cubintegrate function

Unified Cubature Integration Interface

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().

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.

Returns

The returned value is a list of items:

• integral: the value of the integral
• error: 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: forcCuba 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)

See Also

default_args(), hcubature(), pcubature(), cuhre(), vegas(), suave(), divonne()