Solve ndarray Ax=b via LU factorization with pivoting

Given an LUP factorization, this module solves for x in Ax = b. More precisely, it solves for x in LUx = Pb.

var lup = require('ndarray-lup-factorization'),
    solve = require('ndarray-lup-solve'),
    ndarray = require('ndarray'),
    pool = require('ndarray-scratch')
var A = ndarray([2,1,1,0, 4,3,3,1, 8,7,9,5, 6,7,9,8], [4,4])
var b = ndarray([13,38,102,107])
var P = []
// In-place LUP factorization:
//   Note: repeated A tells it L and U are both stored in A
lup(A, A, P)
solve( A, A, P, b)
// b now contains the answer x: [2,5,4,3]
// A and P are unchanged and can be re-used to solve another problem

• L: The n x n ndarray lower-triangular portion of the LUP factorization. The diagonal entries are implicitly assumed to be 1. Unchanged by the algorithm.
• U: The n x n ndarray upper-triangular portion of the LUP factorization. Unchanged by the algorithm.
• P: An Array of length n containg the permutation
• b: An ndarray of length n containing the righthand side of Ax = b
• work: (optional) A vector used to permute the entries. If not provided, it is allocated and released into an ndarray-scratch typed vector pool.

Returns true on successful completion; false otherwise.

If the first two arguments are identical then it's understood that both L and U are stored in a single matrix with the diagonal entries of L (all unity) omitted. Usage and behavior is otherwise identical.

(c) 2015 Ricky Reusser. MIT License