Cannot get the right coefficient from PCHIP fit

Hello,

I want to fit my x, y data using the PCHIP-fit and then I would like to get the coefficients to create several equation that would piecewise fit my data.

I am able to create the fit and to access the single coefficients, but when I try to plot the single polinomial using the coefficients from the PCHIP, the result is wrong.

Here is the code:

y = [0; 600; 843.6; 914.5; 941.1];
x = [0; 100; 500; 1000; 1500];

CurveFit = fit(x,y,'pchip');                % Create the PCHIP fit
pp = pchip(x,y);                            
[breaks,coefs,L,order,dim] = unmkpp(pp);    % Get Coefficientfrom PCHIP

scatter(x,y); grid on; hold on;             % Plot my data x, y
plot(CurveFit,'k');                         % Plot the pchip fit

syms f1(x)                                  % Plot the first polinomial function for the first two set of data using the coefficient from PCHIP
f1(x) = coefs(1,1)*x.^3 + coefs(1,2)*x.^2 + coefs(1,3)*x + coefs(1,4);
fplot(f1,[0 100]);

syms f2(x)                                  % Plot the second polinomial function for the second set of data using the coefficient from PCHIP
f2(x) = coefs(2,1)*x.^3 + coefs(2,2)*x.^2 + coefs(2,3)*x + coefs(2,4);
fplot(f2,[100 500]);

syms f3(x)
f3(x) = coefs(3,1)*x.^3 + coefs(3,2)*x.^2 + coefs(3,3)*x + coefs(3,4);
fplot(f3,[500 1000]);

syms f4(x)
f4(x) = coefs(4,1)*x.^3 + coefs(4,2)*x.^2 + coefs(4,3)*x + coefs(4,4);
fplot(f4,[1000 1500]);

The result I got looks like this! I don't know why only f1(x) is overlapping my PCHIP- fit, while the other functions f2(x), f3(x) and f4(x) are not. Should not all the functions overlap the fit?

Do you know what I am getting wrong? Thank you

Answer 1

[Torsten]

From the documentation:

Since the polynomial coefficients in coefs are local coefficients for each interval, you must subtract the lower endpoint of the corresponding knot interval to use the coefficients in a conventional polynomial equation. In other words, for the coefficients [a,b,c,d] on the interval [x1,x2], the corresponding polynomial is

f(x)=a(x−x1)^3+b(x−x1)^2+c(x−x1)+d .