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.
commat(r, c)Number of rows of \(\mathbf{Y}\).
Number of columns of \(\mathbf{Y}\).
A sparse (\(r c \times r c\)) matrix, \(\mathbf{P}\).
Magnus, J.R., Neudecker, H. (2019), Matrix Differential Calculus with Applications in Statistics and Econometrics, third edition, New York, Wiley, pp. 54-55.
Other utilities:
Cmatrix(),
FoReco2ts(),
agg_ts(),
arrange_hres(),
ctf_tools(),
hts_tools(),
lcmat(),
oct_bounds(),
residuals_matrix(),
score_index(),
shrink_estim(),
thf_tools()
Y <- matrix(rnorm(30), 5, 6)
P <- commat(5, 6)
P %*% as.vector(Y) == as.vector(t(Y)) # check
#> 30 x 1 Matrix of class "lgeMatrix"
#> [,1]
#> [1,] TRUE
#> [2,] TRUE
#> [3,] TRUE
#> [4,] TRUE
#> [5,] TRUE
#> [6,] TRUE
#> [7,] TRUE
#> [8,] TRUE
#> [9,] TRUE
#> [10,] TRUE
#> [11,] TRUE
#> [12,] TRUE
#> [13,] TRUE
#> [14,] TRUE
#> [15,] TRUE
#> [16,] TRUE
#> [17,] TRUE
#> [18,] TRUE
#> [19,] TRUE
#> [20,] TRUE
#> [21,] TRUE
#> [22,] TRUE
#> [23,] TRUE
#> [24,] TRUE
#> [25,] TRUE
#> [26,] TRUE
#> [27,] TRUE
#> [28,] TRUE
#> [29,] TRUE
#> [30,] TRUE