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#!/usr/bin/env python
# Created by John Travers, Robert Hetland, 2007
""" Test functions for rbf module """
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import (assert_, assert_array_almost_equal,
assert_almost_equal, run_module_suite)
from numpy import linspace, sin, random, exp, allclose
from scipy.interpolate.rbf import Rbf
FUNCTIONS = ('multiquadric', 'inverse multiquadric', 'gaussian',
'cubic', 'quintic', 'thin-plate', 'linear')
def check_rbf1d_interpolation(function):
"""Check that the Rbf function interpolates through the nodes (1D)"""
olderr = np.seterr(all="ignore")
try:
x = linspace(0,10,9)
y = sin(x)
rbf = Rbf(x, y, function=function)
yi = rbf(x)
assert_array_almost_equal(y, yi)
assert_almost_equal(rbf(float(x[0])), y[0])
finally:
np.seterr(**olderr)
def check_rbf2d_interpolation(function):
"""Check that the Rbf function interpolates through the nodes (2D)"""
olderr = np.seterr(all="ignore")
try:
x = random.rand(50,1)*4-2
y = random.rand(50,1)*4-2
z = x*exp(-x**2-1j*y**2)
rbf = Rbf(x, y, z, epsilon=2, function=function)
zi = rbf(x, y)
zi.shape = x.shape
assert_array_almost_equal(z, zi)
finally:
np.seterr(**olderr)
def check_rbf3d_interpolation(function):
"""Check that the Rbf function interpolates through the nodes (3D)"""
olderr = np.seterr(all="ignore")
try:
x = random.rand(50,1)*4-2
y = random.rand(50,1)*4-2
z = random.rand(50,1)*4-2
d = x*exp(-x**2-y**2)
rbf = Rbf(x, y, z, d, epsilon=2, function=function)
di = rbf(x, y, z)
di.shape = x.shape
assert_array_almost_equal(di, d)
finally:
np.seterr(**olderr)
def test_rbf_interpolation():
for function in FUNCTIONS:
yield check_rbf1d_interpolation, function
yield check_rbf2d_interpolation, function
yield check_rbf3d_interpolation, function
def check_rbf1d_regularity(function, atol):
"""Check that the Rbf function approximates a smooth function well away
from the nodes."""
olderr = np.seterr(all="ignore")
try:
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, function=function)
xi = linspace(0, 10, 100)
yi = rbf(xi)
#import matplotlib.pyplot as plt
#plt.figure()
#plt.plot(x, y, 'o', xi, sin(xi), ':', xi, yi, '-')
#plt.title(function)
#plt.show()
msg = "abs-diff: %f" % abs(yi - sin(xi)).max()
assert_(allclose(yi, sin(xi), atol=atol), msg)
finally:
np.seterr(**olderr)
def test_rbf_regularity():
tolerances = {
'multiquadric': 0.05,
'inverse multiquadric': 0.02,
'gaussian': 0.01,
'cubic': 0.15,
'quintic': 0.1,
'thin-plate': 0.1,
'linear': 0.2
}
for function in FUNCTIONS:
yield check_rbf1d_regularity, function, tolerances.get(function, 1e-2)
def test_default_construction():
"""Check that the Rbf class can be constructed with the default
multiquadric basis function. Regression test for ticket #1228."""
x = linspace(0,10,9)
y = sin(x)
rbf = Rbf(x, y)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_function_is_callable():
"""Check that the Rbf class can be constructed with function=callable."""
x = linspace(0,10,9)
y = sin(x)
linfunc = lambda x:x
rbf = Rbf(x, y, function=linfunc)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_two_arg_function_is_callable():
"""Check that the Rbf class can be constructed with a two argument
function=callable."""
def _func(self, r):
return self.epsilon + r
x = linspace(0,10,9)
y = sin(x)
rbf = Rbf(x, y, function=_func)
yi = rbf(x)
assert_array_almost_equal(y, yi)
def test_rbf_epsilon_none():
x = linspace(0, 10, 9)
y = sin(x)
rbf = Rbf(x, y, epsilon=None)
if __name__ == "__main__":
run_module_suite()
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