def _gwr_no_memo(fn: Callable[[float], Any], time: float, M: int = 32, precin: int = 0) -> float:
"""
GWR alorithm without memoization. This is a near 1:1 translation from
Mathematica.
"""
tau = mp.log(2.0) / mp.mpf(time)
fni: List[float] = [0.0] * M
for i, n in enumerate(fni):
if i == 0:
continue
fni[i] = fn(n * tau)
G0: List[float] = [0.0] * M
Gp: List[float] = [0.0] * M
M1 = M
for n in range(1, M + 1):
try:
n_fac = mp.fac(n - 1)
G0[n - 1] = tau * mp.fac(2 * n) / (n * n_fac * n_fac)
s = 0.0
for i in range(n + 1):
s += mp.binomial(n, i) * (-1) ** i * fni[n + i]
G0[n - 1] *= s
except:
M1 = n - 1
break
best = G0[M1 - 1]
Gm: List[float] = [0.0] * M1
broken = False
for k in range(M1 - 1):
for n in range(M1 - 1 - k)[::-1]:
try:
expr = G0[n + 1] - G0[n]
except:
expr = 0.0
broken = True
break
expr = Gm[n + 1] + (k + 1) / expr
Gp[n] = expr
if k % 2 == 1 and n == M1 - 2 - k:
best = expr
if broken:
break
for n in range(M1 - k):
Gm[n] = G0[n]
G0[n] = Gp[n]
return best
def radial_indefinite(a, n, m):
# Evaluates the radial indefinite integral at a for n, m
m = abs(m)
# Checks if it is a valid point to evaluate at, or if a == 0
if (n - m) % 2 > 0 or m > n or a == 0:
return 0
# Due to some weird issues with mpmath, if simultaneously n and m
# are zero, the value of hyp3f2 is wrong. Good news is that both
# n and m are zero, then the solution is trivial.
hyp = 1
if m != 0 or n != 0:
hyp = mp.hyp3f2(-1 - n / 2, -m / 2 - n / 2, m / 2 - n / 2, -n, -n / 2,
a**(-2))
binom = mp.binomial(n, 1 / 2 * (-m + n))
return float(a**(2 + n) / (2 + n) * binom * hyp)
def binomial(n, i):
return int(mp.binomial(n, i))
def binomial(n: int, i: int, precin: int) -> float:
return mp.binomial(n, i)
def binompdf(n, p, k):
return mp.binomial(n, k) * p**k * (1 - p)**(n - k)