# quadv: Vectorized Integration In pracma: Practical Numerical Math Functions

## Usage

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

## Arguments

 `f` 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`.

## 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.

## 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.

`quad`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## 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 ```