How to fit quadratic function with plateau condition?

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].

Answer 1

[Matt J]

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

[Matt J]

madhuri's reply moved here:

when i tried to use above code, i have got the following error...

 Undefined function or variable 'F'.

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

[Matt J]

But as you can see from my code, F() is defined. Where did you hide it?

[madhuri dubey]

I did not hide it. I just copied your code and paste it in matlab and i got above error. It did not consider p0 as a function.

[Matt J]

p0? The message you posted above refers to 'F'.

[madhuri dubey]

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]

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

Answer 2

[madhuri dubey]

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).

Answer 3

[madhuri dubey]

Sorry, I forget to attach the file.

[Srishti Vishwakarma]

https://blogs.cornell.edu/agsci-interns/2015/08/20/the-models-used-to-fit-the-data-of-yield-nitrogen-fertilizer-response/

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