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How to create an upper triangular matrix using vector elements in R?
To create an upper triangular matrix using vector elements, we can first create the matrix with appropriate number of columns and rows then take the transpose of that matrix. After that we will assign the lower triangular matrix elements to 0.
The selection of number of rows and columns plays an important role here so we need to be careful while choosing them.
Check out the examples given below to understand how it can be done.
Example 1
Following snippet creates a vector −
x1<-rpois(5,2) x1
The following vector is created −
[1] 2 2 3 0 0
To create an upper triangular matrix using x1, add the following code to the above snippet −
x1<-rpois(5,2) M1<-t(matrix(x1,nrow=9,ncol=5))[,1:5] M1
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2] [,3] [,4] [,5] [1,] 2 2 3 0 0 [2,] 0 2 2 3 0 [3,] 0 0 2 2 3 [4,] 3 0 0 2 2 [5,] 2 3 0 0 2
Add the following code to the above snippet −
M1[lower.tri(M1)]<-0 M1
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2] [,3] [,4] [,5] [1,] 2 2 3 0 0 [2,] 0 2 2 3 0 [3,] 0 0 2 2 3 [4,] 0 0 0 2 2 [5,] 0 0 0 0 2
Example 2
Following snippet creates a vector −
x2<-rpois(10,5) x2
Output
The following vector is created −
[1] 5 8 5 4 3 5 5 5 11 6
To create an upper triangular matrix using x2, add the following code to the above snippet −
x2<-rpois(10,5) M2<-t(matrix(x2,nrow=19,ncol=10))[,1:10] M2
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1][,2][,3][,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] 5 8 5 4 3 5 5 5 11 6 [2,] 6 5 8 5 4 3 5 5 5 11 [3,] 11 6 5 8 5 4 3 5 5 5 [4,] 5 11 6 5 8 5 4 3 5 5 [5,] 5 5 11 6 5 8 5 4 3 5 [6,] 5 5 5 11 6 5 8 5 4 3 [7,] 3 5 5 5 11 6 5 8 5 4 [8,] 4 3 5 5 5 11 6 5 8 5 [9,] 5 4 3 5 5 5 11 6 5 8 [10,] 8 5 4 3 5 5 5 11 6 5
Add the following code to the above snippet −
M2[lower.tri(M2)]<-0 M2
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1][,2][,3][,4][,5][,6][,7][,8][,9][,10] [1,] 5 8 5 4 3 5 5 5 11 6 [2,] 0 5 8 5 4 3 5 5 5 11 [3,] 0 0 5 8 5 4 3 5 5 5 [4,] 0 0 0 5 8 5 4 3 5 5 [5,] 0 0 0 0 5 8 5 4 3 5 [6,] 0 0 0 0 0 5 8 5 4 3 [7,] 0 0 0 0 0 0 5 8 5 4 [8,] 0 0 0 0 0 0 0 5 8 5 [9,] 0 0 0 0 0 0 0 0 5 8 [10,] 0 0 0 0 0 0 0 0 0 5
Example 3
Following snippet creates a vector −
x3<-rpois(3,28) x3
The following vector is created −
[1] 21 33 24
To create an upper triangular matrix using x3, add the following code to the above snippet −
x3<-rpois(3,28) M3<-t(matrix(x3,nrow=5,ncol=3))[,1:3] M3
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2] [,3] [1,] 21 33 24 [2,] 24 21 33 [3,] 33 24 21
Add the following code to the above snippet −
M3[lower.tri(M3)]<-0 M3
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2] [,3] [1,] 21 33 24 [2,] 0 21 33 [3,] 0 0 21
Example 4
Following snippet creates a vector −
x4<-rpois(5,500) x4
The following vector is created −
Output
[1] 495 499 478 502 531
To create an upper triangular matrix using x4, add the following code to the above snippet −
x4<-rpois(5,500) M4<-t(matrix(x4,nrow=9,ncol=5))[,1:5] M4
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2] [,3] [,4] [,5] [1,] 495 499 478 502 531 [2,] 531 495 499 478 502 [3,] 502 531 495 499 478 [4,] 478 502 531 495 499 [5,] 499 478 502 531 495
Add the following code to the above snippet −
M4[lower.tri(M4)]<-0 M4
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2] [,3] [,4] [,5] [1,] 495 499 478 502 531 [2,] 0 495 499 478 502 [3,] 0 0 495 499 478 [4,] 0 0 0 495 499 [5,] 0 0 0 0 495
Example 5
Following snippet creates a vector −
x5<-rpois(10,100) x5
The following vector is created −
[1] 109 85 108 86 76 99 113 75 82 86
To create an upper triangular matrix using x5, add the following code to the above snippet −
x5<-rpois(10,100) M5<-t(matrix(x5,nrow=19,ncol=10))[,1:10] M5
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1] [,2][,3][,4][,5][,6][,7][,8][,9][,10] [1,] 109 85 108 86 76 99 113 75 82 86 [2,] 86 109 85 108 86 76 99 113 75 82 [3,] 82 86 109 85 108 86 76 99 113 75 [4,] 75 82 86 109 85 108 86 76 99 113 [5,] 113 75 82 86 109 85 108 86 76 99 [6,] 99 113 75 82 86 109 85 108 86 76 [7,] 76 99 113 75 82 86 109 85 108 86 [8,] 86 76 99 113 75 82 86 109 85 108 [9,] 108 86 76 99 113 75 82 86 109 85 [10,] 85 108 86 76 99 113 75 82 86 109
Add the following code to the above snippet −
M5[lower.tri(M5)]<-0 M5
Output
If you execute all the above given snippets as a single program, it generates the following Output −
[,1][,2][,3][,4][,5][,6][,7][,8][,9][,10] [1,] 109 85 108 86 76 99 113 75 82 86 [2,] 0 109 85 108 86 76 99 113 75 82 [3,] 0 0 109 85 108 86 76 99 113 75 [4,] 0 0 0 109 85 108 86 76 99 113 [5,] 0 0 0 0 109 85 108 86 76 99 [6,] 0 0 0 0 0 109 85 108 86 76 [7,] 0 0 0 0 0 0 109 85 108 86 [8,] 0 0 0 0 0 0 0 109 85 108 [9,] 0 0 0 0 0 0 0 0 109 85 [10,] 0 0 0 0 0 0 0 0 0 109
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