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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)
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])
def check_rbf2d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (2D).
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)
def check_rbf3d_interpolation(function):
# Check that the Rbf function interpolates through the nodes (3D).
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)
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.
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.plot(x, y, 'o', xi, yi-sin(xi), ':')
# plt.title(function)
# plt.show()
msg = "abs-diff: %f" % abs(yi - sin(xi)).max()
assert_(allclose(yi, sin(xi), atol=atol), msg)
def test_rbf_regularity():
tolerances = {
'multiquadric': 0.1,
'inverse multiquadric': 0.15,
'gaussian': 0.15,
'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 check_rbf1d_stability(function):
# Check that the Rbf function with default epsilon is not subject
# to overshoot. Regression for issue #4523.
#
# Generate some data (fixed random seed hence deterministic)
np.random.seed(1234)
x = np.linspace(0, 10, 50)
z = x + 4.0 * np.random.randn(len(x))
rbf = Rbf(x, z, function=function)
xi = np.linspace(0, 10, 1000)
yi = rbf(xi)
# subtract the linear trend and make sure there no spikes
assert_(np.abs(yi-xi).max() / np.abs(z-x).max() < 1.1)
def test_rbf_stability():
for function in FUNCTIONS:
yield check_rbf1d_stability, function
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)
def test_rbf_epsilon_none_collinear():
# Check that collinear points in one dimension doesn't cause an error
# due to epsilon = 0
x = [1, 2, 3]
y = [4, 4, 4]
z = [5, 6, 7]
rbf = Rbf(x, y, z, epsilon=None)
assert_(rbf.epsilon > 0)
if __name__ == "__main__":
run_module_suite()
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