simple-squiggle

A restricted subset of Squiggle
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slu.md (1702B)


      1 <!-- Note: This file is automatically generated from source code comments. Changes made in this file will be overridden. -->
      2 
      3 # Function slu
      4 
      5 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
      6 
      7 `P * A * Q = L * U`
      8 
      9 
     10 ## Syntax
     11 
     12 ```js
     13 math.slu(A, order, threshold)
     14 ```
     15 
     16 ### Parameters
     17 
     18 Parameter | Type | Description
     19 --------- | ---- | -----------
     20 `A` | SparseMatrix | A two dimensional sparse matrix for which to get the LU decomposition.
     21 `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.
     22 `threshold` | Number | Partial pivoting threshold (1 for partial pivoting)
     23 
     24 ### Returns
     25 
     26 Type | Description
     27 ---- | -----------
     28 Object | The lower triangular matrix, the upper triangular matrix and the permutation vectors.
     29 
     30 
     31 ### Throws
     32 
     33 Type | Description
     34 ---- | -----------
     35 
     36 
     37 ## Examples
     38 
     39 ```js
     40 const A = math.sparse([[4,3], [6, 3]])
     41 math.slu(A, 1, 0.001)
     42 // returns:
     43 // {
     44 //   L: [[1, 0], [1.5, 1]]
     45 //   U: [[4, 3], [0, -1.5]]
     46 //   p: [0, 1]
     47 //   q: [0, 1]
     48 // }
     49 ```
     50 
     51 
     52 ## See also
     53 
     54 [lup](lup.md),
     55 [lsolve](lsolve.md),
     56 [usolve](usolve.md),
     57 [lusolve](lusolve.md)