[Scilab-users] advices in optimizing matrix calculations

[Serge Steer]

Le 24/09/2012 22:46, Paul Carrico a écrit :
>
> Dear all,
>
> May I ask some advice in matrix calculation issue, in order to 
> optimize the code ?
>
> The matrix hereafter is the first trial in treating a (m x 6) matrix 
> where :
>
> -The first line is the upper part of a symmetrical 6x6 tensor (the 3 
> first components are the diagonal terms)
>
> -m may correspond to millions of lines
>
> -(each line is independent from the other)
>
> I had a look in some function (such as schur, spec, bdiag and so on) 
> in order to see if I can use this symmetrical specificity ... but I 
> don't see anything èAm I wrong ?
>
The schur, spec, bdiag function internally check if the matrix is 
symmetric and if yes apply specific algorithm. But the matrix must be 
passed in its full form.

> Several calculations will be done: Eigen values calculation for each 
> submatrix, summation, multiplication and so on ...
>
> Vectorization can be useful to improve speedup ?
>
I did not see any possible vectorization  (there is no way to compute 
several schur decompositions with only one call to a primitive function)
If you have a multicore processor you can try the parallel_run function.

Serge Steer
INRIA
>
> Any advices ?
>
> Thanks in advance
>
> Paul
>
> PS : M is made from a text file ... its structure can be change in 
> order to be as efficient as possible ...
>
> Mat = [
>
>     9.315        9.315        28.41  - 0.0000999  - 3.169      - 
> 3.169     ;
>     2.945        2.945        28.45    0.04826    - 3.175      - 
> 3.175      ;
>     8.486        9.341        25.73    0.0101     - 3.179      - 
> 3.189      ;
>     2.043        2.939        25.73    0.038      - 3.185      - 
> 3.182      ;
>     9.341        8.486        25.73    0.0101     - 3.189      - 
> 3.179      ;
>     2.939        2.043        25.73    0.038      - 3.182      - 
> 3.185      ;
>     8.492        8.492        23.      0.02036    - 3.179      - 
> 3.179      ;
>     2.018        2.018        22.97    0.02779    - 3.172      - 
> 3.172     ;
>     9.108        8.179        25.01    0.01326    - 3.197      - 
> 1.608     ;
>     4.695        2.302        25.04    0.0905     - 3.199      - 
> 1.61       ;
>     8.271        8.186        22.27    0.02824    - 3.212      - 
> 1.601     ;
>     3.842        2.302        22.29    0.07548    - 3.214      - 
> 1.599     ;
>     9.134        8.128        24.91    0.01554    - 3.278      - 
> 1.61      ;
>     4.675        2.145        24.9     0.08819    - 3.276      - 
> 1.612     ;
>
>     ...
>
>     ...
>     8.291        8.129        22.16    0.03055    - 3.263      - 
> 1.598  ] ;
>
>     sub11        sub22       sub33 sub12        sub23       sub13 ... 
> where sub is a submatrix == 1 line
>
>
>
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