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. -->
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# Function slu
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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
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`P * A * Q = L * U`
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## Syntax
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```js
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math.slu(A, order, threshold)
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```
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### Parameters
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Parameter | Type | Description
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--------- | ---- | -----------
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`A` | SparseMatrix | A two dimensional sparse matrix for which to get the LU decomposition.
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`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.
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`threshold` | Number | Partial pivoting threshold (1 for partial pivoting)
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### Returns
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Type | Description
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---- | -----------
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Object | The lower triangular matrix, the upper triangular matrix and the permutation vectors.
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### Throws
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Type | Description
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---- | -----------
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## Examples
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```js
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const A = math.sparse([[4,3], [6, 3]])
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math.slu(A, 1, 0.001)
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// returns:
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// {
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// L: [[1, 0], [1.5, 1]]
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// U: [[4, 3], [0, -1.5]]
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// p: [0, 1]
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// q: [0, 1]
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// }
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```
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## See also
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[lup](lup.md),
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[lsolve](lsolve.md),
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[usolve](usolve.md),
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[lusolve](lusolve.md)
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