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.
0020 %
0021 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0022 %   This program is free software; you can redistribute it and/or modify
0024 %   the Free Software Foundation; either version 2 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 General Public License for more details.
0031 %
0032 %   You can obtain a copy of the GNU General Public License from
0033 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0034 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
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```