RandomCoefficients (version 0.0.2)

PSI_mu_fourier: Auxiliary funciton for the evaluation of the SVD of F_c on a pre-specified grid divided by the singular values to the square.

Description

Computation is done using the Fast Fourier transform for the integration.

Usage

PSI_mu_fourier(x, c, b, Psi, res)

Arguments

x

a pre-specified grid

c

the parameter indexing the singular functions

b

the parameter indexing the smoothness class (see Gaillac and Gautier 2018)

Psi

the Prolate Spheroidal wave functions

res

the resolution level for the FFT.

Value

a list containing, in order:

- ipeven

- ipodd

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)
#### Bandwidth 1
L =15
L1 = L+1
N2 = max(L,3)
twoN = 2*N2
#### Bandwidth 1
c1 = 1
K1 = max(twoN+2,30)
K = K1
c = 1
b=1
bound=1
out <- get_psi_mu(c,N2,twoN,K, L1)
Psi <- out[[1]]
mu<- out[[2]]
xseq = seq(-bound,bound, length.out=10)
resol=2^7
psix <- PSI_mu_fourier(xseq,c,b,Psi,resol)
# }