Module « scipy.optimize »

Fonction nnls - module scipy.optimize

Signature de la fonction nnls

def nnls(A, b, maxiter=None) 

Description

nnls.__doc__

    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)