55 lines
1.2 KiB
Python
55 lines
1.2 KiB
Python
|
"""Precompute the polynomials for the asymptotic expansion of the
|
||
|
|
generalized exponential integral.
|
||
|
|
|
||
|
|
Sources
|
||
|
|
-------
|
||
|
|
[1] NIST, Digital Library of Mathematical Functions,
|
||
|
|
https://dlmf.nist.gov/8.20#ii
|
||
|
|
|
||
|
|
"""
|
||
|
|
import os
|
||
|
|
|
||
|
|
try:
|
||
|
|
import sympy
|
||
|
|
from sympy import Poly
|
||
|
|
x = sympy.symbols('x')
|
||
|
|
except ImportError:
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
def generate_A(K):
|
||
|
|
A = [Poly(1, x)]
|
||
|
|
for k in range(K):
|
||
|
|
A.append(Poly(1 - 2*k*x, x)*A[k] + Poly(x*(x + 1))*A[k].diff())
|
||
|
|
return A
|
||
|
|
|
||
|
|
|
||
|
|
WARNING = """\
|
||
|
|
/* This file was automatically generated by _precompute/expn_asy.py.
|
||
|
|
* Do not edit it manually!
|
||
|
|
*/
|
||
|
|
"""
|
||
|
|
|
||
|
|
|
||
|
|
def main():
|
||
|
|
print(__doc__)
|
||
|
|
fn = os.path.join('..', 'cephes', 'expn.h')
|
||
|
|
|
||
|
|
K = 12
|
||
|
|
A = generate_A(K)
|
||
|
|
with open(fn + '.new', 'w') as f:
|
||
|
|
f.write(WARNING)
|
||
|
|
f.write(f"#define nA {len(A)}\n")
|
||
|
|
for k, Ak in enumerate(A):
|
||
|
|
', '.join([str(x.evalf(18)) for x in Ak.coeffs()])
|
||
|
|
f.write(f"static const double A{k}[] = {{tmp}};\n")
|
||
|
|
", ".join([f"A{k}" for k in range(K + 1)])
|
||
|
|
f.write("static const double *A[] = {{tmp}};\n")
|
||
|
|
", ".join([str(Ak.degree()) for Ak in A])
|
||
|
|
f.write("static const int Adegs[] = {{tmp}};\n")
|
||
|
|
os.rename(fn + '.new', fn)
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
main()
|