def ploteig(an,ev,nd=20):
N = len(an)
x = linspace(-1, 1, nd)
v = zeros(nd, float)
for i, a in enumerate(an):
T = orthogonal.chebyt(2*i)
v[:] += a*T(x)
plot(x, v, 'o-')
return x, v
def ploteig(an,ev,nd=20):
N = len(an)
x = linspace(-1, 1, nd)
v = zeros(nd, float)
for i, a in enumerate(an):
T = orthogonal.chebyt(2*i)
v[:] += a*T(x)
plot(x, v, 'o-')
return x, v
def test_t_roots():
weightf = orth.chebyt(5).weight_func
verify_gauss_quad(orth.t_roots, orth.eval_chebyt, weightf, -1., 1., 5)
verify_gauss_quad(orth.t_roots, orth.eval_chebyt, weightf, -1., 1., 25)
verify_gauss_quad(orth.t_roots, orth.eval_chebyt, weightf, -1., 1., 100)
x, w = orth.t_roots(5, False)
y, v, m = orth.t_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.t_roots, 0)
assert_raises(ValueError, orth.t_roots, 3.3)
def test_roots_chebyt():
weightf = orth.chebyt(5).weight_func
verify_gauss_quad(sc.roots_chebyt, orth.eval_chebyt, weightf, -1., 1., 5)
verify_gauss_quad(sc.roots_chebyt, orth.eval_chebyt, weightf, -1., 1., 25)
verify_gauss_quad(sc.roots_chebyt, orth.eval_chebyt, weightf, -1., 1., 100)
x, w = sc.roots_chebyt(5, False)
y, v, m = sc.roots_chebyt(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_chebyt, 0)
assert_raises(ValueError, sc.roots_chebyt, 3.3)
def test_chebyt(self):
T0 = orth.chebyt(0)
T1 = orth.chebyt(1)
T2 = orth.chebyt(2)
T3 = orth.chebyt(3)
T4 = orth.chebyt(4)
T5 = orth.chebyt(5)
assert_array_almost_equal(T0.c, [1], 13)
assert_array_almost_equal(T1.c, [1, 0], 13)
assert_array_almost_equal(T2.c, [2, 0, -1], 13)
assert_array_almost_equal(T3.c, [4, 0, -3, 0], 13)
assert_array_almost_equal(T4.c, [8, 0, -8, 0, 1], 13)
assert_array_almost_equal(T5.c, [16, 0, -20, 0, 5, 0], 13)
def test_chebyt(self):
T0 = orth.chebyt(0)
T1 = orth.chebyt(1)
T2 = orth.chebyt(2)
T3 = orth.chebyt(3)
T4 = orth.chebyt(4)
T5 = orth.chebyt(5)
assert_array_almost_equal(T0.c,[1],13)
assert_array_almost_equal(T1.c,[1,0],13)
assert_array_almost_equal(T2.c,[2,0,-1],13)
assert_array_almost_equal(T3.c,[4,0,-3,0],13)
assert_array_almost_equal(T4.c,[8,0,-8,0,1],13)
assert_array_almost_equal(T5.c,[16,0,-20,0,5,0],13)
def test_sh_chebyt(self):
# T*_n(x) = T_n(2x-1)
psub = np.poly1d([2, -1])
Ts0 = orth.sh_chebyt(0)
Ts1 = orth.sh_chebyt(1)
Ts2 = orth.sh_chebyt(2)
Ts3 = orth.sh_chebyt(3)
Ts4 = orth.sh_chebyt(4)
Ts5 = orth.sh_chebyt(5)
tse0 = orth.chebyt(0)(psub)
tse1 = orth.chebyt(1)(psub)
tse2 = orth.chebyt(2)(psub)
tse3 = orth.chebyt(3)(psub)
tse4 = orth.chebyt(4)(psub)
tse5 = orth.chebyt(5)(psub)
assert_array_almost_equal(Ts0.c, tse0.c, 13)
assert_array_almost_equal(Ts1.c, tse1.c, 13)
assert_array_almost_equal(Ts2.c, tse2.c, 13)
assert_array_almost_equal(Ts3.c, tse3.c, 13)
assert_array_almost_equal(Ts4.c, tse4.c, 12)
assert_array_almost_equal(Ts5.c, tse5.c, 12)
def test_sh_chebyt(self):
# T*_n(x) = T_n(2x-1)
psub = np.poly1d([2,-1])
Ts0 = orth.sh_chebyt(0)
Ts1 = orth.sh_chebyt(1)
Ts2 = orth.sh_chebyt(2)
Ts3 = orth.sh_chebyt(3)
Ts4 = orth.sh_chebyt(4)
Ts5 = orth.sh_chebyt(5)
tse0 = orth.chebyt(0)(psub)
tse1 = orth.chebyt(1)(psub)
tse2 = orth.chebyt(2)(psub)
tse3 = orth.chebyt(3)(psub)
tse4 = orth.chebyt(4)(psub)
tse5 = orth.chebyt(5)(psub)
assert_array_almost_equal(Ts0.c,tse0.c,13)
assert_array_almost_equal(Ts1.c,tse1.c,13)
assert_array_almost_equal(Ts2.c,tse2.c,13)
assert_array_almost_equal(Ts3.c,tse3.c,13)
assert_array_almost_equal(Ts4.c,tse4.c,12)
assert_array_almost_equal(Ts5.c,tse5.c,12)
