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 |
Throws #
Type | Description —- | ———–
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]]
