def test_chebyshev_u():
x, w = gauss_chebyshev_u(1, 17)
assert [str(r) for r in x] == ["0"]
assert [str(r) for r in w] == ["1.5707963267948966"]
x, w = gauss_chebyshev_u(2, 17)
assert [str(r)
for r in x] == ["0.50000000000000000", "-0.50000000000000000"]
assert [str(r)
for r in w] == ["0.78539816339744831", "0.78539816339744831"]
x, w = gauss_chebyshev_u(3, 17)
assert [str(r) for r in x
] == ["0.70710678118654752", "0", "-0.70710678118654752"]
assert [str(r) for r in w] == [
"0.39269908169872415",
"0.78539816339744831",
"0.39269908169872415",
]
x, w = gauss_chebyshev_u(4, 17)
assert [str(r) for r in x] == [
"0.80901699437494742",
"0.30901699437494742",
"-0.30901699437494742",
"-0.80901699437494742",
]
assert [str(r) for r in w] == [
"0.21707871342270599",
"0.56831944997474231",
"0.56831944997474231",
"0.21707871342270599",
]
x, w = gauss_chebyshev_u(5, 17)
assert [str(r) for r in x] == [
"0.86602540378443865",
"0.50000000000000000",
"0",
"-0.50000000000000000",
"-0.86602540378443865",
]
assert [str(r) for r in w] == [
"0.13089969389957472",
"0.39269908169872415",
"0.52359877559829887",
"0.39269908169872415",
"0.13089969389957472",
]
def test_chebyshev_u():
x, w = gauss_chebyshev_u(1, 17)
assert [str(r) for r in x] == ['0']
assert [str(r) for r in w] == ['1.5707963267948966']
x, w = gauss_chebyshev_u(2, 17)
assert [str(r) for r in x] == [
'0.50000000000000000',
'-0.50000000000000000']
assert [str(r) for r in w] == [
'0.78539816339744831',
'0.78539816339744831']
x, w = gauss_chebyshev_u(3, 17)
assert [str(r) for r in x] == [
'0.70710678118654752',
'0',
'-0.70710678118654752']
assert [str(r) for r in w] == [
'0.39269908169872415',
'0.78539816339744831',
'0.39269908169872415']
x, w = gauss_chebyshev_u(4, 17)
assert [str(r) for r in x] == [
'0.80901699437494742',
'0.30901699437494742',
'-0.30901699437494742',
'-0.80901699437494742']
assert [str(r) for r in w] == [
'0.21707871342270599',
'0.56831944997474231',
'0.56831944997474231',
'0.21707871342270599']
x, w = gauss_chebyshev_u(5, 17)
assert [str(r) for r in x] == [
'0.86602540378443865',
'0.50000000000000000',
'0',
'-0.50000000000000000',
'-0.86602540378443865']
assert [str(r) for r in w] == [
'0.13089969389957472',
'0.39269908169872415',
'0.52359877559829887',
'0.39269908169872415',
'0.13089969389957472']
def test_chebyshev_u():
x, w = gauss_chebyshev_u(1, 17)
assert [str(r) for r in x] == ['0']
assert [str(r) for r in w] == ['1.5707963267948966']
x, w = gauss_chebyshev_u(2, 17)
assert [str(r) for r in x] == [
'0.50000000000000000',
'-0.50000000000000000']
assert [str(r) for r in w] == [
'0.78539816339744831',
'0.78539816339744831']
x, w = gauss_chebyshev_u(3, 17)
assert [str(r) for r in x] == [
'0.70710678118654752',
'0',
'-0.70710678118654752']
assert [str(r) for r in w] == [
'0.39269908169872415',
'0.78539816339744831',
'0.39269908169872415']
x, w = gauss_chebyshev_u(4, 17)
assert [str(r) for r in x] == [
'0.80901699437494742',
'0.30901699437494742',
'-0.30901699437494742',
'-0.80901699437494742']
assert [str(r) for r in w] == [
'0.21707871342270599',
'0.56831944997474231',
'0.56831944997474231',
'0.21707871342270599']
x, w = gauss_chebyshev_u(5, 17)
assert [str(r) for r in x] == [
'0.86602540378443865',
'0.50000000000000000',
'0',
'-0.50000000000000000',
'-0.86602540378443865']
assert [str(r) for r in w] == [
'0.13089969389957472',
'0.39269908169872415',
'0.52359877559829887',
'0.39269908169872415',
'0.13089969389957472']
def test_chebyshev_u_precise():
x, w = gauss_chebyshev_u(3, 40)
assert [str(r) for r in x] == [
'0.7071067811865475244008443621048490392848',
'0',
'-0.7071067811865475244008443621048490392848']
assert [str(r) for r in w] == [
'0.3926990816987241548078304229099378605246',
'0.7853981633974483096156608458198757210493',
'0.3926990816987241548078304229099378605246']
def test_chebyshev_u_precise():
x, w = gauss_chebyshev_u(3, 40)
assert [str(r) for r in x] == [
'0.7071067811865475244008443621048490392848',
'0',
'-0.7071067811865475244008443621048490392848']
assert [str(r) for r in w] == [
'0.3926990816987241548078304229099378605246',
'0.7853981633974483096156608458198757210493',
'0.3926990816987241548078304229099378605246']
def _quad_coeffs_hq(M, collocation_type, digits=20):
if M == 1:
x = np.array([0.0])
w = np.array([2.0])
elif collocation_type == "gauss_legendre":
from sympy.integrals.quadrature import gauss_legendre
x, w = gauss_legendre(M, digits)
elif collocation_type == "gauss_lobatto":
from sympy.integrals.quadrature import gauss_lobatto
x, w = gauss_lobatto(M, digits)
elif collocation_type == "gauss_hermite":
from sympy.integrals.quadrature import gauss_hermite
x, w = gauss_hermite(M, 30)
x = np.array(x, dtype=float)
w = np.array(w, dtype=float)
elif collocation_type == "gauss_jacobi":
from sympy.integrals.quadrature import gauss_jacobi
x, w = gauss_jacobi(M, 0, 0, 30)
x = np.array(x, dtype=float)
w = np.array(w, dtype=float)
elif collocation_type == "gauss_chebyshev_u":
from sympy.integrals.quadrature import gauss_chebyshev_u
x, w = gauss_chebyshev_u(M, 30)
x = np.array(x, dtype=float)
w = np.array(w, dtype=float)
elif collocation_type == "gauss_chebyshev_t":
from sympy.integrals.quadrature import gauss_chebyshev_t
x, w = gauss_chebyshev_t(M, 30)
x = np.array(x, dtype=float)
w = np.array(w, dtype=float)
else:
raise Exception("Unknown collocation method '" +
str(collocation_type) + "'")
assert len(x) == M
return x, w
