Example #1
0
def test_u_roots():
    weightf = orth.chebyu(5).weight_func
    verify_gauss_quad(orth.u_roots, orth.eval_chebyu, weightf, -1., 1., 5)
    verify_gauss_quad(orth.u_roots, orth.eval_chebyu, weightf, -1., 1., 25)
    verify_gauss_quad(orth.u_roots, orth.eval_chebyu, weightf, -1., 1., 100)

    x, w = orth.u_roots(5, False)
    y, v, m = orth.u_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, -1, 1)
    assert_allclose(m, muI, rtol=muI_err)

    assert_raises(ValueError, orth.u_roots, 0)
    assert_raises(ValueError, orth.u_roots, 3.3)
Example #2
0
def test_roots_chebyu():
    weightf = orth.chebyu(5).weight_func
    verify_gauss_quad(sc.roots_chebyu, orth.eval_chebyu, weightf, -1., 1., 5)
    verify_gauss_quad(sc.roots_chebyu, orth.eval_chebyu, weightf, -1., 1., 25)
    verify_gauss_quad(sc.roots_chebyu, orth.eval_chebyu, weightf, -1., 1., 100)

    x, w = sc.roots_chebyu(5, False)
    y, v, m = sc.roots_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, -1, 1)
    assert_allclose(m, muI, rtol=muI_err)

    assert_raises(ValueError, sc.roots_chebyu, 0)
    assert_raises(ValueError, sc.roots_chebyu, 3.3)
Example #3
0
 def test_chebyu(self):
     U0 = orth.chebyu(0)
     U1 = orth.chebyu(1)
     U2 = orth.chebyu(2)
     U3 = orth.chebyu(3)
     U4 = orth.chebyu(4)
     U5 = orth.chebyu(5)
     assert_array_almost_equal(U0.c, [1], 13)
     assert_array_almost_equal(U1.c, [2, 0], 13)
     assert_array_almost_equal(U2.c, [4, 0, -1], 13)
     assert_array_almost_equal(U3.c, [8, 0, -4, 0], 13)
     assert_array_almost_equal(U4.c, [16, 0, -12, 0, 1], 13)
     assert_array_almost_equal(U5.c, [32, 0, -32, 0, 6, 0], 13)
Example #4
0
 def test_chebyu(self):
     U0 = orth.chebyu(0)
     U1 = orth.chebyu(1)
     U2 = orth.chebyu(2)
     U3 = orth.chebyu(3)
     U4 = orth.chebyu(4)
     U5 = orth.chebyu(5)
     assert_array_almost_equal(U0.c,[1],13)
     assert_array_almost_equal(U1.c,[2,0],13)
     assert_array_almost_equal(U2.c,[4,0,-1],13)
     assert_array_almost_equal(U3.c,[8,0,-4,0],13)
     assert_array_almost_equal(U4.c,[16,0,-12,0,1],13)
     assert_array_almost_equal(U5.c,[32,0,-32,0,6,0],13)
Example #5
0
 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)
Example #6
0
 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)