# [R] integration of a discrete function

Thomas Lumley tlumley at u.washington.edu
Sun Apr 21 22:54:31 CEST 2002

On Sat, 20 Apr 2002, Giuseppe  Pagnoni wrote:

> Dear R list
>
> I am looking for a function in R that computes the integration of a
> discrete curve, such as a power spectrum, in a specified interval (in my
> case, that would be 'power in a certain frequency band').  I found only
> analytic functions, and not on a curve specified as a set of (x,y) pairs.
> I have the impression that I am not looking in the right place....  or I
> should code the algorithm myself?

You should probably code it yourself.

When you have a genuinely discrete function the integral will usually be
exactly
sum(w*x)
where w is a vector of weights that will depend on x in a problem-specific
way (that being why you want to do it yourself). You probably don't want

OTOH, if you have data (x,y) and want to integrate a smooth or
interpolated curve you could use approxfun() or splinefun() to create that
smooth curve and integrate it. [Someone will probably point out that you
don't actually need to integrate() it, since linear and spline functions
have closed-form integrals]

-thomas

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