How to reduce running time of diagonal matrix multiplication with full matrix in Matlab?

Question

z cy 2022-7-28

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1769470-how-to-reduce-running-time-of-diagonal-matrix-multiplication-with-full-matrix-in-matlab

评论： z cy 2022-7-28

采纳的回答： Chunru

I need to calculate a matrix multiplication that

, where B is a full matrix with

and D is a digonal matrix with

.The computational complexity is

Acturally, if the matrix D is a full matrix, the computational complexity will be

.

I recorded the running time for both cases in matlab, and find that the running time and time complexity are not consistent, how can I speed it up? I want to use less time to calculate the first case compared with the second case.

Thanks.

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Chunru 2022-7-28

The simplest case is for D=I. Then

. The complexity for this matrix multiplication is

rather than

.

For full matrix D, the complexity is

.

For diagonal D, the complexity is

.

z cy 2022-7-28

Thanks, I made a typo. I have modified it in the question

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Answer 1

Chunru 2022-7-28

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1769470-how-to-reduce-running-time-of-diagonal-matrix-multiplication-with-full-matrix-in-matlab#answer_1016630

编辑：Chunru 2022-7-28

在 MATLAB Online 中打开

n = 2000; d=500;
B = randn(d, n);
dv = randn(n, 1);
D = diag(dv);
% Normal
tic
A = B*D*B';
toc
Elapsed time is 0.052677 seconds.
% Speed up 1
tic
C = B*(dv.*B');
toc
Elapsed time is 0.012931 seconds.
% Speed up 2
tic
E = (B.*dv')*B';
toc
Elapsed time is 0.012015 seconds.
A(1:5, 1:5)
ans = 5×5
    6.0809   11.2463  -58.6430  -66.3057  -24.0124
   11.2463  -49.0177   52.5213   23.6997   18.0264
  -58.6430   52.5213   42.9952   29.0237   23.4184
  -66.3057   23.6997   29.0237  -44.6983   -0.1757
  -24.0124   18.0264   23.4184   -0.1757  -61.5623
C(1:5, 1:5)
ans = 5×5
    6.0809   11.2463  -58.6430  -66.3057  -24.0124
   11.2463  -49.0177   52.5213   23.6997   18.0264
  -58.6430   52.5213   42.9952   29.0237   23.4184
  -66.3057   23.6997   29.0237  -44.6983   -0.1757
  -24.0124   18.0264   23.4184   -0.1757  -61.5623
E(1:5, 1:5)
ans = 5×5
    6.0809   11.2463  -58.6430  -66.3057  -24.0124
   11.2463  -49.0177   52.5213   23.6997   18.0264
  -58.6430   52.5213   42.9952   29.0237   23.4184
  -66.3057   23.6997   29.0237  -44.6983   -0.1757
  -24.0124   18.0264   23.4184   -0.1757  -61.5623