+ /i AtRt^RIt^RIHtHtHtHt^RIH t H t .R Ot R Rlt Rt RtRt!R R] 4tR#) z2Nearly exact trust-region optimization subproblem.N)normget_lapack_funcssolve_triangular cho_solve)_minimize_trust_regionBaseQuadraticSubproblemIterativeSubproblemc Vf \R4h\V4'g \R4h\W3RVRVRVR\/VB#)a Minimization of scalar function of one or more variables using a nearly exact trust-region algorithm. Options ------- initial_trust_radius : float Initial trust-region radius. max_trust_radius : float Maximum value of the trust-region radius. No steps that are longer than this value will be proposed. eta : float Trust region related acceptance stringency for proposed steps. gtol : float Gradient norm must be less than ``gtol`` before successful termination. subproblem_maxiter : int, optional Maximum number of iterations to perform per subproblem. Only affects trust-exact. Default is 25. .. versionadded:: 1.17.0 z9Jacobian is required for trust region exact minimization.z?Hessian matrix is required for trust region exact minimization.argsjachess subproblem) ValueErrorcallablerr)funx0r r r trust_region_optionss&&&&&,_/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/optimize/_trustregion_exact.py_minimize_trustregion_exactr sj0 {/0 0 D>>/0 0 !# : :# :D :-@ :$8 ::c\P!V4pVPwrW8wd \R4h\P!V4p\P !V4p\ V4EFp^W5,, VPWU3,, pRW5,, VPWU3,, pW5^,RVPV^,R1V3,V,,pW5^,RVPV^,R1V3,V,,p \V4\V^4,\V4\V ^4,8dWdV&WV^,R%EK WtV&WV^,R%EK \W4p \V 4p \V4p W, p W, pW3#)aGiven upper triangular matrix ``U`` estimate the smallest singular value and the correspondent right singular vector in O(n**2) operations. Parameters ---------- U : ndarray Square upper triangular matrix. Returns ------- s_min : float Estimated smallest singular value of the provided matrix. z_min : ndarray Estimated right singular vector. Notes ----- The procedure is based on [1]_ and is done in two steps. First, it finds a vector ``e`` with components selected from {+1, -1} such that the solution ``w`` from the system ``U.T w = e`` is as large as possible. Next it estimate ``U v = w``. The smallest singular value is close to ``norm(w)/norm(v)`` and the right singular vector is close to ``v/norm(v)``. The estimation will be better more ill-conditioned is the matrix. References ---------- .. [1] Cline, A. K., Moler, C. B., Stewart, G. W., Wilkinson, J. H. An estimate for the condition number of a matrix. 1979. SIAM Journal on Numerical Analysis, 16(2), 368-375. z.A square triangular matrix should be provided.N) np atleast_2dshaperzerosemptyrangeTabsrr)Umnpwkwpwmpppmvv_normw_norms_minz_mins& r estimate_smallest_singular_valuer/0seD aA 77DAvIJJ  A  A1XfAD !gQT " stWqss1Q347|B & stWqss1Q347|B & r7T"a[ CGd2qk$9 9aDacdGaDacdG A !WF !WF OE JE <rcD\P!V4p\P!V4p\P!\P!V4^R7p\P!W,V, 4p\P !W, V,4pWE3#)z Given a square matrix ``H`` compute upper and lower bounds for its eigenvalues (Gregoshgorin Bounds). Defined ref. [1]. References ---------- .. [1] Conn, A. R., Gould, N. I., & Toint, P. L. Trust region methods. 2000. Siam. pp. 19. )axis)rdiagrsumminmax)HH_diag H_diag_abs H_row_sumslbubs& rgershgorin_boundsr<siWWQZFJq *J #j0 1B #j0 1B 6Mrc\P!VRV^, 1V^, 3,^,4W^, V^, 3,, p\V4p\P!V4p^WR^, &V^8wdL\ VRV^, 1RV^, 13,VRV^, 1V^, 3,)4VRV^, %W53#)a Compute term that makes the leading ``k`` by ``k`` submatrix from ``A`` singular. Parameters ---------- A : ndarray Symmetric matrix that is not positive definite. U : ndarray Upper triangular matrix resulting of an incomplete Cholesky decomposition of matrix ``A``. k : int Positive integer such that the leading k by k submatrix from `A` is the first non-positive definite leading submatrix. Returns ------- delta : float Amount that should be added to the element (k, k) of the leading k by k submatrix of ``A`` to make it singular. v : ndarray A vector such that ``v.T B v = 0``. Where B is the matrix A after ``delta`` is added to its element (k, k). N)rr3lenrr)Ar r%deltar"r*s&&& rsingular_leading_submatrixrAs6 FF1TacT1Q3Y<? #a!QqSk 1E AA  A AcF Av"1TacT4AaC4Z=1TacT1Q3Y<-@$1Q3 8Orcaa]tRt^toRtRt^t]P!] 4Pt RV3Rllt Rt RtRtVtV;t#)raQuadratic subproblem solved by nearly exact iterative method. Notes ----- This subproblem solver was based on [1]_, [2]_ and [3]_, which implement similar algorithms. The algorithm is basically that of [1]_ but ideas from [2]_ and [3]_ were also used. References ---------- .. [1] A.R. Conn, N.I. Gould, and P.L. Toint, "Trust region methods", Siam, pp. 169-200, 2000. .. [2] J. Nocedal and S. Wright, "Numerical optimization", Springer Science & Business Media. pp. 83-91, 2006. .. [3] J.J. More and D.C. Sorensen, "Computing a trust region step", SIAM Journal on Scientific and Statistical Computing, vol. 4(3), pp. 553-572, 1983. g{Gz?c r<\S V`WW44RVnRVn^VnW`nWpnVf VPMTVnVP^8d \R4h\RVP34wVn \VP4Vn\VP4wVnVn\%VP\&P(4Vn\%VPR4VnVPVP.,VP*,VnR#)NzJmaxiter must not be set to a negative number, use np.inf to mean infinite.fror)potrf)super__init__previous_tr_radius lambda_lbniterk_easyk_hardMAXITER_DEFAULTmaxiterrrr choleskyr> dimensionr<hess_gershgorin_lbhess_gershgorin_ubrrinfhess_infhess_froEPS CLOSE_TO_ZERO) selfxrr r hessprLrMrO __class__s &&&&&&&&&rrHIterativeSubproblem.__init__s +#%   07t++G <? ? **tyylC TYY&7 &B $  #TYY/ TYY. 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The values were chosen accordingly to the guidelines on section 7.3.8 (p. 192) from [1]_. )r5jac_magr4rRrVrUr diagonalrSrIrJrsqrt UPDATE_COEFF)rY tr_radius lambda_ubrJlambda_initials&& r_initial_values#IterativeSubproblem._initial_valuess4<< 1C9P9P8P8< 8< 5GGH C 2 2 455 Y.T5L5L59]]59]]2DDE .. .DNNI6I >N )>!?!*->-> @S-T!TVN)33rc n VPV4wr#pVPpRpRp^VnVPVP8EdZV'dRpMEVPV\ P !V4,,pVPVRRRR7wrV;P^, unX ^8XEd[VPVP8Ed?\X R3VP)4p \V 4p W8:d V^8XdRpEM\WRR7p \V 4pW, ^,W, ,V, pW/,pW8Ed\V 4wppVPV VV4wpp\!VV.\"R7p\ P$!V \ P$!XV 44pV^,V^,,VW!^,,,, pVVP&8:dV VV,, p EMTp\)W2V^,, 4pVPV\ P !V4,,pVPVRRRR7wpp V ^8XdTpRpEKO\)VV4p\)\ P*!\ P"!W4,44W0P,WC, ,,4pEK\#W, 4V, pVVP.8:dEMTpTpEKV ^8XdVPVP8:dV^8Xd\ P0!V4p RpEMK\X 4wppTpVV,p V^,V^,,VP&V,V^,,8:dMTp\)W2V^,, 4p\)\ P*!W4,4W0P,WC, ,,4pEK\3XX V 4wpp\V4p\)W2VV^,, ,4p\)\ P*!\ P"!W4,44W0P,WC, ,,4pEKuW0nW nWnX V3#)zSolve quadratic subproblemTF)lower overwrite_acleanr)trans)key)rfrQrKrOr reyerPr_rXrr rrr/get_boundaries_intersectionsr4rdotrMr5rarbrLrrArJlambda_currentrI)rYrcrqrJrdr" hits_boundaryalready_factorizedr6r infor#p_normr$r, delta_lambda lambda_newr-r.tatbstep_lenquadratic_termrelative_errorcr@r*r+s&& rsolveIterativeSubproblem.solve1s04/C/CI/N,9 NN " jj4<<'"%*"IInRVVAY66--49.2(4 JJ!OJqyT\\D,>,>>q%j488)4a&>Q+>$)M%Q5a!' 1V5EFyP +: %#CA#FLE5!>>q%?HJFB #B85H&(VVArvva|% *-GGBFF9+@$AB%(9(99;N(OO*&));%Y Y r)rr/rAr)NN)rnumpyr scipy.linalgrrrr _trustregionrr__all__rr/r<rArrrrrsF8%%K " :FL^*'TL 1L r