scipy.special.gammainccinv#
- scipy.special.gammainccinv(a, y, out=None) = <ufunc 'gammainccinv'>#
Inverse of the regularized upper incomplete gamma function.
Given an input \(y\) between 0 and 1, returns \(x\) such that \(y = Q(a, x)\). Here \(Q\) is the regularized upper incomplete gamma function; see
gammaincc
. This is well-defined because the upper incomplete gamma function is monotonic as can be seen from its definition in [dlmf].- Parameters:
- aarray_like
Positive parameter
- yarray_like
Argument between 0 and 1, inclusive
- outndarray, optional
Optional output array for the function values
- Returns:
- scalar or ndarray
Values of the inverse of the upper incomplete gamma function
See also
gammaincc
regularized upper incomplete gamma function
gammainc
regularized lower incomplete gamma function
gammaincinv
inverse of the regularized lower incomplete gamma function
References
[dlmf]NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/8.2#E4
Examples
>>> import scipy.special as sc
It starts at infinity and monotonically decreases to 0.
>>> sc.gammainccinv(0.5, [0, 0.1, 0.5, 1]) array([ inf, 1.35277173, 0.22746821, 0. ])
It inverts the upper incomplete gamma function.
>>> a, x = 0.5, [0, 0.1, 0.5, 1] >>> sc.gammaincc(a, sc.gammainccinv(a, x)) array([0. , 0.1, 0.5, 1. ])
>>> a, x = 0.5, [0, 10, 50] >>> sc.gammainccinv(a, sc.gammaincc(a, x)) array([ 0., 10., 50.])