natural cubic spline interpolation of y-values: how to get derivative of the spline wrt the y-values?

Prashant Kumar answered . 2025-07-13 02:16:14

x=cumsum(rand(1,10));
y=rand(size(x));
xi=linspace(min(x),max(x),500);
f=ppval(spline(x,y),xi)

f = 1×500
    0.8578    0.8215    0.7861    0.7516    0.7180    0.6852    0.6533    0.6223    0.5920    0.5627    0.5341    0.5063    0.4794    0.4532    0.4278    0.4032    0.3794    0.3563    0.3340    0.3124    0.2915    0.2714    0.2519    0.2332    0.2152    0.1978    0.1812    0.1652    0.1498    0.1351

plot(x,y,'or',xi,f,'b') % 

b=eye(length(x));
yd=spline(x,b);
dfdy=ppval(yd,xi); % dfdy(i,j) is the derivative of f(xi(j)) with respect to y(i))
figure
plot(xi,dfdy')

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