Quote:Dimitris wrote:

Quote:

Dimitris wrote:

So, it seems like there are two cases?

1. Bug in dsyrdb
2. Typo in MKL manual

Neither! It is more of a quality of implementation of issue. The MKL documentation gives a recommendation for the input argument kd that is valid for real life applications where the input matrix A is large. However, if A is small, those recommendations are incorrect. I believe that the MKL routine does not check for incorrect values of kd as well as it should, and you probably did not go beyond the MKL manual to find out what values are appropriate.

The argument kd is defined in the MKL 11 manual as "The bandwidth of the banded matrix B", but what is matrix B? It is certainly not one of the arguments to ?syrdb. If you look up the original paper (http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.4242) and the TOMS issue in which the source code was given (http://www.netlib.org/toms/807) you find that kd is the half-bandwidth of the reduced bandwidth matrix A_band = Q^TAQ that results from applying blocked Householder transformations to the original matrix A. Therefore, kd can never exceed n - 1, if A is n X n.

Recommendations:

• If the kd value that the MKL manual recommends is greater or equal to n, set kd = n - 1.
• If you want to perform meaningful tests of matrix algebra routines, do not try with garbage matrices or null matrices. It is not that difficult to generate an input matrix with suitable properties (in this case, a nonsingular symmetric matrix of size larger than 40 X 40)
• Avoid using routines such as ?syrdb that are labelled "computational". See if your needs could be met by using one of the "driver" routines instead. If you decide to use a "computational" routine directly, be prepared to work with a longer argument list which may include additional variables that are internal to the underlying algorithm, and be prepared to read technical papers in which the algorithm was published.