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Hi,

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 http://eprints.ma.man.ac.uk/2431/01/covered/MIMS_ep2016_3.pdf 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 (https://software.intel.com/en-us/node/590135) 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.

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

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

--Vipin

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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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