# CreateQuadrature: Create a full or sparse numerical quadrature. In GPC: Generalized Polynomial Chaos

## Usage

 `1` ```CreateQuadrature(N,L,QuadPoly,ExpPoly,QuadType,ParamDistrib) ```

## Arguments

 `N` Number of random variables `L` Level of quadrature used in the approximation. `QuadPoly` The type of one-dimensional quadrature rule to be used. For `SPARSE`, one can use `ClenshawCurtis` or `Fejer`. For `FULL`, one could choose `Hermite`,`Legendre`,`Jacobi` or `Laguerre` `ExpPoly` The polynomial used in the expansion. Options are `Hermite`, `Legendre`, `Jacobi`, `Laguerre` `QuadType` Type of quadrature. Options are `SPARSE` or `FULL` `ParamDistrib` Shape parameters used for the definition of random variables.

## Value

 `QuadSize` Number of quadrature points `QuadNodes` A (QuadSize x n) matrix containing the QuadSize d-dimensional quadrature points. `QuadWeights` A n-tuple vector containing the quadrature weights associated with each quadrature point `PolyNodes` A (m x n) matrix containing the m d-dimensional multivariate polynomial evaluated at the n quadrature points.

Jordan Ko

## References

J. Ko, 2009, Applications of the generalized polynomial chaos to the numerical simulationof stochastic shear flows, Doctoral thesis, University of Paris VI.

`tell.GPCE.quad`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```rm(list = setdiff(ls(), lsf.str())) # random variable definitgeion d <- 3 # number of random variables L <- 4 # quadrature level in each dimention. # could be anisotropic eg c(3,4,5) for full quadrature # PCE definition QuadType <- "FULL" # type of quadrature QuadPoly <- rep("LEGENDRE",d) # polynomial to use ExpPoly <- rep("LEGENDRE",d) # polynomial to use ParamDistrib <- NULL # QuadType <- "SPARSE" # type of quadrature # QuadPoly <- 'ClenshawCurtis' # polynomial to use # ExpPoly <- rep("LEGENDRE",d) # polynomial to use Quadrature = CreateQuadrature(d,L,QuadPoly,ExpPoly,QuadType,ParamDistrib) # quadrature ```

GPC documentation built on May 30, 2017, 12:50 a.m.