Thread Subject: Fitting Superquadrics

Hello,

I am trying to fit superquadrics[A.H.Barr] to some data that
I have and Im facing some difficulties.

My objective function is defined as:

function f= super_fitting(a,data)
x=data(1,:);
y=data(2,:);
    term1=((x/a(1)).^(2/a(5)));
    term2=((y/a(2)).^(2/a(5)));
f= a(3)* ((1- ((term1+term2).^(a(5)/a(4))) .^ (a(4)/2))
 
% f = (term1+term2).*a(3)+ a(4) ;
% f= ((data(1,:).^2)/(a(1)^2)) + ((data(2,:).^2)/(a(2)^2));
% f= data(:,1).^2 .*a(1) + data(:,2).^2 .*a(2);.^( a(5)/a(4
end

I have generated data (parabolic) using a script like so:

function [x,y,z,xx,yy,zz] = parabolic_surface_generate(a,b,n)

if nargin ==0
    %Generate around (0,0,0) about n*2 points
    %We assume a and b to be 1
    n=20; a=1;b=1;
end
    x= [-n:2:0; 0:2:n];
    y= [-n:2:0; 0:2:n];
    
    %computing y
    z= ((x.^2)/a^2) + ((y.^2)/b^2);
%For Plotting
     xx=x;yy=y;zz=z;
%Data
 x=[x(1:end,1);x(1:end,2)];
 y=[y(1:end,1);y(1:end,2)];
 z=[z(1:end,1);z(1:end,2)];
end

Once, I've generated the data, I fit it by using a statement
like so,
data=[x;y];
[a,res]=lsqcurvefit(@super_fitting,a0,data,z)

So, I've gotten the following errors at different times

1) I get complex values of the co-efficients
2) I get an error like so,

??? Error using ==> qr
Complex sparse QR is not yet available.

Error in ==> aprecon at 57
   RPCMTX = qr(TM(:,p));

Error in ==> trdog at 47
         [R,permR] = feval(pcmtx,H,pcoptions,DM,DG,varargin{:});

Error in ==> snls at 345
      [sx,snod,qp,posdef,pcgit,Z] = trdog(x,g,A,D,delta,dv,...

Error in ==> lsqncommon at 231
    [x,FVAL,LAMBDA,JACOB,EXITFLAG,OUTPUT,msg]=...

Error in ==> lsqcurvefit at 186
[x,Resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] = ...


I have got co-efficients of a superquadric for a fit at
other times.

Potential issues:
I save my scripts on a network drive and am using Matlab
using a common Egr license.

When I get this error, I usually go back to fitting a sphere
and then up my way to a Super quadric and sometimes it works
(???)

I am lost here and any help would be much appreciated. I
have spent a lot of time poring through the matlab archives
and am hoping John or somebody could help me with this.

Thanks,
M