The new Version 7.1 of INTLAB is available. INTLAB is Matlab toolbox for self-validating algorithms. A number of changes, improvements and speed-ups have been implemented.
It comprises of
The philosophy of INTLAB is that *everything* is written in Matlab code to assure best portability.
The new version handles Hessians in pure floating point and with verified bounds. As an example consider a model problem where the function to be minimized is
function y = f(x) N = length(x); I = 1:N-4; y = sum( (-4*x(I)+3.0).^2 ) + sum( ( x(I).^2 + 2*x(I+1).^2 + ... 3*x(I+2).^2 + 4*x(I+3).^2 + 5*x(N).^2 ).^2 );with initial approximation xs=ones(N,1) for N=1000. This means 1e6 elements in the gradient and 1e9 elements in the Hessian, or 8 GByte in full storage. In our implementation Hessians are stored sparse using a special storage scheme allowing efficient computations.
The following is executable code to calculate an inclusion of a stationary point of f by first performing a simple Newton iteration followed by a verification step for the resulting nonlinear system. Error estimations are completely rigorous.
>> n = 1000; xs = ones(n,1); tic X = verifynlss(@f,xs,'hSparseSPD'); t = toc maxrelerr = max(relerr(X)) t = 23.8040 maxrelerr = 5.5992e-013Inclusions of all components of a stationary point are to some 13 decimal digits and takes 24 seconds on my 800 MHz Pentium III Laptop. Symmetric positive definiteness of the Hessian can be verified as well, ensuring a (local) minimum of f in X.
INTLAB works under Windows, Unix and Mac OS and is tested under Matlab Versions 5.3 to 7.0 . INTLAB is freely available for non-commercial use from
http://www.ti3.tu-harburg.de/intlab/For demonstration, also Matlab-implementations of our new summation and dot product routines are given, S. M. Rump, T. Ogita, and S. Oishi Accurate Floating-Point Summation, SIAM J. Sci. Comput. Vol. 31, Issue 2, pp. 1269-1302 (2008).
Comments always welcome. Best wishes
Siegfried M. Rump, Email firstname.lastname@example.org
Date: 27 June 2013
Prof. Dr. Siegfried M. Rump
Inst. f. Computer Science III
Technical University Hamburg-Harburg