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 个评论
Bruno Luong
2021-4-29
What typical values of n and p ?
Damien GUILLOTIN
2021-4-29
Bruno Luong
2021-4-30
编辑：Bruno Luong
2021-4-30
"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
2021-4-30
采纳的回答
Bruno Luong
2021-4-30
编辑：Bruno Luong
2021-4-30
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.
更多回答（1 个）
Jan
2021-4-29
0 个投票
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?
2 个评论
Damien GUILLOTIN
2021-4-29
Bruno Luong
2021-4-30
编辑：Bruno Luong
2021-4-30
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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