^Mh .ddlZddlmZdgZddddZdS)N)_nnlsnnls)atolc4tj|tjd}tj|tj}t|jdkrt dd|jzt|jdkrt dd |jz|j\}}||jd kr$t d d |d |jd fz|sd|z}t |||\}}}|dkrtd||fS)a Solve ``argmin_x || Ax - b ||_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 Tolerance value used in the algorithm to assess closeness to zero in the projected residual ``(A.T @ (A x - b)`` entries. Increasing this value relaxes the solution constraints. A typical relaxation value can be selected as ``max(m, n) * np.linalg.norm(a, 1) * np.spacing(1.)``. This value is not set as default since the norm operation becomes expensive for large problems hence can be used only when necessary. 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 [2]_ which is an improved version of 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` .. [2] : Bro, Rasmus and de Jong, Sijmen, "A Fast Non-Negativity- Constrained Least Squares Algorithm", Journal Of Chemometrics, 1997, :doi:`10.1002/(SICI)1099-128X(199709/10)11:5<393::AID-CEM483>3.0.CO;2-L` 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 two-dimensional array (matrix)z, but the shape of A is rz)Expected a one-dimensional array (vector)z, 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 ValueErrorr RuntimeError) Abmaxiterrmnxrnorminfos T/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/optimize/_nnls.pyrrsID Qbj<<?? ? 17||qD=AG==>?? ? 7DAqAGAJBEEEagaj^EEFGG G A#1a))NAud rzzBCCC e8O)N)numpyr _cython_nnlsr__all__rrrr#s^ (YTYYYYYYYr