scipy.special.gammaln — SciPy v1.16.0 Manual (original) (raw)

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

Logarithm of the absolute value of the gamma function.

Defined as

\[\ln(\lvert\Gamma(x)\rvert)\]

where \(\Gamma\) is the gamma function. For more details on the gamma function, see [dlmf].

Parameters:

xarray_like

Real argument

outndarray, optional

Optional output array for the function results

Returns:

scalar or ndarray

Values of the log of the absolute value of gamma

See also

gammasgn

sign of the gamma function

loggamma

principal branch of the logarithm of the gamma function

Notes

It is the same function as the Python standard library functionmath.lgamma.

When used in conjunction with gammasgn, this function is useful for working in logspace on the real axis without having to deal with complex numbers via the relation exp(gammaln(x)) = gammasgn(x) * gamma(x).

For complex-valued log-gamma, use loggamma instead of gammaln.

gammaln has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

See Support for the array API standard for more information.

References

Examples

import numpy as np import scipy.special as sc

It has two positive zeros.

sc.gammaln([1, 2]) array([0., 0.])

It has poles at nonpositive integers.

sc.gammaln([0, -1, -2, -3, -4]) array([inf, inf, inf, inf, inf])

It asymptotically approaches x * log(x) (Stirling’s formula).

x = np.array([1e10, 1e20, 1e40, 1e80]) sc.gammaln(x) array([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82]) x * np.log(x) array([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])