diff function taking very long time while differentiating symbolic expressions

Hello all,

I need to make a Jacobian matrix where both the function (f) array and the variable (y) array are of 5420-by-1. f is an array of symbolic expressions. The sample code is below.

for i=1:5420
    for j=1:5420
        jacobian(i,j)=diff(f(i), y(j)); % Finding the jacobian element
    end
end

After running a few iterations, it seems like it will take more than 5 days. Is there any other way to do that so it should take less time? Thanks in advance.

[Walter Roberson]

It is not clear why you are not using the jacobian() function

[M Al Mamun]

Thanks for your quick reply. Yeah, the jacobian fauction works with great speed. However, I wanted to write the code from the elementary level.

Answer 1

[Walter Roberson]

Potentially faster:

numf = length(f);
numy = length(y);
Jac = zeros(numf, numy, 'sym');
for i = 1 : numf
    thisf = f(i);
    thesevars = symvar(thisf);
    [~, varidx] = ismember(thesevars, y);  %convert variable names to indices
    for j = varidx
        Jac(i, j) = diff(thisf, y(j));
    end
end

What this does is query each f element for the unbound variables present in it, and then only tries to differentiate with respect to those variables.

In the form written it will fail if there are unbound variables that are not listed in y; the fix would not be difficult.

[M Al Mamun]

Thanks a lot Walter. This is what I was actually looking for. It is working perfectly and taking very less time compared to my previous approach.