cubature: cubintegrate – R documentation

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cubintegrate

Unified Cubature Integration Interface

Description

Integrate a function within specified limits using method specified. Further arguments specific to method as well as other arguments to f may be passed. For defaults used in each method, see help on the method or default_args's.

Usage

cubintegrate(
  f,
  lower,
  upper,
  fDim = 1,
  method = c("hcubature", "pcubature", "cuhre", "divonne", "suave", "vegas"),
  relTol = 1e-05,
  absTol = 1e-12,
  maxEval = 10^6,
  nVec = 1L,
  ...
)

Arguments

`f`	The function (integrand) to be integrated. Can be vectorized version, but the additional arguments `...` must indicate via either `vectorInterface = TRUE` for `hcubature` and `pcubature`, or a value for `nVec`. See details on each method.
`lower`	The lower limit of integration, a vector for hypercubes.
`upper`	The upper limit of integration, a vector for hypercubes.
`fDim`	The number of components of f, default 1, bears no relation to the dimension of the hypercube over which integration is performed.
`method`	the method to use should be one of "hcubature", "pcubature", "cuhre", "divonne", "suave" or "vegas".
`relTol`	The maximum tolerance, default 1e-5.
`absTol`	the absolute tolerance, default 1e-12.
`maxEval`	The maximum number of function evaluations needed, default 10^6. Note that the actual number of function evaluations performed is only approximately guaranteed not to exceed this number.
`nVec`	the number of vectorization points for Cuba C library, default 1, but can be set to an integer > 1 for vectorization, for example, 1024. The function f above needs to handle the vector of points appropriately; see vignette examples. Unlike Cuba, the cubature C library manages the number of points on its own and can vary between calls. Therefore, any value for nVec greater than one implies vectorization for a cubature method.
`...`	All other arguments which may include integration method specific parameters and those for f. Unrecognized parameters for integration method are presumed to be intended for f and so processed.

Value

The returned value is a list of items: -

integral

the value of the integral

`error`	the estimated relative error for cubature; for Cuba it is the estimated absolute error
`neval`	the number of times the function was evaluated

returnCode

the actual integer return code of the C routine; a non-zero value usually indicates problems; further interpretation depends on method

`nregions`	for Cuba routines, the actual number of subregions needed
`prob`	the Chi2-probability (not the Chi2-value itself!) that `error` is not a reliable estimate of the true integration error.

Examples

I.1d <- function(x) {
  sin(4*x) *
    x * ((x * ( x * (x*x-4) + 1) - 1))
}
I.1d_v <- function(x) {
   matrix(apply(x, 2, function(z)
       sin(4 * z) *
       z * ((z * ( z * (z * z - 4) + 1) - 1))),
       ncol = ncol(x))
}
cubintegrate(f = I.1d, lower = -2, upper = 2, method = "pcubature")
cubintegrate(f = I.1d, lower = -2, upper = 2, method = "cuhre", flags=list(verbose = 2))
cubintegrate(f = I.1d_v, lower = -2, upper = 2, method = "hcubature", nVec = 2L)
cubintegrate(f = I.1d_v, lower = -2, upper = 2, method = "cuhre", nVec = 128L)

cubature

Adaptive Multivariate Integration over Hypercubes

v2.0.4.1

GPL-3

Authors

Balasubramanian Narasimhan [aut, cre], Manuel Koller [ctb], Steven G. Johnson [aut], Thomas Hahn [aut], Annie Bouvier [aut], Kiên Kiêu [aut], Simen Gaure [ctb]

Initial release