[Scipy-svn] r4567 - branches/Interpolate1D

scipy-svn@scip... scipy-svn@scip...
Mon Jul 28 16:16:41 CDT 2008


Author: fcady
Date: 2008-07-28 16:16:39 -0500 (Mon, 28 Jul 2008)
New Revision: 4567

Added:
   branches/Interpolate1D/interp1D.py
Removed:
   branches/Interpolate1D/interpolate1d.py
Log:
changed file name

Copied: branches/Interpolate1D/interp1D.py (from rev 4565, branches/Interpolate1D/interpolate1d.py)

Deleted: branches/Interpolate1D/interpolate1d.py
===================================================================
--- branches/Interpolate1D/interpolate1d.py	2008-07-28 20:55:35 UTC (rev 4566)
+++ branches/Interpolate1D/interpolate1d.py	2008-07-28 21:16:39 UTC (rev 4567)
@@ -1,484 +0,0 @@
-"""
-    Interpolation of 1D data
-
-    This module provides several functions and classes for interpolation
-    and extrapolation of 1D data (1D in both input and output).  The
-    primary function provided is:
-
-        interp1d(x, y, new_x) : from data points x and y, interpolates
-                                        values for points in new_x and
-                                        returns them as an array.
-
-    Classes provided include:
-
-        Interpolate1d  :   an object for interpolation of
-                                various kinds.  interp1d is a wrapper
-                                around this class.
-                                
-        Spline : an object for spline interpolation
-        
-    Functions provided include:
-
-        linear : linear interpolation
-        logarithmic :  logarithmic interpolation
-        block : block interpolation
-        block_average_above : block average above interpolation
-
-"""
-
-# FIXME: information strings giving mathematical descriptions of the actions
-#     of the functions.
-
-from interpolate_wrapper import linear, logarithmic, block, block_average_above
-from fitpack_wrapper import Spline
-import numpy as np
-from numpy import array, arange, empty, float64, NaN
-
-def make_array_safe(ary, typecode=np.float64):
-    """Used to make sure that inputs and outputs are
-    properly formatted.
-    """
-    ary = np.atleast_1d(np.asarray(ary, typecode))
-    if not ary.flags['CONTIGUOUS']:
-        ary = ary.copy()
-    return ary
-    
-def interp1d(x, y, new_x, kind='linear', low=np.NaN, high=np.NaN, \
-                    kindkw={}, lowkw={}, highkw={}, \
-                    remove_bad_data = False, bad_data=[], interp_axis = 0):
-    """ A function for interpolation of 1D data.
-        
-        Parameters
-        -----------
-            
-        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.  Note that y must be
-            one-dimensional.
-            
-        new_x -- list or NumPy array
-            points whose value is to be interpolated from x and y.
-            new_x must be in sorted order, lowest to highest.
-                
-        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.
-        
-        remove_bad_data -- bool
-            indicates whether to remove bad data.
-            
-        bad_data -- list
-            List of values (in x or y) which indicate unacceptable data. All points
-            that have x or y value in missing_data will be removed before
-            any interpolatin is performed if remove_bad_data is true.
-            
-            numpy.NaN is always considered bad data.
-            
-        Acceptable Input Strings
-        ------------------------
-        
-            "linear" -- linear interpolation : default
-            "logarithmic" -- logarithmic interpolation : linear in log space?
-            "block" --
-            "block_average_above' -- block average above
-            "Spline" -- spline interpolation.  keyword k (defaults to 3) 
-                indicates order of spline
-            numpy.NaN -- return numpy.NaN
-        
-        Examples
-        ---------
-        
-            >>> import numpy
-            >>> from Interpolate1D import interp1d
-            >>> x = range(5)        # note list is permitted
-            >>> y = numpy.arange(5.)
-            >>> new_x = [.2, 2.3, 5.6]
-            >>> interp1d(x, y, new_x)
-            array([.2, 2.3, 5.6, NaN])
-    """
-    return Interpolate1d(x, y, kind=kind, low=low, high=high, \
-                                    kindkw=kindkw, lowkw=lowkw, highkw=highkw, \
-                                    remove_bad_data = remove_bad_data, bad_data=bad_data)(new_x)
-
-class Interpolate1d(object):
-    """ A class for interpolation of 1D data.
-        
-        Parameters
-        -----------
-            
-        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.  Note that y must be
-            one-dimensional.
-                
-        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.
-            A constant signifies a function which returns that constant
-            (e.g. val and lambda x : val are equivalent).  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.
-        
-        remove_bad_data -- bool
-            indicates whether to remove bad data points from x and y.
-            
-        bad_data -- list
-            List of values (in x or y) which indicate unacceptable data. All points
-            that have x or y value in missing_data will be removed before
-            any interpolatin is performed if remove_bad_data is true.
-            
-            numpy.NaN is always considered bad data.
-            
-        Some Acceptable Input Strings
-        ------------------------
-        
-            "linear" -- linear interpolation : default
-            "logarithmic" -- logarithmic interpolation : linear in log space?
-            "block" --
-            "block_average_above' -- block average above
-            "Spline" -- spline interpolation.  keyword k (defaults to 3) 
-                indicates order of spline
-            numpy.NaN -- return numpy.NaN
-        
-        Examples
-        ---------
-        
-            >>> import numpy
-            >>> from Interpolate1D import interp1d
-            >>> x = range(5)        # note list is permitted
-            >>> y = numpy.arange(5.)
-            >>> new_x = [.2, 2.3, 5.6]
-            >>> interp1d(x, y, new_x)
-            array([.2, 2.3, 5.6, NaN])
-    """
-    # FIXME: more informative descriptions of sample arguments
-    # FIXME: examples in doc string
-    # FIXME : Allow copying or not of arrays.  non-copy + remove_bad_data should flash 
-    #           a warning (esp if we interpolate missing values), but work anyway.
-    
-    def __init__(self, x, y, kind='linear', low=np.NaN, high=np.NaN, \
-                        kindkw={}, lowkw={}, highkw={}, \
-                        remove_bad_data = False, bad_data=[]):
-        # FIXME: don't allow copying multiple times.
-        # FIXME : allow no copying, in case user has huge dataset
-        
-        # check acceptable size and dimensions
-        x = np.array(x)
-        y = np.array(y)
-        assert len(x) > 0 and len(y) > 0 , "Arrays cannot be of zero 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"
-        
-        # remove bad data, is there is any
-        if remove_bad_data:
-            x, y = self._remove_bad_data(x, y, bad_data)
-        
-        # store data
-        # FIXME : may be good to let x and y be initialized later, or changed after-the-fact
-        self._init_xy(x, y)
-        
-        # store interpolation functions for each range
-        self.kind = self._init_interp_method(kind, kindkw)
-        self.low = self._init_interp_method(low, lowkw)
-        self.high = self._init_interp_method(high, highkw)
-
-    def _remove_bad_data(self, x, y, bad_data = [None, np.NaN]):
-        """ removes data points whose x or y coordinate is
-            either in bad_data or is a NaN.
-        """
-        # FIXME : In the future, it may be good to just replace the bad points with good guesses.
-        #       Especially in generalizing the higher dimensions
-        # FIXME : This step is very inefficient because it iterates over the array
-        mask = np.array([  (xi not in bad_data) and (not np.isnan(xi)) and \
-                                    (y[i] not in bad_data) and (not np.isnan(y[i])) \
-                                for i, xi in enumerate(x) ])
-        x = x[mask]
-        y = y[mask]
-        return x, y
-    
-    def _init_xy(self, x, y):
-        # select proper dataypes and make arrays
-        self._xdtype = {np.float32 : np.float32}.setdefault(type(x[0]), np.float64) # unless data is float32,  cast to float64
-        self._ydtype = {np.float32 : np.float32}.setdefault(type(y[0]), np.float64)
-        self._x = make_array_safe(x, self._xdtype).copy()
-        self._y = make_array_safe(y, self._ydtype).copy()
-        
-    def _init_interp_method(self, interp_arg, kw):
-        """
-            User provides interp_arg and dictionary kw.  _init_interp_method
-            returns the interpolating function from x and y specified by interp_arg,
-            possibly with extra keyword arguments given in kw.
-        
-        """
-        # FIXME : error checking specific to interpolation method.  x and y long
-        #   enough for order-3 spline if that's indicated, etc.  Functions should throw
-        #   errors themselves, but errors at instantiation would be nice.
-        
-        from inspect import isclass, isfunction
-        
-        # primary usage : user passes a string indicating a known function
-        if interp_arg in ['linear', 'logarithmic', 'block', 'block_average_above']:
-            # string used to indicate interpolation method,  Select appropriate function
-            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, **kw)
-        elif interp_arg in ['Spline', Spline, 'spline']:
-            # use the Spline class from fitpack_wrapper
-            result = Spline(self._x, self._y, **kw)
-        elif interp_arg in ['cubic', 'Cubic', 'Quadratic', \
-                                'quadratic', 'Quad', 'quad', 'Quintic', 'quintic']:
-            # specify specific kinds of splines
-            if interp_arg in ['Quadratic', 'quadratic', 'Quad', 'quad']:
-                result = Spline(self._x, self._y, k=2)
-            elif interp_arg in ['cubic', 'Cubic']:
-                result = Spline(self._x, self._y, k=3)
-            elif interp_arg in ['Quintic', 'quintic']:
-                result = Spline(self._x, self._y, k=4)
-                
-        # secondary usage : user passes a callable class
-        elif isclass(interp_arg) and hasattr(interp_arg, '__call__'):
-            if hasattr(interp_arg, 'init_xy'):
-                result = interp_arg(**kw)
-                result.init_xy(self._x, self._y)
-            elif hasattr(interp_arg, 'set_xy'):
-                result = interp_arg(**kw)
-                result.set_xy(self._x, self._y)
-            else:
-                result = interp_arg(x, y, **kw)
-                
-        # user passes an instance of a callable class which has yet
-        # to have its x and y initialized.
-        elif hasattr(interp_arg, 'init_xy') and hasattr(interp_arg, '__call__'):
-            result = interp_arg
-            result.init_xy(self._x, self._y)
-        elif hasattr(interp_arg, 'set_xy') and hasattr(interp_arg, '__call__'):
-            result = interp_arg
-            result.set_xy(self._x, self._y)
-                
-        # user passes a function to be called
-        # Assume function has form of f(x, y, newx, **kw)
-        # FIXME : should other function forms be allowed?
-        elif isfunction(interp_arg):
-            # assume x, y and newx are all passed to interp_arg
-            result = lambda new_x : interp_arg(self._x, self._y, new_x, **kw)
-        
-        # default : user has passed a default value to always be returned
-        else:
-            result = np.vectorize(lambda new_x : interp_arg)
-            
-        return result
-
-    def __call__(self, newx):
-        """
-            Input x must be in sorted order.
-            Breaks x into pieces in-range, below-range, and above range.
-            Performs appropriate operation on each and concatenates results.
-        """
-        # FIXME : make_array_safe may also be called within the interpolation technique.
-        #   waste of time, but ok for the time being.
-        newx = make_array_safe(newx)
-        
-        # masks indicate which elements fall into which interpolation region
-        low_mask = newx<self._x[0]
-        high_mask = newx>self._x[-1]
-        interp_mask = (~low_mask) & (~high_mask)
-        
-        # use correct function for x values in each region
-        if len(newx[low_mask]) == 0: new_low=np.array([])  # FIXME : remove need for if/else.
-                                                                            # if/else is a hack, since vectorize is failing
-                                                                            # to work on lists/arrays of length 0
-                                                                            # on the computer where this is being
-                                                                            # developed
-        else: new_low = self.low(newx[low_mask])
-        if len(newx[interp_mask])==0: new_interp=np.array([])
-        else: new_interp = self.kind(newx[interp_mask])
-        if len(newx[high_mask]) == 0: new_high = np.array([])
-        else: new_high = self.high(newx[high_mask])
-        
-        result = np.concatenate((new_low, new_interp, new_high)) # FIXME : deal with mixed datatypes
-                                                                                          # Would be nice to say result = zeros(dtype=?)
-                                                                                          # and fill in
-        
-        return result
-        
-# unit testing
-import unittest, time
-class Test(unittest.TestCase):
-    
-    def assertAllclose(self, x, y):
-        self.assert_(np.allclose(make_array_safe(x), make_array_safe(y)))
-        
-    def test_interpolate_wrapper(self):
-        """ run unit test contained in interpolate_wrapper.py
-        """
-        #print "\n\nTESTING _interpolate_wrapper MODULE"
-        from interpolate_wrapper import Test
-        T = Test()
-        T.runTest()
-        
-    def test_fitpack_wrapper(self):
-        """ run unit test contained in fitpack_wrapper.py
-        """
-        #print "\n\nTESTING _fitpack_wrapper MODULE"
-        from fitpack_wrapper import Test
-        T = Test()
-        T.runTest()
-        
-    def test_instantiationFormat(self):
-        """ make sure : all allowed instantiation formats are supported
-        """
-        
-        # make sure : an instance of a callable class in which
-        #   x and y haven't been initiated works
-        N = 7 #must be > 5
-        x = np.arange(N)
-        y = np.arange(N)
-        interp_func = Interpolate1d(x, y, kind=Spline(k=2), low=Spline(k=2), high=Spline(k=2))
-        new_x = np.arange(N+1)-0.5
-        new_y = interp_func(new_x)
-        self.assertAllclose(new_x, new_y)
-        
-    def test_callFormat(self):
-        """ make sure : all allowed calling formats are supported
-        """
-        # make sure : having no out-of-range elements in new_x is fine
-        # There was a bug with this earlier.        
-        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)
-        
-    def test_removeBad(self):
-        """make sure : interp1d works with bad data
-        """
-        N = 7.0 # must be >=5
-        x = arange(N); x[2] = np.NaN
-        y = arange(N); y[4] = None; y[0]=np.NaN
-        new_x = arange(N+1)-0.5
-        new_y = interp1d(x, y, new_x, kind='linear', low='linear', high='linear', \
-                                    remove_bad_data = True, bad_data = [None])
-        self.assertAllclose(new_x, new_y)
-        
-    def test_intper1d(self):
-        """ make sure : interp1d works, at least in the linear case
-        """
-        N = 7
-        x = arange(N)
-        y = arange(N)
-        new_x = arange(N+1)-0.5
-        new_y = interp1d(x, y, new_x, kind='linear', low='linear', high='linear')        
-        self.assertAllclose(new_x, new_y)
-        
-    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 # 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):
-        """ make sure : order-2 splines work on linear data
-            make sure : order-2 splines work on non-linear data
-            make sure : 'cubic' and 'quad' as arguments yield
-                                the desired spline
-        """
-        #print "\n\nTESTING 2nd ORDER SPLINE"
-        N = 7 #must be > 5
-        x = np.arange(N)
-        y = np.arange(N)
-        T1 = time.clock()
-        interp_func = Interpolate1d(x, y, kind='Spline', kindkw={'k':2}, low='spline', high='spline')
-        T2 = time.clock()
-        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 "time to evaluate 2nd order spline interp function with N = %i: " % N, t2 - t1
-        self.assertAllclose(new_x, new_y)
-        
-        # 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='quad', high='cubic')
-        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='linear', high='linear')
-        T2 = time.clock()
-        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 "time to create linear interp function with N = %i: " % N, t2 - t1
-        
-        self.assertAllclose(new_x, new_y)
-        
-        
-if __name__ == '__main__':
-    unittest.main()                 
\ No newline at end of file



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