R语言常用的矩阵操作

R语言是一门非常方便的数据分析语言，它内置了许多处理矩阵的方法。下面列出一些常用的矩阵操作方法示例。

矩阵的生成

> mat <- matrix(:, ncol = , nrow = , byrow=TRUE, dimnames=list(c(paste("x", :, sep = ".")), c(paste("y", :, sep = "."))))
> mat
    y. y. y. y.
x.
x.
x.
x.        16
# 矩阵的行列名还可以使用rownames或者colnames进行修改
> rownames(mat) <- paste("row", :, sep=".")
> colnames(mat) <- paste("col", :, sep=".")
> mat
      col. col. col. col.
row.
row.
row.
row.                

矩阵的维度

# 表示这是一个4行4列的矩阵
> dim(mat)
[]  

矩阵的加减

> mat. <- matrix(:, nrow = )
> mat.
     [,] [,] [,] [,]
[,]
[,]
[,]
[,]
> mat.plus <- mat + mat.
> mat.plus
      col. col. col. col.
row.
row.
row.
row.
> mat.minus <- mat - mat.
> mat.minus
      col. col. col. col.
row.   -   -   -   -
row.   -   -   -   -
row.   -   -   -   -
row.   -   -   -   -

矩阵的转置

> t(mat)
      row. row. row. row.
col.
col.
col.
col.                  

矩阵相乘

# 若A矩阵的维度为m*n，那么B矩阵的维度应为n*p
# 生成的结果矩阵的维度为m*p
> mat. <- matrix(:, nrow = )
> mat.
     [,] [,]
[,]
[,]
[,]
[,]
> mat.mcl <- mat %*% mat.
> mat.mcl
      [,] [,]
row.
row.
row.
row.    

返回矩阵的对角

> diag(mat)
[]      

生成上三角或下三角矩阵

# 生成上三角矩阵，注意这里的diag参数如果为TRUE，
# 表示把矩阵对角也包括进来。设置为FALSE就是不包括。
> mat[!upper.tri(mat, diag = TRUE)] <-
> mat
      col. col. col. col.
row.
row.
row.
row.
# 生成下三角矩阵
> mat[!lower.tri(mat, diag = TRUE)] <-
> mat
      col. col. col. col.
row.
row.
row.
row.                

求解逆矩阵

> solve(mat)
            row.         row.       row.  row.
col.  1.00000000  6.832142e-17  0.00000000 0.0000
col. -0.83333333  1.666667e-01  0.00000000 0.0000
col. -0.06060606 -1.515152e-01  0.09090909 0.0000
col. -0.02651515 -3.787879e-03 -0.08522727 0.0625

求行列式的值

> det(mat)
[] 4.733165e-30

矩阵的特征值和特征向量

> mat.e <- eigen(mat)
> mat.e
eigen() decomposition
$values
[]  3.620937e+01 -2.209373e+00 -3.188632e-15 -1.348401e-16
 
$vectors
           [,]       [,]       [,]        [,]
[,] -0.1511543  0.7270500  0.5037002 -0.06456091
[,] -0.3492373  0.2832088 -0.8319577 -0.31932112
[,] -0.5473203 -0.1606324  0.1528148  0.83232496
[,] -0.7454033 -0.6044736  0.1754427 -0.44844294
# 可以使用mat.e$values和mat.e$vectors取出结果

奇异值分解

> svd(mat)
$d
[] 3.862266e+01 2.071323e+00 7.609772e-16 3.860638e-16
 
$u
           [,]        [,]       [,]        [,]
[,] -0.1347221 -0.82574206  0.3812474 -0.39325613
[,] -0.3407577 -0.42881720 -0.2152141  0.80850658
[,] -0.5467933 -0.03189234 -0.7133141 -0.43724476
[,] -0.7528288  0.36503251  0.5472808  0.02199431
 
$v
           [,]       [,]       [,]       [,]
[,] -0.4284124  0.7186535  0.2825595 -0.4692122
[,] -0.4743725  0.2738078 -0.7264762  0.4150089
[,] -0.5203326 -0.1710379  0.6052738  0.5776189
[,] -0.5662928 -0.6158835 -0.1613571 -0.5234156

QR分解

> qr(mat)
$qr
            col.       col.         col.         col.
row. -16.6132477 -18.2986497 -1.998405e+01 -2.166945e+01
row.   0.3009646  -1.0767638 -2.153528e+00 -3.230291e+00
row.   0.5417363  -0.3456506  1.350645e-15  3.139336e-15
row.   0.7825080  -0.9120325  1.643990e-01  7.300782e-17
 
$rank
[] 
 
$qraux
[] 1.060193e+00 1.220731e+00 1.986394e+00 7.300782e-17
 
$pivot
[]    
 
attr(,"class")
[] "qr"
> qr.Q(qr(mat))
            [,]        [,]       [,]       [,]
[,] -0.06019293 -0.83449195 -0.3906679 -0.3838992
[,] -0.30096463 -0.45762462  0.2347489  0.8030523
[,] -0.54173634 -0.08075729  0.7025058 -0.4544068
[,] -0.78250805  0.29611005 -0.5465868  0.0352538
> qr.R(qr(mat))
          col.      col.         col.         col.
row. -16.61325 -18.298650 -1.998405e+01 -2.166945e+01
row.   0.00000  -1.076764 -2.153528e+00 -3.230291e+00
row.   0.00000   0.000000  1.350645e-15  3.139336e-15
row.   0.00000   0.000000  0.000000e+00  7.300782e-17