带行主元的 LU 分解

Question

以下函数不使用行透视进行 LU 分解。 R 中是否存在使用行主元进行 LU 分解的现有函数？

> require(Matrix)
> expand(lu(matrix(rnorm(16),4,4)))
$L
4 x 4 Matrix of class "dtrMatrix"
     [,1]        [,2]        [,3]        [,4]       
[1,]  1.00000000           .           .           .
[2,]  0.13812836  1.00000000           .           .
[3,]  0.27704442  0.39877260  1.00000000           .
[4,] -0.08512341 -0.24699820  0.04347201  1.00000000

$U
4 x 4 Matrix of class "dtrMatrix"
     [,1]       [,2]       [,3]       [,4]      
[1,]  1.5759031 -0.2074224 -1.5334082 -0.5959756
[2,]          . -1.3096874 -0.6301727  1.1953838
[3,]          .          .  1.6316292  0.6256619
[4,]          .          .          .  0.8078140

$P
4 x 4 sparse Matrix of class "pMatrix"

[1,] | . . .
[2,] . | . .
[3,] . . . |
[4,] . . | .