how to make matlab loop over 2d array faster

Question

I have the above loop running on the above variables:

A is a 2d array of size mxn.
mask is a 1d logical array of size 1xn
results is a 1d array of size 1xn
B is a vector of the form mx1
C is a mxm matrix, m is the same as the above.

Edit: expanded foo(x) into the function.

here is the code:

temp = (B.'*C*B);    
for k = 1:n
    x = A(:,k);
    if(mask(k) == 1)
        result(k) = (B.'*C*x)^2 / (temp*(x.'*C*x)); %returns scalar
    end
end

take note, I am already successfully using the above code as a parfor loop instead of for. I was hoping you would be able to suggest some way to use meshgrid or the sort to yield better performance improvement. I don't think I have RAM problems so a solution can also be expensive memory wise.

Many thanks.

Preallocate result. Change if(mask(k) == 1) to if mask(k). You won't get much gain from that, though. — Luis Mendo
– Luis Mendo, Commented Oct 29, 2013 at 15:18
Hi, I don't think there should be any problem with matrix inputs. — user2324712
– user2324712, Commented Oct 29, 2013 at 15:20
Also, with the current size definitions of your variables, you should use A(k,:) in the code and not A(:,k) ... — bla
– bla, Commented Oct 29, 2013 at 15:41

bla · Accepted Answer · 2013-10-29 21:45:49Z

1

try this:

 result=(B.'*C*A).^2./diag(temp*(A.'*C*A))'.*mask;

This vectorization via matrix multiplication will also make sure that result is a 1xn vector. In the code you provided there can be a case where the last elements in mask are zeros, in this case your code will truncate result to a smaller length, whereas, in the answer it'll keep these elements zero.

edited Oct 29, 2013 at 21:45

answered Oct 29, 2013 at 21:39

bla

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Luis Mendo · Accepted Answer · 2013-10-29 16:23:24Z

1

If your foo admits matrix input, you could do:

result = zeros(1,n); % preallocate result with zeros
mask = logical(mask); % make mask logical type
result(mask) = foo(A(mask),:); % compute foo for all selected columns

edited Oct 29, 2013 at 16:23

answered Oct 29, 2013 at 15:23

Luis Mendo

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5 Comments

user2324712 Over a year ago

why do you preallocate with NaN and not zeros?

Luis Mendo Over a year ago

Because I didn't know which result you wanted for the columns not in mask. But yes, 0 is implicit in your code. I have corrected my answer

user2324712 Over a year ago

its currently failing. i guess the function foo isn't that suitable for matrices. i'll look into it. is there anything that can be done without putting matrices into foo?

Eitan T Over a year ago

Why is there an extra logical in the last line? mask is already logical.

Luis Mendo Over a year ago

@user2324712 If you need to feed foo with each column separately, a for loop is probably the best you can do. And it can be parallelized. You could perhaps save some time replacing for k=1:n by for k=find(mask) and removing the if. At the end you would have to "expand" result, along the lines of result(logical(mask))=result;

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