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)
def test_warnings():
# ticket 1334
olderr = np.seterr(all='raise')
try:
# these should raise no fp warnings
orth.eval_legendre(1, 0)
orth.eval_laguerre(1, 1)
orth.eval_gegenbauer(1, 1, 0)
finally:
np.seterr(**olderr)
def test_warnings():
# ticket 1334
olderr = np.seterr(all='raise')
try:
# these should raise no fp warnings
orth.eval_legendre(1, 0)
orth.eval_laguerre(1, 1)
orth.eval_gegenbauer(1, 1, 0)
finally:
np.seterr(**olderr)
def test_cg_roots():
rootf = lambda a: lambda n, mu: orth.cg_roots(n, a, mu)
evalf = lambda a: lambda n, x: orth.eval_gegenbauer(n, a, x)
weightf = lambda a: lambda x: (1 - x**2)**(a - 0.5)
vgq = verify_gauss_quad
vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 5)
vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 25, atol=1e-12)
vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 100, atol=1e-11)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 5)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 25, atol=1e-13)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 100, atol=1e-12)
vgq(rootf(1), evalf(1), weightf(1), -1., 1., 5)
vgq(rootf(1), evalf(1), weightf(1), -1., 1., 25, atol=1e-13)
vgq(rootf(1), evalf(1), weightf(1), -1., 1., 100, atol=1e-12)
vgq(rootf(10), evalf(10), weightf(10), -1., 1., 5)
vgq(rootf(10), evalf(10), weightf(10), -1., 1., 25, atol=1e-13)
vgq(rootf(10), evalf(10), weightf(10), -1., 1., 100, atol=1e-12)
vgq(rootf(50), evalf(50), weightf(50), -1., 1., 5, atol=1e-13)
vgq(rootf(50), evalf(50), weightf(50), -1., 1., 25, atol=1e-12)
vgq(rootf(50), evalf(50), weightf(50), -1., 1., 100, atol=1e-11)
# this is a special case that the old code supported.
# when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
# to a scaled down copy of T_n(x) there.
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 5)
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 25)
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 100)
x, w = orth.cg_roots(5, 2, False)
y, v, m = orth.cg_roots(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), -1, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.cg_roots, 0, 2)
assert_raises(ValueError, orth.cg_roots, 3.3, 2)
assert_raises(ValueError, orth.cg_roots, 3, -.75)
def test_roots_gegenbauer():
rootf = lambda a: lambda n, mu: sc.roots_gegenbauer(n, a, mu)
evalf = lambda a: lambda n, x: orth.eval_gegenbauer(n, a, x)
weightf = lambda a: lambda x: (1 - x**2)**(a - 0.5)
vgq = verify_gauss_quad
vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 5)
vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 25, atol=1e-12)
vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 100, atol=1e-11)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 5)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 25, atol=1e-13)
vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 100, atol=1e-12)
vgq(rootf(1), evalf(1), weightf(1), -1., 1., 5)
vgq(rootf(1), evalf(1), weightf(1), -1., 1., 25, atol=1e-13)
vgq(rootf(1), evalf(1), weightf(1), -1., 1., 100, atol=1e-12)
vgq(rootf(10), evalf(10), weightf(10), -1., 1., 5)
vgq(rootf(10), evalf(10), weightf(10), -1., 1., 25, atol=1e-13)
vgq(rootf(10), evalf(10), weightf(10), -1., 1., 100, atol=1e-12)
vgq(rootf(50), evalf(50), weightf(50), -1., 1., 5, atol=1e-13)
vgq(rootf(50), evalf(50), weightf(50), -1., 1., 25, atol=1e-12)
vgq(rootf(50), evalf(50), weightf(50), -1., 1., 100, atol=1e-11)
# this is a special case that the old code supported.
# when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
# to a scaled down copy of T_n(x) there.
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 5)
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 25)
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 100)
x, w = sc.roots_gegenbauer(5, 2, False)
y, v, m = sc.roots_gegenbauer(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), -1, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, sc.roots_gegenbauer, 0, 2)
assert_raises(ValueError, sc.roots_gegenbauer, 3.3, 2)
assert_raises(ValueError, sc.roots_gegenbauer, 3, -.75)
def test_cg_roots():
root_func = lambda a: lambda n, mu: orth.cg_roots(n, a, mu)
eval_func = lambda a: lambda n, x: orth.eval_gegenbauer(n, a, x)
verify_gauss_quad(root_func(-0.25), eval_func(-0.25), 5)
verify_gauss_quad(root_func(-0.25), eval_func(-0.25), 25, atol=1e-12)
verify_gauss_quad(root_func(-0.25), eval_func(-0.25), 100, atol=1e-11)
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-12)
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-12)
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, atol=1e-13)
verify_gauss_quad(root_func(50), eval_func(50), 25, atol=1e-12)
verify_gauss_quad(root_func(50), eval_func(50), 100, atol=1e-11)
# this is a special case that the old code supported.
# when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
# to a scaled down copy of T_n(x) there.
verify_gauss_quad(root_func(0), orth.eval_chebyt, 5)
verify_gauss_quad(root_func(0), orth.eval_chebyt, 25)
verify_gauss_quad(root_func(0), orth.eval_chebyt, 100)
x, w = orth.cg_roots(5, 2, False)
y, v, m = orth.cg_roots(5, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.cg_roots, 0, 2)
assert_raises(ValueError, orth.cg_roots, 3.3, 2)
assert_raises(ValueError, orth.cg_roots, 3, -.75)
def test_cg_roots():
root_func = lambda a: lambda n, mu: orth.cg_roots(n, a, mu)
eval_func = lambda a: lambda n, x: orth.eval_gegenbauer(n, a, x)
verify_gauss_quad(root_func(-0.25), eval_func(-0.25), 5)
verify_gauss_quad(root_func(-0.25), eval_func(-0.25), 25, atol=1e-12)
verify_gauss_quad(root_func(-0.25), eval_func(-0.25), 100, atol=1e-11)
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-12)
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-12)
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, atol=1e-13)
verify_gauss_quad(root_func(50), eval_func(50), 25, atol=1e-12)
verify_gauss_quad(root_func(50), eval_func(50), 100, atol=1e-11)
# this is a special case that the old code supported.
# when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
# to a scaled down copy of T_n(x) there.
verify_gauss_quad(root_func(0), orth.eval_chebyt, 5)
verify_gauss_quad(root_func(0), orth.eval_chebyt, 25)
verify_gauss_quad(root_func(0), orth.eval_chebyt, 100)
x, w = orth.cg_roots(5, 2, False)
y, v, m = orth.cg_roots(5, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.cg_roots, 0, 2)
assert_raises(ValueError, orth.cg_roots, 3.3, 2)
assert_raises(ValueError, orth.cg_roots, 3, -.75)
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