Help with vectorizing Diag command

I have an MxN matrix, which I would like to turn into an MxNxN matrix, where the elements in the second and third dimensions are a diagonal matrix. It can be done in a for loop by

for ii=1:M
  newMat(ii,:,:)=diag(oldMat(ii,:))
end

Any ideas on how to vectorize this? Thanks

Answer 1

[Jan]

Pre-allocate:

clear
M = 200;
N = 300;
oldMat = rand(M, N);

tic;               % ORIGINAL
for ii=1:M
  newMat(ii,:,:) = diag(oldMat(ii,:));
end
toc    % 16.71 seconds (Matlab 2009a/64, Win7, Core2Duo)

tic;                 % REPMAT
[m, n]  = size(oldMat);
idx     = permute(repmat(logical(eye(n)), [1, 1, m]), [3, 2, 1]);
nM      = idx+0;
nM(idx) = oldMat;
toc    % 1.10 sec 

clear newMat
tic;                % WITH PRE-ALLOCATION
newMat = zeros(M, N, N);  % Pre-allocate!!!
for ii=1:M
  newMat(ii,:,:) = diag(oldMat(ii,:));
end
toc    % 0.68 seconds

clear newMat
tic;                 % BSXFUN
newMat = zeros(M,N,N);
newMat(bsxfun(@plus,(1:M)', (0:N-1)*(M*N+M))) = oldMat;
toc    % 0.076 seconds

Answer 2

[Sven]

Hi Brendan, is this the answer you're looking for?

M = 2, N = 3
oldMat = reshape(1:M*N,M,N)
newMat = zeros(M,N,N)
newMat(bsxfun(@plus,(1:M)',(0:N-1)*M*(N+1))) = oldMat

It uses the bsxfun command to build a list of indices equivalent to the non-zero elements of your newMat, and just populates these elements directly from oldMat.

I haven't tested, but I suspect it will be faster than the loop. Hope it's helpful.

[Edit]

Just tested for M = 200, N = 300:

Elapsed time is 8.962171 seconds. <- loop method
Elapsed time is 1.915089 seconds. <- bsxfun method

[Jan]

In my measurements BSXFUN is much faster.

[Sven]

Oh, I wasn't timing just once... I gave it a few loops which is why my numbers are over 1 second :) Either that or my pc runs like treacle.

And for fairness to the loop method, my comparison used preallocation.

Answer 3

[Andrei Bobrov]

[m,n] = size(oldMat);
idx = permute(repmat(logical(eye(n)),[1,1,m]),[3 2 1]);
nM = idx+0;
nM(idx)=oldMat;

Answer 4

[Brendan]

Thanks a lot!