A Free Interval Arithmetic Toolbox for Matlab

The first official version 1.0.2.004 of b4m is available on this site since

With the release of this version all previously released beta versions are obsolete.

Short Description of b4m

The package b4m is a free interval arithmetic toolbox for Matlab 5.
b4m is an abbreviation of BIAS for Matlab.

b4m has been tested under Matlab 5.1, Matlab 5.2 and Matlab 5.3 with Windows and Unix Systems including

It should be possible to use b4m on a DEC Alpha, but there exists currently only a test version of BIAS for DEC Alpha.

b4m consists of two main parts:

The interface to the Basic Interval Arithmetic Subroutines by Olaf Knüppel (commonly known as BIAS).
A collection of M-Files which either work on these routines or implement small programs.

In the nearest future there will be a complete documentation available in

Since 19.3.1999 documentation in

is available.

This small example shows (hopefully) some of the features of b4m.

Sample output of b4m

It has been generated using the code fragment

      A = interval(rand(10));
      b = A*ones(10,1);
      x = A\b

and afterwards taking a picture.

Prerequisites for b4m are Matlab 5 and BIAS. The Windows version comes with precompiled Mex-files (dll's), so there is no explicit need for BIAS.

It is possible to raise the speed of the Windows version by recompiling the Mex-files (this needs BIAS).

In order to install b4m on a Unix Workstation or Linux PC there are three simple steps to perform.

Download the b4m version for Unix, uncompress the package e.g. in the directory
/usr/local/matlab/toolbox/.
Compile all files (bias_*.c) in the directories
/usr/local/matlab/toolbox/b4m/private/ and
/usr/local/matlab/toolbox/b4m/@interval/private/
using the appropriate Makefiles.
Add the directory
/usr/local/matlab/toolbox/b4m/
to the Matlab searchpath.

For the second step you need a compiled version of BIAS.

For Windows 95/98/NT the package is available with precompiled Mex-files (dll's), so the installation process is much easier.

Download the b4m version for Windows 95/98/NT and uncompress the package in the directory
C:\Matlab\Toolbox\.
Add the directory
C:\Matlab\Toolbox\b4m\
to your path.

The Matlab directory might be somewhere else on your system, in that case simply modify the statements above to fit your system.

A new BIAS building upon BLAS is on the way ;-).

In order to get the users of b4m, PROFIL/BIAS, INTLAB etc. together, a mailing list has been set up with the name

If you want to subscribe to this list, send an e-mail to

with the text 'subscribe validated_numerics' inside.

Jens Zemke zemke∂tu-harburg.de
TU Hamburg - Harburg
Schwarzenbergstr. 95