How to perform non linear least square regression of eigenvalues of a matrix (matrix elements being some function of independent variable and parameters to be optimized)?

Hi, I am a beginner in MATLAB and struggling with this one code. I have a (4x4) matrix whose elements are function of independent variable and parameters (say a,b,c are parameters) and x is independent variable. e.g. M= [a+b*exp(x*b),c*b*exp(x*c)....;c+a*exp(x*b)....] the eigenvalues of this matrix are y(dependent variables) I want to fit my data to.

I have the data set Xexp=[x1,x2,x3......] and Yexp=[y1,y2....]

I am trying to fit the data set (X,Y) to the eigenvalue "y" (say 2nd eigenvalue) of the matrix (M) using "lsqnonlin" where at the end of the function program I calculate "Y-y" so as to be minimized by the lsqnonlin e.g.

phiLSQ= lsqnonlin(@(phi) lambdafn(phi), initial_param); %command to start regression in main program

function LErr = lambdafn(phi) %start of the function

I am providing the data set (X,Y) in function program itself.

when I run the script I get following error

       Error using horzcat
       Dimensions of matrices being concatenated are not consistent.

       Error in lambdafn (line 31)
       Q=[a+b*exp(x*b),c*b*exp(x*c)....;c+a*exp(x*b)....] ; %the complete matrix 

       Error in @(phi)lambdafn(phi)

       Error in lsqnonlin (line 194)
       initVals.F = feval(funfcn{3},xCurrent,varargin{:});

       Error in lambda (line 32)
       phiLSQ= lsqnonlin(@(phi) lambdafn(phi), initial_param);

       Caused by:
       Failure in initial user-supplied objective function evaluation. LSQNONLIN cannot continue.

Thanks

Answer 1

[Matt J]

You should test lambdafn(phi) before you feed it to lsqnonlin to make sure it works, i.e., that it always runs without error messages and returns a finite, real value. LSQNONLIN is complaining that it doesn't.

[Vipultomar]

Hi. Thanks for the reply. I tried running my function code (lambdafn(phi)) from a different script with artificial values. As long as I give a single value for my x(independent variable) it runs, but when I take the entire vector for X (the independent variable) or more than one values of x just to check it starts giving error:

Error using vertcat
Dimensions of matrices being concatenated are not consistent.

Error in lambdafn (line 33)
Q=[a+b*exp(x*b),c*b*exp(x*c)....;c+a*exp(x*b)....] ; %the complete matrix 
Error in test (line 28)
lambdafn(phi)

[Matt J]

Makes sense. Now you know what to fix!

[Vipultomar]

I'm sorry I still dont understand why shouldn't I feed my entire data. As its a regression and so my experimental data (X,Y) needs to be fitted based on the corresponding eigenvalues. Should I feed the value of my X one by one using for loop? But wherever I have seen the use of this code I never saw anyone giving values of x one by one. It would be a great help if you could please provide me details of how the lsqcurvefit and lsqnonlin proceed through the code. I mean how is the program iterating at each step (couldn't find details). e.g we feed entire xdata and ydata in below expression at once, right?

x = lsqcurvefit(fun,x0,xdata,ydata)

(trying with lsqcurvefit now).

Thanks

[Matt J]

It's got nothing to do with lsqcurvefit or lsqnonlin. You need to teach lambdafn() to handle vectorized input. I think you can understand, for example, why this works

    >> eig(rand(5))

    ans =

       2.3013 + 0.0000i
       0.4685 + 0.1426i
       0.4685 - 0.1426i
      -0.1218 + 0.5437i
      -0.1218 - 0.5437i

but this does not,

    >> eig(rand(5:10))
    Error using eig
    For standard eigenproblem EIG(A), A must be 2-D.

[Vipultomar]

Okay. Thanks for reply. I'm trying. Will let you know wherever I get.

[Vipultomar]

As I am giving as input the entire row of xdata, the program is trying to calculate the matrix elements first, and then eigenvalues to be given as output (y) for minimization. The problem I think is that the code is taking the entire row of xdata at once and then processing according to..

Q=[a+b*exp(x*b),c*b*exp(x*c)....;c+a*exp(x*b)....]

after which I calculate my eigencalues. because each element of matrix is being generated for each xdata value, there is problem with concatenation. On the other hand if I try to take just one element of matrix as my function operator (just to check) or just one value of xdata, it works fine.

[Vipultomar]

As I mentioned the program was not taking complete xdata row, I have started a for loop in the function itself. In this way the function calculates the value of y from the model (function) and keeps putting them in a row vector. Finally the entire row vector is output of the function (for lsqcurvefit). And so its working now. Although there is no change in parameter values with each step (which I think should be unrelated to it) so trying to correct that.

Thanks