Levenberg Marquardt Optimisation issue

[lms17]

Hi,

I'm looking to use the Levenberg Marquardt algorithm using a percentage error optimisation technique instead of the absolute error technique. As far as I know the Levenberg Marquardt algorithm in Labview uses the absolute error technique (i.e. Y-f(x)) when calculating out the errors. How do I change this to use the percentage error technique, where the error = [(Y-f(x))/Y]*100? I modified the error calculation within the algorithm to calculate the error this way but the results weren't satisfactory. I'm wondering if I'm overlooking anything or is there a lot more to this than meets the eye? I know in other programs like Mathematica you have the option to choose how you want the error calculated but I don't see this option in the Labview vi. Any help appreciated.

Thanks,

LMS

Additional Information:

I am using Labview version 8.2

I changed the subvi ABX to calculate the error differently. The ABX vi contains a subvi called LM function and gradient. The output of this subvi calculates the error as Y - best fit. I have changed this calculation to be [((Y-best fit)/Y)*100] to get the percentage error instead. This affects alpha, beta and chisqr. I believe that I may need to make more changes to the algorithm to implement the percentage error technique but I'm not sure what changes to make. The results I recieved from the above changes were worse than the results I got from the absolute error method (error = Y - best fit). This shouldn't have been the case. I'm implementing the VI format of the Levenberg Marquardt algorithm and not the formula string. Any help appreciated.

Thanks,

LMS

[Ashish_Naik_NIUK · Accepted solution]

Hi LMS,

I am not sure if I have understood you correctly.

However as the Lev-Mar algorithm calculates Y-f(x). If you divide this output by the best non-linear fit (Y) and multiply by 100. This will give you your desired effect.

I hope this helps you. 

[altenbach]

Levenberg-Marquard uses a weighted chisquare = Sum[(Y-(f(x))² x weight)].

I would think you should get close to what you need if you would make the weights to be a function of Y for example.

Just create an array of weights according to your array of Y data and wire both the the fitting VI.

I would not mess with the NI code. 🙂

[altenbach]

Just wondering: Did you solve your problem?

[lms17]

Hi,

I tried using the weights but this did not work for me as the results were still worse. In the end, I used the NI VI just as it was and I changed the equations I was inputting to this VI. For the percentage error, I set Y = 1 and f(x) = f(x)/Y. In other words, I divided the equation by Y. There was no need to multiply both sides by 100. The results I got were identical to the results I got in Mathematica using the percentage technique. Thanks for all yer help.

LMS17

[mmlf]

Hello,

I'm pretty new at labview.

The last post help me very much to understand the Chisqr. 

I want to understand better the calculation of alpha and beta.

In numerical recipes C, beta=-1/2 plus second derivate of chisqr.

I can´t find the constant factor -1/2 in ABX.

I can´t find the factor 1/2 of the covariance as well.

When I try to understand the calculation of alpha, I´m complete lost.

Is the same equation of Numerical Recipes C (15.5.7) or a different one?

In LM function and gradient is just the gradient or second order partial derivates, I saw there order 2? 

Thank you very much. 

[altenbach]

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mmlf wrote:

I want to understand better the calculation of alpha and beta. 

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... continued here. Let's keep it all in one place. 😉

[altenbach]

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altenbach wrote: 

... continued here. Let's keep it all in one place. 😉

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 Sorry, bad link. Here it is.... 🙂