Symetric matrix power optimization

Hello,

I would like to calculate A^p where A is a symetric matrix. I know that I can use A^p but i would like to know is there is way to calculate only (n²+n)/2 coefficients and just paste the (n²-n)/2 last that are equals ? Or simply do this optimization for A*B where A and B are both symetrics ?

Thank you :)

[Bruno Luong]

What typical values of n and p ?

[Damien GUILLOTIN]

From 1 to 1000 ^^'

[Bruno Luong]

"Or simply do this optimization for A*B where A and B are both symetrics ?"

How? For generic A and B symmetric the product is NOT symmetric. If you decide to access only the upper parts of A and B, you make memory access pattern more complex and inefficient for caching.

[Damien GUILLOTIN]

Exact hehe ! When the words go faster than your maths... it happens ^^

Answer 1

[Bruno Luong]

Youeu can edit MATLAB function mpower.m and try to the basic calculation (line 76 in my case)

D = D*D; % I assume p is integer in your case

With multiplicationfor triu elements then reflect.

However I would doubt you could beat MATLAB generic matrix product.

Answer 2

[Jan]

Are you using this already:

• https://www.mathworks.com/matlabcentral/fileexchange/25782-mpower2-a-faster-matrix-power-function
• https://www.mathworks.com/matlabcentral/fileexchange/44575-matrix-power

Do you have a C compiler such that you can try to modify the above solutions and call LAPACK:DSYMM instead of DGEMM?

[Damien GUILLOTIN]

First, thank you for your answer !

Then, the function you are proposing are still calculating all the terms (faster than the basic operation for sure) but I really want to exploit the symetric aspect of the matrix. (It is more I have to than I want to, you know, school projects)

I don't really understand what you meant at the end ^^'

[Bruno Luong]

I revisit mpower2 and all the speed up around 2010 when the FEX is publiseh becomes very little now wth R2021a.