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bundles / scipy latest / scipy / optimize / _nnls / nnls

function

scipy.optimize._nnls:nnls

source: /scipy/optimize/_nnls.py :9

Signature

def   nnls ( A ,  b ,  * ,  maxiter = None ,  atol = <object object at 0x0000> )

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.

atol : float, optional

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

See also

lsq_linear

Linear least squares with bounds on the variables

Aliases

  • scipy.optimize.nnls

Referenced by

This package