import numpy as np from numpy.testing import assert_, assert_allclose import pytest import scipy.special.orthogonal as orth from scipy.special._testutils import FuncData def test_eval_chebyt(): n = np.arange(0, 10000, 7) x = 2*np.random.rand() - 1 v1 = np.cos(n*np.arccos(x)) v2 = orth.eval_chebyt(n, x) assert_(np.allclose(v1, v2, rtol=1e-15)) def test_eval_genlaguerre_restriction(): # check it returns nan for alpha <= -1 assert_(np.isnan(orth.eval_genlaguerre(0, -1, 0))) assert_(np.isnan(orth.eval_genlaguerre(0.1, -1, 0))) def test_warnings(): # ticket 1334 with np.errstate(all='raise'): # these should raise no fp warnings orth.eval_legendre(1, 0) orth.eval_laguerre(1, 1) orth.eval_gegenbauer(1, 1, 0) class TestPolys(object): """ Check that the eval_* functions agree with the constructed polynomials """ def check_poly(self, func, cls, param_ranges=[], x_range=[], nn=10, nparam=10, nx=10, rtol=1e-8): np.random.seed(1234) dataset = [] for n in np.arange(nn): params = [a + (b-a)*np.random.rand(nparam) for a,b in param_ranges] params = np.asarray(params).T if not param_ranges: params = [0] for p in params: if param_ranges: p = (n,) + tuple(p) else: p = (n,) x = x_range[0] + (x_range[1] - x_range[0])*np.random.rand(nx) x[0] = x_range[0] # always include domain start point x[1] = x_range[1] # always include domain end point poly = np.poly1d(cls(*p).coef) z = np.c_[np.tile(p, (nx,1)), x, poly(x)] dataset.append(z) dataset = np.concatenate(dataset, axis=0) def polyfunc(*p): p = (p[0].astype(int),) + p[1:] return func(*p) with np.errstate(all='raise'): ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1, rtol=rtol) ds.check() def test_jacobi(self): self.check_poly(orth.eval_jacobi, orth.jacobi, param_ranges=[(-0.99, 10), (-0.99, 10)], x_range=[-1, 1], rtol=1e-5) def test_sh_jacobi(self): self.check_poly(orth.eval_sh_jacobi, orth.sh_jacobi, param_ranges=[(1, 10), (0, 1)], x_range=[0, 1], rtol=1e-5) def test_gegenbauer(self): self.check_poly(orth.eval_gegenbauer, orth.gegenbauer, param_ranges=[(-0.499, 10)], x_range=[-1, 1], rtol=1e-7) def test_chebyt(self): self.check_poly(orth.eval_chebyt, orth.chebyt, param_ranges=[], x_range=[-1, 1]) def test_chebyu(self): self.check_poly(orth.eval_chebyu, orth.chebyu, param_ranges=[], x_range=[-1, 1]) def test_chebys(self): self.check_poly(orth.eval_chebys, orth.chebys, param_ranges=[], x_range=[-2, 2]) def test_chebyc(self): self.check_poly(orth.eval_chebyc, orth.chebyc, param_ranges=[], x_range=[-2, 2]) def test_sh_chebyt(self): with np.errstate(all='ignore'): self.check_poly(orth.eval_sh_chebyt, orth.sh_chebyt, param_ranges=[], x_range=[0, 1]) def test_sh_chebyu(self): self.check_poly(orth.eval_sh_chebyu, orth.sh_chebyu, param_ranges=[], x_range=[0, 1]) def test_legendre(self): self.check_poly(orth.eval_legendre, orth.legendre, param_ranges=[], x_range=[-1, 1]) def test_sh_legendre(self): with np.errstate(all='ignore'): self.check_poly(orth.eval_sh_legendre, orth.sh_legendre, param_ranges=[], x_range=[0, 1]) def test_genlaguerre(self): self.check_poly(orth.eval_genlaguerre, orth.genlaguerre, param_ranges=[(-0.99, 10)], x_range=[0, 100]) def test_laguerre(self): self.check_poly(orth.eval_laguerre, orth.laguerre, param_ranges=[], x_range=[0, 100]) def test_hermite(self): self.check_poly(orth.eval_hermite, orth.hermite, param_ranges=[], x_range=[-100, 100]) def test_hermitenorm(self): self.check_poly(orth.eval_hermitenorm, orth.hermitenorm, param_ranges=[], x_range=[-100, 100]) class TestRecurrence(object): """ Check that the eval_* functions sig='ld->d' and 'dd->d' agree. """ def check_poly(self, func, param_ranges=[], x_range=[], nn=10, nparam=10, nx=10, rtol=1e-8): np.random.seed(1234) dataset = [] for n in np.arange(nn): params = [a + (b-a)*np.random.rand(nparam) for a,b in param_ranges] params = np.asarray(params).T if not param_ranges: params = [0] for p in params: if param_ranges: p = (n,) + tuple(p) else: p = (n,) x = x_range[0] + (x_range[1] - x_range[0])*np.random.rand(nx) x[0] = x_range[0] # always include domain start point x[1] = x_range[1] # always include domain end point kw = dict(sig=(len(p)+1)*'d'+'->d') z = np.c_[np.tile(p, (nx,1)), x, func(*(p + (x,)), **kw)] dataset.append(z) dataset = np.concatenate(dataset, axis=0) def polyfunc(*p): p = (p[0].astype(int),) + p[1:] kw = dict(sig='l'+(len(p)-1)*'d'+'->d') return func(*p, **kw) with np.errstate(all='raise'): ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1, rtol=rtol) ds.check() def test_jacobi(self): self.check_poly(orth.eval_jacobi, param_ranges=[(-0.99, 10), (-0.99, 10)], x_range=[-1, 1]) def test_sh_jacobi(self): self.check_poly(orth.eval_sh_jacobi, param_ranges=[(1, 10), (0, 1)], x_range=[0, 1]) def test_gegenbauer(self): self.check_poly(orth.eval_gegenbauer, param_ranges=[(-0.499, 10)], x_range=[-1, 1]) def test_chebyt(self): self.check_poly(orth.eval_chebyt, param_ranges=[], x_range=[-1, 1]) def test_chebyu(self): self.check_poly(orth.eval_chebyu, param_ranges=[], x_range=[-1, 1]) def test_chebys(self): self.check_poly(orth.eval_chebys, param_ranges=[], x_range=[-2, 2]) def test_chebyc(self): self.check_poly(orth.eval_chebyc, param_ranges=[], x_range=[-2, 2]) def test_sh_chebyt(self): self.check_poly(orth.eval_sh_chebyt, param_ranges=[], x_range=[0, 1]) def test_sh_chebyu(self): self.check_poly(orth.eval_sh_chebyu, param_ranges=[], x_range=[0, 1]) def test_legendre(self): self.check_poly(orth.eval_legendre, param_ranges=[], x_range=[-1, 1]) def test_sh_legendre(self): self.check_poly(orth.eval_sh_legendre, param_ranges=[], x_range=[0, 1]) def test_genlaguerre(self): self.check_poly(orth.eval_genlaguerre, param_ranges=[(-0.99, 10)], x_range=[0, 100]) def test_laguerre(self): self.check_poly(orth.eval_laguerre, param_ranges=[], x_range=[0, 100]) def test_hermite(self): v = orth.eval_hermite(70, 1.0) a = -1.457076485701412e60 assert_allclose(v,a) def test_hermite_domain(): # Regression test for gh-11091. assert np.isnan(orth.eval_hermite(-1, 1.0)) assert np.isnan(orth.eval_hermitenorm(-1, 1.0)) @pytest.mark.parametrize("n", [0, 1, 2]) @pytest.mark.parametrize("x", [0, 1, np.nan]) def test_hermite_nan(n, x): # Regression test for gh-11369. assert np.isnan(orth.eval_hermite(n, x)) == np.any(np.isnan([n, x])) assert np.isnan(orth.eval_hermitenorm(n, x)) == np.any(np.isnan([n, x])) @pytest.mark.parametrize('n', [0, 1, 2, 3.2]) @pytest.mark.parametrize('alpha', [1, np.nan]) @pytest.mark.parametrize('x', [2, np.nan]) def test_genlaguerre_nan(n, alpha, x): # Regression test for gh-11361. nan_laguerre = np.isnan(orth.eval_genlaguerre(n, alpha, x)) nan_arg = np.any(np.isnan([n, alpha, x])) assert nan_laguerre == nan_arg @pytest.mark.parametrize('n', [0, 1, 2, 3.2]) @pytest.mark.parametrize('alpha', [0.0, 1, np.nan]) @pytest.mark.parametrize('x', [1e-6, 2, np.nan]) def test_gegenbauer_nan(n, alpha, x): # Regression test for gh-11370. nan_gegenbauer = np.isnan(orth.eval_gegenbauer(n, alpha, x)) nan_arg = np.any(np.isnan([n, alpha, x])) assert nan_gegenbauer == nan_arg