RandomCoefficients (version 0.0.2)

get_u: Computation of the coefficients of the PSWF on the Legendre polynomials basis of L^2(-1,1)

Description

The matrix ueven has columns u^0,u^2,...,u^2N, and the matrix uodd has columns u^1,u^3,...,u^2N+1. Each column has length N+1. Below, note that i must have odd length so that ai and ci have even length and can be split into two subvectors containing alternate entries of ai and ci.

Usage

get_u(c, N)

Arguments

c

parameter indexing the functions of the SVD

N

maximal index of the functions computed in the SVD

Value

a list containing, in order:

- ueven : the coefficients of the decomposition of the SVD on the Legendre polynomials for the even functions

- uodd : the coefficients of the decomposition of the SVD on the Legendre polynomials for the odd functions

Examples

# NOT RUN {
library(orthopolynom)
library(polynom)
library(tmvtnorm)
library(ks)
library(sfsmisc)
library(snowfall)
library(fourierin)
library(rdetools)
library(statmod)
library(RCEIM)
library(robustbase)
library(VGAM)
library(RandomCoefficients)
#### Number of Psis
L =15
L1 = L+1
N2 = max(L,3)
twoN = 2*N2
#### Bandwidth 1
c1 = 1
K1 = max(twoN+2,30)
K = K1
### get the coefficients beta (for the computation of Psi) of the PSWF on the
### basis of Legendre polynomials.
out <- get_u(c1,N2)

# }