222 lines
6.4 KiB
Python
222 lines
6.4 KiB
Python
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# Created by John Travers, Robert Hetland, 2007
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""" Test functions for rbf module """
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import numpy as np
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from numpy.testing import (assert_, assert_array_almost_equal,
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assert_almost_equal)
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from numpy import linspace, sin, cos, random, exp, allclose
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from scipy.interpolate.rbf import Rbf
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FUNCTIONS = ('multiquadric', 'inverse multiquadric', 'gaussian',
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'cubic', 'quintic', 'thin-plate', 'linear')
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def check_rbf1d_interpolation(function):
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# Check that the Rbf function interpolates through the nodes (1D)
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x = linspace(0,10,9)
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y = sin(x)
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rbf = Rbf(x, y, function=function)
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yi = rbf(x)
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assert_array_almost_equal(y, yi)
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assert_almost_equal(rbf(float(x[0])), y[0])
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def check_rbf2d_interpolation(function):
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# Check that the Rbf function interpolates through the nodes (2D).
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x = random.rand(50,1)*4-2
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y = random.rand(50,1)*4-2
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z = x*exp(-x**2-1j*y**2)
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rbf = Rbf(x, y, z, epsilon=2, function=function)
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zi = rbf(x, y)
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zi.shape = x.shape
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assert_array_almost_equal(z, zi)
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def check_rbf3d_interpolation(function):
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# Check that the Rbf function interpolates through the nodes (3D).
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x = random.rand(50, 1)*4 - 2
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y = random.rand(50, 1)*4 - 2
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z = random.rand(50, 1)*4 - 2
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d = x*exp(-x**2 - y**2)
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rbf = Rbf(x, y, z, d, epsilon=2, function=function)
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di = rbf(x, y, z)
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di.shape = x.shape
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assert_array_almost_equal(di, d)
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def test_rbf_interpolation():
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for function in FUNCTIONS:
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check_rbf1d_interpolation(function)
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check_rbf2d_interpolation(function)
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check_rbf3d_interpolation(function)
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def check_2drbf1d_interpolation(function):
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# Check that the 2-D Rbf function interpolates through the nodes (1D)
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x = linspace(0, 10, 9)
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y0 = sin(x)
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y1 = cos(x)
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y = np.vstack([y0, y1]).T
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rbf = Rbf(x, y, function=function, mode='N-D')
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yi = rbf(x)
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assert_array_almost_equal(y, yi)
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assert_almost_equal(rbf(float(x[0])), y[0])
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def check_2drbf2d_interpolation(function):
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# Check that the 2-D Rbf function interpolates through the nodes (2D).
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x = random.rand(50, ) * 4 - 2
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y = random.rand(50, ) * 4 - 2
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z0 = x * exp(-x ** 2 - 1j * y ** 2)
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z1 = y * exp(-y ** 2 - 1j * x ** 2)
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z = np.vstack([z0, z1]).T
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rbf = Rbf(x, y, z, epsilon=2, function=function, mode='N-D')
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zi = rbf(x, y)
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zi.shape = z.shape
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assert_array_almost_equal(z, zi)
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def check_2drbf3d_interpolation(function):
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# Check that the 2-D Rbf function interpolates through the nodes (3D).
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x = random.rand(50, ) * 4 - 2
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y = random.rand(50, ) * 4 - 2
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z = random.rand(50, ) * 4 - 2
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d0 = x * exp(-x ** 2 - y ** 2)
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d1 = y * exp(-y ** 2 - x ** 2)
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d = np.vstack([d0, d1]).T
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rbf = Rbf(x, y, z, d, epsilon=2, function=function, mode='N-D')
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di = rbf(x, y, z)
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di.shape = d.shape
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assert_array_almost_equal(di, d)
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def test_2drbf_interpolation():
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for function in FUNCTIONS:
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check_2drbf1d_interpolation(function)
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check_2drbf2d_interpolation(function)
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check_2drbf3d_interpolation(function)
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def check_rbf1d_regularity(function, atol):
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# Check that the Rbf function approximates a smooth function well away
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# from the nodes.
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x = linspace(0, 10, 9)
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y = sin(x)
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rbf = Rbf(x, y, function=function)
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xi = linspace(0, 10, 100)
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yi = rbf(xi)
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msg = "abs-diff: %f" % abs(yi - sin(xi)).max()
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assert_(allclose(yi, sin(xi), atol=atol), msg)
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def test_rbf_regularity():
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tolerances = {
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'multiquadric': 0.1,
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'inverse multiquadric': 0.15,
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'gaussian': 0.15,
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'cubic': 0.15,
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'quintic': 0.1,
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'thin-plate': 0.1,
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'linear': 0.2
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}
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for function in FUNCTIONS:
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check_rbf1d_regularity(function, tolerances.get(function, 1e-2))
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def check_2drbf1d_regularity(function, atol):
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# Check that the 2-D Rbf function approximates a smooth function well away
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# from the nodes.
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x = linspace(0, 10, 9)
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y0 = sin(x)
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y1 = cos(x)
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y = np.vstack([y0, y1]).T
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rbf = Rbf(x, y, function=function, mode='N-D')
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xi = linspace(0, 10, 100)
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yi = rbf(xi)
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msg = "abs-diff: %f" % abs(yi - np.vstack([sin(xi), cos(xi)]).T).max()
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assert_(allclose(yi, np.vstack([sin(xi), cos(xi)]).T, atol=atol), msg)
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def test_2drbf_regularity():
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tolerances = {
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'multiquadric': 0.1,
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'inverse multiquadric': 0.15,
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'gaussian': 0.15,
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'cubic': 0.15,
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'quintic': 0.1,
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'thin-plate': 0.15,
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'linear': 0.2
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}
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for function in FUNCTIONS:
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check_2drbf1d_regularity(function, tolerances.get(function, 1e-2))
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def check_rbf1d_stability(function):
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# Check that the Rbf function with default epsilon is not subject
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# to overshoot. Regression for issue #4523.
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#
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# Generate some data (fixed random seed hence deterministic)
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np.random.seed(1234)
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x = np.linspace(0, 10, 50)
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z = x + 4.0 * np.random.randn(len(x))
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rbf = Rbf(x, z, function=function)
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xi = np.linspace(0, 10, 1000)
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yi = rbf(xi)
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# subtract the linear trend and make sure there no spikes
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assert_(np.abs(yi-xi).max() / np.abs(z-x).max() < 1.1)
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def test_rbf_stability():
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for function in FUNCTIONS:
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check_rbf1d_stability(function)
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def test_default_construction():
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# Check that the Rbf class can be constructed with the default
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# multiquadric basis function. Regression test for ticket #1228.
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x = linspace(0,10,9)
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y = sin(x)
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rbf = Rbf(x, y)
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yi = rbf(x)
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assert_array_almost_equal(y, yi)
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def test_function_is_callable():
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# Check that the Rbf class can be constructed with function=callable.
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x = linspace(0,10,9)
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y = sin(x)
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linfunc = lambda x:x
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rbf = Rbf(x, y, function=linfunc)
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yi = rbf(x)
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assert_array_almost_equal(y, yi)
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def test_two_arg_function_is_callable():
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# Check that the Rbf class can be constructed with a two argument
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# function=callable.
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def _func(self, r):
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return self.epsilon + r
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x = linspace(0,10,9)
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y = sin(x)
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rbf = Rbf(x, y, function=_func)
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yi = rbf(x)
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assert_array_almost_equal(y, yi)
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def test_rbf_epsilon_none():
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x = linspace(0, 10, 9)
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y = sin(x)
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Rbf(x, y, epsilon=None)
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def test_rbf_epsilon_none_collinear():
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# Check that collinear points in one dimension doesn't cause an error
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# due to epsilon = 0
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x = [1, 2, 3]
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y = [4, 4, 4]
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z = [5, 6, 7]
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rbf = Rbf(x, y, z, epsilon=None)
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assert_(rbf.epsilon > 0)
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