tKgl@ddlZddlmZmZddlZdgZddddZddZy) N)solve LinAlgWarningnnls)atolctj|}tj|}t|jdk7rt dd|jzt|jdk7rt dd|jz|j\}}||jdk7r"t dd |d |jdfzt |||| \}}}|dk7r t d ||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.)npasarray_chkfinitelenshape ValueError_nnls RuntimeError) Abmaxiterrmnxrnormmodes X/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/scipy/optimize/_nnls.pyrrsD QA QA 177|qD3AGG9=>? ? 177|qD3AGG9=>? ? 77DAqAGGAJBs4aggaj^4DEFG G1ad3NAud qyBCC e8Oc|j\}}|j|z}||z}|sd|z}|%dt||ztjdz}tj |tj }tj |tj } tj |t} |jjtj } d} | js| | |kDjrtj| | z} d| | <d| ddtj5tjd d t t#|tj$| | || d d | | <ddd| |kr| | j'dkr| dz } | | dkz}||||| |z z j'}|d|z z}||| zz }d | ||k<tj5tjd d t t#|tj$| | || d d | | <dddd| | <| |kr| | j'dkr| dd|dd|||zz | dd| |k(r|ddfS| js| | |kDjr|tj(j+||z|z dfS#1swY^xYw#1swYxYw)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?)dtyperTgignorezIll-conditioned matrix)messagecategorysymF)assume_a check_finiter )rTmaxr spacingzerosfloat64boolcopyastypeallanyargmaxwarningscatch_warningsfilterwarningsrrix_minlinalgnorm)rrrr rrAtAAtbrsPwiterkindsalphas rrrbs 77DAq ##'C a%C A# {3q!9nrzz"~- "**%A "**%A $A  "**%A DuuwQrUS[--/ IIaA2h !!  $ $ &  # #H6N-: <RVVAq\*CFUQVWAaD' g~AaDHHJN AIDA;DtW$!D' 12779E !e) A qLAAa3hK((*'':R1>@S1.A*/1!+ AqbEg~AaDHHJNt!S1W}! 7? b"9 IuuwQrUS[--/L biinnQqS1W%q ((=' &+*sA K+ A K8+K58L)N)NN) numpyr scipy.linalgrrr2__all__rrrrrFs*- (WTWtB)r