如何在R中用下三角矩阵替换上三角矩阵，反之亦然？
通过对整个矩阵进行转置并从中提取上三角矩阵，然后将其存储在原始矩阵中，可以将上三角矩阵替换为下三角矩阵。例如，如果我们有一个矩阵M，那么M的上三角矩阵可以使用下面的代码替换为下三角矩阵-
M1[upper.tri(M1)]<-t(M1)[upper.tri(M1)]
也可以用类似的方式对下三角矩阵进行。
示例
M1<-matrix(1:25,ncol=5) M1输出结果
[,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
示例
M1[upper.tri(M1)]<-t(M1)[upper.tri(M1)] M1输出结果
[,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
示例
M2<-matrix(rpois(100,10),nrow=10) M2输出结果
[,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
示例
M2[upper.tri(M2)]<-t(M2)[upper.tri(M2)] M2输出结果
[,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
示例
M3<-matrix(rpois(64,5),nrow=8) M3输出结果
[,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
示例
M3[lower.tri(M3)]<-t(M3)[lower.tri(M3)] M3输出结果
[,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
示例
M4<-matrix(rnorm(36),nrow=6) M4输出结果
[,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
示例
M4[lower.tri(M4)]<-t(M4)[lower.tri(M4)] M4输出结果
[,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
示例
M5<-matrix(rexp(9),nrow=3) M5输出结果
[,1] [,2] [,3] [1,] 0.8228933 0.05741123 0.3246455 [2,] 0.1750773 0.08412468 2.1097830 [3,] 0.3997029 1.18019289 0.1099468
示例
M5[upper.tri(M5)]<-t(M5)[upper.tri(M5)] M5输出结果
[,1] [,2] [,3] [1,] 0.8228933 0.17507725 0.3997029 [2,] 0.1750773 0.08412468 1.1801929 [3,] 0.3997029 1.18019289 0.1099468