Module « scipy.special »

Fonction gammaincinv - module scipy.special

Signature de la fonction gammaincinv

Description

gammaincinv.__doc__

gammaincinv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

gammaincinv(a, y)

Inverse to the lower incomplete gamma function with respect to `x`.

Given an input :math:`y` between 0 and 1, returns :math:`x` such
that :math:`y = P(a, x)`. Here :math:`P` is the regularized lower
incomplete gamma function; see `gammainc`. This is well-defined
because the lower incomplete gamma function is monotonic as can be
seen from its definition in [dlmf]_.

Parameters
----------
a : array_like
    Positive parameter
y : array_like
    Parameter between 0 and 1, inclusive

Returns
-------
scalar or ndarray
    Values of the inverse of the lower incomplete gamma function

See Also
--------
gammainc : regularized lower incomplete gamma function
gammaincc : regularized upper incomplete gamma function
gammainccinv : inverse of the regualizred upper incomplete gamma
    function with respect to `x`

References
----------
.. [dlmf] NIST Digital Library of Mathematical Functions
          https://dlmf.nist.gov/8.2#E4

Examples
--------
>>> import scipy.special as sc

It starts at 0 and monotonically increases to infinity.

>>> sc.gammaincinv(0.5, [0, 0.1 ,0.5, 1])
array([0.        , 0.00789539, 0.22746821,        inf])

It inverts the lower incomplete gamma function.

>>> a, x = 0.5, [0, 0.1, 0.5, 1]
>>> sc.gammainc(a, sc.gammaincinv(a, x))
array([0. , 0.1, 0.5, 1. ])

>>> a, x = 0.5, [0, 10, 25]
>>> sc.gammaincinv(a, sc.gammainc(a, x))
array([ 0.        , 10.        , 25.00001465])