FoReco (version 1.1.0)

commat: Commutation matrix

Description

This function returns the (\(r c \times r c\)) commutation matrix \(\mathbf{P}\) such that \(\mathbf{P} \mbox{vec}(\mathbf{Y}) = \mbox{vec}(\mathbf{Y}'),\) where \(\mathbf{Y}\) is a (\(r \times c\)) matrix (Magnus and Neudecker, 2019).

Usage

# Commutation matrix
commat(r, c)
# Vector of indexes for the rows of commutation matrix
commat_index(r, c)

Value

A sparse (\(r c \times r c\)) matrix \(\mathbf{P}\) (commat), or the vector of indexes for the rows of commutation matrix \(\mathbf{P}\)

(commat_index)

Arguments

r

Number of rows of \(\mathbf{Y}\).

c

Number of columns of \(\mathbf{Y}\).

References

Magnus, J.R. and Neudecker, H. (2019), Matrix Differential Calculus with Applications in Statistics and Econometrics, third edition, New York, Wiley, pp. 54-55.

See Also

Utilities: FoReco2matrix(), aggts(), balance_hierarchy(), csprojmat(), cstools(), ctprojmat(), cttools(), df2aggmat(), lcmat(), recoinfo(), res2matrix(), set_bounds(), shrink_estim(), shrink_oasd(), teprojmat(), tetools(), unbalance_hierarchy()

Examples

Y <- matrix(rnorm(30), 5, 6)
P <- commat(5, 6)
P %*% as.vector(Y) == as.vector(t(Y)) # check