def test_roots_sh_chebyu():
weightf = orth.sh_chebyu(5).weight_func
verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 5)
verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 25)
verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1.,
100, atol=1e-13)
x, w = sc.roots_sh_chebyu(5, False)
y, v, m = sc.roots_sh_chebyu(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, 0, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, sc.roots_sh_chebyu, 0)
assert_raises(ValueError, sc.roots_sh_chebyu, 3.3)
def test_sh_chebyu(self):
# U*_n(x) = U_n(2x-1)
psub = np.poly1d([2, -1])
Us0 = orth.sh_chebyu(0)
Us1 = orth.sh_chebyu(1)
Us2 = orth.sh_chebyu(2)
Us3 = orth.sh_chebyu(3)
Us4 = orth.sh_chebyu(4)
Us5 = orth.sh_chebyu(5)
use0 = orth.chebyu(0)(psub)
use1 = orth.chebyu(1)(psub)
use2 = orth.chebyu(2)(psub)
use3 = orth.chebyu(3)(psub)
use4 = orth.chebyu(4)(psub)
use5 = orth.chebyu(5)(psub)
assert_array_almost_equal(Us0.c, use0.c, 13)
assert_array_almost_equal(Us1.c, use1.c, 13)
assert_array_almost_equal(Us2.c, use2.c, 13)
assert_array_almost_equal(Us3.c, use3.c, 13)
assert_array_almost_equal(Us4.c, use4.c, 12)
assert_array_almost_equal(Us5.c, use5.c, 11)