Logrithm of Gamma Function

This module computes the natural logarithm of Gamma function, \(\ln \Gamma(x)\), where \(x \in \mathbb{R}\).

Syntax

This function has the following syntaxes depending on whether it is used in Python or Cython interface.

Interface	Function Signature
Python	lngamma(x)
Cython	double lngamma(double x)

Input Arguments:

x: double

The input argument \(x\) of the function.

Examples

Using in Cython Code

The codes below should be used in a .pyx file and compiled with Cython.

As shown in the codes below, the python’s global lock interpreter, or gil, can be optionally released inside the scope of with nogil: statement. This is especially useful in parallel OpenMP environments.

>>> # cimport module in a *.pyx file
>>> from special_functions cimport lngamma

>>> # Declare typed variables
>>> cdef double x = 2.0
>>> cdef double lg

>>> # Releasing gil to secure maximum cythonic speedup
>>> with nogil:
...     lg = lngamma(x)

Using in Python Code

The codes below should be used in a .py file and no compilation is required. The python’s global lock interpreter, or gil, cannot be released.

>>> # import module in a *.py file
>>> from special_functions import lngamma

>>> x = 2.0
>>> lg = lngamma(x)

Tests

The test script of this module is located at tests/test_lngamma.py. The test compares the results of this module with scipy.special package (function gamma) for several combinations of input parameters with multiple values. Run the test by

git clone https://github.com/ameli/special_functions.git
cd special_functions/tests
python test_lngamma.py

Algorithm

This module is a wrapper around gamma function in the Cephes C library (see [Cephes-1989]).

References

[Cephes-1989]

Moshier, S. L. (1989). C language library with special functions for mathematical physics. Available at http://www.netlib.org/cephes.