Fat diagonal matrices occur when we combine two dimensions of a data set along one edge of a matrix. For example, trade-flow data in the decompr and gvc package have each country-industry combination occur on each edge of the matrix.
A fat diagonal matrix looks like this.
library(diagonals)##
## D I
## A G
## O N
## A Lfatdiag(12, steps=3)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 1 1 1 1 0 0 0 0 0 0 0 0
## [2,] 1 1 1 1 0 0 0 0 0 0 0 0
## [3,] 1 1 1 1 0 0 0 0 0 0 0 0
## [4,] 1 1 1 1 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 1 1 1 0 0 0 0
## [6,] 0 0 0 0 1 1 1 1 0 0 0 0
## [7,] 0 0 0 0 1 1 1 1 0 0 0 0
## [8,] 0 0 0 0 1 1 1 1 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 1 1 1 1
## [10,] 0 0 0 0 0 0 0 0 1 1 1 1
## [11,] 0 0 0 0 0 0 0 0 1 1 1 1
## [12,] 0 0 0 0 0 0 0 0 1 1 1 1The workhorse function of this package is the fatdiag
function, which tries behave similarly to the diag function
from the base package, but then with diagonals being
fat.
We can also use the function to assign values to the diagonal.
( m <- matrix(111, nrow=6, ncol=9) )## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 111 111 111 111 111 111 111 111 111
## [2,] 111 111 111 111 111 111 111 111 111
## [3,] 111 111 111 111 111 111 111 111 111
## [4,] 111 111 111 111 111 111 111 111 111
## [5,] 111 111 111 111 111 111 111 111 111
## [6,] 111 111 111 111 111 111 111 111 111fatdiag(m, steps=3) <- 5
m## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 5 5 5 111 111 111 111 111 111
## [2,] 5 5 5 111 111 111 111 111 111
## [3,] 111 111 111 5 5 5 111 111 111
## [4,] 111 111 111 5 5 5 111 111 111
## [5,] 111 111 111 111 111 111 5 5 5
## [6,] 111 111 111 111 111 111 5 5 5As can be seen from the above example, the blocks and matrices do not have to be square.
The diagonal of a matrix can also be extracted.
fatdiag(m, steps=3)## [1] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5We can also specify the size of the block in stead of the number of steps.
fatdiag(12, size=4)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 1 1 1 1 0 0 0 0 0 0 0 0
## [2,] 1 1 1 1 0 0 0 0 0 0 0 0
## [3,] 1 1 1 1 0 0 0 0 0 0 0 0
## [4,] 1 1 1 1 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 1 1 1 0 0 0 0
## [6,] 0 0 0 0 1 1 1 1 0 0 0 0
## [7,] 0 0 0 0 1 1 1 1 0 0 0 0
## [8,] 0 0 0 0 1 1 1 1 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 1 1 1 1
## [10,] 0 0 0 0 0 0 0 0 1 1 1 1
## [11,] 0 0 0 0 0 0 0 0 1 1 1 1
## [12,] 0 0 0 0 0 0 0 0 1 1 1 1This also gives us flexibility in terms of having non-square blocks (and consequently matrices).
fatdiag(12, size=c(3,4) )## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 1 1 1 1 0 0 0 0 0 0 0 0
## [2,] 1 1 1 1 0 0 0 0 0 0 0 0
## [3,] 1 1 1 1 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 1 1 1 1 0 0 0 0
## [5,] 0 0 0 0 1 1 1 1 0 0 0 0
## [6,] 0 0 0 0 1 1 1 1 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 1 1 1 1
## [8,] 0 0 0 0 0 0 0 0 1 1 1 1
## [9,] 0 0 0 0 0 0 0 0 1 1 1 1