Derivative of piecewise polynomial using ppval
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Bo Wang
am 31 Mär. 2016
Kommentiert: Jon
am 20 Okt. 2021
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
am 31 Mär. 2016
Bearbeitet: John D'Errico
am 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 Kommentare
Dimitry Chuprakov
am 29 Jul. 2021
Here is the path to correct ppder version for taking derivative of any piecewise polynomial including PCHIP.
Jon
am 20 Okt. 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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