MATLAB: Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) for given data and then finding area

area of curveinterpolationMATLABpchip

Hello all
    I am trying to do Piecewise Cubic Hermite Interpolation on the data given below and then I want to get the area covered by the polynomials with x axis. I think, I am misunderstanding the meaning of coefficients returned by pchip command, but not sure. Does anyonw know what could be the problem?
x = [5.8808 6.5137 7.1828 7.8953];
y = [31.2472 33.9977 36.7661 39.3567];
pp = pchip(x,y)
If I see see pp,it gives pp as
   form: 'pp'
    breaks: [5.8808 6.5137 7.1828 7.8953]
     coefs: [3x4 double]
    pieces: 3
     order: 4
       dim: 1
and pp.coefs are
-0.0112 -0.1529 4.4472 31.2472
-0.3613 0.0884 4.2401 33.9977
-0.0422 -0.3028 3.8731 36.7661
I think these are the polynomials representing the three intervals
[5.8808:6.5137],
[6.5137:7.1828],
[7.1828:7.8953]
But when I find the y values corresponding to x values using these polynomials, it gives wrong values.
It gives negative y values for second polynomial . Even third polynomial do not seem to satisfy the points.
I used these commands for obtaining the values
For example:- (for second polynomial)
xs = linspace(6.5137, 7.1828, 200);
y = polyval(pp.coefs(2,:),xs);
plot(xs,y)
I want to find the area under the curve covered by this plot, that's why I am trying to find the polynomial. Is there any other way to do it or if anyone could find the problem in the commands that I am using, please let me know.
Thanks
Bhomik Luthra

Best Answer

x = [5.8808 6.5137 7.1828 7.8953];
y = [31.2472 33.9977 36.7661 39.3567];
pch = pchip(x,y);
out = fnval(fnint(pch),x([2,3]))*[-1;1];    % if you have 'Curve Fitting Toolbox'
or
out = integral(@(x)ppval(pch,x),x(2),x(3)); %
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