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Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``. This is a wrapper
for a FORTRAN non-negative least squares solver.
Parameters
----------
A : ndarray
Matrix ``A`` as shown above.
b : ndarray
Right-hand side vector.
maxiter: int, optional
Maximum number of iterations, optional.
Default is ``3 * A.shape[1]``.
Returns
-------
x : ndarray
Solution vector.
rnorm : float
The residual, ``|| Ax-b ||_2``.
See Also
--------
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)
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