You are creating ‘jac_n’ inside the timing block in the code you posted, and creating a cell array from ‘x’.
If you create the function first, and define the ‘x’ values as a vector (they appear in order as ‘in1’ in ‘jac_n’ in my code here), the code is much faster:
jac_n = matlabFunction(jac, 'Vars',{[x]})
x=[1 2 3];
fv1 = tic
J1 = jac_n(x)
fv2 = toc(fv1)
with:
fv2 =
4.436000000000000e-04
and:
in1 = x;
fv3 = tic
out = reshape([in1(:,1).*2.0,2.0,1.0,2.0,in1(:,2).*2.0+in1(:,2).^2.*3.0,1.0,1.0,0.0,in1(:,3).*4.0],[3,3]);
fv4 = toc(fv3)
with:
fv2 =
1.782000000000000e-04
Function calls are always going to be a bit slower than running the code ourside the function. The times I get are nowhere near as disparate as yours.
Running this:
jac_n = matlabFunction(jac, 'Vars',{[x]})
x=[1 2 3];
for k = 1:100
fv1 = tic
J1 = jac_n(x)
fv2 = toc(fv1)
in1 = x;
fv3 = tic
out = reshape([in1(:,1).*2.0,2.0,1.0,2.0,in1(:,2).*2.0+in1(:,2).^2.*3.0,1.0,1.0,0.0,in1(:,3).*4.0],[3,3]);
fv4 = toc(fv3)
ratio(k) = fv2 / fv4;
end
ratio_stats = [mean(ratio) std(ratio)]
produces:
ratio_stats =
3.146795126810789e+00 8.189169834987492e+00
so the direct code is about three times faster than the function, however there is wide variation.
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