# v_logsum

## PURPOSE

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

## SYNOPSIS

function y=v_logsum(x,d,k)

## DESCRIPTION

    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.

## CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

- v_gaussmixb V_GAUSSMIXB approximate Bhattacharyya divergence between two GMMs
- v_gaussmixk V_GAUSSMIXK approximate Kullback-Leibler divergence between two GMMs + derivatives

## SOURCE CODE

    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 Lesser General Public License as published by
    0030 %   the Free Software Foundation; either version 3 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 Lesser General Public License for more details.
    0037 %
    0038 %   You can obtain a copy of the GNU Lesser General Public License from
    0039 %   https://www.gnu.org/licenses/ .
    0040 %
    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