ai-content-maker/.venv/Lib/site-packages/scipy/special/_precompute/utils.py

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2024-05-03 04:18:51 +03:00
try:
import mpmath as mp
except ImportError:
pass
try:
from sympy.abc import x
except ImportError:
pass
def lagrange_inversion(a):
"""Given a series
f(x) = a[1]*x + a[2]*x**2 + ... + a[n-1]*x**(n - 1),
use the Lagrange inversion formula to compute a series
g(x) = b[1]*x + b[2]*x**2 + ... + b[n-1]*x**(n - 1)
so that f(g(x)) = g(f(x)) = x mod x**n. We must have a[0] = 0, so
necessarily b[0] = 0 too.
The algorithm is naive and could be improved, but speed isn't an
issue here and it's easy to read.
"""
n = len(a)
f = sum(a[i]*x**i for i in range(n))
h = (x/f).series(x, 0, n).removeO()
hpower = [h**0]
for k in range(n):
hpower.append((hpower[-1]*h).expand())
b = [mp.mpf(0)]
for k in range(1, n):
b.append(hpower[k].coeff(x, k - 1)/k)
b = [mp.mpf(x) for x in b]
return b