Conditioning a matrix for loop

Hello Mathworks community! Could someone give me a hand?

I'm having trouble trying to create a matrix for loop. Since my actual code is complex, I'm going to propose a much simple idea.

Imagine I have a matrix A 4x12 input such as:

A = [1,2,3,4,5,6,3,5,4,2,5,1;
    1,2,3,4,5,6,3,5,4,2,5,1;
    12,5,6,9,2,3,5,3,4,3,6,1;
    12,5,6,9,2,3,5,3,4,3,6,1]

And another matrix b:

b = [1, 2, 3;
    2, 2, 1;
    3, 2, 1;
    1, 2, 6]

Let's say each row of A is divided in 3 subarrays with 4 positions each (12 positions in every row). Now, I'd like to sum each A position with the corresponding value of b. So b(1,1) would be added to A(1,1), A(1,2), A(1,3) and A(1,4); b(1,2) would be added to A(1,5), A(1,6), A(1,7) and A(1,8); ...

On the same loop, I would like to substract to every value of that output( the dimensions still are 4x12) the value of c corresponding to its row. (the first row of out minus c(1), the second row of out minus 12, ...

c = [10;12;14;16]

I'm working with much bigger data, so trying to do it "manually" wouldn't be useful.

Thank's for the help!

Santos

Answer 1

[Jon]

You can do this without a loop, for example

out = [A(:,1:4)-b(:,1) A(:,5:8)-b(:,2) A(:,9:12)-b(:,3)]

out = out - c

[Jon]

If you have a large number of subarrays, perhaps that one line of code would get very long, and might be awkward to define. In this case you could use a loop like this. There may also be some other more clever way to vectorize (avoid using loops) this, which others might suggest. I don't do any checking in my example but you should make sure that the number of subarrays evenly divides the number of columns in A

numSub = 3; % number of subarrays

A = [1,2,3,4,5,6,3,5,4,2,5,1;
    1,2,3,4,5,6,3,5,4,2,5,1;
    12,5,6,9,2,3,5,3,4,3,6,1;
    12,5,6,9,2,3,5,3,4,3,6,1]
b = [1, 2, 3;
    2, 2, 1;
    3, 2, 1;
    1, 2, 6]
c = [10;12;14;16]

% find problem dimensions
numCol = size(A,2); % number of column in overall array

% determine number of columns in each sub array
numSubCol = numCol/numSub;

% make loop to build up new overall array from subarrays
out = zeros(size(A)); % preallocate
startIdx = 1:4:numCol; 
endIdx = numSubCol:4:numCol;

for k = 1:numSub
    out(:,startIdx(k):endIdx(k)) = A(:,startIdx(k):endIdx(k)) - b(:,k);
end

% subtract off c from each row
out = out - c;

[Santos García Rosado]

Thank's Jon. As you said, I have very long arrays so I'm forced to use a loop. I'll try to translate your code to mine and chek if it works.