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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 #
```js
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
Throws #
Type | Description
---- | -----------
Examples #
```js
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]]
```
See also #
[lup](lup.html),
[slu](slu.html),
[lsolve](lsolve.html),
[usolve](usolve.html)