ó Bpˆj/ ãó,•SSKrSSKJr S/rSS.Sjrg)éNé)Únnlsr)ÚmaxitercóF•[R"U[RSS9n[R"U[RS9n[UR5S:wa[ SUR35eUR S:”d#UR S:Xa+URSS:wa[ SUR35eUR S:Xa#URSS:XaUR5nURup4X1RS:wa"[ S S US URS43-5eUS:Xa5[R"S5[RRU54$U(dS U-n[XU5upVnUS :Xa [S 5eXV4$)aJ 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``. 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) ÚC)ÚdtypeÚorder)réz+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 éz%Maximum number of iterations reached.) ÚnpÚasarray_chkfiniteÚfloat64ÚlenÚshapeÚ ValueErrorÚndimÚravelÚemptyÚlinalgÚnormÚ_nnlsÚ RuntimeError)ÚAÚbrÚmÚnÚxÚrnormÚinfos ÚP/var/www/html/pdf-tiff/venv/lib/python3.13/site-packages/scipy/optimize/_nnls.pyrrsl€ôp ×Ò˜Q¤b§j¡j¸Ñ<€AÜ ×Ò˜Q¤b§j¡jÑ1€Aä ˆ17‰7ƒ|qÓÜÐFÀqÇwÁwÀiÐPÓQÐQà ‰‹ ˜Ÿ™ 1›¨1¯7©7°1©:¸«?Üð+Ø+,¯7©7¨)ð5ó6ð 6à &‰&A‹+˜AŸG™G A™J¨!›OØ G‰G‹Iˆà 7‰7D€AàG‰GA‰JƒÜØBؘsÐ4°a·g±g¸a±j°^Ð4DÐEñFóGð Gð ˆAƒvÜ—’˜“ œRŸY™YŸ^™^¨AÓ.Ð/Ð/æ ØA‘#ˆÜ˜1 Ó)N€AˆdØ ˆqƒyÜÐBÓCÐCà ˆ8€Oó)Únumpyr Ú _slsqplibrrÚ__all__©r!r Úr&sðÛÝ$ð ˆ(€ðöTr!