v_logsum

V_LOGSUM v_logsum(x,d,k)=log(sum(k.*exp(x),d))

 Usage: (1) y=v_logsum(x)                      % log(sum(exp(x)))
        (2) f=0.1*log(10); y=logsm(x*f)/f;     % add powers expressed in dB

 Identities: (1) v_logsum(x+c)=v_logsum(x)+c   % where c is a constant
             (2) sum(exp(x-logsum(x)))=1       % normalize to make exp(x) sum to 1

 Inputs:  X(M,N,...) data matrix to sum
          D          optional dimension to sum along [1st non-singular dimension]
          K(M,N,...) optional scaling matrix. It must either be idential
                     in size to X, or else be a vector whose length is
                     equal to the size of dimension D of X

 Outputs: Y(1,N,...) = log(sum(exp(X).*K,D))

 This routine evaluates the given expression for Y but takes care to avoid
 overflow or underflow.

0001 function y=v_logsum(x,d,k)
0002 %V_LOGSUM v_logsum(x,d,k)=log(sum(k.*exp(x),d))
0003 %
0004 % Usage: (1) y=v_logsum(x)                      % log(sum(exp(x)))
0005 %        (2) f=0.1*log(10); y=logsm(x*f)/f;     % add powers expressed in dB
0006 %
0007 % Identities: (1) v_logsum(x+c)=v_logsum(x)+c   % where c is a constant
0008 %             (2) sum(exp(x-logsum(x)))=1       % normalize to make exp(x) sum to 1
0009 %
0010 % Inputs:  X(M,N,...) data matrix to sum
0011 %          D          optional dimension to sum along [1st non-singular dimension]
0012 %          K(M,N,...) optional scaling matrix. It must either be idential
0013 %                     in size to X, or else be a vector whose length is
0014 %                     equal to the size of dimension D of X
0015 %
0016 % Outputs: Y(1,N,...) = log(sum(exp(X).*K,D))
0017 %
0018 % This routine evaluates the given expression for Y but takes care to avoid
0019 % overflow or underflow.
0020 
0021 %      Copyright (C) Mike Brookes 1998
0022 %      Version: $Id: v_logsum.m 10865 2018-09-21 17:22:45Z dmb $
0023 %
0024 %   VOICEBOX is a MATLAB toolbox for speech processing.
0025 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
0026 %
0027 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0028 %   This program is free software; you can redistribute it and/or modify
0029 %   it under the terms of the GNU General Public License as published by
0030 %   the Free Software Foundation; either version 2 of the License, or
0031 %   (at your option) any later version.
0032 %
0033 %   This program is distributed in the hope that it will be useful,
0034 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0035 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0036 %   GNU General Public License for more details.
0037 %
0038 %   You can obtain a copy of the GNU General Public License from
0039 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0040 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0041 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0042 
0043 if nargin==1 || ~numel(d)
0044     d=[find(size(x)-1) 1];
0045     d=d(1);
0046 end
0047 n=size(x,d);
0048 if n<=1,            % use efficient computation if only one term in the sum
0049     if nargin<3
0050         y=x;
0051     else
0052         y=x+log(k);
0053     end
0054     return;
0055 end
0056 s=size(x);
0057 p=[d:ndims(x) 1:d-1];
0058 z=reshape(permute(x,p),n,prod(s)/n);
0059 q=max(z,[],1);              % we subtract y from each row to avoid dynamic range problems
0060 a=(q==Inf)|(q==-Inf);       % check for infinities
0061 if nargin<3
0062     y=q+log(sum(exp(z-q(ones(n,1),:)),1));
0063 elseif numel(k)==n
0064     y=q+log(sum(exp(z-q(ones(n,1),:)).*repmat(k(:),1,prod(s)/n),1));
0065 else
0066     y=q+log(sum(exp(z-q(ones(n,1),:)).*reshape(permute(k,p),n,prod(s)/n),1));
0067 end
0068 y(a)=q(a);                  % correct any column whose max is +-Inf
0069 s(d)=1;                     % update the dimension of the summed component
0070 y=ipermute(reshape(y,s(p)),p);
0071