def test_ps_roots():
weightf = orth.sh_legendre(5).weight_func
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0., 1., 5)
verify_gauss_quad(orth.ps_roots,
orth.eval_sh_legendre,
weightf,
0.,
1.,
25,
atol=1e-13)
verify_gauss_quad(orth.ps_roots,
orth.eval_sh_legendre,
weightf,
0.,
1.,
100,
atol=1e-12)
x, w = orth.ps_roots(5, False)
y, v, m = orth.ps_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, 0, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.ps_roots, 0)
assert_raises(ValueError, orth.ps_roots, 3.3)
def test_ps_roots():
weightf = orth.sh_legendre(5).weight_func
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0.0, 1.0, 5)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0.0, 1.0, 25, atol=1e-13)
verify_gauss_quad(orth.ps_roots, orth.eval_sh_legendre, weightf, 0.0, 1.0, 100, atol=1e-12)
x, w = orth.ps_roots(5, False)
y, v, m = orth.ps_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, 0, 1)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.ps_roots, 0)
assert_raises(ValueError, orth.ps_roots, 3.3)
def test_sh_legendre(self):
# P*_n(x) = P_n(2x-1)
psub = np.poly1d([2, -1])
Ps0 = orth.sh_legendre(0)
Ps1 = orth.sh_legendre(1)
Ps2 = orth.sh_legendre(2)
Ps3 = orth.sh_legendre(3)
Ps4 = orth.sh_legendre(4)
Ps5 = orth.sh_legendre(5)
pse0 = orth.legendre(0)(psub)
pse1 = orth.legendre(1)(psub)
pse2 = orth.legendre(2)(psub)
pse3 = orth.legendre(3)(psub)
pse4 = orth.legendre(4)(psub)
pse5 = orth.legendre(5)(psub)
assert_array_almost_equal(Ps0.c, pse0.c, 13)
assert_array_almost_equal(Ps1.c, pse1.c, 13)
assert_array_almost_equal(Ps2.c, pse2.c, 13)
assert_array_almost_equal(Ps3.c, pse3.c, 13)
assert_array_almost_equal(Ps4.c, pse4.c, 12)
assert_array_almost_equal(Ps5.c, pse5.c, 12)
def test_sh_legendre(self):
# P*_n(x) = P_n(2x-1)
psub = np.poly1d([2,-1])
Ps0 = orth.sh_legendre(0)
Ps1 = orth.sh_legendre(1)
Ps2 = orth.sh_legendre(2)
Ps3 = orth.sh_legendre(3)
Ps4 = orth.sh_legendre(4)
Ps5 = orth.sh_legendre(5)
pse0 = orth.legendre(0)(psub)
pse1 = orth.legendre(1)(psub)
pse2 = orth.legendre(2)(psub)
pse3 = orth.legendre(3)(psub)
pse4 = orth.legendre(4)(psub)
pse5 = orth.legendre(5)(psub)
assert_array_almost_equal(Ps0.c,pse0.c,13)
assert_array_almost_equal(Ps1.c,pse1.c,13)
assert_array_almost_equal(Ps2.c,pse2.c,13)
assert_array_almost_equal(Ps3.c,pse3.c,13)
assert_array_almost_equal(Ps4.c,pse4.c,12)
assert_array_almost_equal(Ps5.c,pse5.c,12)