Integrate and subdivisions limit

Hans W Borchers · 2011-01-12T19:02:22Z

> Dear all, > I have some issues with integrate in R thus I would like to request > your help. I am trying to calculate the integral of f(x)*g(x). > The f(x) is a step function while g(x) is a polynomial. > If f(x) (step function) changes its value only few times (5 or 6 'steps') > everything is calulated ok(verified results in scrap paper) but if f(x) > takes like 800 different values I receive the error > > "Error in integrate number of subdivisions reached" > > I did some checks on the

Hans W Borchers

Wed, Jan 12, 2011 11:02 AM

There's obviously a more numerically stable approach. If g(x) is a polynomial
you do know its polynomial antiderivative. Take that and sum up all intervals
where the step function is constant.

Example:  g(x) = 1 constant, integrate x^2 over 0..1 in 10000 subdivisions.
          The antiderivative is 1/3 * x^3, thus

    g <- function(x) 1
    x <- seq(0, 1, len=10001)
    sum((x[2:10001]^3 - x[1:10000]^3)*g(2:10001))/3  #=> 0.3333333

The antiderivative of a polynomial a_1 x^n + ... + a_{n+1} given as vector
c(a1,...) can also be determined automatically, no manual work is necessary.

Hans Werner

Integrate and subdivisions limit

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