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