Function for best fitting

I've got a set of data :Y(d). And I am trying to approximate this set for an polynomial function in the following form :

So the problem is to find the values of each constant : "a,b,c,e" , for the best fitting!

So does someone know an possible way to do it,maybe some function ?

Obs:The set of data is quite big , so by "multiple iterations" I don't think Matlab can process some rotine.

[Azzi Abdelmalek]

It does'nt look like a polynomial function

Answer 1

[Star Strider]

There are several ways to do it.

First, write your function as:

% a = B(1),    b = B(2),    c = B(3),    e = B(4) 
% Y(d)=(a+b*d)/(c + e*d^3)
Y = @(B,d)  (B(1) + B(2).*d) ./ (B(3) + B(4).*d.^3);

then, with d as your dependent variable and y as your independent variable:

Beta0 = rand(4,1);
[Beta,R,J,CovB,MSE] = nlinfit(d, y, Y, Beta0);    % Statistics Toolbox

or:

[Beta,resnorm,residual,exitflag,output,lambda,jacobian] = lsqcurvefit(Y, Beta0, d, y);    % Optimization Toolbox (allows parameter constraints)

If you do not have access to the Statistics or Optimization Toolboxes, I suggest you use fminsearch and the examples in Curve Fitting via Optimization. (The documentation explains it better than I could.) In that example, replace the start_point line with:

start_point = rand(4,1);

and the FittedCurve line with:

FittedCurve = (params(1) + params(2).*xdata) ./ (params(3) + params(4).*xdata.^3);

which is the code for your function.

[Israel]

Thank you

[Star Strider]

My pleasure!

Answer 2

[Matt J]

Use LSQCURVEFIT if you have it.

[Israel]

Thank you

Answer 3

[Matt J]

If noise is sufficiently negligble, you could also rewrite the problem as a linear fitting:

 d=d(:);
 Y=Y(:);
 w=ones(length(d),1);

 A=[w,d,-Y, -Y.*d.^3];

 [~,~,V]=svd(A);

 abce=V(:,end);

If nothing else, this could generate a good initial guess for LSQCURVEFIT.