def test_js_roots():
rf = lambda a, b: lambda n, mu: orth.js_roots(n, a, b, mu)
ef = lambda a, b: lambda n, x: orth.eval_sh_jacobi(n, a, b, x)
wf = lambda a, b: lambda x: (1. - x)**(a - b) * (x)**(b - 1.)
vgq = verify_gauss_quad
vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1., 5)
vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
25, atol=1e-12)
vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
100, atol=1e-11)
vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 5)
vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 25, atol=1e-13)
vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 100, atol=1e-12)
vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 5)
vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 25, atol=1.5e-13)
vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 100, atol=1e-12)
vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 5)
vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 25, atol=1e-13)
vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 100, atol=1e-12)
vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 5)
vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 25)
vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1.,
100, atol=1e-13)
vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 5, atol=1e-12)
vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 25, atol=1e-11)
vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 100, atol=1e-10)
vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 5, atol=3.5e-14)
vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 25, atol=2e-13)
vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1.,
100, atol=1e-12)
x, w = orth.js_roots(5, 3, 2, False)
y, v, m = orth.js_roots(5, 3, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(wf(3,2), 0, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.js_roots, 0, 1, 1)
assert_raises(ValueError, orth.js_roots, 3.3, 1, 1)
assert_raises(ValueError, orth.js_roots, 3, 1, 2) # p - q <= -1
assert_raises(ValueError, orth.js_roots, 3, 2, -1) # q <= 0
assert_raises(ValueError, orth.js_roots, 3, -2, -1) # both
def test_js_roots():
roots = lambda a, b: lambda n, mu: orth.js_roots(n, a, b, mu)
evalf = lambda a, b: lambda n, x: orth.eval_sh_jacobi(n, a, b, x)
verify_gauss_quad(roots(-0.5, 0.25), evalf(-0.5, 0.25), 5)
verify_gauss_quad(roots(-0.5, 0.25), evalf(-0.5, 0.25), 25, atol=1e-12)
verify_gauss_quad(roots(-0.5, 0.25), evalf(-0.5, 0.25), 100, atol=1e-11)
verify_gauss_quad(roots(0.5, 0.5), evalf(0.5, 0.5), 5)
verify_gauss_quad(roots(0.5, 0.5), evalf(0.5, 0.5), 25, atol=1e-13)
verify_gauss_quad(roots(0.5, 0.5), evalf(0.5, 0.5), 100, atol=1e-12)
verify_gauss_quad(roots(1, 0.5), evalf(1, 0.5), 5)
verify_gauss_quad(roots(1, 0.5), evalf(1, 0.5), 25, atol=1e-13)
verify_gauss_quad(roots(1, 0.5), evalf(1, 0.5), 100, atol=1e-12)
verify_gauss_quad(roots(2, 0.9), evalf(2, 0.9), 5)
verify_gauss_quad(roots(2, 0.9), evalf(2, 0.9), 25, atol=1e-13)
verify_gauss_quad(roots(2, 0.9), evalf(2, 0.9), 100, atol=1e-12)
verify_gauss_quad(roots(27.3, 18.24), evalf(27.3, 18.24), 5)
verify_gauss_quad(roots(27.3, 18.24), evalf(27.3, 18.24), 25)
verify_gauss_quad(roots(27.3, 18.24), evalf(27.3, 18.24), 100, atol=1e-13)
verify_gauss_quad(roots(47.1, 0.2), evalf(47.1, 0.2), 5, atol=1e-12)
verify_gauss_quad(roots(47.1, 0.2), evalf(47.1, 0.2), 25, atol=1e-11)
verify_gauss_quad(roots(47.1, 0.2), evalf(47.1, 0.2), 100, atol=1e-10)
verify_gauss_quad(roots(68.9, 2.25), evalf(68.9, 2.25), 5, atol=2e-14)
verify_gauss_quad(roots(68.9, 2.25), evalf(68.9, 2.25), 25, atol=2e-13)
verify_gauss_quad(roots(68.9, 2.25), evalf(68.9, 2.25), 100, atol=1e-12)
x, w = orth.js_roots(5, 3, 2, False)
y, v, m = orth.js_roots(5, 3, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.js_roots, 0, 1, 1)
assert_raises(ValueError, orth.js_roots, 3.3, 1, 1)
assert_raises(ValueError, orth.js_roots, 3, 1, 2) # p - q <= -1
assert_raises(ValueError, orth.js_roots, 3, 2, -1) # q <= 0
assert_raises(ValueError, orth.js_roots, 3, -2, -1) # both
def test_js_roots():
roots = lambda a, b: lambda n, mu: orth.js_roots(n, a, b, mu)
evalf = lambda a, b: lambda n, x: orth.eval_sh_jacobi(n, a, b, x)
verify_gauss_quad(roots(-0.5, 0.25), evalf(-0.5, 0.25), 5)
verify_gauss_quad(roots(-0.5, 0.25), evalf(-0.5, 0.25), 25, atol=1e-12)
verify_gauss_quad(roots(-0.5, 0.25), evalf(-0.5, 0.25), 100, atol=1e-11)
verify_gauss_quad(roots(0.5, 0.5), evalf(0.5, 0.5), 5)
verify_gauss_quad(roots(0.5, 0.5), evalf(0.5, 0.5), 25, atol=1e-13)
verify_gauss_quad(roots(0.5, 0.5), evalf(0.5, 0.5), 100, atol=1e-12)
verify_gauss_quad(roots(1, 0.5), evalf(1, 0.5), 5)
verify_gauss_quad(roots(1, 0.5), evalf(1, 0.5), 25, atol=1e-13)
verify_gauss_quad(roots(1, 0.5), evalf(1, 0.5), 100, atol=1e-12)
verify_gauss_quad(roots(2, 0.9), evalf(2, 0.9), 5)
verify_gauss_quad(roots(2, 0.9), evalf(2, 0.9), 25, atol=1e-13)
verify_gauss_quad(roots(2, 0.9), evalf(2, 0.9), 100, atol=1e-12)
verify_gauss_quad(roots(27.3, 18.24), evalf(27.3, 18.24), 5)
verify_gauss_quad(roots(27.3, 18.24), evalf(27.3, 18.24), 25)
verify_gauss_quad(roots(27.3, 18.24), evalf(27.3, 18.24), 100, atol=1e-13)
verify_gauss_quad(roots(47.1, 0.2), evalf(47.1, 0.2), 5, atol=1e-12)
verify_gauss_quad(roots(47.1, 0.2), evalf(47.1, 0.2), 25, atol=1e-11)
verify_gauss_quad(roots(47.1, 0.2), evalf(47.1, 0.2), 100, atol=1e-10)
verify_gauss_quad(roots(68.9, 2.25), evalf(68.9, 2.25), 5, atol=2e-14)
verify_gauss_quad(roots(68.9, 2.25), evalf(68.9, 2.25), 25, atol=2e-13)
verify_gauss_quad(roots(68.9, 2.25), evalf(68.9, 2.25), 100, atol=1e-12)
x, w = orth.js_roots(5, 3, 2, False)
y, v, m = orth.js_roots(5, 3, 2, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.js_roots, 0, 1, 1)
assert_raises(ValueError, orth.js_roots, 3.3, 1, 1)
assert_raises(ValueError, orth.js_roots, 3, 1, 2) # p - q <= -1
assert_raises(ValueError, orth.js_roots, 3, 2, -1) # q <= 0
assert_raises(ValueError, orth.js_roots, 3, -2, -1) # both
