commat: Commutation matrix

In FoReco: Forecast Reconciliation

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)

Arguments

r	Number of rows of \mathbf{Y}.
c	Number of columns of \mathbf{Y}.

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)

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(), as_ctmatrix(), as_tevector(), 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

FoReco documentation built on March 12, 2026, 5:07 p.m.