row ranking among multiple matrices

Hi there,

I have three matrix A, B, and C. Here A is a complex matrix of size N*M, where each row of A is generated from the same distribution. Each row of A are also related to corresponding rows of B and C, i.e., the first row will related to the first rows of B and C, so if the row position of A changes, then I want B and C's corresponding rows will be changed as well . Now, calculate the power of each row in A, i.e., the first row power will be: abs(A(1,1))^2+abs(A(1,2))^2+...+abs(A(1,M))^2, then ranking the rows of A based on row's power in descending order, i.e., the highest power row to be the first row, and the lowest poewr row. Meanwhile, I want the rows in B and C can align the ranking changes in A. Is there any efficient way to do this?

Answer 1

[Bruno Luong]

Just very standard matlab programming

% Generate test data
N=10; M=3;
A=rand(N,M)+1i*rand(N,M);
MB = 1;
MC = 2;
B=randi(10,N,MB)

B = 10×1

7 4 3 5 3 4 6 3 6 6

C=randi(10,N,MC)

C = 10×2

6 3 3 2 8 8 3 6 1 4 1 9 7 3 3 1 10 10 5 2

p = 2; % power
[Anorm,is] = sort(vecnorm(A,p,2),'descend')

Anorm = 10×1

1.8755 1.7151 1.6110 1.5849 1.4104 1.3776 1.2816 1.2354 1.1222 1.0291

is = 10×1

5 1 8 4 7 6 10 9 3 2

A = A(is,:)

A = 
   0.7121 + 0.3695i   0.4868 + 0.9979i   0.9602 + 0.8479i
   0.9269 + 0.4427i   0.5795 + 0.9249i   0.2050 + 0.8081i
   0.4052 + 0.9197i   0.9609 + 0.1776i   0.3922 + 0.6903i
   0.3646 + 0.2818i   0.1953 + 0.7376i   0.9552 + 0.8972i
   0.0714 + 0.7200i   0.3226 + 0.4563i   0.8747 + 0.6232i
   0.1924 + 0.3216i   0.5120 + 0.6637i   0.8073 + 0.6346i
   0.6943 + 0.0221i   0.5488 + 0.4397i   0.8141 + 0.0525i
   0.3099 + 0.1480i   0.4871 + 0.3865i   0.8718 + 0.5114i
   0.7629 + 0.4168i   0.2592 + 0.0964i   0.4537 + 0.4703i
   0.3264 + 0.1703i   0.5729 + 0.3254i   0.6828 + 0.1528i

B = B(is,:)

B = 10×1

3 7 3 5 6 4 6 6 3 4

C = C(is,:)

C = 10×2

1 4 6 3 3 1 3 6 7 3 1 9 5 2 10 10 8 8 3 2

[DDDD]

Thank you so much for your explaination!

Answer 2

[Steven Lord]

Call sort with two outputs. Use the second output to reorder the other arrays. See the "Sort Vectors in Same Order" example on the sort documentation page; you would need to generalize it to index into matrices rather than vectors, but that's not difficult.

Answer 3

[Jon]

Similar to @Bruno Luong, but since I already coded up example before I saw @Bruno Luong's I will provide it as alternative here

% Make some example data
m = 5;
n = 3;
A = randn(m,n,"like",1+1i)

A = 
   0.0358 - 1.7015i   0.4671 - 0.2650i   0.6336 - 0.5262i
   0.8548 + 0.0416i   0.2163 - 0.9266i   0.6586 - 1.1739i
  -1.6230 + 0.9340i   0.6844 - 1.0415i  -1.2676 - 0.0650i
   0.7128 - 0.1322i   1.0431 + 0.6256i  -0.1131 + 1.5801i
   0.7582 + 0.1192i  -0.6561 + 0.3697i  -0.5786 + 0.2997i

B = repmat((1:m)',1,m)

B = 5×5

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5

C = repmat(10*(1:m)',1,m)

C = 5×5

10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 40 40 40 40 40 50 50 50 50 50

% Calculate power in each row of A
p = sum(abs(A).^2,2)

p = 5×1

3.8630 3.4495 6.6708 4.5145 1.5809

% Find sort index in descending order
[~,idx] = sort(p,1,'descend');

% Sort the arrays
Asort = A(idx,:)

Asort = 
  -1.6230 + 0.9340i   0.6844 - 1.0415i  -1.2676 - 0.0650i
   0.7128 - 0.1322i   1.0431 + 0.6256i  -0.1131 + 1.5801i
   0.0358 - 1.7015i   0.4671 - 0.2650i   0.6336 - 0.5262i
   0.8548 + 0.0416i   0.2163 - 0.9266i   0.6586 - 1.1739i
   0.7582 + 0.1192i  -0.6561 + 0.3697i  -0.5786 + 0.2997i

Bsort = B(idx,:)

Bsort = 5×5

3 3 3 3 3 4 4 4 4 4 1 1 1 1 1 2 2 2 2 2 5 5 5 5 5

Csort = C(idx,:)

Csort = 5×5

30 30 30 30 30 40 40 40 40 40 10 10 10 10 10 20 20 20 20 20 50 50 50 50 50

[Jon]

Just made a quick edit on the repmat dimensions so that the example matrices would be a little more obvious

[DDDD]

Really appreciate for your explaination!