# scipy.optimize.nnls#

scipy.optimize.nnls(A, b, maxiter=None)[source]#

Solve `argmin_x || Ax - b ||_2` for `x>=0`. This is a wrapper for a FORTRAN non-negative least squares solver.

Parameters:
Andarray

Matrix `A` as shown above.

bndarray

Right-hand side vector.

maxiter: int, optional

Maximum number of iterations, optional. Default is `3 * A.shape`.

Returns:
xndarray

Solution vector.

rnormfloat

The residual, `|| Ax-b ||_2`.

`lsq_linear`

Linear least squares with bounds on the variables

Notes

The FORTRAN code was published in the book below. The algorithm is an active set method. It solves the KKT (Karush-Kuhn-Tucker) conditions for the non-negative least squares problem.

References

Lawson C., Hanson R.J., (1987) Solving Least Squares Problems, SIAM

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. ]), 0.7071067811865475)
```
```>>> b = np.array([-1, -1, -1])
>>> nnls(A, b)
(array([0., 0.]), 1.7320508075688772)
```