How to use multiple sets of xDATA with lsqcurvefit?

I have following function

I'd like to get coefficients alpha, beta, gamma, delta and epsilon coefficients by least squares method and use it to fit some data.

So, I have 3 sets of xDATA (for every independent variable) and one set of yData (for dependent variable) and I'd like to put it all into lsqcurvefit function.

According to the answer in this question, I've tried to write my objective function like this

f = @(c, x) c(1).*x(:,2).^(c(2).*x(:,1).^c(3)) + (c(4) + c(5).*x(:,1))./x(:,3);

and to use it like this

lsqcurvefit(f, [1 1 1], [ndoms nDOF nprocs], measuredVals)

but, unfortunately, I'm still getting following error:

Index exceeds matrix dimensions.

Error in factorizatonKGlobRegr>@(c,x)c(1).*x(:,2).^(c(2).*x(:,1).^c(3))+(c(4)+c(5).*x(:,1))./x(:,3)

Error in lsqcurvefit (line 202)
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Caused by:
    Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

What am I doing wrong?

---------------------------------------------------

Data

measuredVals = [
0.1647815
0.06300775
0.05769325
0.04803725
0.04290825
0.0405065
0.03807525
0.03487725
0.284112
0.13495675
0.12740075
0.11109725
0.105036
0.11022575
0.100587
0.09803775
0.48695475
0.30563525
0.30084925
0.283312
0.2745085
0.271998
0.27472625
0.27103925
0.89953925
0.68234025
0.6783635
0.65540225
0.64421475
0.64214725
0.63949875
0.623119
1.588605
1.37335275
1.36082075
1.35097375
1.34813125
1.34932025
1.3519095
1.34521625
2.820884
2.63251325
2.640659
2.6338805
2.636361
2.62748
2.6233345
2.63821
4.81472975
4.65116425
4.664892
4.64225625
4.6734825
4.63981675
4.635483
4.6280245];

n = 56;

ndoms = [];
for i=1:n
    ndoms = [ndoms; 288];
end

tmp = [
        375
        1029
        2187
        3993
        6591
        10125
        14739];
nDOF = [];
for i=1:7
    for j=1:8
        nDOF = [
            nDOF
            tmp(i)];
    end
end

nprocs = [];
for i=1:7
    nprocs = [nprocs; [1 2 3 4 6 8 12 24]'];
end

[Dean]

Hi Martin,

I have discovered your issue as I have the same problem you had a while ago. I was wondering if you have an idea, how to plot the data sets and the fitted cruve in a plot in order to show the fitting accuracy as it is done in the graphic attached below. The xdata set consists in my case of two different vectors, that I implement in my curve fitting. Each vectors has a different magnitude. Can help me with this issue?

Kind regards

Dean

Answer 1

[Alan Weiss]

Thanks you for giving such a complete, detailed question. Your error is clear. Your objective function takes a 5-D variable c:

f = @(c, x) c(1).*x(:,2).^(c(2).*x(:,1).^c(3)) + (c(4) + c(5).*x(:,1))./x(:,3);

However, your initial point x0 is 3-D:

minc = lsqcurvefit(f, [1 1 1], [ndoms nDOF nprocs], measuredVals)

Give a 5-D initial guess, such as rand(5,1), or ones(5,1).

And, in the future, you might want to learn how to use repmat and ones to save yourself some for loops.

Alan Weiss

MATLAB mathematical toolbox documentation