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Function slu #
Calculate the Sparse Matrix LU decomposition with full pivoting. Sparse Matrix `A` is decomposed in two matrices (`L`, `U`) and two permutation vectors (`pinv`, `q`) where
`P * A * Q = L * U`
Syntax #
```js
math.slu(A, order, threshold)
```
Parameters #
Parameter | Type | Description
--------- | ---- | -----------
`A` | SparseMatrix | A two dimensional sparse matrix for which to get the LU decomposition.
`order` | Number | The Symbolic Ordering and Analysis order: 0 - Natural ordering, no permutation vector q is returned 1 - Matrix must be square, symbolic ordering and analisis is performed on M = A + A' 2 - Symbolic ordering and analisis is performed on M = A' * A. Dense columns from A' are dropped, A recreated from A'. This is appropriatefor LU factorization of unsymmetric matrices. 3 - Symbolic ordering and analisis is performed on M = A' * A. This is best used for LU factorization is matrix M has no dense rows. A dense row is a row with more than 10*sqr(columns) entries.
`threshold` | Number | Partial pivoting threshold (1 for partial pivoting)
Returns #
Type | Description
---- | -----------
Object | The lower triangular matrix, the upper triangular matrix and the permutation vectors.
Throws #
Type | Description
---- | -----------
Examples #
```js
const A = math.sparse([[4,3], [6, 3]])
math.slu(A, 1, 0.001)
// returns:
// {
// L: [[1, 0], [1.5, 1]]
// U: [[4, 3], [0, -1.5]]
// p: [0, 1]
// q: [0, 1]
// }
```
See also #
[lup](lup.html),
[lsolve](lsolve.html),
[usolve](usolve.html),
[lusolve](lusolve.html)