maxstar

Natural log of a sum of exponentials

Description

maxstar(x) is the natural log of a sum of exponentials overcoming the numerical failure of log(sum(exp(x))) for extreme values of an argument vector x.

maxstar(x,[],dim) has the N-D array features of the MATLAB max function.
maxstar(x,w,dim) is the natural log of a weighted sum of exponentials.

The max* function is described in Lin & Costello, Error Control Coding, 2nd Edition, equation 12.127.

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[John D'Errico]

Good help with a reference. It works when the direct alternative expression fails. But there are other (faster) alternatives that should be as accurate. Off hand, its not at all obvious to me why maxstar is better. (Perhaps if I've read the reference.)

x = randn(1,100)*100000;

tic,r1=log(sum(exp(x(:))));toc
Elapsed time is 0.000178 seconds.

tic,r2=maxstar(x);toc
Elapsed time is 0.017096 seconds.

tic,M=max(x(:));r3=M+log(sum(exp(sort(x(:))/M)));toc
Elapsed time is 0.000342 seconds.

[r1,r2,r3]
ans =
          Inf 2.7718e+05 2.7718e+05

Its also arguable that this should have a similar syntax to most other matlab operators with similar functionality. It should operate on a specified dimension. (See help for mean, max, etc.)