def test_chebyshev_t():
x, w = gauss_chebyshev_t(1, 17)
assert [str(r) for r in x] == ['0']
assert [str(r) for r in w] == ['3.1415926535897932']
x, w = gauss_chebyshev_t(2, 17)
assert [str(r) for r in x] == [
'0.70710678118654752',
'-0.70710678118654752']
assert [str(r) for r in w] == [
'1.5707963267948966',
'1.5707963267948966']
x, w = gauss_chebyshev_t(3, 17)
assert [str(r) for r in x] == [
'0.86602540378443865',
'0',
'-0.86602540378443865']
assert [str(r) for r in w] == [
'1.0471975511965977',
'1.0471975511965977',
'1.0471975511965977']
x, w = gauss_chebyshev_t(4, 17)
assert [str(r) for r in x] == [
'0.92387953251128676',
'0.38268343236508977',
'-0.38268343236508977',
'-0.92387953251128676']
assert [str(r) for r in w] == [
'0.78539816339744831',
'0.78539816339744831',
'0.78539816339744831',
'0.78539816339744831']
x, w = gauss_chebyshev_t(5, 17)
assert [str(r) for r in x] == [
'0.95105651629515357',
'0.58778525229247313',
'0',
'-0.58778525229247313',
'-0.95105651629515357']
assert [str(r) for r in w] == [
'0.62831853071795865',
'0.62831853071795865',
'0.62831853071795865',
'0.62831853071795865',
'0.62831853071795865']
def test_chebyshev_t():
x, w = gauss_chebyshev_t(1, 17)
assert [str(r) for r in x] == ['0']
assert [str(r) for r in w] == ['3.1415926535897932']
x, w = gauss_chebyshev_t(2, 17)
assert [str(r) for r in x] == [
'0.70710678118654752',
'-0.70710678118654752']
assert [str(r) for r in w] == [
'1.5707963267948966',
'1.5707963267948966']
x, w = gauss_chebyshev_t(3, 17)
assert [str(r) for r in x] == [
'0.86602540378443865',
'0',
'-0.86602540378443865']
assert [str(r) for r in w] == [
'1.0471975511965977',
'1.0471975511965977',
'1.0471975511965977']
x, w = gauss_chebyshev_t(4, 17)
assert [str(r) for r in x] == [
'0.92387953251128676',
'0.38268343236508977',
'-0.38268343236508977',
'-0.92387953251128676']
assert [str(r) for r in w] == [
'0.78539816339744831',
'0.78539816339744831',
'0.78539816339744831',
'0.78539816339744831']
x, w = gauss_chebyshev_t(5, 17)
assert [str(r) for r in x] == [
'0.95105651629515357',
'0.58778525229247313',
'0',
'-0.58778525229247313',
'-0.95105651629515357']
assert [str(r) for r in w] == [
'0.62831853071795865',
'0.62831853071795865',
'0.62831853071795865',
'0.62831853071795865',
'0.62831853071795865']
def test_chebyshev_t():
x, w = gauss_chebyshev_t(1, 17)
assert [str(r) for r in x] == ["0"]
assert [str(r) for r in w] == ["3.1415926535897932"]
x, w = gauss_chebyshev_t(2, 17)
assert [str(r)
for r in x] == ["0.70710678118654752", "-0.70710678118654752"]
assert [str(r) for r in w] == ["1.5707963267948966", "1.5707963267948966"]
x, w = gauss_chebyshev_t(3, 17)
assert [str(r) for r in x
] == ["0.86602540378443865", "0", "-0.86602540378443865"]
assert [str(r) for r in w] == [
"1.0471975511965977",
"1.0471975511965977",
"1.0471975511965977",
]
x, w = gauss_chebyshev_t(4, 17)
assert [str(r) for r in x] == [
"0.92387953251128676",
"0.38268343236508977",
"-0.38268343236508977",
"-0.92387953251128676",
]
assert [str(r) for r in w] == [
"0.78539816339744831",
"0.78539816339744831",
"0.78539816339744831",
"0.78539816339744831",
]
x, w = gauss_chebyshev_t(5, 17)
assert [str(r) for r in x] == [
"0.95105651629515357",
"0.58778525229247313",
"0",
"-0.58778525229247313",
"-0.95105651629515357",
]
assert [str(r) for r in w] == [
"0.62831853071795865",
"0.62831853071795865",
"0.62831853071795865",
"0.62831853071795865",
"0.62831853071795865",
]
def test_chebyshev_t_precise():
x, w = gauss_chebyshev_t(3, 40)
assert [str(r) for r in x] == [
'0.8660254037844386467637231707529361834714',
'0',
'-0.8660254037844386467637231707529361834714']
assert [str(r) for r in w] == [
'1.047197551196597746154214461093167628066',
'1.047197551196597746154214461093167628066',
'1.047197551196597746154214461093167628066']
def test_chebyshev_t_precise():
x, w = gauss_chebyshev_t(3, 40)
assert [str(r) for r in x] == [
'0.8660254037844386467637231707529361834714',
'0',
'-0.8660254037844386467637231707529361834714']
assert [str(r) for r in w] == [
'1.047197551196597746154214461093167628066',
'1.047197551196597746154214461093167628066',
'1.047197551196597746154214461093167628066']
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