Fitting to a function involving a matrix - error For standard eigenproblem EIG(A), A must be square.

I am trying to fit to a function f(x,y) of the form

function[E]=three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx)

a=3.95;

f1=2.*cos(kx.*a)+4.*cos(0.5.*kx.*a).*cos((0.75^0.5).*ky.*a);
f2=exp(1i.*3^(-0.5).*ky.*a)+2.*exp(-0.5.*1i.*3^(-0.5).*ky.*a).*cos(0.5.*kx.*a);
cf2=conj(f2);

H=[Emp+f1.*tmp,f1.*tmps,f2.*tmpx;f1.*tmps,Ems+f1.*tms,f2.*tmsx;cf2.*tmpx,cf2.*tmsx,f1.*tx];

energy=min(eig(H));

E=E0+energy;

When I evaluate this on its own it works fine

e.g.

    three_orbital_dispersion(0.3,0.7,1,1,1,1,-1,1,1,1,0.1)

gives

    ans=-1.658

however, when I try and use the function to fit to a custom model in cftool I get the following error message

    Expression three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx)      is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated:
Error in fittype expression ==> three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx)
??? For standard eigenproblem EIG(A), A must be square.

What's going on? The matrix H is square, and the function seems to work fine outside the fit.

P.S. I get the same problem if I write a script using

    ft = fittype( 'three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx)', 'independent', {'kx', 'ky'}, 'dependent', 'e' );

In which case the error messages are

Error using fittype/testCustomModelEvaluation (line 12) Expression three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx) is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated: Error in fittype expression ==> three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx) ??? For standard eigenproblem EIG(A), A must be square.

Error in fittype>iCreateFittype (line 371) testCustomModelEvaluation( obj );

Error in fittype (line 328) obj = iCreateFittype( obj, varargin{:} );

Error in three_orbital_fit_script (line 5) ft = fittype( 'three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx)', 'independent', {'kx', 'ky'}, 'dependent', 'e' );

Caused by: Error using fittype/evaluate (line 102) Error in fittype expression ==> three_orbital_dispersion(kx,ky,E0,Emp,Ems,tmp,tms,tx,tmps,tmpx,tmsx) ??? For standard eigenproblem EIG(A), A must be square.

[Torsten]

Make sure that "three_orbital_dispersion" is only called with scalar values for the input data, not vectors or matrices.

Best wishes

Torsten.

[Samuel Magorrian]

I'm pretty sure it's only called with scalar values - kx,ky are the x and y data given to the fitting tool, and all the other parameters are scalar parameters. I've fitted to other functions with no problems (being careful to use elementwise multiplication) - it's the determinant of the matrix which seems to be the issue. If cftool is calling the function with the vectors kx,ky, how do I get round this?

Thanks, Sam

[Torsten]

Generate E in a for-loop from ii=1 to ii=length(kx).

Best wishes

Torsten.

[Steven Lord]

Add a DISP statement to display the SIZE of H immediately before you call EIG, then run the code to reproduce the problem. It will show you what size MATLAB thinks H is; if that's not the size you think it should be, then you can work backwards (setting breakpoints on earlier lines and rerunning the example) to debug why it's a different size.

[Samuel Magorrian]

Thanks - all working now!

Sam