Symetric matrix power optimization

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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 :)
  4 Comments
Damien GUILLOTIN
Damien GUILLOTIN on 30 Apr 2021
Exact hehe ! When the words go faster than your maths... it happens ^^

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Accepted Answer

Bruno Luong
Bruno Luong on 30 Apr 2021
Edited: Bruno Luong on 30 Apr 2021
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.

More Answers (1)

Jan
Jan on 29 Apr 2021
Are you using this already:
Do you have a C compiler such that you can try to modify the above solutions and call LAPACK:DSYMM instead of DGEMM?
  2 Comments
Bruno Luong
Bruno Luong on 30 Apr 2021
I revisit mpower2 and all the speed up around 2010 when the FEX is publiseh becomes very little now wth R2021a.

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