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How to create a block diagonal matrix using a matrix in R?
To create a block diagonal matrix using a matrix in R, we can use bdiag function of Matrix package.
For Example, if we have a matrix called M and we want to create block diagonal using M 4 times by using the below command −
bdiag(replicate(4,M,simplify=FALSE))
Check out the Examples given below to understand how it can be done.
Example 1
Following snippet creates a sample matrix −
M1<-matrix(rpois(9,5),ncol=3) M1
The following matrix is created −
[,1] [,2] [,3] [1,] 9 3 10 [2,] 4 4 2 [3,] 5 8 2
To create a block diagonal matrix using a matrix in R on the above created matrix, add the following code to the above snippet −
M1<-matrix(rpois(9,5),ncol=3) library(Matrix) bdiag(replicate(3,M1,simplify=FALSE))
Output
If you execute all the above given snippets as a single program, it generates the following Output −
9 x 9 sparse Matrix of class "dgCMatrix" [1,] 9 3 10 . . . . . . [2,] 4 4 2 . . . . . . [3,] 5 8 2 . . . . . . [4,] . . . 9 3 10 . . . [5,] . . . 4 4 2 . . . [6,] . . . 5 8 2 . . . [7,] . . . . . . 9 3 10 [8,] . . . . . . 4 4 2 [9,] . . . . . . 5 8 2
Example 2
Following snippet creates a sample matrix −
M2<-matrix(rpois(4,2),ncol=2) M2
The following matrix is created −
[,1] [,2] [1,] 1 2 [2,] 4 1
To create a block diagonal matrix using a matrix in R on the above created matrix, add the following code to the above snippet −
M2<-matrix(rpois(4,2),ncol=2) library(Matrix) bdiag(replicate(6,M2,simplify=FALSE))
Output
If you execute all the above given snippets as a single program, it generates the following Output −
12 x 12 sparse Matrix of class "dgCMatrix" [1,] 1 2 . . . . . . . . . . [2,] 4 1 . . . . . . . . . . [3,] . . 1 2 . . . . . . . . [4,] . . 4 1 . . . . . . . . [5,] . . . . 1 2 . . . . . . [6,] . . . . 4 1 . . . . . . [7,] . . . . . . 1 2 . . . . [8,] . . . . . . 4 1 . . . . [9,] . . . . . . . . 1 2 . . [10,] . . . . . . . . 4 1 . . [11,] . . . . . . . . . . 1 2 [12,] . . . . . . . . . . 4 1
Example 3
Following snippet creates a sample matrix −
M3<-matrix(round(rnorm(16),2),ncol=4) M3
The following matrix is created −
[,1] [,2] [,3] [,4] [1,] -0.61 -1.41 0.46 0.67 [2,] -0.08 -0.69 -0.92 -0.61 [3,] -0.44 -0.48 -0.09 -0.42 [4,] -1.79 0.45 1.34 -0.76
To create a block diagonal matrix using a matrix in R on the above created matrix, add the following code to the above snippet −
M3<-matrix(round(rnorm(16),2),ncol=4) library(Matrix) bdiag(replicate(2,M3,simplify=FALSE))
Output
If you execute all the above given snippets as a single program, it generates the following Output −
8 x 8 sparse Matrix of class "dgCMatrix" [1,] -0.61 -1.41 0.46 0.67 . . . . [2,] -0.08 -0.69 -0.92 -0.61 . . . . [3,] -0.44 -0.48 -0.09 -0.42 . . . . [4,] -1.79 0.45 1.34 -0.76 . . . . [5,] . . . . -0.61 -1.41 0.46 0.67 [6,] . . . . -0.08 -0.69 -0.92 -0.61 [7,] . . . . -0.44 -0.48 -0.09 -0.42 [8,] . . . . -1.79 0.45 1.34 -0.76
Example 4
Following snippet creates a sample matrix −
M4<-matrix(round(rnorm(9),2),ncol=3) M4
The following matrix is created −
[,1] [,2] [,3] [1,] -0.11 1.49 0.86 [2,] -0.06 -0.39 0.96 [3,] 1.29 -2.67 -0.03
To create a block diagonal matrix using a matrix in R on the above created matrix, add the following code to the above snippet −
M4<-matrix(round(rnorm(9),2),ncol=3) library(Matrix) bdiag(replicate(3,M4,simplify=FALSE))
Output
If you execute all the above given snippets as a single program, it generates the following Output −
9 x 9 sparse Matrix of class "dgCMatrix" [1,] -0.11 1.49 0.86 . . . . . . [2,] -0.06 -0.39 0.96 . . . . . . [3,] 1.29 -2.67 -0.03 . . . . . . [4,] . . . -0.11 1.49 0.86 . . . [5,] . . . -0.06 -0.39 0.96 . . . [6,] . . . 1.29 -2.67 -0.03 . . . [7,] . . . . . . -0.11 1.49 0.86 [8,] . . . . . . -0.06 -0.39 0.96 [9,] . . . . . . 1.29 -2.67 -0.03
Example 5
Following snippet creates a sample matrix −
M5<-matrix(rpois(4,10),ncol=2) M5
The following matrix is created −
[,1] [,2] [1,] 10 6 [2,] 5 17
To create a block diagonal matrix using a matrix in R on the above created matrix, add the following code to the above snippet −
M5<-matrix(rpois(4,10),ncol=2) library(Matrix) bdiag(replicate(5,M5,simplify=FALSE))
Output
If you execute all the above given snippets as a single program, it generates the following Output −
10 x 10 sparse Matrix of class "dgCMatrix" [1,] 10 6 . . . . . . . . [2,] 5 17 . . . . . . . . [3,] . . 10 6 . . . . . . [4,] . . 5 17 . . . . . . [5,] . . . . 10 6 . . . . [6,] . . . . 5 17 . . . . [7,] . . . . . . 10 6 . . [8,] . . . . . . 5 17 . . [9,] . . . . . . . . 10 6 [10,] . . . . . . . . 5 17
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