How to use the quadpy.s2._helpers.S2Scheme function in quadpy

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github nschloe / quadpy / quadpy / s2 / _albrecht.py View on Github external
def albrecht_2():
    alpha = (2 * numpy.arange(6) + 1) * pi / 6
    t = numpy.array([cos(alpha), sin(alpha)]).T

    data = [(frac(1, 4), z(2)), (frac(1, 8), sqrt(frac(2, 3)) * t)]

    points, weights = untangle(data)
    return S2Scheme("Albrecht 2", weights, points, 5, _source)
github nschloe / quadpy / quadpy / s2 / _kim_song / __init__.py View on Github external
def kim_song_9():
    data = [
        (0.051310052712355, fsd(2, (0.680167267076408, 2))),
        (0.208368275231940, fsd(2, (0.232463234651158, 2))),
        (0.113628206510048, fsd(2, (0.547722557505169, 2))),
        (0.126977836503225, fsd(2, (0.652159581445885, 1), (0.174745633184644, 1))),
        (0.079067977968328, fsd(2, (0.904823085572323, 1), (0.242446615072141, 1))),
    ]
    points, weights = untangle(data)
    weights /= math.pi
    return S2Scheme("Kim-Song 9", weights, points, 11, _source, 1.742e-14)
github nschloe / quadpy / quadpy / s2 / _albrecht.py View on Github external
D = frac(81, 3125)

    u = sqrt(frac(5, 6)) * cos(pi / 8)
    v = sqrt(frac(5, 6)) * sin(pi / 8)

    data = [
        (B[0], fsd(2, (sqrt(sigma2[0]), 1))),
        (B[1], fsd(2, (sqrt(sigma2[1]), 1))),
        (B[2], fsd(2, (sqrt(sigma2[2]), 1))),
        (C1, pm(2, s1)),
        (C2, pm(2, s2)),
        (D, fsd(2, (u, 1), (v, 1))),
    ]

    points, weights = untangle(data)
    return S2Scheme("Albrecht 5", weights, points, 11, _source)
github nschloe / quadpy / quadpy / s2 / _cools_kim.py View on Github external
(4.6214466764876138e-05, _s4(0.77364389614737803)),
        (0.020941123674084990, _s4(0.67975937134823609)),
        (0.044321766954122515, _s4(0.59230560995561076)),
        (0.052715691149269700, _s4(0.41774444740353380)),
        (0.028690025849304919, _s8(0.89789289495208579, 0.13375169526590821)),
        (0.013819709344648730, _s8(0.93927352486965313, 0.27985732696474981)),
        (0.037034888202855274, _s8(0.79099671385625722, 0.39385576573951899)),
        (0.047520136607474831, _s8(0.56605481445792489, 0.10885005806786229)),
        (0.014296165120136605, _s8(0.83180776464845906, 0.51224072541565606)),
        (0.042923763669888949, _s8(0.76010583069266321, 0.12830595415488073)),
        (0.047444099811669938, _s8(0.62209339812108792, 0.34691040719842391)),
        (0.063500222219468438, _s8(0.36200059276768541, 0.16676191877222966)),
    ]
    points, weights = untangle(data)
    weights /= math.pi
    return S2Scheme("Cools-Kim 3", weights, points, 21, _source)
github nschloe / quadpy / quadpy / s2 / _albrecht.py View on Github external
def albrecht_1():
    # Equals Albrecht-Collatz, Lether(2)
    alpha = (2 * numpy.arange(4) + 1) * pi / 4
    t = numpy.array([cos(alpha), sin(alpha)]).T

    data = [(frac(1, 4), sqrt(frac(1, 2)) * t)]

    points, weights = untangle(data)
    return S2Scheme("Albrecht 1", weights, points, 3, _source)
github nschloe / quadpy / quadpy / s2 / _kim_song / __init__.py View on Github external
def kim_song_1():
    data = [
        (1.0, z(2)),
    ]
    points, weights = untangle(data)
    points = points.astype(numpy.float)
    return S2Scheme("Kim-Song 1", weights, points, 1, _source)
github nschloe / quadpy / quadpy / s2 / _mysovskih.py View on Github external
xc = numpy.array([cos(a), sin(a)]).T

    data = [
        (A1, rho1 * xa),
        (A2, rho2 * xa),
        (B1, sigma1 * xb),
        (B2, sigma2 * xb),
        (B3, sigma3 * xb),
        (C1, tau1 * xc),
        (C2, tau2 * xc),
        (C3, tau3 * xc),
        (C4, tau4 * xc),
    ]

    points, weights = untangle(data)
    return S2Scheme("Mysovskih 3", weights, points, 15, _source)
github nschloe / quadpy / quadpy / s2 / _haegemans_piessens.py View on Github external
0.92628529230400928736e-1,
            0.13543229722409008260,
            0.13543229722409008260,
            0.13543229722409008260,
            0.13543229722409008260,
            0.13413379835073218915,
            0.13413379835073218915,
            0.34823837217490051775e-1,
            0.34823837217490051775e-1,
            0.25124094894580772473,
            0.25124094894580772473,
            0.3378210604282018145,
        ]
    )
    weights /= math.pi
    return S2Scheme("Haegemans-Piessens", weights, points, 9, _source)
github nschloe / quadpy / quadpy / s2 / _kim_song / __init__.py View on Github external
def kim_song_3():
    data = [
        (0.25, fsd(2, (0.5, 2))),
    ]
    points, weights = untangle(data)
    return S2Scheme("Kim-Song 3", weights, points, 3, _source)
github nschloe / quadpy / quadpy / s2 / _kim_song / __init__.py View on Github external
def kim_song_11():
    data = [
        (0.125290208564338, fsd(2, (0.252863797091293, 1))),
        (0.016712625496982, fsd(2, (0.989746802511614, 1))),
        (0.109500391126365, fsd(2, (0.577728928444958, 1))),
        (0.066237455796397, fsd(2, (0.873836956645035, 1))),
        (0.026102860184358, fsd(2, (0.689299380791136, 2))),
        (0.066000934661100, fsd(2, (0.597614304667208, 2))),
        (0.127428372681720, fsd(2, (0.375416824626170, 2))),
        (0.042523065826681, fsd(2, (0.883097111318591, 1), (0.365790800400663, 1))),
        (0.081539591616413, fsd(2, (0.707438744960070, 1), (0.293030722710664, 1))),
    ]
    points, weights = untangle(data)
    weights /= math.pi
    return S2Scheme("Kim-Song 11", weights, points, 15, _source, 1.910e-12)