How to reproduce the example figure using lsqcurvefit

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yp78 2021-9-29

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https://ww2.mathworks.cn/matlabcentral/answers/1463194-how-to-reproduce-the-example-figure-using-lsqcurvefit

编辑： yp78 2021-10-1

Hi, I am trying to follow this example for non-linear curve fitting.

Looking at the section 'Splitting the Linear and Nonlinear Problems', I understood upto the point how to estimate two exponents lambda1 & 2 (line 51). However, I don't understand how to recover the estimate for 'c' to produce the 'Global fit' in the last figure in the following section.

More specifically, once I obtain the unknown lambdas, what should I do to obtain the unknown vector 'c' (in the function 'fitvector')? Which of the followings would be the right approach?

c=A \ ydata
c=A \ yEst, or
Once obtained the estimates for lambda, I follow the full parameter estimation using the lambdas.

Thanks in advance for your help!

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Answer 1

Mathieu NOE 2021-9-29

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hello

well, if the question is only about how to use lsqcurvefit, my answer is not gotta help you because I'm using either fminsearch , or , much better and more robust to crude / bad initial guess : Fminspleas - File Exchange - MATLAB Central (mathworks.com)

see the two examples attached if it helps you

all the best

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yp78 2021-9-30

编辑：yp78 2021-9-30

在 MATLAB Online 中打开

Hi Mathieu,

Thanks for the clarification. If I understood correctly, the Fminspleas function is compatible for matrix operations, no? In my working problem, the x and y data look like

x =
1190
2381
3571
4762
5952
7143
8333
0714
4286
1429
y =
3458    0.1737   -0.0417
2848    0.0959    0.0261
2545    0.0085    0.0599
2334   -0.0521    0.0520
2117   -0.0693    0.0225
2023   -0.0863   -0.0028
1952   -0.0878   -0.0185
1836   -0.0662   -0.0465
1689   -0.0378   -0.0483
1543   -0.0618   -0.0279

and I want to simultaneouly estimate the parameters of the functions

where f_1 fits to the first column of y, f_2 for the second column of y, so on. I modified the funlist as follows, but it is not working (it is running, but the solutions are rather strange, the initial guesses stay as they are etc.).

funlist = {1, @(c,xdata) exp(c(1)*xdata), @(c,xdata) exp(c(2)*xdata); ...
    1, @(c,xdata) exp(c(1)*xdata), @(c,xdata) exp(c(2)*xdata);...
    1, @(c,xdata) exp(c(1)*xdata), @(c,xdata) exp(c(2)*xdata)};

I should probably ask the author of the function for the tips. But if you have any clues, would you mind sharing your expertise with me here?

yp78 2021-9-30

编辑：yp78 2021-10-1

Hi Mathieu,

Thanks again for the helpful example files! I wrote the author of the function to ask about the multivariate usage of the function. When I had a reply, I will share the information with you :)