Derivative of piecewise polynomial using ppval

Question

Bo Wang 2016-3-31

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评论： Jon 2021-10-20

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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Answer 1

John D'Errico 2016-3-31

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https://ww2.mathworks.cn/matlabcentral/answers/276471-derivative-of-piecewise-polynomial-using-ppval#answer_215865

编辑：John D'Errico 2016-4-5

在 MATLAB Online 中打开

Well, you could always use ppder. I've not looked at the code, but I imagine it might work.

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.

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Dimitry Chuprakov 2021-7-29

Here is the path to correct ppder version for taking derivative of any piecewise polynomial including PCHIP.

Jon 2021-10-20

在 MATLAB Online 中打开

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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