def ellipk(m):
"""y=ellipk(m) returns the complete integral of the first kind:
integral(1/sqrt(1-m*sin(t)**2),t=0..pi/2)
This function is rather imprecise around m==1. For more precision
around this point, use ellipkm1."""
return ellipkm1(1 - asarray(m))
def ellipk(m):
"""y=ellipk(m) returns the complete integral of the first kind:
integral(1/sqrt(1-m*sin(t)**2),t=0..pi/2)
This function is rather imprecise around m==1. For more precision
around this point, use ellipkm1."""
return ellipkm1(1 - asarray(m))
def agm(a,b):
"""Arithmetic, Geometric Mean
Start with a_0=a and b_0=b and iteratively compute
a_{n+1} = (a_n+b_n)/2
b_{n+1} = sqrt(a_n*b_n)
until a_n=b_n. The result is agm(a,b)
agm(a,b)=agm(b,a)
agm(a,a) = a
min(a,b) < agm(a,b) < max(a,b)
"""
s = a + b + 0.0
return (pi / 4) * s / ellipkm1(4 * a * b / s ** 2)
def agm(a, b):
"""Arithmetic, Geometric Mean
Start with a_0=a and b_0=b and iteratively compute
a_{n+1} = (a_n+b_n)/2
b_{n+1} = sqrt(a_n*b_n)
until a_n=b_n. The result is agm(a,b)
agm(a,b)=agm(b,a)
agm(a,a) = a
min(a,b) < agm(a,b) < max(a,b)
"""
s = a + b + 0.0
return (pi / 4) * s / ellipkm1(4 * a * b / s**2)
