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POPiecewise Cubic Hermite Interpolating Polynomial (PCHIP) for given data in MATLAB and then finding area
 

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  1. POPiecewise Cubic Hermite Interpolating Polynomial (PCHIP) for given data in MATLAB and then finding area
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    <p><strong>Hello friends</strong> </p> <p>I am trying to do Piecewise Cubic Hermite Interpolation on the data given below in MATLAB 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? </p> <pre><code>x = [5.8808 6.5137 7.1828 7.8953]; y = [31.2472 33.9977 36.7661 39.3567]; pp = pchip(x,y) </code></pre> <p>If I see see pp,it gives pp as</p> <pre><code> form: 'pp' breaks: [5.8808 6.5137 7.1828 7.8953] coefs: [3x4 double] pieces: 3 order: 4 dim: 1 </code></pre> <p>and pp.coefs are</p> <pre><code>-0.0112 -0.1529 4.4472 31.2472 -0.3613 0.0884 4.2401 33.9977 -0.0422 -0.3028 3.8731 36.7661 </code></pre> <p>I think these are the polynomials representing the three intervals</p> <pre><code>[5.8808:6.5137], [6.5137:7.1828], [7.1828:7.8953] </code></pre> <p>But when I find the y values corresponding to x values using these polynomials, it gives wrong values.</p> <p>It gives negative y values for second polynomial . Even third polynomial do not seem to satisfy the points.</p> <p>I used these commands for obtaining the values</p> <p>For example:- (for second polynomial)</p> <pre><code>xs = linspace(6.5137, 7.1828, 200); y = polyval(pp.coefs(2,:),xs); plot(xs,y) </code></pre> <p>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.</p> <p><em>Thanks</em></p> <p><em><strong>Bhomik Luthra</em></strong></p>
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    1. COYou may want to try [`ppval`](http://www.mathworks.com/help/matlab/ref/ppval.html) instead of `polyval`.
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