How to replace kth diagonal in a matrix in octave? - matrix

Question

I am trying to replace the sub and super diagonals of a matrix in Octave.
This is the code I am using:
A=[-3 -2 -1 0 1 2 3;0.1 0.2 0.2 0.5 0.6 -0.1 0]'
P=zeros(4,4)
for (k=1:7)
j=A(k,1)
diag(P,j)=A(k,2)
end
This is the error I got: diag(0,_): subscripts must be either integers 1 to (2^63)-1 or logicals
But all the little parts are okay. diag(P,-3) works fine, but when I ask to replace in the loop it refuses!
What can I do about it? Is this: diag(P,j)=e, not the right code to substitute super and sub diagonals?

Answer 1

The reason you're getting an error is that diag(P,j) is not a reference to the diagonal of P, it is a function that returns the values on that diagonal. So what you're doing is assigning the value A(k,2) to the return value of the function and, since it's never assigned to a variable name, the value is lost and nothing changes.
To fix your loop, you would need to provide indices into P and assign to those. One way is to use logical indexing to tell MATLAB which values in P to change. For example,
P = zeros(4)
M = logical(diag([1,1,1], -1))
P(M) = 3
gives us
P =
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
M =
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
P =
0 0 0 0
3 0 0 0
0 3 0 0
0 0 3 0
The unfortunate part is that we can't specify both which diagonal we want to create and the size of the resulting matrix, so we have to calculate the number of elements on the diagonal before creating it.
A=[-3 -2 -1 0 1 2 3;0.1 0.2 0.2 0.5 0.6 -0.1 0].'
n=4; % Number of rows/columns in P...
% If we want a non-square matrix, we'll have to do more math
P=zeros(n);
for k=1:2*n-1 % Remove hardcoded values to make the code more general.
j=A(k,1);
diag_length = n-abs(j);
M=diag(true(1,diag_length),j); % Create logical array with true on jth diagonal
P(M)=A(k,2);
end
The result is:
P =
0.5000 0.6000 -0.1000 0
0.2000 0.5000 0.6000 -0.1000
0.2000 0.2000 0.5000 0.6000
0.1000 0.2000 0.2000 0.5000
Another approach is to use spdiags. One of the uses of spdiags takes the columns of one matrix and uses them to build the diagonals of the output matrix. You pass the indices of the diagonals to set, and the matrix of values for each of the diagonals, along with the matrix size.
If we only pass one value for each diagonal, spdiags will only set one value, so we'll have to duplicate the input vector n times. (spdiags will happily throw away values, but won't fill them in.)
A=[-3 -2 -1 0 1 2 3;0.1 0.2 0.2 0.5 0.6 -0.1 0].'
n = 4;
diag_idx = A(:,1).'; % indices of diagonals
diag_val = A(:,2).'; % corresponding values
diag_val = repmat(diag_val, n, 1); % duplicate values n times
P = spdiags(diag_val, diag_idx, n, n);
P = full(P);
That last line is because spdiags creates a sparse matrix. full turns it into a regular matrix. The final value of P is what you'd expect:
P =
0.5000 0.6000 -0.1000 0
0.2000 0.5000 0.6000 -0.1000
0.2000 0.2000 0.5000 0.6000
0.1000 0.2000 0.2000 0.5000
Of course, if you're into one-liners, you can combine all of these commands together.
P = full(spdiags(repmat(A(:,2).', n, 1), A(:,1).', n, n));