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from . import __nnls from numpy import asarray_chkfinite, zeros, double
__all__ = ['nnls']
def nnls(A, b, maxiter=None): """ 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 -------- >>> 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)
"""
A, b = map(asarray_chkfinite, (A, b))
if len(A.shape) != 2: raise ValueError("Expected a two-dimensional array (matrix)" + ", but the shape of A is %s" % (A.shape, )) if len(b.shape) != 1: raise ValueError("Expected a one-dimensional array (vector" + ", but the shape of b is %s" % (b.shape, ))
m, n = A.shape
if m != b.shape[0]: raise ValueError( "Incompatible dimensions. The first dimension of " + "A is %s, while the shape of b is %s" % (m, (b.shape[0], )))
maxiter = -1 if maxiter is None else int(maxiter)
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, maxiter) if mode != 1: raise RuntimeError("too many iterations")
return x, rnorm |