How to fit quadratic function with plateau condition?

Question

madhuri dubey 2018-7-23

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评论： Srishti Vishwakarma 2019-1-16

I want to fit quadratic function with plateau condition

(y=a(x+n)^2+b(x+n)+c, x < xc(Ymax) ;    
y=yp, x >= xc(Ymax).

Where a,b,c & n are constants, and xc is critical value at which y is maximum. My data is x=[0,80,100,120,150], y=[1865,3608,4057,4343,4389].

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Answer 1

Matt J 2018-7-23

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编辑：Matt J 2018-7-23

在 MATLAB Online 中打开

LSQCURVEFIT seems to do a decent job. There was no guarantee that it would work - it's not clear to me that the model function has a well-defined Jacobian.

      x=[0,80,100,120,150], 
      y=[1865,3608,4057,4343,4389]
      p0=[0,polyfit(x,y,1)];
    [p,resnorm,residual,exitflag,output] = lsqcurvefit(@F,p0, x,y,[],[0,inf,inf]);
    a=p(1);
    b=p(2);
    c=p(3);
    n=0; %redundant parameter
    plot(x,y,'--*',x,polyval(p,x),'-'); 
    xlabel 'x' 
    ylabel 'y'
    function fval=F(p,xdata)
        [a,b,c]=deal(p(1), p(2), p(3));
        xc=-b/2/a;
        if ~isfinite(xc),
            xc=inf;
            yp=inf;
        else
            yp=polyval(p,xc);
        end
        fval=polyval(p,xdata);
        fval(xdata>xc)=yp;
    end

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madhuri dubey 2018-7-23

编辑：Matt J 2018-7-23

在 MATLAB Online 中打开

Ok forget about p0. My question is when I have just copied and pasted your code then what is the problem. Why have I got this error?

Undefined function or variable 'F'.
Error in lsqcurvefit (line 202)
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Matt J 2018-7-23

Because Matlab cannot recognize the function F(). You pasted it somewhere that makes it invisible.

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Answer 2

madhuri dubey 2018-7-24

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I have some doubt related to your code, which you have sent me at first. In my question, I have mentioned that I want to fit quadratic plus plateau. But in your solution graph showed that one curve fit line (red) and another one (blue) is just join the observed data point. Where is the plateau line? Or what is the value of ymax. I have attached one document, I hope it will clear what I want to ask. Kindly see Fig. 1(b) and equation (3) and (4).