MATLAB: Efficient operation on individual matrix rows

matrix manipulationpreallocate

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

Best Answer

"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.
Related Question