58 lines
1.7 KiB
Markdown
58 lines
1.7 KiB
Markdown
|
<!-- Note: This file is automatically generated from source code comments. Changes made in this file will be overridden. -->
|
||
|
|
|
||
|
|
# 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.md),
|
||
|
|
[lsolve](lsolve.md),
|
||
|
|
[usolve](usolve.md),
|
||
|
|
[lusolve](lusolve.md)
|