projektAI/venv/Lib/site-packages/scipy/special/_precompute/gammainc_asy.py

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2021-06-06 22:13:05 +02:00
"""
Precompute coefficients of Temme's asymptotic expansion for gammainc.
This takes about 8 hours to run on a 2.3 GHz Macbook Pro with 4GB ram.
Sources:
[1] NIST, "Digital Library of Mathematical Functions",
https://dlmf.nist.gov/
"""
import os
from scipy.special._precompute.utils import lagrange_inversion
try:
import mpmath as mp # type: ignore[import]
except ImportError:
pass
def compute_a(n):
"""a_k from DLMF 5.11.6"""
a = [mp.sqrt(2)/2]
for k in range(1, n):
ak = a[-1]/k
for j in range(1, len(a)):
ak -= a[j]*a[-j]/(j + 1)
ak /= a[0]*(1 + mp.mpf(1)/(k + 1))
a.append(ak)
return a
def compute_g(n):
"""g_k from DLMF 5.11.3/5.11.5"""
a = compute_a(2*n)
g = [mp.sqrt(2)*mp.rf(0.5, k)*a[2*k] for k in range(n)]
return g
def eta(lam):
"""Function from DLMF 8.12.1 shifted to be centered at 0."""
if lam > 0:
return mp.sqrt(2*(lam - mp.log(lam + 1)))
elif lam < 0:
return -mp.sqrt(2*(lam - mp.log(lam + 1)))
else:
return 0
def compute_alpha(n):
"""alpha_n from DLMF 8.12.13"""
coeffs = mp.taylor(eta, 0, n - 1)
return lagrange_inversion(coeffs)
def compute_d(K, N):
"""d_{k, n} from DLMF 8.12.12"""
M = N + 2*K
d0 = [-mp.mpf(1)/3]
alpha = compute_alpha(M + 2)
for n in range(1, M):
d0.append((n + 2)*alpha[n+2])
d = [d0]
g = compute_g(K)
for k in range(1, K):
dk = []
for n in range(M - 2*k):
dk.append((-1)**k*g[k]*d[0][n] + (n + 2)*d[k-1][n+2])
d.append(dk)
for k in range(K):
d[k] = d[k][:N]
return d
header = \
r"""/* This file was automatically generated by _precomp/gammainc.py.
* Do not edit it manually!
*/
#ifndef IGAM_H
#define IGAM_H
#define K {}
#define N {}
static const double d[K][N] =
{{"""
footer = \
r"""
#endif
"""
def main():
print(__doc__)
K = 25
N = 25
with mp.workdps(50):
d = compute_d(K, N)
fn = os.path.join(os.path.dirname(__file__), '..', 'cephes', 'igam.h')
with open(fn + '.new', 'w') as f:
f.write(header.format(K, N))
for k, row in enumerate(d):
row = map(lambda x: mp.nstr(x, 17, min_fixed=0, max_fixed=0), row)
f.write('{')
f.write(", ".join(row))
if k < K - 1:
f.write('},\n')
else:
f.write('}};\n')
f.write(footer)
os.rename(fn + '.new', fn)
if __name__ == "__main__":
main()