modify only the diagonal entries in a matrix?

How can I Multiply the diagonal of a matrix by a number, for example; by 2?

Answer 1

[Jan]

A     = rand(4,3);
s     = size(A);
index = 1:s(1)+1:s(1)*s(2);  % Indices of the main diagonal

A(index) = A(index) * 2

This touches the elements on the diagonal only.

[Athikah Raihah]

I would like to keep A and display the new modified matrix as A1. Could you please show me how?

[Image Analyst]

A1 = A; % Initialize
A1(index) = A(index) * 2 % Multiply diagonal by 2

[Alvin Chen]

Does not work well on non-square matrices, e.g. MxN, N > M.

[Image Analyst]

@Alvin Chen, a trivial for loop will work fine. For the upper left diagonal:

[rows, columns] = size(A);
n = min([rows, columns]);
for k = 1 : n
    A(k, k) = A(k, k) * 2;
end

You can use a similar loop for the three other diagonals.

[Alvin Chen]

@Image Analyst For loop would work for sure, but would it be more performable without using loop? Just extract the logicals by the positions of the indices in A.

[Image Analyst]

I don't know what you mean by "performable". Sure there are other ways to perform this operation that may work, however I did not understand your explanation of extracting the logicals so I invite you to show your non-for loop way that doubles the values in the 4 diagonals in a non-square matrix, for example a 5 by 10 matrix.

m = ones(5, 10)

Please show us.

Answer 2

[Image Analyst]

Here's a way you can do it using eye() to create indexes of the diagonal. I show two ways,

1. one to create another output matrix and leave the input matrix alone, and
2. another to change the input matrix in place.

% Create a logical mask for the diagonal elements.
d = logical(eye(size(m)))

% First way: Create an output matrix m2, retaining the original m.
m2 = m % Initialize with a copy of m
% Multiply diagonal elements of m2 (in place) by 2.
m2(d) = m(d) * 2  % Input values are replaced.

% Second way: Change/replace the values in original matrix.
% Multiply diagonal elements (in place) by 2.
m(d) = m(d) * 2  % Input values are replaced.

The two ways are the same except if you want a second matrix for the output you have to copy the input matrix first.

[Athikah Raihah]

Thanks a lot! That is very clear, exactly what I need!

[Jan]

At least in current Matlab versions:

d = eye(size(m), 'logical');  % faster than: logical(...)