matrixNormal (version 0.1.1)

vech: Half-Vectorization of a matrix

Description

Stacks elements of the lower triangle of a numeric symmetric matrix A.

Usage

vech(A, use.Names = TRUE, tol = .Machine$double.eps^0.5)

Value

A vector with n(n+1)/2 elements.

Arguments

A

A matrix with m rows and n columns.

use.Names

Logical. If TRUE, the names of A are taken to be names of the stacked matrix. Default: TRUE.

tol

A numeric tolerance level used to check if a matrix is symmetric. That is, a matrix is symmetric if the difference between the matrix and its transpose is between -tol and tol.

Details

For a symmetric matrix A, the vectorization of A contains more information than necessary. The half-vectorization, denoted vech(), of a symmetric square n by n matrix A is the vectorization of the lower triangular portion.

Examples

x <- matrix(c(1, 2, 2, 4),
  nrow = 2, byrow = TRUE,
  dimnames = list(1:2, c("Sex", "Smoker"))
)
print(x)

# Example 1
vech(x)
# If you just want the vectorized form
vech(x, use.Names = FALSE)

# Example 2: If one has NA's
x[1, 2] <- x[2, 1] <- NA
vech(x)