ndarray-lu-solve

solve a system of linear equations from an LU decomposition

example

var solve = require('ndarray-lu-solve');
var show = require('ndarray-show');
var crout = require('ndarray-crout-decomposition');
var ndarray = require('ndarray');
var zeros = require('zeros');
 
var A = ndarray(
    [ 2, 1, -1, 8, -3, -1, 2, -11, -2, 1, 2, -3 ],
    [ 4, 3 ], [ 1, 4 ]
);
var L = zeros([ 3, 3 ]);
var U = zeros([ 3, 3 ]);
crout(A.hi(3,3), L, U);
 
var X = ndarray(new Float64Array(3));
var Y = ndarray(new Float64Array(3));
var solution = solve(L, U, A.lo(3,0).pick(0), X, Y);
 
console.log('input:\n' + show(A), '\n');
console.log('solution:\n' + show(solution));

output:

input:
   2.000    1.000   -1.000    8.000
  -3.000   -1.000    2.000  -11.000
  -2.000    1.000    2.000   -3.000 

solution:
   2.000    3.000   -1.000

You can pass fewer of the parameters if you want and use a packed representation for L and U in the same matrix:

var solve = require('ndarray-lu-solve');
var show = require('ndarray-show');
var crout = require('ndarray-crout-decomposition');
var ndarray = require('ndarray');
var zeros = require('zeros');
 
var A = ndarray(
    [ 2, 1, -1, 8, -3, -1, 2, -11, -2, 1, 2, -3 ],
    [ 4, 3 ], [ 1, 4 ]
);
var LU = zeros([ 3, 3 ]);
crout(A.hi(3,3), LU);
 
var solution = solve(LU, A.lo(3,0).pick(0));
 
console.log('input:\n' + show(A), '\n');
console.log('solution:\n' + show(solution));

output:

input:
   2.000    1.000   -1.000    8.000
  -3.000   -1.000    2.000  -11.000
  -2.000    1.000    2.000   -3.000 

solution:
   2.000    3.000   -1.000

Just note that it's up to you to ndscratch.free() the solution you get back to prevent leaking memory.

methods

var solve = require('ndarray-lu-solve')

var solution = solve(L, U, B, X, Y)

Given an L and U ndarrays from a decomposition and a vector B, solve the system LY = B for Y and UX = Y for X.

L and U can also be the same matrix.

The solution is written to X as the computation procedes but is also the return value.

Optional X and Y parameters are modified in-place and contain elements of the result. If not given, X and Y will be allocated.

var solution = solve(LU, B, X, Y)

You can omit the U parameter if you have a L and U values packed into the same matrix. The other parameters work the same.

install

With npm do:

npm install ndarray-lu-solve

license

MIT