[Scipy-svn] r4567 - branches/Interpolate1D
scipy-svn at scipy.org
scipy-svn at scipy.org
Mon Jul 28 17:16:41 EDT 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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