I have a matrix M which is a function of two variables, x and y, and I want to diagonalize it for many pairs of x and y. If I index x as x(u) and y as y(v), then I can write the elements of the matrix as M(i,j,u,v) where i and j index which element of the matrix.
Currently I am constructing and diagonalizing the matrices with for loops:
x = linspace(0,1,5);
y = linspace(2,3,5);
M = [ y(v)*x(u) , x(u) ; x(u) , -y(v)^2 ];
(:,:,u,v)] = eig(M(:,:,u,v));
I've been able to vectorize almost all the rest of my code, and this is the last part. Is there a way to vectorize this? My experience with vectorization is fairly limited, so please let me know if you have any side comments on this - for example, whether vectorization would actually speed it up.
I should add that although my MWE is a 2x2, I would in practice be doing this with a 4x4 matrix, if that is relevant to whether or not vectorizing the diagonalization would actually do much to accelerate my code.
error: M(_,_,_,2): but M has size 2x2 error: called from test at line 6 column 36
My bad - I started writing this question, tried the MWE, noticed that it didn't work, fixed the code... and apparently forgot to copy the correct code back into the e-mail.
The corrected code is copied below.
x = linspace(0,1,5); y = linspace(2,3,5); for u=1:5 for v=1:5 M(:,:,u,v)=[y(v)*x(u),x(u);x(u),-y(v)^2]; [vecs(:,:,u,v),vals(:,:,u,v)] = eig(M(:,:,u,v)); end end
The space after vals must have been a typo after I copied this to Gmail. Aside from that, the only change is that I added
(:,:,u,v) after M inside the loop.
When I copy this code out of Gmail. it appears garbled in both Notepad++ and Octave both, so there's probably something strange going on with the formatting. To circumvent that, I also attached the script.