from __future__ import division, print_function, absolute_import import numpy as np from numpy import cos, sin, pi from numpy.testing import TestCase, run_module_suite, assert_equal, \ assert_almost_equal, assert_allclose, assert_ from scipy.integrate import quadrature, romberg, romb, newton_cotes, cumtrapz class TestQuadrature(TestCase): def quad(self, x, a, b, args): raise NotImplementedError def test_quadrature(self): # Typical function with two extra arguments: def myfunc(x,n,z): # Bessel function integrand return cos(n*x-z*sin(x))/pi val, err = quadrature(myfunc,0,pi,(2,1.8)) table_val = 0.30614353532540296487 assert_almost_equal(val, table_val, decimal=7) def test_quadrature_rtol(self): def myfunc(x,n,z): # Bessel function integrand return 1e90 * cos(n*x-z*sin(x))/pi val, err = quadrature(myfunc,0,pi,(2,1.8),rtol=1e-10) table_val = 1e90 * 0.30614353532540296487 assert_allclose(val, table_val, rtol=1e-10) def test_quadrature_miniter(self): # Typical function with two extra arguments: def myfunc(x,n,z): # Bessel function integrand return cos(n*x-z*sin(x))/pi table_val = 0.30614353532540296487 for miniter in [5, 52]: val, err = quadrature(myfunc,0,pi,(2,1.8),miniter=miniter) assert_almost_equal(val, table_val, decimal=7) assert_(err < 1.0) def test_quadrature_single_args(self): def myfunc(x,n): return 1e90 * cos(n*x-1.8*sin(x))/pi val, err = quadrature(myfunc,0,pi,args=2,rtol=1e-10) table_val = 1e90 * 0.30614353532540296487 assert_allclose(val, table_val, rtol=1e-10) def test_romberg(self): # Typical function with two extra arguments: def myfunc(x, n, z): # Bessel function integrand return cos(n*x-z*sin(x))/pi val = romberg(myfunc,0,pi, args=(2, 1.8)) table_val = 0.30614353532540296487 assert_almost_equal(val, table_val, decimal=7) def test_romberg_rtol(self): # Typical function with two extra arguments: def myfunc(x, n, z): # Bessel function integrand return 1e19*cos(n*x-z*sin(x))/pi val = romberg(myfunc,0,pi, args=(2, 1.8), rtol=1e-10) table_val = 1e19*0.30614353532540296487 assert_allclose(val, table_val, rtol=1e-10) def test_romb(self): assert_equal(romb(np.arange(17)),128) def test_non_dtype(self): # Check that we work fine with functions returning float import math valmath = romberg(math.sin, 0, 1) expected_val = 0.45969769413185085 assert_almost_equal(valmath, expected_val, decimal=7) def test_newton_cotes(self): """Test the first few degrees, for evenly spaced points.""" n = 1 wts, errcoff = newton_cotes(n, 1) assert_equal(wts, n*np.array([0.5, 0.5])) assert_almost_equal(errcoff, -n**3/12.0) n = 2 wts, errcoff = newton_cotes(n, 1) assert_almost_equal(wts, n*np.array([1.0, 4.0, 1.0])/6.0) assert_almost_equal(errcoff, -n**5/2880.0) n = 3 wts, errcoff = newton_cotes(n, 1) assert_almost_equal(wts, n*np.array([1.0, 3.0, 3.0, 1.0])/8.0) assert_almost_equal(errcoff, -n**5/6480.0) n = 4 wts, errcoff = newton_cotes(n, 1) assert_almost_equal(wts, n*np.array([7.0, 32.0, 12.0, 32.0, 7.0])/90.0) assert_almost_equal(errcoff, -n**7/1935360.0) def test_newton_cotes2(self): """Test newton_cotes with points that are not evenly spaced.""" x = np.array([0.0, 1.5, 2.0]) y = x**2 wts, errcoff = newton_cotes(x) exact_integral = 8.0/3 numeric_integral = np.dot(wts, y) assert_almost_equal(numeric_integral, exact_integral) x = np.array([0.0, 1.4, 2.1, 3.0]) y = x**2 wts, errcoff = newton_cotes(x) exact_integral = 9.0 numeric_integral = np.dot(wts, y) assert_almost_equal(numeric_integral, exact_integral) class TestCumtrapz(TestCase): def test_1d(self): x = np.linspace(-2, 2, num=5) y = x y_int = cumtrapz(y, x, initial=0) y_expected = [0., -1.5, -2., -1.5, 0.] assert_allclose(y_int, y_expected) y_int = cumtrapz(y, x, initial=None) assert_allclose(y_int, y_expected[1:]) def test_y_nd_x_nd(self): x = np.arange(3 * 2 * 4).reshape(3, 2, 4) y = x y_int = cumtrapz(y, x, initial=0) y_expected = np.array([[[0., 0.5, 2., 4.5], [0., 4.5, 10., 16.5]], [[0., 8.5, 18., 28.5], [0., 12.5, 26., 40.5]], [[0., 16.5, 34., 52.5], [0., 20.5, 42., 64.5]]]) assert_allclose(y_int, y_expected) # Try with all axes shapes = [(2, 2, 4), (3, 1, 4), (3, 2, 3)] for axis, shape in zip([0, 1, 2], shapes): y_int = cumtrapz(y, x, initial=3.45, axis=axis) assert_equal(y_int.shape, (3, 2, 4)) y_int = cumtrapz(y, x, initial=None, axis=axis) assert_equal(y_int.shape, shape) def test_y_nd_x_1d(self): y = np.arange(3 * 2 * 4).reshape(3, 2, 4) x = np.arange(4)**2 # Try with all axes ys_expected = ( np.array([[[ 4., 5., 6., 7.], [ 8., 9., 10., 11.]], [[40., 44., 48., 52.], [56., 60., 64., 68.]]]), np.array([[[ 2., 3., 4., 5.]], [[10., 11., 12., 13.]], [[18., 19., 20., 21.]]]), np.array([[[ 0.5, 5., 17.5], [ 4.5, 21., 53.5]], [[ 8.5, 37., 89.5], [12.5, 53., 125.5]], [[16.5, 69., 161.5], [20.5, 85., 197.5]]])) for axis, y_expected in zip([0, 1, 2], ys_expected): y_int = cumtrapz(y, x=x[:y.shape[axis]], axis=axis, initial=None) assert_allclose(y_int, y_expected) def test_x_none(self): y = np.linspace(-2, 2, num=5) y_int = cumtrapz(y) y_expected = [-1.5, -2., -1.5, 0.] assert_allclose(y_int, y_expected) y_int = cumtrapz(y, initial=1.23) y_expected = [1.23, -1.5, -2., -1.5, 0.] assert_allclose(y_int, y_expected) y_int = cumtrapz(y, dx=3) y_expected = [-4.5, -6., -4.5, 0.] assert_allclose(y_int, y_expected) y_int = cumtrapz(y, dx=3, initial=1.23) y_expected = [1.23, -4.5, -6., -4.5, 0.] assert_allclose(y_int, y_expected) if __name__ == "__main__": run_module_suite()