U !?h @sddlZdddZdS) NHz>'Fc sdkrdd} ntr } n fdd} |dkr>t|n|} tj|} t|rh||| } n||| } tj| } | |ks| || kr| S| | }|}t| |}t|D]}| }t|r||}n ||}|t||}| ||7} | ||8} tj| } |dk r6||| || | | | |ksN| || krV| S| | }|rt| |||}t| |}nd|}t| |}||9}||9}||7}qt d|dS)aSolves 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.]) NcSs|SNxrrE/var/www/html/venv/lib/python3.8/site-packages/pymatting/solver/cg.py precondition6szcg..preconditioncs |Sr)dotrMrr r =sg?z@Conjugate gradient descent did not converge within %d iterations) callablenpZ zeros_likecopyZlinalgZnormr innerrange ValueError)AbZx0ZatolZrtolmaxitercallbackr Zreorthogonalizer rZnorm_brZnorm_rzpZrz iterationZr_oldZApalphabetarr r cgsR0              r)NrrrNNF)numpyrrrrrr s