ftjc fddlZddlmZddlmZmZdgZeddhded d ZdS) N)nnls)_deprecate_positional_args_NoValuerz1.18.0atol)versiondeprecated_args)maxiterrctj|tjd}tj|tj}t|jdkrt d|j|jdks|jdkr(|jddkrt d|j|jdkr%|jddkr|}|j\}}||jdkr$t d d |d |jdfz|sd |z}t|||\}}}|d krtd ||fS)a Solve ``argmin_x || Ax - b ||_2^2`` for ``x>=0``. This problem, often called as NonNegative Least Squares, is a convex optimization problem with convex constraints. It typically arises when the ``x`` models quantities for which only nonnegative values are attainable; weight of ingredients, component costs and so on. Parameters ---------- A : (m, n) ndarray Coefficient array b : (m,) ndarray, float Right-hand side vector. maxiter: int, optional Maximum number of iterations, optional. Default value is ``3 * n``. atol : float, optional .. deprecated:: 1.18.0 This parameter is deprecated and will be removed in SciPy 1.18.0. It is not used in the implementation. Returns ------- x : ndarray Solution vector. rnorm : float The 2-norm of the residual, ``|| Ax-b ||_2``. See Also -------- lsq_linear : Linear least squares with bounds on the variables Notes ----- The code is based on the classical algorithm of [1]_. It utilizes an active set method and solves the KKT (Karush-Kuhn-Tucker) conditions for the non-negative least squares problem. References ---------- .. [1] : Lawson C., Hanson R.J., "Solving Least Squares Problems", SIAM, 1995, :doi:`10.1137/1.9781611971217` 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) C)dtypeorder)r z+Expected a 2D array, but the shape of A is rzDExpected a 1D array,(or 2D with one column), but the, shape of b is rz0Incompatible dimensions. The first dimension of zA is z, while the shape of b is z%Maximum number of iterations reached.) npasarray_chkfinitefloat64lenshape ValueErrorndimravel_nnls RuntimeError) Abr rmnxrnorminfos R/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/optimize/_nnls.pyrr sn| Qbj<<r)s$$$$$$GGGGGGGG (H-3H666XUUUU66UUUr#