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

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?

Answer 1

[Paul]

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]

It looks like it counts the constant coefficient as a dimension. I should be able to use this to get the slope values there.

Answer 2

[Matt J]

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