Function for best fitting
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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.
1 个评论
Azzi Abdelmalek
2012-11-21
It does'nt look like a polynomial function
采纳的回答
Star Strider
2012-11-21
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.
更多回答（2 个）
Use LSQCURVEFIT if you have it.
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.
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