nint_integrateNCube: Integrate Hypercube

In docopulae: Optimal Designs for Copula Models

Description

Interface to the integration over interval dimensions.

Usage

nint_integrateNCube(f, lowerLimit, upperLimit, ...)

nint_integrateNCube_integrate(integrate)

nint_integrateNCube_cubature(adaptIntegrate)

nint_integrateNCube_SparseGrid(createIntegrationGrid)

Arguments

integrate	function(f, lowerLimit, upperLimit, ...) which calls integrate.
adaptIntegrate	function(f, lowerLimit, upperLimit, ...) which calls cubature::adaptIntegrate.
createIntegrationGrid	function(dimension) which calls SparseGrid::createIntegrationGrid.
f	the scalar-valued wrapper function to be integrated.
lowerLimit	the lower limits of integration.
upperLimit	the upper limits of integration.
...	other arguments passed to f.

Details

nint_integrate uses nint_integrateNCube to handle interval dimensions. See examples below on how to deploy different solutions.

The function built by nint_integrateNCube_integrate calls integrate (argument) recursively. The number of function evaluations therefore increases exponentially with the number of dimensions ((subdivisions * 21) ** D if integrate, the default, is used). At the moment it is the default method because no additional package is required. However, you most likely want to consider different solutions.

The function built by nint_integrateNCube_cubature is a trivial wrapper for cubature::adaptIntegrate.

The function built by nint_integrateNCube_SparseGrid is an almost trivial wrapper for SparseGrid::createIntegrationGrid. It scales the grid to the integration region.

Value

nint_integrateNCube returns a single numeric.

nint_integrateNCube_integrate returns a recursive implementation for nint_integrateNCube based on one dimensional integration.

nint_integrateNCube_cubature returns a trivial implementation for nint_integrateNCube indirectly based on cubature::adaptIntegrate.

nint_integrateNCube_SparseGrid returns an implementation for nint_integrateNCube indirectly based on SparseGrid::createIntegrationGrid.

See Also

nint_integrate

integrateA, integrate

adaptIntegrate in package cubature

createIntegrationGrid in package SparseGrid

Examples

## integrate with defaults (stats::integrate)
nint_integrate(sin, nint_space(nint_intvDim(pi/4, 3*pi/4)))


dfltNCube = nint_integrateNCube

## prepare for integrateA
ncube = function(f, lowerLimit, upperLimit, ...) {
    cat('using integrateA\n')
    integrateA(f, lowerLimit, upperLimit, ..., subdivisions=2)
}
ncube = nint_integrateNCube_integrate(ncube)
unlockBinding('nint_integrateNCube', environment(nint_integrate))
assign('nint_integrateNCube', ncube, envir=environment(nint_integrate))

## integrate with integrateA
nint_integrate(sin, nint_space(nint_intvDim(pi/4, 3*pi/4)))


## prepare for cubature
ncube = function(f, lowerLimit, upperLimit, ...) {
    cat('using cubature\n')
    r = cubature::adaptIntegrate(f, lowerLimit, upperLimit, ..., maxEval=1e3)
    return(r$integral)
}
unlockBinding('nint_integrateNCube', environment(nint_integrate))
assign('nint_integrateNCube', ncube, envir=environment(nint_integrate))

## integrate with cubature
nint_integrate(sin, nint_space(nint_intvDim(pi/4, 3*pi/4)))


## prepare for SparseGrid
ncube = function(dimension) {
    cat('using SparseGrid\n')
    SparseGrid::createIntegrationGrid('GQU', dimension, 7)
}
ncube = nint_integrateNCube_SparseGrid(ncube)
unlockBinding('nint_integrateNCube', environment(nint_integrate))
assign('nint_integrateNCube', ncube, envir=environment(nint_integrate))

## integrate with SparseGrid
nint_integrate(sin, nint_space(nint_intvDim(pi/4, 3*pi/4)))


assign('nint_integrateNCube', dfltNCube, envir=environment(nint_integrate))

docopulae documentation built on May 2, 2019, 7:53 a.m.