When using the cftool, should I use Trust Region or Levenberg-Marquardt?

Question

Wesley Brown 2020-1-22

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https://ww2.mathworks.cn/matlabcentral/answers/501376-when-using-the-cftool-should-i-use-trust-region-or-levenberg-marquardt

评论： Matt J 2020-1-24

Hello,

I have a data-set that behaves like a sin wave. I need to fit a curve to the data-set using the cftool. In the fit options, there are two algorithms I can choose from: 'trust-region' or 'Levenberg-Marquardt'.

I am trying to figure out the difference between the two algorithms, which algorithm is better, and why. Below is my code, and a screenshot of the curve fitting tool as well as my fit options. Thanks in advance.

%Who: Wesley Brown
%Input: PPP orthometric heights
%Process:Curve fitting 
%Output: a1, a2, etc. 
 
clear 
format longg 
 
%Time matrix in days 
 
x = [0
90
180
270
360
450
540
630
720
810
900
990
1080
1170
1260
1350
1440];
 
%Y matrix (change in orthometric height from day 1)
y = [ 0
       0.00799999999998136
         0.007000000000005
       0.00799999999998136
      0.000999999999976353
       -0.0010000000000332
        0.0129999999999768
        0.0149999999999864
        0.0109999999999673
       0.00200000000000955
                         0
        0.0029999999999859
        -0.007000000000005
                         0
      -0.00300000000004275
       0.00200000000000955
       -0.0080000000000382];
 
 
cftool(x(:,1),y(:,1));

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Walter Roberson 2020-1-22

编辑：Walter Roberson 2020-1-24

I am not able to answer the question of which is better or why. The algorithms are described at https://www.mathworks.com/help/optim/ug/equation-solving-algorithms.html

With the data and model you have, your question is like asking whether a chicken or a platypus is a better approximation for a snake.

Walter Roberson 2020-1-24

在 MATLAB Online 中打开

You can get a slightly better fit near

5.84357338824362e-05 2.58183128710864e-05 0.00521135858653424 -0.199178847293523 0.678796516975015 -2.289596742701e-08

These parameters are not unique! The sign of the 3rd one can change, and the 5th one involves semi-periodic behavior about pi/180 apart. The 4th one is periodic as well...

It is still a pretty ugly fit. The model is a terrible one for explaining the data.

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Answer 1

Matt J 2020-1-22

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https://ww2.mathworks.cn/matlabcentral/answers/501376-when-using-the-cftool-should-i-use-trust-region-or-levenberg-marquardt#answer_411477

编辑：Matt J 2020-1-22

You can read here about the relative limitations of the 2 algorithms,

https://www.mathworks.com/help/optim/ug/lsqcurvefit.html#buun3a1-2

For you, I expect the decision on which algorithm to use will depend on whether you wish to impose bounds on the parameters. Levenberg-Marquardt does not handle bound constraints. It's not really even a decision. If you try to impose bounds, cftool will default to the trust-region algorithm.