solMat {L0TFinv}R Documentation

Generate the inverse of the crossprod matrix

Description

Generate the inverse matrix of (\boldsymbol{X}^{(q+1)}_A)^T \boldsymbol{X}^{(q+1)}_A for the cases where q=0 or q=1, commonly employed in splicing algorithms. Note that an explicit solution exists for the inverse when q=0, but not when q=1.

Usage

solMat(n, q, A)

Arguments

n

The number of data points

q

The order of the difference, 0 or 1

A

The set of indicators, a subset of \{1,2,3,\dots,n\}

Value

The inverse matrix of (\boldsymbol{X}^{(q+1)}_A)^T \boldsymbol{X}^{(q+1)}_A for the cases where q= 0 or 1.

Examples

Mat1 <- XMat(n = 10, q = 0)
A1 = c(1,2,5,8)
mat1 = as.matrix(Mat1[,A1])
S1 <- solMat(n = 10, q = 0, A = A1)
print(S1)
print(round(S1%*%t(mat1)%*%mat1,10))

Mat2 <- XMat(n = 15, q = 1)
A2 = c(1,3,8,10,15)
mat2 = as.matrix(Mat2[,A2])
S2 <- solMat(n = 15, q = 1, A = A2)
print(S2)
print(round(S2%*%t(mat2)%*%mat2,10))

[Package L0TFinv version 0.1.0 Index]