a j@sDddlZddlmZmZddlZdgZdddddZd ddZdS) N)solve LinAlgWarningnnls)atolc Cst|}t|}t|jdkr6tdd|jt|jdkrXtdd|j|j\}}||jdkrtdd |d |jdft||||d \}}}|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) z)Expected a two-dimensional array (matrix)z, but the shape of A is z)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 )tolz%Maximum number of iterations reached.)npZasarray_chkfinitelenshape ValueError_nnls RuntimeError) AbmaxiterrmnxZrnormmoder:E:\soccer\ml_env\Lib\site-packages\scipy/optimize/_nnls.pyrs*B     cCs\|j\}}|j|}||}|s(d|}|durHdt||td}tj|tjd}tj|tjd} tj|td} | tj} d} | sB| | |k rBt | | } d| | <d| dd<t Dt jd d td t|t| | || d d d| | <Wdn1s 0Y| |kr| | dkr| d7} | | dk}||||| |}|d|9}||| 7}d | ||k<t Dt jd d td t|t| | || d d d| | <Wdn1s0Yd| | <q*| dd|dd<|||| dd<| |kr|ddfSq|tj|||dfS)z This is a single RHS algorithm from ref [2] above. For multiple RHS support, the algorithm is given in :doi:`10.1002/cem.889` N g?)ZdtyperTgignorezIll-conditioned matrix)messagecategorysymF)Zassume_aZ check_finiter)r Tmaxr spacingZzerosZfloat64boolcopyZastypeallanyZargmaxwarningscatch_warningsfilterwarningsrrZix_minZlinalgZnorm)rrrrrrZAtAZAtbrsPwiterkZindsalpharrrr bsR    D     * r )N)NN) numpyr Z scipy.linalgrrr&__all__rr rrrrs Z