How to use the quadpy.helpers.z function in quadpy
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nschloe / quadpy / quadpy / s2 / _radon.py View on Github 
def radon(alpha):
r = sqrt(frac(alpha + 4, alpha + 6))
s = sqrt(frac(alpha + 4, 4 * (alpha + 6)))
t = sqrt(frac(3 * (alpha + 4), 4 * (alpha + 6)))
A = frac(4, (alpha + 4) ** 2)
B = frac((alpha + 2) * (alpha + 6), 6 * (alpha + 4) ** 2)
data = [
(A, z(2)),
(B, numpy.array([[+r, 0], [-r, 0]])),
# Stroud is missing +- in front of t.
(B, numpy.array([[+s, +t], [-s, +t], [+s, -t], [-s, -t]])),
]
points, weights = untangle(data)
return S2Scheme(f"Radon({alpha})", weights, points, 5, _source)def f(x):
degree = 11
n = 3
u = 0.871_740_148_509_601
v = 0.591_700_181_433_148
w = 0.209_299_217_902_484
# u = x[0]
# v = x[1]
# w = x[2]
# B = x[3:]
B = x
data = [
(B[0], z(n)),
(B[1], fsd(n, (u, 1))),
(B[2], fsd(n, (v, 1))),
(B[3], fsd(n, (w, 1))),
(B[4], fsd(n, (u, 2))),
(B[5], fsd(n, (v, 2))),
(B[6], fsd(n, (w, 2))),
(B[7], fsd(n, (u, 1), (v, 1))),
(B[8], fsd(n, (u, 1), (w, 1))),
(B[9], fsd(n, (u, 3))),
(B[10], fsd(n, (v, 3))),
(B[11], fsd(n, (w, 3))),
(B[12], fsd(n, (u, 2), (v, 1))),
]
points, weights = untangle(data)def tyler(n):
data = [(frac(3 - n, 3), z(n)), (frac(1, 6), fsd(n, (1, 1)))]
points, weights = untangle(data)
return CnScheme("Tyler", n, weights, points, 3, _source)def ewing(n):
data = [(frac(2, 3), z(n)), (frac(1, 3 * 2 ** n), pm(n, 1))]
points, weights = untangle(data)
return CnScheme("Ewing", n, weights, points, 3, _source)# -0.373831314185824e+02,
# -0.141469445049282e-01,
# +0.104863970436266,
# -0.973070178977534e-03,
# -0.862234640073899e-02,
# +0.654476925250512e+01,
# +0.153312717360660e-02,
# -0.611928443128898e-04,
# +0.622126777947090e-02,
# +0.887274197302674e-05,
# ],
# ),
}[n]
data = [
(B[0], z(n)),
(B[1], fsd(n, (u, 1))),
(B[2], fsd(n, (v, 1))),
(B[3], fsd(n, (w, 1))),
(B[4], fsd(n, (u, 2))),
(B[5], fsd(n, (v, 2))),
(B[6], fsd(n, (w, 2))),
(B[7], fsd(n, (u, 1), (v, 1))),
(B[8], fsd(n, (u, 1), (w, 1))),
(B[9], fsd(n, (u, 3))),
(B[10], fsd(n, (v, 3))),
(B[11], fsd(n, (w, 3))),
(B[12], fsd(n, (u, 2), (v, 1))),
]
if n > 3:
data += [(B[13], fsd(n, (u, 4))), (B[14], fsd(n, (v, 4)))]
if n > 4:[
-0.361840434143098e2,
-0.447936529138517,
+0.112077863004144e2,
+0.392940404320855e-2,
-0.254859786784158e1,
+0.775156917007496e-1,
-0.130980134773619e-2,
+0.509719573568315,
+0.436600449245395e-3,
],
),
}[dim]
data = [
(B[0], z(dim)),
(B[1], fsd(dim, (u, 1))),
(B[2], fsd(dim, (v, 1))),
(B[3], fsd(dim, (u, 2))),
(B[4], fsd(dim, (v, 2))),
(B[5], fsd(dim, (u, 1), (v, 1))),
(B[6], fsd(dim, (u, 3))),
(B[7], fsd(dim, (v, 3))),
]
if dim > 3:
data += [(B[8], fsd(dim, (u, 4)))]
points, weights = untangle(data)
weights /= math.sqrt(math.pi) ** dim
return Enr2Scheme("Stenger 9a", dim, weights, points, 9, source)-0.670700680243651e2,
-0.856090560229205e-2,
+0.794446232770302e-1,
-0.220272863263544e-3,
-0.373515812228225e-2,
+0.123606544052884e2,
+0.537788804557843e-3,
-0.122101861480881e-4,
+0.725117070759373e-2,
+0.331725011358320e-5,
],
),
}[dim]
data = [
(B[0], z(dim)),
(B[1], fsd(dim, (u, 1))),
(B[2], fsd(dim, (v, 1))),
(B[3], fsd(dim, (w, 1))),
(B[4], fsd(dim, (u, 2))),
(B[5], fsd(dim, (v, 2))),
(B[6], fsd(dim, (w, 2))),
(B[7], fsd(dim, (u, 1), (v, 1))),
(B[8], fsd(dim, (u, 1), (w, 1))),
(B[9], fsd(dim, (u, 3))),
(B[10], fsd(dim, (v, 3))),
(B[11], fsd(dim, (w, 3))),
(B[12], fsd(dim, (u, 2), (v, 1))),
]
if dim > 3:
data += [(B[13], fsd(dim, (u, 4))), (B[14], fsd(dim, (v, 4)))]
if dim > 4:6: (
0.165068012388578e1,
0.524647623275290,
[
+0.616293651884027e3,
+0.107529736766179e1,
-0.113807008098269e3,
-0.610828352270520e-1,
+0.127887706992535e2,
+0.239492607623178e-1,
],
),
}[dim]
data = [
(B[0], z(dim)),
(B[1], fsd(dim, (u, 1))),
(B[2], fsd(dim, (v, 1))),
(B[3], fsd(dim, (u, 2))),
(B[4], fsd(dim, (v, 2))),
(B[5], fsd(dim, (u, 3))),
]
points, weights = untangle(data)
weights /= math.sqrt(math.pi) ** dim
return Enr2Scheme("Stenger 7b", dim, weights, points, 7, source)]
A1 = -2 * (n - 1) * A11 + frac(1, 2) * (inv[0][0] * vec[0] + inv[0][1] * vec[1])
A2 = -2 * (n - 1) * A22 + frac(1, 2) * (inv[1][0] * vec[0] + inv[1][1] * vec[1])
A0 = (
I0
- 2 * n * (A1 + A2)
- 2 ** 2 * comb(n, 2) * (A11 + A22)
- 2 ** 3 * comb(n, 3) * A111
)
u = sqrt(u2)
v = sqrt(v2)
data = [
(A0, z(n)),
(A1, fsd(n, (u, 1))),
(A2, fsd(n, (v, 1))),
(A11, fsd(n, (u, 2))),
(A22, fsd(n, (v, 2))),
(A111, fsd(n, (u, 3))),
]
points, weights = untangle(data)
weights /= I0
variant = "a" if not switch_uv else "b"
return f"McNamee-Stenger 7{variant}", n, weights, points, 7, _sourcer2 = (33 - i * sqrt(165)) / 28
s2 = (30 + i * sqrt(165)) / 35
t2 = (195 - i * 4 * sqrt(165)) / 337
r = sqrt(r2)
s = sqrt(s2)
t = sqrt(t2)
B1 = 176 / r2 ** 3 / 945
B2 = 8 / s2 ** 3 / 135
B3 = 8 / t2 ** 3 / 216
B0 = 8 - 6 * B1 - 12 * B2 - 8 * B3
data = [
(B0, z(3)),
(B1, fsd(3, (r, 1))),
(B2, fsd(3, (s, 2))),
(B3, pm([t, t, t])),
]
points, weights = untangle(data)
weights /= 8
variant = "a" if variant_a else "b"
return C3Scheme(f"Hammer-Stroud 5-3{variant}", weights, points, 7, _source)quadpy
Numerical integration, quadrature for various domains
Package Health Score
53 / 100Popular quadpy functions
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