sparseLU-class {Matrix} | R Documentation

## Sparse LU decomposition of a square sparse matrix

### Description

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

### Objects from the Class

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`.

### Slots

`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`.

### Extends

Class `"LU"`, directly. Class `"MatrixFactorization"`, by class `"LU"`.

### Methods

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 PLUQ.

### Note

The decomposition is of the form

A = PLUQ

where all matrices are sparse and of size n by n. The matrices P and Q are permutation matrices, L is lower triangular and U is upper triangular.

### See Also

`lu`, `solve`, `dgCMatrix`

### Examples

      ## see  examples(lu)

[Package Matrix version 0.999375-33 Index]