sparseLU-class {Matrix} | R Documentation |

Objects of this class contain the components of the LU decomposition of a sparse square matrix.

Objects can be created by calls of the form ```
new("sparseLU",
...)
```

but are more commonly created by function `lu()`

applied to a sparse matrix, such as a matrix of class
`dgCMatrix`

.

`L`

:Object of class

`"dtCMatrix"`

, the lower triangular factor from the left.`U`

:Object of class

`"dtCMatrix"`

, the upper triangular factor from the right.`p`

:Object of class

`"integer"`

, permutation applied from the left.`q`

:Object of class

`"integer"`

, permutation applied from the right.`Dim`

:the dimension of the original matrix; inherited from class

`MatrixFactorization`

.

Class `"LU"`

, directly.
Class `"MatrixFactorization"`

, by class `"LU"`

.

- expand
`signature(x = "sparseLU")`

Returns a list with components`P`

,`L`

,`U`

, and`Q`

, where`P`

and`Q`

represent fill-reducing permutations, and`L`

, and`U`

the lower and upper triangular matrices of the decomposition. The original matrix corresponds to the product`P'LUQ`

.

The decomposition is of the form

`A = P'LUQ,`

or equivalently `PAQ' = LU`

,
where all matrices are sparse and of size `n\times n`

.
The matrices `P`

and `Q`

, and their transposes `P'`

and
`Q'`

are permutation matrices,
`L`

is lower triangular and `U`

is upper triangular.

```
## Extending the one in examples(lu), calling the matrix A,
## and confirming the factorization identities :
A <- as(readMM(system.file("external/pores_1.mtx",
package = "Matrix")),
"CsparseMatrix")
## with dimnames(.) - to see that they propagate to L, U :
dimnames(A) <- list(paste0("r", seq_len(nrow(A))),
paste0("C", seq_len(ncol(A))))
str(luA <- lu(A)) # p is a 0-based permutation of the rows
# q is a 0-based permutation of the columns
xA <- expand(luA)
## which is simply doing
stopifnot(identical(xA$ L, luA@L),
identical(xA$ U, luA@U),
identical(xA$ P, as(luA@p +1L, "pMatrix")),
identical(xA$ Q, as(luA@q +1L, "pMatrix")))
P.LUQ <- with(xA, t(P) %*% L %*% U %*% Q)
stopifnot(all.equal(unname(A), unname(P.LUQ), tolerance = 1e-12))
## permute rows and columns of original matrix
pA <- A[luA@p + 1L, luA@q + 1L]
PAQ. <- with(xA, P %*% A %*% t(Q))
stopifnot(all.equal(unname(pA), unname(PAQ.), tolerance = 1e-12))
pLU <- drop0(luA@L %*% luA@U) # L %*% U -- dropping extra zeros
stopifnot(all.equal(pA, pLU, tolerance = 1e-12))
```

[Package *Matrix* version 1.5-3 Index]