[Scipy-svn] r4594 - branches/Interpolate1D
scipy-svn@scip...
scipy-svn@scip...
Fri Aug 1 16:48:33 CDT 2008
Author: fcady
Date: 2008-08-01 16:48:32 -0500 (Fri, 01 Aug 2008)
New Revision: 4594
Added:
branches/Interpolate1D/fitpack_wrapper2d.py
Log:
forgot to add new fitpack wrapper
Added: branches/Interpolate1D/fitpack_wrapper2d.py
===================================================================
--- branches/Interpolate1D/fitpack_wrapper2d.py 2008-08-01 21:47:36 UTC (rev 4593)
+++ branches/Interpolate1D/fitpack_wrapper2d.py 2008-08-01 21:48:32 UTC (rev 4594)
@@ -0,0 +1,194 @@
+import warnings
+from numpy import zeros, concatenate, alltrue, ravel, all, diff
+import numpy as np
+
+import _dfitpack
+
+_surfit_messages = {1:"""
+ The required storage space exceeds the available storage space: nxest
+ or nyest too small, or s too small.
+ The weighted least-squares spline corresponds to the current set of
+ knots.""",
+ 2:"""
+ A theoretically impossible result was found during the iteration
+ process for finding a smoothing spline with fp = s: s too small or
+ badly chosen eps.
+ Weighted sum of squared residuals does not satisfy abs(fp-s)/s < tol.""",
+ 3:"""
+ the maximal number of iterations maxit (set to 20 by the program)
+ allowed for finding a smoothing spline with fp=s has been reached:
+ s too small.
+ Weighted sum of squared residuals does not satisfy abs(fp-s)/s < tol.""",
+ 4:"""
+ No more knots can be added because the number of b-spline coefficients
+ (nx-kx-1)*(ny-ky-1) already exceeds the number of data points m:
+ either s or m too small.
+ The weighted least-squares spline corresponds to the current set of
+ knots.""",
+ 5:"""
+ No more knots can be added because the additional knot would (quasi)
+ coincide with an old one: s too small or too large a weight to an
+ inaccurate data point.
+ The weighted least-squares spline corresponds to the current set of
+ knots.""",
+ 10:"""
+ Error on entry, no approximation returned. The following conditions
+ must hold:
+ xb<=x[i]<=xe, yb<=y[i]<=ye, w[i]>0, i=0..m-1
+ If iopt==-1, then
+ xb<tx[kx+1]<tx[kx+2]<...<tx[nx-kx-2]<xe
+ yb<ty[ky+1]<ty[ky+2]<...<ty[ny-ky-2]<ye""",
+ -3:"""
+ The coefficients of the spline returned have been computed as the
+ minimal norm least-squares solution of a (numerically) rank deficient
+ system (deficiency=%i). If deficiency is large, the results may be
+ inaccurate. Deficiency may strongly depend on the value of eps."""
+ }
+
+class Spline2d(object):
+ """ Bivariate spline s(x,y) of degrees kx and ky on the rectangle
+ [xb,xe] x [yb, ye] calculated from a given set of data points
+ (x,y,z).
+
+ See also:
+
+ bisplrep, bisplev - an older wrapping of FITPACK
+ UnivariateSpline - a similar class for univariate spline interpolation
+ SmoothUnivariateSpline - to create a BivariateSpline through the
+ given points
+ LSQUnivariateSpline - to create a BivariateSpline using weighted
+ least-squares fitting
+ """
+ def __init__(self, x=None, y=None, z=None, w=None, bbox=[None]*4, kx=3, ky=3, s=0.0, eps=None):
+ """
+ Input:
+ x,y,z - 1-d sequences of data points (order is not
+ important)
+ Optional input:
+ w - positive 1-d sequence of weights
+ bbox - 4-sequence specifying the boundary of
+ the rectangular approximation domain.
+ By default, bbox=[min(x,tx),max(x,tx),
+ min(y,ty),max(y,ty)]
+ kx,ky=3,3 - degrees of the bivariate spline.
+ s - positive smoothing factor defined for
+ estimation condition:
+ sum((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0) <= s
+ Default s=len(w) which should be a good value
+ if 1/w[i] is an estimate of the standard
+ deviation of z[i].
+ eps - a threshold for determining the effective rank
+ of an over-determined linear system of
+ equations. 0 < eps < 1, default is 1e-16.
+ """
+
+ self._w = w
+ self._bbox = bbox
+ self._kx = kx
+ self._ky = kx
+ self._s = s
+ self._eps = eps
+
+ if x is not None and y is not None and z is not None:
+ self.init_xyz(x, y, z)
+ self._is_initialized = True
+ else:
+ self._is_initialized = False
+
+ def init_xyz(self, x, y, z):
+ xb,xe,yb,ye = self._bbox
+ nx,tx,ny,ty,c,fp,wrk1,ier = _dfitpack.surfit_smth(x,y,z,
+ self._w,
+ xb, xe, yb, ye,
+ self._kx, self._ky,
+ s=self._s,
+ eps=self._eps, lwrk2=1)
+ if ier in [0,-1,-2]: # normal return
+ pass
+ else:
+ message = _surfit_messages.get(ier,'ier=%s' % (ier))
+ warnings.warn(message)
+
+ self.fp = fp
+ self.tck = tx[:nx],ty[:ny],c[:(nx-self._kx-1)*(ny-self._ky-1)]
+ self.degrees = self._kx,self._ky
+
+ self._is_initialized = True
+
+ def __call__(self, x, y):
+ """ Evaluate spline at positions x[i],y[i].
+ x and y should be 1d arrays.
+ """
+ # what happens when x contains duplicate values?
+
+ if self._is_initialized is not True:
+ raise Error, "x, y and z must be initialized before interpolating"
+
+ # sort only once for efficiency
+ sorted_x = sorted(x)
+ sorted_y = sorted(y)
+
+ data_grid = self.get_grid(sorted_x, sorted_y)
+
+ # fixme : no list comprehension
+ z = np.array([ data_grid[np.searchsorted(sorted(x), x[i]), np.searchsorted(sorted(y),y[i])] \
+ for i,xi in enumerate(x) ])
+
+ return z
+
+
+ def get_grid(self, x, y, mth='array'):
+ """ Evaluate spline at positions x[i],y[j]."""
+
+ if self._is_initialized is not True:
+ raise Error, "x, y and z must be initialized before interpolating"
+
+ if mth=='array':
+ tx,ty,c = self.tck[:3]
+ kx,ky = self.degrees
+ z,ier = _dfitpack.bispev(tx,ty,c,kx,ky,x,y)
+ assert ier==0,'Invalid input: ier='+`ier`
+ return z
+ raise NotImplementedError
+
+ def get_residual(self):
+ """ Return weighted sum of squared residuals of the spline
+ approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)
+ """
+ return self.fp
+ def get_knots(self):
+ """ Return a tuple (tx,ty) where tx,ty contain knots positions
+ of the spline with respect to x-, y-variable, respectively.
+ The position of interior and additional knots are given as
+ t[k+1:-k-1] and t[:k+1]=b, t[-k-1:]=e, respectively.
+ """
+ return self.tck[:2]
+ def get_coeffs(self):
+ """ Return spline coefficients."""
+ return self.tck[2]
+
+
+ def integral(self, xa, xb, ya, yb):
+ """
+ Evaluate the integral of the spline over area [xa,xb] x [ya,yb].
+
+ Parameters
+ ----------
+ xa, xb : float
+ The end-points of the x integration interval.
+ ya, yb : float
+ The end-points of the y integration interval.
+
+ Returns
+ -------
+ integ : float
+ The value of the resulting integral.
+
+ """
+ tx,ty,c = self.tck[:3]
+ kx,ky = self.degrees
+ return _dfitpack.dblint(tx,ty,c,kx,ky,xa,xb,ya,yb)
+
+# RectBivariateSpline in scipy.interpolate is for a rectangular grid and presumably must faster. There are 3 levels of niceness: scattered
+# data, irregular grid, and regular grids. Spline2d is for the first level and thus slow. ndimage is for the 3rd level and thus fast.
+# I vote to no explicitly treat the 3rd level, but RecBivariateSpline does that if we want to implement it in the future.
\ No newline at end of file
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