# Function lusolve #

Solves the linear system `A * x = b`

where `A`

is an [n x n] matrix and `b`

is a [n] column vector.

## Syntax #

```
math.lusolve(A, b) // returns column vector with the solution to the linear system A * x = b
math.lusolve(lup, b) // returns column vector with the solution to the linear system A * x = b, lup = math.lup(A)
```

### Parameters #

Parameter | Type | Description |
---|---|---|

`A` |
Matrix | Array | Object | Invertible Matrix or the Matrix LU decomposition |

`b` |
Matrix | Array | Column Vector |

`order` |
number | The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix |

`threshold` |
Number | Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix. |

### Returns #

Type | Description |
---|---|

DenseMatrix | Array | Column vector with the solution to the linear system A * x = b |

## Examples #

```
const m = [[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]
const x = math.lusolve(m, [-1, -1, -1, -1]) // x = [[-1], [-0.5], [-1/3], [-0.25]]
const f = math.lup(m)
const x1 = math.lusolve(f, [-1, -1, -1, -1]) // x1 = [[-1], [-0.5], [-1/3], [-0.25]]
const x2 = math.lusolve(f, [1, 2, 1, -1]) // x2 = [[1], [1], [1/3], [-0.25]]
const a = [[-2, 3], [2, 1]]
const b = [11, 9]
const x = math.lusolve(a, b) // [[2], [5]]
```