scipy.special.gammasgn#

scipy.special.gammasgn(x, out=None) = <ufunc 'gammasgn'>#

Sign of the gamma function.

It is defined as

\[\begin{split}\text{gammasgn}(x) = \begin{cases} +1 & \Gamma(x) > 0 \\ -1 & \Gamma(x) < 0 \end{cases}\end{split}\]

where \(\Gamma\) is the gamma function; see gamma. This definition is complete since the gamma function is never zero; see the discussion after [dlmf].

Parameters:

xarray_like: Real argument
outndarray, optional: Optional output array for the function values

Returns:

scalar or ndarray: Sign of the gamma function

See also

gamma: the gamma function
gammaln: log of the absolute value of the gamma function
loggamma: analytic continuation of the log of the gamma function

Notes

The gamma function can be computed as gammasgn(x) * np.exp(gammaln(x)).

Array API Standard Support

gammasgn has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	✅	✅
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. gammasgn does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

References

[dlmf]

NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.2#E1

Examples

>>> import numpy as np
>>> import scipy.special as sc

It is 1 for x > 0.

>>> sc.gammasgn([1, 2, 3, 4])
array([1., 1., 1., 1.])

It alternates between -1 and 1 for negative half-integers.

>>> sc.gammasgn([-0.5, -1.5, -2.5, -3.5])
array([-1.,  1., -1.,  1.])

It can be used to compute the gamma function.

>>> x = [1.5, 0.5, -0.5, -1.5]
>>> sc.gammasgn(x) * np.exp(sc.gammaln(x))
array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])
>>> sc.gamma(x)
array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])