How to replace upper triangular matrix with lower triangular matrix and vice versa in R?

The upper triangular matrix can be replaced with lower triangular matrix by transposing the whole matrix and extracting upper triangular matrix from it then storing it in the original matrix. For example, if we have a matrix M then upper triangular matrix of M can be replaced with lower triangular matrix by using the below code −

M1[upper.tri(M1)]<-t(M1)[upper.tri(M1)]

It can be also done for lower triangular matrix in the similar manner.

Example

 Live Demo

M1<-matrix(1:25,ncol=5)
M1

Output

   [,1] [,2] [,3] [,4] [,5]
[1,] 1    6    11   16 21
[2,] 2    7    12   17 22
[3,] 3    8    13   18 23
[4,] 4    9    14   19 24
[5,] 5    10   15   20 25

Example

M1[upper.tri(M1)]<-t(M1)[upper.tri(M1)]
M1

Output

   [,1] [,2] [,3] [,4] [,5]
[1,] 1    2    3    4    5
[2,] 2    7    8    9    10
[3,] 3    8    13   14   15
[4,] 4    9    14   19   20
[5,] 5    10   15   20   25

Example

 Live Demo

M2<-matrix(rpois(100,10),nrow=10)
M2

Output

   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 3    12   16   6    4    11    12 12    9    14
[2,] 12   9    9    11   10    14   13 10    10   13
[3,] 17   14   8    12   12    15   9   8    15   4
[4,] 17   6    9    17   11    8    11 15    14   12
[5,] 11   14   7    7    12    9    9   8    14   13
[6,] 13   7    11   8    10    3    13 11    6    11
[7,] 13   11   7    11   15    9    12 10    11   7
[8,] 13   10   3    8    7    11    13 9      7   11
[9,] 7    18   15   11   12   14    10 5      7   15
[10,] 13   7   15   11   11    9    12 6      11   10

Example

M2[upper.tri(M2)]<-t(M2)[upper.tri(M2)]
M2

Output

   [,1] [,2] [,3]   [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 3   12    17    17   11   13   13    13   7    13
[2,] 12   9    14    6    14   7    11    10   18    7
[3,] 17   14    8    9    7    11    7    3    15    15
[4,] 17   6     9    17   7    8    11    8    11    11
[5,] 11   14    7    7    12   10   15    7    12    11
[6,] 13   7    11    8    10   3    9     11   14    9
[7,] 13   11    7    11   15   9    12    13   10    12
[8,] 13   10    3    8    7    11   13    9    5      6
[9,] 7    18    15   11   12   14   10    5    7      11
[10,] 13   7    15   11   11   9    12    6    11    10

Example

 Live Demo

M3<-matrix(rpois(64,5),nrow=8)
M3

Output

   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 8    5    2    5    6    6    8    3
[2,] 7    6    13   5    6    9    5    8
[3,] 6    3    12   2    2    8    3    3
[4,] 3    6    2    7    3    1    5    6
[5,] 1    8    7    6    9    3    3    10
[6,] 4    4    7    10   4    4    8    4
[7,] 9    3    9    4    5    8    3    11
[8,] 4    4    9    5    5    4    8    6

Example

M3[lower.tri(M3)]<-t(M3)[lower.tri(M3)]
M3

Output

   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 8    5    2    5    6    6    8    3
[2,] 5    6    13   5    6    9    5    8
[3,] 2    13   12   2    2    8    3    3
[4,] 5    5    2    7    3    1    5    6
[5,] 6    6    2    3    9    3    3    10
[6,] 6    9    8    1    3    4    8    4
[7,] 8    5    3    5    3    8    3    11
[8,] 3    8    3    6    10   4    11    6

Example

 Live Demo

M4<-matrix(rnorm(36),nrow=6)
M4

Output

         [,1]       [,2]       [,3]       [,4]       [,5]    [,6]
[1,] 0.05023214 -0.3817478 0.7079296 0.8578374 -1.5239053 0.1864117
[2,] -0.73729460 1.5129931 0.2135871 0.9721983 -0.2416306 -0.5309397
[3,] -0.24488229 -0.6229905 0.8579926 1.3248632 -1.9305997 0.5397310
[4,] -1.24118039 -1.1080773 -0.9903481 0.1033527 0.4685492 0.1691699
[5,] 1.60606286 -0.9149534 -1.3265918 2.0232826 0.5383570 0.9284483
[6,] 1.29482725 -0.7275765 1.1407260 -0.8860395 -0.3185204 -1.0165007

Example

M4[lower.tri(M4)]<-t(M4)[lower.tri(M4)]
M4

Output

      [,1]          [,2]       [,3]      [,4]       [,5]    [,6]
[1,] 0.05023214 -0.3817478 0.7079296 0.8578374 -1.5239053 0.1864117
[2,] -0.38174778 1.5129931 0.2135871 0.9721983 -0.2416306 -0.5309397
[3,] 0.70792961 0.2135871 0.8579926 1.3248632 -1.9305997 0.5397310
[4,] 0.85783742 0.9721983 1.3248632 0.1033527 0.4685492 0.1691699
[5,] -1.52390534 -0.2416306 -1.9305997 0.4685492 0.5383570 0.9284483
[6,] 0.18641175 -0.5309397 0.5397310 0.1691699 0.9284483 -1.0165007

Example

 Live Demo

M5<-matrix(rexp(9),nrow=3)
M5

Output

         [,1]       [,2]    [,3]
[1,] 0.8228933 0.05741123 0.3246455
[2,] 0.1750773 0.08412468 2.1097830
[3,] 0.3997029 1.18019289 0.1099468

Example

M5[upper.tri(M5)]<-t(M5)[upper.tri(M5)]
M5

Output

         [,1]       [,2]    [,3]
[1,] 0.8228933 0.17507725 0.3997029
[2,] 0.1750773 0.08412468 1.1801929
[3,] 0.3997029 1.18019289 0.1099468

Nizamuddin Siddiqui

Published on 07-Dec-2020 05:33:00

• Related Questions & Answers
• Program to print Lower triangular and Upper triangular matrix of an array in C
• C# program to Illustrate Upper Triangular Matrix
• Java Program to display upper triangular matrix
• C# Program to Illustrate Lower Triangular Matrix
• How to create a heatmap for lower triangular matrix in R?
• How to create an upper triangular matrix using vector elements in R?
• Program to check if matrix is upper triangular in C++
• Program to check if matrix is lower triangular in C++
• How to find the row and column index for upper triangular matrix elements in R?
• Print lower triangular matrix pattern from given array in C Program.
• How to solve triangular matrix equations using Python SciPy?
• C program to convert upper case to lower and vice versa by using string concepts
• Create an array with zero above the main diagonal forming a lower triangular matrix in Numpy
• What are forward triangular merger and reverse triangular merger?
• Which linear function of SciPy is used to solve triangular matrix equations?