I have a vector that is 2048 that I have coded up in Julia and Matlab. The values of the vector in both Matlab is given by the following function: nn=2048 ; h= 2 * pi/nn; vec=[cos(-pi/2),sin(-pi/2)]; g = x->exp(im * k * dot(vec,x)); G = [g( [cos(i h),sin(i* h)] ) for i=0:nn-1] Where x is a d…

You are right! Sorry about that. I have included the parameters.

You didn’t say which element of G you are comparing to Matlab, or what you think the correct answer is for that element, or how you are doing the comparison. (For example, for k=9im, the maximum element of G has an absolute value of ≈ 8103.08. An absolute difference of ≈ 6.36646e-12 in that elemen…

The error I calculated was the following: maximum(abs.(G-GM)) Where GM is the corresponding vector calculated from Matlab. So for that entry you calculated the relative error, which looks fine, but for calculations of the sort, shouldn’t the absolute error be smaller than 6.3e-12?

[image] Pulpo: So for that entry you calculated the relative error, which looks fine, but for calculations of the sort, shouldn’t the absolute error be smaller than 6.3e-12? No, that’s not how computer arithmetic works. The absolute error depends on the magnitude of the quantities involved …

Comparing Float64 to BigFloat gives an error of 1.05e-11, which seems to indicate that the error in Matlab is in the same direction as in Julia, but half as big. (The maximum absolute error is at i = 539, at an angle just past pi/2, although the relative error seems to grow with increasing i.) Her…

Just to mention this: You can get different errors via different matlab versions, too.

[image] Per: Comparing Float64 to BigFloat gives an error of 1.05e-11, which seems to indicate that the error in Matlab is in the same direction as in Julia, but half as big. No, because for one thing you don’t know that you’re looking at the same element. The element with the biggest differ…

True. It could also be that the error in Matlab is 1.5 times that of Julia. Either way, it would probably be best to compute this in BigFloat if errors of that magnitude are a concern.

[image] Per: Either way, it would probably be best to compute this in BigFloat if errors of that magnitude are a concern. I think it’s more likely that there is just a misunderstanding here about floating-point arithmetic. Matlab’s algorithms are not any more accurate for this sort of thing …

Julia Complex Exponential Evaluation vs Matlab

New to Julia

stillyslalom March 23, 2021, 12:08am 2

Can you take a look at the guidelines here to make sure your example is reproducible? In particular, you didn’t define nn or h, so we can’t reproduce the behavior you’re seeing.

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Julia Complex Exponential Evaluation vs Matlab

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