[Scipy-svn] r4550 - in branches/Interpolate1D: . fitpack

scipy-svn@scip... scipy-svn@scip...
Fri Jul 18 14:44:23 CDT 2008


Author: fcady
Date: 2008-07-18 14:44:12 -0500 (Fri, 18 Jul 2008)
New Revision: 4550

Added:
   branches/Interpolate1D/fitpack/
   branches/Interpolate1D/fitpack/Makefile
   branches/Interpolate1D/fitpack/README
   branches/Interpolate1D/fitpack/bispev.f
   branches/Interpolate1D/fitpack/clocur.f
   branches/Interpolate1D/fitpack/cocosp.f
   branches/Interpolate1D/fitpack/concon.f
   branches/Interpolate1D/fitpack/concur.f
   branches/Interpolate1D/fitpack/cualde.f
   branches/Interpolate1D/fitpack/curev.f
   branches/Interpolate1D/fitpack/curfit.f
   branches/Interpolate1D/fitpack/dblint.f
   branches/Interpolate1D/fitpack/evapol.f
   branches/Interpolate1D/fitpack/fourco.f
   branches/Interpolate1D/fitpack/fpader.f
   branches/Interpolate1D/fitpack/fpadno.f
   branches/Interpolate1D/fitpack/fpadpo.f
   branches/Interpolate1D/fitpack/fpback.f
   branches/Interpolate1D/fitpack/fpbacp.f
   branches/Interpolate1D/fitpack/fpbfout.f
   branches/Interpolate1D/fitpack/fpbisp.f
   branches/Interpolate1D/fitpack/fpbspl.f
   branches/Interpolate1D/fitpack/fpchec.f
   branches/Interpolate1D/fitpack/fpched.f
   branches/Interpolate1D/fitpack/fpchep.f
   branches/Interpolate1D/fitpack/fpclos.f
   branches/Interpolate1D/fitpack/fpcoco.f
   branches/Interpolate1D/fitpack/fpcons.f
   branches/Interpolate1D/fitpack/fpcosp.f
   branches/Interpolate1D/fitpack/fpcsin.f
   branches/Interpolate1D/fitpack/fpcurf.f
   branches/Interpolate1D/fitpack/fpcuro.f
   branches/Interpolate1D/fitpack/fpcyt1.f
   branches/Interpolate1D/fitpack/fpcyt2.f
   branches/Interpolate1D/fitpack/fpdeno.f
   branches/Interpolate1D/fitpack/fpdisc.f
   branches/Interpolate1D/fitpack/fpfrno.f
   branches/Interpolate1D/fitpack/fpgivs.f
   branches/Interpolate1D/fitpack/fpgrdi.f
   branches/Interpolate1D/fitpack/fpgrpa.f
   branches/Interpolate1D/fitpack/fpgrre.f
   branches/Interpolate1D/fitpack/fpgrsp.f
   branches/Interpolate1D/fitpack/fpinst.f
   branches/Interpolate1D/fitpack/fpintb.f
   branches/Interpolate1D/fitpack/fpknot.f
   branches/Interpolate1D/fitpack/fpopdi.f
   branches/Interpolate1D/fitpack/fpopsp.f
   branches/Interpolate1D/fitpack/fporde.f
   branches/Interpolate1D/fitpack/fppara.f
   branches/Interpolate1D/fitpack/fppasu.f
   branches/Interpolate1D/fitpack/fpperi.f
   branches/Interpolate1D/fitpack/fppocu.f
   branches/Interpolate1D/fitpack/fppogr.f
   branches/Interpolate1D/fitpack/fppola.f
   branches/Interpolate1D/fitpack/fprank.f
   branches/Interpolate1D/fitpack/fprati.f
   branches/Interpolate1D/fitpack/fpregr.f
   branches/Interpolate1D/fitpack/fprota.f
   branches/Interpolate1D/fitpack/fprppo.f
   branches/Interpolate1D/fitpack/fprpsp.f
   branches/Interpolate1D/fitpack/fpseno.f
   branches/Interpolate1D/fitpack/fpspgr.f
   branches/Interpolate1D/fitpack/fpsphe.f
   branches/Interpolate1D/fitpack/fpsuev.f
   branches/Interpolate1D/fitpack/fpsurf.f
   branches/Interpolate1D/fitpack/fpsysy.f
   branches/Interpolate1D/fitpack/fptrnp.f
   branches/Interpolate1D/fitpack/fptrpe.f
   branches/Interpolate1D/fitpack/insert.f
   branches/Interpolate1D/fitpack/parcur.f
   branches/Interpolate1D/fitpack/parder.f
   branches/Interpolate1D/fitpack/parsur.f
   branches/Interpolate1D/fitpack/percur.f
   branches/Interpolate1D/fitpack/pogrid.f
   branches/Interpolate1D/fitpack/polar.f
   branches/Interpolate1D/fitpack/profil.f
   branches/Interpolate1D/fitpack/regrid.f
   branches/Interpolate1D/fitpack/spalde.f
   branches/Interpolate1D/fitpack/spgrid.f
   branches/Interpolate1D/fitpack/sphere.f
   branches/Interpolate1D/fitpack/splder.f
   branches/Interpolate1D/fitpack/splev.f
   branches/Interpolate1D/fitpack/splint.f
   branches/Interpolate1D/fitpack/sproot.f
   branches/Interpolate1D/fitpack/surev.f
   branches/Interpolate1D/fitpack/surfit.f
   branches/Interpolate1D/multipack.h
Removed:
   branches/Interpolate1D/Interpolate1D.pyc
   branches/Interpolate1D/__init__fit.py
   branches/Interpolate1D/_interpolate.pyd
   branches/Interpolate1D/build/
   branches/Interpolate1D/dfitpack.py
   branches/Interpolate1D/dfitpack.pyd
   branches/Interpolate1D/fitpack_wrapper.pyc
   branches/Interpolate1D/info_fit.py
   branches/Interpolate1D/interpolate_wrapper.pyc
Modified:
   branches/Interpolate1D/Interpolate1D.py
   branches/Interpolate1D/__init__.py
   branches/Interpolate1D/fitpack_wrapper.py
   branches/Interpolate1D/interpolate_wrapper.py
   branches/Interpolate1D/setup.py
Log:
Interpolate1D builds correctly, unnecessary files removed, other improvements.

Modified: branches/Interpolate1D/Interpolate1D.py
===================================================================
--- branches/Interpolate1D/Interpolate1D.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/Interpolate1D.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -11,6 +11,7 @@
 
 # fixme: use this to ensure proper type of all inputs and outputs in Interpolate1D
 def make_array_safe(ary, typecode=np.float64):
+    # fixme: could pick correct typecode
     ary = np.atleast_1d(np.asarray(ary, typecode))
     if not ary.flags['CONTIGUOUS']:
         ary = ary.copy()
@@ -18,44 +19,98 @@
     
 
 class Interpolate1D(object):
-    # see enthought.interpolate
     
-    # fixme: Handle other data types.
     
-    def __init__(self, x, y, k=1, kind='linear', low=None, high=None):
-
+    def __init__(self, x, y, kind='linear', low=np.NaN, high=np.NaN, kindkw={}, lowkw={}, highkw={}, missing_data=[None, np.NaN]):
+        """
+        Object for interpolation of 1D data.
+        
+        REQUIRED ARGUMENTS:
+        
+        x -- list or NumPy array
+            x includes the x-values for the data set to
+            interpolate from.  It must be sorted in
+            ascending order
+            
+        y -- list or NumPy array
+            y includes the y-values for the data set  to
+            interpolate from.
+            
+        OPTIONAL ARGUMENTS:
+        
+        kind -- Usu. function or string.  But can be any type.
+            Specifies the type of extrapolation to use for values within
+            the range of x.  If a string is passed, it will look for an object
+            or function with that name and call it when evaluating.  If 
+            a function or object is passed, it will be called when interpolating.
+            If nothing else, assumes the argument is intended as a value
+            to be returned for all arguments.  Defaults to linear interpolation.
+            
+        kindkw -- dictionary
+            If kind is a class, function or string, additional keyword arguments
+            may be needed (example: if you want a 2nd order spline, kind = 'spline'
+            and kindkw = {'k' : 2}.
+            
+        low (high) -- same as for kind
+            Same options as for 'kind'.  Defaults to returning numpy.NaN ('not 
+            a number') for all values outside the range of x.
+            
+        
+    
+        """
         # fixme: Handle checking if they are the correct size.
         self._x = make_array_safe(x).copy()
         self._y = make_array_safe(y).copy()
-        self._xdtype = type(self._x[0])
-        self._ydtype = type(self._y[0])
-
-        assert( len(x) == len(y) , "x and y must be of the same length" )
-        assert( x.ndim == 1 , "x must be one-dimensional" )
-        assert( y.ndim == 1 , "y must be one-dimensional" )
+        
+        assert len(x) == len(y) , "x and y must be of the same length"
+        assert x.ndim == 1 , "x must be one-dimensional"
+        assert y.ndim == 1 , "y must be one-dimensional"
         # fixme: let y be 2-dimensional.  Involves reworking of Interpolate1D.__call__
         # because Spline enumerates y along the last, rather then first, axis,
         # while concatenate works along first axis
         
-        self.kind = self._init_interp_method(self._x, self._y, k, kind)
-        self.low = self._init_interp_method(self._x, self._y, k, low)
-        self.high = self._init_interp_method(self._x, self._y, k, high)
+        self.kind = self._init_interp_method(self._x, self._y, kind, kindkw)
+        self.low = self._init_interp_method(self._x, self._y, low, lowkw)
+        self.high = self._init_interp_method(self._x, self._y, high, highkw)
 
-    def _init_interp_method(self, x, y, k, interp_arg):
+    def _format_array(x, y, missing_data=[None, np.NaN]):
+        # fixme: don't allow copying multiple times.
+                        
+        assert len(x) > 0 and len(y) > 0 , "interpolation does not support\
+                                        array of length 0"
+        assert len(x) == len(y) , "x and y must be of the same length"
+        mask = [((xi not in missing_data) and (y[i] not in missing_data)) \
+                    for i, xi in enumerate(x) ]
+        if isinstance(x, list): 
+            x = [x[i] for (i, good_data) in enumerate(mask) if good_data]
+        else: 
+            x = x[mask]
+        if isinstance(y, list): 
+            y = [y[i] for (i, good_data) in enumerate(mask) if good_data]
+        else: 
+            y = y[mask]
+        self._xdtype = type(x[0])
+        self._x = make_array_safe(x, _xdtype).copy()
+        self._ydtype = type(y[0])
+        self._y = make_array_safe(y, _ydtype).copy()
+            
+        assert self._x.ndim == 1 , "x must be one-dimensional"
+        assert self._y.ndim == 1 , "y must be one-dimensional"    
+    
+    def _init_interp_method(self, x, y, interp_arg, kw):
         from inspect import isclass, isfunction
         
         if interp_arg in ['linear', 'logarithmic', 'block', 'block_average_above']:
             func = {'linear':linear, 'logarithmic':logarithmic, 'block':block, \
                         'block_average_above':block_average_above}[interp_arg]
-            result = lambda new_x : func(self._x, self._y, new_x)
+            result = lambda new_x : func(self._x, self._y, new_x, **kw)
         elif interp_arg in ['Spline', Spline, 'spline']:
-            result = Spline(self._x, self._y, k=k)
+            result = Spline(self._x, self._y, **kw)
         elif isfunction(interp_arg):
-            result = interp_arg
+            result = lambda new_x : interp_arg(new_x, **kw)
         elif isclass(interp_arg):
-            result = interp_arg(x, y)
+            result = interp_arg(x, y, **kw)
         else:
-            print "warning: defaulting on extrapolation"
             result = np.vectorize(lambda new_x : interp_arg)
         return result
 
@@ -65,10 +120,9 @@
         low_mask = x<self._x[0]
         high_mask = x>self._x[-1]
         interp_mask = (~low_mask) & (~high_mask)
-
-        # hack, since getting an error when self.low or self.high gets 0-length array
-        # and they return None or NaN
-        if len(x[low_mask]) == 0: new_low=np.array([])
+        
+        if len(x[low_mask]) == 0: new_low=np.array([]) # hack, since vectorize is failing
+                                                                            # work on lists/arrays of length 0
         else: new_low = self.low(x[low_mask])
         if len(x[interp_mask])==0: new_interp=np.array([])
         else: new_interp = self.kind(x[interp_mask])
@@ -86,45 +140,89 @@
     def assertAllclose(self, x, y):
         self.assert_(np.allclose(make_array_safe(x), make_array_safe(y)))
         
-    # fixme: run the test contained in the wrapper modules
+    def test__interpolate_wrapper(self):
+        print "\n\nTESTING _interpolate_wrapper MODULE"
+        from interpolate_wrapper import Test
+        T = Test()
+        T.runTest()
         
-    def test_Interp_linearSpl(self):
-        #return
+    def test__fitpack_wrapper(self):
+        print "\n\nTESTING _fitpack_wrapper MODULE"
+        from fitpack_wrapper import Test
+        T = Test()
+        T.runTest()
+        
+    def test_spline1_defaultExt(self):
+        # make sure : spline order 1 (linear) interpolation works correctly
+        # make sure : default extrapolation works
         print "\n\nTESTING LINEAR (1st ORDER) SPLINE"
-        N = 7
+        N = 7 # must be > 5
         x = np.arange(N)
         y = np.arange(N)
+        interp_func = Interpolate1D(x, y, kind='Spline', kindkw={'k':1}, low=None, high=599.73)
+        new_x = np.arange(N+1)-0.5
+        new_y = interp_func(new_x)
+        
+        self.assertAllclose(new_y[1:5], [0.5, 1.5, 2.5, 3.5])
+        self.assert_(new_y[0] == None)
+        self.assert_(new_y[-1] == 599.73)
+        
+    def test_spline2(self):
+        print "\n\nTESTING 2nd ORDER SPLINE"
+        # make sure : order-2 splines work on linear data
+        N = 7 #must be > 5
+        x = np.arange(N)
+        y = np.arange(N)
         T1 = time.clock()
-        interp_func = Interpolate1D(x, y, k=1, kind='Spline', low=None, high=None)
+        interp_func = Interpolate1D(x, y, kind='Spline', kindkw={'k':2}, low='spline', high='spline')
         T2 = time.clock()
-        print 'time to create linear interp function: ', T2 - T1
-        new_x = np.arange(N)-0.5
+        print "time to create 2nd order spline interp function with N = %i: " % N, T2 - T1
+        new_x = np.arange(N+1)-0.5
         t1 = time.clock()
         new_y = interp_func(new_x)
         t2 = time.clock()
-        print '1d interp (sec):', t2 - t1
+        print "time to evaluate 2nd order spline interp function with N = %i: " % N, t2 - t1
+        self.assertAllclose(new_x, new_y)
         
-        print "new_y: ", new_y
-        self.assertAllclose(new_y[1:5], [0.5, 1.5, 2.5, 3.5])
-        self.assert_(new_y[0] == None) 
+        # make sure for non-linear data
+        N = 7
+        x = np.arange(N)
+        y = x**2
+        interp_func = Interpolate1D(x, y, kind='Spline', kindkw={'k':2}, low='spline', high='spline')
+        new_x = np.arange(N+1)-0.5
+        new_y = interp_func(new_x)
+        self.assertAllclose(new_x**2, new_y)
         
+        
     def test_linear(self):
+        # make sure : linear interpolation works 
+        # make sure : linear extrapolation works
         print "\n\nTESTING LINEAR INTERPOLATION"
         N = 7
         x = arange(N)
         y = arange(N)
         new_x = arange(N+1)-0.5
         T1 = time.clock()
-        interp_func = Interpolate1D(x, y, kind='linear', low=None, high=None)
+        interp_func = Interpolate1D(x, y, kind='linear', low='linear', high='linear')
         T2 = time.clock()
-        print 'time to create linear interp function: ', T2 - T1
+        print "time to create linear interp function with N = %i: " % N, T2 - T1
         t1 = time.clock()
         new_y = interp_func(new_x)
         t2 = time.clock()
-        print '1d interp (sec):', t2 - t1
+        print "time to create linear interp function with N = %i: " % N, t2 - t1
         
-        self.assertAllclose(new_y[1:5], [0.5, 1.5, 2.5, 3.5])
-        self.assert_(new_y[0] == None)
+        self.assertAllclose(new_x, new_y)
         
+    def test_noLow(self):
+        # make sure : having the out-of-range elements in new_x is fine
+        # there was a bug with this
+        N = 5
+        x = arange(N)
+        y = arange(N)
+        new_x = arange(1,N-1)+.2
+        interp_func = Interpolate1D(x, y, kind='linear', low='linear', high=np.NaN)
+        new_y = interp_func(new_x)
+        self.assertAllclose(new_x, new_y)
+        
 if __name__ == '__main__':
     unittest.main()                 
\ No newline at end of file

Deleted: branches/Interpolate1D/Interpolate1D.pyc
===================================================================
(Binary files differ)

Modified: branches/Interpolate1D/__init__.py
===================================================================
--- branches/Interpolate1D/__init__.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/__init__.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,3 +1,5 @@
-from interpolate_wrapper import linear, logarithmicm, block_average_above
 
+
+from interpolate_wrapper import linear, logarithmic, block, block_average_above
+from fitpack_wrapper import Spline
 from Interpolate1D import Interpolate1D
\ No newline at end of file

Deleted: branches/Interpolate1D/__init__fit.py
===================================================================
--- branches/Interpolate1D/__init__fit.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/__init__fit.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,15 +0,0 @@
-#
-# interpolate - Interpolation Tools
-#
-
-from info import __doc__
-
-#from interpolate import *
-#from fitpack import *
-
-# New interface to fitpack library:
-from fitpack2 import *
-
-__all__ = filter(lambda s:not s.startswith('_'),dir())
-from numpy.testing import NumpyTest
-test = NumpyTest().test

Deleted: branches/Interpolate1D/_interpolate.pyd
===================================================================
(Binary files differ)

Deleted: branches/Interpolate1D/dfitpack.py
===================================================================
--- branches/Interpolate1D/dfitpack.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/dfitpack.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,7 +0,0 @@
-def __bootstrap__():
-   global __bootstrap__, __loader__, __file__
-   import sys, pkg_resources, imp
-   __file__ = pkg_resources.resource_filename(__name__,'dfitpack.pyd')
-   del __bootstrap__, __loader__
-   imp.load_dynamic(__name__,__file__)
-__bootstrap__()

Deleted: branches/Interpolate1D/dfitpack.pyd
===================================================================
(Binary files differ)

Added: branches/Interpolate1D/fitpack/Makefile
===================================================================
--- branches/Interpolate1D/fitpack/Makefile	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/Makefile	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,19 @@
+# Makefile that builts a library lib$(LIB).a from all
+# of the Fortran files found in the current directory.
+# Usage: make LIB=<libname>
+# Pearu
+
+OBJ=$(patsubst %.f,%.o,$(shell ls *.f))
+all: lib$(LIB).a
+$(OBJ):
+	$(FC) -c $(FFLAGS) $(FSHARED) $(patsubst %.o,%.f,$(@F)) -o $@
+lib$(LIB).a: $(OBJ)
+	$(AR) rus lib$(LIB).a $?
+clean:
+	rm *.o
+
+
+
+
+
+

Added: branches/Interpolate1D/fitpack/README
===================================================================
--- branches/Interpolate1D/fitpack/README	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/README	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,3 @@
+- ddierckx is a 'real*8' version of dierckx 
+  generated by Pearu Peterson <pearu@ioc.ee>.
+- dierckx (in netlib) is fitpack by P. Dierckx

Added: branches/Interpolate1D/fitpack/bispev.f
===================================================================
--- branches/Interpolate1D/fitpack/bispev.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/bispev.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,103 @@
+      subroutine bispev(tx,nx,ty,ny,c,kx,ky,x,mx,y,my,z,wrk,lwrk,
+     * iwrk,kwrk,ier)
+c  subroutine bispev evaluates on a grid (x(i),y(j)),i=1,...,mx; j=1,...
+c  ,my a bivariate spline s(x,y) of degrees kx and ky, given in the
+c  b-spline representation.
+c
+c  calling sequence:
+c     call bispev(tx,nx,ty,ny,c,kx,ky,x,mx,y,my,z,wrk,lwrk,
+c    * iwrk,kwrk,ier)
+c
+c  input parameters:
+c   tx    : real array, length nx, which contains the position of the
+c           knots in the x-direction.
+c   nx    : integer, giving the total number of knots in the x-direction
+c   ty    : real array, length ny, which contains the position of the
+c           knots in the y-direction.
+c   ny    : integer, giving the total number of knots in the y-direction
+c   c     : real array, length (nx-kx-1)*(ny-ky-1), which contains the
+c           b-spline coefficients.
+c   kx,ky : integer values, giving the degrees of the spline.
+c   x     : real array of dimension (mx).
+c           before entry x(i) must be set to the x co-ordinate of the
+c           i-th grid point along the x-axis.
+c           tx(kx+1)<=x(i-1)<=x(i)<=tx(nx-kx), i=2,...,mx.
+c   mx    : on entry mx must specify the number of grid points along
+c           the x-axis. mx >=1.
+c   y     : real array of dimension (my).
+c           before entry y(j) must be set to the y co-ordinate of the
+c           j-th grid point along the y-axis.
+c           ty(ky+1)<=y(j-1)<=y(j)<=ty(ny-ky), j=2,...,my.
+c   my    : on entry my must specify the number of grid points along
+c           the y-axis. my >=1.
+c   wrk   : real array of dimension lwrk. used as workspace.
+c   lwrk  : integer, specifying the dimension of wrk.
+c           lwrk >= mx*(kx+1)+my*(ky+1)
+c   iwrk  : integer array of dimension kwrk. used as workspace.
+c   kwrk  : integer, specifying the dimension of iwrk. kwrk >= mx+my.
+c
+c  output parameters:
+c   z     : real array of dimension (mx*my).
+c           on succesful exit z(my*(i-1)+j) contains the value of s(x,y)
+c           at the point (x(i),y(j)),i=1,...,mx;j=1,...,my.
+c   ier   : integer error flag
+c    ier=0 : normal return
+c    ier=10: invalid input data (see restrictions)
+c
+c  restrictions:
+c   mx >=1, my >=1, lwrk>=mx*(kx+1)+my*(ky+1), kwrk>=mx+my
+c   tx(kx+1) <= x(i-1) <= x(i) <= tx(nx-kx), i=2,...,mx
+c   ty(ky+1) <= y(j-1) <= y(j) <= ty(ny-ky), j=2,...,my
+c
+c  other subroutines required:
+c    fpbisp,fpbspl
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer nx,ny,kx,ky,mx,my,lwrk,kwrk,ier
+c  ..array arguments..
+      integer iwrk(kwrk)
+      real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),x(mx),y(my),z(mx*my),
+     * wrk(lwrk)
+c  ..local scalars..
+      integer i,iw,lwest
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      lwest = (kx+1)*mx+(ky+1)*my
+      if(lwrk.lt.lwest) go to 100
+      if(kwrk.lt.(mx+my)) go to 100
+      if (mx.lt.1) go to 100
+      if (mx.eq.1) go to 30
+      go to 10
+  10  do 20 i=2,mx
+        if(x(i).lt.x(i-1)) go to 100
+  20  continue
+  30  if (my.lt.1) go to 100
+      if (my.eq.1) go to 60
+      go to 40
+  40  do 50 i=2,my
+        if(y(i).lt.y(i-1)) go to 100
+  50  continue
+  60  ier = 0
+      iw = mx*(kx+1)+1
+      call fpbisp(tx,nx,ty,ny,c,kx,ky,x,mx,y,my,z,wrk(1),wrk(iw),
+     * iwrk(1),iwrk(mx+1))
+ 100  return
+      end

Added: branches/Interpolate1D/fitpack/clocur.f
===================================================================
--- branches/Interpolate1D/fitpack/clocur.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/clocur.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,352 @@
+      subroutine clocur(iopt,ipar,idim,m,u,mx,x,w,k,s,nest,n,t,nc,c,fp,
+     * wrk,lwrk,iwrk,ier)
+c  given the ordered set of m points x(i) in the idim-dimensional space
+c  with x(1)=x(m), and given also a corresponding set of strictly in-
+c  creasing values u(i) and the set of positive numbers w(i),i=1,2,...,m
+c  subroutine clocur determines a smooth approximating closed spline
+c  curve s(u), i.e.
+c      x1 = s1(u)
+c      x2 = s2(u)       u(1) <= u <= u(m)
+c      .........
+c      xidim = sidim(u)
+c  with sj(u),j=1,2,...,idim periodic spline functions of degree k with
+c  common knots t(j),j=1,2,...,n.
+c  if ipar=1 the values u(i),i=1,2,...,m must be supplied by the user.
+c  if ipar=0 these values are chosen automatically by clocur as
+c      v(1) = 0
+c      v(i) = v(i-1) + dist(x(i),x(i-1)) ,i=2,3,...,m
+c      u(i) = v(i)/v(m) ,i=1,2,...,m
+c  if iopt=-1 clocur calculates the weighted least-squares closed spline
+c  curve according to a given set of knots.
+c  if iopt>=0 the number of knots of the splines sj(u) and the position
+c  t(j),j=1,2,...,n is chosen automatically by the routine. the smooth-
+c  ness of s(u) is then achieved by minimalizing the discontinuity
+c  jumps of the k-th derivative of s(u) at the knots t(j),j=k+2,k+3,...,
+c  n-k-1. the amount of smoothness is determined by the condition that
+c  f(p)=sum((w(i)*dist(x(i),s(u(i))))**2) be <= s, with s a given non-
+c  negative constant, called the smoothing factor.
+c  the fit s(u) is given in the b-spline representation and can be
+c  evaluated by means of subroutine curev.
+c
+c  calling sequence:
+c     call clocur(iopt,ipar,idim,m,u,mx,x,w,k,s,nest,n,t,nc,c,
+c    * fp,wrk,lwrk,iwrk,ier)
+c
+c  parameters:
+c   iopt  : integer flag. on entry iopt must specify whether a weighted
+c           least-squares closed spline curve (iopt=-1) or a smoothing
+c           closed spline curve (iopt=0 or 1) must be determined. if
+c           iopt=0 the routine will start with an initial set of knots
+c           t(i)=u(1)+(u(m)-u(1))*(i-k-1),i=1,2,...,2*k+2. if iopt=1 the
+c           routine will continue with the knots found at the last call.
+c           attention: a call with iopt=1 must always be immediately
+c           preceded by another call with iopt=1 or iopt=0.
+c           unchanged on exit.
+c   ipar  : integer flag. on entry ipar must specify whether (ipar=1)
+c           the user will supply the parameter values u(i),or whether
+c           (ipar=0) these values are to be calculated by clocur.
+c           unchanged on exit.
+c   idim  : integer. on entry idim must specify the dimension of the
+c           curve. 0 < idim < 11.
+c           unchanged on exit.
+c   m     : integer. on entry m must specify the number of data points.
+c           m > 1. unchanged on exit.
+c   u     : real array of dimension at least (m). in case ipar=1,before
+c           entry, u(i) must be set to the i-th value of the parameter
+c           variable u for i=1,2,...,m. these values must then be
+c           supplied in strictly ascending order and will be unchanged
+c           on exit. in case ipar=0, on exit,the array will contain the
+c           values u(i) as determined by clocur.
+c   mx    : integer. on entry mx must specify the actual dimension of
+c           the array x as declared in the calling (sub)program. mx must
+c           not be too small (see x). unchanged on exit.
+c   x     : real array of dimension at least idim*m.
+c           before entry, x(idim*(i-1)+j) must contain the j-th coord-
+c           inate of the i-th data point for i=1,2,...,m and j=1,2,...,
+c           idim. since first and last data point must coincide it
+c           means that x(j)=x(idim*(m-1)+j),j=1,2,...,idim.
+c           unchanged on exit.
+c   w     : real array of dimension at least (m). before entry, w(i)
+c           must be set to the i-th value in the set of weights. the
+c           w(i) must be strictly positive. w(m) is not used.
+c           unchanged on exit. see also further comments.
+c   k     : integer. on entry k must specify the degree of the splines.
+c           1<=k<=5. it is recommended to use cubic splines (k=3).
+c           the user is strongly dissuaded from choosing k even,together
+c           with a small s-value. unchanged on exit.
+c   s     : real.on entry (in case iopt>=0) s must specify the smoothing
+c           factor. s >=0. unchanged on exit.
+c           for advice on the choice of s see further comments.
+c   nest  : integer. on entry nest must contain an over-estimate of the
+c           total number of knots of the splines returned, to indicate
+c           the storage space available to the routine. nest >=2*k+2.
+c           in most practical situation nest=m/2 will be sufficient.
+c           always large enough is nest=m+2*k, the number of knots
+c           needed for interpolation (s=0). unchanged on exit.
+c   n     : integer.
+c           unless ier = 10 (in case iopt >=0), n will contain the
+c           total number of knots of the smoothing spline curve returned
+c           if the computation mode iopt=1 is used this value of n
+c           should be left unchanged between subsequent calls.
+c           in case iopt=-1, the value of n must be specified on entry.
+c   t     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the knots of the
+c           spline curve,i.e. the position of the interior knots t(k+2),
+c           t(k+3),..,t(n-k-1) as well as the position of the additional
+c           t(1),t(2),..,t(k+1)=u(1) and u(m)=t(n-k),...,t(n) needed for
+c           the b-spline representation.
+c           if the computation mode iopt=1 is used, the values of t(1),
+c           t(2),...,t(n) should be left unchanged between subsequent
+c           calls. if the computation mode iopt=-1 is used, the values
+c           t(k+2),...,t(n-k-1) must be supplied by the user, before
+c           entry. see also the restrictions (ier=10).
+c   nc    : integer. on entry nc must specify the actual dimension of
+c           the array c as declared in the calling (sub)program. nc
+c           must not be too small (see c). unchanged on exit.
+c   c     : real array of dimension at least (nest*idim).
+c           on succesful exit, this array will contain the coefficients
+c           in the b-spline representation of the spline curve s(u),i.e.
+c           the b-spline coefficients of the spline sj(u) will be given
+c           in c(n*(j-1)+i),i=1,2,...,n-k-1 for j=1,2,...,idim.
+c   fp    : real. unless ier = 10, fp contains the weighted sum of
+c           squared residuals of the spline curve returned.
+c   wrk   : real array of dimension at least m*(k+1)+nest*(7+idim+5*k).
+c           used as working space. if the computation mode iopt=1 is
+c           used, the values wrk(1),...,wrk(n) should be left unchanged
+c           between subsequent calls.
+c   lwrk  : integer. on entry,lwrk must specify the actual dimension of
+c           the array wrk as declared in the calling (sub)program. lwrk
+c           must not be too small (see wrk). unchanged on exit.
+c   iwrk  : integer array of dimension at least (nest).
+c           used as working space. if the computation mode iopt=1 is
+c           used,the values iwrk(1),...,iwrk(n) should be left unchanged
+c           between subsequent calls.
+c   ier   : integer. unless the routine detects an error, ier contains a
+c           non-positive value on exit, i.e.
+c    ier=0  : normal return. the close curve returned has a residual
+c             sum of squares fp such that abs(fp-s)/s <= tol with tol a
+c             relative tolerance set to 0.001 by the program.
+c    ier=-1 : normal return. the curve returned is an interpolating
+c             spline curve (fp=0).
+c    ier=-2 : normal return. the curve returned is the weighted least-
+c             squares point,i.e. each spline sj(u) is a constant. in
+c             this extreme case fp gives the upper bound fp0 for the
+c             smoothing factor s.
+c    ier=1  : error. the required storage space exceeds the available
+c             storage space, as specified by the parameter nest.
+c             probably causes : nest too small. if nest is already
+c             large (say nest > m/2), it may also indicate that s is
+c             too small
+c             the approximation returned is the least-squares closed
+c             curve according to the knots t(1),t(2),...,t(n). (n=nest)
+c             the parameter fp gives the corresponding weighted sum of
+c             squared residuals (fp>s).
+c    ier=2  : error. a theoretically impossible result was found during
+c             the iteration proces for finding a smoothing curve with
+c             fp = s. probably causes : s too small.
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=3  : error. the maximal number of iterations maxit (set to 20
+c             by the program) allowed for finding a smoothing curve
+c             with fp=s has been reached. probably causes : s too small
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=10 : error. on entry, the input data are controlled on validity
+c             the following restrictions must be satisfied.
+c             -1<=iopt<=1, 1<=k<=5, m>1, nest>2*k+2, w(i)>0,i=1,2,...,m
+c             0<=ipar<=1, 0<idim<=10, lwrk>=(k+1)*m+nest*(7+idim+5*k),
+c             nc>=nest*idim, x(j)=x(idim*(m-1)+j), j=1,2,...,idim
+c             if ipar=0: sum j=1,idim (x(i*idim+j)-x((i-1)*idim+j))**2>0
+c                        i=1,2,...,m-1.
+c             if ipar=1: u(1)<u(2)<...<u(m)
+c             if iopt=-1: 2*k+2<=n<=min(nest,m+2*k)
+c                         u(1)<t(k+2)<t(k+3)<...<t(n-k-1)<u(m)
+c                            (u(1)=0 and u(m)=1 in case ipar=0)
+c                       the schoenberg-whitney conditions, i.e. there
+c                       must be a subset of data points uu(j) with
+c                       uu(j) = u(i) or u(i)+(u(m)-u(1)) such that
+c                         t(j) < uu(j) < t(j+k+1), j=k+1,...,n-k-1
+c             if iopt>=0: s>=0
+c                         if s=0 : nest >= m+2*k
+c             if one of these conditions is found to be violated,control
+c             is immediately repassed to the calling program. in that
+c             case there is no approximation returned.
+c
+c  further comments:
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the curve will be too smooth and signal will be
+c   lost ; if s is too small the curve will pick up too much noise. in
+c   the extreme cases the program will return an interpolating curve if
+c   s=0 and the weighted least-squares point if s is very large.
+c   between these extremes, a properly chosen s will result in a good
+c   compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   x(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in x(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the weighted
+c   least-squares point and the upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximating curve shows more detail) to obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if clocur is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   curve underlying the data. but, if the computation mode iopt=1 is
+c   used, the knots returned may also depend on the s-values at previous
+c   calls (if these were smaller). therefore, if after a number of
+c   trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   clocur once more with the selected value for s but now with iopt=0.
+c   indeed, clocur may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c
+c   the form of the approximating curve can strongly be affected  by
+c   the choice of the parameter values u(i). if there is no physical
+c   reason for choosing a particular parameter u, often good results
+c   will be obtained with the choice of clocur(in case ipar=0), i.e.
+c        v(1)=0, v(i)=v(i-1)+q(i), i=2,...,m, u(i)=v(i)/v(m), i=1,..,m
+c   where
+c        q(i)= sqrt(sum j=1,idim (xj(i)-xj(i-1))**2 )
+c   other possibilities for q(i) are
+c        q(i)= sum j=1,idim (xj(i)-xj(i-1))**2
+c        q(i)= sum j=1,idim abs(xj(i)-xj(i-1))
+c        q(i)= max j=1,idim abs(xj(i)-xj(i-1))
+c        q(i)= 1
+c
+c
+c  other subroutines required:
+c    fpbacp,fpbspl,fpchep,fpclos,fpdisc,fpgivs,fpknot,fprati,fprota
+c
+c  references:
+c   dierckx p. : algorithms for smoothing data with periodic and
+c                parametric splines, computer graphics and image
+c                processing 20 (1982) 171-184.
+c   dierckx p. : algorithms for smoothing data with periodic and param-
+c                etric splines, report tw55, dept. computer science,
+c                k.u.leuven, 1981.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1987
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,fp
+      integer iopt,ipar,idim,m,mx,k,nest,n,nc,lwrk,ier
+c  ..array arguments..
+      real*8 u(m),x(mx),w(m),t(nest),c(nc),wrk(lwrk)
+      integer iwrk(nest)
+c  ..local scalars..
+      real*8 per,tol,dist
+      integer i,ia1,ia2,ib,ifp,ig1,ig2,iq,iz,i1,i2,j1,j2,k1,k2,lwest,
+     * maxit,m1,nmin,ncc,j
+c  ..function references..
+      real*8 sqrt
+c  we set up the parameters tol and maxit
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 90
+      if(ipar.lt.0 .or. ipar.gt.1) go to 90
+      if(idim.le.0 .or. idim.gt.10) go to 90
+      if(k.le.0 .or. k.gt.5) go to 90
+      k1 = k+1
+      k2 = k1+1
+      nmin = 2*k1
+      if(m.lt.2 .or. nest.lt.nmin) go to 90
+      ncc = nest*idim
+      if(mx.lt.m*idim .or. nc.lt.ncc) go to 90
+      lwest = m*k1+nest*(7+idim+5*k)
+      if(lwrk.lt.lwest) go to 90
+      i1 = idim
+      i2 = m*idim
+      do 5 j=1,idim
+         if(x(i1).ne.x(i2)) go to 90
+         i1 = i1-1
+         i2 = i2-1
+   5  continue
+      if(ipar.ne.0 .or. iopt.gt.0) go to 40
+      i1 = 0
+      i2 = idim
+      u(1) = 0.
+      do 20 i=2,m
+         dist = 0.
+         do 10 j1=1,idim
+            i1 = i1+1
+            i2 = i2+1
+            dist = dist+(x(i2)-x(i1))**2
+  10     continue
+         u(i) = u(i-1)+sqrt(dist)
+  20  continue
+      if(u(m).le.0.) go to 90
+      do 30 i=2,m
+         u(i) = u(i)/u(m)
+  30  continue
+      u(m) = 0.1e+01
+  40  if(w(1).le.0.) go to 90
+      m1 = m-1
+      do 50 i=1,m1
+         if(u(i).ge.u(i+1) .or. w(i).le.0.) go to 90
+  50  continue
+      if(iopt.ge.0) go to 70
+      if(n.le.nmin .or. n.gt.nest) go to 90
+      per = u(m)-u(1)
+      j1 = k1
+      t(j1) = u(1)
+      i1 = n-k
+      t(i1) = u(m)
+      j2 = j1
+      i2 = i1
+      do 60 i=1,k
+         i1 = i1+1
+         i2 = i2-1
+         j1 = j1+1
+         j2 = j2-1
+         t(j2) = t(i2)-per
+         t(i1) = t(j1)+per
+  60  continue
+      call fpchep(u,m,t,n,k,ier)
+      if (ier.eq.0) go to 80
+      go to 90
+  70  if(s.lt.0.) go to 90
+      if(s.eq.0. .and. nest.lt.(m+2*k)) go to 90
+      ier = 0
+c we partition the working space and determine the spline approximation.
+  80  ifp = 1
+      iz = ifp+nest
+      ia1 = iz+ncc
+      ia2 = ia1+nest*k1
+      ib = ia2+nest*k
+      ig1 = ib+nest*k2
+      ig2 = ig1+nest*k2
+      iq = ig2+nest*k1
+      call fpclos(iopt,idim,m,u,mx,x,w,k,s,nest,tol,maxit,k1,k2,n,t,
+     * ncc,c,fp,wrk(ifp),wrk(iz),wrk(ia1),wrk(ia2),wrk(ib),wrk(ig1),
+     * wrk(ig2),wrk(iq),iwrk,ier)
+  90  return
+      end

Added: branches/Interpolate1D/fitpack/cocosp.f
===================================================================
--- branches/Interpolate1D/fitpack/cocosp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/cocosp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,180 @@
+      subroutine cocosp(m,x,y,w,n,t,e,maxtr,maxbin,c,sq,sx,bind,wrk,
+     * lwrk,iwrk,kwrk,ier)
+c  given the set of data points (x(i),y(i)) and the set of positive
+c  numbers w(i),i=1,2,...,m, subroutine cocosp determines the weighted
+c  least-squares cubic spline s(x) with given knots t(j),j=1,2,...,n
+c  which satisfies the following concavity/convexity conditions
+c      s''(t(j+3))*e(j) <= 0, j=1,2,...n-6
+c  the fit is given in the b-spline representation( b-spline coef-
+c  ficients c(j),j=1,2,...n-4) and can be evaluated by means of
+c  subroutine splev.
+c
+c  calling sequence:
+c     call cocosp(m,x,y,w,n,t,e,maxtr,maxbin,c,sq,sx,bind,wrk,
+c    * lwrk,iwrk,kwrk,ier)
+c
+c  parameters:
+c    m   : integer. on entry m must specify the number of data points.
+c          m > 3. unchanged on exit.
+c    x   : real array of dimension at least (m). before entry, x(i)
+c          must be set to the i-th value of the independent variable x,
+c          for i=1,2,...,m. these values must be supplied in strictly
+c          ascending order. unchanged on exit.
+c    y   : real array of dimension at least (m). before entry, y(i)
+c          must be set to the i-th value of the dependent variable y,
+c          for i=1,2,...,m. unchanged on exit.
+c    w   : real array of dimension at least (m). before entry, w(i)
+c          must be set to the i-th value in the set of weights. the
+c          w(i) must be strictly positive. unchanged on exit.
+c    n   : integer. on entry n must contain the total number of knots
+c          of the cubic spline. m+4>=n>=8. unchanged on exit.
+c    t   : real array of dimension at least (n). before entry, this
+c          array must contain the knots of the spline, i.e. the position
+c          of the interior knots t(5),t(6),...,t(n-4) as well as the
+c          position of the boundary knots t(1),t(2),t(3),t(4) and t(n-3)
+c          t(n-2),t(n-1),t(n) needed for the b-spline representation.
+c          unchanged on exit. see also the restrictions (ier=10).
+c    e   : real array of dimension at least (n). before entry, e(j)
+c          must be set to 1 if s(x) must be locally concave at t(j+3),
+c          to (-1) if s(x) must be locally convex at t(j+3) and to 0
+c          if no convexity constraint is imposed at t(j+3),j=1,2,..,n-6.
+c          e(n-5),...,e(n) are not used. unchanged on exit.
+c  maxtr : integer. on entry maxtr must contain an over-estimate of the
+c          total number of records in the used tree structure, to indic-
+c          ate the storage space available to the routine. maxtr >=1
+c          in most practical situation maxtr=100 will be sufficient.
+c          always large enough is
+c                         n-5       n-6
+c              maxtr =  (     ) + (     )  with l the greatest
+c                          l        l+1
+c          integer <= (n-6)/2 . unchanged on exit.
+c  maxbin: integer. on entry maxbin must contain an over-estimate of the
+c          number of knots where s(x) will have a zero second derivative
+c          maxbin >=1. in most practical situation maxbin = 10 will be
+c          sufficient. always large enough is maxbin=n-6.
+c          unchanged on exit.
+c    c   : real array of dimension at least (n).
+c          on succesful exit, this array will contain the coefficients
+c          c(1),c(2),..,c(n-4) in the b-spline representation of s(x)
+c    sq  : real. on succesful exit, sq contains the weighted sum of
+c          squared residuals of the spline approximation returned.
+c    sx  : real array of dimension at least m. on succesful exit
+c          this array will contain the spline values s(x(i)),i=1,...,m
+c   bind : logical array of dimension at least (n). on succesful exit
+c          this array will indicate the knots where s''(x)=0, i.e.
+c                s''(t(j+3)) .eq. 0 if  bind(j) = .true.
+c                s''(t(j+3)) .ne. 0 if  bind(j) = .false., j=1,2,...,n-6
+c   wrk  : real array of dimension at least  m*4+n*7+maxbin*(maxbin+n+1)
+c          used as working space.
+c   lwrk : integer. on entry,lwrk must specify the actual dimension of
+c          the array wrk as declared in the calling (sub)program.lwrk
+c          must not be too small (see wrk). unchanged on exit.
+c   iwrk : integer array of dimension at least (maxtr*4+2*(maxbin+1))
+c          used as working space.
+c   kwrk : integer. on entry,kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program. kwrk
+c          must not be too small (see iwrk). unchanged on exit.
+c   ier   : integer. error flag
+c      ier=0 : succesful exit.
+c      ier>0 : abnormal termination: no approximation is returned
+c        ier=1  : the number of knots where s''(x)=0 exceeds maxbin.
+c                 probably causes : maxbin too small.
+c        ier=2  : the number of records in the tree structure exceeds
+c                 maxtr.
+c                 probably causes : maxtr too small.
+c        ier=3  : the algoritm finds no solution to the posed quadratic
+c                 programming problem.
+c                 probably causes : rounding errors.
+c        ier=10 : on entry, the input data are controlled on validity.
+c                 the following restrictions must be satisfied
+c                   m>3, maxtr>=1, maxbin>=1, 8<=n<=m+4,w(i) > 0,
+c                   x(1)<x(2)<...<x(m), t(1)<=t(2)<=t(3)<=t(4)<=x(1),
+c                   x(1)<t(5)<t(6)<...<t(n-4)<x(m)<=t(n-3)<=...<=t(n),
+c                   kwrk>=maxtr*4+2*(maxbin+1),
+c                   lwrk>=m*4+n*7+maxbin*(maxbin+n+1),
+c                   the schoenberg-whitney conditions, i.e. there must
+c                   be a subset of data points xx(j) such that
+c                     t(j) < xx(j) < t(j+4), j=1,2,...,n-4
+c                 if one of these restrictions is found to be violated
+c                 control is immediately repassed to the calling program
+c
+c
+c  other subroutines required:
+c    fpcosp,fpbspl,fpadno,fpdeno,fpseno,fpfrno,fpchec
+c
+c  references:
+c   dierckx p. : an algorithm for cubic spline fitting with convexity
+c                constraints, computing 24 (1980) 349-371.
+c   dierckx p. : an algorithm for least-squares cubic spline fitting
+c                with convexity and concavity constraints, report tw39,
+c                dept. computer science, k.u.leuven, 1978.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c   p. dierckx
+c   dept. computer science, k.u.leuven
+c   celestijnenlaan 200a, b-3001 heverlee, belgium.
+c   e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : march 1978
+c  latest update : march 1987.
+c
+c  ..
+c  ..scalar arguments..
+      real*8 sq
+      integer m,n,maxtr,maxbin,lwrk,kwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),t(n),e(n),c(n),sx(m),wrk(lwrk)
+      integer iwrk(kwrk)
+      logical bind(n)
+c  ..local scalars..
+      integer i,ia,ib,ic,iq,iu,iz,izz,ji,jib,jjb,jl,jr,ju,kwest,
+     * lwest,mb,nm,n6
+      real*8 one
+c  ..
+c  set constant
+      one = 0.1e+01
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(m.lt.4 .or. n.lt.8) go to 40
+      if(maxtr.lt.1 .or. maxbin.lt.1) go to 40
+      lwest = 7*n+m*4+maxbin*(1+n+maxbin)
+      kwest = 4*maxtr+2*(maxbin+1)
+      if(lwrk.lt.lwest .or. kwrk.lt.kwest) go to 40
+      if(w(1).le.0.) go to 40
+      do 10 i=2,m
+         if(x(i-1).ge.x(i) .or. w(i).le.0.) go to 40
+  10  continue
+      call fpchec(x,m,t,n,3,ier)
+      if (ier.eq.0) go to 20
+      go to 40
+c  set numbers e(i)
+  20  n6 = n-6
+      do 30 i=1,n6
+        if(e(i).gt.0.) e(i) = one
+        if(e(i).lt.0.) e(i) = -one
+  30  continue
+c  we partition the working space and determine the spline approximation
+      nm = n+maxbin
+      mb = maxbin+1
+      ia = 1
+      ib = ia+4*n
+      ic = ib+nm*maxbin
+      iz = ic+n
+      izz = iz+n
+      iu = izz+n
+      iq = iu+maxbin
+      ji = 1
+      ju = ji+maxtr
+      jl = ju+maxtr
+      jr = jl+maxtr
+      jjb = jr+maxtr
+      jib = jjb+mb
+      call fpcosp(m,x,y,w,n,t,e,maxtr,maxbin,c,sq,sx,bind,nm,mb,wrk(ia),
+     *
+     * wrk(ib),wrk(ic),wrk(iz),wrk(izz),wrk(iu),wrk(iq),iwrk(ji),
+     * iwrk(ju),iwrk(jl),iwrk(jr),iwrk(jjb),iwrk(jib),ier)
+  40  return
+      end

Added: branches/Interpolate1D/fitpack/concon.f
===================================================================
--- branches/Interpolate1D/fitpack/concon.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/concon.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,233 @@
+      subroutine concon(iopt,m,x,y,w,v,s,nest,maxtr,maxbin,n,t,c,sq,
+     * sx,bind,wrk,lwrk,iwrk,kwrk,ier)
+c  given the set of data points (x(i),y(i)) and the set of positive
+c  numbers w(i), i=1,2,...,m,subroutine concon determines a cubic spline
+c  approximation s(x) which satisfies the following local convexity
+c  constraints  s''(x(i))*v(i) <= 0, i=1,2,...,m.
+c  the number of knots n and the position t(j),j=1,2,...n is chosen
+c  automatically by the routine in a way that
+c       sq = sum((w(i)*(y(i)-s(x(i))))**2) be <= s.
+c  the fit is given in the b-spline representation (b-spline coef-
+c  ficients c(j),j=1,2,...n-4) and can be evaluated by means of
+c  subroutine splev.
+c
+c  calling sequence:
+c
+c     call concon(iopt,m,x,y,w,v,s,nest,maxtr,maxbin,n,t,c,sq,
+c    * sx,bind,wrk,lwrk,iwrk,kwrk,ier)
+c
+c  parameters:
+c    iopt: integer flag.
+c          if iopt=0, the routine will start with the minimal number of
+c          knots to guarantee that the convexity conditions will be
+c          satisfied. if iopt=1, the routine will continue with the set
+c          of knots found at the last call of the routine.
+c          attention: a call with iopt=1 must always be immediately
+c          preceded by another call with iopt=1 or iopt=0.
+c          unchanged on exit.
+c    m   : integer. on entry m must specify the number of data points.
+c          m > 3. unchanged on exit.
+c    x   : real array of dimension at least (m). before entry, x(i)
+c          must be set to the i-th value of the independent variable x,
+c          for i=1,2,...,m. these values must be supplied in strictly
+c          ascending order. unchanged on exit.
+c    y   : real array of dimension at least (m). before entry, y(i)
+c          must be set to the i-th value of the dependent variable y,
+c          for i=1,2,...,m. unchanged on exit.
+c    w   : real array of dimension at least (m). before entry, w(i)
+c          must be set to the i-th value in the set of weights. the
+c          w(i) must be strictly positive. unchanged on exit.
+c    v   : real array of dimension at least (m). before entry, v(i)
+c          must be set to 1 if s(x) must be locally concave at x(i),
+c          to (-1) if s(x) must be locally convex at x(i) and to 0
+c          if no convexity constraint is imposed at x(i).
+c    s   : real. on entry s must specify an over-estimate for the
+c          the weighted sum of squared residuals sq of the requested
+c          spline. s >=0. unchanged on exit.
+c   nest : integer. on entry nest must contain an over-estimate of the
+c          total number of knots of the spline returned, to indicate
+c          the storage space available to the routine. nest >=8.
+c          in most practical situation nest=m/2 will be sufficient.
+c          always large enough is  nest=m+4. unchanged on exit.
+c  maxtr : integer. on entry maxtr must contain an over-estimate of the
+c          total number of records in the used tree structure, to indic-
+c          ate the storage space available to the routine. maxtr >=1
+c          in most practical situation maxtr=100 will be sufficient.
+c          always large enough is
+c                         nest-5      nest-6
+c              maxtr =  (       ) + (        )  with l the greatest
+c                           l          l+1
+c          integer <= (nest-6)/2 . unchanged on exit.
+c  maxbin: integer. on entry maxbin must contain an over-estimate of the
+c          number of knots where s(x) will have a zero second derivative
+c          maxbin >=1. in most practical situation maxbin = 10 will be
+c          sufficient. always large enough is maxbin=nest-6.
+c          unchanged on exit.
+c    n   : integer.
+c          on exit with ier <=0, n will contain the total number of
+c          knots of the spline approximation returned. if the comput-
+c          ation mode iopt=1 is used this value of n should be left
+c          unchanged between subsequent calls.
+c    t   : real array of dimension at least (nest).
+c          on exit with ier<=0, this array will contain the knots of the
+c          spline,i.e. the position of the interior knots t(5),t(6),...,
+c          t(n-4) as well as the position of the additional knots
+c          t(1)=t(2)=t(3)=t(4)=x(1) and t(n-3)=t(n-2)=t(n-1)=t(n)=x(m)
+c          needed for the the b-spline representation.
+c          if the computation mode iopt=1 is used, the values of t(1),
+c          t(2),...,t(n) should be left unchanged between subsequent
+c          calls.
+c    c   : real array of dimension at least (nest).
+c          on succesful exit, this array will contain the coefficients
+c          c(1),c(2),..,c(n-4) in the b-spline representation of s(x)
+c    sq  : real. unless ier>0 , sq contains the weighted sum of
+c          squared residuals of the spline approximation returned.
+c    sx  : real array of dimension at least m. on exit with ier<=0
+c          this array will contain the spline values s(x(i)),i=1,...,m
+c          if the computation mode iopt=1 is used, the values of sx(1),
+c          sx(2),...,sx(m) should be left unchanged between subsequent
+c          calls.
+c    bind: logical array of dimension at least nest. on exit with ier<=0
+c          this array will indicate the knots where s''(x)=0, i.e.
+c                s''(t(j+3)) .eq. 0 if  bind(j) = .true.
+c                s''(t(j+3)) .ne. 0 if  bind(j) = .false., j=1,2,...,n-6
+c          if the computation mode iopt=1 is used, the values of bind(1)
+c          ,...,bind(n-6) should be left unchanged between subsequent
+c          calls.
+c   wrk  : real array of dimension at least (m*4+nest*8+maxbin*(maxbin+
+c          nest+1)). used as working space.
+c   lwrk : integer. on entry,lwrk must specify the actual dimension of
+c          the array wrk as declared in the calling (sub)program.lwrk
+c          must not be too small (see wrk). unchanged on exit.
+c   iwrk : integer array of dimension at least (maxtr*4+2*(maxbin+1))
+c          used as working space.
+c   kwrk : integer. on entry,kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program. kwrk
+c          must not be too small (see iwrk). unchanged on exit.
+c   ier   : integer. error flag
+c      ier=0 : normal return, s(x) satisfies the concavity/convexity
+c              constraints and sq <= s.
+c      ier<0 : abnormal termination: s(x) satisfies the concavity/
+c              convexity constraints but sq > s.
+c        ier=-3 : the requested storage space exceeds the available
+c                 storage space as specified by the parameter nest.
+c                 probably causes: nest too small. if nest is already
+c                 large (say nest > m/2), it may also indicate that s
+c                 is too small.
+c                 the approximation returned is the least-squares cubic
+c                 spline according to the knots t(1),...,t(n) (n=nest)
+c                 which satisfies the convexity constraints.
+c        ier=-2 : the maximal number of knots n=m+4 has been reached.
+c                 probably causes: s too small.
+c        ier=-1 : the number of knots n is less than the maximal number
+c                 m+4 but concon finds that adding one or more knots
+c                 will not further reduce the value of sq.
+c                 probably causes : s too small.
+c      ier>0 : abnormal termination: no approximation is returned
+c        ier=1  : the number of knots where s''(x)=0 exceeds maxbin.
+c                 probably causes : maxbin too small.
+c        ier=2  : the number of records in the tree structure exceeds
+c                 maxtr.
+c                 probably causes : maxtr too small.
+c        ier=3  : the algoritm finds no solution to the posed quadratic
+c                 programming problem.
+c                 probably causes : rounding errors.
+c        ier=4  : the minimum number of knots (given by n) to guarantee
+c                 that the concavity/convexity conditions will be
+c                 satisfied is greater than nest.
+c                 probably causes: nest too small.
+c        ier=5  : the minimum number of knots (given by n) to guarantee
+c                 that the concavity/convexity conditions will be
+c                 satisfied is greater than m+4.
+c                 probably causes: strongly alternating convexity and
+c                 concavity conditions. normally the situation can be
+c                 coped with by adding n-m-4 extra data points (found
+c                 by linear interpolation e.g.) with a small weight w(i)
+c                 and a v(i) number equal to zero.
+c        ier=10 : on entry, the input data are controlled on validity.
+c                 the following restrictions must be satisfied
+c                   0<=iopt<=1, m>3, nest>=8, s>=0, maxtr>=1, maxbin>=1,
+c                   kwrk>=maxtr*4+2*(maxbin+1), w(i)>0, x(i) < x(i+1),
+c                   lwrk>=m*4+nest*8+maxbin*(maxbin+nest+1)
+c                 if one of these restrictions is found to be violated
+c                 control is immediately repassed to the calling program
+c
+c  further comments:
+c    as an example of the use of the computation mode iopt=1, the
+c    following program segment will cause concon to return control
+c    each time a spline with a new set of knots has been computed.
+c     .............
+c     iopt = 0
+c     s = 0.1e+60  (s very large)
+c     do 10 i=1,m
+c       call concon(iopt,m,x,y,w,v,s,nest,maxtr,maxbin,n,t,c,sq,sx,
+c    *  bind,wrk,lwrk,iwrk,kwrk,ier)
+c       ......
+c       s = sq
+c       iopt=1
+c 10  continue
+c     .............
+c
+c  other subroutines required:
+c    fpcoco,fpcosp,fpbspl,fpadno,fpdeno,fpseno,fpfrno
+c
+c  references:
+c   dierckx p. : an algorithm for cubic spline fitting with convexity
+c                constraints, computing 24 (1980) 349-371.
+c   dierckx p. : an algorithm for least-squares cubic spline fitting
+c                with convexity and concavity constraints, report tw39,
+c                dept. computer science, k.u.leuven, 1978.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c   p. dierckx
+c   dept. computer science, k.u.leuven
+c   celestijnenlaan 200a, b-3001 heverlee, belgium.
+c   e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : march 1978
+c  latest update : march 1987.
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,sq
+      integer iopt,m,nest,maxtr,maxbin,n,lwrk,kwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),v(m),t(nest),c(nest),sx(m),wrk(lwrk)
+      integer iwrk(kwrk)
+      logical bind(nest)
+c  ..local scalars..
+      integer i,lwest,kwest,ie,iw,lww
+      real*8 one
+c  ..
+c  set constant
+      one = 0.1e+01
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt.lt.0 .or. iopt.gt.1) go to 30
+      if(m.lt.4 .or. nest.lt.8) go to 30
+      if(s.lt.0.) go to 30
+      if(maxtr.lt.1 .or. maxbin.lt.1) go to 30
+      lwest = 8*nest+m*4+maxbin*(1+nest+maxbin)
+      kwest = 4*maxtr+2*(maxbin+1)
+      if(lwrk.lt.lwest .or. kwrk.lt.kwest) go to 30
+      if(iopt.gt.0) go to 20
+      if(w(1).le.0.) go to 30
+      if(v(1).gt.0.) v(1) = one
+      if(v(1).lt.0.) v(1) = -one
+      do 10 i=2,m
+         if(x(i-1).ge.x(i) .or. w(i).le.0.) go to 30
+         if(v(i).gt.0.) v(i) = one
+         if(v(i).lt.0.) v(i) = -one
+  10  continue
+  20  ier = 0
+c  we partition the working space and determine the spline approximation
+      ie = 1
+      iw = ie+nest
+      lww = lwrk-nest
+      call fpcoco(iopt,m,x,y,w,v,s,nest,maxtr,maxbin,n,t,c,sq,sx,
+     * bind,wrk(ie),wrk(iw),lww,iwrk,kwrk,ier)
+  30  return
+      end

Added: branches/Interpolate1D/fitpack/concur.f
===================================================================
--- branches/Interpolate1D/fitpack/concur.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/concur.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,370 @@
+      subroutine concur(iopt,idim,m,u,mx,x,xx,w,ib,db,nb,ie,de,ne,k,s,
+     * nest,n,t,nc,c,np,cp,fp,wrk,lwrk,iwrk,ier)
+c  given the ordered set of m points x(i) in the idim-dimensional space
+c  and given also a corresponding set of strictly increasing values u(i)
+c  and the set of positive numbers w(i),i=1,2,...,m, subroutine concur
+c  determines a smooth approximating spline curve s(u), i.e.
+c      x1 = s1(u)
+c      x2 = s2(u)      ub = u(1) <= u <= u(m) = ue
+c      .........
+c      xidim = sidim(u)
+c  with sj(u),j=1,2,...,idim spline functions of odd degree k with
+c  common knots t(j),j=1,2,...,n.
+c  in addition these splines will satisfy the following boundary
+c  constraints        (l)
+c      if ib > 0 :  sj   (u(1)) = db(idim*l+j) ,l=0,1,...,ib-1
+c  and                (l)
+c      if ie > 0 :  sj   (u(m)) = de(idim*l+j) ,l=0,1,...,ie-1.
+c  if iopt=-1 concur calculates the weighted least-squares spline curve
+c  according to a given set of knots.
+c  if iopt>=0 the number of knots of the splines sj(u) and the position
+c  t(j),j=1,2,...,n is chosen automatically by the routine. the smooth-
+c  ness of s(u) is then achieved by minimalizing the discontinuity
+c  jumps of the k-th derivative of s(u) at the knots t(j),j=k+2,k+3,...,
+c  n-k-1. the amount of smoothness is determined by the condition that
+c  f(p)=sum((w(i)*dist(x(i),s(u(i))))**2) be <= s, with s a given non-
+c  negative constant, called the smoothing factor.
+c  the fit s(u) is given in the b-spline representation and can be
+c  evaluated by means of subroutine curev.
+c
+c  calling sequence:
+c     call concur(iopt,idim,m,u,mx,x,xx,w,ib,db,nb,ie,de,ne,k,s,nest,n,
+c    * t,nc,c,np,cp,fp,wrk,lwrk,iwrk,ier)
+c
+c  parameters:
+c   iopt  : integer flag. on entry iopt must specify whether a weighted
+c           least-squares spline curve (iopt=-1) or a smoothing spline
+c           curve (iopt=0 or 1) must be determined.if iopt=0 the routine
+c           will start with an initial set of knots t(i)=ub,t(i+k+1)=ue,
+c           i=1,2,...,k+1. if iopt=1 the routine will continue with the
+c           knots found at the last call of the routine.
+c           attention: a call with iopt=1 must always be immediately
+c           preceded by another call with iopt=1 or iopt=0.
+c           unchanged on exit.
+c   idim  : integer. on entry idim must specify the dimension of the
+c           curve. 0 < idim < 11.
+c           unchanged on exit.
+c   m     : integer. on entry m must specify the number of data points.
+c           m > k-max(ib-1,0)-max(ie-1,0). unchanged on exit.
+c   u     : real array of dimension at least (m). before entry,
+c           u(i) must be set to the i-th value of the parameter variable
+c           u for i=1,2,...,m. these values must be supplied in
+c           strictly ascending order and will be unchanged on exit.
+c   mx    : integer. on entry mx must specify the actual dimension of
+c           the arrays x and xx as declared in the calling (sub)program
+c           mx must not be too small (see x). unchanged on exit.
+c   x     : real array of dimension at least idim*m.
+c           before entry, x(idim*(i-1)+j) must contain the j-th coord-
+c           inate of the i-th data point for i=1,2,...,m and j=1,2,...,
+c           idim. unchanged on exit.
+c   xx    : real array of dimension at least idim*m.
+c           used as working space. on exit xx contains the coordinates
+c           of the data points to which a spline curve with zero deriv-
+c           ative constraints has been determined.
+c           if the computation mode iopt =1 is used xx should be left
+c           unchanged between calls.
+c   w     : real array of dimension at least (m). before entry, w(i)
+c           must be set to the i-th value in the set of weights. the
+c           w(i) must be strictly positive. unchanged on exit.
+c           see also further comments.
+c   ib    : integer. on entry ib must specify the number of derivative
+c           constraints for the curve at the begin point. 0<=ib<=(k+1)/2
+c           unchanged on exit.
+c   db    : real array of dimension nb. before entry db(idim*l+j) must
+c           contain the l-th order derivative of sj(u) at u=u(1) for
+c           j=1,2,...,idim and l=0,1,...,ib-1 (if ib>0).
+c           unchanged on exit.
+c   nb    : integer, specifying the dimension of db. nb>=max(1,idim*ib)
+c           unchanged on exit.
+c   ie    : integer. on entry ie must specify the number of derivative
+c           constraints for the curve at the end point. 0<=ie<=(k+1)/2
+c           unchanged on exit.
+c   de    : real array of dimension ne. before entry de(idim*l+j) must
+c           contain the l-th order derivative of sj(u) at u=u(m) for
+c           j=1,2,...,idim and l=0,1,...,ie-1 (if ie>0).
+c           unchanged on exit.
+c   ne    : integer, specifying the dimension of de. ne>=max(1,idim*ie)
+c           unchanged on exit.
+c   k     : integer. on entry k must specify the degree of the splines.
+c           k=1,3 or 5.
+c           unchanged on exit.
+c   s     : real.on entry (in case iopt>=0) s must specify the smoothing
+c           factor. s >=0. unchanged on exit.
+c           for advice on the choice of s see further comments.
+c   nest  : integer. on entry nest must contain an over-estimate of the
+c           total number of knots of the splines returned, to indicate
+c           the storage space available to the routine. nest >=2*k+2.
+c           in most practical situation nest=m/2 will be sufficient.
+c           always large enough is nest=m+k+1+max(0,ib-1)+max(0,ie-1),
+c           the number of knots needed for interpolation (s=0).
+c           unchanged on exit.
+c   n     : integer.
+c           unless ier = 10 (in case iopt >=0), n will contain the
+c           total number of knots of the smoothing spline curve returned
+c           if the computation mode iopt=1 is used this value of n
+c           should be left unchanged between subsequent calls.
+c           in case iopt=-1, the value of n must be specified on entry.
+c   t     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the knots of the
+c           spline curve,i.e. the position of the interior knots t(k+2),
+c           t(k+3),..,t(n-k-1) as well as the position of the additional
+c           t(1)=t(2)=...=t(k+1)=ub and t(n-k)=...=t(n)=ue needed for
+c           the b-spline representation.
+c           if the computation mode iopt=1 is used, the values of t(1),
+c           t(2),...,t(n) should be left unchanged between subsequent
+c           calls. if the computation mode iopt=-1 is used, the values
+c           t(k+2),...,t(n-k-1) must be supplied by the user, before
+c           entry. see also the restrictions (ier=10).
+c   nc    : integer. on entry nc must specify the actual dimension of
+c           the array c as declared in the calling (sub)program. nc
+c           must not be too small (see c). unchanged on exit.
+c   c     : real array of dimension at least (nest*idim).
+c           on succesful exit, this array will contain the coefficients
+c           in the b-spline representation of the spline curve s(u),i.e.
+c           the b-spline coefficients of the spline sj(u) will be given
+c           in c(n*(j-1)+i),i=1,2,...,n-k-1 for j=1,2,...,idim.
+c   cp    : real array of dimension at least 2*(k+1)*idim.
+c           on exit cp will contain the b-spline coefficients of a
+c           polynomial curve which satisfies the boundary constraints.
+c           if the computation mode iopt =1 is used cp should be left
+c           unchanged between calls.
+c   np    : integer. on entry np must specify the actual dimension of
+c           the array cp as declared in the calling (sub)program. np
+c           must not be too small (see cp). unchanged on exit.
+c   fp    : real. unless ier = 10, fp contains the weighted sum of
+c           squared residuals of the spline curve returned.
+c   wrk   : real array of dimension at least m*(k+1)+nest*(6+idim+3*k).
+c           used as working space. if the computation mode iopt=1 is
+c           used, the values wrk(1),...,wrk(n) should be left unchanged
+c           between subsequent calls.
+c   lwrk  : integer. on entry,lwrk must specify the actual dimension of
+c           the array wrk as declared in the calling (sub)program. lwrk
+c           must not be too small (see wrk). unchanged on exit.
+c   iwrk  : integer array of dimension at least (nest).
+c           used as working space. if the computation mode iopt=1 is
+c           used,the values iwrk(1),...,iwrk(n) should be left unchanged
+c           between subsequent calls.
+c   ier   : integer. unless the routine detects an error, ier contains a
+c           non-positive value on exit, i.e.
+c    ier=0  : normal return. the curve returned has a residual sum of
+c             squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c             ive tolerance set to 0.001 by the program.
+c    ier=-1 : normal return. the curve returned is an interpolating
+c             spline curve, satisfying the constraints (fp=0).
+c    ier=-2 : normal return. the curve returned is the weighted least-
+c             squares polynomial curve of degree k, satisfying the
+c             constraints. in this extreme case fp gives the upper
+c             bound fp0 for the smoothing factor s.
+c    ier=1  : error. the required storage space exceeds the available
+c             storage space, as specified by the parameter nest.
+c             probably causes : nest too small. if nest is already
+c             large (say nest > m/2), it may also indicate that s is
+c             too small
+c             the approximation returned is the least-squares spline
+c             curve according to the knots t(1),t(2),...,t(n). (n=nest)
+c             the parameter fp gives the corresponding weighted sum of
+c             squared residuals (fp>s).
+c    ier=2  : error. a theoretically impossible result was found during
+c             the iteration proces for finding a smoothing spline curve
+c             with fp = s. probably causes : s too small.
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=3  : error. the maximal number of iterations maxit (set to 20
+c             by the program) allowed for finding a smoothing curve
+c             with fp=s has been reached. probably causes : s too small
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=10 : error. on entry, the input data are controlled on validity
+c             the following restrictions must be satisfied.
+c             -1<=iopt<=1, k = 1,3 or 5, m>k-max(0,ib-1)-max(0,ie-1),
+c             nest>=2k+2, 0<idim<=10, lwrk>=(k+1)*m+nest*(6+idim+3*k),
+c             nc >=nest*idim ,u(1)<u(2)<...<u(m),w(i)>0 i=1,2,...,m,
+c             mx>=idim*m,0<=ib<=(k+1)/2,0<=ie<=(k+1)/2,nb>=1,ne>=1,
+c             nb>=ib*idim,ne>=ib*idim,np>=2*(k+1)*idim,
+c             if iopt=-1:2*k+2<=n<=min(nest,mmax) with mmax = m+k+1+
+c                        max(0,ib-1)+max(0,ie-1)
+c                        u(1)<t(k+2)<t(k+3)<...<t(n-k-1)<u(m)
+c                       the schoenberg-whitney conditions, i.e. there
+c                       must be a subset of data points uu(j) such that
+c                         t(j) < uu(j) < t(j+k+1), j=1+max(0,ib-1),...
+c                                                   ,n+k-1-max(0,ie-1)
+c             if iopt>=0: s>=0
+c                         if s=0 : nest >=mmax (see above)
+c             if one of these conditions is found to be violated,control
+c             is immediately repassed to the calling program. in that
+c             case there is no approximation returned.
+c
+c  further comments:
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the curve will be too smooth and signal will be
+c   lost ; if s is too small the curve will pick up too much noise. in
+c   the extreme cases the program will return an interpolating curve if
+c   s=0 and the least-squares polynomial curve of degree k if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   x(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in x(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   polynomial curve and the upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximating curve shows more detail) to obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if concur is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   curve underlying the data. but, if the computation mode iopt=1 is
+c   used, the knots returned may also depend on the s-values at previous
+c   calls (if these were smaller). therefore, if after a number of
+c   trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   concur once more with the selected value for s but now with iopt=0.
+c   indeed, concur may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c
+c   the form of the approximating curve can strongly be affected by
+c   the choice of the parameter values u(i). if there is no physical
+c   reason for choosing a particular parameter u, often good results
+c   will be obtained with the choice
+c        v(1)=0, v(i)=v(i-1)+q(i), i=2,...,m, u(i)=v(i)/v(m), i=1,..,m
+c   where
+c        q(i)= sqrt(sum j=1,idim (xj(i)-xj(i-1))**2 )
+c   other possibilities for q(i) are
+c        q(i)= sum j=1,idim (xj(i)-xj(i-1))**2
+c        q(i)= sum j=1,idim abs(xj(i)-xj(i-1))
+c        q(i)= max j=1,idim abs(xj(i)-xj(i-1))
+c        q(i)= 1
+c
+c  other subroutines required:
+c    fpback,fpbspl,fpched,fpcons,fpdisc,fpgivs,fpknot,fprati,fprota
+c    curev,fppocu,fpadpo,fpinst
+c
+c  references:
+c   dierckx p. : algorithms for smoothing data with periodic and
+c                parametric splines, computer graphics and image
+c                processing 20 (1982) 171-184.
+c   dierckx p. : algorithms for smoothing data with periodic and param-
+c                etric splines, report tw55, dept. computer science,
+c                k.u.leuven, 1981.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1987
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,fp
+      integer iopt,idim,m,mx,ib,nb,ie,ne,k,nest,n,nc,np,lwrk,ier
+c  ..array arguments..
+      real*8 u(m),x(mx),xx(mx),db(nb),de(ne),w(m),t(nest),c(nc),wrk(lwrk
+     *)
+      real*8 cp(np)
+      integer iwrk(nest)
+c  ..local scalars..
+      real*8 tol,dist
+      integer i,ib1,ie1,ja,jb,jfp,jg,jq,jz,j,k1,k2,lwest,maxit,nmin,
+     * ncc,kk,mmin,nmax,mxx
+c ..function references
+      integer max0
+c  ..
+c  we set up the parameters tol and maxit
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 90
+      if(idim.le.0 .or. idim.gt.10) go to 90
+      if(k.le.0 .or. k.gt.5) go to 90
+      k1 = k+1
+      kk = k1/2
+      if(kk*2.ne.k1) go to 90
+      k2 = k1+1
+      if(ib.lt.0 .or. ib.gt.kk) go to 90
+      if(ie.lt.0 .or. ie.gt.kk) go to 90
+      nmin = 2*k1
+      ib1 = max0(0,ib-1)
+      ie1 = max0(0,ie-1)
+      mmin = k1-ib1-ie1
+      if(m.lt.mmin .or. nest.lt.nmin) go to 90
+      if(nb.lt.(idim*ib) .or. ne.lt.(idim*ie)) go to 90
+      if(np.lt.(2*k1*idim)) go to 90
+      mxx = m*idim
+      ncc = nest*idim
+      if(mx.lt.mxx .or. nc.lt.ncc) go to 90
+      lwest = m*k1+nest*(6+idim+3*k)
+      if(lwrk.lt.lwest) go to 90
+      if(w(1).le.0.) go to 90
+      do 10 i=2,m
+         if(u(i-1).ge.u(i) .or. w(i).le.0.) go to 90
+  10  continue
+      if(iopt.ge.0) go to 30
+      if(n.lt.nmin .or. n.gt.nest) go to 90
+      j = n
+      do 20 i=1,k1
+         t(i) = u(1)
+         t(j) = u(m)
+         j = j-1
+  20  continue
+      call fpched(u,m,t,n,k,ib,ie,ier)
+      if (ier.eq.0) go to 40
+      go to 90
+  30  if(s.lt.0.) go to 90
+      nmax = m+k1+ib1+ie1
+      if(s.eq.0. .and. nest.lt.nmax) go to 90
+      ier = 0
+      if(iopt.gt.0) go to 70
+c  we determine a polynomial curve satisfying the boundary constraints.
+  40  call fppocu(idim,k,u(1),u(m),ib,db,nb,ie,de,ne,cp,np)
+c  we generate new data points which will be approximated by a spline
+c  with zero derivative constraints.
+      j = nmin
+      do 50 i=1,k1
+        wrk(i) = u(1)
+        wrk(j) = u(m)
+        j = j-1
+  50  continue
+c  evaluate the polynomial curve
+      call curev(idim,wrk,nmin,cp,np,k,u,m,xx,mxx,ier)
+c  substract from the old data, the values of the polynomial curve
+      do 60 i=1,mxx
+        xx(i) = x(i)-xx(i)
+  60  continue
+c we partition the working space and determine the spline curve.
+  70  jfp = 1
+      jz = jfp+nest
+      ja = jz+ncc
+      jb = ja+nest*k1
+      jg = jb+nest*k2
+      jq = jg+nest*k2
+      call fpcons(iopt,idim,m,u,mxx,xx,w,ib,ie,k,s,nest,tol,maxit,k1,
+     * k2,n,t,ncc,c,fp,wrk(jfp),wrk(jz),wrk(ja),wrk(jb),wrk(jg),wrk(jq),
+     *
+     * iwrk,ier)
+c  add the polynomial curve to the calculated spline.
+      call fpadpo(idim,t,n,c,ncc,k,cp,np,wrk(jz),wrk(ja),wrk(jb))
+  90  return
+      end

Added: branches/Interpolate1D/fitpack/cualde.f
===================================================================
--- branches/Interpolate1D/fitpack/cualde.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/cualde.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,91 @@
+      subroutine cualde(idim,t,n,c,nc,k1,u,d,nd,ier)
+c  subroutine cualde evaluates at the point u all the derivatives
+c                     (l)
+c     d(idim*l+j) = sj   (u) ,l=0,1,...,k, j=1,2,...,idim
+c  of a spline curve s(u) of order k1 (degree k=k1-1) and dimension idim
+c  given in its b-spline representation.
+c
+c  calling sequence:
+c     call cualde(idim,t,n,c,nc,k1,u,d,nd,ier)
+c
+c  input parameters:
+c    idim : integer, giving the dimension of the spline curve.
+c    t    : array,length n, which contains the position of the knots.
+c    n    : integer, giving the total number of knots of s(u).
+c    c    : array,length nc, which contains the b-spline coefficients.
+c    nc   : integer, giving the total number of coefficients of s(u).
+c    k1   : integer, giving the order of s(u) (order=degree+1).
+c    u    : real, which contains the point where the derivatives must
+c           be evaluated.
+c    nd   : integer, giving the dimension of the array d. nd >= k1*idim
+c
+c  output parameters:
+c    d    : array,length nd,giving the different curve derivatives.
+c           d(idim*l+j) will contain the j-th coordinate of the l-th
+c           derivative of the curve at the point u.
+c    ier  : error flag
+c      ier = 0 : normal return
+c      ier =10 : invalid input data (see restrictions)
+c
+c  restrictions:
+c    nd >= k1*idim
+c    t(k1) <= u <= t(n-k1+1)
+c
+c  further comments:
+c    if u coincides with a knot, right derivatives are computed
+c    ( left derivatives if u = t(n-k1+1) ).
+c
+c  other subroutines required: fpader.
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer idim,n,nc,k1,nd,ier
+      real*8 u
+c  ..array arguments..
+      real*8 t(n),c(nc),d(nd)
+c  ..local scalars..
+      integer i,j,kk,l,m,nk1
+c  ..local array..
+      real*8 h(6)
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      if(nd.lt.(k1*idim)) go to 500
+      nk1 = n-k1
+      if(u.lt.t(k1) .or. u.gt.t(nk1+1)) go to 500
+c  search for knot interval t(l) <= u < t(l+1)
+      l = k1
+ 100  if(u.lt.t(l+1) .or. l.eq.nk1) go to 200
+      l = l+1
+      go to 100
+ 200  if(t(l).ge.t(l+1)) go to 500
+      ier = 0
+c  calculate the derivatives.
+      j = 1
+      do 400 i=1,idim
+        call fpader(t,n,c(j),k1,u,l,h)
+        m = i
+        do 300 kk=1,k1
+          d(m) = h(kk)
+          m = m+idim
+ 300    continue
+        j = j+n
+ 400  continue
+ 500  return
+      end

Added: branches/Interpolate1D/fitpack/curev.f
===================================================================
--- branches/Interpolate1D/fitpack/curev.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/curev.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,110 @@
+      subroutine curev(idim,t,n,c,nc,k,u,m,x,mx,ier)
+c  subroutine curev evaluates in a number of points u(i),i=1,2,...,m
+c  a spline curve s(u) of degree k and dimension idim, given in its
+c  b-spline representation.
+c
+c  calling sequence:
+c     call curev(idim,t,n,c,nc,k,u,m,x,mx,ier)
+c
+c  input parameters:
+c    idim : integer, giving the dimension of the spline curve.
+c    t    : array,length n, which contains the position of the knots.
+c    n    : integer, giving the total number of knots of s(u).
+c    c    : array,length nc, which contains the b-spline coefficients.
+c    nc   : integer, giving the total number of coefficients of s(u).
+c    k    : integer, giving the degree of s(u).
+c    u    : array,length m, which contains the points where s(u) must
+c           be evaluated.
+c    m    : integer, giving the number of points where s(u) must be
+c           evaluated.
+c    mx   : integer, giving the dimension of the array x. mx >= m*idim
+c
+c  output parameters:
+c    x    : array,length mx,giving the value of s(u) at the different
+c           points. x(idim*(i-1)+j) will contain the j-th coordinate
+c           of the i-th point on the curve.
+c    ier  : error flag
+c      ier = 0 : normal return
+c      ier =10 : invalid input data (see restrictions)
+c
+c  restrictions:
+c    m >= 1
+c    mx >= m*idim
+c    t(k+1) <= u(i) <= u(i+1) <= t(n-k) , i=1,2,...,m-1.
+c
+c  other subroutines required: fpbspl.
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer idim,n,nc,k,m,mx,ier
+c  ..array arguments..
+      real*8 t(n),c(nc),u(m),x(mx)
+c  ..local scalars..
+      integer i,j,jj,j1,k1,l,ll,l1,mm,nk1
+      real*8 arg,sp,tb,te
+c  ..local array..
+      real*8 h(6)
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      if (m.lt.1) go to 100
+      if (m.eq.1) go to 30
+      go to 10
+  10  do 20 i=2,m
+        if(u(i).lt.u(i-1)) go to 100
+  20  continue
+  30  if(mx.lt.(m*idim)) go to 100
+      ier = 0
+c  fetch tb and te, the boundaries of the approximation interval.
+      k1 = k+1
+      nk1 = n-k1
+      tb = t(k1)
+      te = t(nk1+1)
+      l = k1
+      l1 = l+1
+c  main loop for the different points.
+      mm = 0
+      do 80 i=1,m
+c  fetch a new u-value arg.
+        arg = u(i)
+        if(arg.lt.tb) arg = tb
+        if(arg.gt.te) arg = te
+c  search for knot interval t(l) <= arg < t(l+1)
+  40    if(arg.lt.t(l1) .or. l.eq.nk1) go to 50
+        l = l1
+        l1 = l+1
+        go to 40
+c  evaluate the non-zero b-splines at arg.
+  50    call fpbspl(t,n,k,arg,l,h)
+c  find the value of s(u) at u=arg.
+        ll = l-k1
+        do 70 j1=1,idim
+          jj = ll
+          sp = 0.
+          do 60 j=1,k1
+            jj = jj+1
+            sp = sp+c(jj)*h(j)
+  60      continue
+          mm = mm+1
+          x(mm) = sp
+          ll = ll+n
+  70    continue
+  80  continue
+ 100  return
+      end

Added: branches/Interpolate1D/fitpack/curfit.f
===================================================================
--- branches/Interpolate1D/fitpack/curfit.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/curfit.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,261 @@
+      subroutine curfit(iopt,m,x,y,w,xb,xe,k,s,nest,n,t,c,fp,
+     * wrk,lwrk,iwrk,ier)
+c  given the set of data points (x(i),y(i)) and the set of positive
+c  numbers w(i),i=1,2,...,m,subroutine curfit determines a smooth spline
+c  approximation of degree k on the interval xb <= x <= xe.
+c  if iopt=-1 curfit calculates the weighted least-squares spline
+c  according to a given set of knots.
+c  if iopt>=0 the number of knots of the spline s(x) and the position
+c  t(j),j=1,2,...,n is chosen automatically by the routine. the smooth-
+c  ness of s(x) is then achieved by minimalizing the discontinuity
+c  jumps of the k-th derivative of s(x) at the knots t(j),j=k+2,k+3,...,
+c  n-k-1. the amount of smoothness is determined by the condition that
+c  f(p)=sum((w(i)*(y(i)-s(x(i))))**2) be <= s, with s a given non-
+c  negative constant, called the smoothing factor.
+c  the fit s(x) is given in the b-spline representation (b-spline coef-
+c  ficients c(j),j=1,2,...,n-k-1) and can be evaluated by means of
+c  subroutine splev.
+c
+c  calling sequence:
+c     call curfit(iopt,m,x,y,w,xb,xe,k,s,nest,n,t,c,fp,wrk,
+c    * lwrk,iwrk,ier)
+c
+c  parameters:
+c   iopt  : integer flag. on entry iopt must specify whether a weighted
+c           least-squares spline (iopt=-1) or a smoothing spline (iopt=
+c           0 or 1) must be determined. if iopt=0 the routine will start
+c           with an initial set of knots t(i)=xb, t(i+k+1)=xe, i=1,2,...
+c           k+1. if iopt=1 the routine will continue with the knots
+c           found at the last call of the routine.
+c           attention: a call with iopt=1 must always be immediately
+c           preceded by another call with iopt=1 or iopt=0.
+c           unchanged on exit.
+c   m     : integer. on entry m must specify the number of data points.
+c           m > k. unchanged on exit.
+c   x     : real array of dimension at least (m). before entry, x(i)
+c           must be set to the i-th value of the independent variable x,
+c           for i=1,2,...,m. these values must be supplied in strictly
+c           ascending order. unchanged on exit.
+c   y     : real array of dimension at least (m). before entry, y(i)
+c           must be set to the i-th value of the dependent variable y,
+c           for i=1,2,...,m. unchanged on exit.
+c   w     : real array of dimension at least (m). before entry, w(i)
+c           must be set to the i-th value in the set of weights. the
+c           w(i) must be strictly positive. unchanged on exit.
+c           see also further comments.
+c   xb,xe : real values. on entry xb and xe must specify the boundaries
+c           of the approximation interval. xb<=x(1), xe>=x(m).
+c           unchanged on exit.
+c   k     : integer. on entry k must specify the degree of the spline.
+c           1<=k<=5. it is recommended to use cubic splines (k=3).
+c           the user is strongly dissuaded from choosing k even,together
+c           with a small s-value. unchanged on exit.
+c   s     : real.on entry (in case iopt>=0) s must specify the smoothing
+c           factor. s >=0. unchanged on exit.
+c           for advice on the choice of s see further comments.
+c   nest  : integer. on entry nest must contain an over-estimate of the
+c           total number of knots of the spline returned, to indicate
+c           the storage space available to the routine. nest >=2*k+2.
+c           in most practical situation nest=m/2 will be sufficient.
+c           always large enough is  nest=m+k+1, the number of knots
+c           needed for interpolation (s=0). unchanged on exit.
+c   n     : integer.
+c           unless ier =10 (in case iopt >=0), n will contain the
+c           total number of knots of the spline approximation returned.
+c           if the computation mode iopt=1 is used this value of n
+c           should be left unchanged between subsequent calls.
+c           in case iopt=-1, the value of n must be specified on entry.
+c   t     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the knots of the
+c           spline,i.e. the position of the interior knots t(k+2),t(k+3)
+c           ...,t(n-k-1) as well as the position of the additional knots
+c           t(1)=t(2)=...=t(k+1)=xb and t(n-k)=...=t(n)=xe needed for
+c           the b-spline representation.
+c           if the computation mode iopt=1 is used, the values of t(1),
+c           t(2),...,t(n) should be left unchanged between subsequent
+c           calls. if the computation mode iopt=-1 is used, the values
+c           t(k+2),...,t(n-k-1) must be supplied by the user, before
+c           entry. see also the restrictions (ier=10).
+c   c     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the coefficients
+c           c(1),c(2),..,c(n-k-1) in the b-spline representation of s(x)
+c   fp    : real. unless ier=10, fp contains the weighted sum of
+c           squared residuals of the spline approximation returned.
+c   wrk   : real array of dimension at least (m*(k+1)+nest*(7+3*k)).
+c           used as working space. if the computation mode iopt=1 is
+c           used, the values wrk(1),...,wrk(n) should be left unchanged
+c           between subsequent calls.
+c   lwrk  : integer. on entry,lwrk must specify the actual dimension of
+c           the array wrk as declared in the calling (sub)program.lwrk
+c           must not be too small (see wrk). unchanged on exit.
+c   iwrk  : integer array of dimension at least (nest).
+c           used as working space. if the computation mode iopt=1 is
+c           used,the values iwrk(1),...,iwrk(n) should be left unchanged
+c           between subsequent calls.
+c   ier   : integer. unless the routine detects an error, ier contains a
+c           non-positive value on exit, i.e.
+c    ier=0  : normal return. the spline returned has a residual sum of
+c             squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c             ive tolerance set to 0.001 by the program.
+c    ier=-1 : normal return. the spline returned is an interpolating
+c             spline (fp=0).
+c    ier=-2 : normal return. the spline returned is the weighted least-
+c             squares polynomial of degree k. in this extreme case fp
+c             gives the upper bound fp0 for the smoothing factor s.
+c    ier=1  : error. the required storage space exceeds the available
+c             storage space, as specified by the parameter nest.
+c             probably causes : nest too small. if nest is already
+c             large (say nest > m/2), it may also indicate that s is
+c             too small
+c             the approximation returned is the weighted least-squares
+c             spline according to the knots t(1),t(2),...,t(n). (n=nest)
+c             the parameter fp gives the corresponding weighted sum of
+c             squared residuals (fp>s).
+c    ier=2  : error. a theoretically impossible result was found during
+c             the iteration proces for finding a smoothing spline with
+c             fp = s. probably causes : s too small.
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=3  : error. the maximal number of iterations maxit (set to 20
+c             by the program) allowed for finding a smoothing spline
+c             with fp=s has been reached. probably causes : s too small
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=10 : error. on entry, the input data are controlled on validity
+c             the following restrictions must be satisfied.
+c             -1<=iopt<=1, 1<=k<=5, m>k, nest>2*k+2, w(i)>0,i=1,2,...,m
+c             xb<=x(1)<x(2)<...<x(m)<=xe, lwrk>=(k+1)*m+nest*(7+3*k)
+c             if iopt=-1: 2*k+2<=n<=min(nest,m+k+1)
+c                         xb<t(k+2)<t(k+3)<...<t(n-k-1)<xe
+c                       the schoenberg-whitney conditions, i.e. there
+c                       must be a subset of data points xx(j) such that
+c                         t(j) < xx(j) < t(j+k+1), j=1,2,...,n-k-1
+c             if iopt>=0: s>=0
+c                         if s=0 : nest >= m+k+1
+c             if one of these conditions is found to be violated,control
+c             is immediately repassed to the calling program. in that
+c             case there is no approximation returned.
+c
+c  further comments:
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the weighted least-squares polynomial of degree k if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   y(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in y(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   polynomial and the corresponding upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximation shows more detail) to obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if curfit is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. but, if the computation mode iopt=1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   curfit once more with the selected value for s but now with iopt=0.
+c   indeed, curfit may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c
+c  other subroutines required:
+c    fpback,fpbspl,fpchec,fpcurf,fpdisc,fpgivs,fpknot,fprati,fprota
+c
+c  references:
+c   dierckx p. : an algorithm for smoothing, differentiation and integ-
+c                ration of experimental data using spline functions,
+c                j.comp.appl.maths 1 (1975) 165-184.
+c   dierckx p. : a fast algorithm for smoothing data on a rectangular
+c                grid while using spline functions, siam j.numer.anal.
+c                19 (1982) 1286-1304.
+c   dierckx p. : an improved algorithm for curve fitting with spline
+c                functions, report tw54, dept. computer science,k.u.
+c                leuven, 1981.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1987
+c
+c  ..
+c  ..scalar arguments..
+      real*8 xb,xe,s,fp
+      integer iopt,m,k,nest,n,lwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),t(nest),c(nest),wrk(lwrk)
+      integer iwrk(nest)
+c  ..local scalars..
+      real*8 tol
+      integer i,ia,ib,ifp,ig,iq,iz,j,k1,k2,lwest,maxit,nmin
+c  ..
+c  we set up the parameters tol and maxit
+      maxit = 20
+      tol = 0.1d-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(k.le.0 .or. k.gt.5) go to 50
+      k1 = k+1
+      k2 = k1+1
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 50
+      nmin = 2*k1
+      if(m.lt.k1 .or. nest.lt.nmin) go to 50
+      lwest = m*k1+nest*(7+3*k)
+      if(lwrk.lt.lwest) go to 50
+      if(xb.gt.x(1) .or. xe.lt.x(m) .or. w(1).le.0.) go to 50
+      do 10 i=2,m
+         if(x(i-1).ge.x(i) .or. w(i).le.0.) go to 50
+  10  continue
+      if(iopt.ge.0) go to 30
+      if(n.lt.nmin .or. n.gt.nest) go to 50
+      j = n
+      do 20 i=1,k1
+         t(i) = xb
+         t(j) = xe
+         j = j-1
+  20  continue
+      call fpchec(x,m,t,n,k,ier)
+      if (ier.eq.0) go to 40
+      go to 50
+  30  if(s.lt.0.) go to 50
+      if(s.eq.0. .and. nest.lt.(m+k1)) go to 50
+      ier = 0
+c we partition the working space and determine the spline approximation.
+  40  ifp = 1
+      iz = ifp+nest
+      ia = iz+nest
+      ib = ia+nest*k1
+      ig = ib+nest*k2
+      iq = ig+nest*k2
+      call fpcurf(iopt,x,y,w,m,xb,xe,k,s,nest,tol,maxit,k1,k2,n,t,c,fp,
+     * wrk(ifp),wrk(iz),wrk(ia),wrk(ib),wrk(ig),wrk(iq),iwrk,ier)
+  50  return
+      end

Added: branches/Interpolate1D/fitpack/dblint.f
===================================================================
--- branches/Interpolate1D/fitpack/dblint.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/dblint.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,88 @@
+      real*8 function dblint(tx,nx,ty,ny,c,kx,ky,xb,xe,yb,ye,wrk)
+c  function dblint calculates the double integral
+c         / xe  / ye
+c        |     |      s(x,y) dx dy
+c    xb /  yb /
+c  with s(x,y) a bivariate spline of degrees kx and ky, given in the
+c  b-spline representation.
+c
+c  calling sequence:
+c     aint = dblint(tx,nx,ty,ny,c,kx,ky,xb,xe,yb,ye,wrk)
+c
+c  input parameters:
+c   tx    : real array, length nx, which contains the position of the
+c           knots in the x-direction.
+c   nx    : integer, giving the total number of knots in the x-direction
+c   ty    : real array, length ny, which contains the position of the
+c           knots in the y-direction.
+c   ny    : integer, giving the total number of knots in the y-direction
+c   c     : real array, length (nx-kx-1)*(ny-ky-1), which contains the
+c           b-spline coefficients.
+c   kx,ky : integer values, giving the degrees of the spline.
+c   xb,xe : real values, containing the boundaries of the integration
+c   yb,ye   domain. s(x,y) is considered to be identically zero out-
+c           side the rectangle (tx(kx+1),tx(nx-kx))*(ty(ky+1),ty(ny-ky))
+c
+c  output parameters:
+c   aint  : real , containing the double integral of s(x,y).
+c   wrk   : real array of dimension at least (nx+ny-kx-ky-2).
+c           used as working space.
+c           on exit, wrk(i) will contain the integral
+c                / xe
+c               | ni,kx+1(x) dx , i=1,2,...,nx-kx-1
+c           xb /
+c           with ni,kx+1(x) the normalized b-spline defined on
+c           the knots tx(i),...,tx(i+kx+1)
+c           wrk(j+nx-kx-1) will contain the integral
+c                / ye
+c               | nj,ky+1(y) dy , j=1,2,...,ny-ky-1
+c           yb /
+c           with nj,ky+1(y) the normalized b-spline defined on
+c           the knots ty(j),...,ty(j+ky+1)
+c
+c  other subroutines required: fpintb
+c
+c  references :
+c    gaffney p.w. : the calculation of indefinite integrals of b-splines
+c                   j. inst. maths applics 17 (1976) 37-41.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1989
+c
+c  ..scalar arguments..
+      integer nx,ny,kx,ky
+      real*8 xb,xe,yb,ye
+c  ..array arguments..
+      real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),wrk(nx+ny-kx-ky-2)
+c  ..local scalars..
+      integer i,j,l,m,nkx1,nky1
+      real*8 res
+c  ..
+      nkx1 = nx-kx-1
+      nky1 = ny-ky-1
+c  we calculate the integrals of the normalized b-splines ni,kx+1(x)
+      call fpintb(tx,nx,wrk,nkx1,xb,xe)
+c  we calculate the integrals of the normalized b-splines nj,ky+1(y)
+      call fpintb(ty,ny,wrk(nkx1+1),nky1,yb,ye)
+c  calculate the integral of s(x,y)
+      dblint = 0.
+      do 200 i=1,nkx1
+        res = wrk(i)
+        if(res.eq.0.) go to 200
+        m = (i-1)*nky1
+        l = nkx1
+        do 100 j=1,nky1
+          m = m+1
+          l = l+1
+          dblint = dblint+res*wrk(l)*c(m)
+ 100    continue
+ 200  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/evapol.f
===================================================================
--- branches/Interpolate1D/fitpack/evapol.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/evapol.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,82 @@
+      real*8 function evapol(tu,nu,tv,nv,c,rad,x,y)
+c  function program evacir evaluates the function f(x,y) = s(u,v),
+c  defined through the transformation
+c      x = u*rad(v)*cos(v)    y = u*rad(v)*sin(v)
+c  and where s(u,v) is a bicubic spline ( 0<=u<=1 , -pi<=v<=pi ), given
+c  in its standard b-spline representation.
+c
+c  calling sequence:
+c     f = evapol(tu,nu,tv,nv,c,rad,x,y)
+c
+c  input parameters:
+c   tu    : real array, length nu, which contains the position of the
+c           knots in the u-direction.
+c   nu    : integer, giving the total number of knots in the u-direction
+c   tv    : real array, length nv, which contains the position of the
+c           knots in the v-direction.
+c   nv    : integer, giving the total number of knots in the v-direction
+c   c     : real array, length (nu-4)*(nv-4), which contains the
+c           b-spline coefficients.
+c   rad   : real function subprogram, defining the boundary of the
+c           approximation domain. must be declared external in the
+c           calling (sub)-program
+c   x,y   : real values.
+c           before entry x and y must be set to the co-ordinates of
+c           the point where f(x,y) must be evaluated.
+c
+c  output parameter:
+c   f     : real
+c           on exit f contains the value of f(x,y)
+c
+c  other subroutines required:
+c    bispev,fpbisp,fpbspl
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1989
+c
+c  ..scalar arguments..
+      integer nu,nv
+      real*8 x,y
+c  ..array arguments..
+      real*8 tu(nu),tv(nv),c((nu-4)*(nv-4))
+c  ..user specified function
+      real*8 rad
+c  ..local scalars..
+      integer ier
+      real*8 u,v,r,f,one,dist
+c  ..local arrays
+      real*8 wrk(8)
+      integer iwrk(2)
+c  ..function references
+      real*8 atan2,sqrt
+c  ..
+c  calculate the (u,v)-coordinates of the given point.
+      one = 1
+      u = 0.
+      v = 0.
+      dist = x**2+y**2
+      if(dist.le.0.) go to 10
+      v = atan2(y,x)
+      r = rad(v)
+      if(r.le.0.) go to 10
+      u = sqrt(dist)/r
+      if(u.gt.one) u = one
+c  evaluate s(u,v)
+  10  call bispev(tu,nu,tv,nv,c,3,3,u,1,v,1,f,wrk,8,iwrk,2,ier)
+      evapol = f
+      return
+      end
+

Added: branches/Interpolate1D/fitpack/fourco.f
===================================================================
--- branches/Interpolate1D/fitpack/fourco.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fourco.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,96 @@
+      subroutine fourco(t,n,c,alfa,m,ress,resc,wrk1,wrk2,ier)
+c  subroutine fourco calculates the integrals
+c                    /t(n-3)
+c    ress(i) =      !        s(x)*sin(alfa(i)*x) dx    and
+c              t(4)/
+c                    /t(n-3)
+c    resc(i) =      !        s(x)*cos(alfa(i)*x) dx, i=1,...,m,
+c              t(4)/
+c  where s(x) denotes a cubic spline which is given in its
+c  b-spline representation.
+c
+c  calling sequence:
+c     call fourco(t,n,c,alfa,m,ress,resc,wrk1,wrk2,ier)
+c
+c  input parameters:
+c    t    : real array,length n, containing the knots of s(x).
+c    n    : integer, containing the total number of knots. n>=10.
+c    c    : real array,length n, containing the b-spline coefficients.
+c    alfa : real array,length m, containing the parameters alfa(i).
+c    m    : integer, specifying the number of integrals to be computed.
+c    wrk1 : real array,length n. used as working space
+c    wrk2 : real array,length n. used as working space
+c
+c  output parameters:
+c    ress : real array,length m, containing the integrals ress(i).
+c    resc : real array,length m, containing the integrals resc(i).
+c    ier  : error flag:
+c      ier=0 : normal return.
+c      ier=10: invalid input data (see restrictions).
+c
+c  restrictions:
+c    n >= 10
+c    t(4) < t(5) < ... < t(n-4) < t(n-3).
+c    t(1) <= t(2) <= t(3) <= t(4).
+c    t(n-3) <= t(n-2) <= t(n-1) <= t(n).
+c
+c  other subroutines required: fpbfou,fpcsin
+c
+c  references :
+c    dierckx p. : calculation of fouriercoefficients of discrete
+c                 functions using cubic splines. j. computational
+c                 and applied mathematics 3 (1977) 207-209.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer n,m,ier
+c  ..array arguments..
+      real*8 t(n),c(n),wrk1(n),wrk2(n),alfa(m),ress(m),resc(m)
+c  ..local scalars..
+      integer i,j,n4
+      real*8 rs,rc
+c  ..
+      n4 = n-4
+c  before starting computations a data check is made. in the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(n.lt.10) go to 50
+      j = n
+      do 10 i=1,3
+        if(t(i).gt.t(i+1)) go to 50
+        if(t(j).lt.t(j-1)) go to 50
+        j = j-1
+  10  continue
+      do 20 i=4,n4
+        if(t(i).ge.t(i+1)) go to 50
+  20  continue
+      ier = 0
+c  main loop for the different alfa(i).
+      do 40 i=1,m
+c  calculate the integrals
+c    wrk1(j) = integral(nj,4(x)*sin(alfa*x))    and
+c    wrk2(j) = integral(nj,4(x)*cos(alfa*x)),  j=1,2,...,n-4,
+c  where nj,4(x) denotes the normalised cubic b-spline defined on the
+c  knots t(j),t(j+1),...,t(j+4).
+         call fpbfou(t,n,alfa(i),wrk1,wrk2)
+c  calculate the integrals ress(i) and resc(i).
+         rs = 0.
+         rc = 0.
+         do 30 j=1,n4
+            rs = rs+c(j)*wrk1(j)
+            rc = rc+c(j)*wrk2(j)
+  30     continue
+         ress(i) = rs
+         resc(i) = rc
+  40  continue
+  50  return
+      end

Added: branches/Interpolate1D/fitpack/fpader.f
===================================================================
--- branches/Interpolate1D/fitpack/fpader.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpader.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,57 @@
+      subroutine fpader(t,n,c,k1,x,l,d)
+c  subroutine fpader calculates the derivatives
+c             (j-1)
+c     d(j) = s     (x) , j=1,2,...,k1
+c  of a spline of order k1 at the point t(l)<=x<t(l+1), using the
+c  stable recurrence scheme of de boor
+c  ..
+c  ..scalar arguments..
+      real*8 x
+      integer n,k1,l
+c  ..array arguments..
+      real*8 t(n),c(n),d(k1)
+c  ..local scalars..
+      integer i,ik,j,jj,j1,j2,ki,kj,li,lj,lk
+      real*8 ak,fac,one
+c  ..local array..
+      real*8 h(20)
+c  ..
+      one = 0.1d+01
+      lk = l-k1
+      do 100 i=1,k1
+        ik = i+lk
+        h(i) = c(ik)
+ 100  continue
+      kj = k1
+      fac = one
+      do 700 j=1,k1
+        ki = kj
+        j1 = j+1
+        if(j.eq.1) go to 300
+        i = k1
+        do 200 jj=j,k1
+          li = i+lk
+          lj = li+kj
+          h(i) = (h(i)-h(i-1))/(t(lj)-t(li))
+          i = i-1
+ 200    continue
+ 300    do 400 i=j,k1
+          d(i) = h(i)
+ 400    continue
+        if(j.eq.k1) go to 600
+        do 500 jj=j1,k1
+          ki = ki-1
+          i = k1
+          do 500 j2=jj,k1
+            li = i+lk
+            lj = li+ki
+            d(i) = ((x-t(li))*d(i)+(t(lj)-x)*d(i-1))/(t(lj)-t(li))
+            i = i-1
+ 500    continue
+ 600    d(j) = d(k1)*fac
+        ak = k1-j
+        fac = fac*ak
+        kj = kj-1
+ 700  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpadno.f
===================================================================
--- branches/Interpolate1D/fitpack/fpadno.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpadno.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,59 @@
+      subroutine fpadno(maxtr,up,left,right,info,count,merk,jbind,
+     * n1,ier)
+c  subroutine fpadno adds a branch of length n1 to the triply linked
+c  tree,the information of which is kept in the arrays up,left,right
+c  and info. the information field of the nodes of this new branch is
+c  given in the array jbind. in linking the new branch fpadno takes
+c  account of the property of the tree that
+c    info(k) < info(right(k)) ; info(k) < info(left(k))
+c  if necessary the subroutine calls subroutine fpfrno to collect the
+c  free nodes of the tree. if no computer words are available at that
+c  moment, the error parameter ier is set to 1.
+c  ..
+c  ..scalar arguments..
+      integer maxtr,count,merk,n1,ier
+c  ..array arguments..
+      integer up(maxtr),left(maxtr),right(maxtr),info(maxtr),jbind(n1)
+c  ..local scalars..
+      integer k,niveau,point
+      logical bool
+c  ..subroutine references..
+c    fpfrno
+c  ..
+      point = 1
+      niveau = 1
+  10  k = left(point)
+      bool = .true.
+  20  if(k.eq.0) go to 50
+      if (info(k)-jbind(niveau).lt.0) go to 30
+      if (info(k)-jbind(niveau).eq.0) go to 40
+      go to 50
+  30  point = k
+      k = right(point)
+      bool = .false.
+      go to 20
+  40  point = k
+      niveau = niveau+1
+      go to 10
+  50  if(niveau.gt.n1) go to 90
+      count = count+1
+      if(count.le.maxtr) go to 60
+      call fpfrno(maxtr,up,left,right,info,point,merk,n1,count,ier)
+      if(ier.ne.0) go to 100
+  60  info(count) = jbind(niveau)
+      left(count) = 0
+      right(count) = k
+      if(bool) go to 70
+      bool = .true.
+      right(point) = count
+      up(count) = up(point)
+      go to 80
+  70  up(count) = point
+      left(point) = count
+  80  point = count
+      niveau = niveau+1
+      k = 0
+      go to 50
+  90  ier = 0
+ 100  return
+      end

Added: branches/Interpolate1D/fitpack/fpadpo.f
===================================================================
--- branches/Interpolate1D/fitpack/fpadpo.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpadpo.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,70 @@
+      subroutine fpadpo(idim,t,n,c,nc,k,cp,np,cc,t1,t2)
+c  given a idim-dimensional spline curve of degree k, in its b-spline
+c  representation ( knots t(j),j=1,...,n , b-spline coefficients c(j),
+c  j=1,...,nc) and given also a polynomial curve in its b-spline
+c  representation ( coefficients cp(j), j=1,...,np), subroutine fpadpo
+c  calculates the b-spline representation (coefficients c(j),j=1,...,nc)
+c  of the sum of the two curves.
+c
+c  other subroutine required : fpinst
+c
+c  ..
+c  ..scalar arguments..
+      integer idim,k,n,nc,np
+c  ..array arguments..
+      real*8 t(n),c(nc),cp(np),cc(nc),t1(n),t2(n)
+c  ..local scalars..
+      integer i,ii,j,jj,k1,l,l1,n1,n2,nk1,nk2
+c  ..
+      k1 = k+1
+      nk1 = n-k1
+c  initialization
+      j = 1
+      l = 1
+      do 20 jj=1,idim
+        l1 = j
+        do 10 ii=1,k1
+          cc(l1) = cp(l)
+          l1 = l1+1
+          l = l+1
+  10    continue
+        j = j+n
+        l = l+k1
+  20  continue
+      if(nk1.eq.k1) go to 70
+      n1 = k1*2
+      j = n
+      l = n1
+      do 30 i=1,k1
+        t1(i) = t(i)
+        t1(l) = t(j)
+        l = l-1
+        j = j-1
+  30  continue
+c  find the b-spline representation of the given polynomial curve
+c  according to the given set of knots.
+      nk2 = nk1-1
+      do 60 l=k1,nk2
+        l1 = l+1
+        j = 1
+        do 40 i=1,idim
+          call fpinst(0,t1,n1,cc(j),k,t(l1),l,t2,n2,cc(j),n)
+          j = j+n
+  40    continue
+        do 50 i=1,n2
+          t1(i) = t2(i)
+  50    continue
+        n1 = n2
+  60  continue
+c  find the b-spline representation of the resulting curve.
+  70  j = 1
+      do 90 jj=1,idim
+        l = j
+        do 80 i=1,nk1
+          c(l) = cc(l)+c(l)
+          l = l+1
+  80    continue
+        j = j+n
+  90  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpback.f
===================================================================
--- branches/Interpolate1D/fitpack/fpback.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpback.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,31 @@
+      subroutine fpback(a,z,n,k,c,nest)
+c  subroutine fpback calculates the solution of the system of
+c  equations a*c = z with a a n x n upper triangular matrix
+c  of bandwidth k.
+c  ..
+c  ..scalar arguments..
+      integer n,k,nest
+c  ..array arguments..
+      real*8 a(nest,k),z(n),c(n)
+c  ..local scalars..
+      real*8 store
+      integer i,i1,j,k1,l,m
+c  ..
+      k1 = k-1
+      c(n) = z(n)/a(n,1)
+      i = n-1
+      if(i.eq.0) go to 30
+      do 20 j=2,n
+        store = z(i)
+        i1 = k1
+        if(j.le.k1) i1 = j-1
+        m = i
+        do 10 l=1,i1
+          m = m+1
+          store = store-c(m)*a(i,l+1)
+  10    continue
+        c(i) = store/a(i,1)
+        i = i-1
+  20  continue
+  30  return
+      end

Added: branches/Interpolate1D/fitpack/fpbacp.f
===================================================================
--- branches/Interpolate1D/fitpack/fpbacp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpbacp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,58 @@
+      subroutine fpbacp(a,b,z,n,k,c,k1,nest)
+c  subroutine fpbacp calculates the solution of the system of equations
+c  g * c = z  with g  a n x n upper triangular matrix of the form
+c            ! a '   !
+c        g = !   ' b !
+c            ! 0 '   !
+c  with b a n x k matrix and a a (n-k) x (n-k) upper triangular
+c  matrix of bandwidth k1.
+c  ..
+c  ..scalar arguments..
+      integer n,k,k1,nest
+c  ..array arguments..
+      real*8 a(nest,k1),b(nest,k),z(n),c(n)
+c  ..local scalars..
+      integer i,i1,j,l,l0,l1,n2
+      real*8 store
+c  ..
+      n2 = n-k
+      l = n
+      do 30 i=1,k
+        store = z(l)
+        j = k+2-i
+        if(i.eq.1) go to 20
+        l0 = l
+        do 10 l1=j,k
+          l0 = l0+1
+          store = store-c(l0)*b(l,l1)
+  10    continue
+  20    c(l) = store/b(l,j-1)
+        l = l-1
+        if(l.eq.0) go to 80
+  30  continue
+      do 50 i=1,n2
+        store = z(i)
+        l = n2
+        do 40 j=1,k
+          l = l+1
+          store = store-c(l)*b(i,j)
+  40    continue
+        c(i) = store
+  50  continue
+      i = n2
+      c(i) = c(i)/a(i,1)
+      if(i.eq.1) go to 80
+      do 70 j=2,n2
+        i = i-1
+        store = c(i)
+        i1 = k
+        if(j.le.k) i1=j-1
+        l = i
+        do 60 l0=1,i1
+          l = l+1
+          store = store-c(l)*a(i,l0+1)
+  60    continue
+        c(i) = store/a(i,1)
+  70  continue
+  80  return
+      end

Added: branches/Interpolate1D/fitpack/fpbfout.f
===================================================================
--- branches/Interpolate1D/fitpack/fpbfout.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpbfout.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,197 @@
+      subroutine fpbfou(t,n,par,ress,resc)
+c  subroutine fpbfou calculates the integrals
+c                    /t(n-3)
+c    ress(j) =      !        nj,4(x)*sin(par*x) dx    and
+c              t(4)/
+c                    /t(n-3)
+c    resc(j) =      !        nj,4(x)*cos(par*x) dx ,  j=1,2,...n-4
+c              t(4)/
+c  where nj,4(x) denotes the cubic b-spline defined on the knots
+c  t(j),t(j+1),...,t(j+4).
+c
+c  calling sequence:
+c     call fpbfou(t,n,par,ress,resc)
+c
+c  input parameters:
+c    t    : real array,length n, containing the knots.
+c    n    : integer, containing the number of knots.
+c    par  : real, containing the value of the parameter par.
+c
+c  output parameters:
+c    ress  : real array,length n, containing the integrals ress(j).
+c    resc  : real array,length n, containing the integrals resc(j).
+c
+c  restrictions:
+c    n >= 10, t(4) < t(5) < ... < t(n-4) < t(n-3).
+c  ..
+c  ..scalar arguments..
+      integer n
+      real*8 par
+c  ..array arguments..
+      real*8 t(n),ress(n),resc(n)
+c  ..local scalars..
+      integer i,ic,ipj,is,j,jj,jp1,jp4,k,li,lj,ll,nmj,nm3,nm7
+      real*8 ak,beta,con1,con2,c1,c2,delta,eps,fac,f1,f2,f3,one,quart,
+     * sign,six,s1,s2,term
+c  ..local arrays..
+      real*8 co(5),si(5),hs(5),hc(5),rs(3),rc(3)
+c  ..function references..
+      real*8 cos,sin,abs
+c  ..
+c  initialization.
+      one = 0.1e+01
+      six = 0.6e+01
+      eps = 0.1e-07
+      quart = 0.25e0
+      con1 = 0.5e-01
+      con2 = 0.12e+03
+      nm3 = n-3
+      nm7 = n-7
+      if(par.ne.0.) term = six/par
+      beta = par*t(4)
+      co(1) = cos(beta)
+      si(1) = sin(beta)
+c  calculate the integrals ress(j) and resc(j), j=1,2,3 by setting up
+c  a divided difference table.
+      do 30 j=1,3
+        jp1 = j+1
+        jp4 = j+4
+        beta = par*t(jp4)
+        co(jp1) = cos(beta)
+        si(jp1) = sin(beta)
+        call fpcsin(t(4),t(jp4),par,si(1),co(1),si(jp1),co(jp1),
+     *  rs(j),rc(j))
+        i = 5-j
+        hs(i) = 0.
+        hc(i) = 0.
+        do 10 jj=1,j
+          ipj = i+jj
+          hs(ipj) = rs(jj)
+          hc(ipj) = rc(jj)
+  10    continue
+        do 20 jj=1,3
+          if(i.lt.jj) i = jj
+          k = 5
+          li = jp4
+          do 20 ll=i,4
+            lj = li-jj
+            fac = t(li)-t(lj)
+            hs(k) = (hs(k)-hs(k-1))/fac
+            hc(k) = (hc(k)-hc(k-1))/fac
+            k = k-1
+            li = li-1
+  20    continue
+        ress(j) = hs(5)-hs(4)
+        resc(j) = hc(5)-hc(4)
+  30  continue
+      if(nm7.lt.4) go to 160
+c  calculate the integrals ress(j) and resc(j),j=4,5,...,n-7.
+      do 150 j=4,nm7
+        jp4 = j+4
+        beta = par*t(jp4)
+        co(5) = cos(beta)
+        si(5) = sin(beta)
+        delta = t(jp4)-t(j)
+c  the way of computing ress(j) and resc(j) depends on the value of
+c  beta = par*(t(j+4)-t(j)).
+        beta = delta*par
+        if(abs(beta).le.one) go to 60
+c  if !beta! > 1 the integrals are calculated by setting up a divided
+c  difference table.
+        do 40 k=1,5
+          hs(k) = si(k)
+          hc(k) = co(k)
+  40    continue
+        do 50 jj=1,3
+          k = 5
+          li = jp4
+          do 50 ll=jj,4
+            lj = li-jj
+            fac = par*(t(li)-t(lj))
+            hs(k) = (hs(k)-hs(k-1))/fac
+            hc(k) = (hc(k)-hc(k-1))/fac
+            k = k-1
+            li = li-1
+  50    continue
+        s2 = (hs(5)-hs(4))*term
+        c2 = (hc(5)-hc(4))*term
+        go to 130
+c  if !beta! <= 1 the integrals are calculated by evaluating a series
+c  expansion.
+  60    f3 = 0.
+        do 70 i=1,4
+          ipj = i+j
+          hs(i) = par*(t(ipj)-t(j))
+          hc(i) = hs(i)
+          f3 = f3+hs(i)
+  70    continue
+        f3 = f3*con1
+        c1 = quart
+        s1 = f3
+        if(abs(f3).le.eps) go to 120
+        sign = one
+        fac = con2
+        k = 5
+        is = 0
+        do 110 ic=1,20
+          k = k+1
+          ak = k
+          fac = fac*ak
+          f1 = 0.
+          f3 = 0.
+          do 80 i=1,4
+            f1 = f1+hc(i)
+            f2 = f1*hs(i)
+            hc(i) = f2
+            f3 = f3+f2
+  80      continue
+          f3 = f3*six/fac
+          if(is.eq.0) go to 90
+          is = 0
+          s1 = s1+f3*sign
+          go to 100
+  90      sign = -sign
+          is = 1
+          c1 = c1+f3*sign
+ 100      if(abs(f3).le.eps) go to 120
+ 110    continue
+ 120    s2 = delta*(co(1)*s1+si(1)*c1)
+        c2 = delta*(co(1)*c1-si(1)*s1)
+ 130    ress(j) = s2
+        resc(j) = c2
+        do 140 i=1,4
+          co(i) = co(i+1)
+          si(i) = si(i+1)
+ 140    continue
+ 150  continue
+c  calculate the integrals ress(j) and resc(j),j=n-6,n-5,n-4 by setting
+c  up a divided difference table.
+ 160  do 190 j=1,3
+        nmj = nm3-j
+        i = 5-j
+        call fpcsin(t(nm3),t(nmj),par,si(4),co(4),si(i-1),co(i-1),
+     *  rs(j),rc(j))
+        hs(i) = 0.
+        hc(i) = 0.
+        do 170 jj=1,j
+          ipj = i+jj
+          hc(ipj) = rc(jj)
+          hs(ipj) = rs(jj)
+ 170    continue
+        do 180 jj=1,3
+          if(i.lt.jj) i = jj
+          k = 5
+          li = nmj
+          do 180 ll=i,4
+            lj = li+jj
+            fac = t(lj)-t(li)
+            hs(k) = (hs(k-1)-hs(k))/fac
+            hc(k) = (hc(k-1)-hc(k))/fac
+            k = k-1
+            li = li+1
+ 180    continue
+        ress(nmj) = hs(4)-hs(5)
+        resc(nmj) = hc(4)-hc(5)
+ 190  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpbisp.f
===================================================================
--- branches/Interpolate1D/fitpack/fpbisp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpbisp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,79 @@
+      subroutine fpbisp(tx,nx,ty,ny,c,kx,ky,x,mx,y,my,z,wx,wy,lx,ly)
+c  ..scalar arguments..
+      integer nx,ny,kx,ky,mx,my
+c  ..array arguments..
+      integer lx(mx),ly(my)
+      real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),x(mx),y(my),z(mx*my),
+     * wx(mx,kx+1),wy(my,ky+1)
+c  ..local scalars..
+      integer kx1,ky1,l,l1,l2,m,nkx1,nky1
+      real*8 arg,sp,tb,te
+c  ..local arrays..
+      real*8 h(6)
+c  ..subroutine references..
+c    fpbspl
+c  ..
+      kx1 = kx+1
+      nkx1 = nx-kx1
+      tb = tx(kx1)
+      te = tx(nkx1+1)
+      l = kx1
+      l1 = l+1
+      do 40 i=1,mx
+        arg = x(i)
+        if(arg.lt.tb) arg = tb
+        if(arg.gt.te) arg = te
+  10    if(arg.lt.tx(l1) .or. l.eq.nkx1) go to 20
+        l = l1
+        l1 = l+1
+        go to 10
+  20    call fpbspl(tx,nx,kx,arg,l,h)
+        lx(i) = l-kx1
+        do 30 j=1,kx1
+          wx(i,j) = h(j)
+  30    continue
+  40  continue
+      ky1 = ky+1
+      nky1 = ny-ky1
+      tb = ty(ky1)
+      te = ty(nky1+1)
+      l = ky1
+      l1 = l+1
+      do 80 i=1,my
+        arg = y(i)
+        if(arg.lt.tb) arg = tb
+        if(arg.gt.te) arg = te
+  50    if(arg.lt.ty(l1) .or. l.eq.nky1) go to 60
+        l = l1
+        l1 = l+1
+        go to 50
+  60    call fpbspl(ty,ny,ky,arg,l,h)
+        ly(i) = l-ky1
+        do 70 j=1,ky1
+          wy(i,j) = h(j)
+  70    continue
+  80  continue
+      m = 0
+      do 130 i=1,mx
+        l = lx(i)*nky1
+        do 90 i1=1,kx1
+          h(i1) = wx(i,i1)
+  90    continue
+        do 120 j=1,my
+          l1 = l+ly(j)
+          sp = 0.
+          do 110 i1=1,kx1
+            l2 = l1
+            do 100 j1=1,ky1
+              l2 = l2+1
+              sp = sp+c(l2)*h(i1)*wy(j,j1)
+ 100        continue
+            l1 = l1+nky1
+ 110      continue
+          m = m+1
+          z(m) = sp
+ 120    continue
+ 130  continue
+      return
+      end
+

Added: branches/Interpolate1D/fitpack/fpbspl.f
===================================================================
--- branches/Interpolate1D/fitpack/fpbspl.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpbspl.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,42 @@
+      subroutine fpbspl(t,n,k,x,l,h)
+c  subroutine fpbspl evaluates the (k+1) non-zero b-splines of
+c  degree k at t(l) <= x < t(l+1) using the stable recurrence
+c  relation of de boor and cox.
+c  Travis Oliphant  2007
+c    changed so that weighting of 0 is used when knots with
+c      multiplicity are present.
+c    Also, notice that l+k <= n and 1 <= l+1-k
+c      or else the routine will be accessing memory outside t
+c      Thus it is imperative that that k <= l <= n-k but this
+c      is not checked.
+c  ..
+c  ..scalar arguments..
+      real*8 x
+      integer n,k,l
+c  ..array arguments..
+      real*8 t(n),h(20)
+c  ..local scalars..
+      real*8 f,one
+      integer i,j,li,lj
+c  ..local arrays..
+      real*8 hh(19)
+c  ..
+      one = 0.1d+01
+      h(1) = one
+      do 20 j=1,k
+        do 10 i=1,j
+          hh(i) = h(i)
+  10    continue
+        h(1) = 0.0d0
+        do 20 i=1,j
+          li = l+i
+          lj = li-j
+          if (t(li).ne.t(lj)) goto 15
+          h(i+1) = 0.0d0 
+          goto 20
+  15      f = hh(i)/(t(li)-t(lj)) 
+          h(i) = h(i)+f*(t(li)-x)
+          h(i+1) = f*(x-t(lj))
+  20  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpchec.f
===================================================================
--- branches/Interpolate1D/fitpack/fpchec.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpchec.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,62 @@
+      subroutine fpchec(x,m,t,n,k,ier)
+c  subroutine fpchec verifies the number and the position of the knots
+c  t(j),j=1,2,...,n of a spline of degree k, in relation to the number
+c  and the position of the data points x(i),i=1,2,...,m. if all of the
+c  following conditions are fulfilled, the error parameter ier is set
+c  to zero. if one of the conditions is violated ier is set to ten.
+c      1) k+1 <= n-k-1 <= m
+c      2) t(1) <= t(2) <= ... <= t(k+1)
+c         t(n-k) <= t(n-k+1) <= ... <= t(n)
+c      3) t(k+1) < t(k+2) < ... < t(n-k)
+c      4) t(k+1) <= x(i) <= t(n-k)
+c      5) the conditions specified by schoenberg and whitney must hold
+c         for at least one subset of data points, i.e. there must be a
+c         subset of data points y(j) such that
+c             t(j) < y(j) < t(j+k+1), j=1,2,...,n-k-1
+c  ..
+c  ..scalar arguments..
+      integer m,n,k,ier
+c  ..array arguments..
+      real*8 x(m),t(n)
+c  ..local scalars..
+      integer i,j,k1,k2,l,nk1,nk2,nk3
+      real*8 tj,tl
+c  ..
+      k1 = k+1
+      k2 = k1+1
+      nk1 = n-k1
+      nk2 = nk1+1
+      ier = 10
+c  check condition no 1
+      if(nk1.lt.k1 .or. nk1.gt.m) go to 80
+c  check condition no 2
+      j = n
+      do 20 i=1,k
+        if(t(i).gt.t(i+1)) go to 80
+        if(t(j).lt.t(j-1)) go to 80
+        j = j-1
+  20  continue
+c  check condition no 3
+      do 30 i=k2,nk2
+        if(t(i).le.t(i-1)) go to 80
+  30  continue
+c  check condition no 4
+      if(x(1).lt.t(k1) .or. x(m).gt.t(nk2)) go to 80
+c  check condition no 5
+      if(x(1).ge.t(k2) .or. x(m).le.t(nk1)) go to 80
+      i = 1
+      l = k2
+      nk3 = nk1-1
+      if(nk3.lt.2) go to 70
+      do 60 j=2,nk3
+        tj = t(j)
+        l = l+1
+        tl = t(l)
+  40    i = i+1
+        if(i.ge.m) go to 80
+        if(x(i).le.tj) go to 40
+        if(x(i).ge.tl) go to 80
+  60  continue
+  70  ier = 0
+  80  return
+      end

Added: branches/Interpolate1D/fitpack/fpched.f
===================================================================
--- branches/Interpolate1D/fitpack/fpched.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpched.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,69 @@
+      subroutine fpched(x,m,t,n,k,ib,ie,ier)
+c  subroutine fpched verifies the number and the position of the knots
+c  t(j),j=1,2,...,n of a spline of degree k,with ib derative constraints
+c  at x(1) and ie constraints at x(m), in relation to the number and
+c  the position of the data points x(i),i=1,2,...,m. if all of the
+c  following conditions are fulfilled, the error parameter ier is set
+c  to zero. if one of the conditions is violated ier is set to ten.
+c      1) k+1 <= n-k-1 <= m + max(0,ib-1) + max(0,ie-1)
+c      2) t(1) <= t(2) <= ... <= t(k+1)
+c         t(n-k) <= t(n-k+1) <= ... <= t(n)
+c      3) t(k+1) < t(k+2) < ... < t(n-k)
+c      4) t(k+1) <= x(i) <= t(n-k)
+c      5) the conditions specified by schoenberg and whitney must hold
+c         for at least one subset of data points, i.e. there must be a
+c         subset of data points y(j) such that
+c             t(j) < y(j) < t(j+k+1), j=1+ib1,2+ib1,...,n-k-1-ie1
+c               with ib1 = max(0,ib-1), ie1 = max(0,ie-1)
+c  ..
+c  ..scalar arguments..
+      integer m,n,k,ib,ie,ier
+c  ..array arguments..
+      real*8 x(m),t(n)
+c  ..local scalars..
+      integer i,ib1,ie1,j,jj,k1,k2,l,nk1,nk2,nk3
+      real*8 tj,tl
+c  ..
+      k1 = k+1
+      k2 = k1+1
+      nk1 = n-k1
+      nk2 = nk1+1
+      ib1 = ib-1
+      if(ib1.lt.0) ib1 = 0
+      ie1 = ie-1
+      if(ie1.lt.0) ie1 = 0
+      ier = 10
+c  check condition no 1
+      if(nk1.lt.k1 .or. nk1.gt.(m+ib1+ie1)) go to 80
+c  check condition no 2
+      j = n
+      do 20 i=1,k
+        if(t(i).gt.t(i+1)) go to 80
+        if(t(j).lt.t(j-1)) go to 80
+        j = j-1
+  20  continue
+c  check condition no 3
+      do 30 i=k2,nk2
+        if(t(i).le.t(i-1)) go to 80
+  30  continue
+c  check condition no 4
+      if(x(1).lt.t(k1) .or. x(m).gt.t(nk2)) go to 80
+c  check condition no 5
+      if(x(1).ge.t(k2) .or. x(m).le.t(nk1)) go to 80
+      i = 1
+      jj = 2+ib1
+      l = jj+k
+      nk3 = nk1-1-ie1
+      if(nk3.lt.jj) go to 70
+      do 60 j=jj,nk3
+        tj = t(j)
+        l = l+1
+        tl = t(l)
+  40    i = i+1
+        if(i.ge.m) go to 80
+        if(x(i).le.tj) go to 40
+        if(x(i).ge.tl) go to 80
+  60  continue
+  70  ier = 0
+  80  return
+      end

Added: branches/Interpolate1D/fitpack/fpchep.f
===================================================================
--- branches/Interpolate1D/fitpack/fpchep.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpchep.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,81 @@
+      subroutine fpchep(x,m,t,n,k,ier)
+c  subroutine fpchep verifies the number and the position of the knots
+c  t(j),j=1,2,...,n of a periodic spline of degree k, in relation to
+c  the number and the position of the data points x(i),i=1,2,...,m.
+c  if all of the following conditions are fulfilled, ier is set
+c  to zero. if one of the conditions is violated ier is set to ten.
+c      1) k+1 <= n-k-1 <= m+k-1
+c      2) t(1) <= t(2) <= ... <= t(k+1)
+c         t(n-k) <= t(n-k+1) <= ... <= t(n)
+c      3) t(k+1) < t(k+2) < ... < t(n-k)
+c      4) t(k+1) <= x(i) <= t(n-k)
+c      5) the conditions specified by schoenberg and whitney must hold
+c         for at least one subset of data points, i.e. there must be a
+c         subset of data points y(j) such that
+c             t(j) < y(j) < t(j+k+1), j=k+1,...,n-k-1
+c  ..
+c  ..scalar arguments..
+      integer m,n,k,ier
+c  ..array arguments..
+      real*8 x(m),t(n)
+c  ..local scalars..
+      integer i,i1,i2,j,j1,k1,k2,l,l1,l2,mm,m1,nk1,nk2
+      real*8 per,tj,tl,xi
+c  ..
+      k1 = k+1
+      k2 = k1+1
+      nk1 = n-k1
+      nk2 = nk1+1
+      m1 = m-1
+      ier = 10
+c  check condition no 1
+      if(nk1.lt.k1 .or. n.gt.m+2*k) go to 130
+c  check condition no 2
+      j = n
+      do 20 i=1,k
+        if(t(i).gt.t(i+1)) go to 130
+        if(t(j).lt.t(j-1)) go to 130
+        j = j-1
+  20  continue
+c  check condition no 3
+      do 30 i=k2,nk2
+        if(t(i).le.t(i-1)) go to 130
+  30  continue
+c  check condition no 4
+      if(x(1).lt.t(k1) .or. x(m).gt.t(nk2)) go to 130
+c  check condition no 5
+      l1 = k1
+      l2 = 1
+      do 50 l=1,m
+         xi = x(l)
+  40     if(xi.lt.t(l1+1) .or. l.eq.nk1) go to 50
+         l1 = l1+1
+         l2 = l2+1
+         if(l2.gt.k1) go to 60
+         go to 40
+  50  continue
+      l = m
+  60  per = t(nk2)-t(k1)
+      do 120 i1=2,l
+         i = i1-1
+         mm = i+m1
+         do 110 j=k1,nk1
+            tj = t(j)
+            j1 = j+k1
+            tl = t(j1)
+  70        i = i+1
+            if(i.gt.mm) go to 120
+            i2 = i-m1
+            if (i2.le.0) go to 80
+            go to 90
+  80        xi = x(i)
+            go to 100
+  90        xi = x(i2)+per
+ 100        if(xi.le.tj) go to 70
+            if(xi.ge.tl) go to 120
+ 110     continue
+         ier = 0
+         go to 130
+ 120  continue
+ 130  return
+      end

Added: branches/Interpolate1D/fitpack/fpclos.f
===================================================================
--- branches/Interpolate1D/fitpack/fpclos.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpclos.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,714 @@
+      subroutine fpclos(iopt,idim,m,u,mx,x,w,k,s,nest,tol,maxit,k1,k2,
+     * n,t,nc,c,fp,fpint,z,a1,a2,b,g1,g2,q,nrdata,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 s,tol,fp
+      integer iopt,idim,m,mx,k,nest,maxit,k1,k2,n,nc,ier
+c  ..array arguments..
+      real*8 u(m),x(mx),w(m),t(nest),c(nc),fpint(nest),z(nc),a1(nest,k1)
+     *,
+     * a2(nest,k),b(nest,k2),g1(nest,k2),g2(nest,k1),q(m,k1)
+      integer nrdata(nest)
+c  ..local scalars..
+      real*8 acc,cos,d1,fac,fpart,fpms,fpold,fp0,f1,f2,f3,p,per,pinv,piv
+     *,
+     * p1,p2,p3,sin,store,term,ui,wi,rn,one,con1,con4,con9,half
+      integer i,ich1,ich3,ij,ik,it,iter,i1,i2,i3,j,jj,jk,jper,j1,j2,kk,
+     * kk1,k3,l,l0,l1,l5,mm,m1,new,nk1,nk2,nmax,nmin,nplus,npl1,
+     * nrint,n10,n11,n7,n8
+c  ..local arrays..
+      real*8 h(6),h1(7),h2(6),xi(10)
+c  ..function references..
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpbacp,fpbspl,fpgivs,fpdisc,fpknot,fprota
+c  ..
+c  set constants
+      one = 0.1e+01
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      half = 0.5e0
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1: determination of the number of knots and their position     c
+c  **************************************************************      c
+c  given a set of knots we compute the least-squares closed curve      c
+c  sinf(u). if the sum f(p=inf) <= s we accept the choice of knots.    c
+c  if iopt=-1 sinf(u) is the requested curve                           c
+c  if iopt=0 or iopt=1 we check whether we can accept the knots:       c
+c    if fp <=s we will continue with the current set of knots.         c
+c    if fp > s we will increase the number of knots and compute the    c
+c       corresponding least-squares curve until finally fp<=s.         c
+c  the initial choice of knots depends on the value of s and iopt.     c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmax = m+2*k.                                        c
+c    if s > 0 and                                                      c
+c      iopt=0 we first compute the least-squares polynomial curve of   c
+c      degree k; n = nmin = 2*k+2. since s(u) must be periodic we      c
+c      find that s(u) reduces to a fixed point.                        c
+c      iopt=1 we start with the set of knots found at the last         c
+c      call of the routine, except for the case that s > fp0; then     c
+c      we compute directly the least-squares polynomial curve.         c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+      m1 = m-1
+      kk = k
+      kk1 = k1
+      k3 = 3*k+1
+      nmin = 2*k1
+c  determine the length of the period of the splines.
+      per = u(m)-u(1)
+      if(iopt.lt.0) go to 50
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  determine nmax, the number of knots for periodic spline interpolation
+      nmax = m+2*k
+      if(s.gt.0. .or. nmax.eq.nmin) go to 30
+c  if s=0, s(u) is an interpolating curve.
+      n = nmax
+c  test whether the required storage space exceeds the available one.
+      if(n.gt.nest) go to 620
+c  find the position of the interior knots in case of interpolation.
+   5  if((k/2)*2 .eq.k) go to 20
+      do 10 i=2,m1
+        j = i+k
+        t(j) = u(i)
+  10  continue
+      if(s.gt.0.) go to 50
+      kk = k-1
+      kk1 = k
+      if(kk.gt.0) go to 50
+      t(1) = t(m)-per
+      t(2) = u(1)
+      t(m+1) = u(m)
+      t(m+2) = t(3)+per
+      jj = 0
+      do 15 i=1,m1
+        j = i
+        do 12 j1=1,idim
+          jj = jj+1
+          c(j) = x(jj)
+          j = j+n
+  12    continue
+  15  continue
+      jj = 1
+      j = m
+      do 17 j1=1,idim
+        c(j) = c(jj)
+        j = j+n
+        jj = jj+n
+  17  continue
+      fp = 0.
+      fpint(n) = fp0
+      fpint(n-1) = 0.
+      nrdata(n) = 0
+      go to 630
+  20  do 25 i=2,m1
+         j = i+k
+         t(j) = (u(i)+u(i-1))*half
+  25  continue
+      go to 50
+c  if s > 0 our initial choice depends on the value of iopt.
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  polynomial curve. (i.e. a constant point).
+c  if iopt=1 and fp0>s we start computing the least-squares closed
+c  curve according the set of knots found at the last call of the
+c  routine.
+  30  if(iopt.eq.0) go to 35
+      if(n.eq.nmin) go to 35
+      fp0 = fpint(n)
+      fpold = fpint(n-1)
+      nplus = nrdata(n)
+      if(fp0.gt.s) go to 50
+c  the case that s(u) is a fixed point is treated separetely.
+c  fp0 denotes the corresponding sum of squared residuals.
+  35  fp0 = 0.
+      d1 = 0.
+      do 37 j=1,idim
+        z(j) = 0.
+  37  continue
+      jj = 0
+      do 45 it=1,m1
+        wi = w(it)
+        call fpgivs(wi,d1,cos,sin)
+        do 40 j=1,idim
+          jj = jj+1
+          fac = wi*x(jj)
+          call fprota(cos,sin,fac,z(j))
+          fp0 = fp0+fac**2
+  40    continue
+  45  continue
+      do 47 j=1,idim
+        z(j) = z(j)/d1
+  47  continue
+c  test whether that fixed point is a solution of our problem.
+      fpms = fp0-s
+      if(fpms.lt.acc .or. nmax.eq.nmin) go to 640
+      fpold = fp0
+c  test whether the required storage space exceeds the available one.
+      if(n.ge.nest) go to 620
+c  start computing the least-squares closed curve with one
+c  interior knot.
+      nplus = 1
+      n = nmin+1
+      mm = (m+1)/2
+      t(k2) = u(mm)
+      nrdata(1) = mm-2
+      nrdata(2) = m1-mm
+c  main loop for the different sets of knots. m is a save upper
+c  bound for the number of trials.
+  50  do 340 iter=1,m
+c  find nrint, the number of knot intervals.
+        nrint = n-nmin+1
+c  find the position of the additional knots which are needed for
+c  the b-spline representation of s(u). if we take
+c      t(k+1) = u(1), t(n-k) = u(m)
+c      t(k+1-j) = t(n-k-j) - per, j=1,2,...k
+c      t(n-k+j) = t(k+1+j) + per, j=1,2,...k
+c  then s(u) will be a smooth closed curve if the b-spline
+c  coefficients satisfy the following conditions
+c      c((i-1)*n+n7+j) = c((i-1)*n+j), j=1,...k,i=1,2,...,idim (**)
+c  with n7=n-2*k-1.
+        t(k1) = u(1)
+        nk1 = n-k1
+        nk2 = nk1+1
+        t(nk2) = u(m)
+        do 60 j=1,k
+          i1 = nk2+j
+          i2 = nk2-j
+          j1 = k1+j
+          j2 = k1-j
+          t(i1) = t(j1)+per
+          t(j2) = t(i2)-per
+  60    continue
+c  compute the b-spline coefficients of the least-squares closed curve
+c  sinf(u). the observation matrix a is built up row by row while
+c  taking into account condition (**) and is reduced to triangular
+c  form by givens transformations .
+c  at the same time fp=f(p=inf) is computed.
+c  the n7 x n7 triangularised upper matrix a has the form
+c            ! a1 '    !
+c        a = !    ' a2 !
+c            ! 0  '    !
+c  with a2 a n7 x k matrix and a1 a n10 x n10 upper triangular
+c  matrix of bandwith k+1 ( n10 = n7-k).
+c  initialization.
+        do 65 i=1,nc
+          z(i) = 0.
+  65    continue
+        do 70 i=1,nk1
+          do 70 j=1,kk1
+            a1(i,j) = 0.
+  70    continue
+        n7 = nk1-k
+        n10 = n7-kk
+        jper = 0
+        fp = 0.
+        l = k1
+        jj = 0
+        do 290 it=1,m1
+c  fetch the current data point u(it),x(it)
+          ui = u(it)
+          wi = w(it)
+          do 75 j=1,idim
+            jj = jj+1
+            xi(j) = x(jj)*wi
+  75      continue
+c  search for knot interval t(l) <= ui < t(l+1).
+  80      if(ui.lt.t(l+1)) go to 85
+          l = l+1
+          go to 80
+c  evaluate the (k+1) non-zero b-splines at ui and store them in q.
+  85      call fpbspl(t,n,k,ui,l,h)
+          do 90 i=1,k1
+            q(it,i) = h(i)
+            h(i) = h(i)*wi
+  90      continue
+          l5 = l-k1
+c  test whether the b-splines nj,k+1(u),j=1+n7,...nk1 are all zero at ui
+          if(l5.lt.n10) go to 285
+          if(jper.ne.0) go to 160
+c  initialize the matrix a2.
+          do 95 i=1,n7
+          do 95 j=1,kk
+              a2(i,j) = 0.
+  95      continue
+          jk = n10+1
+          do 110 i=1,kk
+            ik = jk
+            do 100 j=1,kk1
+              if(ik.le.0) go to 105
+              a2(ik,i) = a1(ik,j)
+              ik = ik-1
+ 100        continue
+ 105        jk = jk+1
+ 110      continue
+          jper = 1
+c  if one of the b-splines nj,k+1(u),j=n7+1,...nk1 is not zero at ui
+c  we take account of condition (**) for setting up the new row
+c  of the observation matrix a. this row is stored in the arrays h1
+c  (the part with respect to a1) and h2 (the part with
+c  respect to a2).
+ 160      do 170 i=1,kk
+            h1(i) = 0.
+            h2(i) = 0.
+ 170      continue
+          h1(kk1) = 0.
+          j = l5-n10
+          do 210 i=1,kk1
+            j = j+1
+            l0 = j
+ 180        l1 = l0-kk
+            if(l1.le.0) go to 200
+            if(l1.le.n10) go to 190
+            l0 = l1-n10
+            go to 180
+ 190        h1(l1) = h(i)
+            go to 210
+ 200        h2(l0) = h2(l0)+h(i)
+ 210      continue
+c  rotate the new row of the observation matrix into triangle
+c  by givens transformations.
+          if(n10.le.0) go to 250
+c  rotation with the rows 1,2,...n10 of matrix a.
+          do 240 j=1,n10
+            piv = h1(1)
+            if(piv.ne.0.) go to 214
+            do 212 i=1,kk
+              h1(i) = h1(i+1)
+ 212        continue
+            h1(kk1) = 0.
+            go to 240
+c  calculate the parameters of the givens transformation.
+ 214        call fpgivs(piv,a1(j,1),cos,sin)
+c  transformation to the right hand side.
+            j1 = j
+            do 217 j2=1,idim
+              call fprota(cos,sin,xi(j2),z(j1))
+              j1 = j1+n
+ 217        continue
+c  transformations to the left hand side with respect to a2.
+            do 220 i=1,kk
+              call fprota(cos,sin,h2(i),a2(j,i))
+ 220        continue
+            if(j.eq.n10) go to 250
+            i2 = min0(n10-j,kk)
+c  transformations to the left hand side with respect to a1.
+            do 230 i=1,i2
+              i1 = i+1
+              call fprota(cos,sin,h1(i1),a1(j,i1))
+              h1(i) = h1(i1)
+ 230        continue
+            h1(i1) = 0.
+ 240      continue
+c  rotation with the rows n10+1,...n7 of matrix a.
+ 250      do 270 j=1,kk
+            ij = n10+j
+            if(ij.le.0) go to 270
+            piv = h2(j)
+            if(piv.eq.0.) go to 270
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a2(ij,j),cos,sin)
+c  transformations to right hand side.
+            j1 = ij
+            do 255 j2=1,idim
+              call fprota(cos,sin,xi(j2),z(j1))
+              j1 = j1+n
+ 255        continue
+            if(j.eq.kk) go to 280
+            j1 = j+1
+c  transformations to left hand side.
+            do 260 i=j1,kk
+              call fprota(cos,sin,h2(i),a2(ij,i))
+ 260        continue
+ 270      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 280      do 282 j2=1,idim
+            fp = fp+xi(j2)**2
+ 282      continue
+          go to 290
+c  rotation of the new row of the observation matrix into
+c  triangle in case the b-splines nj,k+1(u),j=n7+1,...n-k-1 are all zero
+c  at ui.
+ 285      j = l5
+          do 140 i=1,kk1
+            j = j+1
+            piv = h(i)
+            if(piv.eq.0.) go to 140
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a1(j,1),cos,sin)
+c  transformations to right hand side.
+            j1 = j
+            do 125 j2=1,idim
+              call fprota(cos,sin,xi(j2),z(j1))
+              j1 = j1+n
+ 125        continue
+            if(i.eq.kk1) go to 150
+            i2 = 1
+            i3 = i+1
+c  transformations to left hand side.
+            do 130 i1=i3,kk1
+              i2 = i2+1
+              call fprota(cos,sin,h(i1),a1(j,i2))
+ 130        continue
+ 140      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 150      do 155 j2=1,idim
+            fp = fp+xi(j2)**2
+ 155      continue
+ 290    continue
+        fpint(n) = fp0
+        fpint(n-1) = fpold
+        nrdata(n) = nplus
+c  backward substitution to obtain the b-spline coefficients .
+        j1 = 1
+        do 292 j2=1,idim
+           call fpbacp(a1,a2,z(j1),n7,kk,c(j1),kk1,nest)
+           j1 = j1+n
+ 292    continue
+c  calculate from condition (**) the remaining coefficients.
+        do 297 i=1,k
+          j1 = i
+          do 295 j=1,idim
+            j2 = j1+n7
+            c(j2) = c(j1)
+            j1 = j1+n
+ 295      continue
+ 297    continue
+        if(iopt.lt.0) go to 660
+c  test whether the approximation sinf(u) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 660
+c  if f(p=inf) < s accept the choice of knots.
+        if(fpms.lt.0.) go to 350
+c  if n=nmax, sinf(u) is an interpolating curve.
+        if(n.eq.nmax) go to 630
+c  increase the number of knots.
+c  if n=nest we cannot increase the number of knots because of the
+c  storage capacity limitation.
+        if(n.eq.nest) go to 620
+c  determine the number of knots nplus we are going to add.
+        npl1 = nplus*2
+        rn = nplus
+        if(fpold-fp.gt.acc) npl1 = rn*fpms/(fpold-fp)
+        nplus = min0(nplus*2,max0(npl1,nplus/2,1))
+        fpold = fp
+c  compute the sum of squared residuals for each knot interval
+c  t(j+k) <= ui <= t(j+k+1) and store it in fpint(j),j=1,2,...nrint.
+        fpart = 0.
+        i = 1
+        l = k1
+        jj = 0
+        do 320 it=1,m1
+          if(u(it).lt.t(l)) go to 300
+          new = 1
+          l = l+1
+ 300      term = 0.
+          l0 = l-k2
+          do 310 j2=1,idim
+            fac = 0.
+            j1 = l0
+            do 305 j=1,k1
+              j1 = j1+1
+              fac = fac+c(j1)*q(it,j)
+ 305        continue
+            jj = jj+1
+            term = term+(w(it)*(fac-x(jj)))**2
+            l0 = l0+n
+ 310      continue
+          fpart = fpart+term
+          if(new.eq.0) go to 320
+          if(l.gt.k2) go to 315
+          fpint(nrint) = term
+          new = 0
+          go to 320
+ 315      store = term*half
+          fpint(i) = fpart-store
+          i = i+1
+          fpart = store
+          new = 0
+ 320    continue
+        fpint(nrint) = fpint(nrint)+fpart
+        do 330 l=1,nplus
+c  add a new knot
+          call fpknot(u,m,t,n,fpint,nrdata,nrint,nest,1)
+c  if n=nmax we locate the knots as for interpolation
+          if(n.eq.nmax) go to 5
+c  test whether we cannot further increase the number of knots.
+          if(n.eq.nest) go to 340
+ 330    continue
+c  restart the computations with the new set of knots.
+ 340  continue
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 2: determination of the smoothing closed curve sp(u).          c
+c  **********************************************************          c
+c  we have determined the number of knots and their position.          c
+c  we now compute the b-spline coefficients of the smoothing curve     c
+c  sp(u). the observation matrix a is extended by the rows of matrix   c
+c  b expressing that the kth derivative discontinuities of sp(u) at    c
+c  the interior knots t(k+2),...t(n-k-1) must be zero. the corres-     c
+c  ponding weights of these additional rows are set to 1/p.            c
+c  iteratively we then have to determine the value of p such that f(p),c
+c  the sum of squared residuals be = s. we already know that the least-c
+c  squares polynomial curve corresponds to p=0, and that the least-    c
+c  squares periodic spline curve corresponds to p=infinity. the        c
+c  iteration process which is proposed here, makes use of rational     c
+c  interpolation. since f(p) is a convex and strictly decreasing       c
+c  function of p, it can be approximated by a rational function        c
+c  r(p) = (u*p+v)/(p+w). three values of p(p1,p2,p3) with correspond-  c
+c  ing values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used      c
+c  to calculate the new value of p such that r(p)=s. convergence is    c
+c  guaranteed by taking f1>0 and f3<0.                                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jump of the kth derivative of the
+c  b-splines at the knots t(l),l=k+2,...n-k-1 and store in b.
+ 350  call fpdisc(t,n,k2,b,nest)
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      n11 = n10-1
+      n8 = n7-1
+      p = 0.
+      l = n7
+      do 352 i=1,k
+         j = k+1-i
+         p = p+a2(l,j)
+         l = l-1
+         if(l.eq.0) go to 356
+ 352  continue
+      do 354 i=1,n10
+         p = p+a1(i,1)
+ 354  continue
+ 356  rn = n7
+      p = rn/p
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p) = s.
+      do 595 iter=1,maxit
+c  form the matrix g  as the matrix a extended by the rows of matrix b.
+c  the rows of matrix b with weight 1/p are rotated into
+c  the triangularised observation matrix a.
+c  after triangularisation our n7 x n7 matrix g takes the form
+c            ! g1 '    !
+c        g = !    ' g2 !
+c            ! 0  '    !
+c  with g2 a n7 x (k+1) matrix and g1 a n11 x n11 upper triangular
+c  matrix of bandwidth k+2. ( n11 = n7-k-1)
+        pinv = one/p
+c  store matrix a into g
+        do 358 i=1,nc
+          c(i) = z(i)
+ 358    continue
+        do 360 i=1,n7
+          g1(i,k1) = a1(i,k1)
+          g1(i,k2) = 0.
+          g2(i,1) = 0.
+          do 360 j=1,k
+            g1(i,j) = a1(i,j)
+            g2(i,j+1) = a2(i,j)
+ 360    continue
+        l = n10
+        do 370 j=1,k1
+          if(l.le.0) go to 375
+          g2(l,1) = a1(l,j)
+          l = l-1
+ 370    continue
+ 375    do 540 it=1,n8
+c  fetch a new row of matrix b and store it in the arrays h1 (the part
+c  with respect to g1) and h2 (the part with respect to g2).
+          do 380 j=1,idim
+            xi(j) = 0.
+ 380      continue
+          do 385 i=1,k1
+            h1(i) = 0.
+            h2(i) = 0.
+ 385      continue
+          h1(k2) = 0.
+          if(it.gt.n11) go to 420
+          l = it
+          l0 = it
+          do 390 j=1,k2
+            if(l0.eq.n10) go to 400
+            h1(j) = b(it,j)*pinv
+            l0 = l0+1
+ 390      continue
+          go to 470
+ 400      l0 = 1
+          do 410 l1=j,k2
+            h2(l0) = b(it,l1)*pinv
+            l0 = l0+1
+ 410      continue
+          go to 470
+ 420      l = 1
+          i = it-n10
+          do 460 j=1,k2
+            i = i+1
+            l0 = i
+ 430        l1 = l0-k1
+            if(l1.le.0) go to 450
+            if(l1.le.n11) go to 440
+            l0 = l1-n11
+            go to 430
+ 440        h1(l1) = b(it,j)*pinv
+            go to 460
+ 450        h2(l0) = h2(l0)+b(it,j)*pinv
+ 460      continue
+          if(n11.le.0) go to 510
+c  rotate this row into triangle by givens transformations
+c  rotation with the rows l,l+1,...n11.
+ 470      do 500 j=l,n11
+            piv = h1(1)
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,g1(j,1),cos,sin)
+c  transformation to right hand side.
+            j1 = j
+            do 475 j2=1,idim
+              call fprota(cos,sin,xi(j2),c(j1))
+              j1 = j1+n
+ 475        continue
+c  transformation to the left hand side with respect to g2.
+            do 480 i=1,k1
+              call fprota(cos,sin,h2(i),g2(j,i))
+ 480        continue
+            if(j.eq.n11) go to 510
+            i2 = min0(n11-j,k1)
+c  transformation to the left hand side with respect to g1.
+            do 490 i=1,i2
+              i1 = i+1
+              call fprota(cos,sin,h1(i1),g1(j,i1))
+              h1(i) = h1(i1)
+ 490        continue
+            h1(i1) = 0.
+ 500      continue
+c  rotation with the rows n11+1,...n7
+ 510      do 530 j=1,k1
+            ij = n11+j
+            if(ij.le.0) go to 530
+            piv = h2(j)
+c  calculate the parameters of the givens transformation
+            call fpgivs(piv,g2(ij,j),cos,sin)
+c  transformation to the right hand side.
+            j1 = ij
+            do 515 j2=1,idim
+              call fprota(cos,sin,xi(j2),c(j1))
+              j1 = j1+n
+ 515        continue
+            if(j.eq.k1) go to 540
+            j1 = j+1
+c  transformation to the left hand side.
+            do 520 i=j1,k1
+              call fprota(cos,sin,h2(i),g2(ij,i))
+ 520        continue
+ 530      continue
+ 540    continue
+c  backward substitution to obtain the b-spline coefficients
+        j1 = 1
+        do 542 j2=1,idim
+          call fpbacp(g1,g2,c(j1),n7,k1,c(j1),k2,nest)
+          j1 = j1+n
+ 542    continue
+c  calculate from condition (**) the remaining b-spline coefficients.
+        do 547 i=1,k
+          j1 = i
+          do 545 j=1,idim
+            j2 = j1+n7
+            c(j2) = c(j1)
+            j1 = j1+n
+ 545      continue
+ 547    continue
+c  computation of f(p).
+        fp = 0.
+        l = k1
+        jj = 0
+        do 570 it=1,m1
+          if(u(it).lt.t(l)) go to 550
+          l = l+1
+ 550      l0 = l-k2
+          term = 0.
+          do 565 j2=1,idim
+            fac = 0.
+            j1 = l0
+            do 560 j=1,k1
+              j1 = j1+1
+              fac = fac+c(j1)*q(it,j)
+ 560        continue
+            jj = jj+1
+            term = term+(fac-x(jj))**2
+            l0 = l0+n
+ 565      continue
+          fp = fp+term*w(it)**2
+ 570    continue
+c  test whether the approximation sp(u) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 660
+c  test whether the maximal number of iterations is reached.
+        if(iter.eq.maxit) go to 600
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 580
+        if((f2-f3) .gt. acc) go to 575
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 +p2*con1
+        go to 595
+ 575    if(f2.lt.0.) ich3 = 1
+ 580    if(ich1.ne.0) go to 590
+        if((f1-f2) .gt. acc) go to 585
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 595
+        if(p.ge.p3) p = p2*con1 +p3*con9
+        go to 595
+ 585    if(f2.gt.0.) ich1 = 1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 590    if(f2.ge.f1 .or. f2.le.f3) go to 610
+c  find the new value for p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 595  continue
+c  error codes and messages.
+ 600  ier = 3
+      go to 660
+ 610  ier = 2
+      go to 660
+ 620  ier = 1
+      go to 660
+ 630  ier = -1
+      go to 660
+ 640  ier = -2
+c  the point (z(1),z(2),...,z(idim)) is a solution of our problem.
+c  a constant function is a spline of degree k with all b-spline
+c  coefficients equal to that constant.
+      do 650 i=1,k1
+        rn = k1-i
+        t(i) = u(1)-rn*per
+        j = i+k1
+        rn = i-1
+        t(j) = u(m)+rn*per
+ 650  continue
+      n = nmin
+      j1 = 0
+      do 658 j=1,idim
+        fac = z(j)
+        j2 = j1
+        do 654 i=1,k1
+          j2 = j2+1
+          c(j2) = fac
+ 654    continue
+        j1 = j1+n
+ 658  continue
+      fp = fp0
+      fpint(n) = fp0
+      fpint(n-1) = 0.
+      nrdata(n) = 0
+ 660  return
+      end

Added: branches/Interpolate1D/fitpack/fpcoco.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcoco.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcoco.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,168 @@
+      subroutine fpcoco(iopt,m,x,y,w,v,s,nest,maxtr,maxbin,n,t,c,sq,sx,
+     * bind,e,wrk,lwrk,iwrk,kwrk,ier)
+c  ..scalar arguments..
+      real*8 s,sq
+      integer iopt,m,nest,maxtr,maxbin,n,lwrk,kwrk,ier
+c  ..array arguments..
+      integer iwrk(kwrk)
+      real*8 x(m),y(m),w(m),v(m),t(nest),c(nest),sx(m),e(nest),wrk(lwrk)
+     *
+      logical bind(nest)
+c  ..local scalars..
+      integer i,ia,ib,ic,iq,iu,iz,izz,i1,j,k,l,l1,m1,nmax,nr,n4,n6,n8,
+     * ji,jib,jjb,jl,jr,ju,mb,nm
+      real*8 sql,sqmax,term,tj,xi,half
+c  ..subroutine references..
+c    fpcosp,fpbspl,fpadno,fpdeno,fpseno,fpfrno
+c  ..
+c  set constant
+      half = 0.5e0
+c  determine the maximal admissible number of knots.
+      nmax = m+4
+c  the initial choice of knots depends on the value of iopt.
+c    if iopt=0 the program starts with the minimal number of knots
+c    so that can be guarantied that the concavity/convexity constraints
+c    will be satisfied.
+c    if iopt = 1 the program will continue from the point on where she
+c    left at the foregoing call.
+      if(iopt.gt.0) go to 80
+c  find the minimal number of knots.
+c  a knot is located at the data point x(i), i=2,3,...m-1 if
+c    1) v(i) ^= 0    and
+c    2) v(i)*v(i-1) <= 0  or  v(i)*v(i+1) <= 0.
+      m1 = m-1
+      n = 4
+      do 20 i=2,m1
+        if(v(i).eq.0. .or. (v(i)*v(i-1).gt.0. .and.
+     *  v(i)*v(i+1).gt.0.)) go to 20
+        n = n+1
+c  test whether the required storage space exceeds the available one.
+        if(n+4.gt.nest) go to 200
+        t(n) = x(i)
+  20  continue
+c  find the position of the knots t(1),...t(4) and t(n-3),...t(n) which
+c  are needed for the b-spline representation of s(x).
+      do 30 i=1,4
+        t(i) = x(1)
+        n = n+1
+        t(n) = x(m)
+  30  continue
+c  test whether the minimum number of knots exceeds the maximum number.
+      if(n.gt.nmax) go to 210
+c  main loop for the different sets of knots.
+c  find corresponding values e(j) to the knots t(j+3),j=1,2,...n-6
+c    e(j) will take the value -1,1, or 0 according to the requirement
+c    that s(x) must be locally convex or concave at t(j+3) or that the
+c    sign of s''(x) is unrestricted at that point.
+  40  i= 1
+      xi = x(1)
+      j = 4
+      tj = t(4)
+      n6 = n-6
+      do 70 l=1,n6
+  50    if(xi.eq.tj) go to 60
+        i = i+1
+        xi = x(i)
+        go to 50
+  60    e(l) = v(i)
+        j = j+1
+        tj = t(j)
+  70  continue
+c  we partition the working space
+      nm = n+maxbin
+      mb = maxbin+1
+      ia = 1
+      ib = ia+4*n
+      ic = ib+nm*maxbin
+      iz = ic+n
+      izz = iz+n
+      iu = izz+n
+      iq = iu+maxbin
+      ji = 1
+      ju = ji+maxtr
+      jl = ju+maxtr
+      jr = jl+maxtr
+      jjb = jr+maxtr
+      jib = jjb+mb
+c  given the set of knots t(j),j=1,2,...n, find the least-squares cubic
+c  spline which satisfies the imposed concavity/convexity constraints.
+      call fpcosp(m,x,y,w,n,t,e,maxtr,maxbin,c,sq,sx,bind,nm,mb,wrk(ia),
+     *
+     * wrk(ib),wrk(ic),wrk(iz),wrk(izz),wrk(iu),wrk(iq),iwrk(ji),
+     * iwrk(ju),iwrk(jl),iwrk(jr),iwrk(jjb),iwrk(jib),ier)
+c  if sq <= s or in case of abnormal exit from fpcosp, control is
+c  repassed to the driver program.
+      if(sq.le.s .or. ier.gt.0) go to 300
+c  calculate for each knot interval t(l-1) <= xi <= t(l) the
+c  sum((wi*(yi-s(xi)))**2).
+c  find the interval t(k-1) <= x <= t(k) for which this sum is maximal
+c  on the condition that this interval contains at least one interior
+c  data point x(nr) and that s(x) is not given there by a straight line.
+  80  sqmax = 0.
+      sql = 0.
+      l = 5
+      nr = 0
+      i1 = 1
+      n4 = n-4
+      do 110 i=1,m
+        term = (w(i)*(sx(i)-y(i)))**2
+        if(x(i).lt.t(l) .or. l.gt.n4) go to 100
+        term = term*half
+        sql = sql+term
+        if(i-i1.le.1 .or. (bind(l-4).and.bind(l-3))) go to 90
+        if(sql.le.sqmax) go to 90
+        k = l
+        sqmax = sql
+        nr = i1+(i-i1)/2
+  90    l = l+1
+        i1 = i
+        sql = 0.
+ 100    sql = sql+term
+ 110  continue
+      if(m-i1.le.1 .or. (bind(l-4).and.bind(l-3))) go to 120
+      if(sql.le.sqmax) go to 120
+      k = l
+      nr = i1+(m-i1)/2
+c  if no such interval is found, control is repassed to the driver
+c  program (ier = -1).
+ 120  if(nr.eq.0) go to 190
+c  if s(x) is given by the same straight line in two succeeding knot
+c  intervals t(l-1) <= x <= t(l) and t(l) <= x <= t(l+1),delete t(l)
+      n8 = n-8
+      l1 = 0
+      if(n8.le.0) go to 150
+      do 140 i=1,n8
+        if(.not. (bind(i).and.bind(i+1).and.bind(i+2))) go to 140
+        l = i+4-l1
+        if(k.gt.l) k = k-1
+        n = n-1
+        l1 = l1+1
+        do 130 j=l,n
+          t(j) = t(j+1)
+ 130    continue
+ 140  continue
+c  test whether we cannot further increase the number of knots.
+ 150  if(n.eq.nmax) go to 180
+      if(n.eq.nest) go to 170
+c  locate an additional knot at the point x(nr).
+      j = n
+      do 160 i=k,n
+        t(j+1) = t(j)
+        j = j-1
+ 160  continue
+      t(k) = x(nr)
+      n = n+1
+c  restart the computations with the new set of knots.
+      go to 40
+c  error codes and messages.
+ 170  ier = -3
+      go to 300
+ 180  ier = -2
+      go to 300
+ 190  ier = -1
+      go to 300
+ 200  ier = 4
+      go to 300
+ 210  ier = 5
+ 300  return
+      end

Added: branches/Interpolate1D/fitpack/fpcons.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcons.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcons.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,442 @@
+      subroutine fpcons(iopt,idim,m,u,mx,x,w,ib,ie,k,s,nest,tol,maxit,
+     * k1,k2,n,t,nc,c,fp,fpint,z,a,b,g,q,nrdata,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 s,tol,fp
+      integer iopt,idim,m,mx,ib,ie,k,nest,maxit,k1,k2,n,nc,ier
+c  ..array arguments..
+      real*8 u(m),x(mx),w(m),t(nest),c(nc),fpint(nest),
+     * z(nc),a(nest,k1),b(nest,k2),g(nest,k2),q(m,k1)
+      integer nrdata(nest)
+c  ..local scalars..
+      real*8 acc,con1,con4,con9,cos,fac,fpart,fpms,fpold,fp0,f1,f2,f3,
+     * half,one,p,pinv,piv,p1,p2,p3,rn,sin,store,term,ui,wi
+      integer i,ich1,ich3,it,iter,i1,i2,i3,j,jb,je,jj,j1,j2,j3,kbe,
+     * l,li,lj,l0,mb,me,mm,new,nk1,nmax,nmin,nn,nplus,npl1,nrint,n8
+c  ..local arrays..
+      real*8 h(7),xi(10)
+c  ..function references
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpbacp,fpbspl,fpgivs,fpdisc,fpknot,fprota
+c  ..
+c  set constants
+      one = 0.1e+01
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      half = 0.5e0
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1: determination of the number of knots and their position     c
+c  **************************************************************      c
+c  given a set of knots we compute the least-squares curve sinf(u),    c
+c  and the corresponding sum of squared residuals fp=f(p=inf).         c
+c  if iopt=-1 sinf(u) is the requested curve.                          c
+c  if iopt=0 or iopt=1 we check whether we can accept the knots:       c
+c    if fp <=s we will continue with the current set of knots.         c
+c    if fp > s we will increase the number of knots and compute the    c
+c       corresponding least-squares curve until finally fp<=s.         c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmax = m+k+1-max(0,ib-1)-max(0,ie-1)                 c
+c    if s > 0 and                                                      c
+c      iopt=0 we first compute the least-squares polynomial curve of   c
+c      degree k; n = nmin = 2*k+2                                      c
+c      iopt=1 we start with the set of knots found at the last         c
+c      call of the routine, except for the case that s > fp0; then     c
+c      we compute directly the polynomial curve of degree k.           c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  determine nmin, the number of knots for polynomial approximation.
+      nmin = 2*k1
+c  find which data points are to be concidered.
+      mb = 2
+      jb = ib
+      if(ib.gt.0) go to 10
+      mb = 1
+      jb = 1
+  10  me = m-1
+      je = ie
+      if(ie.gt.0) go to 20
+      me = m
+      je = 1
+  20  if(iopt.lt.0) go to 60
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  determine nmax, the number of knots for spline interpolation.
+      kbe = k1-jb-je
+      mmin = kbe+2
+      mm = m-mmin
+      nmax = nmin+mm
+      if(s.gt.0.) go to 40
+c  if s=0, s(u) is an interpolating curve.
+c  test whether the required storage space exceeds the available one.
+      n = nmax
+      if(nmax.gt.nest) go to 420
+c  find the position of the interior knots in case of interpolation.
+      if(mm.eq.0) go to 60
+  25  i = k2
+      j = 3-jb+k/2
+      do 30 l=1,mm
+        t(i) = u(j)
+        i = i+1
+        j = j+1
+  30  continue
+      go to 60
+c  if s>0 our initial choice of knots depends on the value of iopt.
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  polynomial curve which is a spline curve without interior knots.
+c  if iopt=1 and fp0>s we start computing the least squares spline curve
+c  according to the set of knots found at the last call of the routine.
+  40  if(iopt.eq.0) go to 50
+      if(n.eq.nmin) go to 50
+      fp0 = fpint(n)
+      fpold = fpint(n-1)
+      nplus = nrdata(n)
+      if(fp0.gt.s) go to 60
+  50  n = nmin
+      fpold = 0.
+      nplus = 0
+      nrdata(1) = m-2
+c  main loop for the different sets of knots. m is a save upper bound
+c  for the number of trials.
+  60  do 200 iter = 1,m
+        if(n.eq.nmin) ier = -2
+c  find nrint, tne number of knot intervals.
+        nrint = n-nmin+1
+c  find the position of the additional knots which are needed for
+c  the b-spline representation of s(u).
+        nk1 = n-k1
+        i = n
+        do 70 j=1,k1
+          t(j) = u(1)
+          t(i) = u(m)
+          i = i-1
+  70    continue
+c  compute the b-spline coefficients of the least-squares spline curve
+c  sinf(u). the observation matrix a is built up row by row and
+c  reduced to upper triangular form by givens transformations.
+c  at the same time fp=f(p=inf) is computed.
+        fp = 0.
+c  nn denotes the dimension of the splines
+        nn = nk1-ib-ie
+c  initialize the b-spline coefficients and the observation matrix a.
+        do 75 i=1,nc
+          z(i) = 0.
+          c(i) = 0.
+  75    continue
+        if(me.lt.mb) go to 134
+        if(nn.eq.0) go to 82
+        do 80 i=1,nn
+          do 80 j=1,k1
+            a(i,j) = 0.
+  80    continue
+  82    l = k1
+        jj = (mb-1)*idim
+        do 130 it=mb,me
+c  fetch the current data point u(it),x(it).
+          ui = u(it)
+          wi = w(it)
+          do 84 j=1,idim
+             jj = jj+1
+             xi(j) = x(jj)*wi
+  84      continue
+c  search for knot interval t(l) <= ui < t(l+1).
+  86      if(ui.lt.t(l+1) .or. l.eq.nk1) go to 90
+          l = l+1
+          go to 86
+c  evaluate the (k+1) non-zero b-splines at ui and store them in q.
+  90      call fpbspl(t,n,k,ui,l,h)
+          do 92 i=1,k1
+            q(it,i) = h(i)
+            h(i) = h(i)*wi
+  92      continue
+c  take into account that certain b-spline coefficients must be zero.
+          lj = k1
+          j = nk1-l-ie
+          if(j.ge.0) go to 94
+          lj = lj+j
+  94      li = 1
+          j = l-k1-ib
+          if(j.ge.0) go to 96
+          li = li-j
+          j = 0
+  96      if(li.gt.lj) go to 120
+c  rotate the new row of the observation matrix into triangle.
+          do 110 i=li,lj
+            j = j+1
+            piv = h(i)
+            if(piv.eq.0.) go to 110
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(j,1),cos,sin)
+c  transformations to right hand side.
+            j1 = j
+            do 98 j2 =1,idim
+               call fprota(cos,sin,xi(j2),z(j1))
+               j1 = j1+n
+  98        continue
+            if(i.eq.lj) go to 120
+            i2 = 1
+            i3 = i+1
+            do 100 i1 = i3,lj
+              i2 = i2+1
+c  transformations to left hand side.
+              call fprota(cos,sin,h(i1),a(j,i2))
+ 100        continue
+ 110      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 120      do 125 j2=1,idim
+             fp  = fp+xi(j2)**2
+ 125      continue
+ 130    continue
+        if(ier.eq.(-2)) fp0 = fp
+        fpint(n) = fp0
+        fpint(n-1) = fpold
+        nrdata(n) = nplus
+c  backward substitution to obtain the b-spline coefficients.
+        if(nn.eq.0) go to 134
+        j1 = 1
+        do 132 j2=1,idim
+           j3 = j1+ib
+           call fpback(a,z(j1),nn,k1,c(j3),nest)
+           j1 = j1+n
+ 132    continue
+c  test whether the approximation sinf(u) is an acceptable solution.
+ 134    if(iopt.lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  if f(p=inf) < s accept the choice of knots.
+        if(fpms.lt.0.) go to 250
+c  if n = nmax, sinf(u) is an interpolating spline curve.
+        if(n.eq.nmax) go to 430
+c  increase the number of knots.
+c  if n=nest we cannot increase the number of knots because of
+c  the storage capacity limitation.
+        if(n.eq.nest) go to 420
+c  determine the number of knots nplus we are going to add.
+        if(ier.eq.0) go to 140
+        nplus = 1
+        ier = 0
+        go to 150
+ 140    npl1 = nplus*2
+        rn = nplus
+        if(fpold-fp.gt.acc) npl1 = rn*fpms/(fpold-fp)
+        nplus = min0(nplus*2,max0(npl1,nplus/2,1))
+ 150    fpold = fp
+c  compute the sum of squared residuals for each knot interval
+c  t(j+k) <= u(i) <= t(j+k+1) and store it in fpint(j),j=1,2,...nrint.
+        fpart = 0.
+        i = 1
+        l = k2
+        new = 0
+        jj = (mb-1)*idim
+        do 180 it=mb,me
+          if(u(it).lt.t(l) .or. l.gt.nk1) go to 160
+          new = 1
+          l = l+1
+ 160      term = 0.
+          l0 = l-k2
+          do 175 j2=1,idim
+            fac = 0.
+            j1 = l0
+            do 170 j=1,k1
+              j1 = j1+1
+              fac = fac+c(j1)*q(it,j)
+ 170        continue
+            jj = jj+1
+            term = term+(w(it)*(fac-x(jj)))**2
+            l0 = l0+n
+ 175      continue
+          fpart = fpart+term
+          if(new.eq.0) go to 180
+          store = term*half
+          fpint(i) = fpart-store
+          i = i+1
+          fpart = store
+          new = 0
+ 180    continue
+        fpint(nrint) = fpart
+        do 190 l=1,nplus
+c  add a new knot.
+          call fpknot(u,m,t,n,fpint,nrdata,nrint,nest,1)
+c  if n=nmax we locate the knots as for interpolation
+          if(n.eq.nmax) go to 25
+c  test whether we cannot further increase the number of knots.
+          if(n.eq.nest) go to 200
+ 190    continue
+c  restart the computations with the new set of knots.
+ 200  continue
+c  test whether the least-squares kth degree polynomial curve is a
+c  solution of our approximation problem.
+ 250  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 2: determination of the smoothing spline curve sp(u).          c
+c  **********************************************************          c
+c  we have determined the number of knots and their position.          c
+c  we now compute the b-spline coefficients of the smoothing curve     c
+c  sp(u). the observation matrix a is extended by the rows of matrix   c
+c  b expressing that the kth derivative discontinuities of sp(u) at    c
+c  the interior knots t(k+2),...t(n-k-1) must be zero. the corres-     c
+c  ponding weights of these additional rows are set to 1/p.            c
+c  iteratively we then have to determine the value of p such that f(p),c
+c  the sum of squared residuals be = s. we already know that the least c
+c  squares kth degree polynomial curve corresponds to p=0, and that    c
+c  the least-squares spline curve corresponds to p=infinity. the       c
+c  iteration process which is proposed here, makes use of rational     c
+c  interpolation. since f(p) is a convex and strictly decreasing       c
+c  function of p, it can be approximated by a rational function        c
+c  r(p) = (u*p+v)/(p+w). three values of p(p1,p2,p3) with correspond-  c
+c  ing values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used      c
+c  to calculate the new value of p such that r(p)=s. convergence is    c
+c  guaranteed by taking f1>0 and f3<0.                                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jump of the kth derivative of the
+c  b-splines at the knots t(l),l=k+2,...n-k-1 and store in b.
+      call fpdisc(t,n,k2,b,nest)
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = 0.
+      do 252 i=1,nn
+         p = p+a(i,1)
+ 252  continue
+      rn = nn
+      p = rn/p
+      ich1 = 0
+      ich3 = 0
+      n8 = n-nmin
+c  iteration process to find the root of f(p) = s.
+      do 360 iter=1,maxit
+c  the rows of matrix b with weight 1/p are rotated into the
+c  triangularised observation matrix a which is stored in g.
+        pinv = one/p
+        do 255 i=1,nc
+          c(i) = z(i)
+ 255    continue
+        do 260 i=1,nn
+          g(i,k2) = 0.
+          do 260 j=1,k1
+            g(i,j) = a(i,j)
+ 260    continue
+        do 300 it=1,n8
+c  the row of matrix b is rotated into triangle by givens transformation
+          do 264 i=1,k2
+            h(i) = b(it,i)*pinv
+ 264      continue
+          do 268 j=1,idim
+            xi(j) = 0.
+ 268      continue
+c  take into account that certain b-spline coefficients must be zero.
+          if(it.gt.ib) go to 274
+          j1 = ib-it+2
+          j2 = 1
+          do 270 i=j1,k2
+            h(j2) = h(i)
+            j2 = j2+1
+ 270      continue
+          do 272 i=j2,k2
+            h(i) = 0.
+ 272      continue
+ 274      jj = max0(1,it-ib)
+          do 290 j=jj,nn
+            piv = h(1)
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,g(j,1),cos,sin)
+c  transformations to right hand side.
+            j1 = j
+            do 277 j2=1,idim
+              call fprota(cos,sin,xi(j2),c(j1))
+              j1 = j1+n
+ 277        continue
+            if(j.eq.nn) go to 300
+            i2 = min0(nn-j,k1)
+            do 280 i=1,i2
+c  transformations to left hand side.
+              i1 = i+1
+              call fprota(cos,sin,h(i1),g(j,i1))
+              h(i) = h(i1)
+ 280        continue
+            h(i2+1) = 0.
+ 290      continue
+ 300    continue
+c  backward substitution to obtain the b-spline coefficients.
+        j1 = 1
+        do 308 j2=1,idim
+          j3 = j1+ib
+          call fpback(g,c(j1),nn,k2,c(j3),nest)
+          if(ib.eq.0) go to 306
+          j3 = j1
+          do 304 i=1,ib
+            c(j3) = 0.
+            j3 = j3+1
+ 304      continue
+ 306      j1 =j1+n
+ 308    continue
+c  computation of f(p).
+        fp = 0.
+        l = k2
+        jj = (mb-1)*idim
+        do 330 it=mb,me
+          if(u(it).lt.t(l) .or. l.gt.nk1) go to 310
+          l = l+1
+ 310      l0 = l-k2
+          term = 0.
+          do 325 j2=1,idim
+            fac = 0.
+            j1 = l0
+            do 320 j=1,k1
+              j1 = j1+1
+              fac = fac+c(j1)*q(it,j)
+ 320        continue
+            jj = jj+1
+            term = term+(fac-x(jj))**2
+            l0 = l0+n
+ 325      continue
+          fp = fp+term*w(it)**2
+ 330    continue
+c  test whether the approximation sp(u) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximal number of iterations is reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 340
+        if((f2-f3).gt.acc) go to 335
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p=p1*con9 + p2*con1
+        go to 360
+ 335    if(f2.lt.0.) ich3=1
+ 340    if(ich1.ne.0) go to 350
+        if((f1-f2).gt.acc) go to 345
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 360
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 360
+ 345    if(f2.gt.0.) ich1=1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 350    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value for p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 360  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+ 440  return
+      end

Added: branches/Interpolate1D/fitpack/fpcosp.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcosp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcosp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,362 @@
+      subroutine fpcosp(m,x,y,w,n,t,e,maxtr,maxbin,c,sq,sx,bind,nm,mb,a,
+     *
+     * b,const,z,zz,u,q,info,up,left,right,jbind,ibind,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 sq
+      integer m,n,maxtr,maxbin,nm,mb,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),t(n),e(n),c(n),sx(m),a(n,4),b(nm,maxbin),
+     * const(n),z(n),zz(n),u(maxbin),q(m,4)
+      integer info(maxtr),up(maxtr),left(maxtr),right(maxtr),jbind(mb),
+     * ibind(mb)
+      logical bind(n)
+c  ..local scalars..
+      integer count,i,i1,j,j1,j2,j3,k,kdim,k1,k2,k3,k4,k5,k6,
+     * l,lp1,l1,l2,l3,merk,nbind,number,n1,n4,n6
+      real*8 f,wi,xi
+c  ..local array..
+      real*8 h(4)
+c  ..subroutine references..
+c    fpbspl,fpadno,fpdeno,fpfrno,fpseno
+c  ..
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  if we use the b-spline representation of s(x) our approximation     c
+c  problem results in a quadratic programming problem:                 c
+c    find the b-spline coefficients c(j),j=1,2,...n-4 such that        c
+c        (1) sumi((wi*(yi-sumj(cj*nj(xi))))**2),i=1,2,...m is minimal  c
+c        (2) sumj(cj*n''j(t(l+3)))*e(l) <= 0, l=1,2,...n-6.            c
+c  to solve this problem we use the theil-van de panne procedure.      c
+c  if the inequality constraints (2) are numbered from 1 to n-6,       c
+c  this algorithm finds a subset of constraints ibind(1)..ibind(nbind) c
+c  such that the solution of the minimization problem (1) with these   c
+c  constraints in equality form, satisfies all constraints. such a     c
+c  feasible solution is optimal if the lagrange parameters associated  c
+c  with that problem with equality constraints, are all positive.      c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  determine n6, the number of inequality constraints.
+      n6 = n-6
+c  fix the parameters which determine these constraints.
+      do 10 i=1,n6
+        const(i) = e(i)*(t(i+4)-t(i+1))/(t(i+5)-t(i+2))
+  10  continue
+c  initialize the triply linked tree which is used to find the subset
+c  of constraints ibind(1),...ibind(nbind).
+      count = 1
+      info(1) = 0
+      left(1) = 0
+      right(1) = 0
+      up(1) = 1
+      merk = 1
+c  set up the normal equations  n'nc=n'y  where n denotes the m x (n-4)
+c  observation matrix with elements ni,j = wi*nj(xi)  and y is the
+c  column vector with elements yi*wi.
+c  from the properties of the b-splines nj(x),j=1,2,...n-4, it follows
+c  that  n'n  is a (n-4) x (n-4)  positive definit bandmatrix of
+c  bandwidth 7. the matrices n'n and n'y are built up in a and z.
+      n4 = n-4
+c  initialization
+      do 20 i=1,n4
+        z(i) = 0.
+        do 20 j=1,4
+          a(i,j) = 0.
+  20  continue
+      l = 4
+      lp1 = l+1
+      do 70 i=1,m
+c  fetch the current row of the observation matrix.
+        xi = x(i)
+        wi = w(i)**2
+c  search for knot interval  t(l) <= xi < t(l+1)
+  30    if(xi.lt.t(lp1) .or. l.eq.n4) go to 40
+        l = lp1
+        lp1 = l+1
+        go to 30
+c  evaluate the four non-zero cubic b-splines nj(xi),j=l-3,...l.
+  40    call fpbspl(t,n,3,xi,l,h)
+c  store in q these values h(1),h(2),...h(4).
+        do 50 j=1,4
+          q(i,j) = h(j)
+  50    continue
+c  add the contribution of the current row of the observation matrix
+c  n to the normal equations.
+        l3 = l-3
+        k1 = 0
+        do 60 j1 = l3,l
+          k1 = k1+1
+          f = h(k1)
+          z(j1) = z(j1)+f*wi*y(i)
+          k2 = k1
+          j2 = 4
+          do 60 j3 = j1,l
+            a(j3,j2) = a(j3,j2)+f*wi*h(k2)
+            k2 = k2+1
+            j2 = j2-1
+  60    continue
+  70  continue
+c  since n'n is a symmetric matrix it can be factorized as
+c        (3)  n'n = (r1)'(d1)(r1)
+c  with d1 a diagonal matrix and r1 an (n-4) x (n-4)  unit upper
+c  triangular matrix of bandwidth 4. the matrices r1 and d1 are built
+c  up in a. at the same time we solve the systems of equations
+c        (4)  (r1)'(z2) = n'y
+c        (5)  (d1) (z1) = (z2)
+c  the vectors z2 and z1 are kept in zz and z.
+      do 140 i=1,n4
+        k1 = 1
+        if(i.lt.4) k1 = 5-i
+        k2 = i-4+k1
+        k3 = k2
+        do 100 j=k1,4
+          k4 = j-1
+          k5 = 4-j+k1
+          f = a(i,j)
+          if(k1.gt.k4) go to 90
+          k6 = k2
+          do 80 k=k1,k4
+            f = f-a(i,k)*a(k3,k5)*a(k6,4)
+            k5 = k5+1
+            k6 = k6+1
+  80      continue
+  90      if(j.eq.4) go to 110
+          a(i,j) = f/a(k3,4)
+          k3 = k3+1
+ 100    continue
+ 110    a(i,4) = f
+        f = z(i)
+        if(i.eq.1) go to 130
+        k4 = i
+        do 120 j=k1,3
+          k = k1+3-j
+          k4 = k4-1
+          f = f-a(i,k)*z(k4)*a(k4,4)
+ 120    continue
+ 130    z(i) = f/a(i,4)
+        zz(i) = f
+ 140  continue
+c  start computing the least-squares cubic spline without taking account
+c  of any constraint.
+      nbind = 0
+      n1 = 1
+      ibind(1) = 0
+c  main loop for the least-squares problems with different subsets of
+c  the constraints (2) in equality form. the resulting b-spline coeff.
+c  c and lagrange parameters u are the solution of the system
+c            ! n'n  b' ! ! c !   ! n'y !
+c        (6) !         ! !   ! = !     !
+c            !  b   0  ! ! u !   !  0  !
+c  z1 is stored into array c.
+ 150  do 160 i=1,n4
+        c(i) = z(i)
+ 160  continue
+c  if there are no equality constraints, compute the coeff. c directly.
+      if(nbind.eq.0) go to 370
+c  initialization
+      kdim = n4+nbind
+      do 170 i=1,nbind
+        do 170 j=1,kdim
+          b(j,i) = 0.
+ 170  continue
+c  matrix b is built up,expressing that the constraints nrs ibind(1),...
+c  ibind(nbind) must be satisfied in equality form.
+      do 180 i=1,nbind
+        l = ibind(i)
+        b(l,i) = e(l)
+        b(l+1,i) = -(e(l)+const(l))
+        b(l+2,i) = const(l)
+ 180  continue
+c  find the matrix (b1) as the solution of the system of equations
+c        (7)  (r1)'(d1)(b1) = b'
+c  (b1) is built up in the upper part of the array b(rows 1,...n-4).
+      do 220 k1=1,nbind
+        l = ibind(k1)
+        do 210 i=l,n4
+          f = b(i,k1)
+          if(i.eq.1) go to 200
+          k2 = 3
+          if(i.lt.4) k2 = i-1
+          do 190 k3=1,k2
+            l1 = i-k3
+            l2 = 4-k3
+            f = f-b(l1,k1)*a(i,l2)*a(l1,4)
+ 190      continue
+ 200      b(i,k1) = f/a(i,4)
+ 210    continue
+ 220  continue
+c  factorization of the symmetric matrix  -(b1)'(d1)(b1)
+c        (8)  -(b1)'(d1)(b1) = (r2)'(d2)(r2)
+c  with (d2) a diagonal matrix and (r2) an nbind x nbind unit upper
+c  triangular matrix. the matrices r2 and d2 are built up in the lower
+c  part of the array b (rows n-3,n-2,...n-4+nbind).
+      do 270 i=1,nbind
+        i1 = i-1
+        do 260 j=i,nbind
+          f = 0.
+          do 230 k=1,n4
+            f = f+b(k,i)*b(k,j)*a(k,4)
+ 230      continue
+          k1 = n4+1
+          if(i1.eq.0) go to 250
+          do 240 k=1,i1
+            f = f+b(k1,i)*b(k1,j)*b(k1,k)
+            k1 = k1+1
+ 240      continue
+ 250      b(k1,j) = -f
+          if(j.eq.i) go to 260
+          b(k1,j) = b(k1,j)/b(k1,i)
+ 260    continue
+ 270  continue
+c  according to (3),(7) and (8) the system of equations (6) becomes
+c         ! (r1)'    0  ! ! (d1)    0  ! ! (r1)  (b1) ! ! c !   ! n'y !
+c    (9)  !             ! !            ! !            ! !   ! = !     !
+c         ! (b1)'  (r2)'! !   0   (d2) ! !   0   (r2) ! ! u !   !  0  !
+c  backward substitution to obtain the b-spline coefficients c(j),j=1,..
+c  n-4 and the lagrange parameters u(j),j=1,2,...nbind.
+c  first step of the backward substitution: solve the system
+c             ! (r1)'(d1)      0     ! ! (c1) !   ! n'y !
+c        (10) !                      ! !      ! = !     !
+c             ! (b1)'(d1)  (r2)'(d2) ! ! (u1) !   !  0  !
+c  from (4) and (5) we know that this is equivalent to
+c        (11)  (c1) = (z1)
+c        (12)  (r2)'(d2)(u1) = -(b1)'(z2)
+      do 310 i=1,nbind
+        f = 0.
+        do 280 j=1,n4
+          f = f+b(j,i)*zz(j)
+ 280    continue
+        i1 = i-1
+        k1 = n4+1
+        if(i1.eq.0) go to 300
+        do 290 j=1,i1
+          f = f+u(j)*b(k1,i)*b(k1,j)
+          k1 = k1+1
+ 290    continue
+ 300    u(i) = -f/b(k1,i)
+ 310  continue
+c  second step of the backward substitution: solve the system
+c             ! (r1)  (b1) ! ! c !   ! c1 !
+c        (13) !            ! !   ! = !    !
+c             !   0   (r2) ! ! u !   ! u1 !
+      k1 = nbind
+      k2 = kdim
+c  find the lagrange parameters u.
+      do 340 i=1,nbind
+        f = u(k1)
+        if(i.eq.1) go to 330
+        k3 = k1+1
+        do 320 j=k3,nbind
+          f = f-u(j)*b(k2,j)
+ 320    continue
+ 330    u(k1) = f
+        k1 = k1-1
+        k2 = k2-1
+ 340  continue
+c  find the b-spline coefficients c.
+      do 360 i=1,n4
+        f = c(i)
+        do 350 j=1,nbind
+          f = f-u(j)*b(i,j)
+ 350    continue
+        c(i) = f
+ 360  continue
+ 370  k1 = n4
+      do 390 i=2,n4
+        k1 = k1-1
+        f = c(k1)
+        k2 = 1
+        if(i.lt.5) k2 = 5-i
+        k3 = k1
+        l = 3
+        do 380 j=k2,3
+          k3 = k3+1
+          f = f-a(k3,l)*c(k3)
+          l = l-1
+ 380    continue
+        c(k1) = f
+ 390  continue
+c  test whether the solution of the least-squares problem with the
+c  constraints ibind(1),...ibind(nbind) in equality form, satisfies
+c  all of the constraints (2).
+      k = 1
+c  number counts the number of violated inequality constraints.
+      number = 0
+      do 440 j=1,n6
+        l = ibind(k)
+        k = k+1
+        if(j.eq.l) go to 440
+        k = k-1
+c  test whether constraint j is satisfied
+        f = e(j)*(c(j)-c(j+1))+const(j)*(c(j+2)-c(j+1))
+        if(f.le.0.) go to 440
+c  if constraint j is not satisfied, add a branch of length nbind+1
+c  to the tree. the nodes of this branch contain in their information
+c  field the number of the constraints ibind(1),...ibind(nbind) and j,
+c  arranged in increasing order.
+        number = number+1
+        k1 = k-1
+        if(k1.eq.0) go to 410
+        do 400 i=1,k1
+          jbind(i) = ibind(i)
+ 400    continue
+ 410    jbind(k) = j
+        if(l.eq.0) go to 430
+        do 420 i=k,nbind
+          jbind(i+1) = ibind(i)
+ 420    continue
+ 430    call fpadno(maxtr,up,left,right,info,count,merk,jbind,n1,ier)
+c  test whether the storage space which is required for the tree,exceeds
+c  the available storage space.
+        if(ier.ne.0) go to 560
+ 440  continue
+c  test whether the solution of the least-squares problem with equality
+c  constraints is a feasible solution.
+      if(number.eq.0) go to 470
+c  test whether there are still cases with nbind constraints in
+c  equality form to be considered.
+ 450  if(merk.gt.1) go to 460
+      nbind = n1
+c  test whether the number of knots where s''(x)=0 exceeds maxbin.
+      if(nbind.gt.maxbin) go to 550
+      n1 = n1+1
+      ibind(n1) = 0
+c  search which cases with nbind constraints in equality form
+c  are going to be considered.
+      call fpdeno(maxtr,up,left,right,nbind,merk)
+c  test whether the quadratic programming problem has a solution.
+      if(merk.eq.1) go to 570
+c  find a new case with nbind constraints in equality form.
+ 460  call fpseno(maxtr,up,left,right,info,merk,ibind,nbind)
+      go to 150
+c  test whether the feasible solution is optimal.
+ 470  ier = 0
+      do 480 i=1,n6
+        bind(i) = .false.
+ 480  continue
+      if(nbind.eq.0) go to 500
+      do 490 i=1,nbind
+        if(u(i).le.0.) go to 450
+        j = ibind(i)
+        bind(j) = .true.
+ 490  continue
+c  evaluate s(x) at the data points x(i) and calculate the weighted
+c  sum of squared residual right hand sides sq.
+ 500  sq = 0.
+      l = 4
+      lp1 = 5
+      do 530 i=1,m
+ 510    if(x(i).lt.t(lp1) .or. l.eq.n4) go to 520
+        l = lp1
+        lp1 = l+1
+        go to 510
+ 520    sx(i) = c(l-3)*q(i,1)+c(l-2)*q(i,2)+c(l-1)*q(i,3)+c(l)*q(i,4)
+        sq = sq+(w(i)*(y(i)-sx(i)))**2
+ 530  continue
+      go to 600
+c  error codes and messages.
+ 550  ier = 1
+      go to 600
+ 560  ier = 2
+      go to 600
+ 570  ier = 3
+ 600  return
+      end

Added: branches/Interpolate1D/fitpack/fpcsin.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcsin.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcsin.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,56 @@
+      subroutine fpcsin(a,b,par,sia,coa,sib,cob,ress,resc)
+c  fpcsin calculates the integrals ress=integral((b-x)**3*sin(par*x))
+c  and resc=integral((b-x)**3*cos(par*x)) over the interval (a,b),
+c  given sia=sin(par*a),coa=cos(par*a),sib=sin(par*b) and cob=cos(par*b)
+c  ..
+c  ..scalar arguments..
+      real*8 a,b,par,sia,coa,sib,cob,ress,resc
+c  ..local scalars..
+      integer i,j
+      real*8 ab,ab4,ai,alfa,beta,b2,b4,eps,fac,f1,f2,one,quart,six,
+     * three,two
+c  ..function references..
+      real*8 abs
+c  ..
+      one = 0.1e+01
+      two = 0.2e+01
+      three = 0.3e+01
+      six = 0.6e+01
+      quart = 0.25e+0
+      eps = 0.1e-09
+      ab = b-a
+      ab4 = ab**4
+      alfa = ab*par
+c the way of calculating the integrals ress and resc depends on
+c the value of alfa = (b-a)*par.
+      if(abs(alfa).le.one) go to 100
+c integration by parts.
+      beta = one/alfa
+      b2 = beta**2
+      b4 = six*b2**2
+      f1 = three*b2*(one-two*b2)
+      f2 = beta*(one-six*b2)
+      ress = ab4*(coa*f2+sia*f1+sib*b4)
+      resc = ab4*(coa*f1-sia*f2+cob*b4)
+      go to 400
+c ress and resc are found by evaluating a series expansion.
+ 100  fac = quart
+      f1 = fac
+      f2 = 0.
+      i = 4
+      do 200 j=1,5
+        i = i+1
+        ai = i
+        fac = fac*alfa/ai
+        f2 = f2+fac
+        if(abs(fac).le.eps) go to 300
+        i = i+1
+        ai = i
+        fac = -fac*alfa/ai
+        f1 = f1+fac
+        if(abs(fac).le.eps) go to 300
+ 200  continue
+ 300  ress = ab4*(coa*f2+sia*f1)
+      resc = ab4*(coa*f1-sia*f2)
+ 400  return
+      end

Added: branches/Interpolate1D/fitpack/fpcurf.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcurf.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcurf.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,359 @@
+      subroutine fpcurf(iopt,x,y,w,m,xb,xe,k,s,nest,tol,maxit,k1,k2,
+     * n,t,c,fp,fpint,z,a,b,g,q,nrdata,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 xb,xe,s,tol,fp
+      integer iopt,m,k,nest,maxit,k1,k2,n,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),t(nest),c(nest),fpint(nest),
+     * z(nest),a(nest,k1),b(nest,k2),g(nest,k2),q(m,k1)
+      integer nrdata(nest)
+c  ..local scalars..
+      real*8 acc,con1,con4,con9,cos,half,fpart,fpms,fpold,fp0,f1,f2,f3,
+     * one,p,pinv,piv,p1,p2,p3,rn,sin,store,term,wi,xi,yi
+      integer i,ich1,ich3,it,iter,i1,i2,i3,j,k3,l,l0,
+     * mk1,new,nk1,nmax,nmin,nplus,npl1,nrint,n8
+c  ..local arrays..
+      real*8 h(7)
+c  ..function references
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpback,fpbspl,fpgivs,fpdisc,fpknot,fprota
+c  ..
+c  set constants
+      one = 0.1d+01
+      con1 = 0.1d0
+      con9 = 0.9d0
+      con4 = 0.4d-01
+      half = 0.5d0
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1: determination of the number of knots and their position     c
+c  **************************************************************      c
+c  given a set of knots we compute the least-squares spline sinf(x),   c
+c  and the corresponding sum of squared residuals fp=f(p=inf).         c
+c  if iopt=-1 sinf(x) is the requested approximation.                  c
+c  if iopt=0 or iopt=1 we check whether we can accept the knots:       c
+c    if fp <=s we will continue with the current set of knots.         c
+c    if fp > s we will increase the number of knots and compute the    c
+c       corresponding least-squares spline until finally fp<=s.        c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmax = m+k+1.                                        c
+c    if s > 0 and                                                      c
+c      iopt=0 we first compute the least-squares polynomial of         c
+c      degree k; n = nmin = 2*k+2                                      c
+c      iopt=1 we start with the set of knots found at the last         c
+c      call of the routine, except for the case that s > fp0; then     c
+c      we compute directly the least-squares polynomial of degree k.   c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  determine nmin, the number of knots for polynomial approximation.
+      nmin = 2*k1
+      if(iopt.lt.0) go to 60
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  determine nmax, the number of knots for spline interpolation.
+      nmax = m+k1
+      if(s.gt.0.0d0) go to 45
+c  if s=0, s(x) is an interpolating spline.
+c  test whether the required storage space exceeds the available one.
+      n = nmax
+      if(nmax.gt.nest) go to 420
+c  find the position of the interior knots in case of interpolation.
+  10  mk1 = m-k1
+      if(mk1.eq.0) go to 60
+      k3 = k/2
+      i = k2
+      j = k3+2
+      if(k3*2.eq.k) go to 30
+      do 20 l=1,mk1
+        t(i) = x(j)
+        i = i+1
+        j = j+1
+  20  continue
+      go to 60
+  30  do 40 l=1,mk1
+        t(i) = (x(j)+x(j-1))*half
+        i = i+1
+        j = j+1
+  40  continue
+      go to 60
+c  if s>0 our initial choice of knots depends on the value of iopt.
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  polynomial of degree k which is a spline without interior knots.
+c  if iopt=1 and fp0>s we start computing the least squares spline
+c  according to the set of knots found at the last call of the routine.
+  45  if(iopt.eq.0) go to 50
+      if(n.eq.nmin) go to 50
+      fp0 = fpint(n)
+      fpold = fpint(n-1)
+      nplus = nrdata(n)
+      if(fp0.gt.s) go to 60
+  50  n = nmin
+      fpold = 0.0d0
+      nplus = 0
+      nrdata(1) = m-2
+c  main loop for the different sets of knots. m is a save upper bound
+c  for the number of trials.
+  60  do 200 iter = 1,m
+        if(n.eq.nmin) ier = -2
+c  find nrint, tne number of knot intervals.
+        nrint = n-nmin+1
+c  find the position of the additional knots which are needed for
+c  the b-spline representation of s(x).
+        nk1 = n-k1
+        i = n
+        do 70 j=1,k1
+          t(j) = xb
+          t(i) = xe
+          i = i-1
+  70    continue
+c  compute the b-spline coefficients of the least-squares spline
+c  sinf(x). the observation matrix a is built up row by row and
+c  reduced to upper triangular form by givens transformations.
+c  at the same time fp=f(p=inf) is computed.
+        fp = 0.0d0
+c  initialize the observation matrix a.
+        do 80 i=1,nk1
+          z(i) = 0.0d0
+          do 80 j=1,k1
+            a(i,j) = 0.0d0
+  80    continue
+        l = k1
+        do 130 it=1,m
+c  fetch the current data point x(it),y(it).
+          xi = x(it)
+          wi = w(it)
+          yi = y(it)*wi
+c  search for knot interval t(l) <= xi < t(l+1).
+  85      if(xi.lt.t(l+1) .or. l.eq.nk1) go to 90
+          l = l+1
+          go to 85
+c  evaluate the (k+1) non-zero b-splines at xi and store them in q.
+  90      call fpbspl(t,n,k,xi,l,h)
+          do 95 i=1,k1
+            q(it,i) = h(i)
+            h(i) = h(i)*wi
+  95      continue
+c  rotate the new row of the observation matrix into triangle.
+          j = l-k1
+          do 110 i=1,k1
+            j = j+1
+            piv = h(i)
+            if(piv.eq.0.0d0) go to 110
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(j,1),cos,sin)
+c  transformations to right hand side.
+            call fprota(cos,sin,yi,z(j))
+            if(i.eq.k1) go to 120
+            i2 = 1
+            i3 = i+1
+            do 100 i1 = i3,k1
+              i2 = i2+1
+c  transformations to left hand side.
+              call fprota(cos,sin,h(i1),a(j,i2))
+ 100        continue
+ 110      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 120      fp = fp+yi*yi
+ 130    continue
+        if(ier.eq.(-2)) fp0 = fp
+        fpint(n) = fp0
+        fpint(n-1) = fpold
+        nrdata(n) = nplus
+c  backward substitution to obtain the b-spline coefficients.
+        call fpback(a,z,nk1,k1,c,nest)
+c  test whether the approximation sinf(x) is an acceptable solution.
+        if(iopt.lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  if f(p=inf) < s accept the choice of knots.
+        if(fpms.lt.0.0d0) go to 250
+c  if n = nmax, sinf(x) is an interpolating spline.
+        if(n.eq.nmax) go to 430
+c  increase the number of knots.
+c  if n=nest we cannot increase the number of knots because of
+c  the storage capacity limitation.
+        if(n.eq.nest) go to 420
+c  determine the number of knots nplus we are going to add.
+        if(ier.eq.0) go to 140
+        nplus = 1
+        ier = 0
+        go to 150
+ 140    npl1 = nplus*2
+        rn = nplus
+        if(fpold-fp.gt.acc) npl1 = rn*fpms/(fpold-fp)
+        nplus = min0(nplus*2,max0(npl1,nplus/2,1))
+ 150    fpold = fp
+c  compute the sum((w(i)*(y(i)-s(x(i))))**2) for each knot interval
+c  t(j+k) <= x(i) <= t(j+k+1) and store it in fpint(j),j=1,2,...nrint.
+        fpart = 0.0d0
+        i = 1
+        l = k2
+        new = 0
+        do 180 it=1,m
+          if(x(it).lt.t(l) .or. l.gt.nk1) go to 160
+          new = 1
+          l = l+1
+ 160      term = 0.0d0
+          l0 = l-k2
+          do 170 j=1,k1
+            l0 = l0+1
+            term = term+c(l0)*q(it,j)
+ 170      continue
+          term = (w(it)*(term-y(it)))**2
+          fpart = fpart+term
+          if(new.eq.0) go to 180
+          store = term*half
+          fpint(i) = fpart-store
+          i = i+1
+          fpart = store
+          new = 0
+ 180    continue
+        fpint(nrint) = fpart
+        do 190 l=1,nplus
+c  add a new knot.
+          call fpknot(x,m,t,n,fpint,nrdata,nrint,nest,1)
+c  if n=nmax we locate the knots as for interpolation.
+          if(n.eq.nmax) go to 10
+c  test whether we cannot further increase the number of knots.
+          if(n.eq.nest) go to 200
+ 190    continue
+c  restart the computations with the new set of knots.
+ 200  continue
+c  test whether the least-squares kth degree polynomial is a solution
+c  of our approximation problem.
+ 250  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 2: determination of the smoothing spline sp(x).                c
+c  ***************************************************                 c
+c  we have determined the number of knots and their position.          c
+c  we now compute the b-spline coefficients of the smoothing spline    c
+c  sp(x). the observation matrix a is extended by the rows of matrix   c
+c  b expressing that the kth derivative discontinuities of sp(x) at    c
+c  the interior knots t(k+2),...t(n-k-1) must be zero. the corres-     c
+c  ponding weights of these additional rows are set to 1/p.            c
+c  iteratively we then have to determine the value of p such that      c
+c  f(p)=sum((w(i)*(y(i)-sp(x(i))))**2) be = s. we already know that    c
+c  the least-squares kth degree polynomial corresponds to p=0, and     c
+c  that the least-squares spline corresponds to p=infinity. the        c
+c  iteration process which is proposed here, makes use of rational     c
+c  interpolation. since f(p) is a convex and strictly decreasing       c
+c  function of p, it can be approximated by a rational function        c
+c  r(p) = (u*p+v)/(p+w). three values of p(p1,p2,p3) with correspond-  c
+c  ing values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used      c
+c  to calculate the new value of p such that r(p)=s. convergence is    c
+c  guaranteed by taking f1>0 and f3<0.                                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jump of the kth derivative of the
+c  b-splines at the knots t(l),l=k+2,...n-k-1 and store in b.
+      call fpdisc(t,n,k2,b,nest)
+c  initial value for p.
+      p1 = 0.0d0
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = 0.
+      do 255 i=1,nk1
+         p = p+a(i,1)
+ 255  continue
+      rn = nk1
+      p = rn/p
+      ich1 = 0
+      ich3 = 0
+      n8 = n-nmin
+c  iteration process to find the root of f(p) = s.
+      do 360 iter=1,maxit
+c  the rows of matrix b with weight 1/p are rotated into the
+c  triangularised observation matrix a which is stored in g.
+        pinv = one/p
+        do 260 i=1,nk1
+          c(i) = z(i)
+          g(i,k2) = 0.0d0
+          do 260 j=1,k1
+            g(i,j) = a(i,j)
+ 260    continue
+        do 300 it=1,n8
+c  the row of matrix b is rotated into triangle by givens transformation
+          do 270 i=1,k2
+            h(i) = b(it,i)*pinv
+ 270      continue
+          yi = 0.0d0
+          do 290 j=it,nk1
+            piv = h(1)
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,g(j,1),cos,sin)
+c  transformations to right hand side.
+            call fprota(cos,sin,yi,c(j))
+            if(j.eq.nk1) go to 300
+            i2 = k1
+            if(j.gt.n8) i2 = nk1-j
+            do 280 i=1,i2
+c  transformations to left hand side.
+              i1 = i+1
+              call fprota(cos,sin,h(i1),g(j,i1))
+              h(i) = h(i1)
+ 280        continue
+            h(i2+1) = 0.0d0
+ 290      continue
+ 300    continue
+c  backward substitution to obtain the b-spline coefficients.
+        call fpback(g,c,nk1,k2,c,nest)
+c  computation of f(p).
+        fp = 0.0d0
+        l = k2
+        do 330 it=1,m
+          if(x(it).lt.t(l) .or. l.gt.nk1) go to 310
+          l = l+1
+ 310      l0 = l-k2
+          term = 0.0d0
+          do 320 j=1,k1
+            l0 = l0+1
+            term = term+c(l0)*q(it,j)
+ 320      continue
+          fp = fp+(w(it)*(term-y(it)))**2
+ 330    continue
+c  test whether the approximation sp(x) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximal number of iterations is reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 340
+        if((f2-f3).gt.acc) go to 335
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p=p1*con9 + p2*con1
+        go to 360
+ 335    if(f2.lt.0.0d0) ich3=1
+ 340    if(ich1.ne.0) go to 350
+        if((f1-f2).gt.acc) go to 345
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 360
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 360
+ 345    if(f2.gt.0.0d0) ich1=1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 350    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value for p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 360  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+ 440  return
+      end

Added: branches/Interpolate1D/fitpack/fpcuro.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcuro.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcuro.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,94 @@
+      subroutine fpcuro(a,b,c,d,x,n)
+c  subroutine fpcuro finds the real zeros of a cubic polynomial
+c  p(x) = a*x**3+b*x**2+c*x+d.
+c
+c  calling sequence:
+c     call fpcuro(a,b,c,d,x,n)
+c
+c  input parameters:
+c    a,b,c,d: real values, containing the coefficients of p(x).
+c
+c  output parameters:
+c    x      : real array,length 3, which contains the real zeros of p(x)
+c    n      : integer, giving the number of real zeros of p(x).
+c  ..
+c  ..scalar arguments..
+      real*8 a,b,c,d
+      integer n
+c  ..array argument..
+      real*8 x(3)
+c  ..local scalars..
+      integer i
+      real*8 a1,b1,c1,df,disc,d1,e3,f,four,half,ovfl,pi3,p3,q,r,
+     * step,tent,three,two,u,u1,u2,y
+c  ..function references..
+      real*8 abs,max,datan,atan2,cos,sign,sqrt
+c  set constants
+      two = 0.2d+01
+      three = 0.3d+01
+      four = 0.4d+01
+      ovfl =0.1d+05
+      half = 0.5d+0
+      tent = 0.1d+0
+      e3 = tent/0.3d0
+      pi3 = datan(0.1d+01)/0.75d0
+      a1 = abs(a)
+      b1 = abs(b)
+      c1 = abs(c)
+      d1 = abs(d)
+c  test whether p(x) is a third degree polynomial.
+      if(max(b1,c1,d1).lt.a1*ovfl) go to 300
+c  test whether p(x) is a second degree polynomial.
+      if(max(c1,d1).lt.b1*ovfl) go to 200
+c  test whether p(x) is a first degree polynomial.
+      if(d1.lt.c1*ovfl) go to 100
+c  p(x) is a constant function.
+      n = 0
+      go to 800
+c  p(x) is a first degree polynomial.
+ 100  n = 1
+      x(1) = -d/c
+      go to 500
+c  p(x) is a second degree polynomial.
+ 200  disc = c*c-four*b*d
+      n = 0
+      if(disc.lt.0.) go to 800
+      n = 2
+      u = sqrt(disc)
+      b1 = b+b
+      x(1) = (-c+u)/b1
+      x(2) = (-c-u)/b1
+      go to 500
+c  p(x) is a third degree polynomial.
+ 300  b1 = b/a*e3
+      c1 = c/a
+      d1 = d/a
+      q = c1*e3-b1*b1
+      r = b1*b1*b1+(d1-b1*c1)*half
+      disc = q*q*q+r*r
+      if(disc.gt.0.) go to 400
+      u = sqrt(abs(q))
+      if(r.lt.0.) u = -u
+      p3 = atan2(sqrt(-disc),abs(r))*e3
+      u2 = u+u
+      n = 3
+      x(1) = -u2*cos(p3)-b1
+      x(2) = u2*cos(pi3-p3)-b1
+      x(3) = u2*cos(pi3+p3)-b1
+      go to 500
+ 400  u = sqrt(disc)
+      u1 = -r+u
+      u2 = -r-u
+      n = 1
+      x(1) = sign(abs(u1)**e3,u1)+sign(abs(u2)**e3,u2)-b1
+c  apply a newton iteration to improve the accuracy of the roots.
+ 500  do 700 i=1,n
+        y = x(i)
+        f = ((a*y+b)*y+c)*y+d
+        df = (three*a*y+two*b)*y+c
+        step = 0.
+        if(abs(f).lt.abs(df)*tent) step = f/df
+        x(i) = y-step
+ 700  continue
+ 800  return
+      end

Added: branches/Interpolate1D/fitpack/fpcyt1.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcyt1.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcyt1.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,53 @@
+      subroutine fpcyt1(a,n,nn)
+c (l u)-decomposition of a cyclic tridiagonal matrix with the non-zero
+c elements stored as follows
+c
+c    | a(1,2) a(1,3)                                    a(1,1)  |
+c    | a(2,1) a(2,2) a(2,3)                                     |
+c    |        a(3,1) a(3,2) a(3,3)                              |
+c    |               ...............                            |
+c    |                               a(n-1,1) a(n-1,2) a(n-1,3) |
+c    | a(n,3)                                  a(n,1)   a(n,2)  |
+c
+c  ..
+c  ..scalar arguments..
+      integer n,nn
+c  ..array arguments..
+      real*8 a(nn,6)
+c  ..local scalars..
+      real*8 aa,beta,gamma,sum,teta,v,one
+      integer i,n1,n2
+c  ..
+c  set constant
+      one = 1
+      n2 = n-2
+      beta = one/a(1,2)
+      gamma = a(n,3)
+      teta = a(1,1)*beta
+      a(1,4) = beta
+      a(1,5) = gamma
+      a(1,6) = teta
+      sum = gamma*teta
+      do 10 i=2,n2
+         v = a(i-1,3)*beta
+         aa = a(i,1)
+         beta = one/(a(i,2)-aa*v)
+         gamma = -gamma*v
+         teta = -teta*aa*beta
+         a(i,4) = beta
+         a(i,5) = gamma
+         a(i,6) = teta
+         sum = sum+gamma*teta
+  10  continue
+      n1 = n-1
+      v = a(n2,3)*beta
+      aa = a(n1,1)
+      beta = one/(a(n1,2)-aa*v)
+      gamma = a(n,1)-gamma*v
+      teta = (a(n1,3)-teta*aa)*beta
+      a(n1,4) = beta
+      a(n1,5) = gamma
+      a(n1,6) = teta
+      a(n,4) = one/(a(n,2)-(sum+gamma*teta))
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpcyt2.f
===================================================================
--- branches/Interpolate1D/fitpack/fpcyt2.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpcyt2.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,32 @@
+      subroutine fpcyt2(a,n,b,c,nn)
+c subroutine fpcyt2 solves a linear n x n system
+c         a * c = b
+c where matrix a is a cyclic tridiagonal matrix, decomposed
+c using subroutine fpsyt1.
+c  ..
+c  ..scalar arguments..
+      integer n,nn
+c  ..array arguments..
+      real*8 a(nn,6),b(n),c(n)
+c  ..local scalars..
+      real*8 cc,sum
+      integer i,j,j1,n1
+c  ..
+      c(1) = b(1)*a(1,4)
+      sum = c(1)*a(1,5)
+      n1 = n-1
+      do 10 i=2,n1
+         c(i) = (b(i)-a(i,1)*c(i-1))*a(i,4)
+         sum = sum+c(i)*a(i,5)
+  10  continue
+      cc = (b(n)-sum)*a(n,4)
+      c(n) = cc
+      c(n1) = c(n1)-cc*a(n1,6)
+      j = n1
+      do 20 i=3,n
+         j1 = j-1
+         c(j1) = c(j1)-c(j)*a(j1,3)*a(j1,4)-cc*a(j1,6)
+         j = j1
+  20  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpdeno.f
===================================================================
--- branches/Interpolate1D/fitpack/fpdeno.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpdeno.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,55 @@
+      subroutine fpdeno(maxtr,up,left,right,nbind,merk)
+c  subroutine fpdeno frees the nodes of all branches of a triply linked
+c  tree with length < nbind by putting to zero their up field.
+c  on exit the parameter merk points to the terminal node of the
+c  most left branch of length nbind or takes the value 1 if there
+c  is no such branch.
+c  ..
+c  ..scalar arguments..
+      integer maxtr,nbind,merk
+c  ..array arguments..
+      integer up(maxtr),left(maxtr),right(maxtr)
+c  ..local scalars ..
+      integer i,j,k,l,niveau,point
+c  ..
+      i = 1
+      niveau = 0
+  10  point = i
+      i = left(point)
+      if(i.eq.0) go to 20
+      niveau = niveau+1
+      go to 10
+  20  if(niveau.eq.nbind) go to 70
+  30  i = right(point)
+      j = up(point)
+      up(point) = 0
+      k = left(j)
+      if(point.ne.k) go to 50
+      if(i.ne.0) go to 40
+      niveau = niveau-1
+      if(niveau.eq.0) go to 80
+      point = j
+      go to 30
+  40  left(j) = i
+      go to 10
+  50  l = right(k)
+      if(point.eq.l) go to 60
+      k = l
+      go to 50
+  60  right(k) = i
+      point = k
+  70  i = right(point)
+      if(i.ne.0) go to 10
+      i = up(point)
+      niveau = niveau-1
+      if(niveau.eq.0) go to 80
+      point = i
+      go to 70
+  80  k = 1
+      l = left(k)
+      if(up(l).eq.0) return
+  90  merk = k
+      k = left(k)
+      if(k.ne.0) go to 90
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpdisc.f
===================================================================
--- branches/Interpolate1D/fitpack/fpdisc.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpdisc.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,43 @@
+      subroutine fpdisc(t,n,k2,b,nest)
+c  subroutine fpdisc calculates the discontinuity jumps of the kth
+c  derivative of the b-splines of degree k at the knots t(k+2)..t(n-k-1)
+c  ..scalar arguments..
+      integer n,k2,nest
+c  ..array arguments..
+      real*8 t(n),b(nest,k2)
+c  ..local scalars..
+      real*8 an,fac,prod
+      integer i,ik,j,jk,k,k1,l,lj,lk,lmk,lp,nk1,nrint
+c  ..local array..
+      real*8 h(12)
+c  ..
+      k1 = k2-1
+      k = k1-1
+      nk1 = n-k1
+      nrint = nk1-k
+      an = nrint
+      fac = an/(t(nk1+1)-t(k1))
+      do 40 l=k2,nk1
+        lmk = l-k1
+        do 10 j=1,k1
+          ik = j+k1
+          lj = l+j
+          lk = lj-k2
+          h(j) = t(l)-t(lk)
+          h(ik) = t(l)-t(lj)
+  10    continue
+        lp = lmk
+        do 30 j=1,k2
+          jk = j
+          prod = h(j)
+          do 20 i=1,k
+            jk = jk+1
+            prod = prod*h(jk)*fac
+  20      continue
+          lk = lp+k1
+          b(lmk,j) = (t(lk)-t(lp))/prod
+          lp = lp+1
+  30    continue
+  40  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpfrno.f
===================================================================
--- branches/Interpolate1D/fitpack/fpfrno.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpfrno.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,69 @@
+      subroutine fpfrno(maxtr,up,left,right,info,point,merk,n1,
+     * count,ier)
+c  subroutine fpfrno collects the free nodes (up field zero) of the
+c  triply linked tree the information of which is kept in the arrays
+c  up,left,right and info. the maximal length of the branches of the
+c  tree is given by n1. if no free nodes are found, the error flag
+c  ier is set to 1.
+c  ..
+c  ..scalar arguments..
+      integer maxtr,point,merk,n1,count,ier
+c  ..array arguments..
+      integer up(maxtr),left(maxtr),right(maxtr),info(maxtr)
+c  ..local scalars
+      integer i,j,k,l,n,niveau
+c  ..
+      ier = 1
+      if(n1.eq.2) go to 140
+      niveau = 1
+      count = 2
+  10  j = 0
+      i = 1
+  20  if(j.eq.niveau) go to 30
+      k = 0
+      l = left(i)
+      if(l.eq.0) go to 110
+      i = l
+      j = j+1
+      go to 20
+  30  if (i.lt.count) go to 110
+      if (i.eq.count) go to 100
+      go to 40
+  40  if(up(count).eq.0) go to 50
+      count = count+1
+      go to 30
+  50  up(count) = up(i)
+      left(count) = left(i)
+      right(count) = right(i)
+      info(count) = info(i)
+      if(merk.eq.i) merk = count
+      if(point.eq.i) point = count
+      if(k.eq.0) go to 60
+      right(k) = count
+      go to 70
+  60  n = up(i)
+      left(n) = count
+  70  l = left(i)
+  80  if(l.eq.0) go to 90
+      up(l) = count
+      l = right(l)
+      go to 80
+  90  up(i) = 0
+      i = count
+ 100  count = count+1
+ 110  l = right(i)
+      k = i
+      if(l.eq.0) go to 120
+      i = l
+      go to 20
+ 120  l = up(i)
+      j = j-1
+      if(j.eq.0) go to 130
+      i = l
+      go to 110
+ 130  niveau = niveau+1
+      if(niveau.le.n1) go to 10
+      if(count.gt.maxtr) go to 140
+      ier = 0
+ 140  return
+      end

Added: branches/Interpolate1D/fitpack/fpgivs.f
===================================================================
--- branches/Interpolate1D/fitpack/fpgivs.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpgivs.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,20 @@
+      subroutine fpgivs(piv,ww,cos,sin)
+c  subroutine fpgivs calculates the parameters of a givens
+c  transformation .
+c  ..
+c  ..scalar arguments..
+      real*8 piv,ww,cos,sin
+c  ..local scalars..
+      real*8 dd,one,store
+c  ..function references..
+      real*8 abs,sqrt
+c  ..
+      one = 0.1e+01
+      store = abs(piv)
+      if(store.ge.ww) dd = store*sqrt(one+(ww/piv)**2)
+      if(store.lt.ww) dd = ww*sqrt(one+(piv/ww)**2)
+      cos = ww/dd
+      sin = piv/dd
+      ww = dd
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpgrdi.f
===================================================================
--- branches/Interpolate1D/fitpack/fpgrdi.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpgrdi.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,600 @@
+      subroutine fpgrdi(ifsu,ifsv,ifbu,ifbv,iback,u,mu,v,mv,z,mz,dz,
+     * iop0,iop1,tu,nu,tv,nv,p,c,nc,sq,fp,fpu,fpv,mm,mvnu,spu,spv,
+     * right,q,au,av1,av2,bu,bv,aa,bb,cc,cosi,nru,nrv)
+c  ..
+c  ..scalar arguments..
+      real*8 p,sq,fp
+      integer ifsu,ifsv,ifbu,ifbv,iback,mu,mv,mz,iop0,iop1,nu,nv,nc,
+     * mm,mvnu
+c  ..array arguments..
+      real*8 u(mu),v(mv),z(mz),dz(3),tu(nu),tv(nv),c(nc),fpu(nu),fpv(nv)
+     *,
+     * spu(mu,4),spv(mv,4),right(mm),q(mvnu),au(nu,5),av1(nv,6),
+     * av2(nv,4),aa(2,mv),bb(2,nv),cc(nv),cosi(2,nv),bu(nu,5),bv(nv,5)
+      integer nru(mu),nrv(mv)
+c  ..local scalars..
+      real*8 arg,co,dz1,dz2,dz3,fac,fac0,pinv,piv,si,term,one,three,half
+     *
+      integer i,ic,ii,ij,ik,iq,irot,it,iz,i0,i1,i2,i3,j,jj,jk,jper,
+     * j0,j1,k,k1,k2,l,l0,l1,l2,mvv,ncof,nrold,nroldu,nroldv,number,
+     * numu,numu1,numv,numv1,nuu,nu4,nu7,nu8,nu9,nv11,nv4,nv7,nv8,n1
+c  ..local arrays..
+      real*8 h(5),h1(5),h2(4)
+c  ..function references..
+      integer min0
+      real*8 cos,sin
+c  ..subroutine references..
+c    fpback,fpbspl,fpgivs,fpcyt1,fpcyt2,fpdisc,fpbacp,fprota
+c  ..
+c  let
+c               |   (spu)    |            |   (spv)    |
+c        (au) = | ---------- |     (av) = | ---------- |
+c               | (1/p) (bu) |            | (1/p) (bv) |
+c
+c                                | z  ' 0 |
+c                            q = | ------ |
+c                                | 0  ' 0 |
+c
+c  with c      : the (nu-4) x (nv-4) matrix which contains the b-spline
+c                coefficients.
+c       z      : the mu x mv matrix which contains the function values.
+c       spu,spv: the mu x (nu-4), resp. mv x (nv-4) observation matrices
+c                according to the least-squares problems in the u-,resp.
+c                v-direction.
+c       bu,bv  : the (nu-7) x (nu-4),resp. (nv-7) x (nv-4) matrices
+c                containing the discontinuity jumps of the derivatives
+c                of the b-splines in the u-,resp.v-variable at the knots
+c  the b-spline coefficients of the smoothing spline are then calculated
+c  as the least-squares solution of the following over-determined linear
+c  system of equations
+c
+c    (1)  (av) c (au)' = q
+c
+c  subject to the constraints
+c
+c    (2)  c(i,nv-3+j) = c(i,j), j=1,2,3 ; i=1,2,...,nu-4
+c
+c    (3)  if iop0 = 0  c(1,j) = dz(1)
+c            iop0 = 1  c(1,j) = dz(1)
+c                      c(2,j) = dz(1)+(dz(2)*cosi(1,j)+dz(3)*cosi(2,j))*
+c                               tu(5)/3. = cc(j) , j=1,2,...nv-4
+c
+c    (4)  if iop1 = 1  c(nu-4,j) = 0, j=1,2,...,nv-4.
+c
+c  set constants
+      one = 1
+      three = 3
+      half = 0.5
+c  initialization
+      nu4 = nu-4
+      nu7 = nu-7
+      nu8 = nu-8
+      nu9 = nu-9
+      nv4 = nv-4
+      nv7 = nv-7
+      nv8 = nv-8
+      nv11 = nv-11
+      nuu = nu4-iop0-iop1-1
+      if(p.gt.0.) pinv = one/p
+c  it depends on the value of the flags ifsu,ifsv,ifbu,ifbv and iop0 and
+c  on the value of p whether the matrices (spu), (spv), (bu), (bv) and
+c  (cosi) still must be determined.
+      if(ifsu.ne.0) go to 30
+c  calculate the non-zero elements of the matrix (spu) which is the ob-
+c  servation matrix according to the least-squares spline approximation
+c  problem in the u-direction.
+      l = 4
+      l1 = 5
+      number = 0
+      do 25 it=1,mu
+        arg = u(it)
+  10    if(arg.lt.tu(l1) .or. l.eq.nu4) go to 15
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 10
+  15    call fpbspl(tu,nu,3,arg,l,h)
+        do 20 i=1,4
+          spu(it,i) = h(i)
+  20    continue
+        nru(it) = number
+  25  continue
+      ifsu = 1
+c  calculate the non-zero elements of the matrix (spv) which is the ob-
+c  servation matrix according to the least-squares spline approximation
+c  problem in the v-direction.
+  30  if(ifsv.ne.0) go to 85
+      l = 4
+      l1 = 5
+      number = 0
+      do 50 it=1,mv
+        arg = v(it)
+  35    if(arg.lt.tv(l1) .or. l.eq.nv4) go to 40
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 35
+  40    call fpbspl(tv,nv,3,arg,l,h)
+        do 45 i=1,4
+          spv(it,i) = h(i)
+  45    continue
+        nrv(it) = number
+  50  continue
+      ifsv = 1
+      if(iop0.eq.0) go to 85
+c  calculate the coefficients of the interpolating splines for cos(v)
+c  and sin(v).
+      do 55 i=1,nv4
+         cosi(1,i) = 0.
+         cosi(2,i) = 0.
+  55  continue
+      if(nv7.lt.4) go to 85
+      do 65 i=1,nv7
+         l = i+3
+         arg = tv(l)
+         call fpbspl(tv,nv,3,arg,l,h)
+         do 60 j=1,3
+            av1(i,j) = h(j)
+  60     continue
+         cosi(1,i) = cos(arg)
+         cosi(2,i) = sin(arg)
+  65  continue
+      call fpcyt1(av1,nv7,nv)
+      do 80 j=1,2
+         do 70 i=1,nv7
+            right(i) = cosi(j,i)
+  70     continue
+         call fpcyt2(av1,nv7,right,right,nv)
+         do 75 i=1,nv7
+            cosi(j,i+1) = right(i)
+  75     continue
+         cosi(j,1) = cosi(j,nv7+1)
+         cosi(j,nv7+2) = cosi(j,2)
+         cosi(j,nv4) = cosi(j,3)
+  80  continue
+  85  if(p.le.0.) go to  150
+c  calculate the non-zero elements of the matrix (bu).
+      if(ifbu.ne.0 .or. nu8.eq.0) go to 90
+      call fpdisc(tu,nu,5,bu,nu)
+      ifbu = 1
+c  calculate the non-zero elements of the matrix (bv).
+  90  if(ifbv.ne.0 .or. nv8.eq.0) go to 150
+      call fpdisc(tv,nv,5,bv,nv)
+      ifbv = 1
+c  substituting (2),(3) and (4) into (1), we obtain the overdetermined
+c  system
+c         (5)  (avv) (cr) (auu)' = (qq)
+c  from which the nuu*nv7 remaining coefficients
+c         c(i,j) , i=2+iop0,3+iop0,...,nu-4-iop1 ; j=1,2,...,nv-7 ,
+c  the elements of (cr), are then determined in the least-squares sense.
+c  simultaneously, we compute the resulting sum of squared residuals sq.
+ 150  dz1 = dz(1)
+      do 155 i=1,mv
+         aa(1,i) = dz1
+ 155  continue
+      if(nv8.eq.0 .or. p.le.0.) go to 165
+      do 160 i=1,nv8
+         bb(1,i) = 0.
+ 160  continue
+ 165  mvv = mv
+      if(iop0.eq.0) go to 220
+      fac = tu(5)/three
+      dz2 = dz(2)*fac
+      dz3 = dz(3)*fac
+      do 170 i=1,nv4
+         cc(i) = dz1+dz2*cosi(1,i)+dz3*cosi(2,i)
+ 170  continue
+      do 190 i=1,mv
+         number = nrv(i)
+         fac = 0.
+         do 180 j=1,4
+            number = number+1
+            fac = fac+cc(number)*spv(i,j)
+ 180     continue
+         aa(2,i) = fac
+ 190  continue
+      if(nv8.eq.0 .or. p.le.0.) go to 220
+      do 210 i=1,nv8
+         number = i
+         fac = 0.
+         do 200 j=1,5
+            fac = fac+cc(number)*bv(i,j)
+            number = number+1
+ 200     continue
+         bb(2,i) = fac*pinv
+ 210  continue
+      mvv = mvv+nv8
+c  we first determine the matrices (auu) and (qq). then we reduce the
+c  matrix (auu) to upper triangular form (ru) using givens rotations.
+c  we apply the same transformations to the rows of matrix qq to obtain
+c  the (mv+nv8) x nuu matrix g.
+c  we store matrix (ru) into au and g into q.
+ 220  l = mvv*nuu
+c  initialization.
+      sq = 0.
+      do 230 i=1,l
+        q(i) = 0.
+ 230  continue
+      do 240 i=1,nuu
+        do 240 j=1,5
+          au(i,j) = 0.
+ 240  continue
+      l = 0
+      nrold = 0
+      n1 = nrold+1
+      do 420 it=1,mu
+        number = nru(it)
+c  find the appropriate column of q.
+ 250    do 260 j=1,mvv
+           right(j) = 0.
+ 260    continue
+        if(nrold.eq.number) go to 280
+        if(p.le.0.) go to 410
+c  fetch a new row of matrix (bu).
+        do 270 j=1,5
+          h(j) = bu(n1,j)*pinv
+ 270    continue
+        i0 = 1
+        i1 = 5
+        go to 310
+c  fetch a new row of matrix (spu).
+ 280    do 290 j=1,4
+          h(j) = spu(it,j)
+ 290    continue
+c  find the appropriate column of q.
+        do 300 j=1,mv
+          l = l+1
+          right(j) = z(l)
+ 300    continue
+        i0 = 1
+        i1 = 4
+ 310    if(nu7-number .eq. iop1) i1 = i1-1
+        j0 = n1
+c  take into account that we eliminate the constraints (3)
+ 320     if(j0-1.gt.iop0) go to 360
+         fac0 = h(i0)
+         do 330 j=1,mv
+            right(j) = right(j)-fac0*aa(j0,j)
+ 330     continue
+         if(mv.eq.mvv) go to 350
+         j = mv
+         do 340 jj=1,nv8
+            j = j+1
+            right(j) = right(j)-fac0*bb(j0,jj)
+ 340     continue
+ 350     j0 = j0+1
+         i0 = i0+1
+         go to 320
+ 360     irot = nrold-iop0-1
+         if(irot.lt.0) irot = 0
+c  rotate the new row of matrix (auu) into triangle.
+        do 390 i=i0,i1
+          irot = irot+1
+          piv = h(i)
+          if(piv.eq.0.) go to 390
+c  calculate the parameters of the givens transformation.
+          call fpgivs(piv,au(irot,1),co,si)
+c  apply that transformation to the rows of matrix (qq).
+          iq = (irot-1)*mvv
+          do 370 j=1,mvv
+            iq = iq+1
+            call fprota(co,si,right(j),q(iq))
+ 370      continue
+c  apply that transformation to the columns of (auu).
+          if(i.eq.i1) go to 390
+          i2 = 1
+          i3 = i+1
+          do 380 j=i3,i1
+            i2 = i2+1
+            call fprota(co,si,h(j),au(irot,i2))
+ 380      continue
+ 390    continue
+c we update the sum of squared residuals
+        do 395 j=1,mvv
+          sq = sq+right(j)**2
+ 395    continue
+ 400    if(nrold.eq.number) go to 420
+ 410    nrold = n1
+        n1 = n1+1
+        go to 250
+ 420  continue
+c  we determine the matrix (avv) and then we reduce her to
+c  upper triangular form (rv) using givens rotations.
+c  we apply the same transformations to the columns of matrix
+c  g to obtain the (nv-7) x (nu-5-iop0-iop1) matrix h.
+c  we store matrix (rv) into av1 and av2, h into c.
+c  the nv7 x nv7 upper triangular matrix (rv) has the form
+c              | av1 '     |
+c       (rv) = |     ' av2 |
+c              |  0  '     |
+c  with (av2) a nv7 x 4 matrix and (av1) a nv11 x nv11 upper
+c  triangular matrix of bandwidth 5.
+      ncof = nuu*nv7
+c  initialization.
+      do 430 i=1,ncof
+        c(i) = 0.
+ 430  continue
+      do 440 i=1,nv4
+        av1(i,5) = 0.
+        do 440 j=1,4
+          av1(i,j) = 0.
+          av2(i,j) = 0.
+ 440  continue
+      jper = 0
+      nrold = 0
+      do 770 it=1,mv
+        number = nrv(it)
+ 450    if(nrold.eq.number) go to 480
+        if(p.le.0.) go to 760
+c  fetch a new row of matrix (bv).
+        n1 = nrold+1
+        do 460 j=1,5
+          h(j) = bv(n1,j)*pinv
+ 460    continue
+c  find the appropiate row of g.
+        do 465 j=1,nuu
+          right(j) = 0.
+ 465    continue
+        if(mv.eq.mvv) go to 510
+        l = mv+n1
+        do 470 j=1,nuu
+          right(j) = q(l)
+          l = l+mvv
+ 470    continue
+        go to 510
+c  fetch a new row of matrix (spv)
+ 480    h(5) = 0.
+        do 490 j=1,4
+          h(j) = spv(it,j)
+ 490    continue
+c  find the appropiate row of g.
+        l = it
+        do 500 j=1,nuu
+          right(j) = q(l)
+          l = l+mvv
+ 500    continue
+c  test whether there are non-zero values in the new row of (avv)
+c  corresponding to the b-splines n(j,v),j=nv7+1,...,nv4.
+ 510     if(nrold.lt.nv11) go to 710
+         if(jper.ne.0) go to 550
+c  initialize the matrix (av2).
+         jk = nv11+1
+         do 540 i=1,4
+            ik = jk
+            do 520 j=1,5
+               if(ik.le.0) go to 530
+               av2(ik,i) = av1(ik,j)
+               ik = ik-1
+ 520        continue
+ 530        jk = jk+1
+ 540     continue
+         jper = 1
+c  if one of the non-zero elements of the new row corresponds to one of
+c  the b-splines n(j;v),j=nv7+1,...,nv4, we take account of condition
+c  (2) for setting up this row of (avv). the row is stored in h1( the
+c  part with respect to av1) and h2 (the part with respect to av2).
+ 550     do 560 i=1,4
+            h1(i) = 0.
+            h2(i) = 0.
+ 560     continue
+         h1(5) = 0.
+         j = nrold-nv11
+         do 600 i=1,5
+            j = j+1
+            l0 = j
+ 570        l1 = l0-4
+            if(l1.le.0) go to 590
+            if(l1.le.nv11) go to 580
+            l0 = l1-nv11
+            go to 570
+ 580        h1(l1) = h(i)
+            go to 600
+ 590        h2(l0) = h2(l0) + h(i)
+ 600     continue
+c  rotate the new row of (avv) into triangle.
+         if(nv11.le.0) go to 670
+c  rotations with the rows 1,2,...,nv11 of (avv).
+         do 660 j=1,nv11
+            piv = h1(1)
+            i2 = min0(nv11-j,4)
+            if(piv.eq.0.) go to 640
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,av1(j,1),co,si)
+c  apply that transformation to the columns of matrix g.
+            ic = j
+            do 610 i=1,nuu
+               call fprota(co,si,right(i),c(ic))
+               ic = ic+nv7
+ 610        continue
+c  apply that transformation to the rows of (avv) with respect to av2.
+            do 620 i=1,4
+               call fprota(co,si,h2(i),av2(j,i))
+ 620        continue
+c  apply that transformation to the rows of (avv) with respect to av1.
+            if(i2.eq.0) go to 670
+            do 630 i=1,i2
+               i1 = i+1
+               call fprota(co,si,h1(i1),av1(j,i1))
+ 630        continue
+ 640        do 650 i=1,i2
+               h1(i) = h1(i+1)
+ 650        continue
+            h1(i2+1) = 0.
+ 660     continue
+c  rotations with the rows nv11+1,...,nv7 of avv.
+ 670     do 700 j=1,4
+            ij = nv11+j
+            if(ij.le.0) go to 700
+            piv = h2(j)
+            if(piv.eq.0.) go to 700
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,av2(ij,j),co,si)
+c  apply that transformation to the columns of matrix g.
+            ic = ij
+            do 680 i=1,nuu
+               call fprota(co,si,right(i),c(ic))
+               ic = ic+nv7
+ 680        continue
+            if(j.eq.4) go to 700
+c  apply that transformation to the rows of (avv) with respect to av2.
+            j1 = j+1
+            do 690 i=j1,4
+               call fprota(co,si,h2(i),av2(ij,i))
+ 690        continue
+ 700     continue
+c we update the sum of squared residuals
+         do 705 i=1,nuu
+           sq = sq+right(i)**2
+ 705     continue
+         go to 750
+c  rotation into triangle of the new row of (avv), in case the elements
+c  corresponding to the b-splines n(j;v),j=nv7+1,...,nv4 are all zero.
+ 710     irot =nrold
+         do 740 i=1,5
+            irot = irot+1
+            piv = h(i)
+            if(piv.eq.0.) go to 740
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,av1(irot,1),co,si)
+c  apply that transformation to the columns of matrix g.
+            ic = irot
+            do 720 j=1,nuu
+               call fprota(co,si,right(j),c(ic))
+               ic = ic+nv7
+ 720        continue
+c  apply that transformation to the rows of (avv).
+            if(i.eq.5) go to 740
+            i2 = 1
+            i3 = i+1
+            do 730 j=i3,5
+               i2 = i2+1
+               call fprota(co,si,h(j),av1(irot,i2))
+ 730        continue
+ 740     continue
+c we update the sum of squared residuals
+         do 745 i=1,nuu
+           sq = sq+right(i)**2
+ 745     continue
+ 750     if(nrold.eq.number) go to 770
+ 760     nrold = nrold+1
+         go to 450
+ 770  continue
+c  test whether the b-spline coefficients must be determined.
+      if(iback.ne.0) return
+c  backward substitution to obtain the b-spline coefficients as the
+c  solution of the linear system    (rv) (cr) (ru)' = h.
+c  first step: solve the system  (rv) (c1) = h.
+      k = 1
+      do 780 i=1,nuu
+         call fpbacp(av1,av2,c(k),nv7,4,c(k),5,nv)
+         k = k+nv7
+ 780  continue
+c  second step: solve the system  (cr) (ru)' = (c1).
+      k = 0
+      do 800 j=1,nv7
+        k = k+1
+        l = k
+        do 790 i=1,nuu
+          right(i) = c(l)
+          l = l+nv7
+ 790    continue
+        call fpback(au,right,nuu,5,right,nu)
+        l = k
+        do 795 i=1,nuu
+           c(l) = right(i)
+           l = l+nv7
+ 795    continue
+ 800  continue
+c  calculate from the conditions (2)-(3)-(4), the remaining b-spline
+c  coefficients.
+      ncof = nu4*nv4
+      i = nv4
+      j = 0
+      do 805 l=1,nv4
+         q(l) = dz1
+ 805  continue
+      if(iop0.eq.0) go to 815
+      do 810 l=1,nv4
+         i = i+1
+         q(i) = cc(l)
+ 810  continue
+ 815  if(nuu.eq.0) go to 850
+      do 840 l=1,nuu
+         ii = i
+         do 820 k=1,nv7
+            i = i+1
+            j = j+1
+            q(i) = c(j)
+ 820     continue
+         do 830 k=1,3
+            ii = ii+1
+            i = i+1
+            q(i) = q(ii)
+ 830     continue
+ 840  continue
+ 850  if(iop1.eq.0) go to 870
+      do 860 l=1,nv4
+         i = i+1
+         q(i) = 0.
+ 860  continue
+ 870  do 880 i=1,ncof
+         c(i) = q(i)
+ 880  continue
+c  calculate the quantities
+c    res(i,j) = (z(i,j) - s(u(i),v(j)))**2 , i=1,2,..,mu;j=1,2,..,mv
+c    fp = sumi=1,mu(sumj=1,mv(res(i,j)))
+c    fpu(r) = sum''i(sumj=1,mv(res(i,j))) , r=1,2,...,nu-7
+c                  tu(r+3) <= u(i) <= tu(r+4)
+c    fpv(r) = sumi=1,mu(sum''j(res(i,j))) , r=1,2,...,nv-7
+c                  tv(r+3) <= v(j) <= tv(r+4)
+      fp = 0.
+      do 890 i=1,nu
+        fpu(i) = 0.
+ 890  continue
+      do 900 i=1,nv
+        fpv(i) = 0.
+ 900  continue
+      iz = 0
+      nroldu = 0
+c  main loop for the different grid points.
+      do 950 i1=1,mu
+        numu = nru(i1)
+        numu1 = numu+1
+        nroldv = 0
+        do 940 i2=1,mv
+          numv = nrv(i2)
+          numv1 = numv+1
+          iz = iz+1
+c  evaluate s(u,v) at the current grid point by making the sum of the
+c  cross products of the non-zero b-splines at (u,v), multiplied with
+c  the appropiate b-spline coefficients.
+          term = 0.
+          k1 = numu*nv4+numv
+          do 920 l1=1,4
+            k2 = k1
+            fac = spu(i1,l1)
+            do 910 l2=1,4
+              k2 = k2+1
+              term = term+fac*spv(i2,l2)*c(k2)
+ 910        continue
+            k1 = k1+nv4
+ 920      continue
+c  calculate the squared residual at the current grid point.
+          term = (z(iz)-term)**2
+c  adjust the different parameters.
+          fp = fp+term
+          fpu(numu1) = fpu(numu1)+term
+          fpv(numv1) = fpv(numv1)+term
+          fac = term*half
+          if(numv.eq.nroldv) go to 930
+          fpv(numv1) = fpv(numv1)-fac
+          fpv(numv) = fpv(numv)+fac
+ 930      nroldv = numv
+          if(numu.eq.nroldu) go to 940
+          fpu(numu1) = fpu(numu1)-fac
+          fpu(numu) = fpu(numu)+fac
+ 940    continue
+        nroldu = numu
+ 950  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpgrpa.f
===================================================================
--- branches/Interpolate1D/fitpack/fpgrpa.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpgrpa.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,313 @@
+      subroutine fpgrpa(ifsu,ifsv,ifbu,ifbv,idim,ipar,u,mu,v,mv,z,mz,
+     * tu,nu,tv,nv,p,c,nc,fp,fpu,fpv,mm,mvnu,spu,spv,right,q,au,au1,
+     * av,av1,bu,bv,nru,nrv)
+c  ..
+c  ..scalar arguments..
+      real*8 p,fp
+      integer ifsu,ifsv,ifbu,ifbv,idim,mu,mv,mz,nu,nv,nc,mm,mvnu
+c  ..array arguments..
+      real*8 u(mu),v(mv),z(mz*idim),tu(nu),tv(nv),c(nc*idim),fpu(nu),
+     * fpv(nv),spu(mu,4),spv(mv,4),right(mm*idim),q(mvnu),au(nu,5),
+     * au1(nu,4),av(nv,5),av1(nv,4),bu(nu,5),bv(nv,5)
+      integer ipar(2),nru(mu),nrv(mv)
+c  ..local scalars..
+      real*8 arg,fac,term,one,half,value
+      integer i,id,ii,it,iz,i1,i2,j,jz,k,k1,k2,l,l1,l2,mvv,k0,muu,
+     * ncof,nroldu,nroldv,number,nmd,numu,numu1,numv,numv1,nuu,nvv,
+     * nu4,nu7,nu8,nv4,nv7,nv8
+c  ..local arrays..
+      real*8 h(5)
+c  ..subroutine references..
+c    fpback,fpbspl,fpdisc,fpbacp,fptrnp,fptrpe
+c  ..
+c  let
+c               |   (spu)    |            |   (spv)    |
+c        (au) = | ---------- |     (av) = | ---------- |
+c               | (1/p) (bu) |            | (1/p) (bv) |
+c
+c                                | z  ' 0 |
+c                            q = | ------ |
+c                                | 0  ' 0 |
+c
+c  with c      : the (nu-4) x (nv-4) matrix which contains the b-spline
+c                coefficients.
+c       z      : the mu x mv matrix which contains the function values.
+c       spu,spv: the mu x (nu-4), resp. mv x (nv-4) observation matrices
+c                according to the least-squares problems in the u-,resp.
+c                v-direction.
+c       bu,bv  : the (nu-7) x (nu-4),resp. (nv-7) x (nv-4) matrices
+c                containing the discontinuity jumps of the derivatives
+c                of the b-splines in the u-,resp.v-variable at the knots
+c  the b-spline coefficients of the smoothing spline are then calculated
+c  as the least-squares solution of the following over-determined linear
+c  system of equations
+c
+c    (1)  (av) c (au)' = q
+c
+c  subject to the constraints
+c
+c    (2)  c(nu-3+i,j) = c(i,j), i=1,2,3 ; j=1,2,...,nv-4
+c            if(ipar(1).ne.0)
+c
+c    (3)  c(i,nv-3+j) = c(i,j), j=1,2,3 ; i=1,2,...,nu-4
+c            if(ipar(2).ne.0)
+c
+c  set constants
+      one = 1
+      half = 0.5
+c  initialization
+      nu4 = nu-4
+      nu7 = nu-7
+      nu8 = nu-8
+      nv4 = nv-4
+      nv7 = nv-7
+      nv8 = nv-8
+      muu = mu
+      if(ipar(1).ne.0) muu = mu-1
+      mvv = mv
+      if(ipar(2).ne.0) mvv = mv-1
+c  it depends on the value of the flags ifsu,ifsv,ifbu  and ibvand
+c  on the value of p whether the matrices (spu), (spv), (bu) and (bv)
+c  still must be determined.
+      if(ifsu.ne.0) go to 50
+c  calculate the non-zero elements of the matrix (spu) which is the ob-
+c  servation matrix according to the least-squares spline approximation
+c  problem in the u-direction.
+      l = 4
+      l1 = 5
+      number = 0
+      do 40 it=1,muu
+        arg = u(it)
+  10    if(arg.lt.tu(l1) .or. l.eq.nu4) go to 20
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 10
+  20    call fpbspl(tu,nu,3,arg,l,h)
+        do 30 i=1,4
+          spu(it,i) = h(i)
+  30    continue
+        nru(it) = number
+  40  continue
+      ifsu = 1
+c  calculate the non-zero elements of the matrix (spv) which is the ob-
+c  servation matrix according to the least-squares spline approximation
+c  problem in the v-direction.
+  50  if(ifsv.ne.0) go to 100
+      l = 4
+      l1 = 5
+      number = 0
+      do 90 it=1,mvv
+        arg = v(it)
+  60    if(arg.lt.tv(l1) .or. l.eq.nv4) go to 70
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 60
+  70    call fpbspl(tv,nv,3,arg,l,h)
+        do 80 i=1,4
+          spv(it,i) = h(i)
+  80    continue
+        nrv(it) = number
+  90  continue
+      ifsv = 1
+ 100  if(p.le.0.) go to  150
+c  calculate the non-zero elements of the matrix (bu).
+      if(ifbu.ne.0 .or. nu8.eq.0) go to 110
+      call fpdisc(tu,nu,5,bu,nu)
+      ifbu = 1
+c  calculate the non-zero elements of the matrix (bv).
+ 110  if(ifbv.ne.0 .or. nv8.eq.0) go to 150
+      call fpdisc(tv,nv,5,bv,nv)
+      ifbv = 1
+c  substituting (2)  and (3) into (1), we obtain the overdetermined
+c  system
+c         (4)  (avv) (cr) (auu)' = (qq)
+c  from which the nuu*nvv remaining coefficients
+c         c(i,j) , i=1,...,nu-4-3*ipar(1) ; j=1,...,nv-4-3*ipar(2) ,
+c  the elements of (cr), are then determined in the least-squares sense.
+c  we first determine the matrices (auu) and (qq). then we reduce the
+c  matrix (auu) to upper triangular form (ru) using givens rotations.
+c  we apply the same transformations to the rows of matrix qq to obtain
+c  the (mv) x nuu matrix g.
+c  we store matrix (ru) into au (and au1 if ipar(1)=1) and g into q.
+ 150  if(ipar(1).ne.0) go to 160
+      nuu = nu4
+      call fptrnp(mu,mv,idim,nu,nru,spu,p,bu,z,au,q,right)
+      go to 180
+ 160  nuu = nu7
+      call fptrpe(mu,mv,idim,nu,nru,spu,p,bu,z,au,au1,q,right)
+c  we determine the matrix (avv) and then we reduce this matrix to
+c  upper triangular form (rv) using givens rotations.
+c  we apply the same transformations to the columns of matrix
+c  g to obtain the (nvv) x (nuu) matrix h.
+c  we store matrix (rv) into av (and av1 if ipar(2)=1) and h into c.
+ 180  if(ipar(2).ne.0) go to 190
+      nvv = nv4
+      call fptrnp(mv,nuu,idim,nv,nrv,spv,p,bv,q,av,c,right)
+      go to 200
+ 190  nvv = nv7
+      call fptrpe(mv,nuu,idim,nv,nrv,spv,p,bv,q,av,av1,c,right)
+c  backward substitution to obtain the b-spline coefficients as the
+c  solution of the linear system    (rv) (cr) (ru)' = h.
+c  first step: solve the system  (rv) (c1) = h.
+ 200  ncof = nuu*nvv
+      k = 1
+      if(ipar(2).ne.0) go to 240
+      do 220 ii=1,idim
+      do 220 i=1,nuu
+         call fpback(av,c(k),nvv,5,c(k),nv)
+         k = k+nvv
+ 220  continue
+      go to 300
+ 240  do 260 ii=1,idim
+      do 260 i=1,nuu
+         call fpbacp(av,av1,c(k),nvv,4,c(k),5,nv)
+         k = k+nvv
+ 260  continue
+c  second step: solve the system  (cr) (ru)' = (c1).
+ 300  if(ipar(1).ne.0) go to 400
+      do 360 ii=1,idim
+      k = (ii-1)*ncof
+      do 360 j=1,nvv
+        k = k+1
+        l = k
+        do 320 i=1,nuu
+          right(i) = c(l)
+          l = l+nvv
+ 320    continue
+        call fpback(au,right,nuu,5,right,nu)
+        l = k
+        do 340 i=1,nuu
+           c(l) = right(i)
+           l = l+nvv
+ 340    continue
+ 360  continue
+      go to 500
+ 400  do 460 ii=1,idim
+      k = (ii-1)*ncof
+      do 460 j=1,nvv
+        k = k+1
+        l = k
+        do 420 i=1,nuu
+          right(i) = c(l)
+          l = l+nvv
+ 420    continue
+        call fpbacp(au,au1,right,nuu,4,right,5,nu)
+        l = k
+        do 440 i=1,nuu
+           c(l) = right(i)
+           l = l+nvv
+ 440    continue
+ 460  continue
+c  calculate from the conditions (2)-(3), the remaining b-spline
+c  coefficients.
+ 500  if(ipar(2).eq.0) go to 600
+      i = 0
+      j = 0
+      do 560 id=1,idim
+      do 560 l=1,nuu
+         ii = i
+         do 520 k=1,nvv
+            i = i+1
+            j = j+1
+            q(i) = c(j)
+ 520     continue
+         do 540 k=1,3
+            ii = ii+1
+            i = i+1
+            q(i) = q(ii)
+ 540     continue
+ 560  continue
+      ncof = nv4*nuu
+      nmd = ncof*idim
+      do 580 i=1,nmd
+         c(i) = q(i)
+ 580  continue
+ 600  if(ipar(1).eq.0) go to 700
+      i = 0
+      j = 0
+      n33 = 3*nv4
+      do 660 id=1,idim
+         ii = i
+         do 620 k=1,ncof
+            i = i+1
+            j = j+1
+            q(i) = c(j)
+ 620     continue
+         do 640 k=1,n33
+            ii = ii+1
+            i = i+1
+            q(i) = q(ii)
+ 640     continue
+ 660  continue
+      ncof = nv4*nu4
+      nmd = ncof*idim
+      do 680 i=1,nmd
+         c(i) = q(i)
+ 680  continue
+c  calculate the quantities
+c    res(i,j) = (z(i,j) - s(u(i),v(j)))**2 , i=1,2,..,mu;j=1,2,..,mv
+c    fp = sumi=1,mu(sumj=1,mv(res(i,j)))
+c    fpu(r) = sum''i(sumj=1,mv(res(i,j))) , r=1,2,...,nu-7
+c                  tu(r+3) <= u(i) <= tu(r+4)
+c    fpv(r) = sumi=1,mu(sum''j(res(i,j))) , r=1,2,...,nv-7
+c                  tv(r+3) <= v(j) <= tv(r+4)
+ 700  fp = 0.
+      do 720 i=1,nu
+        fpu(i) = 0.
+ 720  continue
+      do 740 i=1,nv
+        fpv(i) = 0.
+ 740  continue
+      nroldu = 0
+c  main loop for the different grid points.
+      do 860 i1=1,muu
+        numu = nru(i1)
+        numu1 = numu+1
+        nroldv = 0
+        iz = (i1-1)*mv
+        do 840 i2=1,mvv
+          numv = nrv(i2)
+          numv1 = numv+1
+          iz = iz+1
+c  evaluate s(u,v) at the current grid point by making the sum of the
+c  cross products of the non-zero b-splines at (u,v), multiplied with
+c  the appropiate b-spline coefficients.
+          term = 0.
+          k0 = numu*nv4+numv
+          jz = iz
+          do 800 id=1,idim
+          k1 = k0
+          value = 0.
+          do 780 l1=1,4
+            k2 = k1
+            fac = spu(i1,l1)
+            do 760 l2=1,4
+              k2 = k2+1
+              value = value+fac*spv(i2,l2)*c(k2)
+ 760        continue
+            k1 = k1+nv4
+ 780      continue
+c  calculate the squared residual at the current grid point.
+          term = term+(z(jz)-value)**2
+          jz = jz+mz
+          k0 = k0+ncof
+ 800      continue
+c  adjust the different parameters.
+          fp = fp+term
+          fpu(numu1) = fpu(numu1)+term
+          fpv(numv1) = fpv(numv1)+term
+          fac = term*half
+          if(numv.eq.nroldv) go to 820
+          fpv(numv1) = fpv(numv1)-fac
+          fpv(numv) = fpv(numv)+fac
+ 820      nroldv = numv
+          if(numu.eq.nroldu) go to 840
+          fpu(numu1) = fpu(numu1)-fac
+          fpu(numu) = fpu(numu)+fac
+ 840    continue
+        nroldu = numu
+ 860  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpgrre.f
===================================================================
--- branches/Interpolate1D/fitpack/fpgrre.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpgrre.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,328 @@
+      subroutine fpgrre(ifsx,ifsy,ifbx,ifby,x,mx,y,my,z,mz,kx,ky,tx,nx,
+     * ty,ny,p,c,nc,fp,fpx,fpy,mm,mynx,kx1,kx2,ky1,ky2,spx,spy,right,q,
+     * ax,ay,bx,by,nrx,nry)
+c  ..
+c  ..scalar arguments..
+      real*8 p,fp
+      integer ifsx,ifsy,ifbx,ifby,mx,my,mz,kx,ky,nx,ny,nc,mm,mynx,
+     * kx1,kx2,ky1,ky2
+c  ..array arguments..
+      real*8 x(mx),y(my),z(mz),tx(nx),ty(ny),c(nc),spx(mx,kx1),spy(my,ky
+     *1)
+     * ,right(mm),q(mynx),ax(nx,kx2),bx(nx,kx2),ay(ny,ky2),by(ny,ky2),
+     * fpx(nx),fpy(ny)
+      integer nrx(mx),nry(my)
+c  ..local scalars..
+      real*8 arg,cos,fac,pinv,piv,sin,term,one,half
+      integer i,ibandx,ibandy,ic,iq,irot,it,iz,i1,i2,i3,j,k,k1,k2,l,
+     * l1,l2,ncof,nk1x,nk1y,nrold,nroldx,nroldy,number,numx,numx1,
+     * numy,numy1,n1
+c  ..local arrays..
+      real*8 h(7)
+c  ..subroutine references..
+c    fpback,fpbspl,fpgivs,fpdisc,fprota
+c  ..
+c  the b-spline coefficients of the smoothing spline are calculated as
+c  the least-squares solution of the over-determined linear system of
+c  equations  (ay) c (ax)' = q       where
+c
+c               |   (spx)    |            |   (spy)    |
+c        (ax) = | ---------- |     (ay) = | ---------- |
+c               | (1/p) (bx) |            | (1/p) (by) |
+c
+c                                | z  ' 0 |
+c                            q = | ------ |
+c                                | 0  ' 0 |
+c
+c  with c      : the (ny-ky-1) x (nx-kx-1) matrix which contains the
+c                b-spline coefficients.
+c       z      : the my x mx matrix which contains the function values.
+c       spx,spy: the mx x (nx-kx-1) and  my x (ny-ky-1) observation
+c                matrices according to the least-squares problems in
+c                the x- and y-direction.
+c       bx,by  : the (nx-2*kx-1) x (nx-kx-1) and (ny-2*ky-1) x (ny-ky-1)
+c                matrices which contain the discontinuity jumps of the
+c                derivatives of the b-splines in the x- and y-direction.
+      one = 1
+      half = 0.5
+      nk1x = nx-kx1
+      nk1y = ny-ky1
+      if(p.gt.0.) pinv = one/p
+c  it depends on the value of the flags ifsx,ifsy,ifbx and ifby and on
+c  the value of p whether the matrices (spx),(spy),(bx) and (by) still
+c  must be determined.
+      if(ifsx.ne.0) go to 50
+c  calculate the non-zero elements of the matrix (spx) which is the
+c  observation matrix according to the least-squares spline approximat-
+c  ion problem in the x-direction.
+      l = kx1
+      l1 = kx2
+      number = 0
+      do 40 it=1,mx
+        arg = x(it)
+  10    if(arg.lt.tx(l1) .or. l.eq.nk1x) go to 20
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 10
+  20    call fpbspl(tx,nx,kx,arg,l,h)
+        do 30 i=1,kx1
+          spx(it,i) = h(i)
+  30    continue
+        nrx(it) = number
+  40  continue
+      ifsx = 1
+  50  if(ifsy.ne.0) go to 100
+c  calculate the non-zero elements of the matrix (spy) which is the
+c  observation matrix according to the least-squares spline approximat-
+c  ion problem in the y-direction.
+      l = ky1
+      l1 = ky2
+      number = 0
+      do 90 it=1,my
+        arg = y(it)
+  60    if(arg.lt.ty(l1) .or. l.eq.nk1y) go to 70
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 60
+  70    call fpbspl(ty,ny,ky,arg,l,h)
+        do 80 i=1,ky1
+          spy(it,i) = h(i)
+  80    continue
+        nry(it) = number
+  90  continue
+      ifsy = 1
+ 100  if(p.le.0.) go to 120
+c  calculate the non-zero elements of the matrix (bx).
+      if(ifbx.ne.0 .or. nx.eq.2*kx1) go to 110
+      call fpdisc(tx,nx,kx2,bx,nx)
+      ifbx = 1
+c  calculate the non-zero elements of the matrix (by).
+ 110  if(ifby.ne.0 .or. ny.eq.2*ky1) go to 120
+      call fpdisc(ty,ny,ky2,by,ny)
+      ifby = 1
+c  reduce the matrix (ax) to upper triangular form (rx) using givens
+c  rotations. apply the same transformations to the rows of matrix q
+c  to obtain the my x (nx-kx-1) matrix g.
+c  store matrix (rx) into (ax) and g into q.
+ 120  l = my*nk1x
+c  initialization.
+      do 130 i=1,l
+        q(i) = 0.
+ 130  continue
+      do 140 i=1,nk1x
+        do 140 j=1,kx2
+          ax(i,j) = 0.
+ 140  continue
+      l = 0
+      nrold = 0
+c  ibandx denotes the bandwidth of the matrices (ax) and (rx).
+      ibandx = kx1
+      do 270 it=1,mx
+        number = nrx(it)
+ 150    if(nrold.eq.number) go to 180
+        if(p.le.0.) go to 260
+        ibandx = kx2
+c  fetch a new row of matrix (bx).
+        n1 = nrold+1
+        do 160 j=1,kx2
+          h(j) = bx(n1,j)*pinv
+ 160    continue
+c  find the appropriate column of q.
+        do 170 j=1,my
+          right(j) = 0.
+ 170    continue
+        irot = nrold
+        go to 210
+c  fetch a new row of matrix (spx).
+ 180    h(ibandx) = 0.
+        do 190 j=1,kx1
+          h(j) = spx(it,j)
+ 190    continue
+c  find the appropriate column of q.
+        do 200 j=1,my
+          l = l+1
+          right(j) = z(l)
+ 200    continue
+        irot = number
+c  rotate the new row of matrix (ax) into triangle.
+ 210    do 240 i=1,ibandx
+          irot = irot+1
+          piv = h(i)
+          if(piv.eq.0.) go to 240
+c  calculate the parameters of the givens transformation.
+          call fpgivs(piv,ax(irot,1),cos,sin)
+c  apply that transformation to the rows of matrix q.
+          iq = (irot-1)*my
+          do 220 j=1,my
+            iq = iq+1
+            call fprota(cos,sin,right(j),q(iq))
+ 220      continue
+c  apply that transformation to the columns of (ax).
+          if(i.eq.ibandx) go to 250
+          i2 = 1
+          i3 = i+1
+          do 230 j=i3,ibandx
+            i2 = i2+1
+            call fprota(cos,sin,h(j),ax(irot,i2))
+ 230      continue
+ 240    continue
+ 250    if(nrold.eq.number) go to 270
+ 260    nrold = nrold+1
+        go to 150
+ 270  continue
+c  reduce the matrix (ay) to upper triangular form (ry) using givens
+c  rotations. apply the same transformations to the columns of matrix g
+c  to obtain the (ny-ky-1) x (nx-kx-1) matrix h.
+c  store matrix (ry) into (ay) and h into c.
+      ncof = nk1x*nk1y
+c  initialization.
+      do 280 i=1,ncof
+        c(i) = 0.
+ 280  continue
+      do 290 i=1,nk1y
+        do 290 j=1,ky2
+          ay(i,j) = 0.
+ 290  continue
+      nrold = 0
+c  ibandy denotes the bandwidth of the matrices (ay) and (ry).
+      ibandy = ky1
+      do 420 it=1,my
+        number = nry(it)
+ 300    if(nrold.eq.number) go to 330
+        if(p.le.0.) go to 410
+        ibandy = ky2
+c  fetch a new row of matrix (by).
+        n1 = nrold+1
+        do 310 j=1,ky2
+          h(j) = by(n1,j)*pinv
+ 310    continue
+c  find the appropiate row of g.
+        do 320 j=1,nk1x
+          right(j) = 0.
+ 320    continue
+        irot = nrold
+        go to 360
+c  fetch a new row of matrix (spy)
+ 330    h(ibandy) = 0.
+        do 340 j=1,ky1
+          h(j) = spy(it,j)
+ 340    continue
+c  find the appropiate row of g.
+        l = it
+        do 350 j=1,nk1x
+          right(j) = q(l)
+          l = l+my
+ 350    continue
+        irot = number
+c  rotate the new row of matrix (ay) into triangle.
+ 360    do 390 i=1,ibandy
+          irot = irot+1
+          piv = h(i)
+          if(piv.eq.0.) go to 390
+c  calculate the parameters of the givens transformation.
+          call fpgivs(piv,ay(irot,1),cos,sin)
+c  apply that transformation to the colums of matrix g.
+          ic = irot
+          do 370 j=1,nk1x
+            call fprota(cos,sin,right(j),c(ic))
+            ic = ic+nk1y
+ 370      continue
+c  apply that transformation to the columns of matrix (ay).
+          if(i.eq.ibandy) go to 400
+          i2 = 1
+          i3 = i+1
+          do 380 j=i3,ibandy
+            i2 = i2+1
+            call fprota(cos,sin,h(j),ay(irot,i2))
+ 380      continue
+ 390    continue
+ 400    if(nrold.eq.number) go to 420
+ 410    nrold = nrold+1
+        go to 300
+ 420  continue
+c  backward substitution to obtain the b-spline coefficients as the
+c  solution of the linear system    (ry) c (rx)' = h.
+c  first step: solve the system  (ry) (c1) = h.
+      k = 1
+      do 450 i=1,nk1x
+        call fpback(ay,c(k),nk1y,ibandy,c(k),ny)
+        k = k+nk1y
+ 450  continue
+c  second step: solve the system  c (rx)' = (c1).
+      k = 0
+      do 480 j=1,nk1y
+        k = k+1
+        l = k
+        do 460 i=1,nk1x
+          right(i) = c(l)
+          l = l+nk1y
+ 460    continue
+        call fpback(ax,right,nk1x,ibandx,right,nx)
+        l = k
+        do 470 i=1,nk1x
+          c(l) = right(i)
+          l = l+nk1y
+ 470    continue
+ 480  continue
+c  calculate the quantities
+c    res(i,j) = (z(i,j) - s(x(i),y(j)))**2 , i=1,2,..,mx;j=1,2,..,my
+c    fp = sumi=1,mx(sumj=1,my(res(i,j)))
+c    fpx(r) = sum''i(sumj=1,my(res(i,j))) , r=1,2,...,nx-2*kx-1
+c                  tx(r+kx) <= x(i) <= tx(r+kx+1)
+c    fpy(r) = sumi=1,mx(sum''j(res(i,j))) , r=1,2,...,ny-2*ky-1
+c                  ty(r+ky) <= y(j) <= ty(r+ky+1)
+      fp = 0.
+      do 490 i=1,nx
+        fpx(i) = 0.
+ 490  continue
+      do 500 i=1,ny
+        fpy(i) = 0.
+ 500  continue
+      nk1y = ny-ky1
+      iz = 0
+      nroldx = 0
+c  main loop for the different grid points.
+      do 550 i1=1,mx
+        numx = nrx(i1)
+        numx1 = numx+1
+        nroldy = 0
+        do 540 i2=1,my
+          numy = nry(i2)
+          numy1 = numy+1
+          iz = iz+1
+c  evaluate s(x,y) at the current grid point by making the sum of the
+c  cross products of the non-zero b-splines at (x,y), multiplied with
+c  the appropiate b-spline coefficients.
+          term = 0.
+          k1 = numx*nk1y+numy
+          do 520 l1=1,kx1
+            k2 = k1
+            fac = spx(i1,l1)
+            do 510 l2=1,ky1
+              k2 = k2+1
+              term = term+fac*spy(i2,l2)*c(k2)
+ 510        continue
+            k1 = k1+nk1y
+ 520      continue
+c  calculate the squared residual at the current grid point.
+          term = (z(iz)-term)**2
+c  adjust the different parameters.
+          fp = fp+term
+          fpx(numx1) = fpx(numx1)+term
+          fpy(numy1) = fpy(numy1)+term
+          fac = term*half
+          if(numy.eq.nroldy) go to 530
+          fpy(numy1) = fpy(numy1)-fac
+          fpy(numy) = fpy(numy)+fac
+ 530      nroldy = numy
+          if(numx.eq.nroldx) go to 540
+          fpx(numx1) = fpx(numx1)-fac
+          fpx(numx) = fpx(numx)+fac
+ 540    continue
+        nroldx = numx
+ 550  continue
+      return
+      end
+

Added: branches/Interpolate1D/fitpack/fpgrsp.f
===================================================================
--- branches/Interpolate1D/fitpack/fpgrsp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpgrsp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,656 @@
+      subroutine fpgrsp(ifsu,ifsv,ifbu,ifbv,iback,u,mu,v,mv,r,mr,dr,
+     * iop0,iop1,tu,nu,tv,nv,p,c,nc,sq,fp,fpu,fpv,mm,mvnu,spu,spv,
+     * right,q,au,av1,av2,bu,bv,a0,a1,b0,b1,c0,c1,cosi,nru,nrv)
+c  ..
+c  ..scalar arguments..
+      real*8 p,sq,fp
+      integer ifsu,ifsv,ifbu,ifbv,iback,mu,mv,mr,iop0,iop1,nu,nv,nc,
+     * mm,mvnu
+c  ..array arguments..
+      real*8 u(mu),v(mv),r(mr),dr(6),tu(nu),tv(nv),c(nc),fpu(nu),fpv(nv)
+     *,
+     * spu(mu,4),spv(mv,4),right(mm),q(mvnu),au(nu,5),av1(nv,6),c0(nv),
+     * av2(nv,4),a0(2,mv),b0(2,nv),cosi(2,nv),bu(nu,5),bv(nv,5),c1(nv),
+     * a1(2,mv),b1(2,nv)
+      integer nru(mu),nrv(mv)
+c  ..local scalars..
+      real*8 arg,co,dr01,dr02,dr03,dr11,dr12,dr13,fac,fac0,fac1,pinv,piv
+     *,
+     * si,term,one,three,half
+      integer i,ic,ii,ij,ik,iq,irot,it,ir,i0,i1,i2,i3,j,jj,jk,jper,
+     * j0,j1,k,k1,k2,l,l0,l1,l2,mvv,ncof,nrold,nroldu,nroldv,number,
+     * numu,numu1,numv,numv1,nuu,nu4,nu7,nu8,nu9,nv11,nv4,nv7,nv8,n1
+c  ..local arrays..
+      real*8 h(5),h1(5),h2(4)
+c  ..function references..
+      integer min0
+      real*8 cos,sin
+c  ..subroutine references..
+c    fpback,fpbspl,fpgivs,fpcyt1,fpcyt2,fpdisc,fpbacp,fprota
+c  ..
+c  let
+c               |     (spu)      |            |     (spv)      |
+c        (au) = | -------------- |     (av) = | -------------- |
+c               | sqrt(1/p) (bu) |            | sqrt(1/p) (bv) |
+c
+c                                | r  ' 0 |
+c                            q = | ------ |
+c                                | 0  ' 0 |
+c
+c  with c      : the (nu-4) x (nv-4) matrix which contains the b-spline
+c                coefficients.
+c       r      : the mu x mv matrix which contains the function values.
+c       spu,spv: the mu x (nu-4), resp. mv x (nv-4) observation matrices
+c                according to the least-squares problems in the u-,resp.
+c                v-direction.
+c       bu,bv  : the (nu-7) x (nu-4),resp. (nv-7) x (nv-4) matrices
+c                containing the discontinuity jumps of the derivatives
+c                of the b-splines in the u-,resp.v-variable at the knots
+c  the b-spline coefficients of the smoothing spline are then calculated
+c  as the least-squares solution of the following over-determined linear
+c  system of equations
+c
+c  (1)  (av) c (au)' = q
+c
+c  subject to the constraints
+c
+c  (2)  c(i,nv-3+j) = c(i,j), j=1,2,3 ; i=1,2,...,nu-4
+c
+c  (3)  if iop0 = 0  c(1,j) = dr(1)
+c          iop0 = 1  c(1,j) = dr(1)
+c                    c(2,j) = dr(1)+(dr(2)*cosi(1,j)+dr(3)*cosi(2,j))*
+c                            tu(5)/3. = c0(j) , j=1,2,...nv-4
+c
+c  (4)  if iop1 = 0  c(nu-4,j) = dr(4)
+c          iop1 = 1  c(nu-4,j) = dr(4)
+c                    c(nu-5,j) = dr(4)+(dr(5)*cosi(1,j)+dr(6)*cosi(2,j))
+c                                *(tu(nu-4)-tu(nu-3))/3. = c1(j)
+c
+c  set constants
+      one = 1
+      three = 3
+      half = 0.5
+c  initialization
+      nu4 = nu-4
+      nu7 = nu-7
+      nu8 = nu-8
+      nu9 = nu-9
+      nv4 = nv-4
+      nv7 = nv-7
+      nv8 = nv-8
+      nv11 = nv-11
+      nuu = nu4-iop0-iop1-2
+      if(p.gt.0.) pinv = one/p
+c  it depends on the value of the flags ifsu,ifsv,ifbu,ifbv,iop0,iop1
+c  and on the value of p whether the matrices (spu), (spv), (bu), (bv),
+c  (cosi) still must be determined.
+      if(ifsu.ne.0) go to 30
+c  calculate the non-zero elements of the matrix (spu) which is the ob-
+c  servation matrix according to the least-squares spline approximation
+c  problem in the u-direction.
+      l = 4
+      l1 = 5
+      number = 0
+      do 25 it=1,mu
+        arg = u(it)
+  10    if(arg.lt.tu(l1) .or. l.eq.nu4) go to 15
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 10
+  15    call fpbspl(tu,nu,3,arg,l,h)
+        do 20 i=1,4
+          spu(it,i) = h(i)
+  20    continue
+        nru(it) = number
+  25  continue
+      ifsu = 1
+c  calculate the non-zero elements of the matrix (spv) which is the ob-
+c  servation matrix according to the least-squares spline approximation
+c  problem in the v-direction.
+  30  if(ifsv.ne.0) go to 85
+      l = 4
+      l1 = 5
+      number = 0
+      do 50 it=1,mv
+        arg = v(it)
+  35    if(arg.lt.tv(l1) .or. l.eq.nv4) go to 40
+        l = l1
+        l1 = l+1
+        number = number+1
+        go to 35
+  40    call fpbspl(tv,nv,3,arg,l,h)
+        do 45 i=1,4
+          spv(it,i) = h(i)
+  45    continue
+        nrv(it) = number
+  50  continue
+      ifsv = 1
+      if(iop0.eq.0 .and. iop1.eq.0) go to 85
+c  calculate the coefficients of the interpolating splines for cos(v)
+c  and sin(v).
+      do 55 i=1,nv4
+         cosi(1,i) = 0.
+         cosi(2,i) = 0.
+  55  continue
+      if(nv7.lt.4) go to 85
+      do 65 i=1,nv7
+         l = i+3
+         arg = tv(l)
+         call fpbspl(tv,nv,3,arg,l,h)
+         do 60 j=1,3
+            av1(i,j) = h(j)
+  60     continue
+         cosi(1,i) = cos(arg)
+         cosi(2,i) = sin(arg)
+  65  continue
+      call fpcyt1(av1,nv7,nv)
+      do 80 j=1,2
+         do 70 i=1,nv7
+            right(i) = cosi(j,i)
+  70     continue
+         call fpcyt2(av1,nv7,right,right,nv)
+         do 75 i=1,nv7
+            cosi(j,i+1) = right(i)
+  75     continue
+         cosi(j,1) = cosi(j,nv7+1)
+         cosi(j,nv7+2) = cosi(j,2)
+         cosi(j,nv4) = cosi(j,3)
+  80  continue
+  85  if(p.le.0.) go to  150
+c  calculate the non-zero elements of the matrix (bu).
+      if(ifbu.ne.0 .or. nu8.eq.0) go to 90
+      call fpdisc(tu,nu,5,bu,nu)
+      ifbu = 1
+c  calculate the non-zero elements of the matrix (bv).
+  90  if(ifbv.ne.0 .or. nv8.eq.0) go to 150
+      call fpdisc(tv,nv,5,bv,nv)
+      ifbv = 1
+c  substituting (2),(3) and (4) into (1), we obtain the overdetermined
+c  system
+c         (5)  (avv) (cc) (auu)' = (qq)
+c  from which the nuu*nv7 remaining coefficients
+c         c(i,j) , i=2+iop0,3+iop0,...,nu-5-iop1,j=1,2,...,nv-7.
+c  the elements of (cc), are then determined in the least-squares sense.
+c  simultaneously, we compute the resulting sum of squared residuals sq.
+ 150  dr01 = dr(1)
+      dr11 = dr(4)
+      do 155 i=1,mv
+         a0(1,i) = dr01
+         a1(1,i) = dr11
+ 155  continue
+      if(nv8.eq.0 .or. p.le.0.) go to 165
+      do 160 i=1,nv8
+         b0(1,i) = 0.
+         b1(1,i) = 0.
+ 160  continue
+ 165  mvv = mv
+      if(iop0.eq.0) go to 195
+      fac = (tu(5)-tu(4))/three
+      dr02 = dr(2)*fac
+      dr03 = dr(3)*fac
+      do 170 i=1,nv4
+         c0(i) = dr01+dr02*cosi(1,i)+dr03*cosi(2,i)
+ 170  continue
+      do 180 i=1,mv
+         number = nrv(i)
+         fac = 0.
+         do 175 j=1,4
+            number = number+1
+            fac = fac+c0(number)*spv(i,j)
+ 175     continue
+         a0(2,i) = fac
+ 180  continue
+      if(nv8.eq.0 .or. p.le.0.) go to 195
+      do 190 i=1,nv8
+         number = i
+         fac = 0.
+         do 185 j=1,5
+            fac = fac+c0(number)*bv(i,j)
+            number = number+1
+ 185     continue
+         b0(2,i) = fac*pinv
+ 190  continue
+      mvv = mv+nv8
+ 195  if(iop1.eq.0) go to 225
+      fac = (tu(nu4)-tu(nu4+1))/three
+      dr12 = dr(5)*fac
+      dr13 = dr(6)*fac
+      do 200 i=1,nv4
+         c1(i) = dr11+dr12*cosi(1,i)+dr13*cosi(2,i)
+ 200  continue
+      do 210 i=1,mv
+         number = nrv(i)
+         fac = 0.
+         do 205 j=1,4
+            number = number+1
+            fac = fac+c1(number)*spv(i,j)
+ 205     continue
+         a1(2,i) = fac
+ 210  continue
+      if(nv8.eq.0 .or. p.le.0.) go to 225
+      do 220 i=1,nv8
+         number = i
+         fac = 0.
+         do 215 j=1,5
+            fac = fac+c1(number)*bv(i,j)
+            number = number+1
+ 215     continue
+         b1(2,i) = fac*pinv
+ 220  continue
+      mvv = mv+nv8
+c  we first determine the matrices (auu) and (qq). then we reduce the
+c  matrix (auu) to an unit upper triangular form (ru) using givens
+c  rotations without square roots. we apply the same transformations to
+c  the rows of matrix qq to obtain the mv x nuu matrix g.
+c  we store matrix (ru) into au and g into q.
+ 225  l = mvv*nuu
+c  initialization.
+      sq = 0.
+      if(l.eq.0) go to 245
+      do 230 i=1,l
+        q(i) = 0.
+ 230  continue
+      do 240 i=1,nuu
+        do 240 j=1,5
+          au(i,j) = 0.
+ 240  continue
+      l = 0
+ 245  nrold = 0
+      n1 = nrold+1
+      do 420 it=1,mu
+        number = nru(it)
+c  find the appropriate column of q.
+ 250    do 260 j=1,mvv
+           right(j) = 0.
+ 260    continue
+        if(nrold.eq.number) go to 280
+        if(p.le.0.) go to 410
+c  fetch a new row of matrix (bu).
+        do 270 j=1,5
+          h(j) = bu(n1,j)*pinv
+ 270    continue
+        i0 = 1
+        i1 = 5
+        go to 310
+c  fetch a new row of matrix (spu).
+ 280    do 290 j=1,4
+          h(j) = spu(it,j)
+ 290    continue
+c  find the appropriate column of q.
+        do 300 j=1,mv
+          l = l+1
+          right(j) = r(l)
+ 300    continue
+        i0 = 1
+        i1 = 4
+ 310    j0 = n1
+        j1 = nu7-number
+c  take into account that we eliminate the constraints (3)
+ 315     if(j0-1.gt.iop0) go to 335
+         fac0 = h(i0)
+         do 320 j=1,mv
+            right(j) = right(j)-fac0*a0(j0,j)
+ 320     continue
+         if(mv.eq.mvv) go to 330
+         j = mv
+         do 325 jj=1,nv8
+            j = j+1
+            right(j) = right(j)-fac0*b0(j0,jj)
+ 325     continue
+ 330     j0 = j0+1
+         i0 = i0+1
+         go to 315
+c  take into account that we eliminate the constraints (4)
+ 335     if(j1-1.gt.iop1) go to 360
+         fac1 = h(i1)
+         do 340 j=1,mv
+            right(j) = right(j)-fac1*a1(j1,j)
+ 340     continue
+         if(mv.eq.mvv) go to 350
+         j = mv
+         do 345 jj=1,nv8
+            j = j+1
+            right(j) = right(j)-fac1*b1(j1,jj)
+ 345     continue
+ 350     j1 = j1+1
+         i1 = i1-1
+         go to 335
+ 360     irot = nrold-iop0-1
+         if(irot.lt.0) irot = 0
+c  rotate the new row of matrix (auu) into triangle.
+        if(i0.gt.i1) go to 390
+        do 385 i=i0,i1
+          irot = irot+1
+          piv = h(i)
+          if(piv.eq.0.) go to 385
+c  calculate the parameters of the givens transformation.
+          call fpgivs(piv,au(irot,1),co,si)
+c  apply that transformation to the rows of matrix (qq).
+          iq = (irot-1)*mvv
+          do 370 j=1,mvv
+            iq = iq+1
+            call fprota(co,si,right(j),q(iq))
+ 370      continue
+c  apply that transformation to the columns of (auu).
+          if(i.eq.i1) go to 385
+          i2 = 1
+          i3 = i+1
+          do 380 j=i3,i1
+            i2 = i2+1
+            call fprota(co,si,h(j),au(irot,i2))
+ 380      continue
+ 385    continue
+c  we update the sum of squared residuals.
+ 390    do 395 j=1,mvv
+          sq = sq+right(j)**2
+ 395    continue
+ 400    if(nrold.eq.number) go to 420
+ 410    nrold = n1
+        n1 = n1+1
+        go to 250
+ 420  continue
+      if(nuu.eq.0) go to 800
+c  we determine the matrix (avv) and then we reduce her to an unit
+c  upper triangular form (rv) using givens rotations without square
+c  roots. we apply the same transformations to the columns of matrix
+c  g to obtain the (nv-7) x (nu-6-iop0-iop1) matrix h.
+c  we store matrix (rv) into av1 and av2, h into c.
+c  the nv7 x nv7 triangular unit upper matrix (rv) has the form
+c              | av1 '     |
+c       (rv) = |     ' av2 |
+c              |  0  '     |
+c  with (av2) a nv7 x 4 matrix and (av1) a nv11 x nv11 unit upper
+c  triangular matrix of bandwidth 5.
+      ncof = nuu*nv7
+c  initialization.
+      do 430 i=1,ncof
+        c(i) = 0.
+ 430  continue
+      do 440 i=1,nv4
+        av1(i,5) = 0.
+        do 440 j=1,4
+          av1(i,j) = 0.
+          av2(i,j) = 0.
+ 440  continue
+      jper = 0
+      nrold = 0
+      do 770 it=1,mv
+        number = nrv(it)
+ 450    if(nrold.eq.number) go to 480
+        if(p.le.0.) go to 760
+c  fetch a new row of matrix (bv).
+        n1 = nrold+1
+        do 460 j=1,5
+          h(j) = bv(n1,j)*pinv
+ 460    continue
+c  find the appropiate row of g.
+        do 465 j=1,nuu
+          right(j) = 0.
+ 465    continue
+        if(mv.eq.mvv) go to 510
+        l = mv+n1
+        do 470 j=1,nuu
+          right(j) = q(l)
+          l = l+mvv
+ 470    continue
+        go to 510
+c  fetch a new row of matrix (spv)
+ 480    h(5) = 0.
+        do 490 j=1,4
+          h(j) = spv(it,j)
+ 490    continue
+c  find the appropiate row of g.
+        l = it
+        do 500 j=1,nuu
+          right(j) = q(l)
+          l = l+mvv
+ 500    continue
+c  test whether there are non-zero values in the new row of (avv)
+c  corresponding to the b-splines n(j;v),j=nv7+1,...,nv4.
+ 510     if(nrold.lt.nv11) go to 710
+         if(jper.ne.0) go to 550
+c  initialize the matrix (av2).
+         jk = nv11+1
+         do 540 i=1,4
+            ik = jk
+            do 520 j=1,5
+               if(ik.le.0) go to 530
+               av2(ik,i) = av1(ik,j)
+               ik = ik-1
+ 520        continue
+ 530        jk = jk+1
+ 540     continue
+         jper = 1
+c  if one of the non-zero elements of the new row corresponds to one of
+c  the b-splines n(j;v),j=nv7+1,...,nv4, we take account of condition
+c  (2) for setting up this row of (avv). the row is stored in h1( the
+c  part with respect to av1) and h2 (the part with respect to av2).
+ 550     do 560 i=1,4
+            h1(i) = 0.
+            h2(i) = 0.
+ 560     continue
+         h1(5) = 0.
+         j = nrold-nv11
+         do 600 i=1,5
+            j = j+1
+            l0 = j
+ 570        l1 = l0-4
+            if(l1.le.0) go to 590
+            if(l1.le.nv11) go to 580
+            l0 = l1-nv11
+            go to 570
+ 580        h1(l1) = h(i)
+            go to 600
+ 590        h2(l0) = h2(l0) + h(i)
+ 600     continue
+c  rotate the new row of (avv) into triangle.
+         if(nv11.le.0) go to 670
+c  rotations with the rows 1,2,...,nv11 of (avv).
+         do 660 j=1,nv11
+            piv = h1(1)
+            i2 = min0(nv11-j,4)
+            if(piv.eq.0.) go to 640
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,av1(j,1),co,si)
+c  apply that transformation to the columns of matrix g.
+            ic = j
+            do 610 i=1,nuu
+               call fprota(co,si,right(i),c(ic))
+               ic = ic+nv7
+ 610        continue
+c  apply that transformation to the rows of (avv) with respect to av2.
+            do 620 i=1,4
+               call fprota(co,si,h2(i),av2(j,i))
+ 620        continue
+c  apply that transformation to the rows of (avv) with respect to av1.
+            if(i2.eq.0) go to 670
+            do 630 i=1,i2
+               i1 = i+1
+               call fprota(co,si,h1(i1),av1(j,i1))
+ 630        continue
+ 640        do 650 i=1,i2
+               h1(i) = h1(i+1)
+ 650        continue
+            h1(i2+1) = 0.
+ 660     continue
+c  rotations with the rows nv11+1,...,nv7 of avv.
+ 670     do 700 j=1,4
+            ij = nv11+j
+            if(ij.le.0) go to 700
+            piv = h2(j)
+            if(piv.eq.0.) go to 700
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,av2(ij,j),co,si)
+c  apply that transformation to the columns of matrix g.
+            ic = ij
+            do 680 i=1,nuu
+               call fprota(co,si,right(i),c(ic))
+               ic = ic+nv7
+ 680        continue
+            if(j.eq.4) go to 700
+c  apply that transformation to the rows of (avv) with respect to av2.
+            j1 = j+1
+            do 690 i=j1,4
+               call fprota(co,si,h2(i),av2(ij,i))
+ 690        continue
+ 700     continue
+c  we update the sum of squared residuals.
+         do 705 i=1,nuu
+           sq = sq+right(i)**2
+ 705     continue
+         go to 750
+c  rotation into triangle of the new row of (avv), in case the elements
+c  corresponding to the b-splines n(j;v),j=nv7+1,...,nv4 are all zero.
+ 710     irot =nrold
+         do 740 i=1,5
+            irot = irot+1
+            piv = h(i)
+            if(piv.eq.0.) go to 740
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,av1(irot,1),co,si)
+c  apply that transformation to the columns of matrix g.
+            ic = irot
+            do 720 j=1,nuu
+               call fprota(co,si,right(j),c(ic))
+               ic = ic+nv7
+ 720        continue
+c  apply that transformation to the rows of (avv).
+            if(i.eq.5) go to 740
+            i2 = 1
+            i3 = i+1
+            do 730 j=i3,5
+               i2 = i2+1
+               call fprota(co,si,h(j),av1(irot,i2))
+ 730        continue
+ 740     continue
+c  we update the sum of squared residuals.
+         do 745 i=1,nuu
+           sq = sq+right(i)**2
+ 745     continue
+ 750     if(nrold.eq.number) go to 770
+ 760     nrold = nrold+1
+         go to 450
+ 770  continue
+c  test whether the b-spline coefficients must be determined.
+      if(iback.ne.0) return
+c  backward substitution to obtain the b-spline coefficients as the
+c  solution of the linear system    (rv) (cr) (ru)' = h.
+c  first step: solve the system  (rv) (c1) = h.
+      k = 1
+      do 780 i=1,nuu
+         call fpbacp(av1,av2,c(k),nv7,4,c(k),5,nv)
+         k = k+nv7
+ 780  continue
+c  second step: solve the system  (cr) (ru)' = (c1).
+      k = 0
+      do 795 j=1,nv7
+        k = k+1
+        l = k
+        do 785 i=1,nuu
+          right(i) = c(l)
+          l = l+nv7
+ 785    continue
+        call fpback(au,right,nuu,5,right,nu)
+        l = k
+        do 790 i=1,nuu
+           c(l) = right(i)
+           l = l+nv7
+ 790    continue
+ 795  continue
+c  calculate from the conditions (2)-(3)-(4), the remaining b-spline
+c  coefficients.
+ 800  ncof = nu4*nv4
+      j = ncof
+      do 805 l=1,nv4
+         q(l) = dr01
+         q(j) = dr11
+         j = j-1
+ 805  continue
+      i = nv4
+      j = 0
+      if(iop0.eq.0) go to 815
+      do 810 l=1,nv4
+         i = i+1
+         q(i) = c0(l)
+ 810  continue
+ 815  if(nuu.eq.0) go to 835
+      do 830 l=1,nuu
+         ii = i
+         do 820 k=1,nv7
+            i = i+1
+            j = j+1
+            q(i) = c(j)
+ 820     continue
+         do 825 k=1,3
+            ii = ii+1
+            i = i+1
+            q(i) = q(ii)
+ 825     continue
+ 830  continue
+ 835  if(iop1.eq.0) go to 845
+      do 840 l=1,nv4
+         i = i+1
+         q(i) = c1(l)
+ 840  continue
+ 845  do 850 i=1,ncof
+         c(i) = q(i)
+ 850  continue
+c  calculate the quantities
+c    res(i,j) = (r(i,j) - s(u(i),v(j)))**2 , i=1,2,..,mu;j=1,2,..,mv
+c    fp = sumi=1,mu(sumj=1,mv(res(i,j)))
+c    fpu(r) = sum''i(sumj=1,mv(res(i,j))) , r=1,2,...,nu-7
+c                  tu(r+3) <= u(i) <= tu(r+4)
+c    fpv(r) = sumi=1,mu(sum''j(res(i,j))) , r=1,2,...,nv-7
+c                  tv(r+3) <= v(j) <= tv(r+4)
+      fp = 0.
+      do 890 i=1,nu
+        fpu(i) = 0.
+ 890  continue
+      do 900 i=1,nv
+        fpv(i) = 0.
+ 900  continue
+      ir = 0
+      nroldu = 0
+c  main loop for the different grid points.
+      do 950 i1=1,mu
+        numu = nru(i1)
+        numu1 = numu+1
+        nroldv = 0
+        do 940 i2=1,mv
+          numv = nrv(i2)
+          numv1 = numv+1
+          ir = ir+1
+c  evaluate s(u,v) at the current grid point by making the sum of the
+c  cross products of the non-zero b-splines at (u,v), multiplied with
+c  the appropiate b-spline coefficients.
+          term = 0.
+          k1 = numu*nv4+numv
+          do 920 l1=1,4
+            k2 = k1
+            fac = spu(i1,l1)
+            do 910 l2=1,4
+              k2 = k2+1
+              term = term+fac*spv(i2,l2)*c(k2)
+ 910        continue
+            k1 = k1+nv4
+ 920      continue
+c  calculate the squared residual at the current grid point.
+          term = (r(ir)-term)**2
+c  adjust the different parameters.
+          fp = fp+term
+          fpu(numu1) = fpu(numu1)+term
+          fpv(numv1) = fpv(numv1)+term
+          fac = term*half
+          if(numv.eq.nroldv) go to 930
+          fpv(numv1) = fpv(numv1)-fac
+          fpv(numv) = fpv(numv)+fac
+ 930      nroldv = numv
+          if(numu.eq.nroldu) go to 940
+          fpu(numu1) = fpu(numu1)-fac
+          fpu(numu) = fpu(numu)+fac
+ 940    continue
+        nroldu = numu
+ 950  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpinst.f
===================================================================
--- branches/Interpolate1D/fitpack/fpinst.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpinst.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,77 @@
+      subroutine fpinst(iopt,t,n,c,k,x,l,tt,nn,cc,nest)
+c  given the b-spline representation (knots t(j),j=1,2,...,n, b-spline
+c  coefficients c(j),j=1,2,...,n-k-1) of a spline of degree k, fpinst
+c  calculates the b-spline representation (knots tt(j),j=1,2,...,nn,
+c  b-spline coefficients cc(j),j=1,2,...,nn-k-1) of the same spline if
+c  an additional knot is inserted at the point x situated in the inter-
+c  val t(l)<=x<t(l+1). iopt denotes whether (iopt.ne.0) or not (iopt=0)
+c  the given spline is periodic. in case of a periodic spline at least
+c  one of the following conditions must be fulfilled: l>2*k or l<n-2*k.
+c
+c  ..scalar arguments..
+      integer k,n,l,nn,iopt,nest
+      real*8 x
+c  ..array arguments..
+      real*8 t(nest),c(nest),tt(nest),cc(nest)
+c  ..local scalars..
+      real*8 fac,per,one
+      integer i,i1,j,k1,m,mk,nk,nk1,nl,ll
+c  ..
+      one = 0.1e+01
+      k1 = k+1
+      nk1 = n-k1
+c  the new knots
+      ll = l+1
+      i = n
+      do 10 j=ll,n
+         tt(i+1) = t(i)
+         i = i-1
+  10  continue
+      tt(ll) = x
+      do 20 j=1,l
+         tt(j) = t(j)
+  20  continue
+c  the new b-spline coefficients
+      i = nk1
+      do 30 j=l,nk1
+         cc(i+1) = c(i)
+         i = i-1
+  30  continue
+      i = l
+      do 40 j=1,k
+         m = i+k1
+         fac = (x-tt(i))/(tt(m)-tt(i))
+         i1 = i-1
+         cc(i) = fac*c(i)+(one-fac)*c(i1)
+         i = i1
+  40  continue
+      do 50 j=1,i
+         cc(j) = c(j)
+  50  continue
+      nn = n+1
+      if(iopt.eq.0) return
+c   incorporate the boundary conditions for a periodic spline.
+      nk = nn-k
+      nl = nk-k1
+      per = tt(nk)-tt(k1)
+      i = k1
+      j = nk
+      if(ll.le.nl) go to 70
+      do 60 m=1,k
+         mk = m+nl
+         cc(m) = cc(mk)
+         i = i-1
+         j = j-1
+         tt(i) = tt(j)-per
+  60  continue
+      return
+  70  if(ll.gt.(k1+k)) return
+      do 80 m=1,k
+         mk = m+nl
+         cc(mk) = cc(m)
+         i = i+1
+         j = j+1
+         tt(j) = tt(i)+per
+  80  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpintb.f
===================================================================
--- branches/Interpolate1D/fitpack/fpintb.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpintb.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,129 @@
+      subroutine fpintb(t,n,bint,nk1,x,y)
+c  subroutine fpintb calculates integrals of the normalized b-splines
+c  nj,k+1(x) of degree k, defined on the set of knots t(j),j=1,2,...n.
+c  it makes use of the formulae of gaffney for the calculation of
+c  indefinite integrals of b-splines.
+c
+c  calling sequence:
+c     call fpintb(t,n,bint,nk1,x,y)
+c
+c  input parameters:
+c    t    : real array,length n, containing the position of the knots.
+c    n    : integer value, giving the number of knots.
+c    nk1  : integer value, giving the number of b-splines of degree k,
+c           defined on the set of knots ,i.e. nk1 = n-k-1.
+c    x,y  : real values, containing the end points of the integration
+c           interval.
+c  output parameter:
+c    bint : array,length nk1, containing the integrals of the b-splines.
+c  ..
+c  ..scalars arguments..
+      integer n,nk1
+      real*8 x,y
+c  ..array arguments..
+      real*8 t(n),bint(nk1)
+c  ..local scalars..
+      integer i,ia,ib,it,j,j1,k,k1,l,li,lj,lk,l0,min
+      real*8 a,ak,arg,b,f,one
+c  ..local arrays..
+      real*8 aint(6),h(6),h1(6)
+c  initialization.
+      one = 0.1d+01
+      k1 = n-nk1
+      ak = k1
+      k = k1-1
+      do 10 i=1,nk1
+        bint(i) = 0.0d0
+  10  continue
+c  the integration limits are arranged in increasing order.
+      a = x
+      b = y
+      min = 0
+      if (a.lt.b) go to 30
+      if (a.eq.b) go to 160
+      go to 20
+  20  a = y
+      b = x
+      min = 1
+  30  if(a.lt.t(k1)) a = t(k1)
+      if(b.gt.t(nk1+1)) b = t(nk1+1)
+c  using the expression of gaffney for the indefinite integral of a
+c  b-spline we find that
+c  bint(j) = (t(j+k+1)-t(j))*(res(j,b)-res(j,a))/(k+1)
+c    where for t(l) <= x < t(l+1)
+c    res(j,x) = 0, j=1,2,...,l-k-1
+c             = 1, j=l+1,l+2,...,nk1
+c             = aint(j+k-l+1), j=l-k,l-k+1,...,l
+c               = sumi((x-t(j+i))*nj+i,k+1-i(x)/(t(j+k+1)-t(j+i)))
+c                 i=0,1,...,k
+      l = k1
+      l0 = l+1
+c  set arg = a.
+      arg = a
+      do 90 it=1,2
+c  search for the knot interval t(l) <= arg < t(l+1).
+  40    if(arg.lt.t(l0) .or. l.eq.nk1) go to 50
+        l = l0
+        l0 = l+1
+        go to 40
+c  calculation of aint(j), j=1,2,...,k+1.
+c  initialization.
+  50    do 55 j=1,k1
+          aint(j) = 0.0d0
+  55    continue
+        aint(1) = (arg-t(l))/(t(l+1)-t(l))
+        h1(1) = one
+        do 70 j=1,k
+c  evaluation of the non-zero b-splines of degree j at arg,i.e.
+c    h(i+1) = nl-j+i,j(arg), i=0,1,...,j.
+          h(1) = 0.0d0
+          do 60 i=1,j
+            li = l+i
+            lj = li-j
+            f = h1(i)/(t(li)-t(lj))
+            h(i) = h(i)+f*(t(li)-arg)
+            h(i+1) = f*(arg-t(lj))
+  60      continue
+c  updating of the integrals aint.
+          j1 = j+1
+          do 70 i=1,j1
+            li = l+i
+            lj = li-j1
+            aint(i) = aint(i)+h(i)*(arg-t(lj))/(t(li)-t(lj))
+            h1(i) = h(i)
+  70    continue
+        if(it.eq.2) go to 100
+c  updating of the integrals bint
+        lk = l-k
+        ia = lk
+        do 80 i=1,k1
+          bint(lk) = -aint(i)
+          lk = lk+1
+  80    continue
+c  set arg = b.
+        arg = b
+  90  continue
+c  updating of the integrals bint.
+ 100  lk = l-k
+      ib = lk-1
+      do 110 i=1,k1
+        bint(lk) = bint(lk)+aint(i)
+        lk = lk+1
+ 110  continue
+      if(ib.lt.ia) go to 130
+      do 120 i=ia,ib
+        bint(i) = bint(i)+one
+ 120  continue
+c  the scaling factors are taken into account.
+ 130  f = one/ak
+      do 140 i=1,nk1
+        j = i+k1
+        bint(i) = bint(i)*(t(j)-t(i))*f
+ 140  continue
+c  the order of the integration limits is taken into account.
+      if(min.eq.0) go to 160
+      do 150 i=1,nk1
+        bint(i) = -bint(i)
+ 150  continue
+ 160  return
+      end

Added: branches/Interpolate1D/fitpack/fpknot.f
===================================================================
--- branches/Interpolate1D/fitpack/fpknot.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpknot.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,64 @@
+      subroutine fpknot(x,m,t,n,fpint,nrdata,nrint,nest,istart)
+c  subroutine fpknot locates an additional knot for a spline of degree
+c  k and adjusts the corresponding parameters,i.e.
+c    t     : the position of the knots.
+c    n     : the number of knots.
+c    nrint : the number of knotintervals.
+c    fpint : the sum of squares of residual right hand sides
+c            for each knot interval.
+c    nrdata: the number of data points inside each knot interval.
+c  istart indicates that the smallest data point at which the new knot
+c  may be added is x(istart+1)
+c  ..
+c  ..scalar arguments..
+      integer m,n,nrint,nest,istart
+c  ..array arguments..
+      real*8 x(m),t(nest),fpint(nest)
+      integer nrdata(nest)
+c  ..local scalars..
+      real*8 an,am,fpmax
+      integer ihalf,j,jbegin,jj,jk,jpoint,k,maxbeg,maxpt,
+     * next,nrx,number
+c  ..
+      k = (n-nrint-1)/2
+c  search for knot interval t(number+k) <= x <= t(number+k+1) where
+c  fpint(number) is maximal on the condition that nrdata(number)
+c  not equals zero.
+      fpmax = 0.
+      jbegin = istart
+      do 20 j=1,nrint
+        jpoint = nrdata(j)
+        if(fpmax.ge.fpint(j) .or. jpoint.eq.0) go to 10
+        fpmax = fpint(j)
+        number = j
+        maxpt = jpoint
+        maxbeg = jbegin
+  10    jbegin = jbegin+jpoint+1
+  20  continue
+c  let coincide the new knot t(number+k+1) with a data point x(nrx)
+c  inside the old knot interval t(number+k) <= x <= t(number+k+1).
+      ihalf = maxpt/2+1
+      nrx = maxbeg+ihalf
+      next = number+1
+      if(next.gt.nrint) go to 40
+c  adjust the different parameters.
+      do 30 j=next,nrint
+        jj = next+nrint-j
+        fpint(jj+1) = fpint(jj)
+        nrdata(jj+1) = nrdata(jj)
+        jk = jj+k
+        t(jk+1) = t(jk)
+  30  continue
+  40  nrdata(number) = ihalf-1
+      nrdata(next) = maxpt-ihalf
+      am = maxpt
+      an = nrdata(number)
+      fpint(number) = fpmax*an/am
+      an = nrdata(next)
+      fpint(next) = fpmax*an/am
+      jk = next+k
+      t(jk) = x(nrx)
+      n = n+1
+      nrint = nrint+1
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpopdi.f
===================================================================
--- branches/Interpolate1D/fitpack/fpopdi.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpopdi.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,181 @@
+      subroutine fpopdi(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,z,mz,z0,dz,
+     * iopt,ider,tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpu,fpv,
+     * nru,nrv,wrk,lwrk)
+c  given the set of function values z(i,j) defined on the rectangular
+c  grid (u(i),v(j)),i=1,2,...,mu;j=1,2,...,mv, fpopdi determines a
+c  smooth bicubic spline approximation with given knots tu(i),i=1,..,nu
+c  in the u-direction and tv(j),j=1,2,...,nv in the v-direction. this
+c  spline sp(u,v) will be periodic in the variable v and will satisfy
+c  the following constraints
+c
+c     s(tu(1),v) = dz(1) , tv(4) <=v<= tv(nv-3)
+c
+c  and (if iopt(2) = 1)
+c
+c     d s(tu(1),v)
+c     ------------ =  dz(2)*cos(v)+dz(3)*sin(v) , tv(4) <=v<= tv(nv-3)
+c     d u
+c
+c  and (if iopt(3) = 1)
+c
+c     s(tu(nu),v)  =  0   tv(4) <=v<= tv(nv-3)
+c
+c  where the parameters dz(i) correspond to the derivative values g(i,j)
+c  as defined in subroutine pogrid.
+c
+c  the b-spline coefficients of sp(u,v) are determined as the least-
+c  squares solution  of an overdetermined linear system which depends
+c  on the value of p and on the values dz(i),i=1,2,3. the correspond-
+c  ing sum of squared residuals sq is a simple quadratic function in
+c  the variables dz(i). these may or may not be provided. the values
+c  dz(i) which are not given will be determined so as to minimize the
+c  resulting sum of squared residuals sq. in that case the user must
+c  provide some initial guess dz(i) and some estimate (dz(i)-step,
+c  dz(i)+step) of the range of possible values for these latter.
+c
+c  sp(u,v) also depends on the parameter p (p>0) in such a way that
+c    - if p tends to infinity, sp(u,v) becomes the least-squares spline
+c      with given knots, satisfying the constraints.
+c    - if p tends to zero, sp(u,v) becomes the least-squares polynomial,
+c      satisfying the constraints.
+c    - the function  f(p)=sumi=1,mu(sumj=1,mv((z(i,j)-sp(u(i),v(j)))**2)
+c      is continuous and strictly decreasing for p>0.
+c
+c  ..scalar arguments..
+      integer ifsu,ifsv,ifbu,ifbv,mu,mv,mz,nu,nv,nuest,nvest,
+     * nc,lwrk
+      real*8 z0,p,step,fp
+c  ..array arguments..
+      integer ider(2),nru(mu),nrv(mv),iopt(3)
+      real*8 u(mu),v(mv),z(mz),dz(3),tu(nu),tv(nv),c(nc),fpu(nu),fpv(nv)
+     *,
+     * wrk(lwrk)
+c  ..local scalars..
+      real*8 res,sq,sqq,step1,step2,three
+      integer i,id0,iop0,iop1,i1,j,l,laa,lau,lav1,lav2,lbb,lbu,lbv,
+     * lcc,lcs,lq,lri,lsu,lsv,l1,l2,mm,mvnu,number
+c  ..local arrays..
+      integer nr(3)
+      real*8 delta(3),dzz(3),sum(3),a(6,6),g(6)
+c  ..function references..
+      integer max0
+c  ..subroutine references..
+c    fpgrdi,fpsysy
+c  ..
+c  set constant
+      three = 3
+c  we partition the working space
+      lsu = 1
+      lsv = lsu+4*mu
+      lri = lsv+4*mv
+      mm = max0(nuest,mv+nvest)
+      lq = lri+mm
+      mvnu = nuest*(mv+nvest-8)
+      lau = lq+mvnu
+      lav1 = lau+5*nuest
+      lav2 = lav1+6*nvest
+      lbu = lav2+4*nvest
+      lbv = lbu+5*nuest
+      laa = lbv+5*nvest
+      lbb = laa+2*mv
+      lcc = lbb+2*nvest
+      lcs = lcc+nvest
+c  we calculate the smoothing spline sp(u,v) according to the input
+c  values dz(i),i=1,2,3.
+      iop0 = iopt(2)
+      iop1 = iopt(3)
+      call fpgrdi(ifsu,ifsv,ifbu,ifbv,0,u,mu,v,mv,z,mz,dz,
+     * iop0,iop1,tu,nu,tv,nv,p,c,nc,sq,fp,fpu,fpv,mm,mvnu,
+     * wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     * wrk(lav2),wrk(lbu),wrk(lbv),wrk(laa),wrk(lbb),
+     * wrk(lcc),wrk(lcs),nru,nrv)
+      id0 = ider(1)
+      if(id0.ne.0) go to 5
+      res = (z0-dz(1))**2
+      fp = fp+res
+      sq = sq+res
+c in case all derivative values dz(i) are given (step<=0) or in case
+c we have spline interpolation, we accept this spline as a solution.
+  5   if(step.le.0. .or. sq.le.0.) return
+      dzz(1) = dz(1)
+      dzz(2) = dz(2)
+      dzz(3) = dz(3)
+c number denotes the number of derivative values dz(i) that still must
+c be optimized. let us denote these parameters by g(j),j=1,...,number.
+      number = 0
+      if(id0.gt.0) go to 10
+      number = 1
+      nr(1) = 1
+      delta(1) = step
+  10  if(iop0.eq.0) go to 20
+      if(ider(2).ne.0) go to 20
+      step2 = step*three/tu(5)
+      nr(number+1) = 2
+      nr(number+2) = 3
+      delta(number+1) = step2
+      delta(number+2) = step2
+      number = number+2
+  20  if(number.eq.0) return
+c the sum of squared residuals sq is a quadratic polynomial in the
+c parameters g(j). we determine the unknown coefficients of this
+c polymomial by calculating (number+1)*(number+2)/2 different splines
+c according to specific values for g(j).
+      do 30 i=1,number
+         l = nr(i)
+         step1 = delta(i)
+         dzz(l) = dz(l)+step1
+         call fpgrdi(ifsu,ifsv,ifbu,ifbv,1,u,mu,v,mv,z,mz,dzz,
+     *    iop0,iop1,tu,nu,tv,nv,p,c,nc,sum(i),fp,fpu,fpv,mm,mvnu,
+     *    wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     *    wrk(lav2),wrk(lbu),wrk(lbv),wrk(laa),wrk(lbb),
+     *    wrk(lcc),wrk(lcs),nru,nrv)
+         if(id0.eq.0) sum(i) = sum(i)+(z0-dzz(1))**2
+         dzz(l) = dz(l)-step1
+         call fpgrdi(ifsu,ifsv,ifbu,ifbv,1,u,mu,v,mv,z,mz,dzz,
+     *    iop0,iop1,tu,nu,tv,nv,p,c,nc,sqq,fp,fpu,fpv,mm,mvnu,
+     *    wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     *    wrk(lav2),wrk(lbu),wrk(lbv),wrk(laa),wrk(lbb),
+     *    wrk(lcc),wrk(lcs),nru,nrv)
+         if(id0.eq.0) sqq = sqq+(z0-dzz(1))**2
+         a(i,i) = (sum(i)+sqq-sq-sq)/step1**2
+         if(a(i,i).le.0.) go to 80
+         g(i) = (sqq-sum(i))/(step1+step1)
+         dzz(l) = dz(l)
+  30  continue
+      if(number.eq.1) go to 60
+      do 50 i=2,number
+         l1 = nr(i)
+         step1 = delta(i)
+         dzz(l1) = dz(l1)+step1
+         i1 = i-1
+         do 40 j=1,i1
+            l2 = nr(j)
+            step2 = delta(j)
+            dzz(l2) = dz(l2)+step2
+            call fpgrdi(ifsu,ifsv,ifbu,ifbv,1,u,mu,v,mv,z,mz,dzz,
+     *       iop0,iop1,tu,nu,tv,nv,p,c,nc,sqq,fp,fpu,fpv,mm,mvnu,
+     *       wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     *       wrk(lav2),wrk(lbu),wrk(lbv),wrk(laa),wrk(lbb),
+     *       wrk(lcc),wrk(lcs),nru,nrv)
+            if(id0.eq.0) sqq = sqq+(z0-dzz(1))**2
+            a(i,j) = (sq+sqq-sum(i)-sum(j))/(step1*step2)
+            dzz(l2) = dz(l2)
+  40     continue
+         dzz(l1) = dz(l1)
+  50  continue
+c the optimal values g(j) are found as the solution of the system
+c d (sq) / d (g(j)) = 0 , j=1,...,number.
+  60  call fpsysy(a,number,g)
+      do 70 i=1,number
+         l = nr(i)
+         dz(l) = dz(l)+g(i)
+  70  continue
+c we determine the spline sp(u,v) according to the optimal values g(j).
+  80  call fpgrdi(ifsu,ifsv,ifbu,ifbv,0,u,mu,v,mv,z,mz,dz,
+     * iop0,iop1,tu,nu,tv,nv,p,c,nc,sq,fp,fpu,fpv,mm,mvnu,
+     * wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     * wrk(lav2),wrk(lbu),wrk(lbv),wrk(laa),wrk(lbb),
+     * wrk(lcc),wrk(lcs),nru,nrv)
+      if(id0.eq.0) fp = fp+(z0-dz(1))**2
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpopsp.f
===================================================================
--- branches/Interpolate1D/fitpack/fpopsp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpopsp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,211 @@
+      subroutine fpopsp(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,r,mr,r0,r1,dr,
+     * iopt,ider,tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpu,fpv,
+     * nru,nrv,wrk,lwrk)
+c  given the set of function values r(i,j) defined on the rectangular
+c  grid (u(i),v(j)),i=1,2,...,mu;j=1,2,...,mv, fpopsp determines a
+c  smooth bicubic spline approximation with given knots tu(i),i=1,..,nu
+c  in the u-direction and tv(j),j=1,2,...,nv in the v-direction. this
+c  spline sp(u,v) will be periodic in the variable v and will satisfy
+c  the following constraints
+c
+c     s(tu(1),v) = dr(1) , tv(4) <=v<= tv(nv-3)
+c
+c     s(tu(nu),v) = dr(4) , tv(4) <=v<= tv(nv-3)
+c
+c  and (if iopt(2) = 1)
+c
+c     d s(tu(1),v)
+c     ------------ =  dr(2)*cos(v)+dr(3)*sin(v) , tv(4) <=v<= tv(nv-3)
+c     d u
+c
+c  and (if iopt(3) = 1)
+c
+c     d s(tu(nu),v)
+c     ------------- =  dr(5)*cos(v)+dr(6)*sin(v) , tv(4) <=v<= tv(nv-3)
+c     d u
+c
+c  where the parameters dr(i) correspond to the derivative values at the
+c  poles as defined in subroutine spgrid.
+c
+c  the b-spline coefficients of sp(u,v) are determined as the least-
+c  squares solution  of an overdetermined linear system which depends
+c  on the value of p and on the values dr(i),i=1,...,6. the correspond-
+c  ing sum of squared residuals sq is a simple quadratic function in
+c  the variables dr(i). these may or may not be provided. the values
+c  dr(i) which are not given will be determined so as to minimize the
+c  resulting sum of squared residuals sq. in that case the user must
+c  provide some initial guess dr(i) and some estimate (dr(i)-step,
+c  dr(i)+step) of the range of possible values for these latter.
+c
+c  sp(u,v) also depends on the parameter p (p>0) in such a way that
+c    - if p tends to infinity, sp(u,v) becomes the least-squares spline
+c      with given knots, satisfying the constraints.
+c    - if p tends to zero, sp(u,v) becomes the least-squares polynomial,
+c      satisfying the constraints.
+c    - the function  f(p)=sumi=1,mu(sumj=1,mv((r(i,j)-sp(u(i),v(j)))**2)
+c      is continuous and strictly decreasing for p>0.
+c
+c  ..scalar arguments..
+      integer ifsu,ifsv,ifbu,ifbv,mu,mv,mr,nu,nv,nuest,nvest,
+     * nc,lwrk
+      real*8 r0,r1,p,fp
+c  ..array arguments..
+      integer ider(4),nru(mu),nrv(mv),iopt(3)
+      real*8 u(mu),v(mv),r(mr),dr(6),tu(nu),tv(nv),c(nc),fpu(nu),fpv(nv)
+     *,
+     * wrk(lwrk),step(2)
+c  ..local scalars..
+      real*8 res,sq,sqq,sq0,sq1,step1,step2,three
+      integer i,id0,iop0,iop1,i1,j,l,lau,lav1,lav2,la0,la1,lbu,lbv,lb0,
+     * lb1,lc0,lc1,lcs,lq,lri,lsu,lsv,l1,l2,mm,mvnu,number
+c  ..local arrays..
+      integer nr(6)
+      real*8 delta(6),drr(6),sum(6),a(6,6),g(6)
+c  ..function references..
+      integer max0
+c  ..subroutine references..
+c    fpgrsp,fpsysy
+c  ..
+c  set constant
+      three = 3
+c  we partition the working space
+      lsu = 1
+      lsv = lsu+4*mu
+      lri = lsv+4*mv
+      mm = max0(nuest,mv+nvest)
+      lq = lri+mm
+      mvnu = nuest*(mv+nvest-8)
+      lau = lq+mvnu
+      lav1 = lau+5*nuest
+      lav2 = lav1+6*nvest
+      lbu = lav2+4*nvest
+      lbv = lbu+5*nuest
+      la0 = lbv+5*nvest
+      la1 = la0+2*mv
+      lb0 = la1+2*mv
+      lb1 = lb0+2*nvest
+      lc0 = lb1+2*nvest
+      lc1 = lc0+nvest
+      lcs = lc1+nvest
+c  we calculate the smoothing spline sp(u,v) according to the input
+c  values dr(i),i=1,...,6.
+      iop0 = iopt(2)
+      iop1 = iopt(3)
+      id0 = ider(1)
+      id1 = ider(3)
+      call fpgrsp(ifsu,ifsv,ifbu,ifbv,0,u,mu,v,mv,r,mr,dr,
+     * iop0,iop1,tu,nu,tv,nv,p,c,nc,sq,fp,fpu,fpv,mm,mvnu,
+     * wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     * wrk(lav2),wrk(lbu),wrk(lbv),wrk(la0),wrk(la1),wrk(lb0),
+     * wrk(lb1),wrk(lc0),wrk(lc1),wrk(lcs),nru,nrv)
+      sq0 = 0.
+      sq1 = 0.
+      if(id0.eq.0) sq0 = (r0-dr(1))**2
+      if(id1.eq.0) sq1 = (r1-dr(4))**2
+      sq = sq+sq0+sq1
+c in case all derivative values dr(i) are given (step<=0) or in case
+c we have spline interpolation, we accept this spline as a solution.
+      if(sq.le.0.) return
+      if(step(1).le.0. .and. step(2).le.0.) return
+      do 10 i=1,6
+        drr(i) = dr(i)
+  10  continue
+c number denotes the number of derivative values dr(i) that still must
+c be optimized. let us denote these parameters by g(j),j=1,...,number.
+      number = 0
+      if(id0.gt.0) go to 20
+      number = 1
+      nr(1) = 1
+      delta(1) = step(1)
+  20  if(iop0.eq.0) go to 30
+      if(ider(2).ne.0) go to 30
+      step2 = step(1)*three/(tu(5)-tu(4))
+      nr(number+1) = 2
+      nr(number+2) = 3
+      delta(number+1) = step2
+      delta(number+2) = step2
+      number = number+2
+  30  if(id1.gt.0) go to 40
+      number = number+1
+      nr(number) = 4
+      delta(number) = step(2)
+  40  if(iop1.eq.0) go to 50
+      if(ider(4).ne.0) go to 50
+      step2 = step(2)*three/(tu(nu)-tu(nu-4))
+      nr(number+1) = 5
+      nr(number+2) = 6
+      delta(number+1) = step2
+      delta(number+2) = step2
+      number = number+2
+  50  if(number.eq.0) return
+c the sum of squared residulas sq is a quadratic polynomial in the
+c parameters g(j). we determine the unknown coefficients of this
+c polymomial by calculating (number+1)*(number+2)/2 different splines
+c according to specific values for g(j).
+      do 60 i=1,number
+         l = nr(i)
+         step1 = delta(i)
+         drr(l) = dr(l)+step1
+         call fpgrsp(ifsu,ifsv,ifbu,ifbv,1,u,mu,v,mv,r,mr,drr,
+     *    iop0,iop1,tu,nu,tv,nv,p,c,nc,sum(i),fp,fpu,fpv,mm,mvnu,
+     *    wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     *    wrk(lav2),wrk(lbu),wrk(lbv),wrk(la0),wrk(la1),wrk(lb0),
+     *    wrk(lb1),wrk(lc0),wrk(lc1),wrk(lcs),nru,nrv)
+         if(id0.eq.0) sq0 = (r0-drr(1))**2
+         if(id1.eq.0) sq1 = (r1-drr(4))**2
+         sum(i) = sum(i)+sq0+sq1
+         drr(l) = dr(l)-step1
+         call fpgrsp(ifsu,ifsv,ifbu,ifbv,1,u,mu,v,mv,r,mr,drr,
+     *    iop0,iop1,tu,nu,tv,nv,p,c,nc,sqq,fp,fpu,fpv,mm,mvnu,
+     *    wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     *    wrk(lav2),wrk(lbu),wrk(lbv),wrk(la0),wrk(la1),wrk(lb0),
+     *    wrk(lb1),wrk(lc0),wrk(lc1),wrk(lcs),nru,nrv)
+         if(id0.eq.0) sq0 = (r0-drr(1))**2
+         if(id1.eq.0) sq1 = (r1-drr(4))**2
+         sqq = sqq+sq0+sq1
+         drr(l) = dr(l)
+         a(i,i) = (sum(i)+sqq-sq-sq)/step1**2
+         if(a(i,i).le.0.) go to 110
+         g(i) = (sqq-sum(i))/(step1+step1)
+  60  continue
+      if(number.eq.1) go to 90
+      do 80 i=2,number
+         l1 = nr(i)
+         step1 = delta(i)
+         drr(l1) = dr(l1)+step1
+         i1 = i-1
+         do 70 j=1,i1
+            l2 = nr(j)
+            step2 = delta(j)
+            drr(l2) = dr(l2)+step2
+            call fpgrsp(ifsu,ifsv,ifbu,ifbv,1,u,mu,v,mv,r,mr,drr,
+     *       iop0,iop1,tu,nu,tv,nv,p,c,nc,sqq,fp,fpu,fpv,mm,mvnu,
+     *       wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     *       wrk(lav2),wrk(lbu),wrk(lbv),wrk(la0),wrk(la1),wrk(lb0),
+     *       wrk(lb1),wrk(lc0),wrk(lc1),wrk(lcs),nru,nrv)
+            if(id0.eq.0) sq0 = (r0-drr(1))**2
+            if(id1.eq.0) sq1 = (r1-drr(4))**2
+            sqq = sqq+sq0+sq1
+            a(i,j) = (sq+sqq-sum(i)-sum(j))/(step1*step2)
+            drr(l2) = dr(l2)
+  70     continue
+         drr(l1) = dr(l1)
+  80  continue
+c the optimal values g(j) are found as the solution of the system
+c d (sq) / d (g(j)) = 0 , j=1,...,number.
+  90  call fpsysy(a,number,g)
+      do 100 i=1,number
+         l = nr(i)
+         dr(l) = dr(l)+g(i)
+ 100  continue
+c we determine the spline sp(u,v) according to the optimal values g(j).
+ 110  call fpgrsp(ifsu,ifsv,ifbu,ifbv,0,u,mu,v,mv,r,mr,dr,
+     * iop0,iop1,tu,nu,tv,nv,p,c,nc,sq,fp,fpu,fpv,mm,mvnu,
+     * wrk(lsu),wrk(lsv),wrk(lri),wrk(lq),wrk(lau),wrk(lav1),
+     * wrk(lav2),wrk(lbu),wrk(lbv),wrk(la0),wrk(la1),wrk(lb0),
+     * wrk(lb1),wrk(lc0),wrk(lc1),wrk(lcs),nru,nrv)
+      if(id0.eq.0) sq0 = (r0-dr(1))**2
+      if(id1.eq.0) sq1 = (r1-dr(4))**2
+      sq = sq+sq0+sq1
+      return
+      end

Added: branches/Interpolate1D/fitpack/fporde.f
===================================================================
--- branches/Interpolate1D/fitpack/fporde.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fporde.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,47 @@
+      subroutine fporde(x,y,m,kx,ky,tx,nx,ty,ny,nummer,index,nreg)
+c  subroutine fporde sorts the data points (x(i),y(i)),i=1,2,...,m
+c  according to the panel tx(l)<=x<tx(l+1),ty(k)<=y<ty(k+1), they belong
+c  to. for each panel a stack is constructed  containing the numbers
+c  of data points lying inside; index(j),j=1,2,...,nreg points to the
+c  first data point in the jth panel while nummer(i),i=1,2,...,m gives
+c  the number of the next data point in the panel.
+c  ..
+c  ..scalar arguments..
+      integer m,kx,ky,nx,ny,nreg
+c  ..array arguments..
+      real*8 x(m),y(m),tx(nx),ty(ny)
+      integer nummer(m),index(nreg)
+c  ..local scalars..
+      real*8 xi,yi
+      integer i,im,k,kx1,ky1,k1,l,l1,nk1x,nk1y,num,nyy
+c  ..
+      kx1 = kx+1
+      ky1 = ky+1
+      nk1x = nx-kx1
+      nk1y = ny-ky1
+      nyy = nk1y-ky
+      do 10 i=1,nreg
+        index(i) = 0
+  10  continue
+      do 60 im=1,m
+        xi = x(im)
+        yi = y(im)
+        l = kx1
+        l1 = l+1
+  20    if(xi.lt.tx(l1) .or. l.eq.nk1x) go to 30
+        l = l1
+        l1 = l+1
+        go to 20
+  30    k = ky1
+        k1 = k+1
+  40    if(yi.lt.ty(k1) .or. k.eq.nk1y) go to 50
+        k = k1
+        k1 = k+1
+        go to 40
+  50    num = (l-kx1)*nyy+k-ky
+        nummer(im) = index(num)
+        index(num) = im
+  60  continue
+      return
+      end
+

Added: branches/Interpolate1D/fitpack/fppara.f
===================================================================
--- branches/Interpolate1D/fitpack/fppara.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fppara.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,402 @@
+      subroutine fppara(iopt,idim,m,u,mx,x,w,ub,ue,k,s,nest,tol,maxit,
+     * k1,k2,n,t,nc,c,fp,fpint,z,a,b,g,q,nrdata,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 ub,ue,s,tol,fp
+      integer iopt,idim,m,mx,k,nest,maxit,k1,k2,n,nc,ier
+c  ..array arguments..
+      real*8 u(m),x(mx),w(m),t(nest),c(nc),fpint(nest),
+     * z(nc),a(nest,k1),b(nest,k2),g(nest,k2),q(m,k1)
+      integer nrdata(nest)
+c  ..local scalars..
+      real*8 acc,con1,con4,con9,cos,fac,fpart,fpms,fpold,fp0,f1,f2,f3,
+     * half,one,p,pinv,piv,p1,p2,p3,rn,sin,store,term,ui,wi
+      integer i,ich1,ich3,it,iter,i1,i2,i3,j,jj,j1,j2,k3,l,l0,
+     * mk1,new,nk1,nmax,nmin,nplus,npl1,nrint,n8
+c  ..local arrays..
+      real*8 h(7),xi(10)
+c  ..function references
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpback,fpbspl,fpgivs,fpdisc,fpknot,fprota
+c  ..
+c  set constants
+      one = 0.1e+01
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      half = 0.5e0
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1: determination of the number of knots and their position     c
+c  **************************************************************      c
+c  given a set of knots we compute the least-squares curve sinf(u),    c
+c  and the corresponding sum of squared residuals fp=f(p=inf).         c
+c  if iopt=-1 sinf(u) is the requested curve.                          c
+c  if iopt=0 or iopt=1 we check whether we can accept the knots:       c
+c    if fp <=s we will continue with the current set of knots.         c
+c    if fp > s we will increase the number of knots and compute the    c
+c       corresponding least-squares curve until finally fp<=s.         c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmax = m+k+1.                                        c
+c    if s > 0 and                                                      c
+c      iopt=0 we first compute the least-squares polynomial curve of   c
+c      degree k; n = nmin = 2*k+2                                      c
+c      iopt=1 we start with the set of knots found at the last         c
+c      call of the routine, except for the case that s > fp0; then     c
+c      we compute directly the polynomial curve of degree k.           c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  determine nmin, the number of knots for polynomial approximation.
+      nmin = 2*k1
+      if(iopt.lt.0) go to 60
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  determine nmax, the number of knots for spline interpolation.
+      nmax = m+k1
+      if(s.gt.0.) go to 45
+c  if s=0, s(u) is an interpolating curve.
+c  test whether the required storage space exceeds the available one.
+      n = nmax
+      if(nmax.gt.nest) go to 420
+c  find the position of the interior knots in case of interpolation.
+  10  mk1 = m-k1
+      if(mk1.eq.0) go to 60
+      k3 = k/2
+      i = k2
+      j = k3+2
+      if(k3*2.eq.k) go to 30
+      do 20 l=1,mk1
+        t(i) = u(j)
+        i = i+1
+        j = j+1
+  20  continue
+      go to 60
+  30  do 40 l=1,mk1
+        t(i) = (u(j)+u(j-1))*half
+        i = i+1
+        j = j+1
+  40  continue
+      go to 60
+c  if s>0 our initial choice of knots depends on the value of iopt.
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  polynomial curve which is a spline curve without interior knots.
+c  if iopt=1 and fp0>s we start computing the least squares spline curve
+c  according to the set of knots found at the last call of the routine.
+  45  if(iopt.eq.0) go to 50
+      if(n.eq.nmin) go to 50
+      fp0 = fpint(n)
+      fpold = fpint(n-1)
+      nplus = nrdata(n)
+      if(fp0.gt.s) go to 60
+  50  n = nmin
+      fpold = 0.
+      nplus = 0
+      nrdata(1) = m-2
+c  main loop for the different sets of knots. m is a save upper bound
+c  for the number of trials.
+  60  do 200 iter = 1,m
+        if(n.eq.nmin) ier = -2
+c  find nrint, tne number of knot intervals.
+        nrint = n-nmin+1
+c  find the position of the additional knots which are needed for
+c  the b-spline representation of s(u).
+        nk1 = n-k1
+        i = n
+        do 70 j=1,k1
+          t(j) = ub
+          t(i) = ue
+          i = i-1
+  70    continue
+c  compute the b-spline coefficients of the least-squares spline curve
+c  sinf(u). the observation matrix a is built up row by row and
+c  reduced to upper triangular form by givens transformations.
+c  at the same time fp=f(p=inf) is computed.
+        fp = 0.
+c  initialize the b-spline coefficients and the observation matrix a.
+        do 75 i=1,nc
+          z(i) = 0.
+  75    continue
+        do 80 i=1,nk1
+          do 80 j=1,k1
+            a(i,j) = 0.
+  80    continue
+        l = k1
+        jj = 0
+        do 130 it=1,m
+c  fetch the current data point u(it),x(it).
+          ui = u(it)
+          wi = w(it)
+          do 83 j=1,idim
+             jj = jj+1
+             xi(j) = x(jj)*wi
+  83      continue
+c  search for knot interval t(l) <= ui < t(l+1).
+  85      if(ui.lt.t(l+1) .or. l.eq.nk1) go to 90
+          l = l+1
+          go to 85
+c  evaluate the (k+1) non-zero b-splines at ui and store them in q.
+  90      call fpbspl(t,n,k,ui,l,h)
+          do 95 i=1,k1
+            q(it,i) = h(i)
+            h(i) = h(i)*wi
+  95      continue
+c  rotate the new row of the observation matrix into triangle.
+          j = l-k1
+          do 110 i=1,k1
+            j = j+1
+            piv = h(i)
+            if(piv.eq.0.) go to 110
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(j,1),cos,sin)
+c  transformations to right hand side.
+            j1 = j
+            do 97 j2 =1,idim
+               call fprota(cos,sin,xi(j2),z(j1))
+               j1 = j1+n
+  97        continue
+            if(i.eq.k1) go to 120
+            i2 = 1
+            i3 = i+1
+            do 100 i1 = i3,k1
+              i2 = i2+1
+c  transformations to left hand side.
+              call fprota(cos,sin,h(i1),a(j,i2))
+ 100        continue
+ 110      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 120      do 125 j2=1,idim
+             fp  = fp+xi(j2)**2
+ 125      continue
+ 130    continue
+        if(ier.eq.(-2)) fp0 = fp
+        fpint(n) = fp0
+        fpint(n-1) = fpold
+        nrdata(n) = nplus
+c  backward substitution to obtain the b-spline coefficients.
+        j1 = 1
+        do 135 j2=1,idim
+           call fpback(a,z(j1),nk1,k1,c(j1),nest)
+           j1 = j1+n
+ 135    continue
+c  test whether the approximation sinf(u) is an acceptable solution.
+        if(iopt.lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  if f(p=inf) < s accept the choice of knots.
+        if(fpms.lt.0.) go to 250
+c  if n = nmax, sinf(u) is an interpolating spline curve.
+        if(n.eq.nmax) go to 430
+c  increase the number of knots.
+c  if n=nest we cannot increase the number of knots because of
+c  the storage capacity limitation.
+        if(n.eq.nest) go to 420
+c  determine the number of knots nplus we are going to add.
+        if(ier.eq.0) go to 140
+        nplus = 1
+        ier = 0
+        go to 150
+ 140    npl1 = nplus*2
+        rn = nplus
+        if(fpold-fp.gt.acc) npl1 = rn*fpms/(fpold-fp)
+        nplus = min0(nplus*2,max0(npl1,nplus/2,1))
+ 150    fpold = fp
+c  compute the sum of squared residuals for each knot interval
+c  t(j+k) <= u(i) <= t(j+k+1) and store it in fpint(j),j=1,2,...nrint.
+        fpart = 0.
+        i = 1
+        l = k2
+        new = 0
+        jj = 0
+        do 180 it=1,m
+          if(u(it).lt.t(l) .or. l.gt.nk1) go to 160
+          new = 1
+          l = l+1
+ 160      term = 0.
+          l0 = l-k2
+          do 175 j2=1,idim
+            fac = 0.
+            j1 = l0
+            do 170 j=1,k1
+              j1 = j1+1
+              fac = fac+c(j1)*q(it,j)
+ 170        continue
+            jj = jj+1
+            term = term+(w(it)*(fac-x(jj)))**2
+            l0 = l0+n
+ 175      continue
+          fpart = fpart+term
+          if(new.eq.0) go to 180
+          store = term*half
+          fpint(i) = fpart-store
+          i = i+1
+          fpart = store
+          new = 0
+ 180    continue
+        fpint(nrint) = fpart
+        do 190 l=1,nplus
+c  add a new knot.
+          call fpknot(u,m,t,n,fpint,nrdata,nrint,nest,1)
+c  if n=nmax we locate the knots as for interpolation
+          if(n.eq.nmax) go to 10
+c  test whether we cannot further increase the number of knots.
+          if(n.eq.nest) go to 200
+ 190    continue
+c  restart the computations with the new set of knots.
+ 200  continue
+c  test whether the least-squares kth degree polynomial curve is a
+c  solution of our approximation problem.
+ 250  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 2: determination of the smoothing spline curve sp(u).          c
+c  **********************************************************          c
+c  we have determined the number of knots and their position.          c
+c  we now compute the b-spline coefficients of the smoothing curve     c
+c  sp(u). the observation matrix a is extended by the rows of matrix   c
+c  b expressing that the kth derivative discontinuities of sp(u) at    c
+c  the interior knots t(k+2),...t(n-k-1) must be zero. the corres-     c
+c  ponding weights of these additional rows are set to 1/p.            c
+c  iteratively we then have to determine the value of p such that f(p),c
+c  the sum of squared residuals be = s. we already know that the least c
+c  squares kth degree polynomial curve corresponds to p=0, and that    c
+c  the least-squares spline curve corresponds to p=infinity. the       c
+c  iteration process which is proposed here, makes use of rational     c
+c  interpolation. since f(p) is a convex and strictly decreasing       c
+c  function of p, it can be approximated by a rational function        c
+c  r(p) = (u*p+v)/(p+w). three values of p(p1,p2,p3) with correspond-  c
+c  ing values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used      c
+c  to calculate the new value of p such that r(p)=s. convergence is    c
+c  guaranteed by taking f1>0 and f3<0.                                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jump of the kth derivative of the
+c  b-splines at the knots t(l),l=k+2,...n-k-1 and store in b.
+      call fpdisc(t,n,k2,b,nest)
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = 0.
+      do 252 i=1,nk1
+         p = p+a(i,1)
+ 252  continue
+      rn = nk1
+      p = rn/p
+      ich1 = 0
+      ich3 = 0
+      n8 = n-nmin
+c  iteration process to find the root of f(p) = s.
+      do 360 iter=1,maxit
+c  the rows of matrix b with weight 1/p are rotated into the
+c  triangularised observation matrix a which is stored in g.
+        pinv = one/p
+        do 255 i=1,nc
+          c(i) = z(i)
+ 255    continue
+        do 260 i=1,nk1
+          g(i,k2) = 0.
+          do 260 j=1,k1
+            g(i,j) = a(i,j)
+ 260    continue
+        do 300 it=1,n8
+c  the row of matrix b is rotated into triangle by givens transformation
+          do 270 i=1,k2
+            h(i) = b(it,i)*pinv
+ 270      continue
+          do 275 j=1,idim
+            xi(j) = 0.
+ 275      continue
+          do 290 j=it,nk1
+            piv = h(1)
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,g(j,1),cos,sin)
+c  transformations to right hand side.
+            j1 = j
+            do 277 j2=1,idim
+              call fprota(cos,sin,xi(j2),c(j1))
+              j1 = j1+n
+ 277        continue
+            if(j.eq.nk1) go to 300
+            i2 = k1
+            if(j.gt.n8) i2 = nk1-j
+            do 280 i=1,i2
+c  transformations to left hand side.
+              i1 = i+1
+              call fprota(cos,sin,h(i1),g(j,i1))
+              h(i) = h(i1)
+ 280        continue
+            h(i2+1) = 0.
+ 290      continue
+ 300    continue
+c  backward substitution to obtain the b-spline coefficients.
+        j1 = 1
+        do 305 j2=1,idim
+          call fpback(g,c(j1),nk1,k2,c(j1),nest)
+          j1 =j1+n
+ 305    continue
+c  computation of f(p).
+        fp = 0.
+        l = k2
+        jj = 0
+        do 330 it=1,m
+          if(u(it).lt.t(l) .or. l.gt.nk1) go to 310
+          l = l+1
+ 310      l0 = l-k2
+          term = 0.
+          do 325 j2=1,idim
+            fac = 0.
+            j1 = l0
+            do 320 j=1,k1
+              j1 = j1+1
+              fac = fac+c(j1)*q(it,j)
+ 320        continue
+            jj = jj+1
+            term = term+(fac-x(jj))**2
+            l0 = l0+n
+ 325      continue
+          fp = fp+term*w(it)**2
+ 330    continue
+c  test whether the approximation sp(u) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximal number of iterations is reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 340
+        if((f2-f3).gt.acc) go to 335
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p=p1*con9 + p2*con1
+        go to 360
+ 335    if(f2.lt.0.) ich3=1
+ 340    if(ich1.ne.0) go to 350
+        if((f1-f2).gt.acc) go to 345
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 360
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 360
+ 345    if(f2.gt.0.) ich1=1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 350    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value for p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 360  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+ 440  return
+      end

Added: branches/Interpolate1D/fitpack/fppasu.f
===================================================================
--- branches/Interpolate1D/fitpack/fppasu.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fppasu.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,392 @@
+      subroutine fppasu(iopt,ipar,idim,u,mu,v,mv,z,mz,s,nuest,nvest,
+     * tol,maxit,nc,nu,tu,nv,tv,c,fp,fp0,fpold,reducu,reducv,fpintu,
+     * fpintv,lastdi,nplusu,nplusv,nru,nrv,nrdatu,nrdatv,wrk,lwrk,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 s,tol,fp,fp0,fpold,reducu,reducv
+      integer iopt,idim,mu,mv,mz,nuest,nvest,maxit,nc,nu,nv,lastdi,
+     * nplusu,nplusv,lwrk,ier
+c  ..array arguments..
+      real*8 u(mu),v(mv),z(mz*idim),tu(nuest),tv(nvest),c(nc*idim),
+     * fpintu(nuest),fpintv(nvest),wrk(lwrk)
+      integer ipar(2),nrdatu(nuest),nrdatv(nvest),nru(mu),nrv(mv)
+c  ..local scalars
+      real*8 acc,fpms,f1,f2,f3,p,p1,p2,p3,rn,one,con1,con9,con4,
+     * peru,perv,ub,ue,vb,ve
+      integer i,ich1,ich3,ifbu,ifbv,ifsu,ifsv,iter,j,lau1,lav1,laa,
+     * l,lau,lav,lbu,lbv,lq,lri,lsu,lsv,l1,l2,l3,l4,mm,mpm,mvnu,ncof,
+     * nk1u,nk1v,nmaxu,nmaxv,nminu,nminv,nplu,nplv,npl1,nrintu,
+     * nrintv,nue,nuk,nve,nuu,nvv
+c  ..function references..
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpgrpa,fpknot
+c  ..
+c   set constants
+      one = 1
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+c  set boundaries of the approximation domain
+      ub = u(1)
+      ue = u(mu)
+      vb = v(1)
+      ve = v(mv)
+c  we partition the working space.
+      lsu = 1
+      lsv = lsu+mu*4
+      lri = lsv+mv*4
+      mm = max0(nuest,mv)
+      lq = lri+mm*idim
+      mvnu = nuest*mv*idim
+      lau = lq+mvnu
+      nuk = nuest*5
+      lbu = lau+nuk
+      lav = lbu+nuk
+      nuk = nvest*5
+      lbv = lav+nuk
+      laa = lbv+nuk
+      lau1 = lau
+      if(ipar(1).eq.0) go to 10
+      peru = ue-ub
+      lau1 = laa
+      laa = laa+4*nuest
+  10  lav1 = lav
+      if(ipar(2).eq.0) go to 20
+      perv = ve-vb
+      lav1 = laa
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 1: determination of the number of knots and their position.     c
+c ****************************************************************     c
+c  given a set of knots we compute the least-squares spline sinf(u,v), c
+c  and the corresponding sum of squared residuals fp=f(p=inf).         c
+c  if iopt=-1  sinf(u,v) is the requested approximation.               c
+c  if iopt=0 or iopt=1 we check whether we can accept the knots:       c
+c    if fp <=s we will continue with the current set of knots.         c
+c    if fp > s we will increase the number of knots and compute the    c
+c       corresponding least-squares spline until finally fp<=s.        c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmaxu = mu+4+2*ipar(1) and  nmaxv = mv+4+2*ipar(2)   c
+c    if s>0 and                                                        c
+c     *iopt=0 we first compute the least-squares polynomial            c
+c          nu=nminu=8 and nv=nminv=8                                   c
+c     *iopt=1 we start with the knots found at the last call of the    c
+c      routine, except for the case that s > fp0; then we can compute  c
+c      the least-squares polynomial directly.                          c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  determine the number of knots for polynomial approximation.
+  20  nminu = 8
+      nminv = 8
+      if(iopt.lt.0) go to 100
+c  acc denotes the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  find nmaxu and nmaxv which denote the number of knots in u- and v-
+c  direction in case of spline interpolation.
+      nmaxu = mu+4+2*ipar(1)
+      nmaxv = mv+4+2*ipar(2)
+c  find nue and nve which denote the maximum number of knots
+c  allowed in each direction
+      nue = min0(nmaxu,nuest)
+      nve = min0(nmaxv,nvest)
+      if(s.gt.0.) go to 60
+c  if s = 0, s(u,v) is an interpolating spline.
+      nu = nmaxu
+      nv = nmaxv
+c  test whether the required storage space exceeds the available one.
+      if(nv.gt.nvest .or. nu.gt.nuest) go to 420
+c  find the position of the interior knots in case of interpolation.
+c  the knots in the u-direction.
+      nuu = nu-8
+      if(nuu.eq.0) go to 40
+      i = 5
+      j = 3-ipar(1)
+      do 30 l=1,nuu
+        tu(i) = u(j)
+        i = i+1
+        j = j+1
+  30  continue
+c  the knots in the v-direction.
+  40  nvv = nv-8
+      if(nvv.eq.0) go to 60
+      i = 5
+      j = 3-ipar(2)
+      do 50 l=1,nvv
+        tv(i) = v(j)
+        i = i+1
+        j = j+1
+  50  continue
+      go to 100
+c  if s > 0 our initial choice of knots depends on the value of iopt.
+  60  if(iopt.eq.0) go to 90
+      if(fp0.le.s) go to 90
+c  if iopt=1 and fp0 > s we start computing the least- squares spline
+c  according to the set of knots found at the last call of the routine.
+c  we determine the number of grid coordinates u(i) inside each knot
+c  interval (tu(l),tu(l+1)).
+      l = 5
+      j = 1
+      nrdatu(1) = 0
+      mpm = mu-1
+      do 70 i=2,mpm
+        nrdatu(j) = nrdatu(j)+1
+        if(u(i).lt.tu(l)) go to 70
+        nrdatu(j) = nrdatu(j)-1
+        l = l+1
+        j = j+1
+        nrdatu(j) = 0
+  70  continue
+c  we determine the number of grid coordinates v(i) inside each knot
+c  interval (tv(l),tv(l+1)).
+      l = 5
+      j = 1
+      nrdatv(1) = 0
+      mpm = mv-1
+      do 80 i=2,mpm
+        nrdatv(j) = nrdatv(j)+1
+        if(v(i).lt.tv(l)) go to 80
+        nrdatv(j) = nrdatv(j)-1
+        l = l+1
+        j = j+1
+        nrdatv(j) = 0
+  80  continue
+      go to 100
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  polynomial (which is a spline without interior knots).
+  90  nu = nminu
+      nv = nminv
+      nrdatu(1) = mu-2
+      nrdatv(1) = mv-2
+      lastdi = 0
+      nplusu = 0
+      nplusv = 0
+      fp0 = 0.
+      fpold = 0.
+      reducu = 0.
+      reducv = 0.
+ 100  mpm = mu+mv
+      ifsu = 0
+      ifsv = 0
+      ifbu = 0
+      ifbv = 0
+      p = -one
+c  main loop for the different sets of knots.mpm=mu+mv is a save upper
+c  bound for the number of trials.
+      do 250 iter=1,mpm
+        if(nu.eq.nminu .and. nv.eq.nminv) ier = -2
+c  find nrintu (nrintv) which is the number of knot intervals in the
+c  u-direction (v-direction).
+        nrintu = nu-nminu+1
+        nrintv = nv-nminv+1
+c  find ncof, the number of b-spline coefficients for the current set
+c  of knots.
+        nk1u = nu-4
+        nk1v = nv-4
+        ncof = nk1u*nk1v
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(u,v).
+        if(ipar(1).ne.0) go to 110
+        i = nu
+        do 105 j=1,4
+          tu(j) = ub
+          tu(i) = ue
+          i = i-1
+ 105    continue
+        go to 120
+ 110    l1 = 4
+        l2 = l1
+        l3 = nu-3
+        l4 = l3
+        tu(l2) = ub
+        tu(l3) = ue
+        do 115 j=1,3
+          l1 = l1+1
+          l2 = l2-1
+          l3 = l3+1
+          l4 = l4-1
+          tu(l2) = tu(l4)-peru
+          tu(l3) = tu(l1)+peru
+ 115    continue
+ 120    if(ipar(2).ne.0) go to 130
+        i = nv
+        do 125 j=1,4
+          tv(j) = vb
+          tv(i) = ve
+          i = i-1
+ 125    continue
+        go to 140
+ 130    l1 = 4
+        l2 = l1
+        l3 = nv-3
+        l4 = l3
+        tv(l2) = vb
+        tv(l3) = ve
+        do 135 j=1,3
+          l1 = l1+1
+          l2 = l2-1
+          l3 = l3+1
+          l4 = l4-1
+          tv(l2) = tv(l4)-perv
+          tv(l3) = tv(l1)+perv
+ 135    continue
+c  find the least-squares spline sinf(u,v) and calculate for each knot
+c  interval tu(j+3)<=u<=tu(j+4) (tv(j+3)<=v<=tv(j+4)) the sum
+c  of squared residuals fpintu(j),j=1,2,...,nu-7 (fpintv(j),j=1,2,...
+c  ,nv-7) for the data points having their absciss (ordinate)-value
+c  belonging to that interval.
+c  fp gives the total sum of squared residuals.
+ 140    call fpgrpa(ifsu,ifsv,ifbu,ifbv,idim,ipar,u,mu,v,mv,z,mz,tu,
+     *  nu,tv,nv,p,c,nc,fp,fpintu,fpintv,mm,mvnu,wrk(lsu),wrk(lsv),
+     *  wrk(lri),wrk(lq),wrk(lau),wrk(lau1),wrk(lav),wrk(lav1),
+     *  wrk(lbu),wrk(lbv),nru,nrv)
+        if(ier.eq.(-2)) fp0 = fp
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt.lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms) .lt. acc) go to 440
+c  if f(p=inf) < s, we accept the choice of knots.
+        if(fpms.lt.0.) go to 300
+c  if nu=nmaxu and nv=nmaxv, sinf(u,v) is an interpolating spline.
+        if(nu.eq.nmaxu .and. nv.eq.nmaxv) go to 430
+c  increase the number of knots.
+c  if nu=nue and nv=nve we cannot further increase the number of knots
+c  because of the storage capacity limitation.
+        if(nu.eq.nue .and. nv.eq.nve) go to 420
+        ier = 0
+c  adjust the parameter reducu or reducv according to the direction
+c  in which the last added knots were located.
+        if (lastdi.lt.0) go to 150
+        if (lastdi.eq.0) go to 170
+        go to 160
+ 150    reducu = fpold-fp
+        go to 170
+ 160    reducv = fpold-fp
+c  store the sum of squared residuals for the current set of knots.
+ 170    fpold = fp
+c  find nplu, the number of knots we should add in the u-direction.
+        nplu = 1
+        if(nu.eq.nminu) go to 180
+        npl1 = nplusu*2
+        rn = nplusu
+        if(reducu.gt.acc) npl1 = rn*fpms/reducu
+        nplu = min0(nplusu*2,max0(npl1,nplusu/2,1))
+c  find nplv, the number of knots we should add in the v-direction.
+ 180    nplv = 1
+        if(nv.eq.nminv) go to 190
+        npl1 = nplusv*2
+        rn = nplusv
+        if(reducv.gt.acc) npl1 = rn*fpms/reducv
+        nplv = min0(nplusv*2,max0(npl1,nplusv/2,1))
+ 190    if (nplu.lt.nplv) go to 210
+        if (nplu.eq.nplv) go to 200
+        go to 230
+ 200    if(lastdi.lt.0) go to 230
+ 210    if(nu.eq.nue) go to 230
+c  addition in the u-direction.
+        lastdi = -1
+        nplusu = nplu
+        ifsu = 0
+        do 220 l=1,nplusu
+c  add a new knot in the u-direction
+          call fpknot(u,mu,tu,nu,fpintu,nrdatu,nrintu,nuest,1)
+c  test whether we cannot further increase the number of knots in the
+c  u-direction.
+          if(nu.eq.nue) go to 250
+ 220    continue
+        go to 250
+ 230    if(nv.eq.nve) go to 210
+c  addition in the v-direction.
+        lastdi = 1
+        nplusv = nplv
+        ifsv = 0
+        do 240 l=1,nplusv
+c  add a new knot in the v-direction.
+          call fpknot(v,mv,tv,nv,fpintv,nrdatv,nrintv,nvest,1)
+c  test whether we cannot further increase the number of knots in the
+c  v-direction.
+          if(nv.eq.nve) go to 250
+ 240    continue
+c  restart the computations with the new set of knots.
+ 250  continue
+c  test whether the least-squares polynomial is a solution of our
+c  approximation problem.
+ 300  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing spline sp(u,v)                c
+c *****************************************************                c
+c  we have determined the number of knots and their position. we now   c
+c  compute the b-spline coefficients of the smoothing spline sp(u,v).  c
+c  this smoothing spline varies with the parameter p in such a way thatc
+c  f(p)=suml=1,idim(sumi=1,mu(sumj=1,mv((z(i,j,l)-sp(u(i),v(j),l))**2) c
+c  is a continuous, strictly decreasing function of p. moreover the    c
+c  least-squares polynomial corresponds to p=0 and the least-squares   c
+c  spline to p=infinity. iteratively we then have to determine the     c
+c  positive value of p such that f(p)=s. the process which is proposed c
+c  here makes use of rational interpolation. f(p) is approximated by a c
+c  rational function r(p)=(u*p+v)/(p+w); three values of p (p1,p2,p3)  c
+c  with corresponding values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s)c
+c  are used to calculate the new value of p such that r(p)=s.          c
+c  convergence is guaranteed by taking f1 > 0 and f3 < 0.              c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = one
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p)=s.
+      do 350 iter = 1,maxit
+c  find the smoothing spline sp(u,v) and the corresponding sum of
+c  squared residuals fp.
+        call fpgrpa(ifsu,ifsv,ifbu,ifbv,idim,ipar,u,mu,v,mv,z,mz,tu,
+     *  nu,tv,nv,p,c,nc,fp,fpintu,fpintv,mm,mvnu,wrk(lsu),wrk(lsv),
+     *  wrk(lri),wrk(lq),wrk(lau),wrk(lau1),wrk(lav),wrk(lav1),
+     *  wrk(lbu),wrk(lbv),nru,nrv)
+c  test whether the approximation sp(u,v) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 320
+        if((f2-f3).gt.acc) go to 310
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 350
+ 310    if(f2.lt.0.) ich3 = 1
+ 320    if(ich1.ne.0) go to 340
+        if((f1-f2).gt.acc) go to 330
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 350
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 350
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 330    if(f2.gt.0.) ich1 = 1
+ 340    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 350  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+      fp = 0.
+ 440  return
+      end

Added: branches/Interpolate1D/fitpack/fpperi.f
===================================================================
--- branches/Interpolate1D/fitpack/fpperi.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpperi.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,616 @@
+      subroutine fpperi(iopt,x,y,w,m,k,s,nest,tol,maxit,k1,k2,n,t,c,
+     * fp,fpint,z,a1,a2,b,g1,g2,q,nrdata,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 s,tol,fp
+      integer iopt,m,k,nest,maxit,k1,k2,n,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),t(nest),c(nest),fpint(nest),z(nest),
+     * a1(nest,k1),a2(nest,k),b(nest,k2),g1(nest,k2),g2(nest,k1),
+     * q(m,k1)
+      integer nrdata(nest)
+c  ..local scalars..
+      real*8 acc,cos,c1,d1,fpart,fpms,fpold,fp0,f1,f2,f3,p,per,pinv,piv,
+     *
+     * p1,p2,p3,sin,store,term,wi,xi,yi,rn,one,con1,con4,con9,half
+      integer i,ich1,ich3,ij,ik,it,iter,i1,i2,i3,j,jk,jper,j1,j2,kk,
+     * kk1,k3,l,l0,l1,l5,mm,m1,new,nk1,nk2,nmax,nmin,nplus,npl1,
+     * nrint,n10,n11,n7,n8
+c  ..local arrays..
+      real*8 h(6),h1(7),h2(6)
+c  ..function references..
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpbacp,fpbspl,fpgivs,fpdisc,fpknot,fprota
+c  ..
+c  set constants
+      one = 0.1e+01
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      half = 0.5e0
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1: determination of the number of knots and their position     c
+c  **************************************************************      c
+c  given a set of knots we compute the least-squares periodic spline   c
+c  sinf(x). if the sum f(p=inf) <= s we accept the choice of knots.    c
+c  the initial choice of knots depends on the value of s and iopt.     c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmax = m+2*k.                                        c
+c    if s > 0 and                                                      c
+c      iopt=0 we first compute the least-squares polynomial of         c
+c      degree k; n = nmin = 2*k+2. since s(x) must be periodic we      c
+c      find that s(x) is a constant function.                          c
+c      iopt=1 we start with the set of knots found at the last         c
+c      call of the routine, except for the case that s > fp0; then     c
+c      we compute directly the least-squares periodic polynomial.      c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+      m1 = m-1
+      kk = k
+      kk1 = k1
+      k3 = 3*k+1
+      nmin = 2*k1
+c  determine the length of the period of s(x).
+      per = x(m)-x(1)
+      if(iopt.lt.0) go to 50
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  determine nmax, the number of knots for periodic spline interpolation
+      nmax = m+2*k
+      if(s.gt.0. .or. nmax.eq.nmin) go to 30
+c  if s=0, s(x) is an interpolating spline.
+      n = nmax
+c  test whether the required storage space exceeds the available one.
+      if(n.gt.nest) go to 620
+c  find the position of the interior knots in case of interpolation.
+   5  if((k/2)*2 .eq. k) go to 20
+      do 10 i=2,m1
+        j = i+k
+        t(j) = x(i)
+  10  continue
+      if(s.gt.0.) go to 50
+      kk = k-1
+      kk1 = k
+      if(kk.gt.0) go to 50
+      t(1) = t(m)-per
+      t(2) = x(1)
+      t(m+1) = x(m)
+      t(m+2) = t(3)+per
+      do 15 i=1,m1
+        c(i) = y(i)
+  15  continue
+      c(m) = c(1)
+      fp = 0.
+      fpint(n) = fp0
+      fpint(n-1) = 0.
+      nrdata(n) = 0
+      go to 630
+  20  do 25 i=2,m1
+        j = i+k
+        t(j) = (x(i)+x(i-1))*half
+  25  continue
+      go to 50
+c  if s > 0 our initial choice depends on the value of iopt.
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  periodic polynomial. (i.e. a constant function).
+c  if iopt=1 and fp0>s we start computing the least-squares periodic
+c  spline according the set of knots found at the last call of the
+c  routine.
+  30  if(iopt.eq.0) go to 35
+      if(n.eq.nmin) go to 35
+      fp0 = fpint(n)
+      fpold = fpint(n-1)
+      nplus = nrdata(n)
+      if(fp0.gt.s) go to 50
+c  the case that s(x) is a constant function is treated separetely.
+c  find the least-squares constant c1 and compute fp0 at the same time.
+  35  fp0 = 0.
+      d1 = 0.
+      c1 = 0.
+      do 40 it=1,m1
+        wi = w(it)
+        yi = y(it)*wi
+        call fpgivs(wi,d1,cos,sin)
+        call fprota(cos,sin,yi,c1)
+        fp0 = fp0+yi**2
+  40  continue
+      c1 = c1/d1
+c  test whether that constant function is a solution of our problem.
+      fpms = fp0-s
+      if(fpms.lt.acc .or. nmax.eq.nmin) go to 640
+      fpold = fp0
+c  test whether the required storage space exceeds the available one.
+      if(nmin.ge.nest) go to 620
+c  start computing the least-squares periodic spline with one
+c  interior knot.
+      nplus = 1
+      n = nmin+1
+      mm = (m+1)/2
+      t(k2) = x(mm)
+      nrdata(1) = mm-2
+      nrdata(2) = m1-mm
+c  main loop for the different sets of knots. m is a save upper
+c  bound for the number of trials.
+  50  do 340 iter=1,m
+c  find nrint, the number of knot intervals.
+        nrint = n-nmin+1
+c  find the position of the additional knots which are needed for
+c  the b-spline representation of s(x). if we take
+c      t(k+1) = x(1), t(n-k) = x(m)
+c      t(k+1-j) = t(n-k-j) - per, j=1,2,...k
+c      t(n-k+j) = t(k+1+j) + per, j=1,2,...k
+c  then s(x) is a periodic spline with period per if the b-spline
+c  coefficients satisfy the following conditions
+c      c(n7+j) = c(j), j=1,...k   (**)   with n7=n-2*k-1.
+        t(k1) = x(1)
+        nk1 = n-k1
+        nk2 = nk1+1
+        t(nk2) = x(m)
+        do 60 j=1,k
+          i1 = nk2+j
+          i2 = nk2-j
+          j1 = k1+j
+          j2 = k1-j
+          t(i1) = t(j1)+per
+          t(j2) = t(i2)-per
+  60    continue
+c  compute the b-spline coefficients c(j),j=1,...n7 of the least-squares
+c  periodic spline sinf(x). the observation matrix a is built up row
+c  by row while taking into account condition (**) and is reduced to
+c  triangular form by givens transformations .
+c  at the same time fp=f(p=inf) is computed.
+c  the n7 x n7 triangularised upper matrix a has the form
+c            ! a1 '    !
+c        a = !    ' a2 !
+c            ! 0  '    !
+c  with a2 a n7 x k matrix and a1 a n10 x n10 upper triangular
+c  matrix of bandwith k+1 ( n10 = n7-k).
+c  initialization.
+        do 70 i=1,nk1
+          z(i) = 0.
+          do 70 j=1,kk1
+            a1(i,j) = 0.
+  70    continue
+        n7 = nk1-k
+        n10 = n7-kk
+        jper = 0
+        fp = 0.
+        l = k1
+        do 290 it=1,m1
+c  fetch the current data point x(it),y(it)
+          xi = x(it)
+          wi = w(it)
+          yi = y(it)*wi
+c  search for knot interval t(l) <= xi < t(l+1).
+  80      if(xi.lt.t(l+1)) go to 85
+          l = l+1
+          go to 80
+c  evaluate the (k+1) non-zero b-splines at xi and store them in q.
+  85      call fpbspl(t,n,k,xi,l,h)
+          do 90 i=1,k1
+            q(it,i) = h(i)
+            h(i) = h(i)*wi
+  90      continue
+          l5 = l-k1
+c  test whether the b-splines nj,k+1(x),j=1+n7,...nk1 are all zero at xi
+          if(l5.lt.n10) go to 285
+          if(jper.ne.0) go to 160
+c  initialize the matrix a2.
+          do 95 i=1,n7
+          do 95 j=1,kk
+              a2(i,j) = 0.
+  95      continue
+          jk = n10+1
+          do 110 i=1,kk
+            ik = jk
+            do 100 j=1,kk1
+              if(ik.le.0) go to 105
+              a2(ik,i) = a1(ik,j)
+              ik = ik-1
+ 100        continue
+ 105        jk = jk+1
+ 110      continue
+          jper = 1
+c  if one of the b-splines nj,k+1(x),j=n7+1,...nk1 is not zero at xi
+c  we take account of condition (**) for setting up the new row
+c  of the observation matrix a. this row is stored in the arrays h1
+c  (the part with respect to a1) and h2 (the part with
+c  respect to a2).
+ 160      do 170 i=1,kk
+            h1(i) = 0.
+            h2(i) = 0.
+ 170      continue
+          h1(kk1) = 0.
+          j = l5-n10
+          do 210 i=1,kk1
+            j = j+1
+            l0 = j
+ 180        l1 = l0-kk
+            if(l1.le.0) go to 200
+            if(l1.le.n10) go to 190
+            l0 = l1-n10
+            go to 180
+ 190        h1(l1) = h(i)
+            go to 210
+ 200        h2(l0) = h2(l0)+h(i)
+ 210      continue
+c  rotate the new row of the observation matrix into triangle
+c  by givens transformations.
+          if(n10.le.0) go to 250
+c  rotation with the rows 1,2,...n10 of matrix a.
+          do 240 j=1,n10
+            piv = h1(1)
+            if(piv.ne.0.) go to 214
+            do 212 i=1,kk
+              h1(i) = h1(i+1)
+ 212        continue
+            h1(kk1) = 0.
+            go to 240
+c  calculate the parameters of the givens transformation.
+ 214        call fpgivs(piv,a1(j,1),cos,sin)
+c  transformation to the right hand side.
+            call fprota(cos,sin,yi,z(j))
+c  transformations to the left hand side with respect to a2.
+            do 220 i=1,kk
+              call fprota(cos,sin,h2(i),a2(j,i))
+ 220        continue
+            if(j.eq.n10) go to 250
+            i2 = min0(n10-j,kk)
+c  transformations to the left hand side with respect to a1.
+            do 230 i=1,i2
+              i1 = i+1
+              call fprota(cos,sin,h1(i1),a1(j,i1))
+              h1(i) = h1(i1)
+ 230        continue
+            h1(i1) = 0.
+ 240      continue
+c  rotation with the rows n10+1,...n7 of matrix a.
+ 250      do 270 j=1,kk
+            ij = n10+j
+            if(ij.le.0) go to 270
+            piv = h2(j)
+            if(piv.eq.0.) go to 270
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a2(ij,j),cos,sin)
+c  transformations to right hand side.
+            call fprota(cos,sin,yi,z(ij))
+            if(j.eq.kk) go to 280
+            j1 = j+1
+c  transformations to left hand side.
+            do 260 i=j1,kk
+              call fprota(cos,sin,h2(i),a2(ij,i))
+ 260        continue
+ 270      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 280      fp = fp+yi**2
+          go to 290
+c  rotation of the new row of the observation matrix into
+c  triangle in case the b-splines nj,k+1(x),j=n7+1,...n-k-1 are all zero
+c  at xi.
+ 285      j = l5
+          do 140 i=1,kk1
+            j = j+1
+            piv = h(i)
+            if(piv.eq.0.) go to 140
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a1(j,1),cos,sin)
+c  transformations to right hand side.
+            call fprota(cos,sin,yi,z(j))
+            if(i.eq.kk1) go to 150
+            i2 = 1
+            i3 = i+1
+c  transformations to left hand side.
+            do 130 i1=i3,kk1
+              i2 = i2+1
+              call fprota(cos,sin,h(i1),a1(j,i2))
+ 130        continue
+ 140      continue
+c  add contribution of this row to the sum of squares of residual
+c  right hand sides.
+ 150      fp = fp+yi**2
+ 290    continue
+        fpint(n) = fp0
+        fpint(n-1) = fpold
+        nrdata(n) = nplus
+c  backward substitution to obtain the b-spline coefficients c(j),j=1,.n
+        call fpbacp(a1,a2,z,n7,kk,c,kk1,nest)
+c  calculate from condition (**) the coefficients c(j+n7),j=1,2,...k.
+        do 295 i=1,k
+          j = i+n7
+          c(j) = c(i)
+ 295    continue
+        if(iopt.lt.0) go to 660
+c  test whether the approximation sinf(x) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 660
+c  if f(p=inf) < s accept the choice of knots.
+        if(fpms.lt.0.) go to 350
+c  if n=nmax, sinf(x) is an interpolating spline.
+        if(n.eq.nmax) go to 630
+c  increase the number of knots.
+c  if n=nest we cannot increase the number of knots because of the
+c  storage capacity limitation.
+        if(n.eq.nest) go to 620
+c  determine the number of knots nplus we are going to add.
+        npl1 = nplus*2
+        rn = nplus
+        if(fpold-fp.gt.acc) npl1 = rn*fpms/(fpold-fp)
+        nplus = min0(nplus*2,max0(npl1,nplus/2,1))
+        fpold = fp
+c  compute the sum(wi*(yi-s(xi))**2) for each knot interval
+c  t(j+k) <= xi <= t(j+k+1) and store it in fpint(j),j=1,2,...nrint.
+        fpart = 0.
+        i = 1
+        l = k1
+        do 320 it=1,m1
+          if(x(it).lt.t(l)) go to 300
+          new = 1
+          l = l+1
+ 300      term = 0.
+          l0 = l-k2
+          do 310 j=1,k1
+            l0 = l0+1
+            term = term+c(l0)*q(it,j)
+ 310      continue
+          term = (w(it)*(term-y(it)))**2
+          fpart = fpart+term
+          if(new.eq.0) go to 320
+          if(l.gt.k2) go to 315
+          fpint(nrint) = term
+          new = 0
+          go to 320
+ 315      store = term*half
+          fpint(i) = fpart-store
+          i = i+1
+          fpart = store
+          new = 0
+ 320    continue
+        fpint(nrint) = fpint(nrint)+fpart
+        do 330 l=1,nplus
+c  add a new knot
+          call fpknot(x,m,t,n,fpint,nrdata,nrint,nest,1)
+c  if n=nmax we locate the knots as for interpolation.
+          if(n.eq.nmax) go to 5
+c  test whether we cannot further increase the number of knots.
+          if(n.eq.nest) go to 340
+ 330    continue
+c  restart the computations with the new set of knots.
+ 340  continue
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 2: determination of the smoothing periodic spline sp(x).       c
+c  *************************************************************       c
+c  we have determined the number of knots and their position.          c
+c  we now compute the b-spline coefficients of the smoothing spline    c
+c  sp(x). the observation matrix a is extended by the rows of matrix   c
+c  b expressing that the kth derivative discontinuities of sp(x) at    c
+c  the interior knots t(k+2),...t(n-k-1) must be zero. the corres-     c
+c  ponding weights of these additional rows are set to 1/sqrt(p).      c
+c  iteratively we then have to determine the value of p such that      c
+c  f(p)=sum(w(i)*(y(i)-sp(x(i)))**2) be = s. we already know that      c
+c  the least-squares constant function corresponds to p=0, and that    c
+c  the least-squares periodic spline corresponds to p=infinity. the    c
+c  iteration process which is proposed here, makes use of rational     c
+c  interpolation. since f(p) is a convex and strictly decreasing       c
+c  function of p, it can be approximated by a rational function        c
+c  r(p) = (u*p+v)/(p+w). three values of p(p1,p2,p3) with correspond-  c
+c  ing values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used      c
+c  to calculate the new value of p such that r(p)=s. convergence is    c
+c  guaranteed by taking f1>0 and f3<0.                                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jump of the kth derivative of the
+c  b-splines at the knots t(l),l=k+2,...n-k-1 and store in b.
+ 350  call fpdisc(t,n,k2,b,nest)
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      n11 = n10-1
+      n8 = n7-1
+      p = 0.
+      l = n7
+      do 352 i=1,k
+         j = k+1-i
+         p = p+a2(l,j)
+         l = l-1
+         if(l.eq.0) go to 356
+ 352  continue
+      do 354 i=1,n10
+         p = p+a1(i,1)
+ 354  continue
+ 356  rn = n7
+      p = rn/p
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p) = s.
+      do 595 iter=1,maxit
+c  form the matrix g  as the matrix a extended by the rows of matrix b.
+c  the rows of matrix b with weight 1/p are rotated into
+c  the triangularised observation matrix a.
+c  after triangularisation our n7 x n7 matrix g takes the form
+c            ! g1 '    !
+c        g = !    ' g2 !
+c            ! 0  '    !
+c  with g2 a n7 x (k+1) matrix and g1 a n11 x n11 upper triangular
+c  matrix of bandwidth k+2. ( n11 = n7-k-1)
+        pinv = one/p
+c  store matrix a into g
+        do 360 i=1,n7
+          c(i) = z(i)
+          g1(i,k1) = a1(i,k1)
+          g1(i,k2) = 0.
+          g2(i,1) = 0.
+          do 360 j=1,k
+            g1(i,j) = a1(i,j)
+            g2(i,j+1) = a2(i,j)
+ 360    continue
+        l = n10
+        do 370 j=1,k1
+          if(l.le.0) go to 375
+          g2(l,1) = a1(l,j)
+          l = l-1
+ 370    continue
+ 375    do 540 it=1,n8
+c  fetch a new row of matrix b and store it in the arrays h1 (the part
+c  with respect to g1) and h2 (the part with respect to g2).
+          yi = 0.
+          do 380 i=1,k1
+            h1(i) = 0.
+            h2(i) = 0.
+ 380      continue
+          h1(k2) = 0.
+          if(it.gt.n11) go to 420
+          l = it
+          l0 = it
+          do 390 j=1,k2
+            if(l0.eq.n10) go to 400
+            h1(j) = b(it,j)*pinv
+            l0 = l0+1
+ 390      continue
+          go to 470
+ 400      l0 = 1
+          do 410 l1=j,k2
+            h2(l0) = b(it,l1)*pinv
+            l0 = l0+1
+ 410      continue
+          go to 470
+ 420      l = 1
+          i = it-n10
+          do 460 j=1,k2
+            i = i+1
+            l0 = i
+ 430        l1 = l0-k1
+            if(l1.le.0) go to 450
+            if(l1.le.n11) go to 440
+            l0 = l1-n11
+            go to 430
+ 440        h1(l1) = b(it,j)*pinv
+            go to 460
+ 450        h2(l0) = h2(l0)+b(it,j)*pinv
+ 460      continue
+          if(n11.le.0) go to 510
+c  rotate this row into triangle by givens transformations without
+c  square roots.
+c  rotation with the rows l,l+1,...n11.
+ 470      do 500 j=l,n11
+            piv = h1(1)
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,g1(j,1),cos,sin)
+c  transformation to right hand side.
+            call fprota(cos,sin,yi,c(j))
+c  transformation to the left hand side with respect to g2.
+            do 480 i=1,k1
+              call fprota(cos,sin,h2(i),g2(j,i))
+ 480        continue
+            if(j.eq.n11) go to 510
+            i2 = min0(n11-j,k1)
+c  transformation to the left hand side with respect to g1.
+            do 490 i=1,i2
+              i1 = i+1
+              call fprota(cos,sin,h1(i1),g1(j,i1))
+              h1(i) = h1(i1)
+ 490        continue
+            h1(i1) = 0.
+ 500      continue
+c  rotation with the rows n11+1,...n7
+ 510      do 530 j=1,k1
+            ij = n11+j
+            if(ij.le.0) go to 530
+            piv = h2(j)
+c  calculate the parameters of the givens transformation
+            call fpgivs(piv,g2(ij,j),cos,sin)
+c  transformation to the right hand side.
+            call fprota(cos,sin,yi,c(ij))
+            if(j.eq.k1) go to 540
+            j1 = j+1
+c  transformation to the left hand side.
+            do 520 i=j1,k1
+              call fprota(cos,sin,h2(i),g2(ij,i))
+ 520        continue
+ 530      continue
+ 540    continue
+c  backward substitution to obtain the b-spline coefficients
+c  c(j),j=1,2,...n7 of sp(x).
+        call fpbacp(g1,g2,c,n7,k1,c,k2,nest)
+c  calculate from condition (**) the b-spline coefficients c(n7+j),j=1,.
+        do 545 i=1,k
+          j = i+n7
+          c(j) = c(i)
+ 545    continue
+c  computation of f(p).
+        fp = 0.
+        l = k1
+        do 570 it=1,m1
+          if(x(it).lt.t(l)) go to 550
+          l = l+1
+ 550      l0 = l-k2
+          term = 0.
+          do 560 j=1,k1
+            l0 = l0+1
+            term = term+c(l0)*q(it,j)
+ 560      continue
+          fp = fp+(w(it)*(term-y(it)))**2
+ 570    continue
+c  test whether the approximation sp(x) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 660
+c  test whether the maximal number of iterations is reached.
+        if(iter.eq.maxit) go to 600
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 580
+        if((f2-f3) .gt. acc) go to 575
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 +p2*con1
+        go to 595
+ 575    if(f2.lt.0.) ich3 = 1
+ 580    if(ich1.ne.0) go to 590
+        if((f1-f2) .gt. acc) go to 585
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 595
+        if(p.ge.p3) p = p2*con1 +p3*con9
+        go to 595
+ 585    if(f2.gt.0.) ich1 = 1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 590    if(f2.ge.f1 .or. f2.le.f3) go to 610
+c  find the new value for p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 595  continue
+c  error codes and messages.
+ 600  ier = 3
+      go to 660
+ 610  ier = 2
+      go to 660
+ 620  ier = 1
+      go to 660
+ 630  ier = -1
+      go to 660
+ 640  ier = -2
+c  the least-squares constant function c1 is a solution of our problem.
+c  a constant function is a spline of degree k with all b-spline
+c  coefficients equal to that constant c1.
+      do 650 i=1,k1
+        rn = k1-i
+        t(i) = x(1)-rn*per
+        c(i) = c1
+        j = i+k1
+        rn = i-1
+        t(j) = x(m)+rn*per
+ 650  continue
+      n = nmin
+      fp = fp0
+      fpint(n) = fp0
+      fpint(n-1) = 0.
+      nrdata(n) = 0
+ 660  return
+      end

Added: branches/Interpolate1D/fitpack/fppocu.f
===================================================================
--- branches/Interpolate1D/fitpack/fppocu.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fppocu.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,72 @@
+      subroutine fppocu(idim,k,a,b,ib,db,nb,ie,de,ne,cp,np)
+c  subroutine fppocu finds a idim-dimensional polynomial curve p(u) =
+c  (p1(u),p2(u),...,pidim(u)) of degree k, satisfying certain derivative
+c  constraints at the end points a and b, i.e.
+c                  (l)
+c    if ib > 0 : pj   (a) = db(idim*l+j), l=0,1,...,ib-1
+c                  (l)
+c    if ie > 0 : pj   (b) = de(idim*l+j), l=0,1,...,ie-1
+c
+c  the polynomial curve is returned in its b-spline representation
+c  ( coefficients cp(j), j=1,2,...,np )
+c  ..
+c  ..scalar arguments..
+      integer idim,k,ib,nb,ie,ne,np
+      real*8 a,b
+c  ..array arguments..
+      real*8 db(nb),de(ne),cp(np)
+c  ..local scalars..
+      real*8 ab,aki
+      integer i,id,j,jj,l,ll,k1,k2
+c  ..local array..
+      real*8 work(6,6)
+c  ..
+      k1 = k+1
+      k2 = 2*k1
+      ab = b-a
+      do 110 id=1,idim
+        do 10 j=1,k1
+          work(j,1) = 0.
+  10    continue
+        if(ib.eq.0) go to 50
+        l = id
+        do 20 i=1,ib
+          work(1,i) = db(l)
+          l = l+idim
+  20    continue
+        if(ib.eq.1) go to 50
+        ll = ib
+        do 40 j=2,ib
+          ll =  ll-1
+          do 30 i=1,ll
+            aki = k1-i
+            work(j,i) = ab*work(j-1,i+1)/aki + work(j-1,i)
+  30      continue
+  40    continue
+  50    if(ie.eq.0) go to 90
+        l = id
+        j = k1
+        do 60 i=1,ie
+          work(j,i) = de(l)
+          l = l+idim
+          j = j-1
+  60    continue
+        if(ie.eq.1) go to 90
+        ll = ie
+        do 80 jj=2,ie
+          ll =  ll-1
+          j = k1+1-jj
+          do 70 i=1,ll
+            aki = k1-i
+            work(j,i) = work(j+1,i) - ab*work(j,i+1)/aki
+            j = j-1
+  70      continue
+  80    continue
+  90    l = (id-1)*k2
+        do 100 j=1,k1
+          l = l+1
+          cp(l) = work(j,1)
+ 100    continue
+ 110  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fppogr.f
===================================================================
--- branches/Interpolate1D/fitpack/fppogr.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fppogr.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,410 @@
+      subroutine fppogr(iopt,ider,u,mu,v,mv,z,mz,z0,r,s,nuest,nvest,
+     * tol,maxit,nc,nu,tu,nv,tv,c,fp,fp0,fpold,reducu,reducv,fpintu,
+     * fpintv,dz,step,lastdi,nplusu,nplusv,lasttu,nru,nrv,nrdatu,
+     * nrdatv,wrk,lwrk,ier)
+c  ..
+c  ..scalar arguments..
+      integer mu,mv,mz,nuest,nvest,maxit,nc,nu,nv,lastdi,nplusu,nplusv,
+     * lasttu,lwrk,ier
+      real*8 z0,r,s,tol,fp,fp0,fpold,reducu,reducv,step
+c  ..array arguments..
+      integer iopt(3),ider(2),nrdatu(nuest),nrdatv(nvest),nru(mu),
+     * nrv(mv)
+      real*8 u(mu),v(mv),z(mz),tu(nuest),tv(nvest),c(nc),fpintu(nuest),
+     * fpintv(nvest),dz(3),wrk(lwrk)
+c  ..local scalars..
+      real*8 acc,fpms,f1,f2,f3,p,per,pi,p1,p2,p3,vb,ve,zmax,zmin,rn,one,
+     *
+     * con1,con4,con9
+      integer i,ich1,ich3,ifbu,ifbv,ifsu,ifsv,istart,iter,i1,i2,j,ju,
+     * ktu,l,l1,l2,l3,l4,mpm,mumin,mu0,mu1,nn,nplu,nplv,npl1,nrintu,
+     * nrintv,nue,numax,nve,nvmax
+c  ..local arrays..
+      integer idd(2)
+      real*8 dzz(3)
+c  ..function references..
+      real*8 abs,datan2,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpknot,fpopdi
+c  ..
+c   set constants
+      one = 1d0
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+c   initialization
+      ifsu = 0
+      ifsv = 0
+      ifbu = 0
+      ifbv = 0
+      p = -one
+      mumin = 4-iopt(3)
+      if(ider(1).ge.0) mumin = mumin-1
+      if(iopt(2).eq.1 .and. ider(2).eq.1) mumin = mumin-1
+      pi = datan2(0d0,-one)
+      per = pi+pi
+      vb = v(1)
+      ve = vb+per
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 1: determination of the number of knots and their position.     c
+c ****************************************************************     c
+c  given a set of knots we compute the least-squares spline sinf(u,v)  c
+c  and the corresponding sum of squared residuals fp = f(p=inf).       c
+c  if iopt(1)=-1  sinf(u,v) is the requested approximation.            c
+c  if iopt(1)>=0  we check whether we can accept the knots:            c
+c    if fp <= s we will continue with the current set of knots.        c
+c    if fp >  s we will increase the number of knots and compute the   c
+c       corresponding least-squares spline until finally fp <= s.      c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c     knots in the u-direction equals nu=numax=mu+5+iopt(2)+iopt(3)    c
+c     and in the v-direction nv=nvmax=mv+7.                            c
+c    if s>0 and                                                        c
+c      iopt(1)=0 we first compute the least-squares polynomial,i.e. a  c
+c       spline without interior knots : nu=8 ; nv=8.                   c
+c      iopt(1)=1 we start with the set of knots found at the last call c
+c       of the routine, except for the case that s > fp0; then we      c
+c       compute the least-squares polynomial directly.                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+      if(iopt(1).lt.0) go to 120
+c  acc denotes the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  numax and nvmax denote the number of knots needed for interpolation.
+      numax = mu+5+iopt(2)+iopt(3)
+      nvmax = mv+7
+      nue = min0(numax,nuest)
+      nve = min0(nvmax,nvest)
+      if(s.gt.0.) go to 100
+c  if s = 0, s(u,v) is an interpolating spline.
+      nu = numax
+      nv = nvmax
+c  test whether the required storage space exceeds the available one.
+      if(nu.gt.nuest .or. nv.gt.nvest) go to 420
+c  find the position of the knots in the v-direction.
+      do 10 l=1,mv
+        tv(l+3) = v(l)
+  10  continue
+      tv(mv+4) = ve
+      l1 = mv-2
+      l2 = mv+5
+      do 20 i=1,3
+         tv(i) = v(l1)-per
+         tv(l2) = v(i+1)+per
+         l1 = l1+1
+         l2 = l2+1
+  20  continue
+c  if not all the derivative values g(i,j) are given, we will first
+c  estimate these values by computing a least-squares spline
+      idd(1) = ider(1)
+      if(idd(1).eq.0) idd(1) = 1
+      if(idd(1).gt.0) dz(1) = z0
+      idd(2) = ider(2)
+      if(ider(1).lt.0) go to 30
+      if(iopt(2).eq.0 .or. ider(2).ne.0) go to 70
+c we set up the knots in the u-direction for computing the least-squares
+c spline.
+  30  i1 = 3
+      i2 = mu-2
+      nu = 4
+      do 40 i=1,mu
+         if(i1.gt.i2) go to 50
+         nu = nu+1
+         tu(nu) = u(i1)
+         i1 = i1+2
+  40  continue
+  50  do 60 i=1,4
+         tu(i) = 0.
+         nu = nu+1
+         tu(nu) = r
+  60  continue
+c we compute the least-squares spline for estimating the derivatives.
+      call fpopdi(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,z,mz,z0,dz,iopt,idd,
+     *  tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,nrv,
+     *  wrk,lwrk)
+      ifsu = 0
+c if all the derivatives at the origin are known, we compute the
+c interpolating spline.
+c we set up the knots in the u-direction, needed for interpolation.
+  70  nn = numax-8
+      if(nn.eq.0) go to 95
+      ju = 2-iopt(2)
+      do 80 l=1,nn
+        tu(l+4) = u(ju)
+        ju = ju+1
+  80  continue
+      nu = numax
+      l = nu
+      do 90 i=1,4
+         tu(i) = 0.
+         tu(l) = r
+         l = l-1
+  90  continue
+c we compute the interpolating spline.
+  95  call fpopdi(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,z,mz,z0,dz,iopt,idd,
+     *  tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,nrv,
+     *  wrk,lwrk)
+      go to 430
+c  if s>0 our initial choice of knots depends on the value of iopt(1).
+ 100  ier = 0
+      if(iopt(1).eq.0) go to 115
+      step = -step
+      if(fp0.le.s) go to 115
+c  if iopt(1)=1 and fp0 > s we start computing the least-squares spline
+c  according to the set of knots found at the last call of the routine.
+c  we determine the number of grid coordinates u(i) inside each knot
+c  interval (tu(l),tu(l+1)).
+      l = 5
+      j = 1
+      nrdatu(1) = 0
+      mu0 = 2-iopt(2)
+      mu1 = mu-2+iopt(3)
+      do 105 i=mu0,mu1
+        nrdatu(j) = nrdatu(j)+1
+        if(u(i).lt.tu(l)) go to 105
+        nrdatu(j) = nrdatu(j)-1
+        l = l+1
+        j = j+1
+        nrdatu(j) = 0
+ 105  continue
+c  we determine the number of grid coordinates v(i) inside each knot
+c  interval (tv(l),tv(l+1)).
+      l = 5
+      j = 1
+      nrdatv(1) = 0
+      do 110 i=2,mv
+        nrdatv(j) = nrdatv(j)+1
+        if(v(i).lt.tv(l)) go to 110
+        nrdatv(j) = nrdatv(j)-1
+        l = l+1
+        j = j+1
+        nrdatv(j) = 0
+ 110  continue
+      idd(1) = ider(1)
+      idd(2) = ider(2)
+      go to 120
+c  if iopt(1)=0 or iopt(1)=1 and s >= fp0,we start computing the least-
+c  squares polynomial (which is a spline without interior knots).
+ 115  ier = -2
+      idd(1) = ider(1)
+      idd(2) = 1
+      nu = 8
+      nv = 8
+      nrdatu(1) = mu-3+iopt(2)+iopt(3)
+      nrdatv(1) = mv-1
+      lastdi = 0
+      nplusu = 0
+      nplusv = 0
+      fp0 = 0.
+      fpold = 0.
+      reducu = 0.
+      reducv = 0.
+c  main loop for the different sets of knots.mpm=mu+mv is a save upper
+c  bound for the number of trials.
+ 120  mpm = mu+mv
+      do 270 iter=1,mpm
+c  find nrintu (nrintv) which is the number of knot intervals in the
+c  u-direction (v-direction).
+        nrintu = nu-7
+        nrintv = nv-7
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(u,v).
+        i = nu
+        do 130 j=1,4
+          tu(j) = 0.
+          tu(i) = r
+          i = i-1
+ 130    continue
+        l1 = 4
+        l2 = l1
+        l3 = nv-3
+        l4 = l3
+        tv(l2) = vb
+        tv(l3) = ve
+        do 140 j=1,3
+          l1 = l1+1
+          l2 = l2-1
+          l3 = l3+1
+          l4 = l4-1
+          tv(l2) = tv(l4)-per
+          tv(l3) = tv(l1)+per
+ 140    continue
+c  find an estimate of the range of possible values for the optimal
+c  derivatives at the origin.
+        ktu = nrdatu(1)+2-iopt(2)
+        if(nrintu.eq.1) ktu = mu
+        if(ktu.lt.mumin) ktu = mumin
+        if(ktu.eq.lasttu) go to 150
+         zmin = z0
+         zmax = z0
+         l = mv*ktu
+         do 145 i=1,l
+            if(z(i).lt.zmin) zmin = z(i)
+            if(z(i).gt.zmax) zmax = z(i)
+ 145     continue
+         step = zmax-zmin
+         lasttu = ktu
+c  find the least-squares spline sinf(u,v).
+ 150    call fpopdi(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,z,mz,z0,dz,iopt,idd,
+     *   tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,nrv,
+     *   wrk,lwrk)
+        if(step.lt.0.) step = -step
+        if(ier.eq.(-2)) fp0 = fp
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt(1).lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms) .lt. acc) go to 440
+c  if f(p=inf) < s, we accept the choice of knots.
+        if(fpms.lt.0.) go to 300
+c  if nu=numax and nv=nvmax, sinf(u,v) is an interpolating spline
+        if(nu.eq.numax .and. nv.eq.nvmax) go to 430
+c  increase the number of knots.
+c  if nu=nue and nv=nve we cannot further increase the number of knots
+c  because of the storage capacity limitation.
+        if(nu.eq.nue .and. nv.eq.nve) go to 420
+        if(ider(1).eq.0) fpintu(1) = fpintu(1)+(z0-c(1))**2
+        ier = 0
+c  adjust the parameter reducu or reducv according to the direction
+c  in which the last added knots were located.
+        if (lastdi.lt.0) go to 160
+        if (lastdi.eq.0) go to 155
+        go to 170
+ 155     nplv = 3
+         idd(2) = ider(2)
+         fpold = fp
+         go to 230
+ 160    reducu = fpold-fp
+        go to 175
+ 170    reducv = fpold-fp
+c  store the sum of squared residuals for the current set of knots.
+ 175    fpold = fp
+c  find nplu, the number of knots we should add in the u-direction.
+        nplu = 1
+        if(nu.eq.8) go to 180
+        npl1 = nplusu*2
+        rn = nplusu
+        if(reducu.gt.acc) npl1 = rn*fpms/reducu
+        nplu = min0(nplusu*2,max0(npl1,nplusu/2,1))
+c  find nplv, the number of knots we should add in the v-direction.
+ 180    nplv = 3
+        if(nv.eq.8) go to 190
+        npl1 = nplusv*2
+        rn = nplusv
+        if(reducv.gt.acc) npl1 = rn*fpms/reducv
+        nplv = min0(nplusv*2,max0(npl1,nplusv/2,1))
+c  test whether we are going to add knots in the u- or v-direction.
+ 190    if (nplu.lt.nplv) go to 210
+        if (nplu.eq.nplv) go to 200
+        go to 230
+ 200    if(lastdi.lt.0) go to 230
+ 210    if(nu.eq.nue) go to 230
+c  addition in the u-direction.
+        lastdi = -1
+        nplusu = nplu
+        ifsu = 0
+        istart = 0
+        if(iopt(2).eq.0) istart = 1
+        do 220 l=1,nplusu
+c  add a new knot in the u-direction
+          call fpknot(u,mu,tu,nu,fpintu,nrdatu,nrintu,nuest,istart)
+c  test whether we cannot further increase the number of knots in the
+c  u-direction.
+          if(nu.eq.nue) go to 270
+ 220    continue
+        go to 270
+ 230    if(nv.eq.nve) go to 210
+c  addition in the v-direction.
+        lastdi = 1
+        nplusv = nplv
+        ifsv = 0
+        do 240 l=1,nplusv
+c  add a new knot in the v-direction.
+          call fpknot(v,mv,tv,nv,fpintv,nrdatv,nrintv,nvest,1)
+c  test whether we cannot further increase the number of knots in the
+c  v-direction.
+          if(nv.eq.nve) go to 270
+ 240    continue
+c  restart the computations with the new set of knots.
+ 270  continue
+c  test whether the least-squares polynomial is a solution of our
+c  approximation problem.
+ 300  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing spline sp(u,v)                c
+c *****************************************************                c
+c  we have determined the number of knots and their position. we now   c
+c  compute the b-spline coefficients of the smoothing spline sp(u,v).  c
+c  this smoothing spline depends on the parameter p in such a way that c
+c    f(p) = sumi=1,mu(sumj=1,mv((z(i,j)-sp(u(i),v(j)))**2)             c
+c  is a continuous, strictly decreasing function of p. moreover the    c
+c  least-squares polynomial corresponds to p=0 and the least-squares   c
+c  spline to p=infinity. then iteratively we have to determine the     c
+c  positive value of p such that f(p)=s. the process which is proposed c
+c  here makes use of rational interpolation. f(p) is approximated by a c
+c  rational function r(p)=(u*p+v)/(p+w); three values of p (p1,p2,p3)  c
+c  with corresponding values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s)c
+c  are used to calculate the new value of p such that r(p)=s.          c
+c  convergence is guaranteed by taking f1 > 0 and f3 < 0.              c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = one
+      dzz(1) = dz(1)
+      dzz(2) = dz(2)
+      dzz(3) = dz(3)
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p)=s.
+      do 350 iter = 1,maxit
+c  find the smoothing spline sp(u,v) and the corresponding sum f(p).
+        call fpopdi(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,z,mz,z0,dzz,iopt,idd,
+     *   tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,nrv,
+     *   wrk,lwrk)
+c  test whether the approximation sp(u,v) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 320
+        if((f2-f3).gt.acc) go to 310
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 350
+ 310    if(f2.lt.0.) ich3 = 1
+ 320    if(ich1.ne.0) go to 340
+        if((f1-f2).gt.acc) go to 330
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 350
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 350
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 330    if(f2.gt.0.) ich1 = 1
+ 340    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 350  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+      fp = 0.
+ 440  return
+      end

Added: branches/Interpolate1D/fitpack/fppola.f
===================================================================
--- branches/Interpolate1D/fitpack/fppola.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fppola.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,840 @@
+      subroutine fppola(iopt1,iopt2,iopt3,m,u,v,z,w,rad,s,nuest,nvest,
+     * eta,tol,maxit,ib1,ib3,nc,ncc,intest,nrest,nu,tu,nv,tv,c,fp,sup,
+     * fpint,coord,f,ff,row,cs,cosi,a,q,bu,bv,spu,spv,h,index,nummer,
+     * wrk,lwrk,ier)
+c  ..scalar arguments..
+      integer iopt1,iopt2,iopt3,m,nuest,nvest,maxit,ib1,ib3,nc,ncc,
+     * intest,nrest,nu,nv,lwrk,ier
+      real*8 s,eta,tol,fp,sup
+c  ..array arguments..
+      integer index(nrest),nummer(m)
+      real*8 u(m),v(m),z(m),w(m),tu(nuest),tv(nvest),c(nc),fpint(intest)
+     *,
+     * coord(intest),f(ncc),ff(nc),row(nvest),cs(nvest),cosi(5,nvest),
+     * a(ncc,ib1),q(ncc,ib3),bu(nuest,5),bv(nvest,5),spu(m,4),spv(m,4),
+     * h(ib3),wrk(lwrk)
+c  ..user supplied function..
+      real*8 rad
+c  ..local scalars..
+      real*8 acc,arg,co,c1,c2,c3,c4,dmax,eps,fac,fac1,fac2,fpmax,fpms,
+     * f1,f2,f3,hui,huj,p,pi,pinv,piv,pi2,p1,p2,p3,r,ratio,si,sigma,
+     * sq,store,uu,u2,u3,wi,zi,rn,one,two,three,con1,con4,con9,half,ten
+      integer i,iband,iband3,iband4,ich1,ich3,ii,il,in,ipar,ipar1,irot,
+     * iter,i1,i2,i3,j,jl,jrot,j1,j2,k,l,la,lf,lh,ll,lu,lv,lwest,l1,l2,
+     * l3,l4,ncof,ncoff,nvv,nv4,nreg,nrint,nrr,nr1,nuu,nu4,num,num1,
+     * numin,nvmin,rank,iband1
+c  ..local arrays..
+      real*8 hu(4),hv(4)
+c  ..function references..
+      real*8 abs,atan,cos,fprati,sin,sqrt
+      integer min0
+c  ..subroutine references..
+c    fporde,fpbspl,fpback,fpgivs,fprota,fprank,fpdisc,fprppo
+c  ..
+c  set constants
+      one = 1
+      two = 2
+      three = 3
+      ten = 10
+      half = 0.5e0
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      pi = atan(one)*4
+      pi2 = pi+pi
+      ipar = iopt2*(iopt2+3)/2
+      ipar1 = ipar+1
+      eps = sqrt(eta)
+      if(iopt1.lt.0) go to 90
+      numin = 9
+      nvmin = 9+iopt2*(iopt2+1)
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+      if(iopt1.eq.0) go to 10
+      if(s.lt.sup) then
+        if (nv.lt.nvmin) go to 70
+        go to 90
+      endif
+c  if iopt1 = 0 we begin by computing the weighted least-squares
+c  polymomial of the form
+c     s(u,v) = f(1)*(1-u**3)+f(2)*u**3+f(3)*(u**2-u**3)+f(4)*(u-u**3)
+c  where f(4) = 0 if iopt2> 0 , f(3) = 0 if iopt2 > 1 and
+c        f(2) = 0 if iopt3> 0.
+c  the corresponding weighted sum of squared residuals gives the upper
+c  bound sup for the smoothing factor s.
+  10  sup = 0.
+      do 20 i=1,4
+         f(i) = 0.
+         do 20 j=1,4
+            a(i,j) = 0.
+ 20   continue
+      do 50 i=1,m
+         wi = w(i)
+         zi = z(i)*wi
+         uu = u(i)
+         u2 = uu*uu
+         u3 = uu*u2
+         h(1) = (one-u3)*wi
+         h(2) = u3*wi
+         h(3) = u2*(one-uu)*wi
+         h(4) = uu*(one-u2)*wi
+         if(iopt3.ne.0) h(2) = 0.
+         if(iopt2.gt.1) h(3) = 0.
+         if(iopt2.gt.0) h(4) = 0.
+         do 40 j=1,4
+            piv = h(j)
+            if(piv.eq.0.) go to 40
+            call fpgivs(piv,a(j,1),co,si)
+            call fprota(co,si,zi,f(j))
+            if(j.eq.4) go to 40
+            j1 = j+1
+            j2 = 1
+            do 30 l=j1,4
+               j2 = j2+1
+               call fprota(co,si,h(l),a(j,j2))
+  30        continue
+  40     continue
+         sup = sup+zi*zi
+  50  continue
+      if(a(4,1).ne.0.) f(4) = f(4)/a(4,1)
+      if(a(3,1).ne.0.) f(3) = (f(3)-a(3,2)*f(4))/a(3,1)
+      if(a(2,1).ne.0.) f(2) = (f(2)-a(2,2)*f(3)-a(2,3)*f(4))/a(2,1)
+      if(a(1,1).ne.0.)
+     * f(1) = (f(1)-a(1,2)*f(2)-a(1,3)*f(3)-a(1,4)*f(4))/a(1,1)
+c  find the b-spline representation of this least-squares polynomial
+      c1 = f(1)
+      c4 = f(2)
+      c2 = f(4)/three+c1
+      c3 = (f(3)+two*f(4))/three+c1
+      nu = 8
+      nv = 8
+      do 60 i=1,4
+         c(i) = c1
+         c(i+4) = c2
+         c(i+8) = c3
+         c(i+12) = c4
+         tu(i) = 0.
+         tu(i+4) = one
+         rn = 2*i-9
+         tv(i) = rn*pi
+         rn = 2*i-1
+         tv(i+4) = rn*pi
+  60  continue
+      fp = sup
+c  test whether the least-squares polynomial is an acceptable solution
+      fpms = sup-s
+      if(fpms.lt.acc) go to 960
+c  test whether we cannot further increase the number of knots.
+  70  if(nuest.lt.numin .or. nvest.lt.nvmin) go to 950
+c  find the initial set of interior knots of the spline in case iopt1=0.
+      nu = numin
+      nv = nvmin
+      tu(5) = half
+      nvv = nv-8
+      rn = nvv+1
+      fac = pi2/rn
+      do 80 i=1,nvv
+         rn = i
+         tv(i+4) = rn*fac-pi
+  80  continue
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1 : computation of least-squares bicubic splines.              c
+c  ******************************************************              c
+c  if iopt1<0 we compute the least-squares bicubic spline according    c
+c  to the given set of knots.                                          c
+c  if iopt1>=0 we compute least-squares bicubic splines with in-       c
+c  creasing numbers of knots until the corresponding sum f(p=inf)<=s.  c
+c  the initial set of knots then depends on the value of iopt1         c
+c    if iopt1=0 we start with one interior knot in the u-direction     c
+c              (0.5) and 1+iopt2*(iopt2+1) in the v-direction.         c
+c    if iopt1>0 we start with the set of knots found at the last       c
+c              call of the routine.                                    c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  main loop for the different sets of knots. m is a save upper bound
+c  for the number of trials.
+  90  do 570 iter=1,m
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(u,v).
+         l1 = 4
+         l2 = l1
+         l3 = nv-3
+         l4 = l3
+         tv(l2) = -pi
+         tv(l3) = pi
+         do 120 i=1,3
+            l1 = l1+1
+            l2 = l2-1
+            l3 = l3+1
+            l4 = l4-1
+            tv(l2) = tv(l4)-pi2
+            tv(l3) = tv(l1)+pi2
+ 120     continue
+        l = nu
+        do 130 i=1,4
+          tu(i) = 0.
+          tu(l) = one
+          l = l-1
+ 130    continue
+c  find nrint, the total number of knot intervals and nreg, the number
+c  of panels in which the approximation domain is subdivided by the
+c  intersection of knots.
+        nuu = nu-7
+        nvv = nv-7
+        nrr = nvv/2
+        nr1 = nrr+1
+        nrint = nuu+nvv
+        nreg = nuu*nvv
+c  arrange the data points according to the panel they belong to.
+        call fporde(u,v,m,3,3,tu,nu,tv,nv,nummer,index,nreg)
+        if(iopt2.eq.0) go to 195
+c  find the b-spline coefficients cosi of the cubic spline
+c  approximations for cr(v)=rad(v)*cos(v) and sr(v) = rad(v)*sin(v)
+c  if iopt2=1, and additionally also for cr(v)**2,sr(v)**2 and
+c  2*cr(v)*sr(v) if iopt2=2
+        do 140 i=1,nvv
+           do 135 j=1,ipar
+              cosi(j,i) = 0.
+ 135       continue
+           do 140 j=1,nvv
+              a(i,j) = 0.
+ 140    continue
+c  the coefficients cosi are obtained from interpolation conditions
+c  at the knots tv(i),i=4,5,...nv-4.
+        do 175 i=1,nvv
+           l2 = i+3
+           arg = tv(l2)
+           call fpbspl(tv,nv,3,arg,l2,hv)
+           do 145 j=1,nvv
+              row(j) = 0.
+ 145       continue
+           ll = i
+           do 150 j=1,3
+              if(ll.gt.nvv) ll= 1
+              row(ll) = row(ll)+hv(j)
+              ll = ll+1
+ 150       continue
+           co = cos(arg)
+           si = sin(arg)
+           r = rad(arg)
+           cs(1) = co*r
+           cs(2) = si*r
+           if(iopt2.eq.1) go to 155
+           cs(3) = cs(1)*cs(1)
+           cs(4) = cs(2)*cs(2)
+           cs(5) = cs(1)*cs(2)
+ 155       do 170 j=1,nvv
+              piv = row(j)
+              if(piv.eq.0.) go to 170
+              call fpgivs(piv,a(j,1),co,si)
+              do 160 l=1,ipar
+                 call fprota(co,si,cs(l),cosi(l,j))
+ 160          continue
+              if(j.eq.nvv) go to 175
+              j1 = j+1
+              j2 = 1
+              do 165 l=j1,nvv
+                 j2 = j2+1
+                 call fprota(co,si,row(l),a(j,j2))
+ 165          continue
+ 170       continue
+ 175    continue
+         do 190 l=1,ipar
+            do 180 j=1,nvv
+               cs(j) = cosi(l,j)
+ 180        continue
+            call fpback(a,cs,nvv,nvv,cs,ncc)
+            do 185 j=1,nvv
+               cosi(l,j) = cs(j)
+ 185        continue
+ 190     continue
+c  find ncof, the dimension of the spline and ncoff, the number
+c  of coefficients in the standard b-spline representation.
+ 195    nu4 = nu-4
+        nv4 = nv-4
+        ncoff = nu4*nv4
+        ncof = ipar1+nvv*(nu4-1-iopt2-iopt3)
+c  find the bandwidth of the observation matrix a.
+        iband = 4*nvv
+        if(nuu-iopt2-iopt3.le.1) iband = ncof
+        iband1 = iband-1
+c  initialize the observation matrix a.
+        do 200 i=1,ncof
+          f(i) = 0.
+          do 200 j=1,iband
+            a(i,j) = 0.
+ 200    continue
+c  initialize the sum of squared residuals.
+        fp = 0.
+        ratio = one+tu(6)/tu(5)
+c  fetch the data points in the new order. main loop for the
+c  different panels.
+        do 380 num=1,nreg
+c  fix certain constants for the current panel; jrot records the column
+c  number of the first non-zero element in a row of the observation
+c  matrix according to a data point of the panel.
+          num1 = num-1
+          lu = num1/nvv
+          l1 = lu+4
+          lv = num1-lu*nvv+1
+          l2 = lv+3
+          jrot = 0
+          if(lu.gt.iopt2) jrot = ipar1+(lu-iopt2-1)*nvv
+          lu = lu+1
+c  test whether there are still data points in the current panel.
+          in = index(num)
+ 210      if(in.eq.0) go to 380
+c  fetch a new data point.
+          wi = w(in)
+          zi = z(in)*wi
+c  evaluate for the u-direction, the 4 non-zero b-splines at u(in)
+          call fpbspl(tu,nu,3,u(in),l1,hu)
+c  evaluate for the v-direction, the 4 non-zero b-splines at v(in)
+          call fpbspl(tv,nv,3,v(in),l2,hv)
+c  store the value of these b-splines in spu and spv resp.
+          do 220 i=1,4
+            spu(in,i) = hu(i)
+            spv(in,i) = hv(i)
+ 220      continue
+c  initialize the new row of observation matrix.
+          do 240 i=1,iband
+            h(i) = 0.
+ 240      continue
+c  calculate the non-zero elements of the new row by making the cross
+c  products of the non-zero b-splines in u- and v-direction and
+c  by taking into account the conditions of the splines.
+          do 250 i=1,nvv
+             row(i) = 0.
+ 250      continue
+c  take into account the periodicity condition of the bicubic splines.
+          ll = lv
+          do 260 i=1,4
+             if(ll.gt.nvv) ll=1
+             row(ll) = row(ll)+hv(i)
+             ll = ll+1
+ 260      continue
+c  take into account the other conditions of the splines.
+          if(iopt2.eq.0 .or. lu.gt.iopt2+1) go to 280
+          do 270 l=1,ipar
+             cs(l) = 0.
+             do 270 i=1,nvv
+                cs(l) = cs(l)+row(i)*cosi(l,i)
+ 270     continue
+c  fill in the non-zero elements of the new row.
+ 280     j1 = 0
+         do 330 j =1,4
+            jlu = j+lu
+            huj = hu(j)
+            if(jlu.gt.iopt2+2) go to 320
+            go to (290,290,300,310),jlu
+ 290        h(1) = huj
+            j1 = 1
+            go to 330
+ 300        h(1) = h(1)+huj
+            h(2) = huj*cs(1)
+            h(3) = huj*cs(2)
+            j1 = 3
+            go to 330
+ 310        h(1) = h(1)+huj
+            h(2) = h(2)+huj*ratio*cs(1)
+            h(3) = h(3)+huj*ratio*cs(2)
+            h(4) = huj*cs(3)
+            h(5) = huj*cs(4)
+            h(6) = huj*cs(5)
+            j1 = 6
+            go to 330
+ 320        if(jlu.gt.nu4 .and. iopt3.ne.0) go to 330
+            do 325 i=1,nvv
+               j1 = j1+1
+               h(j1) = row(i)*huj
+ 325        continue
+ 330      continue
+          do 335 i=1,iband
+            h(i) = h(i)*wi
+ 335      continue
+c  rotate the row into triangle by givens transformations.
+          irot = jrot
+          do 350 i=1,iband
+            irot = irot+1
+            piv = h(i)
+            if(piv.eq.0.) go to 350
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(irot,1),co,si)
+c  apply that transformation to the right hand side.
+            call fprota(co,si,zi,f(irot))
+            if(i.eq.iband) go to 360
+c  apply that transformation to the left hand side.
+            i2 = 1
+            i3 = i+1
+            do 340 j=i3,iband
+              i2 = i2+1
+              call fprota(co,si,h(j),a(irot,i2))
+ 340        continue
+ 350      continue
+c  add the contribution of the row to the sum of squares of residual
+c  right hand sides.
+ 360      fp = fp+zi**2
+c  find the number of the next data point in the panel.
+ 370      in = nummer(in)
+          go to 210
+ 380    continue
+c  find dmax, the maximum value for the diagonal elements in the reduced
+c  triangle.
+        dmax = 0.
+        do 390 i=1,ncof
+          if(a(i,1).le.dmax) go to 390
+          dmax = a(i,1)
+ 390    continue
+c  check whether the observation matrix is rank deficient.
+        sigma = eps*dmax
+        do 400 i=1,ncof
+          if(a(i,1).le.sigma) go to 410
+ 400    continue
+c  backward substitution in case of full rank.
+        call fpback(a,f,ncof,iband,c,ncc)
+        rank = ncof
+        do 405 i=1,ncof
+          q(i,1) = a(i,1)/dmax
+ 405    continue
+        go to 430
+c  in case of rank deficiency, find the minimum norm solution.
+ 410    lwest = ncof*iband+ncof+iband
+        if(lwrk.lt.lwest) go to 925
+        lf = 1
+        lh = lf+ncof
+        la = lh+iband
+        do 420 i=1,ncof
+          ff(i) = f(i)
+          do 420 j=1,iband
+            q(i,j) = a(i,j)
+ 420    continue
+        call fprank(q,ff,ncof,iband,ncc,sigma,c,sq,rank,wrk(la),
+     *   wrk(lf),wrk(lh))
+        do 425 i=1,ncof
+          q(i,1) = q(i,1)/dmax
+ 425    continue
+c  add to the sum of squared residuals, the contribution of reducing
+c  the rank.
+        fp = fp+sq
+c  find the coefficients in the standard b-spline representation of
+c  the spline.
+ 430    call fprppo(nu,nv,iopt2,iopt3,cosi,ratio,c,ff,ncoff)
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt1.lt.0) then
+          if (fp.le.0) go to 970
+          go to 980
+        endif
+        fpms = fp-s
+        if(abs(fpms).le.acc) then
+            if (fp.le.0) go to 970
+            go to 980
+        endif
+c  if f(p=inf) < s, accept the choice of knots.
+        if(fpms.lt.0.) go to 580
+c  test whether we cannot further increase the number of knots
+        if(m.lt.ncof) go to 935
+c  search where to add a new knot.
+c  find for each interval the sum of squared residuals fpint for the
+c  data points having the coordinate belonging to that knot interval.
+c  calculate also coord which is the same sum, weighted by the position
+c  of the data points considered.
+ 440    do 450 i=1,nrint
+          fpint(i) = 0.
+          coord(i) = 0.
+ 450    continue
+        do 490 num=1,nreg
+          num1 = num-1
+          lu = num1/nvv
+          l1 = lu+1
+          lv = num1-lu*nvv
+          l2 = lv+1+nuu
+          jrot = lu*nv4+lv
+          in = index(num)
+ 460      if(in.eq.0) go to 490
+          store = 0.
+          i1 = jrot
+          do 480 i=1,4
+            hui = spu(in,i)
+            j1 = i1
+            do 470 j=1,4
+              j1 = j1+1
+              store = store+hui*spv(in,j)*c(j1)
+ 470        continue
+            i1 = i1+nv4
+ 480      continue
+          store = (w(in)*(z(in)-store))**2
+          fpint(l1) = fpint(l1)+store
+          coord(l1) = coord(l1)+store*u(in)
+          fpint(l2) = fpint(l2)+store
+          coord(l2) = coord(l2)+store*v(in)
+          in = nummer(in)
+          go to 460
+ 490    continue
+c bring together the information concerning knot panels which are
+c symmetric with respect to the origin.
+        do 495 i=1,nrr
+          l1 = nuu+i
+          l2 = l1+nrr
+          fpint(l1) = fpint(l1)+fpint(l2)
+          coord(l1) = coord(l1)+coord(l2)-pi*fpint(l2)
+ 495    continue
+c  find the interval for which fpint is maximal on the condition that
+c  there still can be added a knot.
+        l1 = 1
+        l2 = nuu+nrr
+        if(nuest.lt.nu+1) l1=nuu+1
+        if(nvest.lt.nv+2) l2=nuu
+c  test whether we cannot further increase the number of knots.
+        if(l1.gt.l2) go to 950
+ 500    fpmax = 0.
+        l = 0
+        do 510 i=l1,l2
+          if(fpmax.ge.fpint(i)) go to 510
+          l = i
+          fpmax = fpint(i)
+ 510    continue
+        if(l.eq.0) go to 930
+c  calculate the position of the new knot.
+        arg = coord(l)/fpint(l)
+c  test in what direction the new knot is going to be added.
+        if(l.gt.nuu) go to 530
+c  addition in the u-direction
+        l4 = l+4
+        fpint(l) = 0.
+        fac1 = tu(l4)-arg
+        fac2 = arg-tu(l4-1)
+        if(fac1.gt.(ten*fac2) .or. fac2.gt.(ten*fac1)) go to 500
+        j = nu
+        do 520 i=l4,nu
+          tu(j+1) = tu(j)
+          j = j-1
+ 520    continue
+        tu(l4) = arg
+        nu = nu+1
+        go to 570
+c  addition in the v-direction
+ 530    l4 = l+4-nuu
+        fpint(l) = 0.
+        fac1 = tv(l4)-arg
+        fac2 = arg-tv(l4-1)
+        if(fac1.gt.(ten*fac2) .or. fac2.gt.(ten*fac1)) go to 500
+        ll = nrr+4
+        j = ll
+        do 550 i=l4,ll
+          tv(j+1) = tv(j)
+          j = j-1
+ 550    continue
+        tv(l4) = arg
+        nv = nv+2
+        nrr = nrr+1
+        do 560 i=5,ll
+          j = i+nrr
+          tv(j) = tv(i)+pi
+ 560    continue
+c  restart the computations with the new set of knots.
+ 570  continue
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing bicubic spline.               c
+c ******************************************************               c
+c we have determined the number of knots and their position. we now    c
+c compute the coefficients of the smoothing spline sp(u,v).            c
+c the observation matrix a is extended by the rows of a matrix, expres-c
+c sing that sp(u,v) must be a constant function in the variable        c
+c v and a cubic polynomial in the variable u. the corresponding        c
+c weights of these additional rows are set to 1/(p). iteratively       c
+c we than have to determine the value of p such that f(p) = sum((w(i)* c
+c (z(i)-sp(u(i),v(i))))**2)  be = s.                                   c
+c we already know that the least-squares polynomial corresponds to p=0,c
+c and that the least-squares bicubic spline corresponds to p=infin.    c
+c the iteration process makes use of rational interpolation. since f(p)c
+c is a convex and strictly decreasing function of p, it can be approx- c
+c imated by a rational function of the form r(p) = (u*p+v)/(p+w).      c
+c three values of p (p1,p2,p3) with corresponding values of f(p) (f1=  c
+c f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used to calculate the new value   c
+c of p such that r(p)=s. convergence is guaranteed by taking f1>0,f3<0.c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jumps of the 3-th order derivative of
+c  the b-splines at the knots tu(l),l=5,...,nu-4.
+ 580  call fpdisc(tu,nu,5,bu,nuest)
+c  evaluate the discontinuity jumps of the 3-th order derivative of
+c  the b-splines at the knots tv(l),l=5,...,nv-4.
+      call fpdisc(tv,nv,5,bv,nvest)
+c  initial value for p.
+      p1 = 0.
+      f1 = sup-s
+      p3 = -one
+      f3 = fpms
+      p = 0.
+      do 590 i=1,ncof
+        p = p+a(i,1)
+ 590  continue
+      rn = ncof
+      p = rn/p
+c  find the bandwidth of the extended observation matrix.
+      iband4 = iband+ipar1
+      if(iband4.gt.ncof) iband4 = ncof
+      iband3 = iband4 -1
+      ich1 = 0
+      ich3 = 0
+      nuu = nu4-iopt3-1
+c  iteration process to find the root of f(p)=s.
+      do 920 iter=1,maxit
+        pinv = one/p
+c  store the triangularized observation matrix into q.
+        do 630 i=1,ncof
+          ff(i) = f(i)
+          do 620 j=1,iband4
+            q(i,j) = 0.
+ 620      continue
+          do 630 j=1,iband
+            q(i,j) = a(i,j)
+ 630    continue
+c  extend the observation matrix with the rows of a matrix, expressing
+c  that for u=constant sp(u,v) must be a constant function.
+        do 720 i=5,nv4
+          ii = i-4
+          do 635 l=1,nvv
+             row(l) = 0.
+ 635      continue
+          ll = ii
+          do 640  l=1,5
+             if(ll.gt.nvv) ll=1
+             row(ll) = row(ll)+bv(ii,l)
+             ll = ll+1
+ 640      continue
+          do 720 j=1,nuu
+c  initialize the new row.
+            do 645 l=1,iband
+              h(l) = 0.
+ 645        continue
+c  fill in the non-zero elements of the row. jrot records the column
+c  number of the first non-zero element in the row.
+            if(j.gt.iopt2) go to 665
+            if(j.eq.2) go to 655
+            do 650 k=1,2
+               cs(k) = 0.
+               do 650 l=1,nvv
+                  cs(k) = cs(k)+cosi(k,l)*row(l)
+ 650        continue
+            h(1) = cs(1)
+            h(2) = cs(2)
+            jrot = 2
+            go to 675
+ 655        do 660 k=3,5
+               cs(k) = 0.
+               do 660 l=1,nvv
+                  cs(k) = cs(k)+cosi(k,l)*row(l)
+ 660        continue
+            h(1) = cs(1)*ratio
+            h(2) = cs(2)*ratio
+            h(3) = cs(3)
+            h(4) = cs(4)
+            h(5) = cs(5)
+            jrot = 2
+            go to 675
+ 665        do 670 l=1,nvv
+               h(l) = row(l)
+ 670        continue
+            jrot = ipar1+1+(j-iopt2-1)*nvv
+ 675        do 677 l=1,iband
+              h(l) = h(l)*pinv
+ 677        continue
+            zi = 0.
+c  rotate the new row into triangle by givens transformations.
+            do 710 irot=jrot,ncof
+              piv = h(1)
+              i2 = min0(iband1,ncof-irot)
+              if(piv.eq.0.) then
+                 if (i2.le.0) go to 720
+                 go to 690
+              endif
+c  calculate the parameters of the givens transformation.
+              call fpgivs(piv,q(irot,1),co,si)
+c  apply that givens transformation to the right hand side.
+              call fprota(co,si,zi,ff(irot))
+              if(i2.eq.0) go to 720
+c  apply that givens transformation to the left hand side.
+              do 680 l=1,i2
+                l1 = l+1
+                call fprota(co,si,h(l1),q(irot,l1))
+ 680          continue
+ 690          do 700 l=1,i2
+                h(l) = h(l+1)
+ 700          continue
+              h(i2+1) = 0.
+ 710        continue
+ 720    continue
+c  extend the observation matrix with the rows of a matrix expressing
+c  that for v=constant. sp(u,v) must be a cubic polynomial.
+        do 810 i=5,nu4
+          ii = i-4
+          do 810 j=1,nvv
+c  initialize the new row
+            do 730 l=1,iband4
+              h(l) = 0.
+ 730        continue
+c  fill in the non-zero elements of the row. jrot records the column
+c  number of the first non-zero element in the row.
+            j1 = 1
+            do 760 l=1,5
+               il = ii+l-1
+               if(il.eq.nu4 .and. iopt3.ne.0) go to 760
+               if(il.gt.iopt2+1) go to 750
+               go to (735,740,745),il
+ 735           h(1) = bu(ii,l)
+               j1 = j+1
+               go to 760
+ 740           h(1) = h(1)+bu(ii,l)
+               h(2) = bu(ii,l)*cosi(1,j)
+               h(3) = bu(ii,l)*cosi(2,j)
+               j1 = j+3
+               go to 760
+ 745           h(1) = h(1)+bu(ii,l)
+               h(2) = bu(ii,l)*cosi(1,j)*ratio
+               h(3) = bu(ii,l)*cosi(2,j)*ratio
+               h(4) = bu(ii,l)*cosi(3,j)
+               h(5) = bu(ii,l)*cosi(4,j)
+               h(6) = bu(ii,l)*cosi(5,j)
+               j1 = j+6
+               go to 760
+ 750           h(j1) = bu(ii,l)
+               j1 = j1+nvv
+ 760        continue
+            do 765 l=1,iband4
+              h(l) = h(l)*pinv
+ 765        continue
+            zi = 0.
+            jrot = 1
+            if(ii.gt.iopt2+1) jrot = ipar1+(ii-iopt2-2)*nvv+j
+c  rotate the new row into triangle by givens transformations.
+            do 800 irot=jrot,ncof
+              piv = h(1)
+              i2 = min0(iband3,ncof-irot)
+              if(piv.eq.0.) then
+                if (i2.le.0) go to 810
+                go to 780
+              endif
+c  calculate the parameters of the givens transformation.
+              call fpgivs(piv,q(irot,1),co,si)
+c  apply that givens transformation to the right hand side.
+              call fprota(co,si,zi,ff(irot))
+              if(i2.eq.0) go to 810
+c  apply that givens transformation to the left hand side.
+              do 770 l=1,i2
+                l1 = l+1
+                call fprota(co,si,h(l1),q(irot,l1))
+ 770          continue
+ 780          do 790 l=1,i2
+                h(l) = h(l+1)
+ 790          continue
+              h(i2+1) = 0.
+ 800        continue
+ 810    continue
+c  find dmax, the maximum value for the diagonal elements in the
+c  reduced triangle.
+        dmax = 0.
+        do 820 i=1,ncof
+          if(q(i,1).le.dmax) go to 820
+          dmax = q(i,1)
+ 820    continue
+c  check whether the matrix is rank deficient.
+        sigma = eps*dmax
+        do 830 i=1,ncof
+          if(q(i,1).le.sigma) go to 840
+ 830    continue
+c  backward substitution in case of full rank.
+        call fpback(q,ff,ncof,iband4,c,ncc)
+        rank = ncof
+        go to 845
+c  in case of rank deficiency, find the minimum norm solution.
+ 840    lwest = ncof*iband4+ncof+iband4
+        if(lwrk.lt.lwest) go to 925
+        lf = 1
+        lh = lf+ncof
+        la = lh+iband4
+        call fprank(q,ff,ncof,iband4,ncc,sigma,c,sq,rank,wrk(la),
+     *   wrk(lf),wrk(lh))
+ 845    do 850 i=1,ncof
+           q(i,1) = q(i,1)/dmax
+ 850    continue
+c  find the coefficients in the standard b-spline representation of
+c  the polar spline.
+        call fprppo(nu,nv,iopt2,iopt3,cosi,ratio,c,ff,ncoff)
+c  compute f(p).
+        fp = 0.
+        do 890 num = 1,nreg
+          num1 = num-1
+          lu = num1/nvv
+          lv = num1-lu*nvv
+          jrot = lu*nv4+lv
+          in = index(num)
+ 860      if(in.eq.0) go to 890
+          store = 0.
+          i1 = jrot
+          do 880 i=1,4
+            hui = spu(in,i)
+            j1 = i1
+            do 870 j=1,4
+              j1 = j1+1
+              store = store+hui*spv(in,j)*c(j1)
+ 870        continue
+            i1 = i1+nv4
+ 880      continue
+          fp = fp+(w(in)*(z(in)-store))**2
+          in = nummer(in)
+          go to 860
+ 890    continue
+c  test whether the approximation sp(u,v) is an acceptable solution
+        fpms = fp-s
+        if(abs(fpms).le.acc) go to 980
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 940
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 900
+        if((f2-f3).gt.acc) go to 895
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 920
+ 895    if(f2.lt.0.) ich3 = 1
+ 900    if(ich1.ne.0) go to 910
+        if((f1-f2).gt.acc) go to 905
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 920
+        if(p.ge.p3) p = p2*con1 +p3*con9
+        go to 920
+ 905    if(f2.gt.0.) ich1 = 1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 910    if(f2.ge.f1 .or. f2.le.f3) go to 945
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 920  continue
+c  error codes and messages.
+ 925  ier = lwest
+      go to 990
+ 930  ier = 5
+      go to 990
+ 935  ier = 4
+      go to 990
+ 940  ier = 3
+      go to 990
+ 945  ier = 2
+      go to 990
+ 950  ier = 1
+      go to 990
+ 960  ier = -2
+      go to 990
+ 970  ier = -1
+      fp = 0.
+ 980  if(ncof.ne.rank) ier = -rank
+ 990  return
+      end
+

Added: branches/Interpolate1D/fitpack/fprank.f
===================================================================
--- branches/Interpolate1D/fitpack/fprank.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fprank.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,236 @@
+      subroutine fprank(a,f,n,m,na,tol,c,sq,rank,aa,ff,h)
+c  subroutine fprank finds the minimum norm solution of a least-
+c  squares problem in case of rank deficiency.
+c
+c  input parameters:
+c    a : array, which contains the non-zero elements of the observation
+c        matrix after triangularization by givens transformations.
+c    f : array, which contains the transformed right hand side.
+c    n : integer,wich contains the dimension of a.
+c    m : integer, which denotes the bandwidth of a.
+c  tol : real value, giving a threshold to determine the rank of a.
+c
+c  output parameters:
+c    c : array, which contains the minimum norm solution.
+c   sq : real value, giving the contribution of reducing the rank
+c        to the sum of squared residuals.
+c rank : integer, which contains the rank of matrix a.
+c
+c  ..scalar arguments..
+      integer n,m,na,rank
+      real*8 tol,sq
+c  ..array arguments..
+      real*8 a(na,m),f(n),c(n),aa(n,m),ff(n),h(m)
+c  ..local scalars..
+      integer i,ii,ij,i1,i2,j,jj,j1,j2,j3,k,kk,m1,nl
+      real*8 cos,fac,piv,sin,yi
+      double precision store,stor1,stor2,stor3
+c  ..function references..
+      integer min0
+c  ..subroutine references..
+c    fpgivs,fprota
+c  ..
+      m1 = m-1
+c  the rank deficiency nl is considered to be the number of sufficient
+c  small diagonal elements of a.
+      nl = 0
+      sq = 0.
+      do 90 i=1,n
+        if(a(i,1).gt.tol) go to 90
+c  if a sufficient small diagonal element is found, we put it to
+c  zero. the remainder of the row corresponding to that zero diagonal
+c  element is then rotated into triangle by givens rotations .
+c  the rank deficiency is increased by one.
+        nl = nl+1
+        if(i.eq.n) go to 90
+        yi = f(i)
+        do 10 j=1,m1
+          h(j) = a(i,j+1)
+  10    continue
+        h(m) = 0.
+        i1 = i+1
+        do 60 ii=i1,n
+          i2 = min0(n-ii,m1)
+          piv = h(1)
+          if(piv.eq.0.) go to 30
+          call fpgivs(piv,a(ii,1),cos,sin)
+          call fprota(cos,sin,yi,f(ii))
+          if(i2.eq.0) go to 70
+          do 20 j=1,i2
+            j1 = j+1
+            call fprota(cos,sin,h(j1),a(ii,j1))
+            h(j) = h(j1)
+  20      continue
+          go to 50
+  30      if(i2.eq.0) go to 70
+          do 40 j=1,i2
+            h(j) = h(j+1)
+  40      continue
+  50      h(i2+1) = 0.
+  60    continue
+c  add to the sum of squared residuals the contribution of deleting
+c  the row with small diagonal element.
+  70    sq = sq+yi**2
+  90  continue
+c  rank denotes the rank of a.
+      rank = n-nl
+c  let b denote the (rank*n) upper trapezoidal matrix which can be
+c  obtained from the (n*n) upper triangular matrix a by deleting
+c  the rows and interchanging the columns corresponding to a zero
+c  diagonal element. if this matrix is factorized using givens
+c  transformations as  b = (r) (u)  where
+c    r is a (rank*rank) upper triangular matrix,
+c    u is a (rank*n) orthonormal matrix
+c  then the minimal least-squares solution c is given by c = b' v,
+c  where v is the solution of the system  (r) (r)' v = g  and
+c  g denotes the vector obtained from the old right hand side f, by
+c  removing the elements corresponding to a zero diagonal element of a.
+c  initialization.
+      do 100 i=1,rank
+        do 100 j=1,m
+          aa(i,j) = 0.
+ 100  continue
+c  form in aa the upper triangular matrix obtained from a by
+c  removing rows and columns with zero diagonal elements. form in ff
+c  the new right hand side by removing the elements of the old right
+c  hand side corresponding to a deleted row.
+      ii = 0
+      do 120 i=1,n
+        if(a(i,1).le.tol) go to 120
+        ii = ii+1
+        ff(ii) = f(i)
+        aa(ii,1) = a(i,1)
+        jj = ii
+        kk = 1
+        j = i
+        j1 = min0(j-1,m1)
+        if(j1.eq.0) go to 120
+        do 110 k=1,j1
+          j = j-1
+          if(a(j,1).le.tol) go to 110
+          kk = kk+1
+          jj = jj-1
+          aa(jj,kk) = a(j,k+1)
+ 110    continue
+ 120  continue
+c  form successively in h the columns of a with a zero diagonal element.
+      ii = 0
+      do 200 i=1,n
+        ii = ii+1
+        if(a(i,1).gt.tol) go to 200
+        ii = ii-1
+        if(ii.eq.0) go to 200
+        jj = 1
+        j = i
+        j1 = min0(j-1,m1)
+        do 130 k=1,j1
+          j = j-1
+          if(a(j,1).le.tol) go to 130
+          h(jj) = a(j,k+1)
+          jj = jj+1
+ 130    continue
+        do 140 kk=jj,m
+          h(kk) = 0.
+ 140    continue
+c  rotate this column into aa by givens transformations.
+        jj = ii
+        do 190 i1=1,ii
+          j1 = min0(jj-1,m1)
+          piv = h(1)
+          if(piv.ne.0.) go to 160
+          if(j1.eq.0) go to 200
+          do 150 j2=1,j1
+            j3 = j2+1
+            h(j2) = h(j3)
+ 150      continue
+          go to 180
+ 160      call fpgivs(piv,aa(jj,1),cos,sin)
+          if(j1.eq.0) go to 200
+          kk = jj
+          do 170 j2=1,j1
+            j3 = j2+1
+            kk = kk-1
+            call fprota(cos,sin,h(j3),aa(kk,j3))
+            h(j2) = h(j3)
+ 170      continue
+ 180      jj = jj-1
+          h(j3) = 0.
+ 190    continue
+ 200  continue
+c  solve the system (aa) (f1) = ff
+      ff(rank) = ff(rank)/aa(rank,1)
+      i = rank-1
+      if(i.eq.0) go to 230
+      do 220 j=2,rank
+        store = ff(i)
+        i1 = min0(j-1,m1)
+        k = i
+        do 210 ii=1,i1
+          k = k+1
+          stor1 = ff(k)
+          stor2 = aa(i,ii+1)
+          store = store-stor1*stor2
+ 210    continue
+        stor1 = aa(i,1)
+        ff(i) = store/stor1
+        i = i-1
+ 220  continue
+c  solve the system  (aa)' (f2) = f1
+ 230  ff(1) = ff(1)/aa(1,1)
+      if(rank.eq.1) go to 260
+      do 250 j=2,rank
+        store = ff(j)
+        i1 = min0(j-1,m1)
+        k = j
+        do 240 ii=1,i1
+          k = k-1
+          stor1 = ff(k)
+          stor2 = aa(k,ii+1)
+          store = store-stor1*stor2
+ 240    continue
+        stor1 = aa(j,1)
+        ff(j) = store/stor1
+ 250  continue
+c  premultiply f2 by the transpoze of a.
+ 260  k = 0
+      do 280 i=1,n
+        store = 0.
+        if(a(i,1).gt.tol) k = k+1
+        j1 = min0(i,m)
+        kk = k
+        ij = i+1
+        do 270 j=1,j1
+          ij = ij-1
+          if(a(ij,1).le.tol) go to 270
+          stor1 = a(ij,j)
+          stor2 = ff(kk)
+          store = store+stor1*stor2
+          kk = kk-1
+ 270    continue
+        c(i) = store
+ 280  continue
+c  add to the sum of squared residuals the contribution of putting
+c  to zero the small diagonal elements of matrix (a).
+      stor3 = 0.
+      do 310 i=1,n
+        if(a(i,1).gt.tol) go to 310
+        store = f(i)
+        i1 = min0(n-i,m1)
+        if(i1.eq.0) go to 300
+        do 290 j=1,i1
+          ij = i+j
+          stor1 = c(ij)
+          stor2 = a(i,j+1)
+          store = store-stor1*stor2
+ 290    continue
+ 300    fac = a(i,1)*c(i)
+        stor1 = a(i,1)
+        stor2 = c(i)
+        stor1 = stor1*stor2
+        stor3 = stor3+stor1*(stor1-store-store)
+ 310  continue
+      fac = stor3
+      sq = sq+fac
+      return
+      end
+

Added: branches/Interpolate1D/fitpack/fprati.f
===================================================================
--- branches/Interpolate1D/fitpack/fprati.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fprati.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,29 @@
+      real*8 function fprati(p1,f1,p2,f2,p3,f3)
+c  given three points (p1,f1),(p2,f2) and (p3,f3), function fprati
+c  gives the value of p such that the rational interpolating function
+c  of the form r(p) = (u*p+v)/(p+w) equals zero at p.
+c  ..
+c  ..scalar arguments..
+      real*8 p1,f1,p2,f2,p3,f3
+c  ..local scalars..
+      real*8 h1,h2,h3,p
+c  ..
+      if(p3.gt.0.) go to 10
+c  value of p in case p3 = infinity.
+      p = (p1*(f1-f3)*f2-p2*(f2-f3)*f1)/((f1-f2)*f3)
+      go to 20
+c  value of p in case p3 ^= infinity.
+  10  h1 = f1*(f2-f3)
+      h2 = f2*(f3-f1)
+      h3 = f3*(f1-f2)
+      p = -(p1*p2*h3+p2*p3*h1+p3*p1*h2)/(p1*h1+p2*h2+p3*h3)
+c  adjust the value of p1,f1,p3 and f3 such that f1 > 0 and f3 < 0.
+  20  if(f2.lt.0.) go to 30
+      p1 = p2
+      f1 = f2
+      go to 40
+  30  p3 = p2
+      f3 = f2
+  40  fprati = p
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpregr.f
===================================================================
--- branches/Interpolate1D/fitpack/fpregr.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpregr.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,367 @@
+      subroutine fpregr(iopt,x,mx,y,my,z,mz,xb,xe,yb,ye,kx,ky,s,
+     * nxest,nyest,tol,maxit,nc,nx,tx,ny,ty,c,fp,fp0,fpold,reducx,
+     * reducy,fpintx,fpinty,lastdi,nplusx,nplusy,nrx,nry,nrdatx,nrdaty,
+     * wrk,lwrk,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 xb,xe,yb,ye,s,tol,fp,fp0,fpold,reducx,reducy
+      integer iopt,mx,my,mz,kx,ky,nxest,nyest,maxit,nc,nx,ny,lastdi,
+     * nplusx,nplusy,lwrk,ier
+c  ..array arguments..
+      real*8 x(mx),y(my),z(mz),tx(nxest),ty(nyest),c(nc),fpintx(nxest),
+     * fpinty(nyest),wrk(lwrk)
+      integer nrdatx(nxest),nrdaty(nyest),nrx(mx),nry(my)
+c  ..local scalars
+      real*8 acc,fpms,f1,f2,f3,p,p1,p2,p3,rn,one,half,con1,con9,con4
+      integer i,ich1,ich3,ifbx,ifby,ifsx,ifsy,iter,j,kx1,kx2,ky1,ky2,
+     * k3,l,lax,lay,lbx,lby,lq,lri,lsx,lsy,mk1,mm,mpm,mynx,ncof,
+     * nk1x,nk1y,nmaxx,nmaxy,nminx,nminy,nplx,nply,npl1,nrintx,
+     * nrinty,nxe,nxk,nye
+c  ..function references..
+      real*8 abs,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpgrre,fpknot
+c  ..
+c   set constants
+      one = 1
+      half = 0.5e0
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+c  we partition the working space.
+      kx1 = kx+1
+      ky1 = ky+1
+      kx2 = kx1+1
+      ky2 = ky1+1
+      lsx = 1
+      lsy = lsx+mx*kx1
+      lri = lsy+my*ky1
+      mm = max0(nxest,my)
+      lq = lri+mm
+      mynx = nxest*my
+      lax = lq+mynx
+      nxk = nxest*kx2
+      lbx = lax+nxk
+      lay = lbx+nxk
+      lby = lay+nyest*ky2
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 1: determination of the number of knots and their position.     c
+c ****************************************************************     c
+c  given a set of knots we compute the least-squares spline sinf(x,y), c
+c  and the corresponding sum of squared residuals fp=f(p=inf).         c
+c  if iopt=-1  sinf(x,y) is the requested approximation.               c
+c  if iopt=0 or iopt=1 we check whether we can accept the knots:       c
+c    if fp <=s we will continue with the current set of knots.         c
+c    if fp > s we will increase the number of knots and compute the    c
+c       corresponding least-squares spline until finally fp<=s.        c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c    knots equals nmaxx = mx+kx+1  and  nmaxy = my+ky+1.               c
+c    if s>0 and                                                        c
+c     *iopt=0 we first compute the least-squares polynomial of degree  c
+c      kx in x and ky in y; nx=nminx=2*kx+2 and ny=nymin=2*ky+2.       c
+c     *iopt=1 we start with the knots found at the last call of the    c
+c      routine, except for the case that s > fp0; then we can compute  c
+c      the least-squares polynomial directly.                          c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  determine the number of knots for polynomial approximation.
+      nminx = 2*kx1
+      nminy = 2*ky1
+      if(iopt.lt.0) go to 120
+c  acc denotes the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  find nmaxx and nmaxy which denote the number of knots in x- and y-
+c  direction in case of spline interpolation.
+      nmaxx = mx+kx1
+      nmaxy = my+ky1
+c  find nxe and nye which denote the maximum number of knots
+c  allowed in each direction
+      nxe = min0(nmaxx,nxest)
+      nye = min0(nmaxy,nyest)
+      if(s.gt.0.) go to 100
+c  if s = 0, s(x,y) is an interpolating spline.
+      nx = nmaxx
+      ny = nmaxy
+c  test whether the required storage space exceeds the available one.
+      if(ny.gt.nyest .or. nx.gt.nxest) go to 420
+c  find the position of the interior knots in case of interpolation.
+c  the knots in the x-direction.
+      mk1 = mx-kx1
+      if(mk1.eq.0) go to 60
+      k3 = kx/2
+      i = kx1+1
+      j = k3+2
+      if(k3*2.eq.kx) go to 40
+      do 30 l=1,mk1
+        tx(i) = x(j)
+        i = i+1
+        j = j+1
+  30  continue
+      go to 60
+  40  do 50 l=1,mk1
+        tx(i) = (x(j)+x(j-1))*half
+        i = i+1
+        j = j+1
+  50  continue
+c  the knots in the y-direction.
+  60  mk1 = my-ky1
+      if(mk1.eq.0) go to 120
+      k3 = ky/2
+      i = ky1+1
+      j = k3+2
+      if(k3*2.eq.ky) go to 80
+      do 70 l=1,mk1
+        ty(i) = y(j)
+        i = i+1
+        j = j+1
+  70  continue
+      go to 120
+  80  do 90 l=1,mk1
+        ty(i) = (y(j)+y(j-1))*half
+        i = i+1
+        j = j+1
+  90  continue
+      go to 120
+c  if s > 0 our initial choice of knots depends on the value of iopt.
+ 100  if(iopt.eq.0) go to 115
+      if(fp0.le.s) go to 115
+c  if iopt=1 and fp0 > s we start computing the least- squares spline
+c  according to the set of knots found at the last call of the routine.
+c  we determine the number of grid coordinates x(i) inside each knot
+c  interval (tx(l),tx(l+1)).
+      l = kx2
+      j = 1
+      nrdatx(1) = 0
+      mpm = mx-1
+      do 105 i=2,mpm
+        nrdatx(j) = nrdatx(j)+1
+        if(x(i).lt.tx(l)) go to 105
+        nrdatx(j) = nrdatx(j)-1
+        l = l+1
+        j = j+1
+        nrdatx(j) = 0
+ 105  continue
+c  we determine the number of grid coordinates y(i) inside each knot
+c  interval (ty(l),ty(l+1)).
+      l = ky2
+      j = 1
+      nrdaty(1) = 0
+      mpm = my-1
+      do 110 i=2,mpm
+        nrdaty(j) = nrdaty(j)+1
+        if(y(i).lt.ty(l)) go to 110
+        nrdaty(j) = nrdaty(j)-1
+        l = l+1
+        j = j+1
+        nrdaty(j) = 0
+ 110  continue
+      go to 120
+c  if iopt=0 or iopt=1 and s>=fp0, we start computing the least-squares
+c  polynomial of degree kx in x and ky in y (which is a spline without
+c  interior knots).
+ 115  nx = nminx
+      ny = nminy
+      nrdatx(1) = mx-2
+      nrdaty(1) = my-2
+      lastdi = 0
+      nplusx = 0
+      nplusy = 0
+      fp0 = 0.
+      fpold = 0.
+      reducx = 0.
+      reducy = 0.
+ 120  mpm = mx+my
+      ifsx = 0
+      ifsy = 0
+      ifbx = 0
+      ifby = 0
+      p = -one
+c  main loop for the different sets of knots.mpm=mx+my is a save upper
+c  bound for the number of trials.
+      do 250 iter=1,mpm
+        if(nx.eq.nminx .and. ny.eq.nminy) ier = -2
+c  find nrintx (nrinty) which is the number of knot intervals in the
+c  x-direction (y-direction).
+        nrintx = nx-nminx+1
+        nrinty = ny-nminy+1
+c  find ncof, the number of b-spline coefficients for the current set
+c  of knots.
+        nk1x = nx-kx1
+        nk1y = ny-ky1
+        ncof = nk1x*nk1y
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(x,y).
+        i = nx
+        do 130 j=1,kx1
+          tx(j) = xb
+          tx(i) = xe
+          i = i-1
+ 130    continue
+        i = ny
+        do 140 j=1,ky1
+          ty(j) = yb
+          ty(i) = ye
+          i = i-1
+ 140    continue
+c  find the least-squares spline sinf(x,y) and calculate for each knot
+c  interval tx(j+kx)<=x<=tx(j+kx+1) (ty(j+ky)<=y<=ty(j+ky+1)) the sum
+c  of squared residuals fpintx(j),j=1,2,...,nx-2*kx-1 (fpinty(j),j=1,2,
+c  ...,ny-2*ky-1) for the data points having their absciss (ordinate)-
+c  value belonging to that interval.
+c  fp gives the total sum of squared residuals.
+        call fpgrre(ifsx,ifsy,ifbx,ifby,x,mx,y,my,z,mz,kx,ky,tx,nx,ty,
+     *  ny,p,c,nc,fp,fpintx,fpinty,mm,mynx,kx1,kx2,ky1,ky2,wrk(lsx),
+     *  wrk(lsy),wrk(lri),wrk(lq),wrk(lax),wrk(lay),wrk(lbx),wrk(lby),
+     *  nrx,nry)
+        if(ier.eq.(-2)) fp0 = fp
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt.lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms) .lt. acc) go to 440
+c  if f(p=inf) < s, we accept the choice of knots.
+        if(fpms.lt.0.) go to 300
+c  if nx=nmaxx and ny=nmaxy, sinf(x,y) is an interpolating spline.
+        if(nx.eq.nmaxx .and. ny.eq.nmaxy) go to 430
+c  increase the number of knots.
+c  if nx=nxe and ny=nye we cannot further increase the number of knots
+c  because of the storage capacity limitation.
+        if(nx.eq.nxe .and. ny.eq.nye) go to 420
+        ier = 0
+c  adjust the parameter reducx or reducy according to the direction
+c  in which the last added knots were located.
+        if (lastdi.lt.0) go to 150
+        if (lastdi.eq.0) go to 170
+        go to 160
+ 150    reducx = fpold-fp
+        go to 170
+ 160    reducy = fpold-fp
+c  store the sum of squared residuals for the current set of knots.
+ 170    fpold = fp
+c  find nplx, the number of knots we should add in the x-direction.
+        nplx = 1
+        if(nx.eq.nminx) go to 180
+        npl1 = nplusx*2
+        rn = nplusx
+        if(reducx.gt.acc) npl1 = rn*fpms/reducx
+        nplx = min0(nplusx*2,max0(npl1,nplusx/2,1))
+c  find nply, the number of knots we should add in the y-direction.
+ 180    nply = 1
+        if(ny.eq.nminy) go to 190
+        npl1 = nplusy*2
+        rn = nplusy
+        if(reducy.gt.acc) npl1 = rn*fpms/reducy
+        nply = min0(nplusy*2,max0(npl1,nplusy/2,1))
+ 190    if (nplx.lt.nply) go to 210
+        if (nplx.eq.nply) go to 200
+        go to 230
+ 200    if(lastdi.lt.0) go to 230
+ 210    if(nx.eq.nxe) go to 230
+c  addition in the x-direction.
+        lastdi = -1
+        nplusx = nplx
+        ifsx = 0
+        do 220 l=1,nplusx
+c  add a new knot in the x-direction
+          call fpknot(x,mx,tx,nx,fpintx,nrdatx,nrintx,nxest,1)
+c  test whether we cannot further increase the number of knots in the
+c  x-direction.
+          if(nx.eq.nxe) go to 250
+ 220    continue
+        go to 250
+ 230    if(ny.eq.nye) go to 210
+c  addition in the y-direction.
+        lastdi = 1
+        nplusy = nply
+        ifsy = 0
+        do 240 l=1,nplusy
+c  add a new knot in the y-direction.
+          call fpknot(y,my,ty,ny,fpinty,nrdaty,nrinty,nyest,1)
+c  test whether we cannot further increase the number of knots in the
+c  y-direction.
+          if(ny.eq.nye) go to 250
+ 240    continue
+c  restart the computations with the new set of knots.
+ 250  continue
+c  test whether the least-squares polynomial is a solution of our
+c  approximation problem.
+ 300  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing spline sp(x,y)                c
+c *****************************************************                c
+c  we have determined the number of knots and their position. we now   c
+c  compute the b-spline coefficients of the smoothing spline sp(x,y).  c
+c  this smoothing spline varies with the parameter p in such a way thatc
+c    f(p) = sumi=1,mx(sumj=1,my((z(i,j)-sp(x(i),y(j)))**2)             c
+c  is a continuous, strictly decreasing function of p. moreover the    c
+c  least-squares polynomial corresponds to p=0 and the least-squares   c
+c  spline to p=infinity. iteratively we then have to determine the     c
+c  positive value of p such that f(p)=s. the process which is proposed c
+c  here makes use of rational interpolation. f(p) is approximated by a c
+c  rational function r(p)=(u*p+v)/(p+w); three values of p (p1,p2,p3)  c
+c  with corresponding values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s)c
+c  are used to calculate the new value of p such that r(p)=s.          c
+c  convergence is guaranteed by taking f1 > 0 and f3 < 0.              c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = one
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p)=s.
+      do 350 iter = 1,maxit
+c  find the smoothing spline sp(x,y) and the corresponding sum of
+c  squared residuals fp.
+        call fpgrre(ifsx,ifsy,ifbx,ifby,x,mx,y,my,z,mz,kx,ky,tx,nx,ty,
+     *  ny,p,c,nc,fp,fpintx,fpinty,mm,mynx,kx1,kx2,ky1,ky2,wrk(lsx),
+     *  wrk(lsy),wrk(lri),wrk(lq),wrk(lax),wrk(lay),wrk(lbx),wrk(lby),
+     *  nrx,nry)
+c  test whether the approximation sp(x,y) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 320
+        if((f2-f3).gt.acc) go to 310
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 350
+ 310    if(f2.lt.0.) ich3 = 1
+ 320    if(ich1.ne.0) go to 340
+        if((f1-f2).gt.acc) go to 330
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 350
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 350
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 330    if(f2.gt.0.) ich1 = 1
+ 340    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 350  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+      fp = 0.
+ 440  return
+      end
+

Added: branches/Interpolate1D/fitpack/fprota.f
===================================================================
--- branches/Interpolate1D/fitpack/fprota.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fprota.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,14 @@
+      subroutine fprota(cos,sin,a,b)
+c  subroutine fprota applies a givens rotation to a and b.
+c  ..
+c  ..scalar arguments..
+      real*8 cos,sin,a,b
+c ..local scalars..
+      real*8 stor1,stor2
+c  ..
+      stor1 = a
+      stor2 = b
+      b = cos*stor2+sin*stor1
+      a = cos*stor1-sin*stor2
+      return
+      end

Added: branches/Interpolate1D/fitpack/fprppo.f
===================================================================
--- branches/Interpolate1D/fitpack/fprppo.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fprppo.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,61 @@
+      subroutine fprppo(nu,nv,if1,if2,cosi,ratio,c,f,ncoff)
+c  given the coefficients of a constrained bicubic spline, as determined
+c  in subroutine fppola, subroutine fprppo calculates the coefficients
+c  in the standard b-spline representation of bicubic splines.
+c  ..
+c  ..scalar arguments..
+      real*8 ratio
+      integer nu,nv,if1,if2,ncoff
+c  ..array arguments
+      real*8 c(ncoff),f(ncoff),cosi(5,nv)
+c  ..local scalars..
+      integer i,iopt,ii,j,k,l,nu4,nvv
+c  ..
+      nu4 = nu-4
+      nvv = nv-7
+      iopt = if1+1
+      do 10 i=1,ncoff
+         f(i) = 0.
+  10  continue
+      i = 0
+      do 120 l=1,nu4
+         ii = i
+         if(l.gt.iopt) go to 80
+         go to (20,40,60),l
+  20     do 30 k=1,nvv
+            i = i+1
+            f(i) = c(1)
+  30     continue
+         j = 1
+         go to 100
+  40     do 50 k=1,nvv
+            i = i+1
+            f(i) = c(1)+c(2)*cosi(1,k)+c(3)*cosi(2,k)
+  50     continue
+         j = 3
+         go to 100
+  60     do 70 k=1,nvv
+            i = i+1
+            f(i) = c(1)+ratio*(c(2)*cosi(1,k)+c(3)*cosi(2,k))+
+     *             c(4)*cosi(3,k)+c(5)*cosi(4,k)+c(6)*cosi(5,k)
+  70     continue
+         j = 6
+         go to 100
+  80     if(l.eq.nu4 .and. if2.ne.0) go to 120
+         do 90 k=1,nvv
+            i = i+1
+            j = j+1
+            f(i) = c(j)
+  90     continue
+ 100     do 110 k=1,3
+            ii = ii+1
+            i = i+1
+            f(i) = f(ii)
+ 110     continue
+ 120  continue
+      do 130 i=1,ncoff
+         c(i) = f(i)
+ 130  continue
+      return
+      end
+

Added: branches/Interpolate1D/fitpack/fprpsp.f
===================================================================
--- branches/Interpolate1D/fitpack/fprpsp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fprpsp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,55 @@
+      subroutine fprpsp(nt,np,co,si,c,f,ncoff)
+c  given the coefficients of a spherical spline function, subroutine
+c  fprpsp calculates the coefficients in the standard b-spline re-
+c  presentation of this bicubic spline.
+c  ..
+c  ..scalar arguments
+      integer nt,np,ncoff
+c  ..array arguments
+      real*8 co(np),si(np),c(ncoff),f(ncoff)
+c  ..local scalars
+      real*8 cn,c1,c2,c3
+      integer i,ii,j,k,l,ncof,npp,np4,nt4
+c  ..
+      nt4 = nt-4
+      np4 = np-4
+      npp = np4-3
+      ncof = 6+npp*(nt4-4)
+      c1 = c(1)
+      cn = c(ncof)
+      j = ncoff
+      do 10 i=1,np4
+         f(i) = c1
+         f(j) = cn
+         j = j-1
+  10  continue
+      i = np4
+      j=1
+      do 70 l=3,nt4
+         ii = i
+         if(l.eq.3 .or. l.eq.nt4) go to 30
+         do 20 k=1,npp
+            i = i+1
+            j = j+1
+            f(i) = c(j)
+  20     continue
+         go to 50
+  30     if(l.eq.nt4) c1 = cn
+         c2 = c(j+1)
+         c3 = c(j+2)
+         j = j+2
+         do 40 k=1,npp
+            i = i+1
+            f(i) = c1+c2*co(k)+c3*si(k)
+  40     continue
+  50     do 60 k=1,3
+            ii = ii+1
+            i = i+1
+            f(i) = f(ii)
+  60     continue
+  70  continue
+      do 80 i=1,ncoff
+         c(i) = f(i)
+  80  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpseno.f
===================================================================
--- branches/Interpolate1D/fitpack/fpseno.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpseno.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,34 @@
+      subroutine fpseno(maxtr,up,left,right,info,merk,ibind,nbind)
+c  subroutine fpseno fetches a branch of a triply linked tree the
+c  information of which is kept in the arrays up,left,right and info.
+c  the branch has a specified length nbind and is determined by the
+c  parameter merk which points to its terminal node. the information
+c  field of the nodes of this branch is stored in the array ibind. on
+c  exit merk points to a new branch of length nbind or takes the value
+c  1 if no such branch was found.
+c  ..
+c  ..scalar arguments..
+      integer maxtr,merk,nbind
+c  ..array arguments..
+      integer up(maxtr),left(maxtr),right(maxtr),info(maxtr),
+     * ibind(nbind)
+c  ..scalar arguments..
+      integer i,j,k
+c  ..
+      k = merk
+      j = nbind
+      do 10 i=1,nbind
+        ibind(j) = info(k)
+        k = up(k)
+        j = j-1
+  10  continue
+  20  k = right(merk)
+      if(k.ne.0) go to 30
+      merk = up(merk)
+      if (merk.le.1) go to 40
+      go to 20
+  30  merk = k
+      k = left(merk)
+      if(k.ne.0) go to 30
+  40  return
+      end

Added: branches/Interpolate1D/fitpack/fpspgr.f
===================================================================
--- branches/Interpolate1D/fitpack/fpspgr.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpspgr.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,439 @@
+      subroutine fpspgr(iopt,ider,u,mu,v,mv,r,mr,r0,r1,s,nuest,nvest,
+     * tol,maxit,nc,nu,tu,nv,tv,c,fp,fp0,fpold,reducu,reducv,fpintu,
+     * fpintv,dr,step,lastdi,nplusu,nplusv,lastu0,lastu1,nru,nrv,
+     * nrdatu,nrdatv,wrk,lwrk,ier)
+c  ..
+c  ..scalar arguments..
+      integer mu,mv,mr,nuest,nvest,maxit,nc,nu,nv,lastdi,nplusu,nplusv,
+     * lastu0,lastu1,lwrk,ier
+      real*8 r0,r1,s,tol,fp,fp0,fpold,reducu,reducv
+c  ..array arguments..
+      integer iopt(3),ider(4),nrdatu(nuest),nrdatv(nvest),nru(mu),
+     * nrv(mv)
+      real*8 u(mu),v(mv),r(mr),tu(nuest),tv(nvest),c(nc),fpintu(nuest),
+     * fpintv(nvest),dr(6),wrk(lwrk),step(2)
+c  ..local scalars..
+      real*8 acc,fpms,f1,f2,f3,p,per,pi,p1,p2,p3,vb,ve,rmax,rmin,rn,one,
+     *
+     * con1,con4,con9
+      integer i,ich1,ich3,ifbu,ifbv,ifsu,ifsv,istart,iter,i1,i2,j,ju,
+     * ktu,l,l1,l2,l3,l4,mpm,mumin,mu0,mu1,nn,nplu,nplv,npl1,nrintu,
+     * nrintv,nue,numax,nve,nvmax
+c  ..local arrays..
+      integer idd(4)
+      real*8 drr(6)
+c  ..function references..
+      real*8 abs,datan2,fprati
+      integer max0,min0
+c  ..subroutine references..
+c    fpknot,fpopsp
+c  ..
+c   set constants
+      one = 1d0
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+c   initialization
+      ifsu = 0
+      ifsv = 0
+      ifbu = 0
+      ifbv = 0
+      p = -one
+      mumin = 4
+      if(ider(1).ge.0) mumin = mumin-1
+      if(iopt(2).eq.1 .and. ider(2).eq.1) mumin = mumin-1
+      if(ider(3).ge.0) mumin = mumin-1
+      if(iopt(3).eq.1 .and. ider(4).eq.1) mumin = mumin-1
+      if(mumin.eq.0) mumin = 1
+      pi = datan2(0d0,-one)
+      per = pi+pi
+      vb = v(1)
+      ve = vb+per
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 1: determination of the number of knots and their position.     c
+c ****************************************************************     c
+c  given a set of knots we compute the least-squares spline sinf(u,v)  c
+c  and the corresponding sum of squared residuals fp = f(p=inf).       c
+c  if iopt(1)=-1  sinf(u,v) is the requested approximation.            c
+c  if iopt(1)>=0  we check whether we can accept the knots:            c
+c    if fp <= s we will continue with the current set of knots.        c
+c    if fp >  s we will increase the number of knots and compute the   c
+c       corresponding least-squares spline until finally fp <= s.      c
+c    the initial choice of knots depends on the value of s and iopt.   c
+c    if s=0 we have spline interpolation; in that case the number of   c
+c     knots in the u-direction equals nu=numax=mu+6+iopt(2)+iopt(3)    c
+c     and in the v-direction nv=nvmax=mv+7.                            c
+c    if s>0 and                                                        c
+c      iopt(1)=0 we first compute the least-squares polynomial,i.e. a  c
+c       spline without interior knots : nu=8 ; nv=8.                   c
+c      iopt(1)=1 we start with the set of knots found at the last call c
+c       of the routine, except for the case that s > fp0; then we      c
+c       compute the least-squares polynomial directly.                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+      if(iopt(1).lt.0) go to 120
+c  acc denotes the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+c  numax and nvmax denote the number of knots needed for interpolation.
+      numax = mu+6+iopt(2)+iopt(3)
+      nvmax = mv+7
+      nue = min0(numax,nuest)
+      nve = min0(nvmax,nvest)
+      if(s.gt.0.) go to 100
+c  if s = 0, s(u,v) is an interpolating spline.
+      nu = numax
+      nv = nvmax
+c  test whether the required storage space exceeds the available one.
+      if(nu.gt.nuest .or. nv.gt.nvest) go to 420
+c  find the position of the knots in the v-direction.
+      do 10 l=1,mv
+        tv(l+3) = v(l)
+  10  continue
+      tv(mv+4) = ve
+      l1 = mv-2
+      l2 = mv+5
+      do 20 i=1,3
+         tv(i) = v(l1)-per
+         tv(l2) = v(i+1)+per
+         l1 = l1+1
+         l2 = l2+1
+  20  continue
+c  if not all the derivative values g(i,j) are given, we will first
+c  estimate these values by computing a least-squares spline
+      idd(1) = ider(1)
+      if(idd(1).eq.0) idd(1) = 1
+      if(idd(1).gt.0) dr(1) = r0
+      idd(2) = ider(2)
+      idd(3) = ider(3)
+      if(idd(3).eq.0) idd(3) = 1
+      if(idd(3).gt.0) dr(4) = r1
+      idd(4) = ider(4)
+      if(ider(1).lt.0 .or. ider(3).lt.0) go to 30
+      if(iopt(2).ne.0 .and. ider(2).eq.0) go to 30
+      if(iopt(3).eq.0 .or. ider(4).ne.0) go to 70
+c we set up the knots in the u-direction for computing the least-squares
+c spline.
+  30  i1 = 3
+      i2 = mu-2
+      nu = 4
+      do 40 i=1,mu
+         if(i1.gt.i2) go to 50
+         nu = nu+1
+         tu(nu) = u(i1)
+         i1 = i1+2
+  40  continue
+  50  do 60 i=1,4
+         tu(i) = 0.
+         nu = nu+1
+         tu(nu) = pi
+  60  continue
+c we compute the least-squares spline for estimating the derivatives.
+      call fpopsp(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,r,mr,r0,r1,dr,iopt,idd,
+     *  tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,nrv,
+     *  wrk,lwrk)
+      ifsu = 0
+c if all the derivatives at the origin are known, we compute the
+c interpolating spline.
+c we set up the knots in the u-direction, needed for interpolation.
+  70  nn = numax-8
+      if(nn.eq.0) go to 95
+      ju = 2-iopt(2)
+      do 80 l=1,nn
+        tu(l+4) = u(ju)
+        ju = ju+1
+  80  continue
+      nu = numax
+      l = nu
+      do 90 i=1,4
+         tu(i) = 0.
+         tu(l) = pi
+         l = l-1
+  90  continue
+c we compute the interpolating spline.
+  95  call fpopsp(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,r,mr,r0,r1,dr,iopt,idd,
+     *  tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,nrv,
+     *  wrk,lwrk)
+      go to 430
+c  if s>0 our initial choice of knots depends on the value of iopt(1).
+ 100  ier = 0
+      if(iopt(1).eq.0) go to 115
+      step(1) = -step(1)
+      step(2) = -step(2)
+      if(fp0.le.s) go to 115
+c  if iopt(1)=1 and fp0 > s we start computing the least-squares spline
+c  according to the set of knots found at the last call of the routine.
+c  we determine the number of grid coordinates u(i) inside each knot
+c  interval (tu(l),tu(l+1)).
+      l = 5
+      j = 1
+      nrdatu(1) = 0
+      mu0 = 2-iopt(2)
+      mu1 = mu-1+iopt(3)
+      do 105 i=mu0,mu1
+        nrdatu(j) = nrdatu(j)+1
+        if(u(i).lt.tu(l)) go to 105
+        nrdatu(j) = nrdatu(j)-1
+        l = l+1
+        j = j+1
+        nrdatu(j) = 0
+ 105  continue
+c  we determine the number of grid coordinates v(i) inside each knot
+c  interval (tv(l),tv(l+1)).
+      l = 5
+      j = 1
+      nrdatv(1) = 0
+      do 110 i=2,mv
+        nrdatv(j) = nrdatv(j)+1
+        if(v(i).lt.tv(l)) go to 110
+        nrdatv(j) = nrdatv(j)-1
+        l = l+1
+        j = j+1
+        nrdatv(j) = 0
+ 110  continue
+      idd(1) = ider(1)
+      idd(2) = ider(2)
+      idd(3) = ider(3)
+      idd(4) = ider(4)
+      go to 120
+c  if iopt(1)=0 or iopt(1)=1 and s >= fp0,we start computing the least-
+c  squares polynomial (which is a spline without interior knots).
+ 115  ier = -2
+      idd(1) = ider(1)
+      idd(2) = 1
+      idd(3) = ider(3)
+      idd(4) = 1
+      nu = 8
+      nv = 8
+      nrdatu(1) = mu-2+iopt(2)+iopt(3)
+      nrdatv(1) = mv-1
+      lastdi = 0
+      nplusu = 0
+      nplusv = 0
+      fp0 = 0.
+      fpold = 0.
+      reducu = 0.
+      reducv = 0.
+c  main loop for the different sets of knots.mpm=mu+mv is a save upper
+c  bound for the number of trials.
+ 120  mpm = mu+mv
+      do 270 iter=1,mpm
+c  find nrintu (nrintv) which is the number of knot intervals in the
+c  u-direction (v-direction).
+        nrintu = nu-7
+        nrintv = nv-7
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(u,v).
+        i = nu
+        do 125 j=1,4
+          tu(j) = 0.
+          tu(i) = pi
+          i = i-1
+ 125    continue
+        l1 = 4
+        l2 = l1
+        l3 = nv-3
+        l4 = l3
+        tv(l2) = vb
+        tv(l3) = ve
+        do 130 j=1,3
+          l1 = l1+1
+          l2 = l2-1
+          l3 = l3+1
+          l4 = l4-1
+          tv(l2) = tv(l4)-per
+          tv(l3) = tv(l1)+per
+ 130    continue
+c  find an estimate of the range of possible values for the optimal
+c  derivatives at the origin.
+        ktu = nrdatu(1)+2-iopt(2)
+        if(ktu.lt.mumin) ktu = mumin
+        if(ktu.eq.lastu0) go to 140
+         rmin = r0
+         rmax = r0
+         l = mv*ktu
+         do 135 i=1,l
+            if(r(i).lt.rmin) rmin = r(i)
+            if(r(i).gt.rmax) rmax = r(i)
+ 135     continue
+         step(1) = rmax-rmin
+         lastu0 = ktu
+ 140    ktu = nrdatu(nrintu)+2-iopt(3)
+        if(ktu.lt.mumin) ktu = mumin
+        if(ktu.eq.lastu1) go to 150
+         rmin = r1
+         rmax = r1
+         l = mv*ktu
+         j = mr
+         do 145 i=1,l
+            if(r(j).lt.rmin) rmin = r(j)
+            if(r(j).gt.rmax) rmax = r(j)
+            j = j-1
+ 145     continue
+         step(2) = rmax-rmin
+         lastu1 = ktu
+c  find the least-squares spline sinf(u,v).
+ 150    call fpopsp(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,r,mr,r0,r1,dr,iopt,
+     *   idd,tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,
+     *   nrv,wrk,lwrk)
+        if(step(1).lt.0.) step(1) = -step(1)
+        if(step(2).lt.0.) step(2) = -step(2)
+        if(ier.eq.(-2)) fp0 = fp
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt(1).lt.0) go to 440
+        fpms = fp-s
+        if(abs(fpms) .lt. acc) go to 440
+c  if f(p=inf) < s, we accept the choice of knots.
+        if(fpms.lt.0.) go to 300
+c  if nu=numax and nv=nvmax, sinf(u,v) is an interpolating spline
+        if(nu.eq.numax .and. nv.eq.nvmax) go to 430
+c  increase the number of knots.
+c  if nu=nue and nv=nve we cannot further increase the number of knots
+c  because of the storage capacity limitation.
+        if(nu.eq.nue .and. nv.eq.nve) go to 420
+        if(ider(1).eq.0) fpintu(1) = fpintu(1)+(r0-dr(1))**2
+        if(ider(3).eq.0) fpintu(nrintu) = fpintu(nrintu)+(r1-dr(4))**2
+        ier = 0
+c  adjust the parameter reducu or reducv according to the direction
+c  in which the last added knots were located.
+        if (lastdi.lt.0) go to 160
+        if (lastdi.eq.0) go to 155
+        go to 170
+ 155     nplv = 3
+         idd(2) = ider(2)
+         idd(4) = ider(4)
+         fpold = fp
+         go to 230
+ 160    reducu = fpold-fp
+        go to 175
+ 170    reducv = fpold-fp
+c  store the sum of squared residuals for the current set of knots.
+ 175    fpold = fp
+c  find nplu, the number of knots we should add in the u-direction.
+        nplu = 1
+        if(nu.eq.8) go to 180
+        npl1 = nplusu*2
+        rn = nplusu
+        if(reducu.gt.acc) npl1 = rn*fpms/reducu
+        nplu = min0(nplusu*2,max0(npl1,nplusu/2,1))
+c  find nplv, the number of knots we should add in the v-direction.
+ 180    nplv = 3
+        if(nv.eq.8) go to 190
+        npl1 = nplusv*2
+        rn = nplusv
+        if(reducv.gt.acc) npl1 = rn*fpms/reducv
+        nplv = min0(nplusv*2,max0(npl1,nplusv/2,1))
+c  test whether we are going to add knots in the u- or v-direction.
+ 190    if (nplu.lt.nplv) go to 210
+        if (nplu.eq.nplv) go to 200
+        go to 230
+ 200    if(lastdi.lt.0) go to 230
+ 210    if(nu.eq.nue) go to 230
+c  addition in the u-direction.
+        lastdi = -1
+        nplusu = nplu
+        ifsu = 0
+        istart = 0
+        if(iopt(2).eq.0) istart = 1
+        do 220 l=1,nplusu
+c  add a new knot in the u-direction
+          call fpknot(u,mu,tu,nu,fpintu,nrdatu,nrintu,nuest,istart)
+c  test whether we cannot further increase the number of knots in the
+c  u-direction.
+          if(nu.eq.nue) go to 270
+ 220    continue
+        go to 270
+ 230    if(nv.eq.nve) go to 210
+c  addition in the v-direction.
+        lastdi = 1
+        nplusv = nplv
+        ifsv = 0
+        do 240 l=1,nplusv
+c  add a new knot in the v-direction.
+          call fpknot(v,mv,tv,nv,fpintv,nrdatv,nrintv,nvest,1)
+c  test whether we cannot further increase the number of knots in the
+c  v-direction.
+          if(nv.eq.nve) go to 270
+ 240    continue
+c  restart the computations with the new set of knots.
+ 270  continue
+c  test whether the least-squares polynomial is a solution of our
+c  approximation problem.
+ 300  if(ier.eq.(-2)) go to 440
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing spline sp(u,v)                c
+c *****************************************************                c
+c  we have determined the number of knots and their position. we now   c
+c  compute the b-spline coefficients of the smoothing spline sp(u,v).  c
+c  this smoothing spline depends on the parameter p in such a way that c
+c    f(p) = sumi=1,mu(sumj=1,mv((z(i,j)-sp(u(i),v(j)))**2)             c
+c  is a continuous, strictly decreasing function of p. moreover the    c
+c  least-squares polynomial corresponds to p=0 and the least-squares   c
+c  spline to p=infinity. then iteratively we have to determine the     c
+c  positive value of p such that f(p)=s. the process which is proposed c
+c  here makes use of rational interpolation. f(p) is approximated by a c
+c  rational function r(p)=(u*p+v)/(p+w); three values of p (p1,p2,p3)  c
+c  with corresponding values of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s)c
+c  are used to calculate the new value of p such that r(p)=s.          c
+c  convergence is guaranteed by taking f1 > 0 and f3 < 0.              c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  initial value for p.
+      p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = one
+      do 305 i=1,6
+        drr(i) = dr(i)
+ 305  continue
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p)=s.
+      do 350 iter = 1,maxit
+c  find the smoothing spline sp(u,v) and the corresponding sum f(p).
+        call fpopsp(ifsu,ifsv,ifbu,ifbv,u,mu,v,mv,r,mr,r0,r1,drr,iopt,
+     *   idd,tu,nu,tv,nv,nuest,nvest,p,step,c,nc,fp,fpintu,fpintv,nru,
+     *   nrv,wrk,lwrk)
+c  test whether the approximation sp(u,v) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).lt.acc) go to 440
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 400
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 320
+        if((f2-f3).gt.acc) go to 310
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 350
+ 310    if(f2.lt.0.) ich3 = 1
+ 320    if(ich1.ne.0) go to 340
+        if((f1-f2).gt.acc) go to 330
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 350
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 350
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 330    if(f2.gt.0.) ich1 = 1
+ 340    if(f2.ge.f1 .or. f2.le.f3) go to 410
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 350  continue
+c  error codes and messages.
+ 400  ier = 3
+      go to 440
+ 410  ier = 2
+      go to 440
+ 420  ier = 1
+      go to 440
+ 430  ier = -1
+      fp = 0.
+ 440  return
+      end

Added: branches/Interpolate1D/fitpack/fpsphe.f
===================================================================
--- branches/Interpolate1D/fitpack/fpsphe.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpsphe.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,764 @@
+      subroutine fpsphe(iopt,m,teta,phi,r,w,s,ntest,npest,eta,tol,maxit,
+     *
+     * ib1,ib3,nc,ncc,intest,nrest,nt,tt,np,tp,c,fp,sup,fpint,coord,f,
+     * ff,row,coco,cosi,a,q,bt,bp,spt,spp,h,index,nummer,wrk,lwrk,ier)
+c  ..
+c  ..scalar arguments..
+      integer iopt,m,ntest,npest,maxit,ib1,ib3,nc,ncc,intest,nrest,
+     * nt,np,lwrk,ier
+      real*8 s,eta,tol,fp,sup
+c  ..array arguments..
+      real*8 teta(m),phi(m),r(m),w(m),tt(ntest),tp(npest),c(nc),
+     * fpint(intest),coord(intest),f(ncc),ff(nc),row(npest),coco(npest),
+     *
+     * cosi(npest),a(ncc,ib1),q(ncc,ib3),bt(ntest,5),bp(npest,5),
+     * spt(m,4),spp(m,4),h(ib3),wrk(lwrk)
+      integer index(nrest),nummer(m)
+c  ..local scalars..
+      real*8 aa,acc,arg,cn,co,c1,dmax,d1,d2,eps,facc,facs,fac1,fac2,fn,
+     * fpmax,fpms,f1,f2,f3,hti,htj,p,pi,pinv,piv,pi2,p1,p2,p3,ri,si,
+     * sigma,sq,store,wi,rn,one,con1,con9,con4,half,ten
+      integer i,iband,iband1,iband3,iband4,ich1,ich3,ii,ij,il,in,irot,
+     * iter,i1,i2,i3,j,jlt,jrot,j1,j2,l,la,lf,lh,ll,lp,lt,lwest,l1,l2,
+     * l3,l4,ncof,ncoff,npp,np4,nreg,nrint,nrr,nr1,ntt,nt4,nt6,num,
+     * num1,rank
+c  ..local arrays..
+      real*8 ht(4),hp(4)
+c  ..function references..
+      real*8 abs,atan,fprati,sqrt,cos,sin
+      integer min0
+c  ..subroutine references..
+c   fpback,fpbspl,fpgivs,fpdisc,fporde,fprank,fprota,fprpsp
+c  ..
+c  set constants
+      one = 0.1e+01
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      half = 0.5e0
+      ten = 0.1e+02
+      pi = atan(one)*4
+      pi2 = pi+pi
+      eps = sqrt(eta)
+      if(iopt.lt.0) go to 70
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+      if(iopt.eq.0) go to 10
+      if(s.lt.sup) then
+        if (np.lt.11) go to 60
+        go to 70
+      endif
+c  if iopt=0 we begin by computing the weighted least-squares polynomial
+c  of the form
+c     s(teta,phi) = c1*f1(teta) + cn*fn(teta)
+c  where f1(teta) and fn(teta) are the cubic polynomials satisfying
+c     f1(0) = 1, f1(pi) = f1'(0) = f1'(pi) = 0 ; fn(teta) = 1-f1(teta).
+c  the corresponding weighted sum of squared residuals gives the upper
+c  bound sup for the smoothing factor s.
+  10  sup = 0.
+      d1 = 0.
+      d2 = 0.
+      c1 = 0.
+      cn = 0.
+      fac1 = pi*(one + half)
+      fac2 = (one + one)/pi**3
+      aa = 0.
+      do 40 i=1,m
+         wi = w(i)
+         ri = r(i)*wi
+         arg = teta(i)
+         fn = fac2*arg*arg*(fac1-arg)
+         f1 = (one-fn)*wi
+         fn = fn*wi
+         if(fn.eq.0.) go to 20
+         call fpgivs(fn,d1,co,si)
+         call fprota(co,si,f1,aa)
+         call fprota(co,si,ri,cn)
+ 20      if(f1.eq.0.) go to 30
+         call fpgivs(f1,d2,co,si)
+         call fprota(co,si,ri,c1)
+ 30      sup = sup+ri*ri
+ 40   continue
+      if(d2.ne.0.) c1 = c1/d2
+      if(d1.ne.0.) cn = (cn-aa*c1)/d1
+c  find the b-spline representation of this least-squares polynomial
+      nt = 8
+      np = 8
+      do 50 i=1,4
+         c(i) = c1
+         c(i+4) = c1
+         c(i+8) = cn
+         c(i+12) = cn
+         tt(i) = 0.
+         tt(i+4) = pi
+         tp(i) = 0.
+         tp(i+4) = pi2
+  50  continue
+      fp = sup
+c  test whether the least-squares polynomial is an acceptable solution
+      fpms = sup-s
+      if(fpms.lt.acc) go to 960
+c  test whether we cannot further increase the number of knots.
+  60  if(npest.lt.11 .or. ntest.lt.9) go to 950
+c  find the initial set of interior knots of the spherical spline in
+c  case iopt = 0.
+      np = 11
+      tp(5) = pi*half
+      tp(6) = pi
+      tp(7) = tp(5)+pi
+      nt = 9
+      tt(5) = tp(5)
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  part 1 : computation of least-squares spherical splines.            c
+c  ********************************************************            c
+c  if iopt < 0 we compute the least-squares spherical spline according c
+c  to the given set of knots.                                          c
+c  if iopt >=0 we compute least-squares spherical splines with increas-c
+c  ing numbers of knots until the corresponding sum f(p=inf)<=s.       c
+c  the initial set of knots then depends on the value of iopt:         c
+c    if iopt=0 we start with one interior knot in the teta-direction   c
+c              (pi/2) and three in the phi-direction (pi/2,pi,3*pi/2). c
+c    if iopt>0 we start with the set of knots found at the last call   c
+c              of the routine.                                         c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  main loop for the different sets of knots. m is a save upper bound
+c  for the number of trials.
+  70  do 570 iter=1,m
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(teta,phi).
+         l1 = 4
+         l2 = l1
+         l3 = np-3
+         l4 = l3
+         tp(l2) = 0.
+         tp(l3) = pi2
+         do 80 i=1,3
+            l1 = l1+1
+            l2 = l2-1
+            l3 = l3+1
+            l4 = l4-1
+            tp(l2) = tp(l4)-pi2
+            tp(l3) = tp(l1)+pi2
+  80     continue
+        l = nt
+        do 90 i=1,4
+          tt(i) = 0.
+          tt(l) = pi
+          l = l-1
+  90    continue
+c  find nrint, the total number of knot intervals and nreg, the number
+c  of panels in which the approximation domain is subdivided by the
+c  intersection of knots.
+        ntt = nt-7
+        npp = np-7
+        nrr = npp/2
+        nr1 = nrr+1
+        nrint = ntt+npp
+        nreg = ntt*npp
+c  arrange the data points according to the panel they belong to.
+        call fporde(teta,phi,m,3,3,tt,nt,tp,np,nummer,index,nreg)
+c  find the b-spline coefficients coco and cosi of the cubic spline
+c  approximations sc(phi) and ss(phi) for cos(phi) and sin(phi).
+        do 100 i=1,npp
+           coco(i) = 0.
+           cosi(i) = 0.
+           do 100 j=1,npp
+              a(i,j) = 0.
+ 100    continue
+c  the coefficients coco and cosi are obtained from the conditions
+c  sc(tp(i))=cos(tp(i)),resp. ss(tp(i))=sin(tp(i)),i=4,5,...np-4.
+        do 150 i=1,npp
+           l2 = i+3
+           arg = tp(l2)
+           call fpbspl(tp,np,3,arg,l2,hp)
+           do 110 j=1,npp
+              row(j) = 0.
+ 110       continue
+           ll = i
+           do 120 j=1,3
+              if(ll.gt.npp) ll= 1
+              row(ll) = row(ll)+hp(j)
+              ll = ll+1
+ 120       continue
+           facc = cos(arg)
+           facs = sin(arg)
+           do 140 j=1,npp
+              piv = row(j)
+              if(piv.eq.0.) go to 140
+              call fpgivs(piv,a(j,1),co,si)
+              call fprota(co,si,facc,coco(j))
+              call fprota(co,si,facs,cosi(j))
+              if(j.eq.npp) go to 150
+              j1 = j+1
+              i2 = 1
+              do 130 l=j1,npp
+                 i2 = i2+1
+                 call fprota(co,si,row(l),a(j,i2))
+ 130          continue
+ 140       continue
+ 150    continue
+        call fpback(a,coco,npp,npp,coco,ncc)
+        call fpback(a,cosi,npp,npp,cosi,ncc)
+c  find ncof, the dimension of the spherical spline and ncoff, the
+c  number of coefficients in the standard b-spline representation.
+        nt4 = nt-4
+        np4 = np-4
+        ncoff = nt4*np4
+        ncof = 6+npp*(ntt-1)
+c  find the bandwidth of the observation matrix a.
+        iband = 4*npp
+        if(ntt.eq.4) iband = 3*(npp+1)
+        if(ntt.lt.4) iband = ncof
+        iband1 = iband-1
+c  initialize the observation matrix a.
+        do 160 i=1,ncof
+          f(i) = 0.
+          do 160 j=1,iband
+            a(i,j) = 0.
+ 160    continue
+c  initialize the sum of squared residuals.
+        fp = 0.
+c  fetch the data points in the new order. main loop for the
+c  different panels.
+        do 340 num=1,nreg
+c  fix certain constants for the current panel; jrot records the column
+c  number of the first non-zero element in a row of the observation
+c  matrix according to a data point of the panel.
+          num1 = num-1
+          lt = num1/npp
+          l1 = lt+4
+          lp = num1-lt*npp+1
+          l2 = lp+3
+          lt = lt+1
+          jrot = 0
+          if(lt.gt.2) jrot = 3+(lt-3)*npp
+c  test whether there are still data points in the current panel.
+          in = index(num)
+ 170      if(in.eq.0) go to 340
+c  fetch a new data point.
+          wi = w(in)
+          ri = r(in)*wi
+c  evaluate for the teta-direction, the 4 non-zero b-splines at teta(in)
+          call fpbspl(tt,nt,3,teta(in),l1,ht)
+c  evaluate for the phi-direction, the 4 non-zero b-splines at phi(in)
+          call fpbspl(tp,np,3,phi(in),l2,hp)
+c  store the value of these b-splines in spt and spp resp.
+          do 180 i=1,4
+            spp(in,i) = hp(i)
+            spt(in,i) = ht(i)
+ 180      continue
+c  initialize the new row of observation matrix.
+          do 190 i=1,iband
+            h(i) = 0.
+ 190      continue
+c  calculate the non-zero elements of the new row by making the cross
+c  products of the non-zero b-splines in teta- and phi-direction and
+c  by taking into account the conditions of the spherical splines.
+          do 200 i=1,npp
+             row(i) = 0.
+ 200      continue
+c  take into account the condition (3) of the spherical splines.
+          ll = lp
+          do 210 i=1,4
+             if(ll.gt.npp) ll=1
+             row(ll) = row(ll)+hp(i)
+             ll = ll+1
+ 210      continue
+c  take into account the other conditions of the spherical splines.
+          if(lt.gt.2 .and. lt.lt.(ntt-1)) go to 230
+          facc = 0.
+          facs = 0.
+          do 220 i=1,npp
+             facc = facc+row(i)*coco(i)
+             facs = facs+row(i)*cosi(i)
+ 220     continue
+c  fill in the non-zero elements of the new row.
+ 230     j1 = 0
+         do 280 j =1,4
+            jlt = j+lt
+            htj = ht(j)
+            if(jlt.gt.2 .and. jlt.le.nt4) go to 240
+            j1 = j1+1
+            h(j1) = h(j1)+htj
+            go to 280
+ 240        if(jlt.eq.3 .or. jlt.eq.nt4) go to 260
+            do 250 i=1,npp
+               j1 = j1+1
+               h(j1) = row(i)*htj
+ 250        continue
+            go to 280
+ 260        if(jlt.eq.3) go to 270
+            h(j1+1) = facc*htj
+            h(j1+2) = facs*htj
+            h(j1+3) = htj
+            j1 = j1+2
+            go to 280
+ 270        h(1) = h(1)+htj
+            h(2) = facc*htj
+            h(3) = facs*htj
+            j1 = 3
+ 280      continue
+          do 290 i=1,iband
+            h(i) = h(i)*wi
+ 290      continue
+c  rotate the row into triangle by givens transformations.
+          irot = jrot
+          do 310 i=1,iband
+            irot = irot+1
+            piv = h(i)
+            if(piv.eq.0.) go to 310
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(irot,1),co,si)
+c  apply that transformation to the right hand side.
+            call fprota(co,si,ri,f(irot))
+            if(i.eq.iband) go to 320
+c  apply that transformation to the left hand side.
+            i2 = 1
+            i3 = i+1
+            do 300 j=i3,iband
+              i2 = i2+1
+              call fprota(co,si,h(j),a(irot,i2))
+ 300        continue
+ 310      continue
+c  add the contribution of the row to the sum of squares of residual
+c  right hand sides.
+ 320      fp = fp+ri**2
+c  find the number of the next data point in the panel.
+ 330      in = nummer(in)
+          go to 170
+ 340    continue
+c  find dmax, the maximum value for the diagonal elements in the reduced
+c  triangle.
+        dmax = 0.
+        do 350 i=1,ncof
+          if(a(i,1).le.dmax) go to 350
+          dmax = a(i,1)
+ 350    continue
+c  check whether the observation matrix is rank deficient.
+        sigma = eps*dmax
+        do 360 i=1,ncof
+          if(a(i,1).le.sigma) go to 370
+ 360    continue
+c  backward substitution in case of full rank.
+        call fpback(a,f,ncof,iband,c,ncc)
+        rank = ncof
+        do 365 i=1,ncof
+          q(i,1) = a(i,1)/dmax
+ 365    continue
+        go to 390
+c  in case of rank deficiency, find the minimum norm solution.
+ 370    lwest = ncof*iband+ncof+iband
+        if(lwrk.lt.lwest) go to 925
+        lf = 1
+        lh = lf+ncof
+        la = lh+iband
+        do 380 i=1,ncof
+          ff(i) = f(i)
+          do 380 j=1,iband
+            q(i,j) = a(i,j)
+ 380    continue
+        call fprank(q,ff,ncof,iband,ncc,sigma,c,sq,rank,wrk(la),
+     *   wrk(lf),wrk(lh))
+        do 385 i=1,ncof
+          q(i,1) = q(i,1)/dmax
+ 385    continue
+c  add to the sum of squared residuals, the contribution of reducing
+c  the rank.
+        fp = fp+sq
+c  find the coefficients in the standard b-spline representation of
+c  the spherical spline.
+ 390    call fprpsp(nt,np,coco,cosi,c,ff,ncoff)
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt.lt.0) then
+          if (fp.le.0) go to 970
+          go to 980
+        endif
+        fpms = fp-s
+        if(abs(fpms).le.acc) then
+          if (fp.le.0) go to 970
+          go to 980
+        endif
+c  if f(p=inf) < s, accept the choice of knots.
+        if(fpms.lt.0.) go to 580
+c  test whether we cannot further increase the number of knots.
+        if(ncof.gt.m) go to 935
+c  search where to add a new knot.
+c  find for each interval the sum of squared residuals fpint for the
+c  data points having the coordinate belonging to that knot interval.
+c  calculate also coord which is the same sum, weighted by the position
+c  of the data points considered.
+ 440    do 450 i=1,nrint
+          fpint(i) = 0.
+          coord(i) = 0.
+ 450    continue
+        do 490 num=1,nreg
+          num1 = num-1
+          lt = num1/npp
+          l1 = lt+1
+          lp = num1-lt*npp
+          l2 = lp+1+ntt
+          jrot = lt*np4+lp
+          in = index(num)
+ 460      if(in.eq.0) go to 490
+          store = 0.
+          i1 = jrot
+          do 480 i=1,4
+            hti = spt(in,i)
+            j1 = i1
+            do 470 j=1,4
+              j1 = j1+1
+              store = store+hti*spp(in,j)*c(j1)
+ 470        continue
+            i1 = i1+np4
+ 480      continue
+          store = (w(in)*(r(in)-store))**2
+          fpint(l1) = fpint(l1)+store
+          coord(l1) = coord(l1)+store*teta(in)
+          fpint(l2) = fpint(l2)+store
+          coord(l2) = coord(l2)+store*phi(in)
+          in = nummer(in)
+          go to 460
+ 490    continue
+c  find the interval for which fpint is maximal on the condition that
+c  there still can be added a knot.
+        l1 = 1
+        l2 = nrint
+        if(ntest.lt.nt+1) l1=ntt+1
+        if(npest.lt.np+2) l2=ntt
+c  test whether we cannot further increase the number of knots.
+        if(l1.gt.l2) go to 950
+ 500    fpmax = 0.
+        l = 0
+        do 510 i=l1,l2
+          if(fpmax.ge.fpint(i)) go to 510
+          l = i
+          fpmax = fpint(i)
+ 510    continue
+        if(l.eq.0) go to 930
+c  calculate the position of the new knot.
+        arg = coord(l)/fpint(l)
+c  test in what direction the new knot is going to be added.
+        if(l.gt.ntt) go to 530
+c  addition in the teta-direction
+        l4 = l+4
+        fpint(l) = 0.
+        fac1 = tt(l4)-arg
+        fac2 = arg-tt(l4-1)
+        if(fac1.gt.(ten*fac2) .or. fac2.gt.(ten*fac1)) go to 500
+        j = nt
+        do 520 i=l4,nt
+          tt(j+1) = tt(j)
+          j = j-1
+ 520    continue
+        tt(l4) = arg
+        nt = nt+1
+        go to 570
+c  addition in the phi-direction
+ 530    l4 = l+4-ntt
+        if(arg.lt.pi) go to 540
+        arg = arg-pi
+        l4 = l4-nrr
+ 540    fpint(l) = 0.
+        fac1 = tp(l4)-arg
+        fac2 = arg-tp(l4-1)
+        if(fac1.gt.(ten*fac2) .or. fac2.gt.(ten*fac1)) go to 500
+        ll = nrr+4
+        j = ll
+        do 550 i=l4,ll
+          tp(j+1) = tp(j)
+          j = j-1
+ 550    continue
+        tp(l4) = arg
+        np = np+2
+        nrr = nrr+1
+        do 560 i=5,ll
+          j = i+nrr
+          tp(j) = tp(i)+pi
+ 560    continue
+c  restart the computations with the new set of knots.
+ 570  continue
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing spherical spline.             c
+c ********************************************************             c
+c we have determined the number of knots and their position. we now    c
+c compute the coefficients of the smoothing spline sp(teta,phi).       c
+c the observation matrix a is extended by the rows of a matrix, expres-c
+c sing that sp(teta,phi) must be a constant function in the variable   c
+c phi and a cubic polynomial in the variable teta. the corresponding   c
+c weights of these additional rows are set to 1/(p). iteratively       c
+c we than have to determine the value of p such that f(p) = sum((w(i)* c
+c (r(i)-sp(teta(i),phi(i))))**2)  be = s.                              c
+c we already know that the least-squares polynomial corresponds to p=0,c
+c and that the least-squares spherical spline corresponds to p=infin.  c
+c the iteration process makes use of rational interpolation. since f(p)c
+c is a convex and strictly decreasing function of p, it can be approx- c
+c imated by a rational function of the form r(p) = (u*p+v)/(p+w).      c
+c three values of p (p1,p2,p3) with corresponding values of f(p) (f1=  c
+c f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used to calculate the new value   c
+c of p such that r(p)=s. convergence is guaranteed by taking f1>0,f3<0.c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  evaluate the discontinuity jumps of the 3-th order derivative of
+c  the b-splines at the knots tt(l),l=5,...,nt-4.
+ 580  call fpdisc(tt,nt,5,bt,ntest)
+c  evaluate the discontinuity jumps of the 3-th order derivative of
+c  the b-splines at the knots tp(l),l=5,...,np-4.
+      call fpdisc(tp,np,5,bp,npest)
+c  initial value for p.
+      p1 = 0.
+      f1 = sup-s
+      p3 = -one
+      f3 = fpms
+      p = 0.
+      do 585 i=1,ncof
+        p = p+a(i,1)
+ 585  continue
+      rn = ncof
+      p = rn/p
+c  find the bandwidth of the extended observation matrix.
+      iband4 = iband+3
+      if(ntt.le.4) iband4 = ncof
+      iband3 = iband4 -1
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p)=s.
+      do 920 iter=1,maxit
+        pinv = one/p
+c  store the triangularized observation matrix into q.
+        do 600 i=1,ncof
+          ff(i) = f(i)
+          do 590 j=1,iband4
+            q(i,j) = 0.
+ 590      continue
+          do 600 j=1,iband
+            q(i,j) = a(i,j)
+ 600    continue
+c  extend the observation matrix with the rows of a matrix, expressing
+c  that for teta=cst. sp(teta,phi) must be a constant function.
+        nt6 = nt-6
+        do 720 i=5,np4
+          ii = i-4
+          do 610 l=1,npp
+             row(l) = 0.
+ 610      continue
+          ll = ii
+          do 620  l=1,5
+             if(ll.gt.npp) ll=1
+             row(ll) = row(ll)+bp(ii,l)
+             ll = ll+1
+ 620      continue
+          facc = 0.
+          facs = 0.
+          do 630 l=1,npp
+             facc = facc+row(l)*coco(l)
+             facs = facs+row(l)*cosi(l)
+ 630      continue
+          do 720 j=1,nt6
+c  initialize the new row.
+            do 640 l=1,iband
+              h(l) = 0.
+ 640        continue
+c  fill in the non-zero elements of the row. jrot records the column
+c  number of the first non-zero element in the row.
+            jrot = 4+(j-2)*npp
+            if(j.gt.1 .and. j.lt.nt6) go to 650
+            h(1) = facc
+            h(2) = facs
+            if(j.eq.1) jrot = 2
+            go to 670
+ 650        do 660 l=1,npp
+               h(l)=row(l)
+ 660        continue
+ 670        do 675 l=1,iband
+               h(l) = h(l)*pinv
+ 675        continue
+            ri = 0.
+c  rotate the new row into triangle by givens transformations.
+            do 710 irot=jrot,ncof
+              piv = h(1)
+              i2 = min0(iband1,ncof-irot)
+              if(piv.eq.0.) then
+                if (i2.le.0) go to 720
+                go to 690
+              endif
+c  calculate the parameters of the givens transformation.
+              call fpgivs(piv,q(irot,1),co,si)
+c  apply that givens transformation to the right hand side.
+              call fprota(co,si,ri,ff(irot))
+              if(i2.eq.0) go to 720
+c  apply that givens transformation to the left hand side.
+              do 680 l=1,i2
+                l1 = l+1
+                call fprota(co,si,h(l1),q(irot,l1))
+ 680          continue
+ 690          do 700 l=1,i2
+                h(l) = h(l+1)
+ 700          continue
+              h(i2+1) = 0.
+ 710        continue
+ 720    continue
+c  extend the observation matrix with the rows of a matrix expressing
+c  that for phi=cst. sp(teta,phi) must be a cubic polynomial.
+        do 810 i=5,nt4
+          ii = i-4
+          do 810 j=1,npp
+c  initialize the new row
+            do 730 l=1,iband4
+              h(l) = 0.
+ 730        continue
+c  fill in the non-zero elements of the row. jrot records the column
+c  number of the first non-zero element in the row.
+            j1 = 1
+            do 760 l=1,5
+               il = ii+l
+               ij = npp
+               if(il.ne.3 .and. il.ne.nt4) go to 750
+               j1 = j1+3-j
+               j2 = j1-2
+               ij = 0
+               if(il.ne.3) go to 740
+               j1 = 1
+               j2 = 2
+               ij = j+2
+ 740           h(j2) = bt(ii,l)*coco(j)
+               h(j2+1) = bt(ii,l)*cosi(j)
+ 750           h(j1) = h(j1)+bt(ii,l)
+               j1 = j1+ij
+ 760        continue
+            do 765 l=1,iband4
+               h(l) = h(l)*pinv
+ 765        continue
+            ri = 0.
+            jrot = 1
+            if(ii.gt.2) jrot = 3+j+(ii-3)*npp
+c  rotate the new row into triangle by givens transformations.
+            do 800 irot=jrot,ncof
+              piv = h(1)
+              i2 = min0(iband3,ncof-irot)
+              if(piv.eq.0.) then
+                if (i2.le.0) go to 810
+                go to 780
+              endif
+c  calculate the parameters of the givens transformation.
+              call fpgivs(piv,q(irot,1),co,si)
+c  apply that givens transformation to the right hand side.
+              call fprota(co,si,ri,ff(irot))
+              if(i2.eq.0) go to 810
+c  apply that givens transformation to the left hand side.
+              do 770 l=1,i2
+                l1 = l+1
+                call fprota(co,si,h(l1),q(irot,l1))
+ 770          continue
+ 780          do 790 l=1,i2
+                h(l) = h(l+1)
+ 790          continue
+              h(i2+1) = 0.
+ 800        continue
+ 810    continue
+c  find dmax, the maximum value for the diagonal elements in the
+c  reduced triangle.
+        dmax = 0.
+        do 820 i=1,ncof
+          if(q(i,1).le.dmax) go to 820
+          dmax = q(i,1)
+ 820    continue
+c  check whether the matrix is rank deficient.
+        sigma = eps*dmax
+        do 830 i=1,ncof
+          if(q(i,1).le.sigma) go to 840
+ 830    continue
+c  backward substitution in case of full rank.
+        call fpback(q,ff,ncof,iband4,c,ncc)
+        rank = ncof
+        go to 845
+c  in case of rank deficiency, find the minimum norm solution.
+ 840    lwest = ncof*iband4+ncof+iband4
+        if(lwrk.lt.lwest) go to 925
+        lf = 1
+        lh = lf+ncof
+        la = lh+iband4
+        call fprank(q,ff,ncof,iband4,ncc,sigma,c,sq,rank,wrk(la),
+     *   wrk(lf),wrk(lh))
+ 845    do 850 i=1,ncof
+           q(i,1) = q(i,1)/dmax
+ 850    continue
+c  find the coefficients in the standard b-spline representation of
+c  the spherical spline.
+        call fprpsp(nt,np,coco,cosi,c,ff,ncoff)
+c  compute f(p).
+        fp = 0.
+        do 890 num = 1,nreg
+          num1 = num-1
+          lt = num1/npp
+          lp = num1-lt*npp
+          jrot = lt*np4+lp
+          in = index(num)
+ 860      if(in.eq.0) go to 890
+          store = 0.
+          i1 = jrot
+          do 880 i=1,4
+            hti = spt(in,i)
+            j1 = i1
+            do 870 j=1,4
+              j1 = j1+1
+              store = store+hti*spp(in,j)*c(j1)
+ 870        continue
+            i1 = i1+np4
+ 880      continue
+          fp = fp+(w(in)*(r(in)-store))**2
+          in = nummer(in)
+          go to 860
+ 890    continue
+c  test whether the approximation sp(teta,phi) is an acceptable solution
+        fpms = fp-s
+        if(abs(fpms).le.acc) go to 980
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 940
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 900
+        if((f2-f3).gt.acc) go to 895
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 920
+ 895    if(f2.lt.0.) ich3 = 1
+ 900    if(ich1.ne.0) go to 910
+        if((f1-f2).gt.acc) go to 905
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 920
+        if(p.ge.p3) p = p2*con1 +p3*con9
+        go to 920
+ 905    if(f2.gt.0.) ich1 = 1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 910    if(f2.ge.f1 .or. f2.le.f3) go to 945
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 920  continue
+c  error codes and messages.
+ 925  ier = lwest
+      go to 990
+ 930  ier = 5
+      go to 990
+ 935  ier = 4
+      go to 990
+ 940  ier = 3
+      go to 990
+ 945  ier = 2
+      go to 990
+ 950  ier = 1
+      go to 990
+ 960  ier = -2
+      go to 990
+ 970  ier = -1
+      fp = 0.
+ 980  if(ncof.ne.rank) ier = -rank
+ 990  return
+      end

Added: branches/Interpolate1D/fitpack/fpsuev.f
===================================================================
--- branches/Interpolate1D/fitpack/fpsuev.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpsuev.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,80 @@
+      subroutine fpsuev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,wu,wv,lu,lv)
+c  ..scalar arguments..
+      integer idim,nu,nv,mu,mv
+c  ..array arguments..
+      integer lu(mu),lv(mv)
+      real*8 tu(nu),tv(nv),c((nu-4)*(nv-4)*idim),u(mu),v(mv),
+     * f(mu*mv*idim),wu(mu,4),wv(mv,4)
+c  ..local scalars..
+      integer i,i1,j,j1,k,l,l1,l2,l3,m,nuv,nu4,nv4
+      real*8 arg,sp,tb,te
+c  ..local arrays..
+      real*8 h(4)
+c  ..subroutine references..
+c    fpbspl
+c  ..
+      nu4 = nu-4
+      tb = tu(4)
+      te = tu(nu4+1)
+      l = 4
+      l1 = l+1
+      do 40 i=1,mu
+        arg = u(i)
+        if(arg.lt.tb) arg = tb
+        if(arg.gt.te) arg = te
+  10    if(arg.lt.tu(l1) .or. l.eq.nu4) go to 20
+        l = l1
+        l1 = l+1
+        go to 10
+  20    call fpbspl(tu,nu,3,arg,l,h)
+        lu(i) = l-4
+        do 30 j=1,4
+          wu(i,j) = h(j)
+  30    continue
+  40  continue
+      nv4 = nv-4
+      tb = tv(4)
+      te = tv(nv4+1)
+      l = 4
+      l1 = l+1
+      do 80 i=1,mv
+        arg = v(i)
+        if(arg.lt.tb) arg = tb
+        if(arg.gt.te) arg = te
+  50    if(arg.lt.tv(l1) .or. l.eq.nv4) go to 60
+        l = l1
+        l1 = l+1
+        go to 50
+  60    call fpbspl(tv,nv,3,arg,l,h)
+        lv(i) = l-4
+        do 70 j=1,4
+          wv(i,j) = h(j)
+  70    continue
+  80  continue
+      m = 0
+      nuv = nu4*nv4
+      do 140 k=1,idim
+        l3 = (k-1)*nuv
+        do 130 i=1,mu
+          l = lu(i)*nv4+l3
+          do 90 i1=1,4
+            h(i1) = wu(i,i1)
+  90      continue
+          do 120 j=1,mv
+            l1 = l+lv(j)
+            sp = 0.
+            do 110 i1=1,4
+              l2 = l1
+              do 100 j1=1,4
+                l2 = l2+1
+                sp = sp+c(l2)*h(i1)*wv(j,j1)
+ 100          continue
+              l1 = l1+nv4
+ 110        continue
+            m = m+1
+            f(m) = sp
+ 120      continue
+ 130    continue
+ 140  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fpsurf.f
===================================================================
--- branches/Interpolate1D/fitpack/fpsurf.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpsurf.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,680 @@
+      subroutine fpsurf(iopt,m,x,y,z,w,xb,xe,yb,ye,kxx,kyy,s,nxest,
+     * nyest,eta,tol,maxit,nmax,km1,km2,ib1,ib3,nc,intest,nrest,
+     * nx0,tx,ny0,ty,c,fp,fp0,fpint,coord,f,ff,a,q,bx,by,spx,spy,h,
+     * index,nummer,wrk,lwrk,ier)
+c  ..
+c  ..scalar arguments..
+      real*8 xb,xe,yb,ye,s,eta,tol,fp,fp0
+      integer iopt,m,kxx,kyy,nxest,nyest,maxit,nmax,km1,km2,ib1,ib3,
+     * nc,intest,nrest,nx0,ny0,lwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),z(m),w(m),tx(nmax),ty(nmax),c(nc),fpint(intest),
+     * coord(intest),f(nc),ff(nc),a(nc,ib1),q(nc,ib3),bx(nmax,km2),
+     * by(nmax,km2),spx(m,km1),spy(m,km1),h(ib3),wrk(lwrk)
+      integer index(nrest),nummer(m)
+c  ..local scalars..
+      real*8 acc,arg,cos,dmax,fac1,fac2,fpmax,fpms,f1,f2,f3,hxi,p,pinv,
+     * piv,p1,p2,p3,sigma,sin,sq,store,wi,x0,x1,y0,y1,zi,eps,
+     * rn,one,con1,con9,con4,half,ten
+      integer i,iband,iband1,iband3,iband4,ibb,ichang,ich1,ich3,ii,
+     * in,irot,iter,i1,i2,i3,j,jrot,jxy,j1,kx,kx1,kx2,ky,ky1,ky2,l,
+     * la,lf,lh,lwest,lx,ly,l1,l2,n,ncof,nk1x,nk1y,nminx,nminy,nreg,
+     * nrint,num,num1,nx,nxe,nxx,ny,nye,nyy,n1,rank
+c  ..local arrays..
+      real*8 hx(6),hy(6)
+c  ..function references..
+      real*8 abs,fprati,sqrt
+      integer min0
+c  ..subroutine references..
+c    fpback,fpbspl,fpgivs,fpdisc,fporde,fprank,fprota
+c  ..
+c  set constants
+      one = 0.1e+01
+      con1 = 0.1e0
+      con9 = 0.9e0
+      con4 = 0.4e-01
+      half = 0.5e0
+      ten = 0.1e+02
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 1: determination of the number of knots and their position.     c
+c ****************************************************************     c
+c given a set of knots we compute the least-squares spline sinf(x,y),  c
+c and the corresponding weighted sum of squared residuals fp=f(p=inf). c
+c if iopt=-1  sinf(x,y) is the requested approximation.                c
+c if iopt=0 or iopt=1 we check whether we can accept the knots:        c
+c   if fp <=s we will continue with the current set of knots.          c
+c   if fp > s we will increase the number of knots and compute the     c
+c      corresponding least-squares spline until finally  fp<=s.        c
+c the initial choice of knots depends on the value of s and iopt.      c
+c   if iopt=0 we first compute the least-squares polynomial of degree  c
+c     kx in x and ky in y; nx=nminx=2*kx+2 and ny=nminy=2*ky+2.        c
+c     fp0=f(0) denotes the corresponding weighted sum of squared       c
+c     residuals                                                        c
+c   if iopt=1 we start with the knots found at the last call of the    c
+c     routine, except for the case that s>=fp0; then we can compute    c
+c     the least-squares polynomial directly.                           c
+c eventually the independent variables x and y (and the corresponding  c
+c parameters) will be switched if this can reduce the bandwidth of the c
+c system to be solved.                                                 c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c  ichang denotes whether(1) or not(-1) the directions have been inter-
+c  changed.
+      ichang = -1
+      x0 = xb
+      x1 = xe
+      y0 = yb
+      y1 = ye
+      kx = kxx
+      ky = kyy
+      kx1 = kx+1
+      ky1 = ky+1
+      nxe = nxest
+      nye = nyest
+      eps = sqrt(eta)
+      if(iopt.lt.0) go to 20
+c  calculation of acc, the absolute tolerance for the root of f(p)=s.
+      acc = tol*s
+      if(iopt.eq.0) go to 10
+      if(fp0.gt.s) go to 20
+c  initialization for the least-squares polynomial.
+  10  nminx = 2*kx1
+      nminy = 2*ky1
+      nx = nminx
+      ny = nminy
+      ier = -2
+      go to 30
+  20  nx = nx0
+      ny = ny0
+c  main loop for the different sets of knots. m is a save upper bound
+c  for the number of trials.
+  30  do 420 iter=1,m
+c  find the position of the additional knots which are needed for the
+c  b-spline representation of s(x,y).
+        l = nx
+        do 40 i=1,kx1
+          tx(i) = x0
+          tx(l) = x1
+          l = l-1
+  40    continue
+        l = ny
+        do 50 i=1,ky1
+          ty(i) = y0
+          ty(l) = y1
+          l = l-1
+  50    continue
+c  find nrint, the total number of knot intervals and nreg, the number
+c  of panels in which the approximation domain is subdivided by the
+c  intersection of knots.
+        nxx = nx-2*kx1+1
+        nyy = ny-2*ky1+1
+        nrint = nxx+nyy
+        nreg = nxx*nyy
+c  find the bandwidth of the observation matrix a.
+c  if necessary, interchange the variables x and y, in order to obtain
+c  a minimal bandwidth.
+        iband1 = kx*(ny-ky1)+ky
+        l = ky*(nx-kx1)+kx
+        if(iband1.le.l) go to 130
+        iband1 = l
+        ichang = -ichang
+        do 60 i=1,m
+          store = x(i)
+          x(i) = y(i)
+          y(i) = store
+  60    continue
+        store = x0
+        x0 = y0
+        y0 = store
+        store = x1
+        x1 = y1
+        y1 = store
+        n = min0(nx,ny)
+        do 70 i=1,n
+          store = tx(i)
+          tx(i) = ty(i)
+          ty(i) = store
+  70    continue
+        n1 = n+1
+        if (nx.lt.ny) go to 80
+        if (nx.eq.ny) go to 120
+        go to 100
+  80    do 90 i=n1,ny
+          tx(i) = ty(i)
+  90    continue
+        go to 120
+ 100    do 110 i=n1,nx
+          ty(i) = tx(i)
+ 110    continue
+ 120    l = nx
+        nx = ny
+        ny = l
+        l = nxe
+        nxe = nye
+        nye = l
+        l = nxx
+        nxx = nyy
+        nyy = l
+        l = kx
+        kx = ky
+        ky = l
+        kx1 = kx+1
+        ky1 = ky+1
+ 130    iband = iband1+1
+c  arrange the data points according to the panel they belong to.
+        call fporde(x,y,m,kx,ky,tx,nx,ty,ny,nummer,index,nreg)
+c  find ncof, the number of b-spline coefficients.
+        nk1x = nx-kx1
+        nk1y = ny-ky1
+        ncof = nk1x*nk1y
+c  initialize the observation matrix a.
+        do 140 i=1,ncof
+          f(i) = 0.
+          do 140 j=1,iband
+            a(i,j) = 0.
+ 140    continue
+c  initialize the sum of squared residuals.
+        fp = 0.
+c  fetch the data points in the new order. main loop for the
+c  different panels.
+        do 250 num=1,nreg
+c  fix certain constants for the current panel; jrot records the column
+c  number of the first non-zero element in a row of the observation
+c  matrix according to a data point of the panel.
+          num1 = num-1
+          lx = num1/nyy
+          l1 = lx+kx1
+          ly = num1-lx*nyy
+          l2 = ly+ky1
+          jrot = lx*nk1y+ly
+c  test whether there are still data points in the panel.
+          in = index(num)
+ 150      if(in.eq.0) go to 250
+c  fetch a new data point.
+          wi = w(in)
+          zi = z(in)*wi
+c  evaluate for the x-direction, the (kx+1) non-zero b-splines at x(in).
+          call fpbspl(tx,nx,kx,x(in),l1,hx)
+c  evaluate for the y-direction, the (ky+1) non-zero b-splines at y(in).
+          call fpbspl(ty,ny,ky,y(in),l2,hy)
+c  store the value of these b-splines in spx and spy respectively.
+          do 160 i=1,kx1
+            spx(in,i) = hx(i)
+ 160      continue
+          do 170 i=1,ky1
+            spy(in,i) = hy(i)
+ 170      continue
+c  initialize the new row of observation matrix.
+          do 180 i=1,iband
+            h(i) = 0.
+ 180      continue
+c  calculate the non-zero elements of the new row by making the cross
+c  products of the non-zero b-splines in x- and y-direction.
+          i1 = 0
+          do 200 i=1,kx1
+            hxi = hx(i)
+            j1 = i1
+            do 190 j=1,ky1
+              j1 = j1+1
+              h(j1) = hxi*hy(j)*wi
+ 190        continue
+            i1 = i1+nk1y
+ 200      continue
+c  rotate the row into triangle by givens transformations .
+          irot = jrot
+          do 220 i=1,iband
+            irot = irot+1
+            piv = h(i)
+            if(piv.eq.0.) go to 220
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(irot,1),cos,sin)
+c  apply that transformation to the right hand side.
+            call fprota(cos,sin,zi,f(irot))
+            if(i.eq.iband) go to 230
+c  apply that transformation to the left hand side.
+            i2 = 1
+            i3 = i+1
+            do 210 j=i3,iband
+              i2 = i2+1
+              call fprota(cos,sin,h(j),a(irot,i2))
+ 210        continue
+ 220      continue
+c  add the contribution of the row to the sum of squares of residual
+c  right hand sides.
+ 230      fp = fp+zi**2
+c  find the number of the next data point in the panel.
+ 240      in = nummer(in)
+          go to 150
+ 250    continue
+c  find dmax, the maximum value for the diagonal elements in the reduced
+c  triangle.
+        dmax = 0.
+        do 260 i=1,ncof
+          if(a(i,1).le.dmax) go to 260
+          dmax = a(i,1)
+ 260    continue
+c  check whether the observation matrix is rank deficient.
+        sigma = eps*dmax
+        do 270 i=1,ncof
+          if(a(i,1).le.sigma) go to 280
+ 270    continue
+c  backward substitution in case of full rank.
+        call fpback(a,f,ncof,iband,c,nc)
+        rank = ncof
+        do 275 i=1,ncof
+          q(i,1) = a(i,1)/dmax
+ 275    continue
+        go to 300
+c  in case of rank deficiency, find the minimum norm solution.
+c  check whether there is sufficient working space
+ 280    lwest = ncof*iband+ncof+iband
+        if(lwrk.lt.lwest) go to 780
+        do 290 i=1,ncof
+          ff(i) = f(i)
+          do 290 j=1,iband
+            q(i,j) = a(i,j)
+ 290    continue
+        lf =1
+        lh = lf+ncof
+        la = lh+iband
+        call fprank(q,ff,ncof,iband,nc,sigma,c,sq,rank,wrk(la),
+     *    wrk(lf),wrk(lh))
+        do 295 i=1,ncof
+          q(i,1) = q(i,1)/dmax
+ 295    continue
+c  add to the sum of squared residuals, the contribution of reducing
+c  the rank.
+        fp = fp+sq
+ 300    if(ier.eq.(-2)) fp0 = fp
+c  test whether the least-squares spline is an acceptable solution.
+        if(iopt.lt.0) go to 820
+        fpms = fp-s
+        if(abs(fpms).le.acc) then
+          if (fp.le.0) go to 815
+          go to 820
+        endif
+c  test whether we can accept the choice of knots.
+        if(fpms.lt.0.) go to 430
+c  test whether we cannot further increase the number of knots.
+        if(ncof.gt.m) go to 790
+        ier = 0
+c  search where to add a new knot.
+c  find for each interval the sum of squared residuals fpint for the
+c  data points having the coordinate belonging to that knot interval.
+c  calculate also coord which is the same sum, weighted by the position
+c  of the data points considered.
+ 310    do 320 i=1,nrint
+          fpint(i) = 0.
+          coord(i) = 0.
+ 320    continue
+        do 360 num=1,nreg
+          num1 = num-1
+          lx = num1/nyy
+          l1 = lx+1
+          ly = num1-lx*nyy
+          l2 = ly+1+nxx
+          jrot = lx*nk1y+ly
+          in = index(num)
+ 330      if(in.eq.0) go to 360
+          store = 0.
+          i1 = jrot
+          do 350 i=1,kx1
+            hxi = spx(in,i)
+            j1 = i1
+            do 340 j=1,ky1
+              j1 = j1+1
+              store = store+hxi*spy(in,j)*c(j1)
+ 340        continue
+            i1 = i1+nk1y
+ 350      continue
+          store = (w(in)*(z(in)-store))**2
+          fpint(l1) = fpint(l1)+store
+          coord(l1) = coord(l1)+store*x(in)
+          fpint(l2) = fpint(l2)+store
+          coord(l2) = coord(l2)+store*y(in)
+          in = nummer(in)
+          go to 330
+ 360    continue
+c  find the interval for which fpint is maximal on the condition that
+c  there still can be added a knot.
+ 370    l = 0
+        fpmax = 0.
+        l1 = 1
+        l2 = nrint
+        if(nx.eq.nxe) l1 = nxx+1
+        if(ny.eq.nye) l2 = nxx
+        if(l1.gt.l2) go to 810
+        do 380 i=l1,l2
+          if(fpmax.ge.fpint(i)) go to 380
+          l = i
+          fpmax = fpint(i)
+ 380    continue
+c  test whether we cannot further increase the number of knots.
+        if(l.eq.0) go to 785
+c  calculate the position of the new knot.
+        arg = coord(l)/fpint(l)
+c  test in what direction the new knot is going to be added.
+        if(l.gt.nxx) go to 400
+c  addition in the x-direction.
+        jxy = l+kx1
+        fpint(l) = 0.
+        fac1 = tx(jxy)-arg
+        fac2 = arg-tx(jxy-1)
+        if(fac1.gt.(ten*fac2) .or. fac2.gt.(ten*fac1)) go to 370
+        j = nx
+        do 390 i=jxy,nx
+          tx(j+1) = tx(j)
+          j = j-1
+ 390    continue
+        tx(jxy) = arg
+        nx = nx+1
+        go to 420
+c  addition in the y-direction.
+ 400    jxy = l+ky1-nxx
+        fpint(l) = 0.
+        fac1 = ty(jxy)-arg
+        fac2 = arg-ty(jxy-1)
+        if(fac1.gt.(ten*fac2) .or. fac2.gt.(ten*fac1)) go to 370
+        j = ny
+        do 410 i=jxy,ny
+          ty(j+1) = ty(j)
+          j = j-1
+ 410    continue
+        ty(jxy) = arg
+        ny = ny+1
+c  restart the computations with the new set of knots.
+ 420  continue
+c  test whether the least-squares polynomial is a solution of our
+c  approximation problem.
+ 430  if(ier.eq.(-2)) go to 830
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+c part 2: determination of the smoothing spline sp(x,y)                c
+c *****************************************************                c
+c we have determined the number of knots and their position. we now    c
+c compute the b-spline coefficients of the smoothing spline sp(x,y).   c
+c the observation matrix a is extended by the rows of a matrix,        c
+c expressing that sp(x,y) must be a polynomial of degree kx in x and   c
+c ky in y. the corresponding weights of these additional rows are set  c
+c to 1./p.  iteratively we than have to determine the value of p       c
+c such that f(p)=sum((w(i)*(z(i)-sp(x(i),y(i))))**2) be = s.           c
+c we already know that the least-squares polynomial corresponds to     c
+c p=0  and that the least-squares spline corresponds to p=infinity.    c
+c the iteration process which is proposed here makes use of rational   c
+c interpolation. since f(p) is a convex and strictly decreasing        c
+c function of p, it can be approximated by a rational function r(p)=   c
+c (u*p+v)/(p+w). three values of p(p1,p2,p3) with corresponding values c
+c of f(p) (f1=f(p1)-s,f2=f(p2)-s,f3=f(p3)-s) are used to calculate the c
+c new value of p such that r(p)=s. convergence is guaranteed by taking c
+c f1 > 0 and f3 < 0.                                                   c
+cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
+      kx2 = kx1+1
+c  test whether there are interior knots in the x-direction.
+      if(nk1x.eq.kx1) go to 440
+c  evaluate the discotinuity jumps of the kx-th order derivative of
+c  the b-splines at the knots tx(l),l=kx+2,...,nx-kx-1.
+      call fpdisc(tx,nx,kx2,bx,nmax)
+ 440  ky2 = ky1 + 1
+c  test whether there are interior knots in the y-direction.
+      if(nk1y.eq.ky1) go to 450
+c  evaluate the discontinuity jumps of the ky-th order derivative of
+c  the b-splines at the knots ty(l),l=ky+2,...,ny-ky-1.
+      call fpdisc(ty,ny,ky2,by,nmax)
+c  initial value for p.
+ 450  p1 = 0.
+      f1 = fp0-s
+      p3 = -one
+      f3 = fpms
+      p = 0.
+      do 460 i=1,ncof
+        p = p+a(i,1)
+ 460  continue
+      rn = ncof
+      p = rn/p
+c  find the bandwidth of the extended observation matrix.
+      iband3 = kx1*nk1y
+      iband4 = iband3 +1
+      ich1 = 0
+      ich3 = 0
+c  iteration process to find the root of f(p)=s.
+      do 770 iter=1,maxit
+        pinv = one/p
+c  store the triangularized observation matrix into q.
+        do 480 i=1,ncof
+          ff(i) = f(i)
+          do 470 j=1,iband
+            q(i,j) = a(i,j)
+ 470      continue
+          ibb = iband+1
+          do 480 j=ibb,iband4
+            q(i,j) = 0.
+ 480    continue
+        if(nk1y.eq.ky1) go to 560
+c  extend the observation matrix with the rows of a matrix, expressing
+c  that for x=cst. sp(x,y) must be a polynomial in y of degree ky.
+        do 550 i=ky2,nk1y
+          ii = i-ky1
+          do 550 j=1,nk1x
+c  initialize the new row.
+            do 490 l=1,iband
+              h(l) = 0.
+ 490        continue
+c  fill in the non-zero elements of the row. jrot records the column
+c  number of the first non-zero element in the row.
+            do 500 l=1,ky2
+              h(l) = by(ii,l)*pinv
+ 500        continue
+            zi = 0.
+            jrot = (j-1)*nk1y+ii
+c  rotate the new row into triangle by givens transformations without
+c  square roots.
+            do 540 irot=jrot,ncof
+              piv = h(1)
+              i2 = min0(iband1,ncof-irot)
+              if(piv.eq.0.) then
+                if (i2.le.0) go to 550
+                go to 520
+              endif
+c  calculate the parameters of the givens transformation.
+              call fpgivs(piv,q(irot,1),cos,sin)
+c  apply that givens transformation to the right hand side.
+              call fprota(cos,sin,zi,ff(irot))
+              if(i2.eq.0) go to 550
+c  apply that givens transformation to the left hand side.
+              do 510 l=1,i2
+                l1 = l+1
+                call fprota(cos,sin,h(l1),q(irot,l1))
+ 510          continue
+ 520          do 530 l=1,i2
+                h(l) = h(l+1)
+ 530          continue
+              h(i2+1) = 0.
+ 540        continue
+ 550    continue
+ 560    if(nk1x.eq.kx1) go to 640
+c  extend the observation matrix with the rows of a matrix expressing
+c  that for y=cst. sp(x,y) must be a polynomial in x of degree kx.
+        do 630 i=kx2,nk1x
+          ii = i-kx1
+          do 630 j=1,nk1y
+c  initialize the new row
+            do 570 l=1,iband4
+              h(l) = 0.
+ 570        continue
+c  fill in the non-zero elements of the row. jrot records the column
+c  number of the first non-zero element in the row.
+            j1 = 1
+            do 580 l=1,kx2
+              h(j1) = bx(ii,l)*pinv
+              j1 = j1+nk1y
+ 580        continue
+            zi = 0.
+            jrot = (i-kx2)*nk1y+j
+c  rotate the new row into triangle by givens transformations .
+            do 620 irot=jrot,ncof
+              piv = h(1)
+              i2 = min0(iband3,ncof-irot)
+              if(piv.eq.0.) then
+                if (i2.le.0) go to 630
+                go to 600
+              endif
+c  calculate the parameters of the givens transformation.
+              call fpgivs(piv,q(irot,1),cos,sin)
+c  apply that givens transformation to the right hand side.
+              call fprota(cos,sin,zi,ff(irot))
+              if(i2.eq.0) go to 630
+c  apply that givens transformation to the left hand side.
+              do 590 l=1,i2
+                l1 = l+1
+                call fprota(cos,sin,h(l1),q(irot,l1))
+ 590          continue
+ 600          do 610 l=1,i2
+                h(l) = h(l+1)
+ 610          continue
+              h(i2+1) = 0.
+ 620        continue
+ 630    continue
+c  find dmax, the maximum value for the diagonal elements in the
+c  reduced triangle.
+ 640    dmax = 0.
+        do 650 i=1,ncof
+          if(q(i,1).le.dmax) go to 650
+          dmax = q(i,1)
+ 650    continue
+c  check whether the matrix is rank deficient.
+        sigma = eps*dmax
+        do 660 i=1,ncof
+          if(q(i,1).le.sigma) go to 670
+ 660    continue
+c  backward substitution in case of full rank.
+        call fpback(q,ff,ncof,iband4,c,nc)
+        rank = ncof
+        go to 675
+c  in case of rank deficiency, find the minimum norm solution.
+ 670    lwest = ncof*iband4+ncof+iband4
+        if(lwrk.lt.lwest) go to 780
+        lf = 1
+        lh = lf+ncof
+        la = lh+iband4
+        call fprank(q,ff,ncof,iband4,nc,sigma,c,sq,rank,wrk(la),
+     *   wrk(lf),wrk(lh))
+ 675    do 680 i=1,ncof
+          q(i,1) = q(i,1)/dmax
+ 680    continue
+c  compute f(p).
+        fp = 0.
+        do 720 num = 1,nreg
+          num1 = num-1
+          lx = num1/nyy
+          ly = num1-lx*nyy
+          jrot = lx*nk1y+ly
+          in = index(num)
+ 690      if(in.eq.0) go to 720
+          store = 0.
+          i1 = jrot
+          do 710 i=1,kx1
+            hxi = spx(in,i)
+            j1 = i1
+            do 700 j=1,ky1
+              j1 = j1+1
+              store = store+hxi*spy(in,j)*c(j1)
+ 700        continue
+            i1 = i1+nk1y
+ 710      continue
+          fp = fp+(w(in)*(z(in)-store))**2
+          in = nummer(in)
+          go to 690
+ 720    continue
+c  test whether the approximation sp(x,y) is an acceptable solution.
+        fpms = fp-s
+        if(abs(fpms).le.acc) go to 820
+c  test whether the maximum allowable number of iterations has been
+c  reached.
+        if(iter.eq.maxit) go to 795
+c  carry out one more step of the iteration process.
+        p2 = p
+        f2 = fpms
+        if(ich3.ne.0) go to 740
+        if((f2-f3).gt.acc) go to 730
+c  our initial choice of p is too large.
+        p3 = p2
+        f3 = f2
+        p = p*con4
+        if(p.le.p1) p = p1*con9 + p2*con1
+        go to 770
+ 730    if(f2.lt.0.) ich3 = 1
+ 740    if(ich1.ne.0) go to 760
+        if((f1-f2).gt.acc) go to 750
+c  our initial choice of p is too small
+        p1 = p2
+        f1 = f2
+        p = p/con4
+        if(p3.lt.0.) go to 770
+        if(p.ge.p3) p = p2*con1 + p3*con9
+        go to 770
+ 750    if(f2.gt.0.) ich1 = 1
+c  test whether the iteration process proceeds as theoretically
+c  expected.
+ 760    if(f2.ge.f1 .or. f2.le.f3) go to 800
+c  find the new value of p.
+        p = fprati(p1,f1,p2,f2,p3,f3)
+ 770  continue
+c  error codes and messages.
+ 780  ier = lwest
+      go to 830
+ 785  ier = 5
+      go to 830
+ 790  ier = 4
+      go to 830
+ 795  ier = 3
+      go to 830
+ 800  ier = 2
+      go to 830
+ 810  ier = 1
+      go to 830
+ 815  ier = -1
+      fp = 0.
+ 820  if(ncof.ne.rank) ier = -rank
+c  test whether x and y are in the original order.
+ 830  if(ichang.lt.0) go to 930
+c  if not, interchange x and y once more.
+      l1 = 1
+      do 840 i=1,nk1x
+        l2 = i
+        do 840 j=1,nk1y
+          f(l2) = c(l1)
+          l1 = l1+1
+          l2 = l2+nk1x
+ 840  continue
+      do 850 i=1,ncof
+        c(i) = f(i)
+ 850  continue
+      do 860 i=1,m
+        store = x(i)
+        x(i) = y(i)
+        y(i) = store
+ 860  continue
+      n = min0(nx,ny)
+      do 870 i=1,n
+        store = tx(i)
+        tx(i) = ty(i)
+        ty(i) = store
+ 870  continue
+      n1 = n+1
+      if (nx.lt.ny) go to 880
+      if (nx.eq.ny) go to 920
+      go to 900
+ 880  do 890 i=n1,ny
+        tx(i) = ty(i)
+ 890  continue
+      go to 920
+ 900  do 910 i=n1,nx
+        ty(i) = tx(i)
+ 910  continue
+ 920  l = nx
+      nx = ny
+      ny = l
+ 930  if(iopt.lt.0) go to 940
+      nx0 = nx
+      ny0 = ny
+ 940  return
+      end
+

Added: branches/Interpolate1D/fitpack/fpsysy.f
===================================================================
--- branches/Interpolate1D/fitpack/fpsysy.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fpsysy.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,56 @@
+      subroutine fpsysy(a,n,g)
+c subroutine fpsysy solves a linear n x n symmetric system
+c    (a) * (b) = (g)
+c on input, vector g contains the right hand side ; on output it will
+c contain the solution (b).
+c  ..
+c  ..scalar arguments..
+      integer n
+c  ..array arguments..
+      real*8 a(6,6),g(6)
+c  ..local scalars..
+      real*8 fac
+      integer i,i1,j,k
+c  ..
+      g(1) = g(1)/a(1,1)
+      if(n.eq.1) return
+c  decomposition of the symmetric matrix (a) = (l) * (d) *(l)'
+c  with (l) a unit lower triangular matrix and (d) a diagonal
+c  matrix
+      do 10 k=2,n
+         a(k,1) = a(k,1)/a(1,1)
+  10  continue
+      do 40 i=2,n
+         i1 = i-1
+         do 30 k=i,n
+            fac = a(k,i)
+            do 20 j=1,i1
+               fac = fac-a(j,j)*a(k,j)*a(i,j)
+  20        continue
+            a(k,i) = fac
+            if(k.gt.i) a(k,i) = fac/a(i,i)
+  30     continue
+  40  continue
+c  solve the system (l)*(d)*(l)'*(b) = (g).
+c  first step : solve (l)*(d)*(c) = (g).
+      do 60 i=2,n
+         i1 = i-1
+         fac = g(i)
+         do 50 j=1,i1
+            fac = fac-g(j)*a(j,j)*a(i,j)
+  50     continue
+         g(i) = fac/a(i,i)
+  60  continue
+c  second step : solve (l)'*(b) = (c)
+      i = n
+      do 80 j=2,n
+         i1 = i
+         i = i-1
+         fac = g(i)
+         do 70 k=i1,n
+            fac = fac-g(k)*a(k,i)
+  70     continue
+         g(i) = fac
+  80  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fptrnp.f
===================================================================
--- branches/Interpolate1D/fitpack/fptrnp.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fptrnp.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,106 @@
+      subroutine fptrnp(m,mm,idim,n,nr,sp,p,b,z,a,q,right)
+c  subroutine fptrnp reduces the (m+n-7) x (n-4) matrix a to upper
+c  triangular form and applies the same givens transformations to
+c  the (m) x (mm) x (idim) matrix z to obtain the (n-4) x (mm) x
+c  (idim) matrix q
+c  ..
+c  ..scalar arguments..
+      real*8 p
+      integer m,mm,idim,n
+c  ..array arguments..
+      real*8 sp(m,4),b(n,5),z(m*mm*idim),a(n,5),q((n-4)*mm*idim),
+     * right(mm*idim)
+      integer nr(m)
+c  ..local scalars..
+      real*8 cos,pinv,piv,sin,one
+      integer i,iband,irot,it,ii,i2,i3,j,jj,l,mid,nmd,m2,m3,
+     * nrold,n4,number,n1
+c  ..local arrays..
+      real*8 h(7)
+c  ..subroutine references..
+c    fpgivs,fprota
+c  ..
+      one = 1
+      if(p.gt.0.) pinv = one/p
+      n4 = n-4
+      mid = mm*idim
+      m2 = m*mm
+      m3 = n4*mm
+c  reduce the matrix (a) to upper triangular form (r) using givens
+c  rotations. apply the same transformations to the rows of matrix z
+c  to obtain the mm x (n-4) matrix g.
+c  store matrix (r) into (a) and g into q.
+c  initialization.
+      nmd = n4*mid
+      do 50 i=1,nmd
+        q(i) = 0.
+  50  continue
+      do 100 i=1,n4
+        do 100 j=1,5
+          a(i,j) = 0.
+ 100  continue
+      nrold = 0
+c  iband denotes the bandwidth of the matrices (a) and (r).
+      iband = 4
+      do 750 it=1,m
+        number = nr(it)
+ 150    if(nrold.eq.number) go to 300
+        if(p.le.0.) go to 700
+        iband = 5
+c  fetch a new row of matrix (b).
+        n1 = nrold+1
+        do 200 j=1,5
+          h(j) = b(n1,j)*pinv
+ 200    continue
+c  find the appropriate column of q.
+        do 250 j=1,mid
+          right(j) = 0.
+ 250    continue
+        irot = nrold
+        go to 450
+c  fetch a new row of matrix (sp).
+ 300    h(iband) = 0.
+        do 350 j=1,4
+          h(j) = sp(it,j)
+ 350    continue
+c  find the appropriate column of q.
+        j = 0
+        do 400 ii=1,idim
+          l = (ii-1)*m2+(it-1)*mm
+          do 400 jj=1,mm
+            j = j+1
+            l = l+1
+            right(j) = z(l)
+ 400    continue
+        irot = number
+c  rotate the new row of matrix (a) into triangle.
+ 450    do 600 i=1,iband
+          irot = irot+1
+          piv = h(i)
+          if(piv.eq.0.) go to 600
+c  calculate the parameters of the givens transformation.
+          call fpgivs(piv,a(irot,1),cos,sin)
+c  apply that transformation to the rows of matrix q.
+          j = 0
+          do 500 ii=1,idim
+            l = (ii-1)*m3+irot
+            do 500 jj=1,mm
+              j = j+1
+              call fprota(cos,sin,right(j),q(l))
+              l = l+n4
+ 500      continue
+c  apply that transformation to the columns of (a).
+          if(i.eq.iband) go to 650
+          i2 = 1
+          i3 = i+1
+          do 550 j=i3,iband
+            i2 = i2+1
+            call fprota(cos,sin,h(j),a(irot,i2))
+ 550      continue
+ 600    continue
+ 650    if(nrold.eq.number) go to 750
+ 700    nrold = nrold+1
+        go to 150
+ 750  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/fptrpe.f
===================================================================
--- branches/Interpolate1D/fitpack/fptrpe.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/fptrpe.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,212 @@
+      subroutine fptrpe(m,mm,idim,n,nr,sp,p,b,z,a,aa,q,right)
+c  subroutine fptrpe reduces the (m+n-7) x (n-7) cyclic bandmatrix a
+c  to upper triangular form and applies the same givens transformations
+c  to the (m) x (mm) x (idim) matrix z to obtain the (n-7) x (mm) x
+c  (idim) matrix q.
+c  ..
+c  ..scalar arguments..
+      real*8 p
+      integer m,mm,idim,n
+c  ..array arguments..
+      real*8 sp(m,4),b(n,5),z(m*mm*idim),a(n,5),aa(n,4),q((n-7)*mm*idim)
+     *,
+     * right(mm*idim)
+      integer nr(m)
+c  ..local scalars..
+      real*8 co,pinv,piv,si,one
+      integer i,iband,irot,it,ii,i2,i3,j,jj,l,mid,nmd,m2,m3,
+     * nrold,n4,number,n1,n7,n11,m1
+c  ..local arrays..
+      real*8 h(5),h1(5),h2(4)
+c  ..subroutine references..
+c    fpgivs,fprota
+c  ..
+      one = 1
+      if(p.gt.0.) pinv = one/p
+      n4 = n-4
+      n7 = n-7
+      n11 = n-11
+      mid = mm*idim
+      m2 = m*mm
+      m3 = n7*mm
+      m1 = m-1
+c  we determine the matrix (a) and then we reduce her to
+c  upper triangular form (r) using givens rotations.
+c  we apply the same transformations to the rows of matrix
+c  z to obtain the (mm) x (n-7) matrix g.
+c  we store matrix (r) into a and aa, g into q.
+c  the n7 x n7 upper triangular matrix (r) has the form
+c             | a1 '     |
+c       (r) = |    ' a2  |
+c             |  0 '     |
+c  with (a2) a n7 x 4 matrix and (a1) a n11 x n11 upper
+c  triangular matrix of bandwidth 5.
+c  initialization.
+      nmd = n7*mid
+      do 50 i=1,nmd
+        q(i) = 0.
+  50  continue
+      do 100 i=1,n4
+        a(i,5) = 0.
+        do 100 j=1,4
+          a(i,j) = 0.
+          aa(i,j) = 0.
+ 100  continue
+      jper = 0
+      nrold = 0
+      do 760 it=1,m1
+        number = nr(it)
+ 120    if(nrold.eq.number) go to 180
+        if(p.le.0.) go to 740
+c  fetch a new row of matrix (b).
+        n1 = nrold+1
+        do 140 j=1,5
+          h(j) = b(n1,j)*pinv
+ 140    continue
+c  find the appropiate row of q.
+        do 160 j=1,mid
+          right(j) = 0.
+ 160    continue
+        go to 240
+c  fetch a new row of matrix (sp)
+ 180    h(5) = 0.
+        do 200 j=1,4
+          h(j) = sp(it,j)
+ 200    continue
+c  find the appropiate row of q.
+        j = 0
+        do 220 ii=1,idim
+          l = (ii-1)*m2+(it-1)*mm
+          do 220 jj=1,mm
+            j = j+1
+            l = l+1
+            right(j) = z(l)
+ 220    continue
+c  test whether there are non-zero values in the new row of (a)
+c  corresponding to the b-splines n(j,*),j=n7+1,...,n4.
+ 240     if(nrold.lt.n11) go to 640
+         if(jper.ne.0) go to 320
+c  initialize the matrix (aa).
+         jk = n11+1
+         do 300 i=1,4
+            ik = jk
+            do 260 j=1,5
+               if(ik.le.0) go to 280
+               aa(ik,i) = a(ik,j)
+               ik = ik-1
+ 260        continue
+ 280        jk = jk+1
+ 300     continue
+         jper = 1
+c  if one of the non-zero elements of the new row corresponds to one of
+c  the b-splines n(j;*),j=n7+1,...,n4,we take account of the periodicity
+c  conditions for setting up this row of (a).
+ 320     do 340 i=1,4
+            h1(i) = 0.
+            h2(i) = 0.
+ 340     continue
+         h1(5) = 0.
+         j = nrold-n11
+         do 420 i=1,5
+            j = j+1
+            l0 = j
+ 360        l1 = l0-4
+            if(l1.le.0) go to 400
+            if(l1.le.n11) go to 380
+            l0 = l1-n11
+            go to 360
+ 380        h1(l1) = h(i)
+            go to 420
+ 400        h2(l0) = h2(l0) + h(i)
+ 420     continue
+c  rotate the new row of (a) into triangle.
+         if(n11.le.0) go to 560
+c  rotations with the rows 1,2,...,n11 of (a).
+         do 540 irot=1,n11
+            piv = h1(1)
+            i2 = min0(n11-irot,4)
+            if(piv.eq.0.) go to 500
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(irot,1),co,si)
+c  apply that transformation to the columns of matrix q.
+            j = 0
+            do 440 ii=1,idim
+               l = (ii-1)*m3+irot
+               do 440 jj=1,mm
+                 j = j+1
+                 call fprota(co,si,right(j),q(l))
+                 l = l+n7
+ 440        continue
+c  apply that transformation to the rows of (a) with respect to aa.
+            do 460 i=1,4
+               call fprota(co,si,h2(i),aa(irot,i))
+ 460        continue
+c  apply that transformation to the rows of (a) with respect to a.
+            if(i2.eq.0) go to 560
+            do 480 i=1,i2
+               i1 = i+1
+               call fprota(co,si,h1(i1),a(irot,i1))
+ 480        continue
+ 500        do 520 i=1,i2
+               h1(i) = h1(i+1)
+ 520        continue
+            h1(i2+1) = 0.
+ 540     continue
+c  rotations with the rows n11+1,...,n7 of a.
+ 560     do 620 irot=1,4
+            ij = n11+irot
+            if(ij.le.0) go to 620
+            piv = h2(irot)
+            if(piv.eq.0.) go to 620
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,aa(ij,irot),co,si)
+c  apply that transformation to the columns of matrix q.
+            j = 0
+            do 580 ii=1,idim
+               l = (ii-1)*m3+ij
+               do 580 jj=1,mm
+                 j = j+1
+                 call fprota(co,si,right(j),q(l))
+                 l = l+n7
+ 580        continue
+            if(irot.eq.4) go to 620
+c  apply that transformation to the rows of (a) with respect to aa.
+            j1 = irot+1
+            do 600 i=j1,4
+               call fprota(co,si,h2(i),aa(ij,i))
+ 600        continue
+ 620     continue
+         go to 720
+c  rotation into triangle of the new row of (a), in case the elements
+c  corresponding to the b-splines n(j;*),j=n7+1,...,n4 are all zero.
+ 640     irot =nrold
+         do 700 i=1,5
+            irot = irot+1
+            piv = h(i)
+            if(piv.eq.0.) go to 700
+c  calculate the parameters of the givens transformation.
+            call fpgivs(piv,a(irot,1),co,si)
+c  apply that transformation to the columns of matrix g.
+            j = 0
+            do 660 ii=1,idim
+               l = (ii-1)*m3+irot
+               do 660 jj=1,mm
+                 j = j+1
+                 call fprota(co,si,right(j),q(l))
+                 l = l+n7
+ 660        continue
+c  apply that transformation to the rows of (a).
+            if(i.eq.5) go to 700
+            i2 = 1
+            i3 = i+1
+            do 680 j=i3,5
+               i2 = i2+1
+               call fprota(co,si,h(j),a(irot,i2))
+ 680        continue
+ 700     continue
+ 720     if(nrold.eq.number) go to 760
+ 740     nrold = nrold+1
+         go to 120
+ 760  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/insert.f
===================================================================
--- branches/Interpolate1D/fitpack/insert.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/insert.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,102 @@
+      subroutine insert(iopt,t,n,c,k,x,tt,nn,cc,nest,ier)
+c  subroutine insert inserts a new knot x into a spline function s(x)
+c  of degree k and calculates the b-spline representation of s(x) with
+c  respect to the new set of knots. in addition, if iopt.ne.0, s(x)
+c  will be considered as a periodic spline with period per=t(n-k)-t(k+1)
+c  satisfying the boundary constraints
+c       t(i+n-2*k-1) = t(i)+per  ,i=1,2,...,2*k+1
+c       c(i+n-2*k-1) = c(i)      ,i=1,2,...,k
+c  in that case, the knots and b-spline coefficients returned will also
+c  satisfy these boundary constraints, i.e.
+c       tt(i+nn-2*k-1) = tt(i)+per  ,i=1,2,...,2*k+1
+c       cc(i+nn-2*k-1) = cc(i)      ,i=1,2,...,k
+c
+c  calling sequence:
+c     call insert(iopt,t,n,c,k,x,tt,nn,cc,nest,ier)
+c
+c  input parameters:
+c    iopt : integer flag, specifying whether (iopt.ne.0) or not (iopt=0)
+c           the given spline must be considered as being periodic.
+c    t    : array,length nest, which contains the position of the knots.
+c    n    : integer, giving the total number of knots of s(x).
+c    c    : array,length nest, which contains the b-spline coefficients.
+c    k    : integer, giving the degree of s(x).
+c    x    : real, which gives the location of the knot to be inserted.
+c    nest : integer specifying the dimension of the arrays t,c,tt and cc
+c           nest > n.
+c
+c  output parameters:
+c    tt   : array,length nest, which contains the position of the knots
+c           after insertion.
+c    nn   : integer, giving the total number of knots after insertion
+c    cc   : array,length nest, which contains the b-spline coefficients
+c           of s(x) with respect to the new set of knots.
+c    ier  : error flag
+c      ier = 0 : normal return
+c      ier =10 : invalid input data (see restrictions)
+c
+c  restrictions:
+c    nest > n
+c    t(k+1) <= x <= t(n-k)
+c    in case of a periodic spline (iopt.ne.0) there must be
+c       either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x
+c       or at least k interior knots t(j) satisfying x<=t(j)<t(n-k)
+c
+c  other subroutines required: fpinst.
+c
+c  further comments:
+c   subroutine insert may be called as follows
+c        call insert(iopt,t,n,c,k,x,t,n,c,nest,ier)
+c   in which case the new representation will simply replace the old one
+c
+c  references :
+c    boehm w : inserting new knots into b-spline curves. computer aided
+c              design 12 (1980) 199-201.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : february 2007 (second interval search added)
+c
+c  ..scalar arguments..
+      integer iopt,n,k,nn,nest,ier
+      real*8 x
+c  ..array arguments..
+      real*8 t(nest),c(nest),tt(nest),cc(nest)
+c  ..local scalars..
+      integer kk,k1,l,nk
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      if(nest.le.n) go to 40
+      k1 = k+1
+      nk = n-k
+      if(x.lt.t(k1) .or. x.gt.t(nk)) go to 40
+c  search for knot interval t(l) <= x < t(l+1).
+      l = k1
+  10  if(x.lt.t(l+1)) go to 20
+      l = l+1
+      if(l.eq.nk) go to 14
+      go to 10
+c  if no interval found above, then reverse the search and 
+c  look for knot interval t(l) < x <= t(l+1).
+  14  l = nk-1
+  16  if(x.gt.t(l)) go to 20
+      l = l-1
+      if(l.eq.k) go to 40
+      go to 16
+  20  if(t(l).ge.t(l+1)) go to 40
+      if(iopt.eq.0) go to 30
+      kk = 2*k
+      if(l.le.kk .and. l.ge.(n-kk)) go to 40
+  30  ier = 0
+c  insert the new knot.
+      call fpinst(iopt,t,n,c,k,x,l,tt,nn,cc,nest)
+  40  return
+      end

Added: branches/Interpolate1D/fitpack/parcur.f
===================================================================
--- branches/Interpolate1D/fitpack/parcur.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/parcur.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,334 @@
+      subroutine parcur(iopt,ipar,idim,m,u,mx,x,w,ub,ue,k,s,nest,n,t,
+     * nc,c,fp,wrk,lwrk,iwrk,ier)
+c  given the ordered set of m points x(i) in the idim-dimensional space
+c  and given also a corresponding set of strictly increasing values u(i)
+c  and the set of positive numbers w(i),i=1,2,...,m, subroutine parcur
+c  determines a smooth approximating spline curve s(u), i.e.
+c      x1 = s1(u)
+c      x2 = s2(u)       ub <= u <= ue
+c      .........
+c      xidim = sidim(u)
+c  with sj(u),j=1,2,...,idim spline functions of degree k with common
+c  knots t(j),j=1,2,...,n.
+c  if ipar=1 the values ub,ue and u(i),i=1,2,...,m must be supplied by
+c  the user. if ipar=0 these values are chosen automatically by parcur
+c  as  v(1) = 0
+c      v(i) = v(i-1) + dist(x(i),x(i-1)) ,i=2,3,...,m
+c      u(i) = v(i)/v(m) ,i=1,2,...,m
+c      ub = u(1) = 0, ue = u(m) = 1.
+c  if iopt=-1 parcur calculates the weighted least-squares spline curve
+c  according to a given set of knots.
+c  if iopt>=0 the number of knots of the splines sj(u) and the position
+c  t(j),j=1,2,...,n is chosen automatically by the routine. the smooth-
+c  ness of s(u) is then achieved by minimalizing the discontinuity
+c  jumps of the k-th derivative of s(u) at the knots t(j),j=k+2,k+3,...,
+c  n-k-1. the amount of smoothness is determined by the condition that
+c  f(p)=sum((w(i)*dist(x(i),s(u(i))))**2) be <= s, with s a given non-
+c  negative constant, called the smoothing factor.
+c  the fit s(u) is given in the b-spline representation and can be
+c  evaluated by means of subroutine curev.
+c
+c  calling sequence:
+c     call parcur(iopt,ipar,idim,m,u,mx,x,w,ub,ue,k,s,nest,n,t,nc,c,
+c    * fp,wrk,lwrk,iwrk,ier)
+c
+c  parameters:
+c   iopt  : integer flag. on entry iopt must specify whether a weighted
+c           least-squares spline curve (iopt=-1) or a smoothing spline
+c           curve (iopt=0 or 1) must be determined.if iopt=0 the routine
+c           will start with an initial set of knots t(i)=ub,t(i+k+1)=ue,
+c           i=1,2,...,k+1. if iopt=1 the routine will continue with the
+c           knots found at the last call of the routine.
+c           attention: a call with iopt=1 must always be immediately
+c           preceded by another call with iopt=1 or iopt=0.
+c           unchanged on exit.
+c   ipar  : integer flag. on entry ipar must specify whether (ipar=1)
+c           the user will supply the parameter values u(i),ub and ue
+c           or whether (ipar=0) these values are to be calculated by
+c           parcur. unchanged on exit.
+c   idim  : integer. on entry idim must specify the dimension of the
+c           curve. 0 < idim < 11.
+c           unchanged on exit.
+c   m     : integer. on entry m must specify the number of data points.
+c           m > k. unchanged on exit.
+c   u     : real array of dimension at least (m). in case ipar=1,before
+c           entry, u(i) must be set to the i-th value of the parameter
+c           variable u for i=1,2,...,m. these values must then be
+c           supplied in strictly ascending order and will be unchanged
+c           on exit. in case ipar=0, on exit,array u will contain the
+c           values u(i) as determined by parcur.
+c   mx    : integer. on entry mx must specify the actual dimension of
+c           the array x as declared in the calling (sub)program. mx must
+c           not be too small (see x). unchanged on exit.
+c   x     : real array of dimension at least idim*m.
+c           before entry, x(idim*(i-1)+j) must contain the j-th coord-
+c           inate of the i-th data point for i=1,2,...,m and j=1,2,...,
+c           idim. unchanged on exit.
+c   w     : real array of dimension at least (m). before entry, w(i)
+c           must be set to the i-th value in the set of weights. the
+c           w(i) must be strictly positive. unchanged on exit.
+c           see also further comments.
+c   ub,ue : real values. on entry (in case ipar=1) ub and ue must
+c           contain the lower and upper bound for the parameter u.
+c           ub <=u(1), ue>= u(m). if ipar = 0 these values will
+c           automatically be set to 0 and 1 by parcur.
+c   k     : integer. on entry k must specify the degree of the splines.
+c           1<=k<=5. it is recommended to use cubic splines (k=3).
+c           the user is strongly dissuaded from choosing k even,together
+c           with a small s-value. unchanged on exit.
+c   s     : real.on entry (in case iopt>=0) s must specify the smoothing
+c           factor. s >=0. unchanged on exit.
+c           for advice on the choice of s see further comments.
+c   nest  : integer. on entry nest must contain an over-estimate of the
+c           total number of knots of the splines returned, to indicate
+c           the storage space available to the routine. nest >=2*k+2.
+c           in most practical situation nest=m/2 will be sufficient.
+c           always large enough is nest=m+k+1, the number of knots
+c           needed for interpolation (s=0). unchanged on exit.
+c   n     : integer.
+c           unless ier = 10 (in case iopt >=0), n will contain the
+c           total number of knots of the smoothing spline curve returned
+c           if the computation mode iopt=1 is used this value of n
+c           should be left unchanged between subsequent calls.
+c           in case iopt=-1, the value of n must be specified on entry.
+c   t     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the knots of the
+c           spline curve,i.e. the position of the interior knots t(k+2),
+c           t(k+3),..,t(n-k-1) as well as the position of the additional
+c           t(1)=t(2)=...=t(k+1)=ub and t(n-k)=...=t(n)=ue needed for
+c           the b-spline representation.
+c           if the computation mode iopt=1 is used, the values of t(1),
+c           t(2),...,t(n) should be left unchanged between subsequent
+c           calls. if the computation mode iopt=-1 is used, the values
+c           t(k+2),...,t(n-k-1) must be supplied by the user, before
+c           entry. see also the restrictions (ier=10).
+c   nc    : integer. on entry nc must specify the actual dimension of
+c           the array c as declared in the calling (sub)program. nc
+c           must not be too small (see c). unchanged on exit.
+c   c     : real array of dimension at least (nest*idim).
+c           on succesful exit, this array will contain the coefficients
+c           in the b-spline representation of the spline curve s(u),i.e.
+c           the b-spline coefficients of the spline sj(u) will be given
+c           in c(n*(j-1)+i),i=1,2,...,n-k-1 for j=1,2,...,idim.
+c   fp    : real. unless ier = 10, fp contains the weighted sum of
+c           squared residuals of the spline curve returned.
+c   wrk   : real array of dimension at least m*(k+1)+nest*(6+idim+3*k).
+c           used as working space. if the computation mode iopt=1 is
+c           used, the values wrk(1),...,wrk(n) should be left unchanged
+c           between subsequent calls.
+c   lwrk  : integer. on entry,lwrk must specify the actual dimension of
+c           the array wrk as declared in the calling (sub)program. lwrk
+c           must not be too small (see wrk). unchanged on exit.
+c   iwrk  : integer array of dimension at least (nest).
+c           used as working space. if the computation mode iopt=1 is
+c           used,the values iwrk(1),...,iwrk(n) should be left unchanged
+c           between subsequent calls.
+c   ier   : integer. unless the routine detects an error, ier contains a
+c           non-positive value on exit, i.e.
+c    ier=0  : normal return. the curve returned has a residual sum of
+c             squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c             ive tolerance set to 0.001 by the program.
+c    ier=-1 : normal return. the curve returned is an interpolating
+c             spline curve (fp=0).
+c    ier=-2 : normal return. the curve returned is the weighted least-
+c             squares polynomial curve of degree k.in this extreme case
+c             fp gives the upper bound fp0 for the smoothing factor s.
+c    ier=1  : error. the required storage space exceeds the available
+c             storage space, as specified by the parameter nest.
+c             probably causes : nest too small. if nest is already
+c             large (say nest > m/2), it may also indicate that s is
+c             too small
+c             the approximation returned is the least-squares spline
+c             curve according to the knots t(1),t(2),...,t(n). (n=nest)
+c             the parameter fp gives the corresponding weighted sum of
+c             squared residuals (fp>s).
+c    ier=2  : error. a theoretically impossible result was found during
+c             the iteration proces for finding a smoothing spline curve
+c             with fp = s. probably causes : s too small.
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=3  : error. the maximal number of iterations maxit (set to 20
+c             by the program) allowed for finding a smoothing curve
+c             with fp=s has been reached. probably causes : s too small
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=10 : error. on entry, the input data are controlled on validity
+c             the following restrictions must be satisfied.
+c             -1<=iopt<=1, 1<=k<=5, m>k, nest>2*k+2, w(i)>0,i=1,2,...,m
+c             0<=ipar<=1, 0<idim<=10, lwrk>=(k+1)*m+nest*(6+idim+3*k),
+c             nc>=nest*idim
+c             if ipar=0: sum j=1,idim (x(idim*i+j)-x(idim*(i-1)+j))**2>0
+c                        i=1,2,...,m-1.
+c             if ipar=1: ub<=u(1)<u(2)<...<u(m)<=ue
+c             if iopt=-1: 2*k+2<=n<=min(nest,m+k+1)
+c                         ub<t(k+2)<t(k+3)<...<t(n-k-1)<ue
+c                            (ub=0 and ue=1 in case ipar=0)
+c                       the schoenberg-whitney conditions, i.e. there
+c                       must be a subset of data points uu(j) such that
+c                         t(j) < uu(j) < t(j+k+1), j=1,2,...,n-k-1
+c             if iopt>=0: s>=0
+c                         if s=0 : nest >= m+k+1
+c             if one of these conditions is found to be violated,control
+c             is immediately repassed to the calling program. in that
+c             case there is no approximation returned.
+c
+c  further comments:
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the curve will be too smooth and signal will be
+c   lost ; if s is too small the curve will pick up too much noise. in
+c   the extreme cases the program will return an interpolating curve if
+c   s=0 and the least-squares polynomial curve of degree k if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   x(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in x(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   polynomial curve and the upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximating curve shows more detail) to obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if parcur is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   curve underlying the data. but, if the computation mode iopt=1 is
+c   used, the knots returned may also depend on the s-values at previous
+c   calls (if these were smaller). therefore, if after a number of
+c   trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   parcur once more with the selected value for s but now with iopt=0.
+c   indeed, parcur may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c
+c   the form of the approximating curve can strongly be affected by
+c   the choice of the parameter values u(i). if there is no physical
+c   reason for choosing a particular parameter u, often good results
+c   will be obtained with the choice of parcur (in case ipar=0), i.e.
+c        v(1)=0, v(i)=v(i-1)+q(i), i=2,...,m, u(i)=v(i)/v(m), i=1,..,m
+c   where
+c        q(i)= sqrt(sum j=1,idim (xj(i)-xj(i-1))**2 )
+c   other possibilities for q(i) are
+c        q(i)= sum j=1,idim (xj(i)-xj(i-1))**2
+c        q(i)= sum j=1,idim abs(xj(i)-xj(i-1))
+c        q(i)= max j=1,idim abs(xj(i)-xj(i-1))
+c        q(i)= 1
+c
+c  other subroutines required:
+c    fpback,fpbspl,fpchec,fppara,fpdisc,fpgivs,fpknot,fprati,fprota
+c
+c  references:
+c   dierckx p. : algorithms for smoothing data with periodic and
+c                parametric splines, computer graphics and image
+c                processing 20 (1982) 171-184.
+c   dierckx p. : algorithms for smoothing data with periodic and param-
+c                etric splines, report tw55, dept. computer science,
+c                k.u.leuven, 1981.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1987
+c
+c  ..
+c  ..scalar arguments..
+      real*8 ub,ue,s,fp
+      integer iopt,ipar,idim,m,mx,k,nest,n,nc,lwrk,ier
+c  ..array arguments..
+      real*8 u(m),x(mx),w(m),t(nest),c(nc),wrk(lwrk)
+      integer iwrk(nest)
+c  ..local scalars..
+      real*8 tol,dist
+      integer i,ia,ib,ifp,ig,iq,iz,i1,i2,j,k1,k2,lwest,maxit,nmin,ncc
+c ..function references
+      real*8 sqrt
+c  ..
+c  we set up the parameters tol and maxit
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 90
+      if(ipar.lt.0 .or. ipar.gt.1) go to 90
+      if(idim.le.0 .or. idim.gt.10) go to 90
+      if(k.le.0 .or. k.gt.5) go to 90
+      k1 = k+1
+      k2 = k1+1
+      nmin = 2*k1
+      if(m.lt.k1 .or. nest.lt.nmin) go to 90
+      ncc = nest*idim
+      if(mx.lt.m*idim .or. nc.lt.ncc) go to 90
+      lwest = m*k1+nest*(6+idim+3*k)
+      if(lwrk.lt.lwest) go to 90
+      if(ipar.ne.0 .or. iopt.gt.0) go to 40
+      i1 = 0
+      i2 = idim
+      u(1) = 0.
+      do 20 i=2,m
+         dist = 0.
+         do 10 j=1,idim
+            i1 = i1+1
+            i2 = i2+1
+            dist = dist+(x(i2)-x(i1))**2
+  10     continue
+         u(i) = u(i-1)+sqrt(dist)
+  20  continue
+      if(u(m).le.0.) go to 90
+      do 30 i=2,m
+         u(i) = u(i)/u(m)
+  30  continue
+      ub = 0.
+      ue = 1.
+      u(m) = ue
+  40  if(ub.gt.u(1) .or. ue.lt.u(m) .or. w(1).le.0.) go to 90
+      do 50 i=2,m
+         if(u(i-1).ge.u(i) .or. w(i).le.0.) go to 90
+  50  continue
+      if(iopt.ge.0) go to 70
+      if(n.lt.nmin .or. n.gt.nest) go to 90
+      j = n
+      do 60 i=1,k1
+         t(i) = ub
+         t(j) = ue
+         j = j-1
+  60  continue
+      call fpchec(u,m,t,n,k,ier)
+      if (ier.eq.0) go to 80
+      go to 90
+  70  if(s.lt.0.) go to 90
+      if(s.eq.0. .and. nest.lt.(m+k1)) go to 90
+      ier = 0
+c we partition the working space and determine the spline curve.
+  80  ifp = 1
+      iz = ifp+nest
+      ia = iz+ncc
+      ib = ia+nest*k1
+      ig = ib+nest*k2
+      iq = ig+nest*k2
+      call fppara(iopt,idim,m,u,mx,x,w,ub,ue,k,s,nest,tol,maxit,k1,k2,
+     * n,t,ncc,c,fp,wrk(ifp),wrk(iz),wrk(ia),wrk(ib),wrk(ig),wrk(iq),
+     * iwrk,ier)
+  90  return
+      end

Added: branches/Interpolate1D/fitpack/parder.f
===================================================================
--- branches/Interpolate1D/fitpack/parder.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/parder.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,179 @@
+      subroutine parder(tx,nx,ty,ny,c,kx,ky,nux,nuy,x,mx,y,my,z,
+     * wrk,lwrk,iwrk,kwrk,ier)
+c  subroutine parder evaluates on a grid (x(i),y(j)),i=1,...,mx; j=1,...
+c  ,my the partial derivative ( order nux,nuy) of a bivariate spline
+c  s(x,y) of degrees kx and ky, given in the b-spline representation.
+c
+c  calling sequence:
+c     call parder(tx,nx,ty,ny,c,kx,ky,nux,nuy,x,mx,y,my,z,wrk,lwrk,
+c    * iwrk,kwrk,ier)
+c
+c  input parameters:
+c   tx    : real array, length nx, which contains the position of the
+c           knots in the x-direction.
+c   nx    : integer, giving the total number of knots in the x-direction
+c   ty    : real array, length ny, which contains the position of the
+c           knots in the y-direction.
+c   ny    : integer, giving the total number of knots in the y-direction
+c   c     : real array, length (nx-kx-1)*(ny-ky-1), which contains the
+c           b-spline coefficients.
+c   kx,ky : integer values, giving the degrees of the spline.
+c   nux   : integer values, specifying the order of the partial
+c   nuy     derivative. 0<=nux<kx, 0<=nuy<ky.
+c   x     : real array of dimension (mx).
+c           before entry x(i) must be set to the x co-ordinate of the
+c           i-th grid point along the x-axis.
+c           tx(kx+1)<=x(i-1)<=x(i)<=tx(nx-kx), i=2,...,mx.
+c   mx    : on entry mx must specify the number of grid points along
+c           the x-axis. mx >=1.
+c   y     : real array of dimension (my).
+c           before entry y(j) must be set to the y co-ordinate of the
+c           j-th grid point along the y-axis.
+c           ty(ky+1)<=y(j-1)<=y(j)<=ty(ny-ky), j=2,...,my.
+c   my    : on entry my must specify the number of grid points along
+c           the y-axis. my >=1.
+c   wrk   : real array of dimension lwrk. used as workspace.
+c   lwrk  : integer, specifying the dimension of wrk.
+c           lwrk >= mx*(kx+1-nux)+my*(ky+1-nuy)+(nx-kx-1)*(ny-ky-1)
+c   iwrk  : integer array of dimension kwrk. used as workspace.
+c   kwrk  : integer, specifying the dimension of iwrk. kwrk >= mx+my.
+c
+c  output parameters:
+c   z     : real array of dimension (mx*my).
+c           on succesful exit z(my*(i-1)+j) contains the value of the
+c           specified partial derivative of s(x,y) at the point
+c           (x(i),y(j)),i=1,...,mx;j=1,...,my.
+c   ier   : integer error flag
+c    ier=0 : normal return
+c    ier=10: invalid input data (see restrictions)
+c
+c  restrictions:
+c   mx >=1, my >=1, 0 <= nux < kx, 0 <= nuy < ky, kwrk>=mx+my
+c   lwrk>=mx*(kx+1-nux)+my*(ky+1-nuy)+(nx-kx-1)*(ny-ky-1),
+c   tx(kx+1) <= x(i-1) <= x(i) <= tx(nx-kx), i=2,...,mx
+c   ty(ky+1) <= y(j-1) <= y(j) <= ty(ny-ky), j=2,...,my
+c
+c  other subroutines required:
+c    fpbisp,fpbspl
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1989
+c
+c  ..scalar arguments..
+      integer nx,ny,kx,ky,nux,nuy,mx,my,lwrk,kwrk,ier
+c  ..array arguments..
+      integer iwrk(kwrk)
+      real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),x(mx),y(my),z(mx*my),
+     * wrk(lwrk)
+c  ..local scalars..
+      integer i,iwx,iwy,j,kkx,kky,kx1,ky1,lx,ly,lwest,l1,l2,m,m0,m1,
+     * nc,nkx1,nky1,nxx,nyy
+      real*8 ak,fac
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      kx1 = kx+1
+      ky1 = ky+1
+      nkx1 = nx-kx1
+      nky1 = ny-ky1
+      nc = nkx1*nky1
+      if(nux.lt.0 .or. nux.ge.kx) go to 400
+      if(nuy.lt.0 .or. nuy.ge.ky) go to 400
+      lwest = nc +(kx1-nux)*mx+(ky1-nuy)*my
+      if(lwrk.lt.lwest) go to 400
+      if(kwrk.lt.(mx+my)) go to 400
+      if (mx.lt.1) go to 400
+      if (mx.eq.1) go to 30
+      go to 10
+  10  do 20 i=2,mx
+        if(x(i).lt.x(i-1)) go to 400
+  20  continue
+  30  if (my.lt.1) go to 400
+      if (my.eq.1) go to 60
+      go to 40
+  40  do 50 i=2,my
+        if(y(i).lt.y(i-1)) go to 400
+  50  continue
+  60  ier = 0
+      nxx = nkx1
+      nyy = nky1
+      kkx = kx
+      kky = ky
+c  the partial derivative of order (nux,nuy) of a bivariate spline of
+c  degrees kx,ky is a bivariate spline of degrees kx-nux,ky-nuy.
+c  we calculate the b-spline coefficients of this spline
+      do 70 i=1,nc
+        wrk(i) = c(i)
+  70  continue
+      if(nux.eq.0) go to 200
+      lx = 1
+      do 100 j=1,nux
+        ak = kkx
+        nxx = nxx-1
+        l1 = lx
+        m0 = 1
+        do 90 i=1,nxx
+          l1 = l1+1
+          l2 = l1+kkx
+          fac = tx(l2)-tx(l1)
+          if(fac.le.0.) go to 90
+          do 80 m=1,nyy
+            m1 = m0+nyy
+            wrk(m0) = (wrk(m1)-wrk(m0))*ak/fac
+            m0  = m0+1
+  80      continue
+  90    continue
+        lx = lx+1
+        kkx = kkx-1
+ 100  continue
+ 200  if(nuy.eq.0) go to 300
+      ly = 1
+      do 230 j=1,nuy
+        ak = kky
+        nyy = nyy-1
+        l1 = ly
+        do 220 i=1,nyy
+          l1 = l1+1
+          l2 = l1+kky
+          fac = ty(l2)-ty(l1)
+          if(fac.le.0.) go to 220
+          m0 = i
+          do 210 m=1,nxx
+            m1 = m0+1
+            wrk(m0) = (wrk(m1)-wrk(m0))*ak/fac
+            m0  = m0+nky1
+ 210      continue
+ 220    continue
+        ly = ly+1
+        kky = kky-1
+ 230  continue
+      m0 = nyy
+      m1 = nky1
+      do 250 m=2,nxx
+        do 240 i=1,nyy
+          m0 = m0+1
+          m1 = m1+1
+          wrk(m0) = wrk(m1)
+ 240    continue
+        m1 = m1+nuy
+ 250  continue
+c  we partition the working space and evaluate the partial derivative
+ 300  iwx = 1+nxx*nyy
+      iwy = iwx+mx*(kx1-nux)
+      call fpbisp(tx(nux+1),nx-2*nux,ty(nuy+1),ny-2*nuy,wrk,kkx,kky,
+     * x,mx,y,my,z,wrk(iwx),wrk(iwy),iwrk(1),iwrk(mx+1))
+ 400  return
+      end
+

Added: branches/Interpolate1D/fitpack/parsur.f
===================================================================
--- branches/Interpolate1D/fitpack/parsur.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/parsur.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,391 @@
+      subroutine parsur(iopt,ipar,idim,mu,u,mv,v,f,s,nuest,nvest,
+     * nu,tu,nv,tv,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c  given the set of ordered points f(i,j) in the idim-dimensional space,
+c  corresponding to grid values (u(i),v(j)) ,i=1,...,mu ; j=1,...,mv,
+c  parsur determines a smooth approximating spline surface s(u,v) , i.e.
+c    f1 = s1(u,v)
+c      ...                u(1) <= u <= u(mu) ; v(1) <= v <= v(mv)
+c    fidim = sidim(u,v)
+c  with sl(u,v), l=1,2,...,idim bicubic spline functions with common
+c  knots tu(i),i=1,...,nu in the u-variable and tv(j),j=1,...,nv in the
+c  v-variable.
+c  in addition, these splines will be periodic in the variable u if
+c  ipar(1) = 1 and periodic in the variable v if ipar(2) = 1.
+c  if iopt=-1, parsur determines the least-squares bicubic spline
+c  surface according to a given set of knots.
+c  if iopt>=0, the number of knots of s(u,v) and their position
+c  is chosen automatically by the routine. the smoothness of s(u,v) is
+c  achieved by minimalizing the discontinuity jumps of the derivatives
+c  of the splines at the knots. the amount of smoothness of s(u,v) is
+c  determined by the condition that
+c  fp=sumi=1,mu(sumj=1,mv(dist(f(i,j)-s(u(i),v(j)))**2))<=s,
+c  with s a given non-negative constant.
+c  the fit s(u,v) is given in its b-spline representation and can be
+c  evaluated by means of routine surev.
+c
+c calling sequence:
+c     call parsur(iopt,ipar,idim,mu,u,mv,v,f,s,nuest,nvest,nu,tu,
+c    *  nv,tv,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer flag. unchanged on exit.
+c          on entry iopt must specify whether a least-squares surface
+c          (iopt=-1) or a smoothing surface (iopt=0 or 1)must be
+c          determined.
+c          if iopt=0 the routine will start with the initial set of
+c          knots needed for determining the least-squares polynomial
+c          surface.
+c          if iopt=1 the routine will continue with the set of knots
+c          found at the last call of the routine.
+c          attention: a call with iopt=1 must always be immediately
+c          preceded by another call with iopt = 1 or iopt = 0.
+c  ipar  : integer array of dimension 2. unchanged on exit.
+c          on entry ipar(1) must specify whether (ipar(1)=1) or not
+c          (ipar(1)=0) the splines must be periodic in the variable u.
+c          on entry ipar(2) must specify whether (ipar(2)=1) or not
+c          (ipar(2)=0) the splines must be periodic in the variable v.
+c  idim  : integer. on entry idim must specify the dimension of the
+c          surface. 1 <= idim <= 3. unchanged on exit.
+c  mu    : integer. on entry mu must specify the number of grid points
+c          along the u-axis. unchanged on exit.
+c          mu >= mumin where mumin=4-2*ipar(1)
+c  u     : real array of dimension at least (mu). before entry, u(i)
+c          must be set to the u-co-ordinate of the i-th grid point
+c          along the u-axis, for i=1,2,...,mu. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c  mv    : integer. on entry mv must specify the number of grid points
+c          along the v-axis. unchanged on exit.
+c          mv >= mvmin where mvmin=4-2*ipar(2)
+c  v     : real array of dimension at least (mv). before entry, v(j)
+c          must be set to the v-co-ordinate of the j-th grid point
+c          along the v-axis, for j=1,2,...,mv. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c  f     : real array of dimension at least (mu*mv*idim).
+c          before entry, f(mu*mv*(l-1)+mv*(i-1)+j) must be set to the
+c          l-th co-ordinate of the data point corresponding to the
+c          the grid point (u(i),v(j)) for l=1,...,idim ,i=1,...,mu
+c          and j=1,...,mv. unchanged on exit.
+c          if ipar(1)=1 it is expected that f(mu*mv*(l-1)+mv*(mu-1)+j)
+c          = f(mu*mv*(l-1)+j), l=1,...,idim ; j=1,...,mv
+c          if ipar(2)=1 it is expected that f(mu*mv*(l-1)+mv*(i-1)+mv)
+c          = f(mu*mv*(l-1)+mv*(i-1)+1), l=1,...,idim ; i=1,...,mu
+c  s     : real. on entry (if iopt>=0) s must specify the smoothing
+c          factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  nuest : integer. unchanged on exit.
+c  nvest : integer. unchanged on exit.
+c          on entry, nuest and nvest must specify an upper bound for the
+c          number of knots required in the u- and v-directions respect.
+c          these numbers will also determine the storage space needed by
+c          the routine. nuest >= 8, nvest >= 8.
+c          in most practical situation nuest = mu/2, nvest=mv/2, will
+c          be sufficient. always large enough are nuest=mu+4+2*ipar(1),
+c          nvest = mv+4+2*ipar(2), the number of knots needed for
+c          interpolation (s=0). see also further comments.
+c  nu    : integer.
+c          unless ier=10 (in case iopt>=0), nu will contain the total
+c          number of knots with respect to the u-variable, of the spline
+c          surface returned. if the computation mode iopt=1 is used,
+c          the value of nu should be left unchanged between subsequent
+c          calls. in case iopt=-1, the value of nu should be specified
+c          on entry.
+c  tu    : real array of dimension at least (nuest).
+c          on succesful exit, this array will contain the knots of the
+c          splines with respect to the u-variable, i.e. the position of
+c          the interior knots tu(5),...,tu(nu-4) as well as the position
+c          of the additional knots tu(1),...,tu(4) and tu(nu-3),...,
+c          tu(nu) needed for the b-spline representation.
+c          if the computation mode iopt=1 is used,the values of tu(1)
+c          ...,tu(nu) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values tu(5),
+c          ...tu(nu-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  nv    : integer.
+c          unless ier=10 (in case iopt>=0), nv will contain the total
+c          number of knots with respect to the v-variable, of the spline
+c          surface returned. if the computation mode iopt=1 is used,
+c          the value of nv should be left unchanged between subsequent
+c          calls. in case iopt=-1, the value of nv should be specified
+c          on entry.
+c  tv    : real array of dimension at least (nvest).
+c          on succesful exit, this array will contain the knots of the
+c          splines with respect to the v-variable, i.e. the position of
+c          the interior knots tv(5),...,tv(nv-4) as well as the position
+c          of the additional knots tv(1),...,tv(4) and tv(nv-3),...,
+c          tv(nv) needed for the b-spline representation.
+c          if the computation mode iopt=1 is used,the values of tv(1)
+c          ...,tv(nv) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values tv(5),
+c          ...tv(nv-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  c     : real array of dimension at least (nuest-4)*(nvest-4)*idim.
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(u,v)
+c  fp    : real. unless ier=10, fp contains the sum of squared
+c          residuals of the spline surface returned.
+c  wrk   : real array of dimension (lwrk). used as workspace.
+c          if the computation mode iopt=1 is used the values of
+c          wrk(1),...,wrk(4) should be left unchanged between subsequent
+c          calls.
+c  lwrk  : integer. on entry lwrk must specify the actual dimension of
+c          the array wrk as declared in the calling (sub)program.
+c          lwrk must not be too small.
+c           lwrk >= 4+nuest*(mv*idim+11+4*ipar(1))+nvest*(11+4*ipar(2))+
+c           4*(mu+mv)+q*idim where q is the larger of mv and nuest.
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c          if the computation mode iopt=1 is used the values of
+c          iwrk(1),.,iwrk(3) should be left unchanged between subsequent
+c          calls.
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= 3+mu+mv+nuest+nvest.
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the surface returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline surface returned is an
+c            interpolating surface (fp=0).
+c   ier=-2 : normal return. the surface returned is the least-squares
+c            polynomial surface. in this extreme case fp gives the
+c            upper bound for the smoothing factor s.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters nuest and
+c            nvest.
+c            probably causes : nuest or nvest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the least-squares surface
+c            according to the current set of knots. the parameter fp
+c            gives the corresponding sum of squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing surface with
+c            fp = s. probably causes : s too small.
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing surface
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt<=1, 0<=ipar(1)<=1, 0<=ipar(2)<=1, 1 <=idim<=3
+c            mu >= 4-2*ipar(1),mv >= 4-2*ipar(2), nuest >=8, nvest >= 8,
+c            kwrk>=3+mu+mv+nuest+nvest,
+c            lwrk >= 4+nuest*(mv*idim+11+4*ipar(1))+nvest*(11+4*ipar(2))
+c             +4*(mu+mv)+max(nuest,mv)*idim
+c            u(i-1)<u(i),i=2,..,mu, v(i-1)<v(i),i=2,...,mv
+c            if iopt=-1: 8<=nu<=min(nuest,mu+4+2*ipar(1))
+c                        u(1)<tu(5)<tu(6)<...<tu(nu-4)<u(mu)
+c                        8<=nv<=min(nvest,mv+4+2*ipar(2))
+c                        v(1)<tv(5)<tv(6)<...<tv(nv-4)<v(mv)
+c                    the schoenberg-whitney conditions, i.e. there must
+c                    be subset of grid co-ordinates uu(p) and vv(q) such
+c                    that   tu(p) < uu(p) < tu(p+4) ,p=1,...,nu-4
+c                           tv(q) < vv(q) < tv(q+4) ,q=1,...,nv-4
+c                     (see fpchec or fpchep)
+c            if iopt>=0: s>=0
+c                       if s=0: nuest>=mu+4+2*ipar(1)
+c                               nvest>=mv+4+2*ipar(2)
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c
+c further comments:
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the surface will be too smooth and signal will be
+c   lost ; if s is too small the surface will pick up too much noise. in
+c   the extreme cases the program will return an interpolating surface
+c   if s=0 and the constrained least-squares polynomial surface if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the accuracy of the data values.
+c   if the user has an idea of the statistical errors on the data, he
+c   can also find a proper estimate for s. for, by assuming that, if he
+c   specifies the right s, parsur will return a surface s(u,v) which
+c   exactly reproduces the surface underlying the data he can evaluate
+c   the sum(dist(f(i,j)-s(u(i),v(j)))**2) to find a good estimate for s.
+c   for example, if he knows that the statistical errors on his f(i,j)-
+c   values is not greater than 0.1, he may expect that a good s should
+c   have a value not larger than mu*mv*(0.1)**2.
+c   if nothing is known about the statistical error in f(i,j), s must
+c   be determined by trial and error, taking account of the comments
+c   above. the best is then to start with a very large value of s (to
+c   determine the le-sq polynomial surface and the corresponding upper
+c   bound fp0 for s) and then to progressively decrease the value of s
+c   ( say by a factor 10 in the beginning, i.e. s=fp0/10,fp0/100,...
+c   and more carefully as the approximation shows more detail) to
+c   obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt = 1 the program will continue with the knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if parsur is called repeatedly for different values of s.
+c   the number of knots of the surface returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   surface underlying the data. if the computation mode iopt = 1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt=1,the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   parsur once more with the chosen value for s but now with iopt=0.
+c   indeed, parsur may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds nuest and
+c   nvest. indeed, if at a certain stage in parsur the number of knots
+c   in one direction (say nu) has reached the value of its upper bound
+c   (nuest), then from that moment on all subsequent knots are added
+c   in the other (v) direction. this may indicate that the value of
+c   nuest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c   for example, by setting nuest=8 (the lowest allowable value for
+c   nuest), the user can indicate that he wants an approximation with
+c   splines which are simple cubic polynomials in the variable u.
+c
+c  other subroutines required:
+c    fppasu,fpchec,fpchep,fpknot,fprati,fpgrpa,fptrnp,fpback,
+c    fpbacp,fpbspl,fptrpe,fpdisc,fpgivs,fprota
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1989
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,fp
+      integer iopt,idim,mu,mv,nuest,nvest,nu,nv,lwrk,kwrk,ier
+c  ..array arguments..
+      real*8 u(mu),v(mv),f(mu*mv*idim),tu(nuest),tv(nvest),
+     * c((nuest-4)*(nvest-4)*idim),wrk(lwrk)
+      integer ipar(2),iwrk(kwrk)
+c  ..local scalars..
+      real*8 tol,ub,ue,vb,ve,peru,perv
+      integer i,j,jwrk,kndu,kndv,knru,knrv,kwest,l1,l2,l3,l4,
+     * lfpu,lfpv,lwest,lww,maxit,nc,mf,mumin,mvmin
+c  ..function references..
+      integer max0
+c  ..subroutine references..
+c    fppasu,fpchec,fpchep
+c  ..
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 200
+      if(ipar(1).lt.0 .or. ipar(1).gt.1) go to 200
+      if(ipar(2).lt.0 .or. ipar(2).gt.1) go to 200
+      if(idim.le.0 .or. idim.gt.3) go to 200
+      mumin = 4-2*ipar(1)
+      if(mu.lt.mumin .or. nuest.lt.8) go to 200
+      mvmin = 4-2*ipar(2)
+      if(mv.lt.mvmin .or. nvest.lt.8) go to 200
+      mf = mu*mv
+      nc = (nuest-4)*(nvest-4)
+      lwest = 4+nuest*(mv*idim+11+4*ipar(1))+nvest*(11+4*ipar(2))+
+     * 4*(mu+mv)+max0(nuest,mv)*idim
+      kwest = 3+mu+mv+nuest+nvest
+      if(lwrk.lt.lwest .or. kwrk.lt.kwest) go to 200
+      do 10 i=2,mu
+        if(u(i-1).ge.u(i)) go to 200
+  10  continue
+      do 20 i=2,mv
+        if(v(i-1).ge.v(i)) go to 200
+  20  continue
+      if(iopt.ge.0) go to 100
+      if(nu.lt.8 .or. nu.gt.nuest) go to 200
+      ub = u(1)
+      ue = u(mu)
+      if (ipar(1).ne.0) go to 40
+      j = nu
+      do 30 i=1,4
+        tu(i) = ub
+        tu(j) = ue
+        j = j-1
+  30  continue
+      call fpchec(u,mu,tu,nu,3,ier)
+      if(ier.ne.0) go to 200
+      go to 60
+  40  l1 = 4
+      l2 = l1
+      l3 = nu-3
+      l4 = l3
+      peru = ue-ub
+      tu(l2) = ub
+      tu(l3) = ue
+      do 50 j=1,3
+        l1 = l1+1
+        l2 = l2-1
+        l3 = l3+1
+        l4 = l4-1
+        tu(l2) = tu(l4)-peru
+        tu(l3) = tu(l1)+peru
+  50  continue
+      call fpchep(u,mu,tu,nu,3,ier)
+      if(ier.ne.0) go to 200
+  60  if(nv.lt.8 .or. nv.gt.nvest) go to 200
+      vb = v(1)
+      ve = v(mv)
+      if (ipar(2).ne.0) go to 80
+      j = nv
+      do 70 i=1,4
+        tv(i) = vb
+        tv(j) = ve
+        j = j-1
+  70  continue
+      call fpchec(v,mv,tv,nv,3,ier)
+      if(ier.ne.0) go to 200
+      go to 150
+  80  l1 = 4
+      l2 = l1
+      l3 = nv-3
+      l4 = l3
+      perv = ve-vb
+      tv(l2) = vb
+      tv(l3) = ve
+      do 90 j=1,3
+        l1 = l1+1
+        l2 = l2-1
+        l3 = l3+1
+        l4 = l4-1
+        tv(l2) = tv(l4)-perv
+        tv(l3) = tv(l1)+perv
+  90  continue
+      call fpchep(v,mv,tv,nv,3,ier)
+      if (ier.eq.0) go to 150
+      go to 200
+ 100  if(s.lt.0.) go to 200
+      if(s.eq.0. .and. (nuest.lt.(mu+4+2*ipar(1)) .or.
+     * nvest.lt.(mv+4+2*ipar(2))) )go to 200
+      ier = 0
+c  we partition the working space and determine the spline approximation
+ 150  lfpu = 5
+      lfpv = lfpu+nuest
+      lww = lfpv+nvest
+      jwrk = lwrk-4-nuest-nvest
+      knru = 4
+      knrv = knru+mu
+      kndu = knrv+mv
+      kndv = kndu+nuest
+      call fppasu(iopt,ipar,idim,u,mu,v,mv,f,mf,s,nuest,nvest,
+     * tol,maxit,nc,nu,tu,nv,tv,c,fp,wrk(1),wrk(2),wrk(3),wrk(4),
+     * wrk(lfpu),wrk(lfpv),iwrk(1),iwrk(2),iwrk(3),iwrk(knru),
+     * iwrk(knrv),iwrk(kndu),iwrk(kndv),wrk(lww),jwrk,ier)
+ 200  return
+      end
+

Added: branches/Interpolate1D/fitpack/percur.f
===================================================================
--- branches/Interpolate1D/fitpack/percur.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/percur.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,274 @@
+      subroutine percur(iopt,m,x,y,w,k,s,nest,n,t,c,fp,
+     * wrk,lwrk,iwrk,ier)
+c  given the set of data points (x(i),y(i)) and the set of positive
+c  numbers w(i),i=1,2,...,m-1, subroutine percur determines a smooth
+c  periodic spline approximation of degree k with period per=x(m)-x(1).
+c  if iopt=-1 percur calculates the weighted least-squares periodic
+c  spline according to a given set of knots.
+c  if iopt>=0 the number of knots of the spline s(x) and the position
+c  t(j),j=1,2,...,n is chosen automatically by the routine. the smooth-
+c  ness of s(x) is then achieved by minimalizing the discontinuity
+c  jumps of the k-th derivative of s(x) at the knots t(j),j=k+2,k+3,...,
+c  n-k-1. the amount of smoothness is determined by the condition that
+c  f(p)=sum((w(i)*(y(i)-s(x(i))))**2) be <= s, with s a given non-
+c  negative constant, called the smoothing factor.
+c  the fit s(x) is given in the b-spline representation (b-spline coef-
+c  ficients c(j),j=1,2,...,n-k-1) and can be evaluated by means of
+c  subroutine splev.
+c
+c  calling sequence:
+c     call percur(iopt,m,x,y,w,k,s,nest,n,t,c,fp,wrk,
+c    * lwrk,iwrk,ier)
+c
+c  parameters:
+c   iopt  : integer flag. on entry iopt must specify whether a weighted
+c           least-squares spline (iopt=-1) or a smoothing spline (iopt=
+c           0 or 1) must be determined. if iopt=0 the routine will start
+c           with an initial set of knots t(i)=x(1)+(x(m)-x(1))*(i-k-1),
+c           i=1,2,...,2*k+2. if iopt=1 the routine will continue with
+c           the knots found at the last call of the routine.
+c           attention: a call with iopt=1 must always be immediately
+c           preceded by another call with iopt=1 or iopt=0.
+c           unchanged on exit.
+c   m     : integer. on entry m must specify the number of data points.
+c           m > 1. unchanged on exit.
+c   x     : real array of dimension at least (m). before entry, x(i)
+c           must be set to the i-th value of the independent variable x,
+c           for i=1,2,...,m. these values must be supplied in strictly
+c           ascending order. x(m) only indicates the length of the
+c           period of the spline, i.e per=x(m)-x(1).
+c           unchanged on exit.
+c   y     : real array of dimension at least (m). before entry, y(i)
+c           must be set to the i-th value of the dependent variable y,
+c           for i=1,2,...,m-1. the element y(m) is not used.
+c           unchanged on exit.
+c   w     : real array of dimension at least (m). before entry, w(i)
+c           must be set to the i-th value in the set of weights. the
+c           w(i) must be strictly positive. w(m) is not used.
+c           see also further comments. unchanged on exit.
+c   k     : integer. on entry k must specify the degree of the spline.
+c           1<=k<=5. it is recommended to use cubic splines (k=3).
+c           the user is strongly dissuaded from choosing k even,together
+c           with a small s-value. unchanged on exit.
+c   s     : real.on entry (in case iopt>=0) s must specify the smoothing
+c           factor. s >=0. unchanged on exit.
+c           for advice on the choice of s see further comments.
+c   nest  : integer. on entry nest must contain an over-estimate of the
+c           total number of knots of the spline returned, to indicate
+c           the storage space available to the routine. nest >=2*k+2.
+c           in most practical situation nest=m/2 will be sufficient.
+c           always large enough is nest=m+2*k,the number of knots needed
+c           for interpolation (s=0). unchanged on exit.
+c   n     : integer.
+c           unless ier = 10 (in case iopt >=0), n will contain the
+c           total number of knots of the spline approximation returned.
+c           if the computation mode iopt=1 is used this value of n
+c           should be left unchanged between subsequent calls.
+c           in case iopt=-1, the value of n must be specified on entry.
+c   t     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the knots of the
+c           spline,i.e. the position of the interior knots t(k+2),t(k+3)
+c           ...,t(n-k-1) as well as the position of the additional knots
+c           t(1),t(2),...,t(k+1)=x(1) and t(n-k)=x(m),..,t(n) needed for
+c           the b-spline representation.
+c           if the computation mode iopt=1 is used, the values of t(1),
+c           t(2),...,t(n) should be left unchanged between subsequent
+c           calls. if the computation mode iopt=-1 is used, the values
+c           t(k+2),...,t(n-k-1) must be supplied by the user, before
+c           entry. see also the restrictions (ier=10).
+c   c     : real array of dimension at least (nest).
+c           on succesful exit, this array will contain the coefficients
+c           c(1),c(2),..,c(n-k-1) in the b-spline representation of s(x)
+c   fp    : real. unless ier = 10, fp contains the weighted sum of
+c           squared residuals of the spline approximation returned.
+c   wrk   : real array of dimension at least (m*(k+1)+nest*(8+5*k)).
+c           used as working space. if the computation mode iopt=1 is
+c           used, the values wrk(1),...,wrk(n) should be left unchanged
+c           between subsequent calls.
+c   lwrk  : integer. on entry,lwrk must specify the actual dimension of
+c           the array wrk as declared in the calling (sub)program. lwrk
+c           must not be too small (see wrk). unchanged on exit.
+c   iwrk  : integer array of dimension at least (nest).
+c           used as working space. if the computation mode iopt=1 is
+c           used,the values iwrk(1),...,iwrk(n) should be left unchanged
+c           between subsequent calls.
+c   ier   : integer. unless the routine detects an error, ier contains a
+c           non-positive value on exit, i.e.
+c    ier=0  : normal return. the spline returned has a residual sum of
+c             squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c             ive tolerance set to 0.001 by the program.
+c    ier=-1 : normal return. the spline returned is an interpolating
+c             periodic spline (fp=0).
+c    ier=-2 : normal return. the spline returned is the weighted least-
+c             squares constant. in this extreme case fp gives the upper
+c             bound fp0 for the smoothing factor s.
+c    ier=1  : error. the required storage space exceeds the available
+c             storage space, as specified by the parameter nest.
+c             probably causes : nest too small. if nest is already
+c             large (say nest > m/2), it may also indicate that s is
+c             too small
+c             the approximation returned is the least-squares periodic
+c             spline according to the knots t(1),t(2),...,t(n). (n=nest)
+c             the parameter fp gives the corresponding weighted sum of
+c             squared residuals (fp>s).
+c    ier=2  : error. a theoretically impossible result was found during
+c             the iteration proces for finding a smoothing spline with
+c             fp = s. probably causes : s too small.
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=3  : error. the maximal number of iterations maxit (set to 20
+c             by the program) allowed for finding a smoothing spline
+c             with fp=s has been reached. probably causes : s too small
+c             there is an approximation returned but the corresponding
+c             weighted sum of squared residuals does not satisfy the
+c             condition abs(fp-s)/s < tol.
+c    ier=10 : error. on entry, the input data are controlled on validity
+c             the following restrictions must be satisfied.
+c             -1<=iopt<=1, 1<=k<=5, m>1, nest>2*k+2, w(i)>0,i=1,...,m-1
+c             x(1)<x(2)<...<x(m), lwrk>=(k+1)*m+nest*(8+5*k)
+c             if iopt=-1: 2*k+2<=n<=min(nest,m+2*k)
+c                         x(1)<t(k+2)<t(k+3)<...<t(n-k-1)<x(m)
+c                       the schoenberg-whitney conditions, i.e. there
+c                       must be a subset of data points xx(j) with
+c                       xx(j) = x(i) or x(i)+(x(m)-x(1)) such that
+c                         t(j) < xx(j) < t(j+k+1), j=k+1,...,n-k-1
+c             if iopt>=0: s>=0
+c                         if s=0 : nest >= m+2*k
+c             if one of these conditions is found to be violated,control
+c             is immediately repassed to the calling program. in that
+c             case there is no approximation returned.
+c
+c  further comments:
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating periodic
+c   spline if s=0 and the weighted least-squares constant if s is very
+c   large. between these extremes, a properly chosen s will result in
+c   a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   y(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in y(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   constant and the corresponding upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximation shows more detail) to obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if percur is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. but, if the computation mode iopt=1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   percur once more with the selected value for s but now with iopt=0.
+c   indeed, percur may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c
+c  other subroutines required:
+c    fpbacp,fpbspl,fpchep,fpperi,fpdisc,fpgivs,fpknot,fprati,fprota
+c
+c  references:
+c   dierckx p. : algorithms for smoothing data with periodic and
+c                parametric splines, computer graphics and image
+c                processing 20 (1982) 171-184.
+c   dierckx p. : algorithms for smoothing data with periodic and param-
+c                etric splines, report tw55, dept. computer science,
+c                k.u.leuven, 1981.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1987
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,fp
+      integer iopt,m,k,nest,n,lwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),w(m),t(nest),c(nest),wrk(lwrk)
+      integer iwrk(nest)
+c  ..local scalars..
+      real*8 per,tol
+      integer i,ia1,ia2,ib,ifp,ig1,ig2,iq,iz,i1,i2,j1,j2,k1,k2,lwest,
+     * maxit,m1,nmin
+c  ..subroutine references..
+c    perper,pcheck
+c  ..
+c  we set up the parameters tol and maxit
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(k.le.0 .or. k.gt.5) go to 50
+      k1 = k+1
+      k2 = k1+1
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 50
+      nmin = 2*k1
+      if(m.lt.2 .or. nest.lt.nmin) go to 50
+      lwest = m*k1+nest*(8+5*k)
+      if(lwrk.lt.lwest) go to 50
+      m1 = m-1
+      do 10 i=1,m1
+         if(x(i).ge.x(i+1) .or. w(i).le.0.) go to 50
+  10  continue
+      if(iopt.ge.0) go to 30
+      if(n.le.nmin .or. n.gt.nest) go to 50
+      per = x(m)-x(1)
+      j1 = k1
+      t(j1) = x(1)
+      i1 = n-k
+      t(i1) = x(m)
+      j2 = j1
+      i2 = i1
+      do 20 i=1,k
+         i1 = i1+1
+         i2 = i2-1
+         j1 = j1+1
+         j2 = j2-1
+         t(j2) = t(i2)-per
+         t(i1) = t(j1)+per
+  20  continue
+      call fpchep(x,m,t,n,k,ier)
+      if (ier.eq.0) go to 40
+      go to 50
+  30  if(s.lt.0.) go to 50
+      if(s.eq.0. .and. nest.lt.(m+2*k)) go to 50
+      ier = 0
+c we partition the working space and determine the spline approximation.
+  40  ifp = 1
+      iz = ifp+nest
+      ia1 = iz+nest
+      ia2 = ia1+nest*k1
+      ib = ia2+nest*k
+      ig1 = ib+nest*k2
+      ig2 = ig1+nest*k2
+      iq = ig2+nest*k1
+      call fpperi(iopt,x,y,w,m,k,s,nest,tol,maxit,k1,k2,n,t,c,fp,
+     * wrk(ifp),wrk(iz),wrk(ia1),wrk(ia2),wrk(ib),wrk(ig1),wrk(ig2),
+     * wrk(iq),iwrk,ier)
+  50  return
+      end

Added: branches/Interpolate1D/fitpack/pogrid.f
===================================================================
--- branches/Interpolate1D/fitpack/pogrid.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/pogrid.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,466 @@
+      subroutine pogrid(iopt,ider,mu,u,mv,v,z,z0,r,s,nuest,nvest,
+     * nu,tu,nv,tv,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c  subroutine pogrid fits a function f(x,y) to a set of data points
+c  z(i,j) given at the nodes (x,y)=(u(i)*cos(v(j)),u(i)*sin(v(j))),
+c  i=1,...,mu ; j=1,...,mv , of a radius-angle grid over a disc
+c    x ** 2  +  y ** 2  <=  r ** 2 .
+c
+c  this approximation problem is reduced to the determination of a
+c  bicubic spline s(u,v) smoothing the data (u(i),v(j),z(i,j)) on the
+c  rectangle 0<=u<=r, v(1)<=v<=v(1)+2*pi
+c  in order to have continuous partial derivatives
+c              i+j
+c             d   f(0,0)
+c    g(i,j) = ----------
+c                i   j
+c              dx  dy
+c
+c  s(u,v)=f(x,y) must satisfy the following conditions
+c
+c    (1) s(0,v) = g(0,0)   v(1)<=v<= v(1)+2*pi
+c
+c        d s(0,v)
+c    (2) -------- = cos(v)*g(1,0)+sin(v)*g(0,1)  v(1)<=v<= v(1)+2*pi
+c        d u
+c
+c  moreover, s(u,v) must be periodic in the variable v, i.e.
+c
+c         j            j
+c        d s(u,vb)   d s(u,ve)
+c    (3) ---------- = ---------   0 <=u<= r, j=0,1,2 , vb=v(1),
+c           j            j                             ve=vb+2*pi
+c        d v          d v
+c
+c  the number of knots of s(u,v) and their position tu(i),i=1,2,...,nu;
+c  tv(j),j=1,2,...,nv, is chosen automatically by the routine. the
+c  smoothness of s(u,v) is achieved by minimalizing the discontinuity
+c  jumps of the derivatives of the spline at the knots. the amount of
+c  smoothness of s(u,v) is determined by the condition that
+c  fp=sumi=1,mu(sumj=1,mv((z(i,j)-s(u(i),v(j)))**2))+(z0-g(0,0))**2<=s,
+c  with s a given non-negative constant.
+c  the fit s(u,v) is given in its b-spline representation and can be
+c  evaluated by means of routine bispev. f(x,y) = s(u,v) can also be
+c  evaluated by means of function program evapol.
+c
+c calling sequence:
+c     call pogrid(iopt,ider,mu,u,mv,v,z,z0,r,s,nuest,nvest,nu,tu,
+c    *  ,nv,tv,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer array of dimension 3, specifying different options.
+c          unchanged on exit.
+c  iopt(1):on entry iopt(1) must specify whether a least-squares spline
+c          (iopt(1)=-1) or a smoothing spline (iopt(1)=0 or 1) must be
+c          determined.
+c          if iopt(1)=0 the routine will start with an initial set of
+c          knots tu(i)=0,tu(i+4)=r,i=1,...,4;tv(i)=v(1)+(i-4)*2*pi,i=1,.
+c          ...,8.
+c          if iopt(1)=1 the routine will continue with the set of knots
+c          found at the last call of the routine.
+c          attention: a call with iopt(1)=1 must always be immediately
+c          preceded by another call with iopt(1) = 1 or iopt(1) = 0.
+c  iopt(2):on entry iopt(2) must specify the requested order of conti-
+c          nuity for f(x,y) at the origin.
+c          if iopt(2)=0 only condition (1) must be fulfilled and
+c          if iopt(2)=1 conditions (1)+(2) must be fulfilled.
+c  iopt(3):on entry iopt(3) must specify whether (iopt(3)=1) or not
+c          (iopt(3)=0) the approximation f(x,y) must vanish at the
+c          boundary of the approximation domain.
+c  ider  : integer array of dimension 2, specifying different options.
+c          unchanged on exit.
+c  ider(1):on entry ider(1) must specify whether (ider(1)=0 or 1) or not
+c          (ider(1)=-1) there is a data value z0 at the origin.
+c          if ider(1)=1, z0 will be considered to be the right function
+c          value, and it will be fitted exactly (g(0,0)=z0=c(1)).
+c          if ider(1)=0, z0 will be considered to be a data value just
+c          like the other data values z(i,j).
+c  ider(2):on entry ider(2) must specify whether (ider(2)=1) or not
+c          (ider(2)=0) f(x,y) must have vanishing partial derivatives
+c          g(1,0) and g(0,1) at the origin. (in case iopt(2)=1)
+c  mu    : integer. on entry mu must specify the number of grid points
+c          along the u-axis. unchanged on exit.
+c          mu >= mumin where mumin=4-iopt(3)-ider(2) if ider(1)<0
+c                                 =3-iopt(3)-ider(2) if ider(1)>=0
+c  u     : real array of dimension at least (mu). before entry, u(i)
+c          must be set to the u-co-ordinate of the i-th grid point
+c          along the u-axis, for i=1,2,...,mu. these values must be
+c          positive and supplied in strictly ascending order.
+c          unchanged on exit.
+c  mv    : integer. on entry mv must specify the number of grid points
+c          along the v-axis. mv > 3 . unchanged on exit.
+c  v     : real array of dimension at least (mv). before entry, v(j)
+c          must be set to the v-co-ordinate of the j-th grid point
+c          along the v-axis, for j=1,2,...,mv. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c          -pi <= v(1) < pi , v(mv) < v(1)+2*pi.
+c  z     : real array of dimension at least (mu*mv).
+c          before entry, z(mv*(i-1)+j) must be set to the data value at
+c          the grid point (u(i),v(j)) for i=1,...,mu and j=1,...,mv.
+c          unchanged on exit.
+c  z0    : real value. on entry (if ider(1) >=0 ) z0 must specify the
+c          data value at the origin. unchanged on exit.
+c  r     : real value. on entry r must specify the radius of the disk.
+c          r>=u(mu) (>u(mu) if iopt(3)=1). unchanged on exit.
+c  s     : real. on entry (if iopt(1)>=0) s must specify the smoothing
+c          factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  nuest : integer. unchanged on exit.
+c  nvest : integer. unchanged on exit.
+c          on entry, nuest and nvest must specify an upper bound for the
+c          number of knots required in the u- and v-directions respect.
+c          these numbers will also determine the storage space needed by
+c          the routine. nuest >= 8, nvest >= 8.
+c          in most practical situation nuest = mu/2, nvest=mv/2, will
+c          be sufficient. always large enough are nuest=mu+5+iopt(2)+
+c          iopt(3), nvest = mv+7, the number of knots needed for
+c          interpolation (s=0). see also further comments.
+c  nu    : integer.
+c          unless ier=10 (in case iopt(1)>=0), nu will contain the total
+c          number of knots with respect to the u-variable, of the spline
+c          approximation returned. if the computation mode iopt(1)=1 is
+c          used, the value of nu should be left unchanged between sub-
+c          sequent calls. in case iopt(1)=-1, the value of nu should be
+c          specified on entry.
+c  tu    : real array of dimension at least (nuest).
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the u-variable, i.e. the position of
+c          the interior knots tu(5),...,tu(nu-4) as well as the position
+c          of the additional knots tu(1)=...=tu(4)=0 and tu(nu-3)=...=
+c          tu(nu)=r needed for the b-spline representation.
+c          if the computation mode iopt(1)=1 is used,the values of tu(1)
+c          ...,tu(nu) should be left unchanged between subsequent calls.
+c          if the computation mode iopt(1)=-1 is used, the values tu(5),
+c          ...tu(nu-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  nv    : integer.
+c          unless ier=10 (in case iopt(1)>=0), nv will contain the total
+c          number of knots with respect to the v-variable, of the spline
+c          approximation returned. if the computation mode iopt(1)=1 is
+c          used, the value of nv should be left unchanged between sub-
+c          sequent calls. in case iopt(1) = -1, the value of nv should
+c          be specified on entry.
+c  tv    : real array of dimension at least (nvest).
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the v-variable, i.e. the position of
+c          the interior knots tv(5),...,tv(nv-4) as well as the position
+c          of the additional knots tv(1),...,tv(4) and tv(nv-3),...,
+c          tv(nv) needed for the b-spline representation.
+c          if the computation mode iopt(1)=1 is used,the values of tv(1)
+c          ...,tv(nv) should be left unchanged between subsequent calls.
+c          if the computation mode iopt(1)=-1 is used, the values tv(5),
+c          ...tv(nv-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  c     : real array of dimension at least (nuest-4)*(nvest-4).
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(u,v)
+c  fp    : real. unless ier=10, fp contains the sum of squared
+c          residuals of the spline approximation returned.
+c  wrk   : real array of dimension (lwrk). used as workspace.
+c          if the computation mode iopt(1)=1 is used the values of
+c          wrk(1),...,wrk(8) should be left unchanged between subsequent
+c          calls.
+c  lwrk  : integer. on entry lwrk must specify the actual dimension of
+c          the array wrk as declared in the calling (sub)program.
+c          lwrk must not be too small.
+c           lwrk >= 8+nuest*(mv+nvest+3)+nvest*21+4*mu+6*mv+q
+c           where q is the larger of (mv+nvest) and nuest.
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c          if the computation mode iopt(1)=1 is used the values of
+c          iwrk(1),.,iwrk(4) should be left unchanged between subsequent
+c          calls.
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= 4+mu+mv+nuest+nvest.
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the spline returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline returned is an interpolating
+c            spline (fp=0).
+c   ier=-2 : normal return. the spline returned is the least-squares
+c            constrained polynomial. in this extreme case fp gives the
+c            upper bound for the smoothing factor s.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters nuest and
+c            nvest.
+c            probably causes : nuest or nvest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the least-squares spline
+c            according to the current set of knots. the parameter fp
+c            gives the corresponding sum of squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing spline with
+c            fp = s. probably causes : s too small.
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing spline
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt(1)<=1, 0<=iopt(2)<=1, 0<=iopt(3)<=1,
+c            -1<=ider(1)<=1, 0<=ider(2)<=1, ider(2)=0 if iopt(2)=0.
+c            mu >= mumin (see above), mv >= 4, nuest >=8, nvest >= 8,
+c            kwrk>=4+mu+mv+nuest+nvest,
+c            lwrk >= 8+nuest*(mv+nvest+3)+nvest*21+4*mu+6*mv+
+c             max(nuest,mv+nvest)
+c            0< u(i-1)<u(i)<=r,i=2,..,mu, (< r if iopt(3)=1)
+c            -pi<=v(1)< pi, v(1)<v(i-1)<v(i)<v(1)+2*pi, i=3,...,mv
+c            if iopt(1)=-1: 8<=nu<=min(nuest,mu+5+iopt(2)+iopt(3))
+c                           0<tu(5)<tu(6)<...<tu(nu-4)<r
+c                           8<=nv<=min(nvest,mv+7)
+c                           v(1)<tv(5)<tv(6)<...<tv(nv-4)<v(1)+2*pi
+c                    the schoenberg-whitney conditions, i.e. there must
+c                    be subset of grid co-ordinates uu(p) and vv(q) such
+c                    that   tu(p) < uu(p) < tu(p+4) ,p=1,...,nu-4
+c                     (iopt(2)=1 and iopt(3)=1 also count for a uu-value
+c                           tv(q) < vv(q) < tv(q+4) ,q=1,...,nv-4
+c                     (vv(q) is either a value v(j) or v(j)+2*pi)
+c            if iopt(1)>=0: s>=0
+c                       if s=0: nuest>=mu+5+iopt(2)+iopt(3), nvest>=mv+7
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c
+c further comments:
+c   pogrid does not allow individual weighting of the data-values.
+c   so, if these were determined to widely different accuracies, then
+c   perhaps the general data set routine polar should rather be used
+c   in spite of efficiency.
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the constrained least-squares polynomial(degrees 3,0)if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the accuracy of the data values.
+c   if the user has an idea of the statistical errors on the data, he
+c   can also find a proper estimate for s. for, by assuming that, if he
+c   specifies the right s, pogrid will return a spline s(u,v) which
+c   exactly reproduces the function underlying the data he can evaluate
+c   the sum((z(i,j)-s(u(i),v(j)))**2) to find a good estimate for this s
+c   for example, if he knows that the statistical errors on his z(i,j)-
+c   values is not greater than 0.1, he may expect that a good s should
+c   have a value not larger than mu*mv*(0.1)**2.
+c   if nothing is known about the statistical error in z(i,j), s must
+c   be determined by trial and error, taking account of the comments
+c   above. the best is then to start with a very large value of s (to
+c   determine the least-squares polynomial and the corresponding upper
+c   bound fp0 for s) and then to progressively decrease the value of s
+c   ( say by a factor 10 in the beginning, i.e. s=fp0/10,fp0/100,...
+c   and more carefully as the approximation shows more detail) to
+c   obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt(1)=0.
+c   if iopt(1) = 1 the program will continue with the knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if pogrid is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. if the computation mode iopt(1) = 1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt(1)=1,the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   pogrid once more with the chosen value for s but now with iopt(1)=0.
+c   indeed, pogrid may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds nuest and
+c   nvest. indeed, if at a certain stage in pogrid the number of knots
+c   in one direction (say nu) has reached the value of its upper bound
+c   (nuest), then from that moment on all subsequent knots are added
+c   in the other (v) direction. this may indicate that the value of
+c   nuest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c   for example, by setting nuest=8 (the lowest allowable value for
+c   nuest), the user can indicate that he wants an approximation which
+c   is a simple cubic polynomial in the variable u.
+c
+c  other subroutines required:
+c    fppogr,fpchec,fpchep,fpknot,fpopdi,fprati,fpgrdi,fpsysy,fpback,
+c    fpbacp,fpbspl,fpcyt1,fpcyt2,fpdisc,fpgivs,fprota
+c
+c  references:
+c   dierckx p. : fast algorithms for smoothing data over a disc or a
+c                sphere using tensor product splines, in "algorithms
+c                for approximation", ed. j.c.mason and m.g.cox,
+c                clarendon press oxford, 1987, pp. 51-65
+c   dierckx p. : fast algorithms for smoothing data over a disc or a
+c                sphere using tensor product splines, report tw73, dept.
+c                computer science,k.u.leuven, 1985.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : july 1985
+c  latest update : march 1989
+c
+c  ..
+c  ..scalar arguments..
+      real*8 z0,r,s,fp
+      integer mu,mv,nuest,nvest,nu,nv,lwrk,kwrk,ier
+c  ..array arguments..
+      integer iopt(3),ider(2),iwrk(kwrk)
+      real*8 u(mu),v(mv),z(mu*mv),c((nuest-4)*(nvest-4)),tu(nuest),
+     * tv(nvest),wrk(lwrk)
+c  ..local scalars..
+      real*8 per,pi,tol,uu,ve,zmax,zmin,one,half,rn,zb
+      integer i,i1,i2,j,jwrk,j1,j2,kndu,kndv,knru,knrv,kwest,l,
+     * ldz,lfpu,lfpv,lwest,lww,m,maxit,mumin,muu,nc
+c  ..function references..
+      real*8 datan2
+      integer max0
+c  ..subroutine references..
+c    fpchec,fpchep,fppogr
+c  ..
+c  set constants
+      one = 1d0
+      half = 0.5e0
+      pi = datan2(0d0,-one)
+      per = pi+pi
+      ve = v(1)+per
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations, a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt(1).lt.(-1) .or. iopt(1).gt.1) go to 200
+      if(iopt(2).lt.0 .or. iopt(2).gt.1) go to 200
+      if(iopt(3).lt.0 .or. iopt(3).gt.1) go to 200
+      if(ider(1).lt.(-1) .or. ider(1).gt.1) go to 200
+      if(ider(2).lt.0 .or. ider(2).gt.1) go to 200
+      if(ider(2).eq.1 .and. iopt(2).eq.0) go to 200
+      mumin = 4-iopt(3)-ider(2)
+      if(ider(1).ge.0) mumin = mumin-1
+      if(mu.lt.mumin .or. mv.lt.4) go to 200
+      if(nuest.lt.8 .or. nvest.lt.8) go to 200
+      m = mu*mv
+      nc = (nuest-4)*(nvest-4)
+      lwest = 8+nuest*(mv+nvest+3)+21*nvest+4*mu+6*mv+
+     * max0(nuest,mv+nvest)
+      kwest = 4+mu+mv+nuest+nvest
+      if(lwrk.lt.lwest .or. kwrk.lt.kwest) go to 200
+      if(u(1).le.0. .or. u(mu).gt.r) go to 200
+      if(iopt(3).eq.0) go to 10
+      if(u(mu).eq.r) go to 200
+  10  if(mu.eq.1) go to 30
+      do 20 i=2,mu
+        if(u(i-1).ge.u(i)) go to 200
+  20  continue
+  30  if(v(1).lt. (-pi) .or. v(1).ge.pi ) go to 200
+      if(v(mv).ge.v(1)+per) go to 200
+      do 40 i=2,mv
+        if(v(i-1).ge.v(i)) go to 200
+  40  continue
+      if(iopt(1).gt.0) go to 140
+c  if not given, we compute an estimate for z0.
+      if(ider(1).lt.0) go to 50
+      zb = z0
+      go to 70
+  50  zb = 0.
+      do 60 i=1,mv
+         zb = zb+z(i)
+  60  continue
+      rn = mv
+      zb = zb/rn
+c  we determine the range of z-values.
+  70  zmin = zb
+      zmax = zb
+      do 80 i=1,m
+         if(z(i).lt.zmin) zmin = z(i)
+         if(z(i).gt.zmax) zmax = z(i)
+  80  continue
+      wrk(5) = zb
+      wrk(6) = 0.
+      wrk(7) = 0.
+      wrk(8) = zmax -zmin
+      iwrk(4) = mu
+      if(iopt(1).eq.0) go to 140
+      if(nu.lt.8 .or. nu.gt.nuest) go to 200
+      if(nv.lt.11 .or. nv.gt.nvest) go to 200
+      j = nu
+      do 90 i=1,4
+        tu(i) = 0.
+        tu(j) = r
+        j = j-1
+  90  continue
+      l = 9
+      wrk(l) = 0.
+      if(iopt(2).eq.0) go to 100
+      l = l+1
+      uu = u(1)
+      if(uu.gt.tu(5)) uu = tu(5)
+      wrk(l) = uu*half
+ 100  do 110 i=1,mu
+        l = l+1
+        wrk(l) = u(i)
+ 110  continue
+      if(iopt(3).eq.0) go to 120
+      l = l+1
+      wrk(l) = r
+ 120  muu = l-8
+      call fpchec(wrk(9),muu,tu,nu,3,ier)
+      if(ier.ne.0) go to 200
+      j1 = 4
+      tv(j1) = v(1)
+      i1 = nv-3
+      tv(i1) = ve
+      j2 = j1
+      i2 = i1
+      do 130 i=1,3
+        i1 = i1+1
+        i2 = i2-1
+        j1 = j1+1
+        j2 = j2-1
+        tv(j2) = tv(i2)-per
+        tv(i1) = tv(j1)+per
+ 130  continue
+      l = 9
+      do 135 i=1,mv
+        wrk(l) = v(i)
+        l = l+1
+ 135  continue
+      wrk(l) = ve
+      call fpchep(wrk(9),mv+1,tv,nv,3,ier)
+      if (ier.eq.0) go to 150
+      go to 200
+ 140  if(s.lt.0.) go to 200
+      if(s.eq.0. .and. (nuest.lt.(mu+5+iopt(2)+iopt(3)) .or.
+     * nvest.lt.(mv+7)) ) go to 200
+c  we partition the working space and determine the spline approximation
+ 150  ldz = 5
+      lfpu = 9
+      lfpv = lfpu+nuest
+      lww = lfpv+nvest
+      jwrk = lwrk-8-nuest-nvest
+      knru = 5
+      knrv = knru+mu
+      kndu = knrv+mv
+      kndv = kndu+nuest
+      call fppogr(iopt,ider,u,mu,v,mv,z,m,zb,r,s,nuest,nvest,tol,maxit,
+     * nc,nu,tu,nv,tv,c,fp,wrk(1),wrk(2),wrk(3),wrk(4),wrk(lfpu),
+     * wrk(lfpv),wrk(ldz),wrk(8),iwrk(1),iwrk(2),iwrk(3),iwrk(4),
+     * iwrk(knru),iwrk(knrv),iwrk(kndu),iwrk(kndv),wrk(lww),jwrk,ier)
+ 200  return
+      end
+

Added: branches/Interpolate1D/fitpack/polar.f
===================================================================
--- branches/Interpolate1D/fitpack/polar.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/polar.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,450 @@
+      subroutine polar(iopt,m,x,y,z,w,rad,s,nuest,nvest,eps,nu,tu,
+     *  nv,tv,u,v,c,fp,wrk1,lwrk1,wrk2,lwrk2,iwrk,kwrk,ier)
+c  subroutine polar fits a smooth function f(x,y) to a set of data
+c  points (x(i),y(i),z(i)) scattered arbitrarily over an approximation
+c  domain  x**2+y**2 <= rad(atan(y/x))**2. through the transformation
+c    x = u*rad(v)*cos(v) , y = u*rad(v)*sin(v)
+c  the approximation problem is reduced to the determination of a bi-
+c  cubic spline s(u,v) fitting a corresponding set of data points
+c  (u(i),v(i),z(i)) on the rectangle 0<=u<=1,-pi<=v<=pi.
+c  in order to have continuous partial derivatives
+c              i+j
+c             d   f(0,0)
+c    g(i,j) = ----------
+c                i   j
+c              dx  dy
+c
+c  s(u,v)=f(x,y) must satisfy the following conditions
+c
+c    (1) s(0,v) = g(0,0)   -pi <=v<= pi.
+c
+c        d s(0,v)
+c    (2) -------- = rad(v)*(cos(v)*g(1,0)+sin(v)*g(0,1))
+c        d u
+c                                                    -pi <=v<= pi
+c         2
+c        d s(0,v)         2       2             2
+c    (3) -------- = rad(v)*(cos(v)*g(2,0)+sin(v)*g(0,2)+sin(2*v)*g(1,1))
+c           2
+c        d u                                         -pi <=v<= pi
+c
+c  moreover, s(u,v) must be periodic in the variable v, i.e.
+c
+c         j            j
+c        d s(u,-pi)   d s(u,pi)
+c    (4) ---------- = ---------   0 <=u<= 1, j=0,1,2
+c           j           j
+c        d v         d v
+c
+c  if iopt(1) < 0 circle calculates a weighted least-squares spline
+c  according to a given set of knots in u- and v- direction.
+c  if iopt(1) >=0, the number of knots in each direction and their pos-
+c  ition tu(j),j=1,2,...,nu ; tv(j),j=1,2,...,nv are chosen automatical-
+c  ly by the routine. the smoothness of s(u,v) is then achieved by mini-
+c  malizing the discontinuity jumps of the derivatives of the spline
+c  at the knots. the amount of smoothness of s(u,v) is determined  by
+c  the condition that fp = sum((w(i)*(z(i)-s(u(i),v(i))))**2) be <= s,
+c  with s a given non-negative constant.
+c  the bicubic spline is given in its standard b-spline representation
+c  and the corresponding function f(x,y) can be evaluated by means of
+c  function program evapol.
+c
+c calling sequence:
+c     call polar(iopt,m,x,y,z,w,rad,s,nuest,nvest,eps,nu,tu,
+c    *  nv,tv,u,v,wrk1,lwrk1,wrk2,lwrk2,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer array of dimension 3, specifying different options.
+c          unchanged on exit.
+c  iopt(1):on entry iopt(1) must specify whether a weighted
+c          least-squares polar spline (iopt(1)=-1) or a smoothing
+c          polar spline (iopt(1)=0 or 1) must be determined.
+c          if iopt(1)=0 the routine will start with an initial set of
+c          knots tu(i)=0,tu(i+4)=1,i=1,...,4;tv(i)=(2*i-9)*pi,i=1,...,8.
+c          if iopt(1)=1 the routine will continue with the set of knots
+c          found at the last call of the routine.
+c          attention: a call with iopt(1)=1 must always be immediately
+c          preceded by another call with iopt(1) = 1 or iopt(1) = 0.
+c  iopt(2):on entry iopt(2) must specify the requested order of conti-
+c          nuity for f(x,y) at the origin.
+c          if iopt(2)=0 only condition (1) must be fulfilled,
+c          if iopt(2)=1 conditions (1)+(2) must be fulfilled and
+c          if iopt(2)=2 conditions (1)+(2)+(3) must be fulfilled.
+c  iopt(3):on entry iopt(3) must specify whether (iopt(3)=1) or not
+c          (iopt(3)=0) the approximation f(x,y) must vanish at the
+c          boundary of the approximation domain.
+c  m     : integer. on entry m must specify the number of data points.
+c          m >= 4-iopt(2)-iopt(3) unchanged on exit.
+c  x     : real array of dimension at least (m).
+c  y     : real array of dimension at least (m).
+c  z     : real array of dimension at least (m).
+c          before entry, x(i),y(i),z(i) must be set to the co-ordinates
+c          of the i-th data point, for i=1,...,m. the order of the data
+c          points is immaterial. unchanged on exit.
+c  w     : real array of dimension at least (m). before entry, w(i) must
+c          be set to the i-th value in the set of weights. the w(i) must
+c          be strictly positive. unchanged on exit.
+c  rad   : real function subprogram defining the boundary of the approx-
+c          imation domain, i.e   x = rad(v)*cos(v) , y = rad(v)*sin(v),
+c          -pi <= v <= pi.
+c          must be declared external in the calling (sub)program.
+c  s     : real. on entry (in case iopt(1) >=0) s must specify the
+c          smoothing factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  nuest : integer. unchanged on exit.
+c  nvest : integer. unchanged on exit.
+c          on entry, nuest and nvest must specify an upper bound for the
+c          number of knots required in the u- and v-directions resp.
+c          these numbers will also determine the storage space needed by
+c          the routine. nuest >= 8, nvest >= 8.
+c          in most practical situation nuest = nvest = 8+sqrt(m/2) will
+c          be sufficient. see also further comments.
+c  eps   : real.
+c          on entry, eps must specify a threshold for determining the
+c          effective rank of an over-determined linear system of equat-
+c          ions. 0 < eps < 1.  if the number of decimal digits in the
+c          computer representation of a real number is q, then 10**(-q)
+c          is a suitable value for eps in most practical applications.
+c          unchanged on exit.
+c  nu    : integer.
+c          unless ier=10 (in case iopt(1) >=0),nu will contain the total
+c          number of knots with respect to the u-variable, of the spline
+c          approximation returned. if the computation mode iopt(1)=1
+c          is used, the value of nu should be left unchanged between
+c          subsequent calls.
+c          in case iopt(1)=-1,the value of nu must be specified on entry
+c  tu    : real array of dimension at least nuest.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the u-variable, i.e. the position
+c          of the interior knots tu(5),...,tu(nu-4) as well as the
+c          position of the additional knots tu(1)=...=tu(4)=0 and
+c          tu(nu-3)=...=tu(nu)=1 needed for the b-spline representation
+c          if the computation mode iopt(1)=1 is used,the values of
+c          tu(1),...,tu(nu) should be left unchanged between subsequent
+c          calls. if the computation mode iopt(1)=-1 is used,the values
+c          tu(5),...tu(nu-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  nv    : integer.
+c          unless ier=10 (in case iopt(1)>=0), nv will contain the total
+c          number of knots with respect to the v-variable, of the spline
+c          approximation returned. if the computation mode iopt(1)=1
+c          is used, the value of nv should be left unchanged between
+c          subsequent calls. in case iopt(1)=-1, the value of nv should
+c          be specified on entry.
+c  tv    : real array of dimension at least nvest.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the v-variable, i.e. the position of
+c          the interior knots tv(5),...,tv(nv-4) as well as the position
+c          of the additional knots tv(1),...,tv(4) and tv(nv-3),...,
+c          tv(nv) needed for the b-spline representation.
+c          if the computation mode iopt(1)=1 is used, the values of
+c          tv(1),...,tv(nv) should be left unchanged between subsequent
+c          calls. if the computation mode iopt(1)=-1 is used,the values
+c          tv(5),...tv(nv-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  u     : real array of dimension at least (m).
+c  v     : real array of dimension at least (m).
+c          on succesful exit, u(i),v(i) contains the co-ordinates of
+c          the i-th data point with respect to the transformed rectan-
+c          gular approximation domain, for i=1,2,...,m.
+c          if the computation mode iopt(1)=1 is used the values of
+c          u(i),v(i) should be left unchanged between subsequent calls.
+c  c     : real array of dimension at least (nuest-4)*(nvest-4).
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(u,v).
+c  fp    : real. unless ier=10, fp contains the weighted sum of
+c          squared residuals of the spline approximation returned.
+c  wrk1  : real array of dimension (lwrk1). used as workspace.
+c          if the computation mode iopt(1)=1 is used the value of
+c          wrk1(1) should be left unchanged between subsequent calls.
+c          on exit wrk1(2),wrk1(3),...,wrk1(1+ncof) will contain the
+c          values d(i)/max(d(i)),i=1,...,ncof=1+iopt(2)*(iopt(2)+3)/2+
+c          (nv-7)*(nu-5-iopt(2)-iopt(3)) with d(i) the i-th diagonal el-
+c          ement of the triangular matrix for calculating the b-spline
+c          coefficients.it includes those elements whose square is < eps
+c          which are treated as 0 in the case of rank deficiency(ier=-2)
+c  lwrk1 : integer. on entry lwrk1 must specify the actual dimension of
+c          the array wrk1 as declared in the calling (sub)program.
+c          lwrk1 must not be too small. let
+c            k = nuest-7, l = nvest-7, p = 1+iopt(2)*(iopt(2)+3)/2,
+c            q = k+2-iopt(2)-iopt(3) then
+c          lwrk1 >= 129+10*k+21*l+k*l+(p+l*q)*(1+8*l+p)+8*m
+c  wrk2  : real array of dimension (lwrk2). used as workspace, but
+c          only in the case a rank deficient system is encountered.
+c  lwrk2 : integer. on entry lwrk2 must specify the actual dimension of
+c          the array wrk2 as declared in the calling (sub)program.
+c          lwrk2 > 0 . a save upper bound  for lwrk2 = (p+l*q+1)*(4*l+p)
+c          +p+l*q where p,l,q are as above. if there are enough data
+c          points, scattered uniformly over the approximation domain
+c          and if the smoothing factor s is not too small, there is a
+c          good chance that this extra workspace is not needed. a lot
+c          of memory might therefore be saved by setting lwrk2=1.
+c          (see also ier > 10)
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= m+(nuest-7)*(nvest-7).
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the spline returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline returned is an interpolating
+c            spline (fp=0).
+c   ier=-2 : normal return. the spline returned is the weighted least-
+c            squares constrained polynomial . in this extreme case
+c            fp gives the upper bound for the smoothing factor s.
+c   ier<-2 : warning. the coefficients of the spline returned have been
+c            computed as the minimal norm least-squares solution of a
+c            (numerically) rank deficient system. (-ier) gives the rank.
+c            especially if the rank deficiency which can be computed as
+c            1+iopt(2)*(iopt(2)+3)/2+(nv-7)*(nu-5-iopt(2)-iopt(3))+ier
+c            is large the results may be inaccurate.
+c            they could also seriously depend on the value of eps.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters nuest and
+c            nvest.
+c            probably causes : nuest or nvest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the weighted least-squares
+c            polar spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing spline with
+c            fp = s. probably causes : s too small or badly chosen eps.
+c            there is an approximation returned but the corresponding
+c            weighted sum of squared residuals does not satisfy the
+c            condition abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing spline
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            weighted sum of squared residuals does not satisfy the
+c            condition abs(fp-s)/s < tol.
+c   ier=4  : error. no more knots can be added because the dimension
+c            of the spline 1+iopt(2)*(iopt(2)+3)/2+(nv-7)*(nu-5-iopt(2)
+c            -iopt(3)) already exceeds the number of data points m.
+c            probably causes : either s or m too small.
+c            the approximation returned is the weighted least-squares
+c            polar spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=5  : error. no more knots can be added because the additional
+c            knot would (quasi) coincide with an old one.
+c            probably causes : s too small or too large a weight to an
+c            inaccurate data point.
+c            the approximation returned is the weighted least-squares
+c            polar spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt(1)<=1 , 0<=iopt(2)<=2 , 0<=iopt(3)<=1 ,
+c            m>=4-iopt(2)-iopt(3) , nuest>=8 ,nvest >=8, 0<eps<1,
+c            0<=teta(i)<=pi, 0<=phi(i)<=2*pi, w(i)>0, i=1,...,m
+c            lwrk1 >= 129+10*k+21*l+k*l+(p+l*q)*(1+8*l+p)+8*m
+c            kwrk >= m+(nuest-7)*(nvest-7)
+c            if iopt(1)=-1:9<=nu<=nuest,9+iopt(2)*(iopt(2)+1)<=nv<=nvest
+c                          0<tu(5)<tu(6)<...<tu(nu-4)<1
+c                          -pi<tv(5)<tv(6)<...<tv(nv-4)<pi
+c            if iopt(1)>=0: s>=0
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c   ier>10 : error. lwrk2 is too small, i.e. there is not enough work-
+c            space for computing the minimal least-squares solution of
+c            a rank deficient system of linear equations. ier gives the
+c            requested value for lwrk2. there is no approximation re-
+c            turned but, having saved the information contained in nu,
+c            nv,tu,tv,wrk1,u,v and having adjusted the value of lwrk2
+c            and the dimension of the array wrk2 accordingly, the user
+c            can continue at the point the program was left, by calling
+c            polar with iopt(1)=1.
+c
+c further comments:
+c  by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the constrained weighted least-squares polynomial if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   z(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in z(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   polynomial and the corresponding upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximation shows more detail) to obtain closer fits.
+c   to choose s very small is strongly discouraged. this considerably
+c   increases computation time and memory requirements. it may also
+c   cause rank-deficiency (ier<-2) and endager numerical stability.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt(1)=0.
+c   if iopt(1)=1 the program will continue with the set of knots found
+c   at the last call of the routine. this will save a lot of computation
+c   time if polar is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. if the computation mode iopt(1)=1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt(1)=1,the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   polar once more with the selected value for s but now with iopt(1)=0
+c   indeed, polar may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds nuest and
+c   nvest. indeed, if at a certain stage in polar the number of knots
+c   in one direction (say nu) has reached the value of its upper bound
+c   (nuest), then from that moment on all subsequent knots are added
+c   in the other (v) direction. this may indicate that the value of
+c   nuest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c
+c  other subroutines required:
+c    fpback,fpbspl,fppola,fpdisc,fpgivs,fprank,fprati,fprota,fporde,
+c    fprppo
+c
+c  references:
+c   dierckx p.: an algorithm for fitting data over a circle using tensor
+c               product splines,j.comp.appl.maths 15 (1986) 161-173.
+c   dierckx p.: an algorithm for fitting data on a circle using tensor
+c               product splines, report tw68, dept. computer science,
+c               k.u.leuven, 1984.
+c   dierckx p.: curve and surface fitting with splines, monographs on
+c               numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : june 1984
+c  latest update : march 1989
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,eps,fp
+      integer m,nuest,nvest,nu,nv,lwrk1,lwrk2,kwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),z(m),w(m),tu(nuest),tv(nvest),u(m),v(m),
+     * c((nuest-4)*(nvest-4)),wrk1(lwrk1),wrk2(lwrk2)
+      integer iopt(3),iwrk(kwrk)
+c  ..user specified function
+      real*8 rad
+c  ..local scalars..
+      real*8 tol,pi,dist,r,one
+      integer i,ib1,ib3,ki,kn,kwest,la,lbu,lcc,lcs,lro,j
+     * lbv,lco,lf,lff,lfp,lh,lq,lsu,lsv,lwest,maxit,ncest,ncc,nuu,
+     * nvv,nreg,nrint,nu4,nv4,iopt1,iopt2,iopt3,ipar,nvmin
+c  ..function references..
+      real*8 datan2,sqrt
+      external rad
+c  ..subroutine references..
+c    fppola
+c  ..
+c  set up constants
+      one = 1d0
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid,control is immediately repassed to the calling program.
+      ier = 10
+      if(eps.le.0. .or. eps.ge.1.) go to 60
+      iopt1 = iopt(1)
+      if(iopt1.lt.(-1) .or. iopt1.gt.1) go to 60
+      iopt2 = iopt(2)
+      if(iopt2.lt.0 .or. iopt2.gt.2) go to 60
+      iopt3 = iopt(3)
+      if(iopt3.lt.0 .or. iopt3.gt.1) go to 60
+      if(m.lt.(4-iopt2-iopt3)) go to 60
+      if(nuest.lt.8 .or. nvest.lt.8) go to 60
+      nu4 = nuest-4
+      nv4 = nvest-4
+      ncest = nu4*nv4
+      nuu = nuest-7
+      nvv = nvest-7
+      ipar = 1+iopt2*(iopt2+3)/2
+      ncc = ipar+nvv*(nuest-5-iopt2-iopt3)
+      nrint = nuu+nvv
+      nreg = nuu*nvv
+      ib1 = 4*nvv
+      ib3 = ib1+ipar
+      lwest = ncc*(1+ib1+ib3)+2*nrint+ncest+m*8+ib3+5*nuest+12*nvest
+      kwest = m+nreg
+      if(lwrk1.lt.lwest .or. kwrk.lt.kwest) go to 60
+      if(iopt1.gt.0) go to 40
+      do 10 i=1,m
+        if(w(i).le.0.) go to 60
+        dist = x(i)**2+y(i)**2
+        u(i) = 0.
+        v(i) = 0.
+        if(dist.le.0.) go to 10
+        v(i) = datan2(y(i),x(i))
+        r = rad(v(i))
+        if(r.le.0.) go to 60
+        u(i) = sqrt(dist)/r
+        if(u(i).gt.one) go to 60
+  10  continue
+      if(iopt1.eq.0) go to 40
+      nuu = nu-8
+      if(nuu.lt.1 .or. nu.gt.nuest) go to 60
+      tu(4) = 0.
+      do 20 i=1,nuu
+         j = i+4
+         if(tu(j).le.tu(j-1) .or. tu(j).ge.one) go to 60
+  20  continue
+      nvv = nv-8
+      nvmin = 9+iopt2*(iopt2+1)
+      if(nv.lt.nvmin .or. nv.gt.nvest) go to 60
+      pi = datan2(0d0,-one)
+      tv(4) = -pi
+      do 30 i=1,nvv
+         j = i+4
+         if(tv(j).le.tv(j-1) .or. tv(j).ge.pi) go to 60
+  30  continue
+      go to 50
+  40  if(s.lt.0.) go to 60
+  50  ier = 0
+c  we partition the working space and determine the spline approximation
+      kn = 1
+      ki = kn+m
+      lq = 2
+      la = lq+ncc*ib3
+      lf = la+ncc*ib1
+      lff = lf+ncc
+      lfp = lff+ncest
+      lco = lfp+nrint
+      lh = lco+nrint
+      lbu = lh+ib3
+      lbv = lbu+5*nuest
+      lro = lbv+5*nvest
+      lcc = lro+nvest
+      lcs = lcc+nvest
+      lsu = lcs+nvest*5
+      lsv = lsu+m*4
+      call fppola(iopt1,iopt2,iopt3,m,u,v,z,w,rad,s,nuest,nvest,eps,tol,
+     *
+     * maxit,ib1,ib3,ncest,ncc,nrint,nreg,nu,tu,nv,tv,c,fp,wrk1(1),
+     * wrk1(lfp),wrk1(lco),wrk1(lf),wrk1(lff),wrk1(lro),wrk1(lcc),
+     * wrk1(lcs),wrk1(la),wrk1(lq),wrk1(lbu),wrk1(lbv),wrk1(lsu),
+     * wrk1(lsv),wrk1(lh),iwrk(ki),iwrk(kn),wrk2,lwrk2,ier)
+  60  return
+      end
+

Added: branches/Interpolate1D/fitpack/profil.f
===================================================================
--- branches/Interpolate1D/fitpack/profil.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/profil.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,117 @@
+      subroutine profil(iopt,tx,nx,ty,ny,c,kx,ky,u,nu,cu,ier)
+c  if iopt=0 subroutine profil calculates the b-spline coefficients of
+c  the univariate spline f(y) = s(u,y) with s(x,y) a bivariate spline of
+c  degrees kx and ky, given in the b-spline representation.
+c  if iopt = 1 it calculates the b-spline coefficients of the univariate
+c  spline g(x) = s(x,u)
+c
+c  calling sequence:
+c     call profil(iopt,tx,nx,ty,ny,c,kx,ky,u,nu,cu,ier)
+c
+c  input parameters:
+c   iopt  : integer flag, specifying whether the profile f(y) (iopt=0)
+c           or the profile g(x) (iopt=1) must be determined.
+c   tx    : real array, length nx, which contains the position of the
+c           knots in the x-direction.
+c   nx    : integer, giving the total number of knots in the x-direction
+c   ty    : real array, length ny, which contains the position of the
+c           knots in the y-direction.
+c   ny    : integer, giving the total number of knots in the y-direction
+c   c     : real array, length (nx-kx-1)*(ny-ky-1), which contains the
+c           b-spline coefficients.
+c   kx,ky : integer values, giving the degrees of the spline.
+c   u     : real value, specifying the requested profile.
+c           tx(kx+1)<=u<=tx(nx-kx), if iopt=0.
+c           ty(ky+1)<=u<=ty(ny-ky), if iopt=1.
+c   nu    : on entry nu must specify the dimension of the array cu.
+c           nu >= ny if iopt=0, nu >= nx if iopt=1.
+c
+c  output parameters:
+c   cu    : real array of dimension (nu).
+c           on succesful exit this array contains the b-spline
+c   ier   : integer error flag
+c    ier=0 : normal return
+c    ier=10: invalid input data (see restrictions)
+c
+c  restrictions:
+c   if iopt=0 : tx(kx+1) <= u <= tx(nx-kx), nu >=ny.
+c   if iopt=1 : ty(ky+1) <= u <= ty(ny-ky), nu >=nx.
+c
+c  other subroutines required:
+c    fpbspl
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer iopt,nx,ny,kx,ky,nu,ier
+      real*8 u
+c  ..array arguments..
+      real*8 tx(nx),ty(ny),c((nx-kx-1)*(ny-ky-1)),cu(nu)
+c  ..local scalars..
+      integer i,j,kx1,ky1,l,l1,m,m0,nkx1,nky1
+      real*8 sum
+c  ..local array
+      real*8 h(6)
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      kx1 = kx+1
+      ky1 = ky+1
+      nkx1 = nx-kx1
+      nky1 = ny-ky1
+      ier = 10
+      if(iopt.ne.0) go to 200
+      if(nu.lt.ny) go to 300
+      if(u.lt.tx(kx1) .or. u.gt.tx(nkx1+1)) go to 300
+c  the b-splinecoefficients of f(y) = s(u,y).
+      ier = 0
+      l = kx1
+      l1 = l+1
+ 110  if(u.lt.tx(l1) .or. l.eq.nkx1) go to 120
+      l = l1
+      l1 = l+1
+      go to 110
+ 120  call fpbspl(tx,nx,kx,u,l,h)
+      m0 = (l-kx1)*nky1+1
+      do 140 i=1,nky1
+        m = m0
+        sum = 0.
+        do 130 j=1,kx1
+          sum = sum+h(j)*c(m)
+          m = m+nky1
+ 130    continue
+        cu(i) = sum
+        m0 = m0+1
+ 140  continue
+      go to 300
+ 200  if(nu.lt.nx) go to 300
+      if(u.lt.ty(ky1) .or. u.gt.ty(nky1+1)) go to 300
+c  the b-splinecoefficients of g(x) = s(x,u).
+      ier = 0
+      l = ky1
+      l1 = l+1
+ 210  if(u.lt.ty(l1) .or. l.eq.nky1) go to 220
+      l = l1
+      l1 = l+1
+      go to 210
+ 220  call fpbspl(ty,ny,ky,u,l,h)
+      m0 = l-ky
+      do 240 i=1,nkx1
+        m = m0
+        sum = 0.
+        do 230 j=1,ky1
+          sum = sum+h(j)*c(m)
+          m = m+1
+ 230    continue
+        cu(i) = sum
+        m0 = m0+nky1
+ 240  continue
+ 300  return
+      end
+

Added: branches/Interpolate1D/fitpack/regrid.f
===================================================================
--- branches/Interpolate1D/fitpack/regrid.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/regrid.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,353 @@
+      subroutine regrid(iopt,mx,x,my,y,z,xb,xe,yb,ye,kx,ky,s,
+     * nxest,nyest,nx,tx,ny,ty,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c given the set of values z(i,j) on the rectangular grid (x(i),y(j)),
+c i=1,...,mx;j=1,...,my, subroutine regrid determines a smooth bivar-
+c iate spline approximation s(x,y) of degrees kx and ky on the rect-
+c angle xb <= x <= xe, yb <= y <= ye.
+c if iopt = -1 regrid calculates the least-squares spline according
+c to a given set of knots.
+c if iopt >= 0 the total numbers nx and ny of these knots and their
+c position tx(j),j=1,...,nx and ty(j),j=1,...,ny are chosen automatic-
+c ally by the routine. the smoothness of s(x,y) is then achieved by
+c minimalizing the discontinuity jumps in the derivatives of s(x,y)
+c across the boundaries of the subpanels (tx(i),tx(i+1))*(ty(j),ty(j+1).
+c the amounth of smoothness is determined by the condition that f(p) =
+c sum ((z(i,j)-s(x(i),y(j))))**2) be <= s, with s a given non-negative
+c constant, called the smoothing factor.
+c the fit is given in the b-spline representation (b-spline coefficients
+c c((ny-ky-1)*(i-1)+j),i=1,...,nx-kx-1;j=1,...,ny-ky-1) and can be eval-
+c uated by means of subroutine bispev.
+c
+c calling sequence:
+c     call regrid(iopt,mx,x,my,y,z,xb,xe,yb,ye,kx,ky,s,nxest,nyest,
+c    *  nx,tx,ny,ty,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer flag. on entry iopt must specify whether a least-
+c          squares spline (iopt=-1) or a smoothing spline (iopt=0 or 1)
+c          must be determined.
+c          if iopt=0 the routine will start with an initial set of knots
+c          tx(i)=xb,tx(i+kx+1)=xe,i=1,...,kx+1;ty(i)=yb,ty(i+ky+1)=ye,i=
+c          1,...,ky+1. if iopt=1 the routine will continue with the set
+c          of knots found at the last call of the routine.
+c          attention: a call with iopt=1 must always be immediately pre-
+c                     ceded by another call with iopt=1 or iopt=0 and
+c                     s.ne.0.
+c          unchanged on exit.
+c  mx    : integer. on entry mx must specify the number of grid points
+c          along the x-axis. mx > kx . unchanged on exit.
+c  x     : real array of dimension at least (mx). before entry, x(i)
+c          must be set to the x-co-ordinate of the i-th grid point
+c          along the x-axis, for i=1,2,...,mx. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c  my    : integer. on entry my must specify the number of grid points
+c          along the y-axis. my > ky . unchanged on exit.
+c  y     : real array of dimension at least (my). before entry, y(j)
+c          must be set to the y-co-ordinate of the j-th grid point
+c          along the y-axis, for j=1,2,...,my. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c  z     : real array of dimension at least (mx*my).
+c          before entry, z(my*(i-1)+j) must be set to the data value at
+c          the grid point (x(i),y(j)) for i=1,...,mx and j=1,...,my.
+c          unchanged on exit.
+c  xb,xe : real values. on entry xb,xe,yb and ye must specify the bound-
+c  yb,ye   aries of the rectangular approximation domain.
+c          xb<=x(i)<=xe,i=1,...,mx; yb<=y(j)<=ye,j=1,...,my.
+c          unchanged on exit.
+c  kx,ky : integer values. on entry kx and ky must specify the degrees
+c          of the spline. 1<=kx,ky<=5. it is recommended to use bicubic
+c          (kx=ky=3) splines. unchanged on exit.
+c  s     : real. on entry (in case iopt>=0) s must specify the smoothing
+c          factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  nxest : integer. unchanged on exit.
+c  nyest : integer. unchanged on exit.
+c          on entry, nxest and nyest must specify an upper bound for the
+c          number of knots required in the x- and y-directions respect.
+c          these numbers will also determine the storage space needed by
+c          the routine. nxest >= 2*(kx+1), nyest >= 2*(ky+1).
+c          in most practical situation nxest = mx/2, nyest=my/2, will
+c          be sufficient. always large enough are nxest=mx+kx+1, nyest=
+c          my+ky+1, the number of knots needed for interpolation (s=0).
+c          see also further comments.
+c  nx    : integer.
+c          unless ier=10 (in case iopt >=0), nx will contain the total
+c          number of knots with respect to the x-variable, of the spline
+c          approximation returned. if the computation mode iopt=1 is
+c          used, the value of nx should be left unchanged between sub-
+c          sequent calls.
+c          in case iopt=-1, the value of nx should be specified on entry
+c  tx    : real array of dimension nmax.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the x-variable, i.e. the position of
+c          the interior knots tx(kx+2),...,tx(nx-kx-1) as well as the
+c          position of the additional knots tx(1)=...=tx(kx+1)=xb and
+c          tx(nx-kx)=...=tx(nx)=xe needed for the b-spline representat.
+c          if the computation mode iopt=1 is used, the values of tx(1),
+c          ...,tx(nx) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values tx(kx+2),
+c          ...tx(nx-kx-1) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  ny    : integer.
+c          unless ier=10 (in case iopt >=0), ny will contain the total
+c          number of knots with respect to the y-variable, of the spline
+c          approximation returned. if the computation mode iopt=1 is
+c          used, the value of ny should be left unchanged between sub-
+c          sequent calls.
+c          in case iopt=-1, the value of ny should be specified on entry
+c  ty    : real array of dimension nmax.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the y-variable, i.e. the position of
+c          the interior knots ty(ky+2),...,ty(ny-ky-1) as well as the
+c          position of the additional knots ty(1)=...=ty(ky+1)=yb and
+c          ty(ny-ky)=...=ty(ny)=ye needed for the b-spline representat.
+c          if the computation mode iopt=1 is used, the values of ty(1),
+c          ...,ty(ny) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values ty(ky+2),
+c          ...ty(ny-ky-1) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  c     : real array of dimension at least (nxest-kx-1)*(nyest-ky-1).
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(x,y)
+c  fp    : real. unless ier=10, fp contains the sum of squared
+c          residuals of the spline approximation returned.
+c  wrk   : real array of dimension (lwrk). used as workspace.
+c          if the computation mode iopt=1 is used the values of wrk(1),
+c          ...,wrk(4) should be left unchanged between subsequent calls.
+c  lwrk  : integer. on entry lwrk must specify the actual dimension of
+c          the array wrk as declared in the calling (sub)program.
+c          lwrk must not be too small.
+c           lwrk >= 4+nxest*(my+2*kx+5)+nyest*(2*ky+5)+mx*(kx+1)+
+c            my*(ky+1) +u
+c           where u is the larger of my and nxest.
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c          if the computation mode iopt=1 is used the values of iwrk(1),
+c          ...,iwrk(3) should be left unchanged between subsequent calls
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= 3+mx+my+nxest+nyest.
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the spline returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline returned is an interpolating
+c            spline (fp=0).
+c   ier=-2 : normal return. the spline returned is the least-squares
+c            polynomial of degrees kx and ky. in this extreme case fp
+c            gives the upper bound for the smoothing factor s.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters nxest and
+c            nyest.
+c            probably causes : nxest or nyest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the least-squares spline
+c            according to the current set of knots. the parameter fp
+c            gives the corresponding sum of squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing spline with
+c            fp = s. probably causes : s too small.
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing spline
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt<=1, 1<=kx,ky<=5, mx>kx, my>ky, nxest>=2*kx+2,
+c            nyest>=2*ky+2, kwrk>=3+mx+my+nxest+nyest,
+c            lwrk >= 4+nxest*(my+2*kx+5)+nyest*(2*ky+5)+mx*(kx+1)+
+c             my*(ky+1) +max(my,nxest),
+c            xb<=x(i-1)<x(i)<=xe,i=2,..,mx,yb<=y(j-1)<y(j)<=ye,j=2,..,my
+c            if iopt=-1: 2*kx+2<=nx<=min(nxest,mx+kx+1)
+c                        xb<tx(kx+2)<tx(kx+3)<...<tx(nx-kx-1)<xe
+c                        2*ky+2<=ny<=min(nyest,my+ky+1)
+c                        yb<ty(ky+2)<ty(ky+3)<...<ty(ny-ky-1)<ye
+c                    the schoenberg-whitney conditions, i.e. there must
+c                    be subset of grid co-ordinates xx(p) and yy(q) such
+c                    that   tx(p) < xx(p) < tx(p+kx+1) ,p=1,...,nx-kx-1
+c                           ty(q) < yy(q) < ty(q+ky+1) ,q=1,...,ny-ky-1
+c            if iopt>=0: s>=0
+c                        if s=0 : nxest>=mx+kx+1, nyest>=my+ky+1
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c
+c further comments:
+c   regrid does not allow individual weighting of the data-values.
+c   so, if these were determined to widely different accuracies, then
+c   perhaps the general data set routine surfit should rather be used
+c   in spite of efficiency.
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the least-squares polynomial (degrees kx,ky) if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the accuracy of the data values.
+c   if the user has an idea of the statistical errors on the data, he
+c   can also find a proper estimate for s. for, by assuming that, if he
+c   specifies the right s, regrid will return a spline s(x,y) which
+c   exactly reproduces the function underlying the data he can evaluate
+c   the sum((z(i,j)-s(x(i),y(j)))**2) to find a good estimate for this s
+c   for example, if he knows that the statistical errors on his z(i,j)-
+c   values is not greater than 0.1, he may expect that a good s should
+c   have a value not larger than mx*my*(0.1)**2.
+c   if nothing is known about the statistical error in z(i,j), s must
+c   be determined by trial and error, taking account of the comments
+c   above. the best is then to start with a very large value of s (to
+c   determine the least-squares polynomial and the corresponding upper
+c   bound fp0 for s) and then to progressively decrease the value of s
+c   ( say by a factor 10 in the beginning, i.e. s=fp0/10,fp0/100,...
+c   and more carefully as the approximation shows more detail) to
+c   obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if regrid is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. if the computation mode iopt=1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   regrid once more with the selected value for s but now with iopt=0.
+c   indeed, regrid may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds nxest and
+c   nyest. indeed, if at a certain stage in regrid the number of knots
+c   in one direction (say nx) has reached the value of its upper bound
+c   (nxest), then from that moment on all subsequent knots are added
+c   in the other (y) direction. this may indicate that the value of
+c   nxest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c   for example, by setting nxest=2*kx+2 (the lowest allowable value for
+c   nxest), the user can indicate that he wants an approximation which
+c   is a simple polynomial of degree kx in the variable x.
+c
+c  other subroutines required:
+c    fpback,fpbspl,fpregr,fpdisc,fpgivs,fpgrre,fprati,fprota,fpchec,
+c    fpknot
+c
+c  references:
+c   dierckx p. : a fast algorithm for smoothing data on a rectangular
+c                grid while using spline functions, siam j.numer.anal.
+c                19 (1982) 1286-1304.
+c   dierckx p. : a fast algorithm for smoothing data on a rectangular
+c                grid while using spline functions, report tw53, dept.
+c                computer science,k.u.leuven, 1980.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1989
+c
+c  ..
+c  ..scalar arguments..
+      real*8 xb,xe,yb,ye,s,fp
+      integer iopt,mx,my,kx,ky,nxest,nyest,nx,ny,lwrk,kwrk,ier
+c  ..array arguments..
+      real*8 x(mx),y(my),z(mx*my),tx(nxest),ty(nyest),
+     * c((nxest-kx-1)*(nyest-ky-1)),wrk(lwrk)
+      integer iwrk(kwrk)
+c  ..local scalars..
+      real*8 tol
+      integer i,j,jwrk,kndx,kndy,knrx,knry,kwest,kx1,kx2,ky1,ky2,
+     * lfpx,lfpy,lwest,lww,maxit,nc,nminx,nminy,mz
+c  ..function references..
+      integer max0
+c  ..subroutine references..
+c    fpregr,fpchec
+c  ..
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(kx.le.0 .or. kx.gt.5) go to 70
+      kx1 = kx+1
+      kx2 = kx1+1
+      if(ky.le.0 .or. ky.gt.5) go to 70
+      ky1 = ky+1
+      ky2 = ky1+1
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 70
+      nminx = 2*kx1
+      if(mx.lt.kx1 .or. nxest.lt.nminx) go to 70
+      nminy = 2*ky1
+      if(my.lt.ky1 .or. nyest.lt.nminy) go to 70
+      mz = mx*my
+      nc = (nxest-kx1)*(nyest-ky1)
+      lwest = 4+nxest*(my+2*kx2+1)+nyest*(2*ky2+1)+mx*kx1+
+     * my*ky1+max0(nxest,my)
+      kwest = 3+mx+my+nxest+nyest
+      if(lwrk.lt.lwest .or. kwrk.lt.kwest) go to 70
+      if(xb.gt.x(1) .or. xe.lt.x(mx)) go to 70
+      do 10 i=2,mx
+        if(x(i-1).ge.x(i)) go to 70
+  10  continue
+      if(yb.gt.y(1) .or. ye.lt.y(my)) go to 70
+      do 20 i=2,my
+        if(y(i-1).ge.y(i)) go to 70
+  20  continue
+      if(iopt.ge.0) go to 50
+      if(nx.lt.nminx .or. nx.gt.nxest) go to 70
+      j = nx
+      do 30 i=1,kx1
+        tx(i) = xb
+        tx(j) = xe
+        j = j-1
+  30  continue
+      call fpchec(x,mx,tx,nx,kx,ier)
+      if(ier.ne.0) go to 70
+      if(ny.lt.nminy .or. ny.gt.nyest) go to 70
+      j = ny
+      do 40 i=1,ky1
+        ty(i) = yb
+        ty(j) = ye
+        j = j-1
+  40  continue
+      call fpchec(y,my,ty,ny,ky,ier)
+      if (ier.eq.0) go to 60
+      go to 70
+  50  if(s.lt.0.) go to 70
+      if(s.eq.0. .and. (nxest.lt.(mx+kx1) .or. nyest.lt.(my+ky1)) )
+     * go to 70
+      ier = 0
+c  we partition the working space and determine the spline approximation
+  60  lfpx = 5
+      lfpy = lfpx+nxest
+      lww = lfpy+nyest
+      jwrk = lwrk-4-nxest-nyest
+      knrx = 4
+      knry = knrx+mx
+      kndx = knry+my
+      kndy = kndx+nxest
+      call fpregr(iopt,x,mx,y,my,z,mz,xb,xe,yb,ye,kx,ky,s,nxest,nyest,
+     * tol,maxit,nc,nx,tx,ny,ty,c,fp,wrk(1),wrk(2),wrk(3),wrk(4),
+     * wrk(lfpx),wrk(lfpy),iwrk(1),iwrk(2),iwrk(3),iwrk(knrx),
+     * iwrk(knry),iwrk(kndx),iwrk(kndy),wrk(lww),jwrk,ier)
+  70  return
+      end
+

Added: branches/Interpolate1D/fitpack/spalde.f
===================================================================
--- branches/Interpolate1D/fitpack/spalde.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/spalde.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,73 @@
+      subroutine spalde(t,n,c,k1,x,d,ier)
+c  subroutine spalde evaluates at a point x all the derivatives
+c              (j-1)
+c      d(j) = s     (x) , j=1,2,...,k1
+c  of a spline s(x) of order k1 (degree k=k1-1), given in its b-spline
+c  representation.
+c
+c  calling sequence:
+c     call spalde(t,n,c,k1,x,d,ier)
+c
+c  input parameters:
+c    t    : array,length n, which contains the position of the knots.
+c    n    : integer, giving the total number of knots of s(x).
+c    c    : array,length n, which contains the b-spline coefficients.
+c    k1   : integer, giving the order of s(x) (order=degree+1)
+c    x    : real, which contains the point where the derivatives must
+c           be evaluated.
+c
+c  output parameters:
+c    d    : array,length k1, containing the derivative values of s(x).
+c    ier  : error flag
+c      ier = 0 : normal return
+c      ier =10 : invalid input data (see restrictions)
+c
+c  restrictions:
+c    t(k1) <= x <= t(n-k1+1)
+c
+c  further comments:
+c    if x coincides with a knot, right derivatives are computed
+c    ( left derivatives if x = t(n-k1+1) ).
+c
+c  other subroutines required: fpader.
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer n,k1,ier
+      real*8 x
+c  ..array arguments..
+      real*8 t(n),c(n),d(k1)
+c  ..local scalars..
+      integer l,nk1
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      nk1 = n-k1
+      if(x.lt.t(k1) .or. x.gt.t(nk1+1)) go to 300
+c  search for knot interval t(l) <= x < t(l+1)
+      l = k1
+ 100  if(x.lt.t(l+1) .or. l.eq.nk1) go to 200
+      l = l+1
+      go to 100
+ 200  if(t(l).ge.t(l+1)) go to 300
+      ier = 0
+c  calculate the derivatives.
+      call fpader(t,n,c,k1,x,l,d)
+ 300  return
+      end

Added: branches/Interpolate1D/fitpack/spgrid.f
===================================================================
--- branches/Interpolate1D/fitpack/spgrid.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/spgrid.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,501 @@
+      subroutine spgrid(iopt,ider,mu,u,mv,v,r,r0,r1,s,nuest,nvest,
+     * nu,tu,nv,tv,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c  given the function values r(i,j) on the latitude-longitude grid
+c  (u(i),v(j)), i=1,...,mu ; j=1,...,mv , spgrid determines a smooth
+c  bicubic spline approximation on the rectangular domain 0<=u<=pi,
+c  vb<=v<=ve (vb = v(1), ve=vb+2*pi).
+c  this approximation s(u,v) will satisfy the properties
+c
+c    (1) s(0,v) = s(0,0) = dr(1)
+c
+c        d s(0,v)           d s(0,0)           d s(0,pi/2)
+c    (2) -------- = cos(v)* -------- + sin(v)* -----------
+c        d u                d u                d u
+c
+c                 = cos(v)*dr(2)+sin(v)*dr(3)
+c                                                     vb <= v <= ve
+c    (3) s(pi,v) = s(pi,0) = dr(4)
+c
+c        d s(pi,v)           d s(pi,0)           d s(pi,pi/2)
+c    (4) -------- = cos(v)*  --------- + sin(v)* ------------
+c        d u                 d u                 d u
+c
+c                 = cos(v)*dr(5)+sin(v)*dr(6)
+c
+c  and will be periodic in the variable v, i.e.
+c
+c         j           j
+c        d s(u,vb)   d s(u,ve)
+c    (5) --------- = ---------   0 <=u<= pi , j=0,1,2
+c           j           j
+c        d v         d v
+c
+c  the number of knots of s(u,v) and their position tu(i),i=1,2,...,nu;
+c  tv(j),j=1,2,...,nv, is chosen automatically by the routine. the
+c  smoothness of s(u,v) is achieved by minimalizing the discontinuity
+c  jumps of the derivatives of the spline at the knots. the amount of
+c  smoothness of s(u,v) is determined by the condition that
+c  fp=sumi=1,mu(sumj=1,mv((r(i,j)-s(u(i),v(j)))**2))+(r0-s(0,v))**2
+c  + (r1-s(pi,v))**2 <= s, with s a given non-negative constant.
+c  the fit s(u,v) is given in its b-spline representation and can be
+c  evaluated by means of routine bispev
+c
+c calling sequence:
+c     call spgrid(iopt,ider,mu,u,mv,v,r,r0,r1,s,nuest,nvest,nu,tu,
+c    *  ,nv,tv,c,fp,wrk,lwrk,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer array of dimension 3, specifying different options.
+c          unchanged on exit.
+c  iopt(1):on entry iopt(1) must specify whether a least-squares spline
+c          (iopt(1)=-1) or a smoothing spline (iopt(1)=0 or 1) must be
+c          determined.
+c          if iopt(1)=0 the routine will start with an initial set of
+c          knots tu(i)=0,tu(i+4)=pi,i=1,...,4;tv(i)=v(1)+(i-4)*2*pi,
+c          i=1,...,8.
+c          if iopt(1)=1 the routine will continue with the set of knots
+c          found at the last call of the routine.
+c          attention: a call with iopt(1)=1 must always be immediately
+c          preceded by another call with iopt(1) = 1 or iopt(1) = 0.
+c  iopt(2):on entry iopt(2) must specify the requested order of conti-
+c          nuity at the pole u=0.
+c          if iopt(2)=0 only condition (1) must be fulfilled and
+c          if iopt(2)=1 conditions (1)+(2) must be fulfilled.
+c  iopt(3):on entry iopt(3) must specify the requested order of conti-
+c          nuity at the pole u=pi.
+c          if iopt(3)=0 only condition (3) must be fulfilled and
+c          if iopt(3)=1 conditions (3)+(4) must be fulfilled.
+c  ider  : integer array of dimension 4, specifying different options.
+c          unchanged on exit.
+c  ider(1):on entry ider(1) must specify whether (ider(1)=0 or 1) or not
+c          (ider(1)=-1) there is a data value r0 at the pole u=0.
+c          if ider(1)=1, r0 will be considered to be the right function
+c          value, and it will be fitted exactly (s(0,v)=r0).
+c          if ider(1)=0, r0 will be considered to be a data value just
+c          like the other data values r(i,j).
+c  ider(2):on entry ider(2) must specify whether (ider(2)=1) or not
+c          (ider(2)=0) the approximation has vanishing derivatives
+c          dr(2) and dr(3) at the pole u=0  (in case iopt(2)=1)
+c  ider(3):on entry ider(3) must specify whether (ider(3)=0 or 1) or not
+c          (ider(3)=-1) there is a data value r1 at the pole u=pi.
+c          if ider(3)=1, r1 will be considered to be the right function
+c          value, and it will be fitted exactly (s(pi,v)=r1).
+c          if ider(3)=0, r1 will be considered to be a data value just
+c          like the other data values r(i,j).
+c  ider(4):on entry ider(4) must specify whether (ider(4)=1) or not
+c          (ider(4)=0) the approximation has vanishing derivatives
+c          dr(5) and dr(6) at the pole u=pi (in case iopt(3)=1)
+c  mu    : integer. on entry mu must specify the number of grid points
+c          along the u-axis. unchanged on exit.
+c          mu >= 1, mu >=mumin=4-i0-i1-ider(2)-ider(4) with
+c            i0=min(1,ider(1)+1), i1=min(1,ider(3)+1)
+c  u     : real array of dimension at least (mu). before entry, u(i)
+c          must be set to the u-co-ordinate of the i-th grid point
+c          along the u-axis, for i=1,2,...,mu. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c          0 < u(i) < pi.
+c  mv    : integer. on entry mv must specify the number of grid points
+c          along the v-axis. mv > 3 . unchanged on exit.
+c  v     : real array of dimension at least (mv). before entry, v(j)
+c          must be set to the v-co-ordinate of the j-th grid point
+c          along the v-axis, for j=1,2,...,mv. these values must be
+c          supplied in strictly ascending order. unchanged on exit.
+c          -pi <= v(1) < pi , v(mv) < v(1)+2*pi.
+c  r     : real array of dimension at least (mu*mv).
+c          before entry, r(mv*(i-1)+j) must be set to the data value at
+c          the grid point (u(i),v(j)) for i=1,...,mu and j=1,...,mv.
+c          unchanged on exit.
+c  r0    : real value. on entry (if ider(1) >=0 ) r0 must specify the
+c          data value at the pole u=0. unchanged on exit.
+c  r1    : real value. on entry (if ider(1) >=0 ) r1 must specify the
+c          data value at the pole u=pi. unchanged on exit.
+c  s     : real. on entry (if iopt(1)>=0) s must specify the smoothing
+c          factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  nuest : integer. unchanged on exit.
+c  nvest : integer. unchanged on exit.
+c          on entry, nuest and nvest must specify an upper bound for the
+c          number of knots required in the u- and v-directions respect.
+c          these numbers will also determine the storage space needed by
+c          the routine. nuest >= 8, nvest >= 8.
+c          in most practical situation nuest = mu/2, nvest=mv/2, will
+c          be sufficient. always large enough are nuest=mu+6+iopt(2)+
+c          iopt(3), nvest = mv+7, the number of knots needed for
+c          interpolation (s=0). see also further comments.
+c  nu    : integer.
+c          unless ier=10 (in case iopt(1)>=0), nu will contain the total
+c          number of knots with respect to the u-variable, of the spline
+c          approximation returned. if the computation mode iopt(1)=1 is
+c          used, the value of nu should be left unchanged between sub-
+c          sequent calls. in case iopt(1)=-1, the value of nu should be
+c          specified on entry.
+c  tu    : real array of dimension at least (nuest).
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the u-variable, i.e. the position of
+c          the interior knots tu(5),...,tu(nu-4) as well as the position
+c          of the additional knots tu(1)=...=tu(4)=0 and tu(nu-3)=...=
+c          tu(nu)=pi needed for the b-spline representation.
+c          if the computation mode iopt(1)=1 is used,the values of tu(1)
+c          ...,tu(nu) should be left unchanged between subsequent calls.
+c          if the computation mode iopt(1)=-1 is used, the values tu(5),
+c          ...tu(nu-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  nv    : integer.
+c          unless ier=10 (in case iopt(1)>=0), nv will contain the total
+c          number of knots with respect to the v-variable, of the spline
+c          approximation returned. if the computation mode iopt(1)=1 is
+c          used, the value of nv should be left unchanged between sub-
+c          sequent calls. in case iopt(1) = -1, the value of nv should
+c          be specified on entry.
+c  tv    : real array of dimension at least (nvest).
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the v-variable, i.e. the position of
+c          the interior knots tv(5),...,tv(nv-4) as well as the position
+c          of the additional knots tv(1),...,tv(4) and tv(nv-3),...,
+c          tv(nv) needed for the b-spline representation.
+c          if the computation mode iopt(1)=1 is used,the values of tv(1)
+c          ...,tv(nv) should be left unchanged between subsequent calls.
+c          if the computation mode iopt(1)=-1 is used, the values tv(5),
+c          ...tv(nv-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  c     : real array of dimension at least (nuest-4)*(nvest-4).
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(u,v)
+c  fp    : real. unless ier=10, fp contains the sum of squared
+c          residuals of the spline approximation returned.
+c  wrk   : real array of dimension (lwrk). used as workspace.
+c          if the computation mode iopt(1)=1 is used the values of
+c          wrk(1),..,wrk(12) should be left unchanged between subsequent
+c          calls.
+c  lwrk  : integer. on entry lwrk must specify the actual dimension of
+c          the array wrk as declared in the calling (sub)program.
+c          lwrk must not be too small.
+c           lwrk >= 12+nuest*(mv+nvest+3)+nvest*24+4*mu+8*mv+q
+c           where q is the larger of (mv+nvest) and nuest.
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c          if the computation mode iopt(1)=1 is used the values of
+c          iwrk(1),.,iwrk(5) should be left unchanged between subsequent
+c          calls.
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= 5+mu+mv+nuest+nvest.
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the spline returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline returned is an interpolating
+c            spline (fp=0).
+c   ier=-2 : normal return. the spline returned is the least-squares
+c            constrained polynomial. in this extreme case fp gives the
+c            upper bound for the smoothing factor s.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters nuest and
+c            nvest.
+c            probably causes : nuest or nvest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the least-squares spline
+c            according to the current set of knots. the parameter fp
+c            gives the corresponding sum of squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing spline with
+c            fp = s. probably causes : s too small.
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing spline
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            sum of squared residuals does not satisfy the condition
+c            abs(fp-s)/s < tol.
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt(1)<=1, 0<=iopt(2)<=1, 0<=iopt(3)<=1,
+c            -1<=ider(1)<=1, 0<=ider(2)<=1, ider(2)=0 if iopt(2)=0.
+c            -1<=ider(3)<=1, 0<=ider(4)<=1, ider(4)=0 if iopt(3)=0.
+c            mu >= mumin (see above), mv >= 4, nuest >=8, nvest >= 8,
+c            kwrk>=5+mu+mv+nuest+nvest,
+c            lwrk >= 12+nuest*(mv+nvest+3)+nvest*24+4*mu+8*mv+
+c             max(nuest,mv+nvest)
+c            0< u(i-1)<u(i)< pi,i=2,..,mu,
+c            -pi<=v(1)< pi, v(1)<v(i-1)<v(i)<v(1)+2*pi, i=3,...,mv
+c            if iopt(1)=-1: 8<=nu<=min(nuest,mu+6+iopt(2)+iopt(3))
+c                           0<tu(5)<tu(6)<...<tu(nu-4)< pi
+c                           8<=nv<=min(nvest,mv+7)
+c                           v(1)<tv(5)<tv(6)<...<tv(nv-4)<v(1)+2*pi
+c                    the schoenberg-whitney conditions, i.e. there must
+c                    be subset of grid co-ordinates uu(p) and vv(q) such
+c                    that   tu(p) < uu(p) < tu(p+4) ,p=1,...,nu-4
+c                     (iopt(2)=1 and iopt(3)=1 also count for a uu-value
+c                           tv(q) < vv(q) < tv(q+4) ,q=1,...,nv-4
+c                     (vv(q) is either a value v(j) or v(j)+2*pi)
+c            if iopt(1)>=0: s>=0
+c                       if s=0: nuest>=mu+6+iopt(2)+iopt(3), nvest>=mv+7
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c
+c further comments:
+c   spgrid does not allow individual weighting of the data-values.
+c   so, if these were determined to widely different accuracies, then
+c   perhaps the general data set routine sphere should rather be used
+c   in spite of efficiency.
+c   by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the constrained least-squares polynomial(degrees 3,0)if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the accuracy of the data values.
+c   if the user has an idea of the statistical errors on the data, he
+c   can also find a proper estimate for s. for, by assuming that, if he
+c   specifies the right s, spgrid will return a spline s(u,v) which
+c   exactly reproduces the function underlying the data he can evaluate
+c   the sum((r(i,j)-s(u(i),v(j)))**2) to find a good estimate for this s
+c   for example, if he knows that the statistical errors on his r(i,j)-
+c   values is not greater than 0.1, he may expect that a good s should
+c   have a value not larger than mu*mv*(0.1)**2.
+c   if nothing is known about the statistical error in r(i,j), s must
+c   be determined by trial and error, taking account of the comments
+c   above. the best is then to start with a very large value of s (to
+c   determine the least-squares polynomial and the corresponding upper
+c   bound fp0 for s) and then to progressively decrease the value of s
+c   ( say by a factor 10 in the beginning, i.e. s=fp0/10,fp0/100,...
+c   and more carefully as the approximation shows more detail) to
+c   obtain closer fits.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt(1)=0.
+c   if iopt(1) = 1 the program will continue with the knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if spgrid is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. if the computation mode iopt(1) = 1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt(1)=1,the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   spgrid once more with the chosen value for s but now with iopt(1)=0.
+c   indeed, spgrid may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds nuest and
+c   nvest. indeed, if at a certain stage in spgrid the number of knots
+c   in one direction (say nu) has reached the value of its upper bound
+c   (nuest), then from that moment on all subsequent knots are added
+c   in the other (v) direction. this may indicate that the value of
+c   nuest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c   for example, by setting nuest=8 (the lowest allowable value for
+c   nuest), the user can indicate that he wants an approximation which
+c   is a simple cubic polynomial in the variable u.
+c
+c  other subroutines required:
+c    fpspgr,fpchec,fpchep,fpknot,fpopsp,fprati,fpgrsp,fpsysy,fpback,
+c    fpbacp,fpbspl,fpcyt1,fpcyt2,fpdisc,fpgivs,fprota
+c
+c  references:
+c   dierckx p. : fast algorithms for smoothing data over a disc or a
+c                sphere using tensor product splines, in "algorithms
+c                for approximation", ed. j.c.mason and m.g.cox,
+c                clarendon press oxford, 1987, pp. 51-65
+c   dierckx p. : fast algorithms for smoothing data over a disc or a
+c                sphere using tensor product splines, report tw73, dept.
+c                computer science,k.u.leuven, 1985.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : july 1985
+c  latest update : march 1989
+c
+c  ..
+c  ..scalar arguments..
+      real*8 r0,r1,s,fp
+      integer mu,mv,nuest,nvest,nu,nv,lwrk,kwrk,ier
+c  ..array arguments..
+      integer iopt(3),ider(4),iwrk(kwrk)
+      real*8 u(mu),v(mv),r(mu*mv),c((nuest-4)*(nvest-4)),tu(nuest),
+     * tv(nvest),wrk(lwrk)
+c  ..local scalars..
+      real*8 per,pi,tol,uu,ve,rmax,rmin,one,half,rn,rb,re
+      integer i,i1,i2,j,jwrk,j1,j2,kndu,kndv,knru,knrv,kwest,l,
+     * ldr,lfpu,lfpv,lwest,lww,m,maxit,mumin,muu,nc
+c  ..function references..
+      real*8 datan2
+      integer max0
+c  ..subroutine references..
+c    fpchec,fpchep,fpspgr
+c  ..
+c  set constants
+      one = 1d0
+      half = 0.5e0
+      pi = datan2(0d0,-one)
+      per = pi+pi
+      ve = v(1)+per
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations, a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      ier = 10
+      if(iopt(1).lt.(-1) .or. iopt(1).gt.1) go to 200
+      if(iopt(2).lt.0 .or. iopt(2).gt.1) go to 200
+      if(iopt(3).lt.0 .or. iopt(3).gt.1) go to 200
+      if(ider(1).lt.(-1) .or. ider(1).gt.1) go to 200
+      if(ider(2).lt.0 .or. ider(2).gt.1) go to 200
+      if(ider(2).eq.1 .and. iopt(2).eq.0) go to 200
+      if(ider(3).lt.(-1) .or. ider(3).gt.1) go to 200
+      if(ider(4).lt.0 .or. ider(4).gt.1) go to 200
+      if(ider(4).eq.1 .and. iopt(3).eq.0) go to 200
+      mumin = 4
+      if(ider(1).ge.0) mumin = mumin-1
+      if(iopt(2).eq.1 .and. ider(2).eq.1) mumin = mumin-1
+      if(ider(3).ge.0) mumin = mumin-1
+      if(iopt(3).eq.1 .and. ider(4).eq.1) mumin = mumin-1
+      if(mumin.eq.0) mumin = 1
+      if(mu.lt.mumin .or. mv.lt.4) go to 200
+      if(nuest.lt.8 .or. nvest.lt.8) go to 200
+      m = mu*mv
+      nc = (nuest-4)*(nvest-4)
+      lwest = 12+nuest*(mv+nvest+3)+24*nvest+4*mu+8*mv+
+     * max0(nuest,mv+nvest)
+      kwest = 5+mu+mv+nuest+nvest
+      if(lwrk.lt.lwest .or. kwrk.lt.kwest) go to 200
+      if(u(1).le.0. .or. u(mu).ge.pi) go to 200
+      if(mu.eq.1) go to 30
+      do 20 i=2,mu
+        if(u(i-1).ge.u(i)) go to 200
+  20  continue
+  30  if(v(1).lt. (-pi) .or. v(1).ge.pi ) go to 200
+      if(v(mv).ge.v(1)+per) go to 200
+      do 40 i=2,mv
+        if(v(i-1).ge.v(i)) go to 200
+  40  continue
+      if(iopt(1).gt.0) go to 140
+c  if not given, we compute an estimate for r0.
+      rn = mv
+      if(ider(1).lt.0) go to 45
+      rb = r0
+      go to 55
+  45  rb = 0.
+      do 50 i=1,mv
+         rb = rb+r(i)
+  50  continue
+      rb = rb/rn
+c  if not given, we compute an estimate for r1.
+  55  if(ider(3).lt.0) go to 60
+      re = r1
+      go to 70
+  60  re = 0.
+      j = m
+      do 65 i=1,mv
+         re = re+r(j)
+         j = j-1
+  65  continue
+      re = re/rn
+c  we determine the range of r-values.
+  70  rmin = rb
+      rmax = re
+      do 80 i=1,m
+         if(r(i).lt.rmin) rmin = r(i)
+         if(r(i).gt.rmax) rmax = r(i)
+  80  continue
+      wrk(5) = rb
+      wrk(6) = 0.
+      wrk(7) = 0.
+      wrk(8) = re
+      wrk(9) = 0.
+      wrk(10) = 0.
+      wrk(11) = rmax -rmin
+      wrk(12) = wrk(11)
+      iwrk(4) = mu
+      iwrk(5) = mu
+      if(iopt(1).eq.0) go to 140
+      if(nu.lt.8 .or. nu.gt.nuest) go to 200
+      if(nv.lt.11 .or. nv.gt.nvest) go to 200
+      j = nu
+      do 90 i=1,4
+        tu(i) = 0.
+        tu(j) = pi
+        j = j-1
+  90  continue
+      l = 13
+      wrk(l) = 0.
+      if(iopt(2).eq.0) go to 100
+      l = l+1
+      uu = u(1)
+      if(uu.gt.tu(5)) uu = tu(5)
+      wrk(l) = uu*half
+ 100  do 110 i=1,mu
+        l = l+1
+        wrk(l) = u(i)
+ 110  continue
+      if(iopt(3).eq.0) go to 120
+      l = l+1
+      uu = u(mu)
+      if(uu.lt.tu(nu-4)) uu = tu(nu-4)
+      wrk(l) = uu+(pi-uu)*half
+ 120  l = l+1
+      wrk(l) = pi
+      muu = l-12
+      call fpchec(wrk(13),muu,tu,nu,3,ier)
+      if(ier.ne.0) go to 200
+      j1 = 4
+      tv(j1) = v(1)
+      i1 = nv-3
+      tv(i1) = ve
+      j2 = j1
+      i2 = i1
+      do 130 i=1,3
+        i1 = i1+1
+        i2 = i2-1
+        j1 = j1+1
+        j2 = j2-1
+        tv(j2) = tv(i2)-per
+        tv(i1) = tv(j1)+per
+ 130  continue
+      l = 13
+      do 135 i=1,mv
+        wrk(l) = v(i)
+        l = l+1
+ 135  continue
+      wrk(l) = ve
+      call fpchep(wrk(13),mv+1,tv,nv,3,ier)
+      if (ier.eq.0) go to 150
+      go to 200
+ 140  if(s.lt.0.) go to 200
+      if(s.eq.0. .and. (nuest.lt.(mu+6+iopt(2)+iopt(3)) .or.
+     * nvest.lt.(mv+7)) ) go to 200
+c  we partition the working space and determine the spline approximation
+ 150  ldr = 5
+      lfpu = 13
+      lfpv = lfpu+nuest
+      lww = lfpv+nvest
+      jwrk = lwrk-12-nuest-nvest
+      knru = 6
+      knrv = knru+mu
+      kndu = knrv+mv
+      kndv = kndu+nuest
+      call fpspgr(iopt,ider,u,mu,v,mv,r,m,rb,re,s,nuest,nvest,tol,maxit,
+     *
+     * nc,nu,tu,nv,tv,c,fp,wrk(1),wrk(2),wrk(3),wrk(4),wrk(lfpu),
+     * wrk(lfpv),wrk(ldr),wrk(11),iwrk(1),iwrk(2),iwrk(3),iwrk(4),
+     * iwrk(5),iwrk(knru),iwrk(knrv),iwrk(kndu),iwrk(kndv),wrk(lww),
+     * jwrk,ier)
+ 200  return
+      end

Added: branches/Interpolate1D/fitpack/sphere.f
===================================================================
--- branches/Interpolate1D/fitpack/sphere.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/sphere.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,404 @@
+      subroutine sphere(iopt,m,teta,phi,r,w,s,ntest,npest,eps,
+     *  nt,tt,np,tp,c,fp,wrk1,lwrk1,wrk2,lwrk2,iwrk,kwrk,ier)
+c  subroutine sphere determines a smooth bicubic spherical spline
+c  approximation s(teta,phi), 0 <= teta <= pi ; 0 <= phi <= 2*pi
+c  to a given set of data points (teta(i),phi(i),r(i)),i=1,2,...,m.
+c  such a spline has the following specific properties
+c
+c    (1) s(0,phi)  = constant   0 <=phi<= 2*pi.
+c
+c    (2) s(pi,phi) = constant   0 <=phi<= 2*pi
+c
+c         j             j
+c        d s(teta,0)   d s(teta,2*pi)
+c    (3) ----------- = ------------   0 <=teta<=pi, j=0,1,2
+c             j             j
+c        d phi         d phi
+c
+c        d s(0,phi)    d s(0,0)             d s(0,pi/2)
+c    (4) ----------  = -------- *cos(phi) + ----------- *sin(phi)
+c        d teta        d teta               d teta
+c
+c        d s(pi,phi)   d s(pi,0)            d s(pi,pi/2)
+c    (5) ----------- = ---------*cos(phi) + ------------*sin(phi)
+c        d teta        d teta               d teta
+c
+c  if iopt =-1 sphere calculates a weighted least-squares spherical
+c  spline according to a given set of knots in teta- and phi- direction.
+c  if iopt >=0, the number of knots in each direction and their position
+c  tt(j),j=1,2,...,nt ; tp(j),j=1,2,...,np are chosen automatically by
+c  the routine. the smoothness of s(teta,phi) is then achieved by mini-
+c  malizing the discontinuity jumps of the derivatives of the spline
+c  at the knots. the amount of smoothness of s(teta,phi) is determined
+c  by the condition that fp = sum((w(i)*(r(i)-s(teta(i),phi(i))))**2)
+c  be <= s, with s a given non-negative constant.
+c  the spherical spline is given in the standard b-spline representation
+c  of bicubic splines and can be evaluated by means of subroutine bispev
+c
+c calling sequence:
+c     call sphere(iopt,m,teta,phi,r,w,s,ntest,npest,eps,
+c    *  nt,tt,np,tp,c,fp,wrk1,lwrk1,wrk2,lwrk2,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer flag. on entry iopt must specify whether a weighted
+c          least-squares spherical spline (iopt=-1) or a smoothing
+c          spherical spline (iopt=0 or 1) must be determined.
+c          if iopt=0 the routine will start with an initial set of knots
+c          tt(i)=0,tt(i+4)=pi,i=1,...,4;tp(i)=0,tp(i+4)=2*pi,i=1,...,4.
+c          if iopt=1 the routine will continue with the set of knots
+c          found at the last call of the routine.
+c          attention: a call with iopt=1 must always be immediately pre-
+c                     ceded by another call with iopt=1 or iopt=0.
+c          unchanged on exit.
+c  m     : integer. on entry m must specify the number of data points.
+c          m >= 2. unchanged on exit.
+c  teta  : real array of dimension at least (m).
+c  phi   : real array of dimension at least (m).
+c  r     : real array of dimension at least (m).
+c          before entry,teta(i),phi(i),r(i) must be set to the spherical
+c          co-ordinates of the i-th data point, for i=1,...,m.the order
+c          of the data points is immaterial. unchanged on exit.
+c  w     : real array of dimension at least (m). before entry, w(i) must
+c          be set to the i-th value in the set of weights. the w(i) must
+c          be strictly positive. unchanged on exit.
+c  s     : real. on entry (in case iopt>=0) s must specify the smoothing
+c          factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  ntest : integer. unchanged on exit.
+c  npest : integer. unchanged on exit.
+c          on entry, ntest and npest must specify an upper bound for the
+c          number of knots required in the teta- and phi-directions.
+c          these numbers will also determine the storage space needed by
+c          the routine. ntest >= 8, npest >= 8.
+c          in most practical situation ntest = npest = 8+sqrt(m/2) will
+c          be sufficient. see also further comments.
+c  eps   : real.
+c          on entry, eps must specify a threshold for determining the
+c          effective rank of an over-determined linear system of equat-
+c          ions. 0 < eps < 1.  if the number of decimal digits in the
+c          computer representation of a real number is q, then 10**(-q)
+c          is a suitable value for eps in most practical applications.
+c          unchanged on exit.
+c  nt    : integer.
+c          unless ier=10 (in case iopt >=0), nt will contain the total
+c          number of knots with respect to the teta-variable, of the
+c          spline approximation returned. if the computation mode iopt=1
+c          is used, the value of nt should be left unchanged between
+c          subsequent calls.
+c          in case iopt=-1, the value of nt should be specified on entry
+c  tt    : real array of dimension at least ntest.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the teta-variable, i.e. the position
+c          of the interior knots tt(5),...,tt(nt-4) as well as the
+c          position of the additional knots tt(1)=...=tt(4)=0 and
+c          tt(nt-3)=...=tt(nt)=pi needed for the b-spline representation
+c          if the computation mode iopt=1 is used, the values of tt(1),
+c          ...,tt(nt) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values tt(5),
+c          ...tt(nt-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  np    : integer.
+c          unless ier=10 (in case iopt >=0), np will contain the total
+c          number of knots with respect to the phi-variable, of the
+c          spline approximation returned. if the computation mode iopt=1
+c          is used, the value of np should be left unchanged between
+c          subsequent calls.
+c          in case iopt=-1, the value of np (>=9) should be specified
+c          on entry.
+c  tp    : real array of dimension at least npest.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the phi-variable, i.e. the position of
+c          the interior knots tp(5),...,tp(np-4) as well as the position
+c          of the additional knots tp(1),...,tp(4) and tp(np-3),...,
+c          tp(np) needed for the b-spline representation.
+c          if the computation mode iopt=1 is used, the values of tp(1),
+c          ...,tp(np) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values tp(5),
+c          ...tp(np-4) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  c     : real array of dimension at least (ntest-4)*(npest-4).
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(teta,phi).
+c  fp    : real. unless ier=10, fp contains the weighted sum of
+c          squared residuals of the spline approximation returned.
+c  wrk1  : real array of dimension (lwrk1). used as workspace.
+c          if the computation mode iopt=1 is used the value of wrk1(1)
+c          should be left unchanged between subsequent calls.
+c          on exit wrk1(2),wrk1(3),...,wrk1(1+ncof) will contain the
+c          values d(i)/max(d(i)),i=1,...,ncof=6+(np-7)*(nt-8)
+c          with d(i) the i-th diagonal element of the reduced triangular
+c          matrix for calculating the b-spline coefficients. it includes
+c          those elements whose square is less than eps,which are treat-
+c          ed as 0 in the case of presumed rank deficiency (ier<-2).
+c  lwrk1 : integer. on entry lwrk1 must specify the actual dimension of
+c          the array wrk1 as declared in the calling (sub)program.
+c          lwrk1 must not be too small. let
+c            u = ntest-7, v = npest-7, then
+c          lwrk1 >= 185+52*v+10*u+14*u*v+8*(u-1)*v**2+8*m
+c  wrk2  : real array of dimension (lwrk2). used as workspace, but
+c          only in the case a rank deficient system is encountered.
+c  lwrk2 : integer. on entry lwrk2 must specify the actual dimension of
+c          the array wrk2 as declared in the calling (sub)program.
+c          lwrk2 > 0 . a save upper bound  for lwrk2 = 48+21*v+7*u*v+
+c          4*(u-1)*v**2 where u,v are as above. if there are enough data
+c          points, scattered uniformly over the approximation domain
+c          and if the smoothing factor s is not too small, there is a
+c          good chance that this extra workspace is not needed. a lot
+c          of memory might therefore be saved by setting lwrk2=1.
+c          (see also ier > 10)
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= m+(ntest-7)*(npest-7).
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the spline returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline returned is a spherical
+c            interpolating spline (fp=0).
+c   ier=-2 : normal return. the spline returned is the weighted least-
+c            squares constrained polynomial . in this extreme case
+c            fp gives the upper bound for the smoothing factor s.
+c   ier<-2 : warning. the coefficients of the spline returned have been
+c            computed as the minimal norm least-squares solution of a
+c            (numerically) rank deficient system. (-ier) gives the rank.
+c            especially if the rank deficiency which can be computed as
+c            6+(nt-8)*(np-7)+ier, is large the results may be inaccurate
+c            they could also seriously depend on the value of eps.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters ntest and
+c            npest.
+c            probably causes : ntest or npest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the weighted least-squares
+c            spherical spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing spline with
+c            fp = s. probably causes : s too small or badly chosen eps.
+c            there is an approximation returned but the corresponding
+c            weighted sum of squared residuals does not satisfy the
+c            condition abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing spline
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            weighted sum of squared residuals does not satisfy the
+c            condition abs(fp-s)/s < tol.
+c   ier=4  : error. no more knots can be added because the dimension
+c            of the spherical spline 6+(nt-8)*(np-7) already exceeds
+c            the number of data points m.
+c            probably causes : either s or m too small.
+c            the approximation returned is the weighted least-squares
+c            spherical spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=5  : error. no more knots can be added because the additional
+c            knot would (quasi) coincide with an old one.
+c            probably causes : s too small or too large a weight to an
+c            inaccurate data point.
+c            the approximation returned is the weighted least-squares
+c            spherical spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt<=1,  m>=2, ntest>=8 ,npest >=8, 0<eps<1,
+c            0<=teta(i)<=pi, 0<=phi(i)<=2*pi, w(i)>0, i=1,...,m
+c            lwrk1 >= 185+52*v+10*u+14*u*v+8*(u-1)*v**2+8*m
+c            kwrk >= m+(ntest-7)*(npest-7)
+c            if iopt=-1: 8<=nt<=ntest , 9<=np<=npest
+c                        0<tt(5)<tt(6)<...<tt(nt-4)<pi
+c                        0<tp(5)<tp(6)<...<tp(np-4)<2*pi
+c            if iopt>=0: s>=0
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c   ier>10 : error. lwrk2 is too small, i.e. there is not enough work-
+c            space for computing the minimal least-squares solution of
+c            a rank deficient system of linear equations. ier gives the
+c            requested value for lwrk2. there is no approximation re-
+c            turned but, having saved the information contained in nt,
+c            np,tt,tp,wrk1, and having adjusted the value of lwrk2 and
+c            the dimension of the array wrk2 accordingly, the user can
+c            continue at the point the program was left, by calling
+c            sphere with iopt=1.
+c
+c further comments:
+c  by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the constrained weighted least-squares polynomial if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   r(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in r(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   polynomial and the corresponding upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximation shows more detail) to obtain closer fits.
+c   to choose s very small is strongly discouraged. this considerably
+c   increases computation time and memory requirements. it may also
+c   cause rank-deficiency (ier<-2) and endager numerical stability.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if sphere is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. if the computation mode iopt=1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   sphere once more with the selected value for s but now with iopt=0.
+c   indeed, sphere may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds ntest and
+c   npest. indeed, if at a certain stage in sphere the number of knots
+c   in one direction (say nt) has reached the value of its upper bound
+c   (ntest), then from that moment on all subsequent knots are added
+c   in the other (phi) direction. this may indicate that the value of
+c   ntest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c   for example, by setting ntest=8 (the lowest allowable value for
+c   ntest), the user can indicate that he wants an approximation which
+c   is a cubic polynomial in the variable teta.
+c
+c  other subroutines required:
+c    fpback,fpbspl,fpsphe,fpdisc,fpgivs,fprank,fprati,fprota,fporde,
+c    fprpsp
+c
+c  references:
+c   dierckx p. : algorithms for smoothing data on the sphere with tensor
+c                product splines, computing 32 (1984) 319-342.
+c   dierckx p. : algorithms for smoothing data on the sphere with tensor
+c                product splines, report tw62, dept. computer science,
+c                k.u.leuven, 1983.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : july 1983
+c  latest update : march 1989
+c
+c  ..
+c  ..scalar arguments..
+      real*8 s,eps,fp
+      integer iopt,m,ntest,npest,nt,np,lwrk1,lwrk2,kwrk,ier
+c  ..array arguments..
+      real*8 teta(m),phi(m),r(m),w(m),tt(ntest),tp(npest),
+     * c((ntest-4)*(npest-4)),wrk1(lwrk1),wrk2(lwrk2)
+      integer iwrk(kwrk)
+c  ..local scalars..
+      real*8 tol,pi,pi2,one
+      integer i,ib1,ib3,ki,kn,kwest,la,lbt,lcc,lcs,lro,j
+     * lbp,lco,lf,lff,lfp,lh,lq,lst,lsp,lwest,maxit,ncest,ncc,ntt,
+     * npp,nreg,nrint,ncof,nt4,np4
+c  ..function references..
+      real*8 atan
+c  ..subroutine references..
+c    fpsphe
+c  ..
+c  set constants
+      one = 0.1e+01
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid,control is immediately repassed to the calling program.
+      ier = 10
+      if(eps.le.0. .or. eps.ge.1.) go to 80
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 80
+      if(m.lt.2) go to 80
+      if(ntest.lt.8 .or. npest.lt.8) go to 80
+      nt4 = ntest-4
+      np4 = npest-4
+      ncest = nt4*np4
+      ntt = ntest-7
+      npp = npest-7
+      ncc = 6+npp*(ntt-1)
+      nrint = ntt+npp
+      nreg = ntt*npp
+      ncof = 6+3*npp
+      ib1 = 4*npp
+      ib3 = ib1+3
+      if(ncof.gt.ib1) ib1 = ncof
+      if(ncof.gt.ib3) ib3 = ncof
+      lwest = 185+52*npp+10*ntt+14*ntt*npp+8*(m+(ntt-1)*npp**2)
+      kwest = m+nreg
+      if(lwrk1.lt.lwest .or. kwrk.lt.kwest) go to 80
+      if(iopt.gt.0) go to 60
+      pi = atan(one)*4
+      pi2 = pi+pi
+      do 20 i=1,m
+        if(w(i).le.0.) go to 80
+        if(teta(i).lt.0. .or. teta(i).gt.pi) go to 80
+        if(phi(i) .lt.0. .or. phi(i).gt.pi2) go to 80
+  20  continue
+      if(iopt.eq.0) go to 60
+      ntt = nt-8
+      if(ntt.lt.0 .or. nt.gt.ntest) go to 80
+      if(ntt.eq.0) go to 40
+      tt(4) = 0.
+      do 30 i=1,ntt
+         j = i+4
+         if(tt(j).le.tt(j-1) .or. tt(j).ge.pi) go to 80
+  30  continue
+  40  npp = np-8
+      if(npp.lt.1 .or. np.gt.npest) go to 80
+      tp(4) = 0.
+      do 50 i=1,npp
+         j = i+4
+         if(tp(j).le.tp(j-1) .or. tp(j).ge.pi2) go to 80
+  50  continue
+      go to 70
+  60  if(s.lt.0.) go to 80
+  70  ier = 0
+c  we partition the working space and determine the spline approximation
+      kn = 1
+      ki = kn+m
+      lq = 2
+      la = lq+ncc*ib3
+      lf = la+ncc*ib1
+      lff = lf+ncc
+      lfp = lff+ncest
+      lco = lfp+nrint
+      lh = lco+nrint
+      lbt = lh+ib3
+      lbp = lbt+5*ntest
+      lro = lbp+5*npest
+      lcc = lro+npest
+      lcs = lcc+npest
+      lst = lcs+npest
+      lsp = lst+m*4
+      call fpsphe(iopt,m,teta,phi,r,w,s,ntest,npest,eps,tol,maxit,
+     * ib1,ib3,ncest,ncc,nrint,nreg,nt,tt,np,tp,c,fp,wrk1(1),wrk1(lfp),
+     * wrk1(lco),wrk1(lf),wrk1(lff),wrk1(lro),wrk1(lcc),wrk1(lcs),
+     * wrk1(la),wrk1(lq),wrk1(lbt),wrk1(lbp),wrk1(lst),wrk1(lsp),
+     * wrk1(lh),iwrk(ki),iwrk(kn),wrk2,lwrk2,ier)
+  80  return
+      end
+

Added: branches/Interpolate1D/fitpack/splder.f
===================================================================
--- branches/Interpolate1D/fitpack/splder.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/splder.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,162 @@
+      subroutine splder(t,n,c,k,nu,x,y,m,wrk,ier)
+c  subroutine splder evaluates in a number of points x(i),i=1,2,...,m
+c  the derivative of order nu of a spline s(x) of degree k,given in
+c  its b-spline representation.
+c
+c  calling sequence:
+c     call splder(t,n,c,k,nu,x,y,m,wrk,ier)
+c
+c  input parameters:
+c    t    : array,length n, which contains the position of the knots.
+c    n    : integer, giving the total number of knots of s(x).
+c    c    : array,length n, which contains the b-spline coefficients.
+c    k    : integer, giving the degree of s(x).
+c    nu   : integer, specifying the order of the derivative. 0<=nu<=k
+c    x    : array,length m, which contains the points where the deriv-
+c           ative of s(x) must be evaluated.
+c    m    : integer, giving the number of points where the derivative
+c           of s(x) must be evaluated
+c    wrk  : real array of dimension n. used as working space.
+c
+c  output parameters:
+c    y    : array,length m, giving the value of the derivative of s(x)
+c           at the different points.
+c    ier  : error flag
+c      ier = 0 : normal return
+c      ier =10 : invalid input data (see restrictions)
+c
+c  restrictions:
+c    0 <= nu <= k
+c    m >= 1
+c    t(k+1) <= x(i) <= x(i+1) <= t(n-k) , i=1,2,...,m-1.
+c
+c  other subroutines required: fpbspl
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c++ pearu: 13 aug 20003
+c++   - disabled cliping x values to interval [min(t),max(t)]
+c++   - removed the restriction of the orderness of x values
+c++   - fixed initialization of sp to double precision value
+c
+c  ..scalar arguments..
+      integer n,k,nu,m,ier
+c  ..array arguments..
+      real*8 t(n),c(n),x(m),y(m),wrk(n)
+c  ..local scalars..
+      integer i,j,kk,k1,k2,l,ll,l1,l2,nk1,nk2,nn
+      real*8 ak,arg,fac,sp,tb,te
+c++..
+      integer k3
+c..++
+c  ..local arrays ..
+      real*8 h(6)
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      if(nu.lt.0 .or. nu.gt.k) go to 200
+c--      if(m-1) 200,30,10
+c++..
+      if(m.lt.1) go to 200
+c..++
+c--  10  do 20 i=2,m
+c--        if(x(i).lt.x(i-1)) go to 200
+c--  20  continue
+  30  ier = 0
+c  fetch tb and te, the boundaries of the approximation interval.
+      k1 = k+1
+      k3 = k1+1
+      nk1 = n-k1
+      tb = t(k1)
+      te = t(nk1+1)
+c  the derivative of order nu of a spline of degree k is a spline of
+c  degree k-nu,the b-spline coefficients wrk(i) of which can be found
+c  using the recurrence scheme of de boor.
+      l = 1
+      kk = k
+      nn = n
+      do 40 i=1,nk1
+         wrk(i) = c(i)
+  40  continue
+      if(nu.eq.0) go to 100
+      nk2 = nk1
+      do 60 j=1,nu
+         ak = kk
+         nk2 = nk2-1
+         l1 = l
+         do 50 i=1,nk2
+            l1 = l1+1
+            l2 = l1+kk
+            fac = t(l2)-t(l1)
+            if(fac.le.0.) go to 50
+            wrk(i) = ak*(wrk(i+1)-wrk(i))/fac
+  50     continue
+         l = l+1
+         kk = kk-1
+  60  continue
+      if(kk.ne.0) go to 100
+c  if nu=k the derivative is a piecewise constant function
+      j = 1
+      do 90 i=1,m
+         arg = x(i)
+c++..
+ 65      if(arg.ge.t(l) .or. l+1.eq.k2) go to 70
+         l1 = l
+         l = l-1
+         j = j-1
+         go to 65
+c..++
+  70     if(arg.lt.t(l+1) .or. l.eq.nk1) go to 80
+         l = l+1
+         j = j+1
+         go to 70
+  80     y(i) = wrk(j)
+  90  continue
+      go to 200
+ 100  l = k1
+      l1 = l+1
+      k2 = k1-nu
+c  main loop for the different points.
+      do 180 i=1,m
+c  fetch a new x-value arg.
+        arg = x(i)
+c--        if(arg.lt.tb) arg = tb
+c--        if(arg.gt.te) arg = te
+c  search for knot interval t(l) <= arg < t(l+1)
+c++..
+ 135    if(arg.ge.t(l) .or. l1.eq.k3) go to 140
+        l1 = l
+        l = l-1
+        go to 135
+c..++
+ 140    if(arg.lt.t(l1) .or. l.eq.nk1) go to 150
+        l = l1
+        l1 = l+1
+        go to 140
+c  evaluate the non-zero b-splines of degree k-nu at arg.
+ 150    call fpbspl(t,n,kk,arg,l,h)
+c  find the value of the derivative at x=arg.
+        sp = 0.0d0
+        ll = l-k1
+        do 160 j=1,k2
+          ll = ll+1
+          sp = sp+wrk(ll)*h(j)
+ 160    continue
+        y(i) = sp
+ 180  continue
+ 200  return
+      end

Added: branches/Interpolate1D/fitpack/splev.f
===================================================================
--- branches/Interpolate1D/fitpack/splev.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/splev.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,115 @@
+      subroutine splev(t,n,c,k,x,y,m,ier)
+c  subroutine splev evaluates in a number of points x(i),i=1,2,...,m
+c  a spline s(x) of degree k, given in its b-spline representation.
+c
+c  calling sequence:
+c     call splev(t,n,c,k,x,y,m,ier)
+c
+c  input parameters:
+c    t    : array,length n, which contains the position of the knots.
+c    n    : integer, giving the total number of knots of s(x).
+c    c    : array,length n, which contains the b-spline coefficients.
+c    k    : integer, giving the degree of s(x).
+c    x    : array,length m, which contains the points where s(x) must
+c           be evaluated.
+c    m    : integer, giving the number of points where s(x) must be
+c           evaluated.
+c
+c  output parameter:
+c    y    : array,length m, giving the value of s(x) at the different
+c           points.
+c    ier  : error flag
+c      ier = 0 : normal return
+c      ier =10 : invalid input data (see restrictions)
+c
+c  restrictions:
+c    m >= 1
+c--    t(k+1) <= x(i) <= x(i+1) <= t(n-k) , i=1,2,...,m-1.
+c
+c  other subroutines required: fpbspl.
+c
+c  references :
+c    de boor c  : on calculating with b-splines, j. approximation theory
+c                 6 (1972) 50-62.
+c    cox m.g.   : the numerical evaluation of b-splines, j. inst. maths
+c                 applics 10 (1972) 134-149.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c++ pearu: 11 aug 2003
+c++   - disabled cliping x values to interval [min(t),max(t)]
+c++   - removed the restriction of the orderness of x values
+c++   - fixed initialization of sp to double precision value
+c
+c  ..scalar arguments..
+      integer n,k,m,ier
+c  ..array arguments..
+      real*8 t(n),c(n),x(m),y(m)
+c  ..local scalars..
+      integer i,j,k1,l,ll,l1,nk1
+c++..
+      integer k2
+c..++
+      real*8 arg,sp,tb,te
+c  ..local array..
+      real*8 h(20)
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+c--      if(m-1) 100,30,10
+c++..
+      if(m.lt.1) go to 100
+c..++
+c--  10  do 20 i=2,m
+c--        if(x(i).lt.x(i-1)) go to 100
+c--  20  continue
+  30  ier = 0
+c  fetch tb and te, the boundaries of the approximation interval.
+      k1 = k+1
+c++..
+      k2 = k1+1
+c..++
+      nk1 = n-k1
+      tb = t(k1)
+      te = t(nk1+1)
+      l = k1
+      l1 = l+1
+c  main loop for the different points.
+      do 80 i=1,m
+c  fetch a new x-value arg.
+        arg = x(i)
+c--        if(arg.lt.tb) arg = tb
+c--        if(arg.gt.te) arg = te
+c  search for knot interval t(l) <= arg < t(l+1)
+c++..
+ 35     if(arg.ge.t(l) .or. l1.eq.k2) go to 40
+        l1 = l
+        l = l-1
+        go to 35
+c..++
+  40    if(arg.lt.t(l1) .or. l.eq.nk1) go to 50
+        l = l1
+        l1 = l+1
+        go to 40
+c  evaluate the non-zero b-splines at arg.
+  50    call fpbspl(t,n,k,arg,l,h)
+c  find the value of s(x) at x=arg.
+        sp = 0.0d0
+        ll = l-k1
+        do 60 j=1,k1
+          ll = ll+1
+          sp = sp+c(ll)*h(j)
+  60    continue
+        y(i) = sp
+  80  continue
+ 100  return
+      end

Added: branches/Interpolate1D/fitpack/splint.f
===================================================================
--- branches/Interpolate1D/fitpack/splint.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/splint.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,58 @@
+      real*8 function splint(t,n,c,k,a,b,wrk)
+c  function splint calculates the integral of a spline function s(x)
+c  of degree k, which is given in its normalized b-spline representation
+c
+c  calling sequence:
+c     aint = splint(t,n,c,k,a,b,wrk)
+c
+c  input parameters:
+c    t    : array,length n,which contains the position of the knots
+c           of s(x).
+c    n    : integer, giving the total number of knots of s(x).
+c    c    : array,length n, containing the b-spline coefficients.
+c    k    : integer, giving the degree of s(x).
+c    a,b  : real values, containing the end points of the integration
+c           interval. s(x) is considered to be identically zero outside
+c           the interval (t(k+1),t(n-k)).
+c
+c  output parameter:
+c    aint : real, containing the integral of s(x) between a and b.
+c    wrk  : real array, length n.  used as working space
+c           on output, wrk will contain the integrals of the normalized
+c           b-splines defined on the set of knots.
+c
+c  other subroutines required: fpintb.
+c
+c  references :
+c    gaffney p.w. : the calculation of indefinite integrals of b-splines
+c                   j. inst. maths applics 17 (1976) 37-41.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      real*8 a,b
+      integer n,k
+c  ..array arguments..
+      real*8 t(n),c(n),wrk(n)
+c  ..local scalars..
+      integer i,nk1
+c  ..
+      nk1 = n-k-1
+c  calculate the integrals wrk(i) of the normalized b-splines
+c  ni,k+1(x), i=1,2,...nk1.
+      call fpintb(t,n,wrk,nk1,a,b)
+c  calculate the integral of s(x).
+      splint = 0.0d0
+      do 10 i=1,nk1
+        splint = splint+c(i)*wrk(i)
+  10  continue
+      return
+      end

Added: branches/Interpolate1D/fitpack/sproot.f
===================================================================
--- branches/Interpolate1D/fitpack/sproot.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/sproot.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,183 @@
+      subroutine sproot(t,n,c,zero,mest,m,ier)
+c  subroutine sproot finds the zeros of a cubic spline s(x),which is
+c  given in its normalized b-spline representation.
+c
+c  calling sequence:
+c     call sproot(t,n,c,zero,mest,m,ier)
+c
+c  input parameters:
+c    t    : real array,length n, containing the knots of s(x).
+c    n    : integer, containing the number of knots.  n>=8
+c    c    : real array,length n, containing the b-spline coefficients.
+c    mest : integer, specifying the dimension of array zero.
+c
+c  output parameters:
+c    zero : real array,lenth mest, containing the zeros of s(x).
+c    m    : integer,giving the number of zeros.
+c    ier  : error flag:
+c      ier = 0: normal return.
+c      ier = 1: the number of zeros exceeds mest.
+c      ier =10: invalid input data (see restrictions).
+c
+c  other subroutines required: fpcuro
+c
+c  restrictions:
+c    1) n>= 8.
+c    2) t(4) < t(5) < ... < t(n-4) < t(n-3).
+c       t(1) <= t(2) <= t(3) <= t(4)
+c       t(n-3) <= t(n-2) <= t(n-1) <= t(n)
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c ..
+c ..scalar arguments..
+      integer n,mest,m,ier
+c  ..array arguments..
+      real*8 t(n),c(n),zero(mest)
+c  ..local scalars..
+      integer i,j,j1,l,n4
+      real*8 ah,a0,a1,a2,a3,bh,b0,b1,c1,c2,c3,c4,c5,d4,d5,h1,h2,
+     * three,two,t1,t2,t3,t4,t5,zz
+      logical z0,z1,z2,z3,z4,nz0,nz1,nz2,nz3,nz4
+c  ..local array..
+      real*8 y(3)
+c  ..
+c  set some constants
+      two = 0.2d+01
+      three = 0.3d+01
+c  before starting computations a data check is made. if the input data
+c  are invalid, control is immediately repassed to the calling program.
+      n4 = n-4
+      ier = 10
+      if(n.lt.8) go to 800
+      j = n
+      do 10 i=1,3
+        if(t(i).gt.t(i+1)) go to 800
+        if(t(j).lt.t(j-1)) go to 800
+        j = j-1
+  10  continue
+      do 20 i=4,n4
+        if(t(i).ge.t(i+1)) go to 800
+  20  continue
+c  the problem considered reduces to finding the zeros of the cubic
+c  polynomials pl(x) which define the cubic spline in each knot
+c  interval t(l)<=x<=t(l+1). a zero of pl(x) is also a zero of s(x) on
+c  the condition that it belongs to the knot interval.
+c  the cubic polynomial pl(x) is determined by computing s(t(l)),
+c  s'(t(l)),s(t(l+1)) and s'(t(l+1)). in fact we only have to compute
+c  s(t(l+1)) and s'(t(l+1)); because of the continuity conditions of
+c  splines and their derivatives, the value of s(t(l)) and s'(t(l))
+c  is already known from the foregoing knot interval.
+      ier = 0
+c  evaluate some constants for the first knot interval
+      h1 = t(4)-t(3)
+      h2 = t(5)-t(4)
+      t1 = t(4)-t(2)
+      t2 = t(5)-t(3)
+      t3 = t(6)-t(4)
+      t4 = t(5)-t(2)
+      t5 = t(6)-t(3)
+c  calculate a0 = s(t(4)) and ah = s'(t(4)).
+      c1 = c(1)
+      c2 = c(2)
+      c3 = c(3)
+      c4 = (c2-c1)/t4
+      c5 = (c3-c2)/t5
+      d4 = (h2*c1+t1*c2)/t4
+      d5 = (t3*c2+h1*c3)/t5
+      a0 = (h2*d4+h1*d5)/t2
+      ah = three*(h2*c4+h1*c5)/t2
+      z1 = .true.
+      if(ah.lt.0.0d0) z1 = .false.
+      nz1 = .not.z1
+      m = 0
+c  main loop for the different knot intervals.
+      do 300 l=4,n4
+c  evaluate some constants for the knot interval t(l) <= x <= t(l+1).
+        h1 = h2
+        h2 = t(l+2)-t(l+1)
+        t1 = t2
+        t2 = t3
+        t3 = t(l+3)-t(l+1)
+        t4 = t5
+        t5 = t(l+3)-t(l)
+c  find a0 = s(t(l)), ah = s'(t(l)), b0 = s(t(l+1)) and bh = s'(t(l+1)).
+        c1 = c2
+        c2 = c3
+        c3 = c(l)
+        c4 = c5
+        c5 = (c3-c2)/t5
+        d4 = (h2*c1+t1*c2)/t4
+        d5 = (h1*c3+t3*c2)/t5
+        b0 = (h2*d4+h1*d5)/t2
+        bh = three*(h2*c4+h1*c5)/t2
+c  calculate the coefficients a0,a1,a2 and a3 of the cubic polynomial
+c  pl(x) = ql(y) = a0+a1*y+a2*y**2+a3*y**3 ; y = (x-t(l))/(t(l+1)-t(l)).
+        a1 = ah*h1
+        b1 = bh*h1
+        a2 = three*(b0-a0)-b1-two*a1
+        a3 = two*(a0-b0)+b1+a1
+c  test whether or not pl(x) could have a zero in the range
+c  t(l) <= x <= t(l+1).
+        z3 = .true.
+        if(b1.lt.0.0d0) z3 = .false.
+        nz3 = .not.z3
+        if(a0*b0.le.0.0d0) go to 100
+        z0 = .true.
+        if(a0.lt.0.0d0) z0 = .false.
+        nz0 = .not.z0
+        z2 = .true.
+        if(a2.lt.0.) z2 = .false.
+        nz2 = .not.z2
+        z4 = .true.
+        if(3.0d0*a3+a2.lt.0.0d0) z4 = .false.
+        nz4 = .not.z4
+        if(.not.((z0.and.(nz1.and.(z3.or.z2.and.nz4).or.nz2.and.
+     * z3.and.z4).or.nz0.and.(z1.and.(nz3.or.nz2.and.z4).or.z2.and.
+     * nz3.and.nz4))))go to 200
+c  find the zeros of ql(y).
+ 100    call fpcuro(a3,a2,a1,a0,y,j)
+        if(j.eq.0) go to 200
+c  find which zeros of pl(x) are zeros of s(x).
+        do 150 i=1,j
+          if(y(i).lt.0.0d0 .or. y(i).gt.1.0d0) go to 150
+c  test whether the number of zeros of s(x) exceeds mest.
+          if(m.ge.mest) go to 700
+          m = m+1
+          zero(m) = t(l)+h1*y(i)
+ 150    continue
+ 200    a0 = b0
+        ah = bh
+        z1 = z3
+        nz1 = nz3
+ 300  continue
+c  the zeros of s(x) are arranged in increasing order.
+      if(m.lt.2) go to 800
+      do 400 i=2,m
+        j = i
+ 350    j1 = j-1
+        if(j1.eq.0) go to 400
+        if(zero(j).ge.zero(j1)) go to 400
+        zz = zero(j)
+        zero(j) = zero(j1)
+        zero(j1) = zz
+        j = j1
+        go to 350
+ 400  continue
+      j = m
+      m = 1
+      do 500 i=2,j
+        if(zero(i).eq.zero(m)) go to 500
+        m = m+1
+        zero(m) = zero(i)
+ 500  continue
+      go to 800
+ 700  ier = 1
+ 800  return
+      end

Added: branches/Interpolate1D/fitpack/surev.f
===================================================================
--- branches/Interpolate1D/fitpack/surev.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/surev.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,106 @@
+      subroutine surev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,mf,wrk,lwrk,
+     * iwrk,kwrk,ier)
+c  subroutine surev evaluates on a grid (u(i),v(j)),i=1,...,mu; j=1,...
+c  ,mv a bicubic spline surface of dimension idim, given in the
+c  b-spline representation.
+c
+c  calling sequence:
+c     call surev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,mf,wrk,lwrk,
+c    * iwrk,kwrk,ier)
+c
+c  input parameters:
+c   idim  : integer, specifying the dimension of the spline surface.
+c   tu    : real array, length nu, which contains the position of the
+c           knots in the u-direction.
+c   nu    : integer, giving the total number of knots in the u-direction
+c   tv    : real array, length nv, which contains the position of the
+c           knots in the v-direction.
+c   nv    : integer, giving the total number of knots in the v-direction
+c   c     : real array, length (nu-4)*(nv-4)*idim, which contains the
+c           b-spline coefficients.
+c   u     : real array of dimension (mu).
+c           before entry u(i) must be set to the u co-ordinate of the
+c           i-th grid point along the u-axis.
+c           tu(4)<=u(i-1)<=u(i)<=tu(nu-3), i=2,...,mu.
+c   mu    : on entry mu must specify the number of grid points along
+c           the u-axis. mu >=1.
+c   v     : real array of dimension (mv).
+c           before entry v(j) must be set to the v co-ordinate of the
+c           j-th grid point along the v-axis.
+c           tv(4)<=v(j-1)<=v(j)<=tv(nv-3), j=2,...,mv.
+c   mv    : on entry mv must specify the number of grid points along
+c           the v-axis. mv >=1.
+c   mf    : on entry, mf must specify the dimension of the array f.
+c           mf >= mu*mv*idim
+c   wrk   : real array of dimension lwrk. used as workspace.
+c   lwrk  : integer, specifying the dimension of wrk.
+c           lwrk >= 4*(mu+mv)
+c   iwrk  : integer array of dimension kwrk. used as workspace.
+c   kwrk  : integer, specifying the dimension of iwrk. kwrk >= mu+mv.
+c
+c  output parameters:
+c   f     : real array of dimension (mf).
+c           on succesful exit f(mu*mv*(l-1)+mv*(i-1)+j) contains the
+c           l-th co-ordinate of the bicubic spline surface at the
+c           point (u(i),v(j)),l=1,...,idim,i=1,...,mu;j=1,...,mv.
+c   ier   : integer error flag
+c    ier=0 : normal return
+c    ier=10: invalid input data (see restrictions)
+c
+c  restrictions:
+c   mu >=1, mv >=1, lwrk>=4*(mu+mv), kwrk>=mu+mv , mf>=mu*mv*idim
+c   tu(4) <= u(i-1) <= u(i) <= tu(nu-3), i=2,...,mu
+c   tv(4) <= v(j-1) <= v(j) <= tv(nv-3), j=2,...,mv
+c
+c  other subroutines required:
+c    fpsuev,fpbspl
+c
+c  references :
+c    de boor c : on calculating with b-splines, j. approximation theory
+c                6 (1972) 50-62.
+c    cox m.g.  : the numerical evaluation of b-splines, j. inst. maths
+c                applics 10 (1972) 134-149.
+c    dierckx p. : curve and surface fitting with splines, monographs on
+c                 numerical analysis, oxford university press, 1993.
+c
+c  author :
+c    p.dierckx
+c    dept. computer science, k.u.leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  latest update : march 1987
+c
+c  ..scalar arguments..
+      integer idim,nu,nv,mu,mv,mf,lwrk,kwrk,ier
+c  ..array arguments..
+      integer iwrk(kwrk)
+      real*8 tu(nu),tv(nv),c((nu-4)*(nv-4)*idim),u(mu),v(mv),f(mf),
+     * wrk(lwrk)
+c  ..local scalars..
+      integer i,muv
+c  ..
+c  before starting computations a data check is made. if the input data
+c  are invalid control is immediately repassed to the calling program.
+      ier = 10
+      if(mf.lt.mu*mv*idim) go to 100
+      muv = mu+mv
+      if(lwrk.lt.4*muv) go to 100
+      if(kwrk.lt.muv) go to 100
+      if (mu.lt.1) go to 100
+      if (mu.eq.1) go to 30
+      go to 10
+  10  do 20 i=2,mu
+        if(u(i).lt.u(i-1)) go to 100
+  20  continue
+  30  if (mv.lt.1) go to 100
+      if (mv.eq.1) go to 60
+      go to 40
+  40  do 50 i=2,mv
+        if(v(i).lt.v(i-1)) go to 100
+  50  continue
+  60  ier = 0
+      call fpsuev(idim,tu,nu,tv,nv,c,u,mu,v,mv,f,wrk(1),wrk(4*mu+1),
+     * iwrk(1),iwrk(mu+1))
+ 100  return
+      end

Added: branches/Interpolate1D/fitpack/surfit.f
===================================================================
--- branches/Interpolate1D/fitpack/surfit.f	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack/surfit.f	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,412 @@
+      subroutine surfit(iopt,m,x,y,z,w,xb,xe,yb,ye,kx,ky,s,nxest,nyest,
+     *  nmax,eps,nx,tx,ny,ty,c,fp,wrk1,lwrk1,wrk2,lwrk2,iwrk,kwrk,ier)
+c given the set of data points (x(i),y(i),z(i)) and the set of positive
+c numbers w(i),i=1,...,m, subroutine surfit determines a smooth bivar-
+c iate spline approximation s(x,y) of degrees kx and ky on the rect-
+c angle xb <= x <= xe, yb <= y <= ye.
+c if iopt = -1 surfit calculates the weighted least-squares spline
+c according to a given set of knots.
+c if iopt >= 0 the total numbers nx and ny of these knots and their
+c position tx(j),j=1,...,nx and ty(j),j=1,...,ny are chosen automatic-
+c ally by the routine. the smoothness of s(x,y) is then achieved by
+c minimalizing the discontinuity jumps in the derivatives of s(x,y)
+c across the boundaries of the subpanels (tx(i),tx(i+1))*(ty(j),ty(j+1).
+c the amounth of smoothness is determined by the condition that f(p) =
+c sum ((w(i)*(z(i)-s(x(i),y(i))))**2) be <= s, with s a given non-neg-
+c ative constant, called the smoothing factor.
+c the fit is given in the b-spline representation (b-spline coefficients
+c c((ny-ky-1)*(i-1)+j),i=1,...,nx-kx-1;j=1,...,ny-ky-1) and can be eval-
+c uated by means of subroutine bispev.
+c
+c calling sequence:
+c     call surfit(iopt,m,x,y,z,w,xb,xe,yb,ye,kx,ky,s,nxest,nyest,
+c    *  nmax,eps,nx,tx,ny,ty,c,fp,wrk1,lwrk1,wrk2,lwrk2,iwrk,kwrk,ier)
+c
+c parameters:
+c  iopt  : integer flag. on entry iopt must specify whether a weighted
+c          least-squares spline (iopt=-1) or a smoothing spline (iopt=0
+c          or 1) must be determined.
+c          if iopt=0 the routine will start with an initial set of knots
+c          tx(i)=xb,tx(i+kx+1)=xe,i=1,...,kx+1;ty(i)=yb,ty(i+ky+1)=ye,i=
+c          1,...,ky+1. if iopt=1 the routine will continue with the set
+c          of knots found at the last call of the routine.
+c          attention: a call with iopt=1 must always be immediately pre-
+c                     ceded by another call with iopt=1 or iopt=0.
+c          unchanged on exit.
+c  m     : integer. on entry m must specify the number of data points.
+c          m >= (kx+1)*(ky+1). unchanged on exit.
+c  x     : real array of dimension at least (m).
+c  y     : real array of dimension at least (m).
+c  z     : real array of dimension at least (m).
+c          before entry, x(i),y(i),z(i) must be set to the co-ordinates
+c          of the i-th data point, for i=1,...,m. the order of the data
+c          points is immaterial. unchanged on exit.
+c  w     : real array of dimension at least (m). before entry, w(i) must
+c          be set to the i-th value in the set of weights. the w(i) must
+c          be strictly positive. unchanged on exit.
+c  xb,xe : real values. on entry xb,xe,yb and ye must specify the bound-
+c  yb,ye   aries of the rectangular approximation domain.
+c          xb<=x(i)<=xe,yb<=y(i)<=ye,i=1,...,m. unchanged on exit.
+c  kx,ky : integer values. on entry kx and ky must specify the degrees
+c          of the spline. 1<=kx,ky<=5. it is recommended to use bicubic
+c          (kx=ky=3) splines. unchanged on exit.
+c  s     : real. on entry (in case iopt>=0) s must specify the smoothing
+c          factor. s >=0. unchanged on exit.
+c          for advice on the choice of s see further comments
+c  nxest : integer. unchanged on exit.
+c  nyest : integer. unchanged on exit.
+c          on entry, nxest and nyest must specify an upper bound for the
+c          number of knots required in the x- and y-directions respect.
+c          these numbers will also determine the storage space needed by
+c          the routine. nxest >= 2*(kx+1), nyest >= 2*(ky+1).
+c          in most practical situation nxest = kx+1+sqrt(m/2), nyest =
+c          ky+1+sqrt(m/2) will be sufficient. see also further comments.
+c  nmax  : integer. on entry nmax must specify the actual dimension of
+c          the arrays tx and ty. nmax >= nxest, nmax >=nyest.
+c          unchanged on exit.
+c  eps   : real.
+c          on entry, eps must specify a threshold for determining the
+c          effective rank of an over-determined linear system of equat-
+c          ions. 0 < eps < 1.  if the number of decimal digits in the
+c          computer representation of a real number is q, then 10**(-q)
+c          is a suitable value for eps in most practical applications.
+c          unchanged on exit.
+c  nx    : integer.
+c          unless ier=10 (in case iopt >=0), nx will contain the total
+c          number of knots with respect to the x-variable, of the spline
+c          approximation returned. if the computation mode iopt=1 is
+c          used, the value of nx should be left unchanged between sub-
+c          sequent calls.
+c          in case iopt=-1, the value of nx should be specified on entry
+c  tx    : real array of dimension nmax.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the x-variable, i.e. the position of
+c          the interior knots tx(kx+2),...,tx(nx-kx-1) as well as the
+c          position of the additional knots tx(1)=...=tx(kx+1)=xb and
+c          tx(nx-kx)=...=tx(nx)=xe needed for the b-spline representat.
+c          if the computation mode iopt=1 is used, the values of tx(1),
+c          ...,tx(nx) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values tx(kx+2),
+c          ...tx(nx-kx-1) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  ny    : integer.
+c          unless ier=10 (in case iopt >=0), ny will contain the total
+c          number of knots with respect to the y-variable, of the spline
+c          approximation returned. if the computation mode iopt=1 is
+c          used, the value of ny should be left unchanged between sub-
+c          sequent calls.
+c          in case iopt=-1, the value of ny should be specified on entry
+c  ty    : real array of dimension nmax.
+c          on succesful exit, this array will contain the knots of the
+c          spline with respect to the y-variable, i.e. the position of
+c          the interior knots ty(ky+2),...,ty(ny-ky-1) as well as the
+c          position of the additional knots ty(1)=...=ty(ky+1)=yb and
+c          ty(ny-ky)=...=ty(ny)=ye needed for the b-spline representat.
+c          if the computation mode iopt=1 is used, the values of ty(1),
+c          ...,ty(ny) should be left unchanged between subsequent calls.
+c          if the computation mode iopt=-1 is used, the values ty(ky+2),
+c          ...ty(ny-ky-1) must be supplied by the user, before entry.
+c          see also the restrictions (ier=10).
+c  c     : real array of dimension at least (nxest-kx-1)*(nyest-ky-1).
+c          on succesful exit, c contains the coefficients of the spline
+c          approximation s(x,y)
+c  fp    : real. unless ier=10, fp contains the weighted sum of
+c          squared residuals of the spline approximation returned.
+c  wrk1  : real array of dimension (lwrk1). used as workspace.
+c          if the computation mode iopt=1 is used the value of wrk1(1)
+c          should be left unchanged between subsequent calls.
+c          on exit wrk1(2),wrk1(3),...,wrk1(1+(nx-kx-1)*(ny-ky-1)) will
+c          contain the values d(i)/max(d(i)),i=1,...,(nx-kx-1)*(ny-ky-1)
+c          with d(i) the i-th diagonal element of the reduced triangular
+c          matrix for calculating the b-spline coefficients. it includes
+c          those elements whose square is less than eps,which are treat-
+c          ed as 0 in the case of presumed rank deficiency (ier<-2).
+c  lwrk1 : integer. on entry lwrk1 must specify the actual dimension of
+c          the array wrk1 as declared in the calling (sub)program.
+c          lwrk1 must not be too small. let
+c            u = nxest-kx-1, v = nyest-ky-1, km = max(kx,ky)+1,
+c            ne = max(nxest,nyest), bx = kx*v+ky+1, by = ky*u+kx+1,
+c            if(bx.le.by) b1 = bx, b2 = b1+v-ky
+c            if(bx.gt.by) b1 = by, b2 = b1+u-kx  then
+c          lwrk1 >= u*v*(2+b1+b2)+2*(u+v+km*(m+ne)+ne-kx-ky)+b2+1
+c  wrk2  : real array of dimension (lwrk2). used as workspace, but
+c          only in the case a rank deficient system is encountered.
+c  lwrk2 : integer. on entry lwrk2 must specify the actual dimension of
+c          the array wrk2 as declared in the calling (sub)program.
+c          lwrk2 > 0 . a save upper boundfor lwrk2 = u*v*(b2+1)+b2
+c          where u,v and b2 are as above. if there are enough data
+c          points, scattered uniformly over the approximation domain
+c          and if the smoothing factor s is not too small, there is a
+c          good chance that this extra workspace is not needed. a lot
+c          of memory might therefore be saved by setting lwrk2=1.
+c          (see also ier > 10)
+c  iwrk  : integer array of dimension (kwrk). used as workspace.
+c  kwrk  : integer. on entry kwrk must specify the actual dimension of
+c          the array iwrk as declared in the calling (sub)program.
+c          kwrk >= m+(nxest-2*kx-1)*(nyest-2*ky-1).
+c  ier   : integer. unless the routine detects an error, ier contains a
+c          non-positive value on exit, i.e.
+c   ier=0  : normal return. the spline returned has a residual sum of
+c            squares fp such that abs(fp-s)/s <= tol with tol a relat-
+c            ive tolerance set to 0.001 by the program.
+c   ier=-1 : normal return. the spline returned is an interpolating
+c            spline (fp=0).
+c   ier=-2 : normal return. the spline returned is the weighted least-
+c            squares polynomial of degrees kx and ky. in this extreme
+c            case fp gives the upper bound for the smoothing factor s.
+c   ier<-2 : warning. the coefficients of the spline returned have been
+c            computed as the minimal norm least-squares solution of a
+c            (numerically) rank deficient system. (-ier) gives the rank.
+c            especially if the rank deficiency which can be computed as
+c            (nx-kx-1)*(ny-ky-1)+ier, is large the results may be inac-
+c            curate. they could also seriously depend on the value of
+c            eps.
+c   ier=1  : error. the required storage space exceeds the available
+c            storage space, as specified by the parameters nxest and
+c            nyest.
+c            probably causes : nxest or nyest too small. if these param-
+c            eters are already large, it may also indicate that s is
+c            too small
+c            the approximation returned is the weighted least-squares
+c            spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=2  : error. a theoretically impossible result was found during
+c            the iteration proces for finding a smoothing spline with
+c            fp = s. probably causes : s too small or badly chosen eps.
+c            there is an approximation returned but the corresponding
+c            weighted sum of squared residuals does not satisfy the
+c            condition abs(fp-s)/s < tol.
+c   ier=3  : error. the maximal number of iterations maxit (set to 20
+c            by the program) allowed for finding a smoothing spline
+c            with fp=s has been reached. probably causes : s too small
+c            there is an approximation returned but the corresponding
+c            weighted sum of squared residuals does not satisfy the
+c            condition abs(fp-s)/s < tol.
+c   ier=4  : error. no more knots can be added because the number of
+c            b-spline coefficients (nx-kx-1)*(ny-ky-1) already exceeds
+c            the number of data points m.
+c            probably causes : either s or m too small.
+c            the approximation returned is the weighted least-squares
+c            spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=5  : error. no more knots can be added because the additional
+c            knot would (quasi) coincide with an old one.
+c            probably causes : s too small or too large a weight to an
+c            inaccurate data point.
+c            the approximation returned is the weighted least-squares
+c            spline according to the current set of knots.
+c            the parameter fp gives the corresponding weighted sum of
+c            squared residuals (fp>s).
+c   ier=10 : error. on entry, the input data are controlled on validity
+c            the following restrictions must be satisfied.
+c            -1<=iopt<=1, 1<=kx,ky<=5, m>=(kx+1)*(ky+1), nxest>=2*kx+2,
+c            nyest>=2*ky+2, 0<eps<1, nmax>=nxest, nmax>=nyest,
+c            xb<=x(i)<=xe, yb<=y(i)<=ye, w(i)>0, i=1,...,m
+c            lwrk1 >= u*v*(2+b1+b2)+2*(u+v+km*(m+ne)+ne-kx-ky)+b2+1
+c            kwrk >= m+(nxest-2*kx-1)*(nyest-2*ky-1)
+c            if iopt=-1: 2*kx+2<=nx<=nxest
+c                        xb<tx(kx+2)<tx(kx+3)<...<tx(nx-kx-1)<xe
+c                        2*ky+2<=ny<=nyest
+c                        yb<ty(ky+2)<ty(ky+3)<...<ty(ny-ky-1)<ye
+c            if iopt>=0: s>=0
+c            if one of these conditions is found to be violated,control
+c            is immediately repassed to the calling program. in that
+c            case there is no approximation returned.
+c   ier>10 : error. lwrk2 is too small, i.e. there is not enough work-
+c            space for computing the minimal least-squares solution of
+c            a rank deficient system of linear equations. ier gives the
+c            requested value for lwrk2. there is no approximation re-
+c            turned but, having saved the information contained in nx,
+c            ny,tx,ty,wrk1, and having adjusted the value of lwrk2 and
+c            the dimension of the array wrk2 accordingly, the user can
+c            continue at the point the program was left, by calling
+c            surfit with iopt=1.
+c
+c further comments:
+c  by means of the parameter s, the user can control the tradeoff
+c   between closeness of fit and smoothness of fit of the approximation.
+c   if s is too large, the spline will be too smooth and signal will be
+c   lost ; if s is too small the spline will pick up too much noise. in
+c   the extreme cases the program will return an interpolating spline if
+c   s=0 and the weighted least-squares polynomial (degrees kx,ky)if s is
+c   very large. between these extremes, a properly chosen s will result
+c   in a good compromise between closeness of fit and smoothness of fit.
+c   to decide whether an approximation, corresponding to a certain s is
+c   satisfactory the user is highly recommended to inspect the fits
+c   graphically.
+c   recommended values for s depend on the weights w(i). if these are
+c   taken as 1/d(i) with d(i) an estimate of the standard deviation of
+c   z(i), a good s-value should be found in the range (m-sqrt(2*m),m+
+c   sqrt(2*m)). if nothing is known about the statistical error in z(i)
+c   each w(i) can be set equal to one and s determined by trial and
+c   error, taking account of the comments above. the best is then to
+c   start with a very large value of s ( to determine the least-squares
+c   polynomial and the corresponding upper bound fp0 for s) and then to
+c   progressively decrease the value of s ( say by a factor 10 in the
+c   beginning, i.e. s=fp0/10, fp0/100,...and more carefully as the
+c   approximation shows more detail) to obtain closer fits.
+c   to choose s very small is strongly discouraged. this considerably
+c   increases computation time and memory requirements. it may also
+c   cause rank-deficiency (ier<-2) and endager numerical stability.
+c   to economize the search for a good s-value the program provides with
+c   different modes of computation. at the first call of the routine, or
+c   whenever he wants to restart with the initial set of knots the user
+c   must set iopt=0.
+c   if iopt=1 the program will continue with the set of knots found at
+c   the last call of the routine. this will save a lot of computation
+c   time if surfit is called repeatedly for different values of s.
+c   the number of knots of the spline returned and their location will
+c   depend on the value of s and on the complexity of the shape of the
+c   function underlying the data. if the computation mode iopt=1
+c   is used, the knots returned may also depend on the s-values at
+c   previous calls (if these were smaller). therefore, if after a number
+c   of trials with different s-values and iopt=1, the user can finally
+c   accept a fit as satisfactory, it may be worthwhile for him to call
+c   surfit once more with the selected value for s but now with iopt=0.
+c   indeed, surfit may then return an approximation of the same quality
+c   of fit but with fewer knots and therefore better if data reduction
+c   is also an important objective for the user.
+c   the number of knots may also depend on the upper bounds nxest and
+c   nyest. indeed, if at a certain stage in surfit the number of knots
+c   in one direction (say nx) has reached the value of its upper bound
+c   (nxest), then from that moment on all subsequent knots are added
+c   in the other (y) direction. this may indicate that the value of
+c   nxest is too small. on the other hand, it gives the user the option
+c   of limiting the number of knots the routine locates in any direction
+c   for example, by setting nxest=2*kx+2 (the lowest allowable value for
+c   nxest), the user can indicate that he wants an approximation which
+c   is a simple polynomial of degree kx in the variable x.
+c
+c  other subroutines required:
+c    fpback,fpbspl,fpsurf,fpdisc,fpgivs,fprank,fprati,fprota,fporde
+c
+c  references:
+c   dierckx p. : an algorithm for surface fitting with spline functions
+c                ima j. numer. anal. 1 (1981) 267-283.
+c   dierckx p. : an algorithm for surface fitting with spline functions
+c                report tw50, dept. computer science,k.u.leuven, 1980.
+c   dierckx p. : curve and surface fitting with splines, monographs on
+c                numerical analysis, oxford university press, 1993.
+c
+c  author:
+c    p.dierckx
+c    dept. computer science, k.u. leuven
+c    celestijnenlaan 200a, b-3001 heverlee, belgium.
+c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
+c
+c  creation date : may 1979
+c  latest update : march 1987
+c
+c  ..
+c  ..scalar arguments..
+      real*8 xb,xe,yb,ye,s,eps,fp
+      integer iopt,m,kx,ky,nxest,nyest,nmax,nx,ny,lwrk1,lwrk2,kwrk,ier
+c  ..array arguments..
+      real*8 x(m),y(m),z(m),w(m),tx(nmax),ty(nmax),
+     * c((nxest-kx-1)*(nyest-ky-1)),wrk1(lwrk1),wrk2(lwrk2)
+      integer iwrk(kwrk)
+c  ..local scalars..
+      real*8 tol
+      integer i,ib1,ib3,jb1,ki,kmax,km1,km2,kn,kwest,kx1,ky1,la,lbx,
+     * lby,lco,lf,lff,lfp,lh,lq,lsx,lsy,lwest,maxit,ncest,nest,nek,
+     * nminx,nminy,nmx,nmy,nreg,nrint,nxk,nyk
+c  ..function references..
+      integer max0
+c  ..subroutine references..
+c    fpsurf
+c  ..
+c  we set up the parameters tol and maxit.
+      maxit = 20
+      tol = 0.1e-02
+c  before starting computations a data check is made. if the input data
+c  are invalid,control is immediately repassed to the calling program.
+      ier = 10
+      if(eps.le.0. .or. eps.ge.1.) go to 71
+      if(kx.le.0 .or. kx.gt.5) go to 71
+      kx1 = kx+1
+      if(ky.le.0 .or. ky.gt.5) go to 71
+      ky1 = ky+1
+      kmax = max0(kx,ky)
+      km1 = kmax+1
+      km2 = km1+1
+      if(iopt.lt.(-1) .or. iopt.gt.1) go to 71
+      if(m.lt.(kx1*ky1)) go to 71
+      nminx = 2*kx1
+      if(nxest.lt.nminx .or. nxest.gt.nmax) go to 71
+      nminy = 2*ky1
+      if(nyest.lt.nminy .or. nyest.gt.nmax) go to 71
+      nest = max0(nxest,nyest)
+      nxk = nxest-kx1
+      nyk = nyest-ky1
+      ncest = nxk*nyk
+      nmx = nxest-nminx+1
+      nmy = nyest-nminy+1
+      nrint = nmx+nmy
+      nreg = nmx*nmy
+      ib1 = kx*nyk+ky1
+      jb1 = ky*nxk+kx1
+      ib3 = kx1*nyk+1
+      if(ib1.le.jb1) go to 10
+      ib1 = jb1
+      ib3 = ky1*nxk+1
+  10  lwest = ncest*(2+ib1+ib3)+2*(nrint+nest*km2+m*km1)+ib3
+      kwest = m+nreg
+      if(lwrk1.lt.lwest .or. kwrk.lt.kwest) go to 71
+      if(xb.ge.xe .or. yb.ge.ye) go to 71
+      do 20 i=1,m
+        if(w(i).le.0.) go to 70
+        if(x(i).lt.xb .or. x(i).gt.xe) go to 71
+        if(y(i).lt.yb .or. y(i).gt.ye) go to 71
+  20  continue
+      if(iopt.ge.0) go to 50
+      if(nx.lt.nminx .or. nx.gt.nxest) go to 71
+      nxk = nx-kx1
+      tx(kx1) = xb
+      tx(nxk+1) = xe
+      do 30 i=kx1,nxk
+        if(tx(i+1).le.tx(i)) go to 72
+  30  continue
+      if(ny.lt.nminy .or. ny.gt.nyest) go to 71
+      nyk = ny-ky1
+      ty(ky1) = yb
+      ty(nyk+1) = ye
+      do 40 i=ky1,nyk
+        if(ty(i+1).le.ty(i)) go to 73
+  40  continue
+      go to 60
+  50  if(s.lt.0.) go to 71
+  60  ier = 0
+c  we partition the working space and determine the spline approximation
+      kn = 1
+      ki = kn+m
+      lq = 2
+      la = lq+ncest*ib3
+      lf = la+ncest*ib1
+      lff = lf+ncest
+      lfp = lff+ncest
+      lco = lfp+nrint
+      lh = lco+nrint
+      lbx = lh+ib3
+      nek = nest*km2
+      lby = lbx+nek
+      lsx = lby+nek
+      lsy = lsx+m*km1
+      call fpsurf(iopt,m,x,y,z,w,xb,xe,yb,ye,kx,ky,s,nxest,nyest,
+     * eps,tol,maxit,nest,km1,km2,ib1,ib3,ncest,nrint,nreg,nx,tx,
+     * ny,ty,c,fp,wrk1(1),wrk1(lfp),wrk1(lco),wrk1(lf),wrk1(lff),
+     * wrk1(la),wrk1(lq),wrk1(lbx),wrk1(lby),wrk1(lsx),wrk1(lsy),
+     * wrk1(lh),iwrk(ki),iwrk(kn),wrk2,lwrk2,ier)
+ 70   return
+ 71   print*,"iopt,kx,ky,m=",iopt,kx,ky,m
+      print*,"nxest,nyest,nmax=",nxest,nyest,nmax
+      print*,"lwrk1,lwrk2,kwrk=",lwrk1,lwrk2,kwrk
+      print*,"xb,xe,yb,ye=",xb,xe,yb,ye
+      print*,"eps,s",eps,s
+      return
+ 72   print*,"tx=",tx
+      return
+ 73   print*,"ty=",ty
+      return
+      end

Modified: branches/Interpolate1D/fitpack_wrapper.py
===================================================================
--- branches/Interpolate1D/fitpack_wrapper.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/fitpack_wrapper.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,13 +1,20 @@
-""" fit_helper.py
+"""
+This module is used for spline interpolation, and functions
+as a wrapper around the FITPACK Fortran interpolation
+package.  It is not intended to be directly accessed by
+the user, but rather through the class Interpolate1D.
 
-mimics the functionality of enthought.interpolate that is
-contained in the module fitting.py
+The code has been modified from an older version of
+scipy.interpolate, where it was directly called by the
+user.  As such, it includes functionality not available through
+Interpolate1D.  For this reason, users may wish to get
+under the hood.
 
 """
 
 import numpy as np
 
-import dfitpack #fixme: rename module fitpack_wrapper
+import dfitpack
 
 
 class Spline(object):
@@ -119,7 +126,7 @@
         if x is (partially) ordered.
         
         """
-        print 'length of x: ', len(x)
+        
         if len(x) == 0: return np.array([]) #hack to cope with shape (0,)
         if nu is None:
             return dfitpack.splev(*(self._eval_args+(x,)))
@@ -190,13 +197,16 @@
         T1 = time.clock()
         interp_func = Spline(x, y, k=1)
         T2 = time.clock()
-        print 'time to create linear interp function: ', T2 - T1
+        print "time to create order 1 spline interpolation function with N = %i:" % N, T2 - T1
         new_x = np.arange(N)+0.5
         t1 = time.clock()
         new_y = interp_func(new_x)
         t2 = time.clock()
-        print '1d interp (sec):', t2 - t1
+        print "time for order 1 spline interpolation with N = %i:" % N, t2 - t1
         self.assertAllclose(new_y[:5], [0.5, 1.5, 2.5, 3.5, 4.5])
+    
+    def runTest(self):
+        self.test_linearSpl()
                              
 if __name__ == '__main__':
     unittest.main()

Deleted: branches/Interpolate1D/fitpack_wrapper.pyc
===================================================================
(Binary files differ)

Deleted: branches/Interpolate1D/info_fit.py
===================================================================
--- branches/Interpolate1D/info_fit.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/info_fit.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,12 +0,0 @@
-"""
-Interpolation Tools
-===================
-
-Primary interpolation agent:
-
-    Interpolate1D  --  callable class, initialized with x and y to interpolate
-                            from and indicator of how to deal with 
-                            extrapolation
-"""
-
-postpone_import = 1

Modified: branches/Interpolate1D/interpolate_wrapper.py
===================================================================
--- branches/Interpolate1D/interpolate_wrapper.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/interpolate_wrapper.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,12 +1,12 @@
 """ helper_funcs.py
 """
 
-import numpy
-import sys; sys.path.append('C:\home\python\branches\interpolate2\entinterp')
+import numpy as np
+import sys
 import _interpolate
 
-def make_array_safe(ary, typecode = numpy.float64):
-    ary = numpy.atleast_1d(numpy.asarray(ary, typecode))
+def make_array_safe(ary, typecode = np.float64):
+    ary = np.atleast_1d(np.asarray(ary, typecode))
     if not ary.flags['CONTIGUOUS']:
         ary = ary.copy()
     return ary
@@ -24,17 +24,17 @@
         new_x
             1-D array
     """
-    x = make_array_safe(x, numpy.float64)
-    y = make_array_safe(y, numpy.float64)
-    new_x = make_array_safe(new_x, numpy.float64)
+    x = make_array_safe(x, np.float64)
+    y = make_array_safe(y, np.float64)
+    new_x = make_array_safe(new_x, np.float64)
 
     assert len(y.shape) < 3, "function only works with 1D or 2D arrays"
     if len(y.shape) == 2:
-        new_y = numpy.zeros((y.shape[0], len(new_x)), numpy.float64)
+        new_y = np.zeros((y.shape[0], len(new_x)), np.float64)
         for i in range(len(new_y)):
             _interpolate.linear_dddd(x, y[i], new_x, new_y[i])
     else:
-        new_y = numpy.zeros(len(new_x), numpy.float64)
+        new_y = np.zeros(len(new_x), np.float64)
         _interpolate.linear_dddd(x, y, new_x, new_y)
 
     return new_y
@@ -51,17 +51,17 @@
         new_x
             1-D array
     """
-    x = make_array_safe(x, numpy.float64)
-    y = make_array_safe(y, numpy.float64)
-    new_x = make_array_safe(new_x, numpy.float64)
+    x = make_array_safe(x, np.float64)
+    y = make_array_safe(y, np.float64)
+    new_x = make_array_safe(new_x, np.float64)
 
     assert len(y.shape) < 3, "function only works with 1D or 2D arrays"
     if len(y.shape) == 2:
-        new_y = numpy.zeros((y.shape[0], len(new_x)), numpy.float64)
+        new_y = np.zeros((y.shape[0], len(new_x)), np.float64)
         for i in range(len(new_y)):
             _interpolate.loginterp_dddd(x, y[i], new_x, new_y[i])
     else:
-        new_y = numpy.zeros(len(new_x), numpy.float64)
+        new_y = np.zeros(len(new_x), np.float64)
         _interpolate.loginterp_dddd(x, y, new_x, new_y)
 
     return new_y
@@ -79,20 +79,20 @@
             1-D array
     """
     bad_index = None
-    x = make_array_safe(x, numpy.float64)
-    y = make_array_safe(y, numpy.float64)
-    new_x = make_array_safe(new_x, numpy.float64)
+    x = make_array_safe(x, np.float64)
+    y = make_array_safe(y, np.float64)
+    new_x = make_array_safe(new_x, np.float64)
 
     assert len(y.shape) < 3, "function only works with 1D or 2D arrays"
     if len(y.shape) == 2:
-        new_y = numpy.zeros((y.shape[0], len(new_x)), numpy.float64)
+        new_y = np.zeros((y.shape[0], len(new_x)), np.float64)
         for i in range(len(new_y)):
             bad_index = _interpolate.block_averave_above_dddd(x, y[i], 
                                                             new_x, new_y[i])
             if bad_index is not None:
                 break                                                
     else:
-        new_y = numpy.zeros(len(new_x), numpy.float64)
+        new_y = np.zeros(len(new_x), np.float64)
         bad_index = _interpolate.block_average_above_dddd(x, y, new_x, new_y)
 
     if bad_index is not None:
@@ -111,13 +111,13 @@
         # This code is a little strange -- we really want a routine that
         # returns the index of values where x[j] < x[index]
         TINY = 1e-10
-        indices = numpy.searchsorted(x, new_x+TINY)-1
+        indices = np.searchsorted(x, new_x+TINY)-1
 
         # If the value is at the front of the list, it'll have -1.
         # In this case, we will use the first (0), element in the array.
         # take requires the index array to be an Int
-        indices = numpy.atleast_1d(numpy.clip(indices, 0, numpy.Inf).astype(numpy.int))
-        new_y = numpy.take(y, indices, axis=-1)
+        indices = np.atleast_1d(np.clip(indices, 0, np.Inf).astype(np.int))
+        new_y = np.take(y, indices, axis=-1)
         return new_y
 def test_helper():
     """ use numpy.allclose to test
@@ -125,78 +125,24 @@
     
     print "now testing accuracy of interpolation of linear data"
     
-    x = numpy.arange(10.)
+    x = np.arange(10.)
     y = 2.0*x
-    c = numpy.array([-1.0, 2.3, 10.5])
+    c = np.array([-1.0, 2.3, 10.5])
     
-    assert numpy.allclose( linear(x, y, c) , [-2.0, 4.6, 21.0] ), "problem in linear"
-    assert numpy.allclose( logarithmic(x, y, c) , [0. , 4.51738774 , 21.47836848] ), \
+    assert np.allclose( linear(x, y, c) , [-2.0, 4.6, 21.0] ), "problem in linear"
+    assert np.allclose( logarithmic(x, y, c) , [0. , 4.51738774 , 21.47836848] ), \
                     "problem with logarithmic"
-    assert numpy.allclose( block_average_above(x, y, c) , [0., 2., 4.] ), \
+    assert np.allclose( block_average_above(x, y, c) , [0., 2., 4.] ), \
                     "problem with block_average_above"
 
-def compare_runtimes():
-    from scipy import arange, ones
-    import time
-    
-    # basic linear interp
-    N = 3000.
-    x = arange(N)
-    y = arange(N)
-    new_x = arange(N)+0.5
-    t1 = time.clock()
-    new_y = linear(x, y, new_x)
-    t2 = time.clock()
-    print '1d interp (sec):', t2 - t1
-    print new_y[:5]
 
-    # basic block_average_above
-    N = 3000.
-    x = arange(N)
-    y = arange(N)
-    new_x = arange(N/2)*2
-    t1 = time.clock()
-    new_y = block_average_above(x, y, new_x)
-    t2 = time.clock()
-    print '1d block_average_above (sec):', t2 - t1
-    print new_y[:5]
-    
-    # y linear with y having multiple params
-    N = 3000.
-    x = arange(N)
-    y = ones((100,N)) * arange(N)
-    new_x = arange(N)+0.5
-    t1 = time.clock()
-    new_y = linear(x, y, new_x)
-    t2 = time.clock()
-    print 'fast interpolate (sec):', t2 - t1
-    print new_y[:5,:5]
-
-    # scipy with multiple params
-    import scipy
-    N = 3000.
-    x = arange(N)
-    y = ones((100, N)) * arange(N)
-    new_x = arange(N)
-    t1 = time.clock()
-    interp = scipy.interpolate.interp1d(x, y)
-    new_y = interp(new_x)
-    t2 = time.clock()
-    print 'scipy interp1d (sec):', t2 - t1
-    print new_y[:5,:5]
-
-
-# Below is stuff from scipy.interpolate and fitpack
-
 # Unit Test
 import unittest
 import time
 from numpy import arange, allclose, ones, NaN, isnan
 class Test(unittest.TestCase):
     
-    #def assertAllclose(self, x, y, rtol = 1.0e-5):
-      #  self.assert_(numpy.allclose(x, y, rtol = rtol))
-     
+    
     def assertAllclose(self, x, y, rtol=1.0e-5):
         for i, xi in enumerate(x):
             self.assert_(allclose(xi, y[i], rtol) or (isnan(xi) and isnan(y[i])))
@@ -209,7 +155,7 @@
         t1 = time.clock()
         new_y = linear(x, y, new_x)
         t2 = time.clock()
-        print '1d interp (sec):', t2 - t1
+        print "time for linear interpolation with N = %i:" % N, t2 - t1
         
         self.assertAllclose(new_y[:5], [0.5, 1.5, 2.5, 3.5, 4.5])
         
@@ -222,7 +168,7 @@
         t1 = time.clock()
         new_y = block_average_above(x, y, new_x)
         t2 = time.clock()
-        print '1d block_average_above (sec):', t2 - t1
+        print "time for block_avg_above interpolation with N = %i:" % N, t2 - t1
         self.assertAllclose(new_y[:5], [0.0, 0.5, 2.5, 4.5, 6.5])
 
     def test_linear2(self):
@@ -233,7 +179,7 @@
         t1 = time.clock()
         new_y = linear(x, y, new_x)
         t2 = time.clock()
-        print 'fast interpolate (sec):', t2 - t1
+        print "time for 2D linear interpolation with N = %i:" % N, t2 - t1
         self.assertAllclose(new_y[:5,:5],
                             [[ 0.5, 1.5, 2.5, 3.5, 4.5],
                              [ 0.5, 1.5, 2.5, 3.5, 4.5],
@@ -249,11 +195,16 @@
         t1 = time.clock()
         new_y = logarithmic(x, y, new_x)
         t2 = time.clock()
-        print 'logarithmic interp (sec):', t2 - t1
-        correct_y = [numpy.NaN, 1.41421356, 2.44948974, 3.46410162, 4.47213595]
+        print "time for logarithmic interpolation with N = %i:" % N, t2 - t1
+        correct_y = [np.NaN, 1.41421356, 2.44948974, 3.46410162, 4.47213595]
         self.assertAllclose(new_y[:5], correct_y)
-        print "logo"
         
+    def runTest(self):
+        self.test_linear()
+        self.test_block_average_above()
+        self.test_linear2()
+        self.test_logarithmic()
+    
 if __name__ == '__main__':
     unittest.main()
     
\ No newline at end of file

Deleted: branches/Interpolate1D/interpolate_wrapper.pyc
===================================================================
(Binary files differ)

Added: branches/Interpolate1D/multipack.h
===================================================================
--- branches/Interpolate1D/multipack.h	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/multipack.h	2008-07-18 19:44:12 UTC (rev 4550)
@@ -0,0 +1,211 @@
+/* MULTIPACK module by Travis Oliphant
+
+Copyright (c) 2002 Travis Oliphant all rights reserved
+Oliphant.Travis@altavista.net
+Permission to use, modify, and distribute this software is given under the 
+terms of the SciPy (BSD style) license.  See LICENSE.txt that came with
+this distribution for specifics.
+
+NO WARRANTY IS EXPRESSED OR IMPLIED.  USE AT YOUR OWN RISK.
+*/
+
+
+/* This extension module is a collection of wrapper functions around
+common FORTRAN code in the packages MINPACK, ODEPACK, and QUADPACK plus
+some differential algebraic equation solvers.
+
+The wrappers are meant to be nearly direct translations between the
+FORTAN code and Python.  Some parameters like sizes do not need to be 
+passed since they are available from the objects.  
+
+It is anticipated that a pure Python module be written to call these lower
+level routines and make a simpler user interface.  All of the routines define
+default values for little-used parameters so that even the raw routines are
+quite useful without a separate wrapper. 
+
+FORTRAN Outputs that are not either an error indicator or the sought-after
+results are placed in a dictionary and returned as an optional member of
+the result tuple when the full_output argument is non-zero.
+*/
+
+#include "Python.h"
+#include "numpy/arrayobject.h"
+
+#define PYERR(errobj,message) {PyErr_SetString(errobj,message); goto fail;}
+#define PYERR2(errobj,message) {PyErr_Print(); PyErr_SetString(errobj, message); goto fail;}
+#define ISCONTIGUOUS(m) ((m)->flags & CONTIGUOUS)
+
+#define STORE_VARS() PyObject *store_multipack_globals[4]; int store_multipack_globals3;
+
+#define INIT_FUNC(fun,arg,errobj) { /* Get extra arguments or set to zero length tuple */ \
+  store_multipack_globals[0] = multipack_python_function; \
+  store_multipack_globals[1] = multipack_extra_arguments; \
+  if (arg == NULL) { \
+    if ((arg = PyTuple_New(0)) == NULL) goto fail; \
+  } \
+  else \
+    Py_INCREF(arg);   /* We decrement on exit. */ \
+  if (!PyTuple_Check(arg))  \
+    PYERR(errobj,"Extra Arguments must be in a tuple"); \
+  /* Set up callback functions */ \
+  if (!PyCallable_Check(fun)) \
+    PYERR(errobj,"First argument must be a callable function."); \
+  multipack_python_function = fun; \
+  multipack_extra_arguments = arg; }
+
+#define INIT_JAC_FUNC(fun,Dfun,arg,col_deriv,errobj) { \
+  store_multipack_globals[0] = multipack_python_function; \
+  store_multipack_globals[1] = multipack_extra_arguments; \
+  store_multipack_globals[2] = multipack_python_jacobian; \
+  store_multipack_globals3 = multipack_jac_transpose; \
+  if (arg == NULL) { \
+    if ((arg = PyTuple_New(0)) == NULL) goto fail; \
+  } \
+  else \
+    Py_INCREF(arg);   /* We decrement on exit. */ \
+  if (!PyTuple_Check(arg))  \
+    PYERR(errobj,"Extra Arguments must be in a tuple"); \
+  /* Set up callback functions */ \
+  if (!PyCallable_Check(fun) || (Dfun != Py_None && !PyCallable_Check(Dfun))) \
+    PYERR(errobj,"The function and its Jacobian must be callable functions."); \
+  multipack_python_function = fun; \
+  multipack_extra_arguments = arg; \
+  multipack_python_jacobian = Dfun; \
+  multipack_jac_transpose = !(col_deriv);}
+
+#define RESTORE_JAC_FUNC() multipack_python_function = store_multipack_globals[0]; \
+  multipack_extra_arguments = store_multipack_globals[1]; \
+  multipack_python_jacobian = store_multipack_globals[2]; \
+  multipack_jac_transpose = store_multipack_globals3;
+
+#define RESTORE_FUNC() multipack_python_function = store_multipack_globals[0]; \
+  multipack_extra_arguments = store_multipack_globals[1];
+
+#define SET_DIAG(ap_diag,o_diag,mode) { /* Set the diag vector from input */ \
+  if (o_diag == NULL || o_diag == Py_None) { \
+    ap_diag = (PyArrayObject *)PyArray_FromDims(1,&n,PyArray_DOUBLE); \
+    if (ap_diag == NULL) goto fail; \
+    diag = (double *)ap_diag -> data; \
+    mode = 1; \
+  } \
+  else { \
+    ap_diag = (PyArrayObject *)PyArray_ContiguousFromObject(o_diag, PyArray_DOUBLE, 1, 1); \
+    if (ap_diag == NULL) goto fail; \
+    diag = (double *)ap_diag -> data; \
+    mode = 2; } }
+
+#define MATRIXC2F(jac,data,n,m) {double *p1=(double *)(jac), *p2, *p3=(double *)(data);\
+int i,j;\
+for (j=0;j<(m);p3++,j++) \
+  for (p2=p3,i=0;i<(n);p2+=(m),i++,p1++) \
+    *p1 = *p2; }
+/*
+static PyObject *multipack_python_function=NULL;
+static PyObject *multipack_python_jacobian=NULL;
+static PyObject *multipack_extra_arguments=NULL;
+static int multipack_jac_transpose=1;
+*/
+
+static PyArrayObject * my_make_numpy_array(PyObject *y0, int type, int mindim, int maxdim)
+     /* This is just like PyArray_ContiguousFromObject except it handles
+      * single numeric datatypes as 1-element, rank-1 arrays instead of as
+      * scalars.
+      */
+{
+  PyArrayObject *new_array;
+  PyObject *tmpobj;
+
+  Py_INCREF(y0);
+
+  if (PyInt_Check(y0) || PyFloat_Check(y0)) {
+    tmpobj = PyList_New(1);
+    PyList_SET_ITEM(tmpobj, 0, y0);   /* reference now belongs to tmpobj */
+  }
+  else
+    tmpobj = y0;
+  
+  new_array = (PyArrayObject *)PyArray_ContiguousFromObject(tmpobj, type, mindim, maxdim);
+  
+  Py_DECREF(tmpobj);
+  return new_array;
+}
+
+static PyObject *call_python_function(PyObject *func, int n, double *x, PyObject *args, int dim, PyObject *error_obj)
+{
+  /*
+    This is a generic function to call a python function that takes a 1-D
+    sequence as a first argument and optional extra_arguments (should be a
+    zero-length tuple if none desired).  The result of the function is 
+    returned in a multiarray object.
+        -- build sequence object from values in x.
+	-- add extra arguments (if any) to an argument list.
+	-- call Python callable object
+ 	-- check if error occurred:
+	         if so return NULL
+	-- if no error, place result of Python code into multiarray object.
+  */
+
+  PyArrayObject *sequence = NULL;
+  PyObject *arglist = NULL, *tmpobj = NULL;
+  PyObject *arg1 = NULL, *str1 = NULL;
+  PyObject *result = NULL;
+  PyArrayObject *result_array = NULL;
+
+  /* Build sequence argument from inputs */
+  sequence = (PyArrayObject *)PyArray_FromDimsAndData(1, &n, PyArray_DOUBLE, (char *)x);
+  if (sequence == NULL) PYERR2(error_obj,"Internal failure to make an array of doubles out of first\n                 argument to function call.");
+
+  /* Build argument list */
+  if ((arg1 = PyTuple_New(1)) == NULL) {
+    Py_DECREF(sequence);
+    return NULL;
+  }
+  PyTuple_SET_ITEM(arg1, 0, (PyObject *)sequence); 
+                /* arg1 now owns sequence reference */
+  if ((arglist = PySequence_Concat( arg1, args)) == NULL)
+    PYERR2(error_obj,"Internal error constructing argument list.");
+
+  Py_DECREF(arg1);    /* arglist has a reference to sequence, now. */
+    
+
+  /* Call function object --- variable passed to routine.  Extra
+          arguments are in another passed variable.
+   */
+  if ((result = PyEval_CallObject(func, arglist))==NULL) {
+    PyErr_Print();
+    tmpobj = PyObject_GetAttrString(func, "func_name");
+    if (tmpobj == NULL) goto fail;
+    str1 = PyString_FromString("Error occured while calling the Python function named ");
+    if (str1 == NULL) { Py_DECREF(tmpobj); goto fail;}
+    PyString_ConcatAndDel(&str1, tmpobj);
+    PyErr_SetString(error_obj, PyString_AsString(str1));
+    Py_DECREF(str1);
+    goto fail;
+  }
+
+  if ((result_array = (PyArrayObject *)PyArray_ContiguousFromObject(result, PyArray_DOUBLE, dim-1, dim))==NULL) 
+    PYERR2(error_obj,"Result from function call is not a proper array of floats.");
+
+  Py_DECREF(result);
+  Py_DECREF(arglist);
+  return (PyObject *)result_array;
+
+ fail:
+  Py_XDECREF(arglist);
+  Py_XDECREF(result);
+  Py_XDECREF(arg1);
+  return NULL;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+

Modified: branches/Interpolate1D/setup.py
===================================================================
--- branches/Interpolate1D/setup.py	2008-07-18 13:19:37 UTC (rev 4549)
+++ branches/Interpolate1D/setup.py	2008-07-18 19:44:12 UTC (rev 4550)
@@ -1,24 +1,30 @@
 #!/usr/bin/env python
 
+import os
 from os.path import join
 
 def configuration(parent_package='',top_path=None):
     from numpy.distutils.misc_util import Configuration
 
-    config = Configuration('', parent_package, top_path)
+    config = Configuration('', parent_package, top_path) #first arg was 'interpolate'
 
+
     config.add_extension('_interpolate',
                          ['_interpolate.cpp'],
                          include_dirs = ['.'],
                          depends = ['interpolate.h'])
 
+    config.add_library('fitpack',
+                       sources=[join('fitpack', '*.f')],
+                      )
+
     config.add_extension('dfitpack',
                          sources=['fitpack.pyf'],
                          libraries=['fitpack'],
                         )
-                        
+
     return config
 
 if __name__ == '__main__':
     from numpy.distutils.core import setup
-    setup(**configuration(top_path='').todict() )
\ No newline at end of file
+    setup(**configuration().todict())
\ No newline at end of file



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