Computes the direct sum of all matrices passed in via the list.
direct_sum(x)A field<matrix> or list containing matrices
Matrix containing the direct sum of all matrices in the list.
Consider matrix \(A\) (\(M \times N\)) and \(B\) (\(K \times P\)). A direct sum is a diagonal matrix \(A (+) B\) with dimensions \((m + k) x (n + p)\).
x = list(matrix(0, nrow = 5, ncol = 3),
matrix(1, nrow = 5, ncol = 3))
direct_sum(x)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0
#> [6,] 0 0 0 1 1 1
#> [7,] 0 0 0 1 1 1
#> [8,] 0 0 0 1 1 1
#> [9,] 0 0 0 1 1 1
#> [10,] 0 0 0 1 1 1
x = list(matrix(rnorm(15), nrow = 5, ncol = 3),
matrix(rnorm(30), nrow = 5, ncol = 6),
matrix(rnorm(18), nrow = 2, ncol = 9))
direct_sum(x)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.8679492 -0.079081199 2.0359604 0.000000000 0.0000000 0.0000000
#> [2,] 0.4738486 1.931351096 -0.9596798 0.000000000 0.0000000 0.0000000
#> [3,] 0.4878884 2.120571320 -0.6044085 0.000000000 0.0000000 0.0000000
#> [4,] 1.8528172 0.003966124 -0.2421029 0.000000000 0.0000000 0.0000000
#> [5,] 0.5814289 0.965862275 1.2115386 0.000000000 0.0000000 0.0000000
#> [6,] 0.0000000 0.000000000 0.0000000 1.578944645 -1.7151922 -1.0106199
#> [7,] 0.0000000 0.000000000 0.0000000 0.440601529 -0.2396853 0.5514397
#> [8,] 0.0000000 0.000000000 0.0000000 1.781942012 -0.2209881 -0.1385003
#> [9,] 0.0000000 0.000000000 0.0000000 0.504170155 -0.9121694 -1.0621207
#> [10,] 0.0000000 0.000000000 0.0000000 -0.006280381 -1.5767439 -1.1798228
#> [11,] 0.0000000 0.000000000 0.0000000 0.000000000 0.0000000 0.0000000
#> [12,] 0.0000000 0.000000000 0.0000000 0.000000000 0.0000000 0.0000000
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [3,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [6,] -1.0138381 -0.2800320 -2.8901024 0.0000000 0.0000000 0.0000000
#> [7,] -0.3489747 2.2259691 -0.2767730 0.0000000 0.0000000 0.0000000
#> [8,] 0.8411251 -1.7624051 -0.1669105 0.0000000 0.0000000 0.0000000
#> [9,] -1.2904265 -0.7177486 1.3225655 0.0000000 0.0000000 0.0000000
#> [10,] -0.2503535 -0.3741344 1.7872447 0.0000000 0.0000000 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 -0.4072574 1.9481586 0.3655616
#> [12,] 0.0000000 0.0000000 0.0000000 -0.7192638 -0.9286569 -0.1275307
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> [1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [3,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [11,] 0.4920717 -0.1978193 1.0157872 0.3581453 1.2529534 -1.2678879
#> [12,] -1.0691865 0.7393204 0.2089057 0.1224596 -0.6101309 0.8349744