fastmatrix (version 0.5-7721)

symmetrizer: Symmetrizer matrix

Description

This function returns the symmetrizer matrix of order \(n\) which transforms, for every \(n\times n\) matrix \(\bold{A}\), vec\((\bold{A})\) into vec\(((\bold{A} + \bold{A}^T)/2)\).

Usage

symmetrizer(n = 1, matrix = FALSE)

Value

Returns an \(n^2\) by \(n^2\) matrix (if requested).

Arguments

n

order of the symmetrizer matrix.

matrix

a logical indicating whether the symmetrizer matrix will be returned.

Details

This function is a wrapper function for the function symm.info. This function provides the information required to create the symmetrizer matrix. If option matrix = FALSE the symmetrizer matrix is stored in three vectors containing the coordinate list of indexes for rows, columns and the values.

Warning: matrix = TRUE is not recommended, unless the order n be small. This matrix can require a huge amount of storage.

References

Abadir, K.M., Magnus, J.R. (2005). Matrix Algebra. Cambridge University Press.

Magnus, J.R., Neudecker, H. (2007). Matrix Differential Calculus with Applications in Statistics and Econometrics, 3rd Edition. Wiley, New York.

See Also

symm.info

Examples

z <- symmetrizer(n = 100)
object.size(z) # 319 Kb of storage

N100 <- symmetrizer(n = 100, matrix = TRUE) # time: < 2 secs
object.size(N100) # 800 Mb of storage, do not request this matrix!

# a small example
N3 <- symmetrizer(n = 3, matrix = TRUE)
a <- matrix(rep(c(2,4,6), each = 3), ncol = 3)
a
b <- 0.5 * (a + t(a))
b
v <- N3 %*% vec(a)
all(vec(b) == as.vector(v)) # vectors are equal!