# 3j $SSKrSSjrg)Nc F^TcSn O[T5(aTn OU4Sjn Uc[R"U5OUR5n [RR U5n [U5(a X"U 5- n OXR U 5- n [RR U 5n X:dXU -:aU $U "U 5nUR5n[R"X5n[U5GHnU R5n[U5(a U"U5nOUR U5nU[R"UU5- nU UU-- n U UU--n [RR U 5n Ub U"X XX5 X:dXU -:aU s $U "U 5nU(a4[R"U U- U5U- n[R"X5nO SU- n[R"X5nUU-nUU-nX- nGM [SU-5e)a$Solves a system of linear equations :math:`Ax=b` using conjugate gradient descent :cite:`hestenes1952methods` Parameters ---------- A: scipy.sparse.csr_matrix Square matrix b: numpy.ndarray Vector describing the right-hand side of the system x0: numpy.ndarray Initialization, if `None` then :code:`x=np.zeros_like(b)` atol: float Absolute tolerance. The loop terminates if the :math:`||r||` is smaller than `atol`, where :math:`r` denotes the residual of the current iterate. rtol: float Relative tolerance. The loop terminates if :math:`{||r||}/{||b||}` is smaller than `rtol`, where :math:`r` denotes the residual of the current iterate. callback: function Function :code:`callback(A, x, b, norm_b, r, norm_r)` called after each iteration, defaults to `None` M: function or scipy.sparse.csr_matrix Function that applies the preconditioner to a vector. Alternatively, `M` can be a matrix describing the precondioner. reorthogonalize: boolean Whether to apply reorthogonalization of the residuals after each update, defaults to `False` Returns ------- x: numpy.ndarray Solution of the system Example ------- >>> from pymatting import * >>> import numpy as np >>> A = np.array([[3.0, 1.0], [1.0, 2.0]]) >>> M = jacobi(A) >>> b = np.array([4.0, 3.0]) >>> cg(A, b, M=M) array([1., 1.]) cU$N)xs M/home/wildlama/miniconda3/lib/python3.13/site-packages/pymatting/solver/cg.py preconditioncg..precondition6sHc&>TRU5$r)dot)rMs rr r =s558Or g?z@Conjugate gradient descent did not converge within %d iterations) callablenp zeros_likecopylinalgnormr innerrange ValueError)Abx0atolrtolmaxitercallbackrreorthogonalizer rnorm_brnorm_rzprz iterationr_oldApalphabetas ` rcgr+s` y  !  J aBGGIA YY^^A F{{ !H aL YY^^A F }.QA A !B7^  A;;1BqBRXXa_$ UQY URZ"   Q1a 0 =FF]2H O 88AIq)B.D!B8D!B BJD T  ?$B JWT r )NggHz>i'NNF)numpyrr+rr rr-s%    qr