How can I fit to a growing spiral

So far my function looks like this

 function [x,y] = fitspiral(th, param)
  a = param(1);
  b = param(2);
  c = param(3);
  d = param(4);
  e = param(5);
  f = param(5);
  g = param(5);
  R=((a+(f+g).*th).^2.*(b+(f+g).*th).^2./((a+(f+g).*th).^2.*sin(th).^2+(b+(f+g).*th).^2.*cos(th).^2)).^(.5);
  x=R.*cos(th)+c;
  y=R.*sin(th)+d+(th/pi).^e;
 end

I've been trying to do a lsqcurvefit, but I can't seem to set it up to work. It's a bit of a crazy equation but it fits very close to my current data.

th=linspace(0,2.2*pi);
xdata=[399 347 292 235 167 109 76 96 197 262 323 410 463 559 566 557 527];
ydata= [413 434 440 435 410 367 325 184 106 70 70 80 128 278 338 381 458];

const=[ 196 156 301 266 5.40 10 .8];
param = lsqcurvefit(@fitspiral, const, th, xdata,ydata)

Answer 1

[Star Strider]

There are a few problems with your code, the most significant of which is that in all nonlinear curve fitting functions in MATLAB, the parameter argument comes first and the xdata argument second:

function [xy] = fitspiral(param, th)

Beyond that, lsqcurvefit will easily fit multiple dependent variables, but you have to concatenate them into one matrix:

xydata = [xdata; ydata]';

and be sure your objective function returns a vector of the same size:

xy = [x; y]';

Your independent variable has to be the same length as your dependent variable:

th=linspace(0, 2.2*pi, length(xdata));

With those changes, it works and produces what looks to me as an acceptable fit.

The full code, with revisions (and a plot):

   function [xy] = fitspiral(param, th)
    a = param(1);
    b = param(2);
    c = param(3);
    d = param(4);
    e = param(5);
    f = param(5);
    g = param(5);
    R=((a+(f+g).*th).^2.*(b+(f+g).*th).^2./((a+(f+g).*th).^2.*sin(th).^2+(b+(f+g).*th).^2.*cos(th).^2)).^(.5);
    x=R.*cos(th)+c;
    y=R.*sin(th)+d+(th/pi).^e;
    xy = [x; y]';
   end

xdata = [399 347 292 235 167 109  76  96 197 262 323 410 463 559 566 557 527];
ydata = [413 434 440 435 410 367 325 184 106  70  70  80 128 278 338 381 458];
xydata = [xdata; ydata]';
th=linspace(0, 2.2*pi, length(xdata));

const=[ 196 156 301 266 5.40 10 .8];

param = lsqcurvefit(@fitspiral, const, th, xydata)

[xyfit] = fitspiral(param,th);

figure(1)
plot(xdata, ydata, 'bp')
hold on
plot(xyfit(:,1), xyfit(:,2), '-m')
hold off
grid