+ 0in*r^RIHtHtHtHt^RIHt^RIHt^RI H t R.t RRRR R R RR RR RRRRR/Rllt R#))innerzerosinffinfo)norm)sqrt) make_systemminresNrtolgh㈵>shiftgmaxiterMcallbackshowFcheckcD\WW!4wrrVPp VPp Rp RpVP^,pVf ^V,p.R#OpV'dQ\V R,4\V RVR RVR 2,4\V RVR R VR 2,4\4^p^p^p^p^p^pV Pp\ V4P pVfVP4pMWV ,, pV !V4p\VV4pV^8d \R 4hV^8XdV ^3#\V4pV^8XdTp V ^3#\V4pV 'dV !V4pV !V4p\VV4p\VV4p \VV , 4p!VV,VR$,,p"V!V"8d \R 4hV !V4p\VV4p\VV4p \VV , 4p!VV,VR$,,p"V!V"8d \R4h^p#Tp$^p%^p&Tp'Tp(Tp)^p*^p+^p,\ V4Pp-R%p.^p/\VVR7p\VVR7p0TpV'd \4\4\R4VV8EdV^, pR V$, pVV,p1V !V14pVVV1,, pV^8dVV$V#, V,, p\V1V4p2VV2V$, V,, pTpTpV !V4pT$p#\VV4p$V$^8d \R 4h\V$4p$V+V2^,V#^,,V$^,,, p+V^8XdV$V, ^ V,8:dR%pT&p3V.V%,V/V2,,p4V/V%,V.V2,, p5V/V$,p&V.)V$,p%\V5V%.4p6V(V6,p7\V5V$.4p8\V8V4p8V5V8, p.V$V8, p/V.V(,p9V/V(,p(R V8, p:T0p;Tp0V1V3V;,, V4V0,, V:,pV V9V,,p \V,V84p,\V-V84p-V)V8, p!V*V4V!,, p)V&)V!,p*\V+4p\V 4pVV,p"VV,V,pV>^8XdT"p>T(p'T'pV^8XgV^8Xd\ p?MVVV,, p?V^8Xd\ p@M V6V, p@V,V-, pV^8XdY^V?,pA^X@,pBVB^8:d^pXA^8:d^pVV8d^pVRV, 8d^pV0 : 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. zSolution of symmetric Ax = bz n = 3gz shift = z23.14ez itnlim = z rtol = z11.2ezindefinite preconditionerg?znon-symmetric matrixznon-symmetric preconditioner)dtypezD Itn x(1) Compatible LS norm(A) cond(A) gbar/|A|g?FTg{Gz?6g z12.5ez10.3ez8.1ez istop = z itn =5gz Anorm = z12.4ez Acond = z rnorm = z ynorm = z Arnorm = ) 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 gUUUUUU?)r matvecshapeprintrrepscopyr ValueErrorrrabsmaxrminr)HAbx0r r r rrrrxrpsolvefirstlastnmsgistopitnAnormAcondrnormynormxtyperr1ybeta1bnormwr2stzepsaoldbbetadbarepslnqrnormphibarrhs1rhs2tnorm2gmaxgmincssnw2valfaoldepsdeltagbarrootArnormgammaphidenomw1epsxepsrdiagtest1test2t1t2prntstr1str2str3infosH&&&$$$$$$$ `/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/sparse/linalg/_isolve/minres.pyr r sMdQ2)JA! XXF XXF E D  Aa% CC  e445 e 1R&f~FFG e 72,od5\JJK  E C E E E E GGE ,  C  z VVX 1Wr A "aLE qy455 !1v GE z 1v KE  1I AY !AJ !BK AJC3>) t834 4AY !AJ "RL AJC3>) t8;< < D D D E F F D D F D <  D B B auA q B B    TU - q H aC 1I  M !8T$YN"AQqz dB    2JR{ !834 4Dz$'D!G#dAg-- !8EzRV# T BI%Dy29$T td{T4L!$dD\"E3 E\ E\6kfE    ]U2X % . AI44 5LeAg~wqyV Qs{u}s"u}t# 19D A:!EU5[)E A:E5LET  A:UBUBQwQwg~Cu}}} 7D "9D '"* D 8q=D RW D RW D DH D A:D D"XQqtEl!E%=9DuUm$DuTl!E$223 dSq\!" z d8O d8O)N) numpyrrrr numpy.linalgrmathrutilsr __all__r rbraris]** *j$jcj4j j j',j49jrb