The new Version 9 of INTLAB, the Matlab toolbox for Reliable Compting, is now available for Matlab and Octave.
The main progress in Version 8 are two new toolboxes:
It comprises of
The philosophy of INTLAB is that *everything* is written in Matlab code to assure best portability.
The 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.
Some higher transcendental functions like erf, erfc and gamma have been added. For arguments close to negative integers the result of the built-in Matlab function has sometimes no correct digit, whereas INTLAB verifies bounds of almost maximum accuracy.
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
For Octave the INTLAB package is self-contained including Octave Version 3.8.2.
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 email@example.com
Dates: May 15, 2014 and February 9, 2015
Prof. Dr. Siegfried M. Rump
Inst. f. Computer Science III
Technical University Hamburg-Harburg