XMat {L0TFinv} | R Documentation |
Generate an artificial design matrix
Description
This matrix corresponds to the difference matrix, transforming the L0 trend filtering model into an inverse statistical problem.
Usage
XMat(n, q)
Arguments
n |
The number of data points |
q |
The order of the difference |
Details
Noticing the correspondence between \boldsymbol{D}^{(q+1)}
and \boldsymbol{X}^{(q+1)}
, the result of their matrix multiplication is a combination of a zero matrix and an identity matrix. Expressed as \boldsymbol{D}^{(q+1)} \boldsymbol{X}^{(q+1)}=(\boldsymbol{O}_{(n-q-1)\times(q+1)},\quad \boldsymbol{I}_{(n-q-1)\times(n-q-1)})
. The result is advantageous for the invertible processing of the original L0 trend filtering problem.
Value
A matrix with dimensions n
by n
, whose elements correspond to the difference matrix.
Examples
mat1 <- XMat(n = 10, q = 0)
print(mat1)
mat2 <- XMat(n = 15, q = 1)
print(mat2)
mat3 <- XMat(n = 15, q = 2)
print(mat3)
Mat1 <- DiffMat(n = 10, q = 0)
Mat2 <- DiffMat(n = 15, q = 1)
Mat3 <- DiffMat(n = 15, q = 2)
print(Mat1%*%mat1)
print(Mat2%*%mat2)
print(Mat3%*%mat3)
[Package L0TFinv version 0.1.0 Index]