How to evaluate a first/second derivative for 5th order spline?

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Abdul Mannan
Abdul Mannan 2015-9-8
编辑： Abdul Mannan 2015-9-8
I am using 5th order spline for my function. I want to evaluate its first and second derivative. For example, I am using the code as follows
if true
x = [0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1];
y = [0,0.7071,1,0.7071,0,-0.7071,-1,-0.7071,0];
k = 5;
sp = spapi( optknt(x,k), x, y );
xx = 0:.005:1;
yy = fnval(xx,sp);
v_o = 2*pi*cos(2*pi*xx); % First Derivative
a_o = -(2*pi)^2*sin(2*pi*xx); % Second Derivative
plot(xx,yy);
hold on; figure, plot(xx,v_o);
plot(diff(yy,1)); hold off % inaccurate first difference
hold on; figure, plot(xx,a_o);
plot(diff(yy,2)); hold off % inaccurate second difference
end
Please, tell me how can I find first and second derivative for 5th order spline. Thanks
  1 个评论
Abdul Mannan
Abdul Mannan 2015-9-8
编辑：Abdul Mannan 2015-9-8
OK. I got the answer but I am not erasing the question for the future use.
if true
x = [0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1];
y = [0,0.7071,1,0.7071,0,-0.7071,-1,-0.7071,0];
k = 5;
sp = spapi( optknt(x,k), x, y );
xx = 0:.005:1;
yy = fnval(xx,sp);
dsp = fnder(sp);
dyy = fnval(xx,dsp);
ddsp = fnder(sp,2);
ddyy = fnval(xx,ddsp);
v_o = 2*pi*cos(2*pi*xx); % First Derivative
a_o = -(2*pi)^2*sin(2*pi*xx); % Second Derivative
plot(xx,yy);
hold on; figure, plot(xx,v_o);
plot(xx,dyy), title('first derivative'); hold off
hold on; figure, plot(xx,a_o);
plot(xx,ddyy); title('second derivative'); hold off
end
Use it and please wish me peace and blessings.

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