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Real and Imaginary element Separation from square matrix and stacking into a vector

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Karthik Nagaraj
Karthik Nagaraj on 10 Nov 2020
Commented: Karthik Nagaraj on 19 Nov 2020
Around 10000 matrices are stored in a folder in .mat format.
The matrices are square in nature with order NxN in my case N=15.
Important characteristics of the matrix
1) Diagonal elements D11,D22 etc are real in nature
2) The other elements in the matrices are complex in nature.
3) The elements in the lower triangle are equal to the complex conjugates of the upper triangle matrix, so the real part remains the same.
Requirement:
1) Separate all the diagonal elements and store in a column vector.
So Nx1 column vector-1
2) Separate all the Real parts of the upper triangle matrix and lower triangle matrix and store in another column vector.
Since for NxN matrix the number of elements the upper triangle is given by is N(N-1)/2 and similarly for lower triangle is given by N(N-1)/2
So in total 2 x (N(N-1))/2)= [N(N-1)] x1 column vector-2
3) At the end stacking a column vector-1 and column vector-2 to form a column vector-3 of N2x1 order.
Like-
Please help me in getting Column vector-3 which is very crucial. Manually could be done for few matrices but at present the task is tobe done for 10000 matrices, which may even increase. Thanks

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Accepted Answer

Jon
Jon on 10 Nov 2020
Edited: Jon on 10 Nov 2020
D = diag(A)
L = triu(A,1)
U = tril(A,-1)
[D; real(U(:)); real(L(:))]
is close but you still have zero elements in L and U to get rid off
If you know that none of the original elements are zero you could use
D = diag(A)
L = triu(A,1)
L = L(L~=0)
U = tril(A,-1)
U = U(U~=0)
[D; real(U); real(L)]

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Karthik Nagaraj
Karthik Nagaraj on 19 Nov 2020
Hi Jon, I tried another apporach using for loops and saved the data in a cell.
clear all;
close all;
clc;
N=15;
k=6;
C=cell(k,1)
for j = 1:k
C{j}= rand(N,N) + 1i*rand(N,N); % Complex Matrix
end
Now the cell C contains 6 x1 data with each each cell has 15x15 data in 6 cell.
Is it better to split the cell and perform the operations
D = diag(C)
L = triu(C,1)
U = tril(C,-1)
[D; real(U(:)); real(L(:))]
Jon
Jon on 19 Nov 2020
Yes, better to just keep the data within the local workspace and utilize existing programming elements such as cell arrays. I wasn't sure why you were saving the data in files. I thought that was just to simulate the real application where you had to use some experimental data that had been stored in files.So are you all set now?
Karthik Nagaraj
Karthik Nagaraj on 19 Nov 2020
What you thought in the last two sentences are perfectly accurate. Thanks a lot for your patience. I hope I am all set now. If something is there, I will come back. Thanks

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More Answers (1)

Bastian Arturo Romero Mardones
with a matrix of example "a":
a = [1 1+3*i 2+3*i; 3+4*i 2 4+4*i; 5+4*i 6+4*i 3];
realMatrix = zeros(1,length(a));
realMatrixx = zeros(1,(length(a)*(length(a)-1))/2);
k=1; l = 1;
for i=1:length(a)
for j=1:length(a)
if(a(i,j) == real(a(i,j))) %Only if real (a+0*j)
realMatrix(k) = a(i,j);
k=k+1;
elseif(a(i,j) == complex(a(i,j))) %only is complex (a+b*j)
realMatrixx(l) = real(a(i,j));
l=l+1;
end
end
end
realMatrix=realMatrix'; %V1
realMatrixx=realMatrixx'; %V2
final = [realMatrix;realMatrixx]; %V3

  2 Comments

Karthik Nagaraj
Karthik Nagaraj on 11 Nov 2020
Also, I used this to code to fetch mat files in the folder.
files = dir('*.mat');
for i = 1:numel(files)
filename = files(i).name;
data = load(filename);
As I have 10000 matrices stored in a folder in .mat format. Could you help me how to perform the same 3 tasks on those 10000 matrices, which is shown by you for a single A matrix and save those vectors in another folder

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