Calculate the derivative of a data-function in r
Is there an easy way to calculate the derivative of non-liner functions that are give by data?
for example:
x = 1 / c(1000:1)
y = x^-1.5
ycs = cumsum(y)
plot (x, ycs, log="xy")
How can I calculate the derivative function from the function given by ´x´ and ´ycs´?
Answer
Was also going to suggest an example of a smoothed spline fit followed by prediction of the derivative. In this case, the results are very similar to the diff calculation described by @dbaupp:
spl <- smooth.spline(x, y=ycs)
pred <- predict(spl)
plot (x, ycs, log="xy")
lines(pred, col=2)
ycs.prime <- diff(ycs)/diff(x)
pred.prime <- predict(spl, deriv=1)
plot(ycs.prime)
lines(pred.prime$y, col=2)