Efficient operation on individual matrix rows

Hello,

I'm searching for a way to apply the Jacobian function to each row of a matrix. Essentially I need to access each row of a matrix and apply a function. I could use a "for loop" which is quite slow:

for i=1:size(a,1)
    tmp = jacobian(a(i,:),b);
    result=cat(1,result,tmp);
end

I also found this solution:

function dNdv = matjacobian(N,v)
    rz = arrayfun(@(ii)jacobian(N(ii,:),v),(1:numel(N(:,1))).','un',0);
    dNdv = cat(1,rz{:});
end

The second solution is faster but I'm wondering if there is a more efficient way. Or even a way to apply the jacobian to a multi row matrix.

Thanks in advance,

Chris

Answer 1

[Stephen23]

"I could use a "for loop" which is quite slow:"

The problem is not the for loop, but the fact that you expand the array result on each loop iteration. Expanding arrays is slow. Read this to know why:

https://www.mathworks.com/help/matlab/matlab_prog/preallocating-arrays.html

Using a loop (with a properly preallocated output) will be faster than using arrayfun. You can simply preallocate the output array to be the correct size before the loop, and your code will be quite fast:

out = nan(...); % defined to be the final size!
for k = ...
    ...
    out(k,...) = ...
end

the correct size to use for preallocation depends on a and b: I am sure that can figure that out.

[Chris B]

Perfect, that worked. The for loop with preallocation is indeed faster. Thanks.