# 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. ## 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)