def test_he_roots():
verify_gauss_quad(orth.he_roots, orth.eval_hermitenorm, 5)
verify_gauss_quad(orth.he_roots, orth.eval_hermitenorm, 25, atol=1e-13)
verify_gauss_quad(orth.he_roots, orth.eval_hermitenorm, 100, atol=1e-12)
x, w = orth.he_roots(5, False)
y, v, m = orth.he_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.he_roots, 0)
assert_raises(ValueError, orth.he_roots, 3.3)
def test_he_roots():
verify_gauss_quad(orth.he_roots, orth.eval_hermitenorm, 5)
verify_gauss_quad(orth.he_roots, orth.eval_hermitenorm, 25, atol=1e-13)
verify_gauss_quad(orth.he_roots, orth.eval_hermitenorm, 100, atol=1e-12)
x, w = orth.he_roots(5, False)
y, v, m = orth.he_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.he_roots, 0)
assert_raises(ValueError, orth.he_roots, 3.3)
def test_he_roots():
rootf = orth.he_roots
evalf = orth.eval_hermitenorm
weightf = orth.hermitenorm(5).weight_func
verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
x, w = orth.he_roots(5, False)
y, v, m = orth.he_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.he_roots, 0)
assert_raises(ValueError, orth.he_roots, 3.3)
def test_he_roots():
rootf = orth.he_roots
evalf = orth.eval_hermitenorm
weightf = orth.hermitenorm(5).weight_func
verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
x, w = orth.he_roots(5, False)
y, v, m = orth.he_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.he_roots, 0)
assert_raises(ValueError, orth.he_roots, 3.3)
def qnwnorm1(n):
"""Gauss-Hermite normal quadrature nodes and weights in 1 dimension
Parameters
------------
n : int
Number of quadrature nodes
Returns
----------
x : (n, ) ndarray
Quadrature nodes
w : (n, ) ndarray
Quadrature weights
"""
x, w = orthogonal.he_roots(n)
## normalize weights to sum to 1
w /= sum(w)
return (x.real, w)