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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)
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)
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)
(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)
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)
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)
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)
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)
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)
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)