# v_gammalns

## PURPOSE

V_GAMMALNS Log of Gamma(x) for positive or negative real x [y,s]=(x)

## SYNOPSIS

function [y,s]=v_gammalns(x)

## DESCRIPTION

    V_GAMMALNS Log of Gamma(x) for positive or negative real x [y,s]=(x)

      Inputs: x      real matrix of input values

     Outputs: y      log(gamma(x)) or, if s is present, log(abs(gamma(x)))
              s      sign(gamma(x))

     If s is not specified then y will b complex if gamma(x) is negative (i.e. if floor(x) is negative and odd).
     Uses gamma(x) = pi/gamma(1-z)/sin(pi*z) which is 5.5.3 from [1]

     [1]    F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors.
           NIST Handbook of Mathematical Functions. CUP, 2010. ISBN 978-0-521-14063-8.

## CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

- v_hypergeom1f1 V_HYPERGEOM1F1 Confluent hypergeometric function, 1F1 a.k.a Kummer's M function [h,l]=(a,b,z,tol,maxj)

## SOURCE CODE

    0001 function [y,s]=v_gammalns(x)
    0002 %V_GAMMALNS Log of Gamma(x) for positive or negative real x [y,s]=(x)
    0003 %
    0004 %  Inputs: x      real matrix of input values
    0005 %
    0006 % Outputs: y      log(gamma(x)) or, if s is present, log(abs(gamma(x)))
    0007 %          s      sign(gamma(x))
    0008 %
    0009 % If s is not specified then y will b complex if gamma(x) is negative (i.e. if floor(x) is negative and odd).
    0010 % Uses gamma(x) = pi/gamma(1-z)/sin(pi*z) which is 5.5.3 from [1]
    0011 %
    0012 % [1]    F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors.
    0013 %       NIST Handbook of Mathematical Functions. CUP, 2010. ISBN 978-0-521-14063-8.
    0014
    0015 %      Copyright (C) Mike Brookes 2017
    0016 %      Version: $Id: v_gammalns.m 10865 2018-09-21 17:22:45Z dmb $
    0017 %
    0018 %   VOICEBOX is a MATLAB toolbox for speech processing.
    0019 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
    0020 %
    0021 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0022 %   This program is free software; you can redistribute it and/or modify
    0023 %   it under the terms of the GNU Lesser General Public License as published by
    0024 %   the Free Software Foundation; either version 3 of the License, or
    0025 %   (at your option) any later version.
    0026 %
    0027 %   This program is distributed in the hope that it will be useful,
    0028 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
    0029 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    0030 %   GNU Lesser General Public License for more details.
    0031 %
    0032 %   You can obtain a copy of the GNU Lesser General Public License from
    0033 %   https://www.gnu.org/licenses/ .
    0034 %
    0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0036 persistent l
    0037 m=x<=0;
    0038 y=zeros(size(x));
    0039 s=ones(size(x));
    0040 if ~all(m(:)) % non-negative x values
    0041     y(~m)=gammaln(x(~m));
    0042 end
    0043 f=m & (x==fix(x)); % find and non-positive integers
    0044 if any(f(:))
    0045     y(f)=Inf; % set output to infinity
    0046     m=m & ~f; % do not consider these values furhter
    0047 end
    0048 if any(m(:)) % negative x values
    0049     if isempty(l)
    0050         l=log(pi);
    0051     end
    0052     t=sin(pi*x(m));
    0053     if nargout>1
    0054         p=t<0;
    0055         s(m)=1-2*(p);
    0056         y(m)=l-gammaln(1-x(m))-log(abs(t));
    0057     else
    0058         y(m)=l-gammaln(1-x(m))-log(t);
    0059     end
    0060 end
    0061