Proposed GEMM Extension: Triangle Triangle Matrix Multiply

Proposed GEMM Extension: Triangle Triangle Matrix Multiply


After speaking to one of the MKL developers recently I was wondering whether it might be beneficial to add some new functionality to MKL in order to compute triangular-triangular matrix products. As triangular matrices form a subgroup, the result will always remain triangular and can therefore be computed highly efficiently by performing only the minimal number of flops required.

In particular, I work with matrix functions where we often require powers of the Schur factor of a matrix, which is triangular. This would be beneficial for anyone wishing to compute a polynomial or rational function of a matrix, for instance. In particular this would be used extensively to compute the logarithm, powers, and trigonometric functions of a matrix (see for a list of software that could potentially benefit from such a specialized routine). These algorithms are used in various applications including the solution of PDEs and in network analysis etc.

This new routine could perhaps have a similar calling sequence to <?>GEMMT ( since this is targeted at solving a similar problem.

I am sure there are plenty of other applications that I currently don't know about that would highly benefit from this functionality. If you know of any, please leave a comment so that the developers of MKL receive some feedback and can consider implementing this extension.

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I would also be very interested to see this functionality implemented.

At we implemented out own version so we are interested too. We need it in our optimizer for semidefinite problems.

Thank you for all your interests in this request. I am adding this to our engineering tracker.


This would be very useful for computing matrix functions of upper triangular matrices, e.g. when working with the Schur normal form.

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