Debugging equations. vectorized vs. for-loop

[Pythagorean]

I get different results from these two functions. I need a fresh pair of eyes to help me find the discrepancy. The old way I did it, with the for-loop, gave proper results (but is slower, I think).VECTORIZED (wrong):

Nss = .5*(1+tanh((y(1,:)-V3)/V4)); %N as t --> inf
tau = 1./(phi*cosh((y(1,:)-V3)./(2*V4)));

dy(:,2) = (Nss-y(2,:))./tau;

a4 = (Nss(1)-y(2,1))./tau(1);

save newodeset a4

vectorized result:
a4 = 0.5300

FOR-LOOP (right):

 Nss = .5*(1+tanh((y(1)-V3)/V4)); %N as t --> inf
tau = 1/(phi*cosh((y(1)-V3)/(2*V4)));
    
dy(2) = (Nss-y(2))/tau;

a4 = a4 = (Nss-y(2))/tau;

for-loop result:
a4 = 0.4572

 

[Pythagorean]

MATLAB, by the way.

 

[MRFMengineer]

On first glance, why no ./ or .* in line 1 of the vectorized? Don't you get a dimension mismatch error?

 

[Pythagorean]

Matlab doesn't have a problem with the vector in the numerator, so onlly the 1./() was necessary. I added the . in the second line out of desperation. Upon your suggestion, I also tried adding the . in but I get the same result (it diverges to Inf/NaN)

I also further dissected the (Nss-y(2,./tau term

and found the problem to be in the "y(2,:)" which is the second variable in the ODE, so it's possibly not even anything to do with this code. All the other values in the expression remain the same in both codes... maybe I'm not catching the right time to compare, I don't know.

This is just an excerpt of my whole code. I'd hoped I'd narrowed it down, but not sure anymore.

 

[alphy]

As a scientist, it is important to carefully examine and understand the differences between vectorized and for-loop methods of debugging equations. While both methods may produce different results, it is important to identify the source of the discrepancy and determine which method is more accurate and efficient.

First, it is important to understand the differences between vectorized and for-loop methods. Vectorized methods operate on entire arrays or matrices at once, while for-loop methods operate on each element individually. This means that vectorized methods can be more efficient for large datasets, but may also introduce errors if the data is not properly formatted. On the other hand, for-loop methods may be slower but can be more precise when dealing with individual elements.

In this case, it seems that the for-loop method is producing the correct results while the vectorized method is giving incorrect results. This could be due to a formatting error in the vectorized code, or it could be a more fundamental issue with the equations themselves. It is important to carefully check the equations and ensure that they are being applied correctly in both methods.

One strategy for identifying the source of the discrepancy is to compare the output of each method for a small subset of the data. This can help to pinpoint where the error is occurring and provide clues for how to fix it. It may also be helpful to consult with a colleague or seek out additional resources to gain a fresh perspective on the problem.

In conclusion, as a scientist, it is important to carefully examine and understand the differences between vectorized and for-loop methods when debugging equations. By carefully analyzing the results and seeking out additional help if needed, it is possible to identify and resolve any discrepancies and ensure the accuracy and efficiency of the equations.