sandy4321 / fcnnls

Fast Combinatorial Non-negative Least Squares

fcnnls

Fast Combinatorial Non-negative Least Squares.

Fast algorithm for the solution of large‐scale non‐negativity‐constrained least squares problems from Van Benthem and Keenan (10.1002/cem.889), based on the active-set method algorithm published by Lawson and Hanson.

It solves the following optimisation problem. Given an matrix and an matrix, find subject to , where is an matrix and is the Frobenius norm. In fact, is the best solution to the equation: , where . Note that if is a column vector, it performs the regular Non-negative Least Squares algorithm and finds a vector as a solution to the problem. Also, performing this algorithm when is a matrix is like running the algorithm on each column of , it will give the same result but in a much more efficient way.

https://en.wikipedia.org/wiki/Non-negative_least_squares

Installation

$ npm i ml-fcnnls

API Documentation

Usage

import { Matrix } from 'ml-matrix';
import { fcnnls } from 'ml-fcnnls';

// Example with multiple RHS

let X = new Matrix([
  [1, 1, 2],
  [10, 11, -9],
  [-1, 0, 0],
  [-5, 6, -7],
]);

// Y can either be a Matrix of an array of array
let Y = new Matrix([
  [-1, 0, 0, 9],
  [11, -20, 103, 5],
  [0, 0, 0, 0],
  [1, 2, 3, 4],
]);

let K = fcnnls(X, Y);

/*
K = Matrix([
  [0.461, 0, 4.9714, 0],
  [0.5611, 0, 4.7362, 2.2404],
  [0, 1.2388, 0, 1.9136],
    ])
*/

import { fcnnlsVector } from 'ml-fcnnls';

// Example with single RHS and same X
// Should be giving a vector with the element of the first column of K in the previous example, since y is the first column of Y

let X = new Matrix([
  [1, 1, 2],
  [10, 11, -9],
  [-1, 0, 0],
  [-5, 6, -7],
]);

let y = [-1, 11, 0, 1];

let k = fcnnlsVector(X, y);

/*
k = [0.461, 0.5611, 0]
*/

License

MIT