# How to get the value of slopes of pchip at the enpoints?

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David Gillcrist on 7 Jan 2024
Commented: David Gillcrist on 8 Jan 2024
I'm using pchip to interpolate a set of data X. After getting the interpolation, I'm trying to have functions g and f, connect to the endpoints of the interpolation. I want g and f to have the same slopes where they connect to the endpoints. Is there a convenient way to get the values of the slopes of the pchip interpolation?

Paul on 7 Jan 2024
The doc page pchip (under the Output Arguments, pp section) shows how the interpolationg polynominal is formed for each interval based on the breakpoints and the pp coefficients, from which it should be straighforward to compute the derivative at the leading and trailing edges of the first and last intervals respectively.
x = 0:.1:1;y=sin(x);
pp = pchip(x,y);
pp
pp = struct with fields:
form: 'pp' breaks: [0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1] coefs: [10×4 double] pieces: 10 order: 4 dim: 1
Not sure why pp.oder = 4. That seems odd for a cubic polynomial.
David Gillcrist on 8 Jan 2024
It looks like it counts the constant coefficient as a dimension. I should be able to use this to get the slope values there.

Matt J on 7 Jan 2024
Edited: Matt J on 7 Jan 2024
You don't need to determine the end slopes to extrapolate X. Just use the 'extrap' option to obtain values where desired outside the boundaries of X.
You could also do a finite-difference approximation, e.g.,
x=sort(rand(1,10)); y=rand(size(x)); f=@(z) interp1(x,y,z,'pchip','extrap');
ye=y(end); delta=eps(ye);
endslope = ( f(ye+delta) - f(ye) )/delta
endslope = 24

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