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.
parameter indexing the functions of the SVD
maximal index of the functions computed in the SVD
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
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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)
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