def test_la_roots():
root_func = lambda a: lambda n, mu: orth.la_roots(n, a, mu)
eval_func = lambda a: lambda n, x: orth.eval_genlaguerre(n, a, x)
verify_gauss_quad(root_func(-0.5), eval_func(-0.5), 5)
verify_gauss_quad(root_func(-0.5), eval_func(-0.5), 25, atol=1e-13)
verify_gauss_quad(root_func(-0.5), eval_func(-0.5), 100, atol=1e-12)
verify_gauss_quad(root_func(0.1), eval_func(0.1), 5)
verify_gauss_quad(root_func(0.1), eval_func(0.1), 25, atol=1e-13)
verify_gauss_quad(root_func(0.1), eval_func(0.1), 100, atol=1e-13)
verify_gauss_quad(root_func(1), eval_func(1), 5)
verify_gauss_quad(root_func(1), eval_func(1), 25, atol=1e-13)
verify_gauss_quad(root_func(1), eval_func(1), 100, atol=1e-13)
verify_gauss_quad(root_func(10), eval_func(10), 5)
verify_gauss_quad(root_func(10), eval_func(10), 25, atol=1e-13)
verify_gauss_quad(root_func(10), eval_func(10), 100, atol=1e-12)
verify_gauss_quad(root_func(50), eval_func(50), 5)
verify_gauss_quad(root_func(50), eval_func(50), 25, atol=1e-13)
verify_gauss_quad(root_func(50), eval_func(50), 100, atol=1e-13)
x, w = orth.la_roots(5, 2, False)
y, v, m = orth.la_roots(5, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.la_roots, 0, 2)
assert_raises(ValueError, orth.la_roots, 3.3, 2)
assert_raises(ValueError, orth.la_roots, 3, -1.1)
def test_la_roots():
root_func = lambda a: lambda n, mu: orth.la_roots(n, a, mu)
eval_func = lambda a: lambda n, x: orth.eval_genlaguerre(n, a, x)
verify_gauss_quad(root_func(-0.5), eval_func(-0.5), 5)
verify_gauss_quad(root_func(-0.5), eval_func(-0.5), 25, atol=1e-13)
verify_gauss_quad(root_func(-0.5), eval_func(-0.5), 100, atol=1e-12)
verify_gauss_quad(root_func(0.1), eval_func(0.1), 5)
verify_gauss_quad(root_func(0.1), eval_func(0.1), 25, atol=1e-13)
verify_gauss_quad(root_func(0.1), eval_func(0.1), 100, atol=1e-13)
verify_gauss_quad(root_func(1), eval_func(1), 5)
verify_gauss_quad(root_func(1), eval_func(1), 25, atol=1e-13)
verify_gauss_quad(root_func(1), eval_func(1), 100, atol=1e-13)
verify_gauss_quad(root_func(10), eval_func(10), 5)
verify_gauss_quad(root_func(10), eval_func(10), 25, atol=1e-13)
verify_gauss_quad(root_func(10), eval_func(10), 100, atol=1e-12)
verify_gauss_quad(root_func(50), eval_func(50), 5)
verify_gauss_quad(root_func(50), eval_func(50), 25, atol=1e-13)
verify_gauss_quad(root_func(50), eval_func(50), 100, atol=1e-13)
x, w = orth.la_roots(5, 2, False)
y, v, m = orth.la_roots(5, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.la_roots, 0, 2)
assert_raises(ValueError, orth.la_roots, 3.3, 2)
assert_raises(ValueError, orth.la_roots, 3, -1.1)
def eval_harmonicBasis(n, l, r, r0=1.):
"""
For testing purposes
Evaluates the harmonic basis function at positions r
"""
N = norm_harmonicBasis(n, l, r0)
return (N * r**l * exp(-0.5 * r**2 / r0**2) *
eval_genlaguerre(n, l + 0.5, r**2 / r0**2))
def test_roots_genlaguerre():
rootf = lambda a: lambda n, mu: sc.roots_genlaguerre(n, a, mu)
evalf = lambda a: lambda n, x: orth.eval_genlaguerre(n, a, x)
weightf = lambda a: lambda x: x**a * np.exp(-x)
vgq = verify_gauss_quad
vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 5)
vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 25, atol=1e-13)
vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 100, atol=1e-12)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 5)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 25, atol=1e-13)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 100, atol=1.6e-13)
vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 5)
vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 25, atol=1e-13)
vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 100, atol=1.03e-13)
vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 5)
vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 25, atol=1e-13)
vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 100, atol=1e-12)
vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 5)
vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 25, atol=1e-13)
vgq(rootf(50),
evalf(50),
weightf(50),
0.,
np.inf,
100,
rtol=1e-14,
atol=2e-13)
x, w = sc.roots_genlaguerre(5, 2, False)
y, v, m = sc.roots_genlaguerre(5, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf(2.), 0., np.inf)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, sc.roots_genlaguerre, 0, 2)
assert_raises(ValueError, sc.roots_genlaguerre, 3.3, 2)
assert_raises(ValueError, sc.roots_genlaguerre, 3, -1.1)
def test_roots_genlaguerre():
rootf = lambda a: lambda n, mu: sc.roots_genlaguerre(n, a, mu)
evalf = lambda a: lambda n, x: orth.eval_genlaguerre(n, a, x)
weightf = lambda a: lambda x: x**a * np.exp(-x)
vgq = verify_gauss_quad
vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 5)
vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 25, atol=1e-13)
vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 100, atol=1e-12)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 5)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 25, atol=1e-13)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 100, atol=1e-13)
vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 5)
vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 25, atol=1e-13)
vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 100, atol=1e-13)
vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 5)
vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 25, atol=1e-13)
vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 100, atol=1e-12)
vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 5)
vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 25, atol=1e-13)
vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 100, rtol=1e-14, atol=2e-13)
x, w = sc.roots_genlaguerre(5, 2, False)
y, v, m = sc.roots_genlaguerre(5, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf(2.), 0., np.inf)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, sc.roots_genlaguerre, 0, 2)
assert_raises(ValueError, sc.roots_genlaguerre, 3.3, 2)
assert_raises(ValueError, sc.roots_genlaguerre, 3, -1.1)
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_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
