quadv: Vectorized Integration

Description

Vectorized adaptive Simpson integration.

Usage

quadv(f, a, b, tol = .Machine$double.eps^(1/2), ...)

Arguments

univariate, vector-valued function; need not be vectorized.

a, b

endpoints of the integration interval.

tol

acuracy required for the recursion step.

...

further parameters to be passed to the function f.

Value

Returns a list with components Q the integral value, fcnt the number of function calls, and estim.prec the estimated precision that normally will be much too high.

Details

Recursive version of the adaptive Simpson quadrature, recursion is based on the maximum of all components of the function calls.

quad is not suitable for functions with singularities in the interval or at end points.

Examples

Run this code

##  Examples
f1 <- function(x) c(sin(x), cos(x))
quadv(f1, 0, pi)
# $Q
#  [1] 2.000000e+00 1.110223e-16
# $fcnt
#  [1] 65
# $estim.prec
#  [1] 4.321337e-07

f2 <- function(x) x^c(1:10)
quadv(f2, 0, 1, tol = 1e-12)
# $Q
#  [1] 0.50000000 0.33333333 0.25000000 0.20000000 0.16666667
#  [6] 0.14285714 0.12500000 0.11111111 0.10000000 0.09090909
# $fcnt
#  [1] 505
# $estim.prec
#  [1] 2.49e-10