How to fit quadratic function with plateau condition, where the plateau condition is achieved by linear fit?

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madhuri dubey 2018-7-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/412576-how-to-fit-quadratic-function-with-plateau-condition-where-the-plateau-condition-is-achieved-by-li

编辑： dpb 2018-7-29

The values of x and y are as follows:

x=[0,80,100,120,150], 
y=[1865,3608,4057,4343,4389]

My equations are as follows:

y=a(x)^2+b(x)+c, x < xc(Ymax) ....(1)  
y=yp, x >= xc(Ymax) ....(2)

I want to fit these two equations, where first equation will provide a quadratic fit whereas the second equation will provide a linear one. The problem is when we are trying to fit, it provide us best fit in quadratic form (eq.1), it did not include the linear fit (eq.2).

We are also providing the code that we have used:

yf = @(b,x) b(1).*x.^2+b(2)*x+b(3);
B0 = [0.006; 21; 1878];
[Bm,normresm] = fminsearch(@(b) norm(y - yf(b,x)), B0);
a=Bm(1);
b=Bm(2);
c=Bm(3);
xc=-b/(2*a);
p=c-(b^2/(4*a));
 if (x < xc) 
      yfit = a.*x.^2+ b*x+c;
 else yfit = p;
 end
plot(x,yfit, '*')
hold on 
plot(x,y)
hold off

We are providing the graph (fig(1)) which we got from our results. For further understanding, we are also proving a graph (fig(2)) which shows how the result should come.