`scipy.optimize._nnls:nnls`

source: /scipy/optimize/_nnls.py:8

Signature

def nnls(A, b, *, maxiter = None)

Summary

Solve argmin_x || Ax - b ||_2^2 for x>=0.

Extended Summary

This problem, often called as NonNegative Least Squares, is a convex optimization problem with convex constraints. It typically arises when the x models quantities for which only nonnegative values are attainable; weight of ingredients, component costs and so on.

Parameters

A : (m, n) ndarray: Coefficient array
b : (m,) ndarray, float: Right-hand side vector.
maxiter : int, optional: Maximum number of iterations, optional. Default value is 3 * n.

Returns

x : ndarray: Solution vector.
rnorm : float: The 2-norm of the residual, || Ax-b ||_2.

Notes

The code is based on the classical algorithm of ^[1]. It utilizes an active set method and solves the KKT (Karush-Kuhn-Tucker) conditions for the non-negative least squares problem.

Examples

import numpy as np
from scipy.optimize import nnls
A = np.array([[1, 0], [1, 0], [0, 1]])
b = np.array([2, 1, 1])

✓

nnls(A, b)

✗

(array([1.5, 1. ]), 0.7071067811865476)

b = np.array([-1, -1, -1])
nnls(A, b)

✓

(array([0., 0.]), 1.7320508075688772)

Aliases

scipy.optimize.nnls