R: Vectorized Integration

quadv {pracma} | R Documentation

## Vectorized Integration

### Description

Vectorized adaptive Simpson integration.

### Usage

    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.

### See Also

`quad`

### Examples

    ##  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

[Package pracma version 2.0.4 Index]