関数として用意されているものいろいろ　　　　　Last modified: Feb 17, 2009

行列式　　det　　　・ 直前のページへ戻る


> (a <- matrix(c(1, 2, 4, 9), nrow=2))
     [,1] [,2]
[1,]    1    4
[2,]    2    9
> det(a)
[1] 1

> (b <- matrix(c(2,5,4,3, 5,7,6,3, 5,8,7,9, 1,2,5,3), byrow=TRUE, ncol=4))
     [,1] [,2] [,3] [,4]
[1,]    2    5    4    3
[2,]    5    7    6    3
[3,]    5    8    7    9
[4,]    1    2    5    3
> det(b)
[1] 186

> det(matrix(rnorm(12), 3))
 以下にエラー determinant.matrix(x, logarithm = TRUE, ...) : 
   'x' は正方行列でなければなりません
逆行列　　solve　　　・ 直前のページへ戻る

> (a <- matrix(c(1, 2, 4, 9), nrow=2))
     [,1] [,2]
[1,]    1    4
[2,]    2    9
> solve(a)
     [,1] [,2]
[1,]    9   -4
[2,]   -2    1

>  (b <- matrix(c(2,5,4,3, 5,7,6,3, 5,8,7,9, 1,2,5,3), byrow=TRUE, ncol=4))
     [,1] [,2] [,3] [,4]
[1,]    2    5    4    3
[2,]    5    7    6    3
[3,]    5    8    7    9
[4,]    1    2    5    3
> solve(b)
            [,1]        [,2]        [,3]        [,4]
[1,] -0.67741935  0.35483871  0.12903226 -0.06451613
[2,]  0.54838710 -0.09677419 -0.08064516 -0.20967742
[3,] -0.03225806  0.06451613 -0.11290323  0.30645161
[4,] -0.08602151 -0.16129032  0.19892473 -0.01612903

> solve(matrix(rnorm(12), 3))
 以下にエラー solve.default(matrix(rnorm(12), 3)) : 
   逆行列は正方行列だけにしか定義できません
一般化逆行列　　MASS:::ginv　　　・ 直前のページへ戻る

> library(MASS)
> (x <- matrix(c(1,3,2, 5,3,2), byrow=TRUE, ncol=3))
     [,1] [,2] [,3]
[1,]    1    3    2
[2,]    5    3    2
> ginv(x)
           [,1]        [,2]
[1,] -0.2500000  0.25000000
[2,]  0.2884615 -0.05769231
[3,]  0.1923077 -0.03846154
連立方程式　　solve　　　・ 直前のページへ戻る

> (a <- c(3,2,1,5))
[1] 3 2 1 5
> (b <- matrix(c(2,5,4,3, 5,7,6,3, 5,8,7,9, 1,2,5,3), byrow=TRUE, ncol=4))
     [,1] [,2] [,3] [,4]
[1,]    2    5    4    3
[2,]    5    7    6    3
[3,]    5    8    7    9
[4,]    1    2    5    3
> solve(b, a)
[1] -1.5161290  0.3225806  1.4516129 -0.4623656

> (c <- matrix(c(3,2,1,5, 4,3,2,7), nrow=4))
     [,1] [,2]
[1,]    3    4
[2,]    2    3
[3,]    1    2
[4,]    5    7
> solve(b, c)
           [,1]       [,2]
[1,] -1.5161290 -1.8387097
[2,]  0.3225806  0.2741935
[3,]  1.4516129  1.9838710
[4,] -0.4623656 -0.5430108
固有値・固有ベクトル　　eigen　　　・ 直前のページへ戻る

> (x <- matrix(c(1,2,3, 2,1,5, 3,5,1), 3))
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    1    5
[3,]    3    5    1
> eigen(x)
$values
[1]  7.8390863 -0.7106916 -4.1283947

$vectors
           [,1]       [,2]       [,3]
[1,] -0.4612978  0.8691432 -0.1783099
[2,] -0.6075927 -0.4559069 -0.6503692
[3,] -0.6465566 -0.1916741  0.7383939

> (y <- matrix(c(1,3,2, 7,5,3, 2,4,8), 3))
     [,1] [,2] [,3]
[1,]    1    7    2
[2,]    3    5    4
[3,]    2    3    8
> eigen(y)
$values
[1] 12.087767  3.789629 -1.877395

$vectors
           [,1]       [,2]       [,3]
[1,] -0.4828242 -0.6512015 -0.9297536
[2,] -0.5764175 -0.4368246  0.3595983
[3,] -0.6592600  0.6205811  0.0790403
特異値分解　　svd　　　・ 直前のページへ戻る

> (x <- matrix(c(1,2,3, 2,1,5, 3,5,1), 3))
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    1    5
[3,]    3    5    1

> svd(x)
$d
[1] 7.8390863 4.1283947 0.7106916

$u
           [,1]       [,2]       [,3]
[1,] -0.4612978 -0.1783099 -0.8691432
[2,] -0.6075927 -0.6503692  0.4559069
[3,] -0.6465566  0.7383939  0.1916741

$v
           [,1]       [,2]       [,3]
[1,] -0.4612978  0.1783099  0.8691432
[2,] -0.6075927  0.6503692 -0.4559069
[3,] -0.6465566 -0.7383939 -0.1916741

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