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[1].

Returns

xndarray: Solution vector.
rnormfloat: 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

>>> 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)