mvQuad (version 1.0-2)

createNIGrid: creates a grid for numerical integration.

Description

createNIGrid Creates a grid for multivariate numerical integration. The Grid can be based on different quadrature- and construction-rules.

Usage

createNIGrid(dim = NULL, type = NULL, level = NULL,
  ndConstruction = "product", level.trans = NULL)

Arguments

dim

number of dimensions

type

quadrature rule (see Details)

level

accuracy level (typically number of grid points for the underlying 1D quadrature rule)

ndConstruction

character vector which denotes the construction rule for multidimensional grids. [object Object],[object Object]

level.trans

logical variable denotes either to take the levels as number of grid points (FALSE = default) or to transform in that manner that number of grid points = 2^(levels-1) (TRUE). Alternatively level.trans can be a function, which takes (n x d)-ma

Value

• Returns an object of class 'NIGrid'. This object is basically an environment containing nodes and weights and a list of features for this special grid. This grid can be used for numerical integration (via quadrature)

Details

The following quadrature rules are supported (build-in). [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object] The argument type and level can also be vector-value, different for each dimension (the later only for "product rule"; see examples)

References

Philip J. Davis, Philip Rabinowitz (1984): Methods of Numerical Integration

F. Heiss, V. Winschel (2008): Likelihood approximation by numerical integration on sparse grids, Journal of Econometrics

H.-J. Bungartz, M. Griebel (2004): Sparse grids, Acta Numerica

See Also

rescale, quadrature, print, plot and size

Examples

## 1D-Grid --> closed Newton-Cotes Formula of degree 1 (trapeziodal-rule)
myGrid <- createNIGrid(dim=1, type="cNC1", level=10)
print(myGrid)
## 2D-Grid --> nested Gauss-Legendre rule
myGrid <- createNIGrid(dim=2, type=c("GLe","nLe"), level=c(4, 7))
rescale(myGrid, domain = rbind(c(-1,1),c(-1,1)))
plot(myGrid)
print(myGrid)
myFun <- function(x){
   1-x[,1]^2*x[,2]^2
}
quadrature(f = myFun, grid = myGrid)
## level transformation
levelTrans <- function(x){
  tmp <- as.matrix(x)
  tmp[, 2] <- 2*tmp[ ,2]
  return(tmp)
}
nw <- createNIGrid(dim=2, type="cNC1", level = 3,
   level.trans = levelTrans, ndConstruction = "sparse")
plot(nw)