EVOLUTION-MANAGER

Edit File: test_rbf.py

# 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) from numpy import linspace, sin, cos, 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: check_rbf1d_interpolation(function) check_rbf2d_interpolation(function) check_rbf3d_interpolation(function) def check_2drbf1d_interpolation(function): # Check that the 2-dim Rbf function interpolates through the nodes (1D) x = linspace(0, 10, 9) y0 = sin(x) y1 = cos(x) y = np.vstack([y0, y1]).T rbf = Rbf(x, y, function=function, mode='N-D') yi = rbf(x) assert_array_almost_equal(y, yi) assert_almost_equal(rbf(float(x[0])), y[0]) def check_2drbf2d_interpolation(function): # Check that the 2-dim Rbf function interpolates through the nodes (2D). x = random.rand(50, ) * 4 - 2 y = random.rand(50, ) * 4 - 2 z0 = x * exp(-x ** 2 - 1j * y ** 2) z1 = y * exp(-y ** 2 - 1j * x ** 2) z = np.vstack([z0, z1]).T rbf = Rbf(x, y, z, epsilon=2, function=function, mode='N-D') zi = rbf(x, y) zi.shape = z.shape assert_array_almost_equal(z, zi) def check_2drbf3d_interpolation(function): # Check that the 2-dim Rbf function interpolates through the nodes (3D). x = random.rand(50, ) * 4 - 2 y = random.rand(50, ) * 4 - 2 z = random.rand(50, ) * 4 - 2 d0 = x * exp(-x ** 2 - y ** 2) d1 = y * exp(-y ** 2 - x ** 2) d = np.vstack([d0, d1]).T rbf = Rbf(x, y, z, d, epsilon=2, function=function, mode='N-D') di = rbf(x, y, z) di.shape = d.shape assert_array_almost_equal(di, d) def test_2drbf_interpolation(): for function in FUNCTIONS: check_2drbf1d_interpolation(function) check_2drbf2d_interpolation(function) check_2drbf3d_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: check_rbf1d_regularity(function, tolerances.get(function, 1e-2)) def check_2drbf1d_regularity(function, atol): # Check that the 2-dim Rbf function approximates a smooth function well away # from the nodes. x = linspace(0, 10, 9) y0 = sin(x) y1 = cos(x) y = np.vstack([y0, y1]).T rbf = Rbf(x, y, function=function, mode='N-D') xi = linspace(0, 10, 100) yi = rbf(xi) msg = "abs-diff: %f" % abs(yi - np.vstack([sin(xi), cos(xi)]).T).max() assert_(allclose(yi, np.vstack([sin(xi), cos(xi)]).T, atol=atol), msg) def test_2drbf_regularity(): tolerances = { 'multiquadric': 0.1, 'inverse multiquadric': 0.15, 'gaussian': 0.15, 'cubic': 0.15, 'quintic': 0.1, 'thin-plate': 0.15, 'linear': 0.2 } for function in FUNCTIONS: check_2drbf1d_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: 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)