indexCardinal: Get the order of canonical polynomial chaos expansion

In GPC: Generalized Polynomial Chaos

Description

For a d-dimensional polynomial chaos expansion up to order p, there are a total of M polynomials, determine from get(d,p). Each polynomial $phi_m(x)$ is expressed as the product of the polynomial from each random variables, i.e. $phi_m(x) = phi_m,1(x_1)phi_m,2(x_2)...phi_m,d(x_d)$, each with a different polynomial order. We can thus very succintly denote phi_m(x) with a n-tuple vector containing the polynomial order from each dimension and the entire canonical PCE expansion can be express as a (m x n) matrix.

Usage

indexCardinal(d,p,m,index)

Arguments

d	Number of input random variables
p	Order of the polynomial chaos expansion
m	Pointer to the current n-tuple vector being calculated
index	A dummy variable that stores the polynoial order calculated so far

Value

Index

A (m x d) matrix that donates the polynomial order for each random variables in the canonical construction of PCE

Author(s)

Jordan Ko

References

R. Ghanem and P. Spanos, 1991, Stochastic Finite Elements: A Spectral Approach. Berlin: Springer.

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

See Also

getM

Examples

d <- 3
p <- 5
m <- getM(d,p)
index <- indexCardinal(d,p)
print(t(index))

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