def test_jacobi_precise():
x, w = gauss_jacobi(3, -S.Half, S.Half, 40)
assert [str(r) for r in x] == [
'-0.6234898018587335305250048840042398106323',
'0.2225209339563144042889025644967947594664',
'0.9009688679024191262361023195074450511659']
assert [str(r) for r in w] == [
'0.3379547635663543330553835737094171534907',
'1.097332224279111467485302294320899710461',
'1.706305665744327437921957515249186020246']
x, w = gauss_jacobi(3, 2, 3, 40)
assert [str(r) for r in x] == [
'-0.4611587037808976179121958105554375981274',
'0.1043853303832390210914918407615869143233',
'0.6295006461249313240934312425211234110769']
assert [str(r) for r in w] == [
'0.1793761350221326596137764371503859752628',
'0.6159564099114715430909548532229749439714',
'0.2713341217330624639619353762933057474325']
def test_jacobi_precise():
x, w = gauss_jacobi(3, -S.Half, S.Half, 40)
assert [str(r) for r in x] == [
'-0.6234898018587335305250048840042398106323',
'0.2225209339563144042889025644967947594664',
'0.9009688679024191262361023195074450511659']
assert [str(r) for r in w] == [
'0.3379547635663543330553835737094171534907',
'1.097332224279111467485302294320899710461',
'1.706305665744327437921957515249186020246']
x, w = gauss_jacobi(3, 2, 3, 40)
assert [str(r) for r in x] == [
'-0.4611587037808976179121958105554375981274',
'0.1043853303832390210914918407615869143233',
'0.6295006461249313240934312425211234110769']
assert [str(r) for r in w] == [
'0.1793761350221326596137764371503859752628',
'0.6159564099114715430909548532229749439714',
'0.2713341217330624639619353762933057474325']
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
def test_jacobi():
x, w = gauss_jacobi(1, Rational(-1, 2), S.Half, 17)
assert [str(r) for r in x] == ['0.50000000000000000']
assert [str(r) for r in w] == ['3.1415926535897932']
x, w = gauss_jacobi(2, Rational(-1, 2), S.Half, 17)
assert [str(r)
for r in x] == ['-0.30901699437494742', '0.80901699437494742']
assert [str(r) for r in w] == ['0.86831485369082398', '2.2732777998989693']
x, w = gauss_jacobi(3, Rational(-1, 2), S.Half, 17)
assert [str(r) for r in x] == [
'-0.62348980185873353', '0.22252093395631440', '0.90096886790241913'
]
assert [str(r) for r in w] == [
'0.33795476356635433', '1.0973322242791115', '1.7063056657443274'
]
x, w = gauss_jacobi(4, Rational(-1, 2), S.Half, 17)
assert [str(r) for r in x] == [
'-0.76604444311897804', '-0.17364817766693035', '0.50000000000000000',
'0.93969262078590838'
]
assert [str(r) for r in w] == [
'0.16333179083642836', '0.57690240318269103', '1.0471975511965977',
'1.3541609083740761'
]
x, w = gauss_jacobi(5, Rational(-1, 2), S.Half, 17)
assert [str(r) for r in x] == [
'-0.84125353283118117', '-0.41541501300188643', '0.14231483827328514',
'0.65486073394528506', '0.95949297361449739'
]
assert [str(r) for r in w] == [
'0.090675770007435372', '0.33391416373675607', '0.65248870981926643',
'0.94525424081394926', '1.1192597692123861'
]
x, w = gauss_jacobi(1, 2, 3, 17)
assert [str(r) for r in x] == ['0.14285714285714286']
assert [str(r) for r in w] == ['1.0666666666666667']
x, w = gauss_jacobi(2, 2, 3, 17)
assert [str(r)
for r in x] == ['-0.24025307335204215', '0.46247529557426437']
assert [str(r)
for r in w] == ['0.48514624517838660', '0.58152042148828007']
x, w = gauss_jacobi(3, 2, 3, 17)
assert [str(r) for r in x] == [
'-0.46115870378089762', '0.10438533038323902', '0.62950064612493132'
]
assert [str(r) for r in w] == [
'0.17937613502213266', '0.61595640991147154', '0.27133412173306246'
]
x, w = gauss_jacobi(4, 2, 3, 17)
assert [str(r) for r in x] == [
'-0.59903470850824782', '-0.14761105199952565', '0.32554377081188859',
'0.72879429738819258'
]
assert [str(r) for r in w] == [
'0.067809641836772187', '0.38956404952032481', '0.47995970868024150',
'0.12933326662932816'
]
x, w = gauss_jacobi(5, 2, 3, 17)
assert [str(r) for r in x] == [
'-0.69045775012676106', '-0.32651993134900065', '0.082337849552034905',
'0.47517887061283164', '0.79279429464422850'
]
assert [str(r) for r in w] == [
'0.027410178066337099', '0.21291786060364828', '0.43908437944395081',
'0.32220656547221822', '0.065047683080512268'
]
def test_jacobi():
x, w = gauss_jacobi(1, -S.Half, S.Half, 17)
assert [str(r) for r in x] == ['0.50000000000000000']
assert [str(r) for r in w] == ['3.1415926535897932']
x, w = gauss_jacobi(2, -S.Half, S.Half, 17)
assert [str(r) for r in x] == ['-0.30901699437494742',
'0.80901699437494742']
assert [str(r) for r in w] == ['0.86831485369082398',
'2.2732777998989693']
x, w = gauss_jacobi(3, -S.Half, S.Half, 17)
assert [str(r) for r in x] == ['-0.62348980185873353',
'0.22252093395631440',
'0.90096886790241913']
assert [str(r) for r in w] == ['0.33795476356635433',
'1.0973322242791115',
'1.7063056657443274']
x, w = gauss_jacobi(4, -S.Half, S.Half, 17)
assert [str(r) for r in x] == ['-0.76604444311897804',
'-0.17364817766693035',
'0.50000000000000000',
'0.93969262078590838']
assert [str(r) for r in w] == ['0.16333179083642836',
'0.57690240318269103',
'1.0471975511965977',
'1.3541609083740761']
x, w = gauss_jacobi(5, -S.Half, S.Half, 17)
assert [str(r) for r in x] == ['-0.84125353283118117',
'-0.41541501300188643',
'0.14231483827328514',
'0.65486073394528506',
'0.95949297361449739']
assert [str(r) for r in w] == ['0.090675770007435371',
'0.33391416373675607',
'0.65248870981926643',
'0.94525424081394926',
'1.1192597692123861']
x, w = gauss_jacobi(1, 2, 3, 17)
assert [str(r) for r in x] == ['0.14285714285714286']
assert [str(r) for r in w] == ['1.0666666666666667']
x, w = gauss_jacobi(2, 2, 3, 17)
assert [str(r) for r in x] == ['-0.24025307335204215',
'0.46247529557426437']
assert [str(r) for r in w] == ['0.48514624517838660',
'0.58152042148828007']
x, w = gauss_jacobi(3, 2, 3, 17)
assert [str(r) for r in x] == ['-0.46115870378089762',
'0.10438533038323902',
'0.62950064612493132']
assert [str(r) for r in w] == ['0.17937613502213266',
'0.61595640991147154',
'0.27133412173306246']
x, w = gauss_jacobi(4, 2, 3, 17)
assert [str(r) for r in x] == ['-0.59903470850824782',
'-0.14761105199952565',
'0.32554377081188859',
'0.72879429738819258']
assert [str(r) for r in w] == ['0.067809641836772187',
'0.38956404952032481',
'0.47995970868024150',
'0.12933326662932816']
x, w = gauss_jacobi(5, 2, 3, 17)
assert [str(r) for r in x] == ['-0.69045775012676106',
'-0.32651993134900065',
'0.082337849552034905',
'0.47517887061283164',
'0.79279429464422850']
assert [str(r) for r in w] ==['0.027410178066337099',
'0.21291786060364828',
'0.43908437944395081',
'0.32220656547221822',
'0.065047683080512268']
