Speeding up matrix operations

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federico nutarelli 2022-12-2

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评论： federico nutarelli 2022-12-2

Hi all,

say A and B are big matrices and u,s,v are the svd decomposition of another big matrix. Now, is there a way to speed up the following operation?

mat=(A-u*s*v').*B

I have read that MATLAB has a tool called BLAS but have not understood how to use it and if it is useful in this case.

Thank you

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Matt J 2022-12-2

编辑：Matt J 2022-12-2

What are the dimensions of all the matrices? Are they all square? Are any of the singular values zero?

federico nutarelli 2022-12-2

So the matrices are 1000x700. Singular values decay after a lot of time. There are but I would say they are a 10% of the entire singular value matrix.

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Answer 1

Jan 2022-12-2

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https://ww2.mathworks.cn/matlabcentral/answers/1869627-speeding-up-matrix-operations#answer_1118617

在 MATLAB Online 中打开

Matlab calls optimized libraries to solve linear algebra operations. These libraries are based on BLAS and LAPACK, but modern versions as ATLAS and MKL are tune automatically to improve the performance.

These functions are called automatically if you apply a matrix multiplication or SVD, and inversion or LU or QR decomposition. You do not have to call these functions manually. This was the purpose of designing Matlab.

If u,s,v is the SVD decomposition of another matrix C, wouldn't it be more efficient to use

(A - C) .* B

instead of:

(A - u*s*v') .* B