MATLAB: Derivative of piecewise polynomial using ppval

ppval polynomial

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

Best Answer

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.

Related Solutions

MATLAB: How to find the derivative of a spline curve in MATLAB 7.9 (R2009b)

The POLYDER function is meant to be used to differentiate polynomials, and not piece-wise polynomials, such as splines.

If you have Spline Toolbox, you can use FNDER function to find the derivative of a spline:

pp=spline(x,y);
p_der=fnder(pp,1);
y_prime=ppval(p_der,x);

For more information on the FNDER function, please refer to the documentation by executing the following in the MATLAB command prompt:

doc fnder

If you do not have access to the Spline Toolbox, you can use UNMKPP function to break down your polynomial and then use MKPP function to assemble a new polynomial that will be a derivative of the first polynomial as in the following example:

% create points we will use to construct the spline
x = 0:10;
y = (x-5).^3+3*3+x+5;
% points the spline will be plotted at
xx = linspace(0,10,20);
% create the spline
pp = spline(x,y);
% plot the spline and the initial points used to create it
figure
plot(x,y,'o',xx,ppval(pp,xx))
hold on
% extract details from piece-wise polynomial by breaking it apart
[breaks,coefs,l,k,d] = unmkpp(pp);
% make the polynomial that describes the derivative
pp2 = mkpp(breaks,repmat(k-1:-1:1,d*l,1).*coefs(:,1:k-1),d);
% plot the derivative of the polynomial
plot(xx,ppval(pp2,xx),'-r')
% to calculate 2nd derivative differentiate the 1st derivative
[breaks,coefs,l,k,d] = unmkpp(pp2);
pp3 = mkpp(breaks,repmat(k-1:-1:1,d*l,1).*coefs(:,1:k-1),d);
plot(xx,ppval(pp3,xx),'-g')

For more information on the UNMKPP and MKPP functions please refer to the documentation by executing the following in the MATLAB command prompt:

doc unmkpp
doc mkpp

MATLAB: How to calculate spline of the function

X = [args;args]
Y = [vals;derivs]
P = spapi(4,X(:),Y(:))

after comment

ppp = csape([-1 1],[3 -1 1 3],[1 1])

polyval(ppp.coefs,1)

Best Answer

Related Solutions

MATLAB: How to find the derivative of a spline curve in MATLAB 7.9 (R2009b)

MATLAB: How to calculate spline of the function

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