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#program spuRs/resources/scripts/simpson_n.r
simpson_n <- function(ftn, a, b, n = 100) {
# numerical integral of ftn from a to b
# using Simpson's rule with n subdivisions
#
# ftn is a function of a single variable
# we assume a < b and n is a positive even integer
n <- max(c(2*(n %/% 2), 4))
h <- (b-a)/n
x.vec1 <- seq(a+h, b-h, by = 2*h)
x.vec2 <- seq(a+2*h, b-2*h, by = 2*h)
f.vec1 <- sapply(x.vec1, ftn)
f.vec2 <- sapply(x.vec2, ftn)
S <- h/3*(ftn(a) + ftn(b) + 4*sum(f.vec1) + 2*sum(f.vec2))
return(S)
}
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