ftjn* bddlmZmZmZmZddlmZddlmZddl m Z dgZ d dd dddd d d d Z dS))innerzerosinffinfo)norm)sqrt) make_systemminresNgh㈵>gF)rtolshiftmaxiterMcallbackshowcheckc^ t||||\}}} }|j} |j} d} d}|jd}|d|z}gd}|rTt| dzt| d|d d |d zt| d |d d |dztd}d}d}d}d}d}| j}t |j}||}n||| zz }| |}t||}|dkrtd|dkr| dfSt|}|dkr|} | dfSt|}| r| |}| |}t||}t||} t|| z }!||z|dzz}"|!|"krtd| |}t||}t||} t|| z }!||z|dzz}"|!|"krtdd}#|}$d}%d}&|}'|}(|})d}*d}+d},t |j }-d}.d}/t||}t||}0|}|r+tttd||kr|dz }d|$z }||z}1| |1}|||1zz }|dkr ||$|#z |zz }t|1|}2||2|$z |zz }|}|}| |}|$}#t||}$|$dkrtdt|$}$|+|2dz|#dzz|$dzzz }+|dkr|$|z d|zkrd}|&}3|.|%z|/|2zz}4|/|%z|.|2zz }5|/|$z}&|. |$z}%t|5|%g}6|(|6z}7t|5|$g}8t|8|}8|5|8z }.|$|8z }/|.|(z}9|/|(z}(d|8z }:|0};|}0|1|3|;zz |4|0zz |:z}| |9|zz} t|,|8},t|-|8}-|)|8z }!|*|4|!zz })|& |!z}*t|+}t| }||z}"||z|z}<||z|z}=|5}>|>dkr|"}>|(}'|'}|dks|dkrt }?n|||zz }?|dkrt }@n|6|z }@|,|-z }|dkrEd|?z}Ad|@z}B|Bdkrd}|Adkrd}||krd}|d|z krd}|<|krd}|@|krd}|?|krd}d}C|dkrd }C|dkrd }C||dz krd }C|dzdkrd }C|'d|0 : convergence to tolerance not achieved, number of iterations <0 : illegal input or breakdown Other Parameters ---------------- x0 : ndarray Starting guess for the solution. shift : float Value to apply to the system ``(A - shift * I)x = b``. Default is 0. rtol : float Tolerance to achieve. The algorithm terminates when the relative residual is below ``rtol``. maxiter : integer Maximum number of iterations. Iteration will stop after maxiter steps even if the specified tolerance has not been achieved. M : {sparse array, ndarray, LinearOperator} Preconditioner for A. The preconditioner should approximate the inverse of A. Effective preconditioning dramatically improves the rate of convergence, which implies that fewer iterations are needed to reach a given error tolerance. callback : function User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector. show : bool If ``True``, print out a summary and metrics related to the solution during iterations. Default is ``False``. check : bool If ``True``, run additional input validation to check that `A` and `M` (if specified) are symmetric. Default is ``False``. Examples -------- >>> import numpy as np >>> from scipy.sparse import csc_array >>> from scipy.sparse.linalg import minres >>> A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float) >>> A = A + A.T >>> b = np.array([2, 4, -1], dtype=float) >>> x, exitCode = minres(A, b) >>> print(exitCode) # 0 indicates successful convergence 0 >>> np.allclose(A.dot(x), b) True References ---------- Solution of sparse indefinite systems of linear equations, C. C. Paige and M. A. Saunders (1975), SIAM J. Numer. Anal. 12(4), pp. 617-629. https://web.stanford.edu/group/SOL/software/minres/ This file is a translation of the following MATLAB implementation: https://web.stanford.edu/group/SOL/software/minres/minres-matlab.zip zEnter minres. zExit minres. rN) z3 beta2 = 0. If M = I, b and x are eigenvectors z/ beta1 = 0. The exact solution is x0 z3 A solution to Ax = b was found, given rtol z3 A least-squares solution was found, given rtol z3 Reasonable accuracy achieved, given eps z3 x has converged to an eigenvector z3 acond has exceeded 0.1/eps z3 The iteration limit was reached z3 A does not define a symmetric matrix z3 M does not define a symmetric matrix z3 M does not define a pos-def preconditioner zSolution of symmetric Ax = bz n = 3gz shift = z23.14ez itnlim = z rtol = z11.2ezindefinite preconditionergUUUUUU?znon-symmetric matrixznon-symmetric preconditioner)dtypezD Itn x(1) Compatible LS norm(A) cond(A) gbar/|A|r g? g?F(Tg{Gz?6g z12.5ez10.3ez8.1ez istop = z itn =5gz Anorm = z12.4ez Acond = z rnorm = z ynorm = z Arnorm = )r matvecshapeprintrrepscopyr ValueErrorrrabsmaxrminr)HAbx0r r rrrrrxr!psolvefirstlastnmsgistopitnAnormAcondrnormynormxtyper$r1ybeta1bnormwr2stzepsaoldbbetadbarepslnqrnormphibarrhs1rhs2tnorm2gmaxgmincssnw2valfaoldepsdeltagbarrootArnormgammaphidenomw1epsxepsrdiagtest1test2t1t2prntstr1str2str3infosH `/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/sparse/linalg/_isolve/minres.pyr r sdQ2q))JAq!Q XF XF E D  Aa% C C CC  e44555 eF1FFFFFFFGGG eJ7JJJdJJJJKKK  E C E E E E GE ,, C  z VVXX 1Wr A "aLLE qyy4555 !1v GGE zz 1v KKE = F1II VAYY !AJJ !BKK AJJC3>) t88344 4VAYY !AJJ "RLL AJJC3>) t88;<< < D D D E F F D D F D << D B B auA q   B B V   TUUU -- q H aC F1II  M !88T$YN"AQqzz dB    F2JJR{{ !88344 4Dzz$'D!G#dAg-- !88EzRV## T BI%Dy29$T td{T4L!!$dD\""E3 E\ E\6kfE    ]U2X % . AI44 5LeAg~wqyV Qs{u}s"u}t# 199D A::!EEU5[)E A::EE5LET  A::UBUBQwwQwwg~~Cu}}}}}} 77D "99D '"*  D 8q==D RW  D RW  D DH  D A::D  D 999qt999E999D$u$$$DBuBBBEBBBeBBBD $+$ % % %Rx1}}   HQKKK A:: u --x #  dLELLLCLLLLMMM dMEMMMMMMMNNN dMEMMMMMMMNNN d2F2222333 dSq\!""" zz d8O)N) numpyrrrr numpy.linalgrmathrutilsr __all__r rjrirqs************ *j$c4 DuEjjjjjjjrj