# scipy/scipy

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 from __future__ import division, print_function, absolute_import from . import _nnls from numpy import asarray_chkfinite, zeros, double __all__ = ['nnls'] def nnls(A, b): """ 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. Returns ------- x : ndarray Solution vector. rnorm : float The residual, ``|| Ax-b ||_2``. 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 """ A, b = map(asarray_chkfinite, (A, b)) if len(A.shape) != 2: raise ValueError("expected matrix") if len(b.shape) != 1: raise ValueError("expected vector") m, n = A.shape if m != b.shape[0]: raise ValueError("incompatible dimensions") w = zeros((n,), dtype=double) zz = zeros((m,), dtype=double) index = zeros((n,), dtype=int) x, rnorm, mode = _nnls.nnls(A, m, n, b, w, zz, index) if mode != 1: raise RuntimeError("too many iterations") return x, rnorm