Derivative of piecewise polynomial using ppval
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I have a problem about derivative of piecewise polynomial. Here is my code
function y=ppval_drv(pp,x,deriv)
%x=0:10;
%y=f(x);
%xx=linspace(0,10,200);
y=f(x);
pp=spline(x,y);
t=pp.coefs;
[m n]=size(t);
d=[n-deriv:-1:1;ones(deriv-1,n-deriv)];
d=cumsum(d,1);
d=prod(d,1);
I don't know what to do next. Can anyone give me a hint for this one? Thanks
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John D'Errico
il 31 Mar 2016
Modificato: John D'Errico
il 5 Apr 2016
For a cubic spline, a derivative is actually pretty easy to do, as just a matrix multiply. (For that matter any order spline in a pp form is trivial to differentiate.)
% pd is the polynomial degree of the polynomial segments,
% so for a spline created by spline, we have pd=3.
pd = 3;
D = diag(pd:-1:1,1);
% given deriv as the order of the derivative to compute
% just loop
for i = 1:deriv
pp.coefs = pp.coefs*D;
end
Untested code, but it should work.
2 Commenti
Dimitry Chuprakov
il 29 Lug 2021
Here is the path to correct ppder version for taking derivative of any piecewise polynomial including PCHIP.
Jon
il 20 Ott 2021
Inspired approach! I love its simplicity just using a single matrix multiply. I think you were aiming for clarifying the approach here, but, I think you actually could even further vectorize it using
pp.coefs = pp.coefs*D^deriv
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