+ /i/Rt^RIt^RIHtHt^RIHtHtH t ^RI H t ^RI H t ^RIHtHtHtHtHtHtHtHtHtHtHtHtRtRtR tR R ltR#) a Dogleg algorithm with rectangular trust regions for least-squares minimization. The description of the algorithm can be found in [Voglis]_. The algorithm does trust-region iterations, but the shape of trust regions is rectangular as opposed to conventional elliptical. The intersection of a trust region and an initial feasible region is again some rectangle. Thus, on each iteration a bound-constrained quadratic optimization problem is solved. A quadratic problem is solved by well-known dogleg approach, where the function is minimized along piecewise-linear "dogleg" path [NumOpt]_, Chapter 4. If Jacobian is not rank-deficient then the function is decreasing along this path, and optimization amounts to simply following along this path as long as a point stays within the bounds. A constrained Cauchy step (along the anti-gradient) is considered for safety in rank deficient cases, in this situations the convergence might be slow. If during iterations some variable hit the initial bound and the component of anti-gradient points outside the feasible region, then a next dogleg step won't make any progress. At this state such variables satisfy first-order optimality conditions and they are excluded before computing a next dogleg step. Gauss-Newton step can be computed exactly by `numpy.linalg.lstsq` (for dense Jacobian matrices) or by iterative procedure `scipy.sparse.linalg.lsmr` (for dense and sparse matrices, or Jacobian being LinearOperator). The second option allows to solve very large problems (up to couple of millions of residuals on a regular PC), provided the Jacobian matrix is sufficiently sparse. But note that dogbox is not very good for solving problems with large number of constraints, because of variables exclusion-inclusion on each iteration (a required number of function evaluations might be high or accuracy of a solution will be poor), thus its large-scale usage is probably limited to unconstrained problems. References ---------- .. [Voglis] C. Voglis and I. E. Lagaris, "A Rectangular Trust Region Dogleg Approach for Unconstrained and Bound Constrained Nonlinear Optimization", WSEAS International Conference on Applied Mathematics, Corfu, Greece, 2004. .. [NumOpt] J. Nocedal and S. J. Wright, "Numerical optimization, 2nd edition". N)lstsqnorm)LinearOperatoraslinearoperatorlsmr)OptimizeResult)_call_callback_maybe_halt) step_size_to_bound in_boundsupdate_tr_radiusevaluate_quadraticbuild_quadratic_1dminimize_quadratic_1d compute_gradcompute_jac_scalecheck_terminationscale_for_robust_loss_functionprint_header_nonlinearprint_iteration_nonlinearcjaaaSPwr4VVV3RlpVVV3Rlp\W43WV\R7#)zCompute LinearOperator to use in LSMR by dogbox algorithm. `active_set` mask is used to excluded active variables from computations of matrix-vector products. cz<VP4P4p^VS&SPVS,4#)ravelcopymatvec)xx_freeJop active_setds& X/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/optimize/_lsq/dogbox.pyrlsmr_operator..matvecBs2!zzz!a%  cB<SSPV4,p^VS&V#r)rmatvec)rrrrr s& r!r%lsmr_operator..rmatvecGs#  A * r#)rr%dtype)shaperfloat)rr rmnrr%sfff r! lsmr_operatorr-:s- 99DA!  1& NNr#c8W , pW0, p\P!WA)4p\P!WQ4p\P!Wd4p\P!Wu4p \P!Wa)4p \P!Wq4p WgWW3#)aFind intersection of trust-region bounds and initial bounds. Returns ------- lb_total, ub_total : ndarray with shape of x Lower and upper bounds of the intersection region. orig_l, orig_u : ndarray of bool with shape of x True means that an original bound is taken as a corresponding bound in the intersection region. tr_l, tr_u : ndarray of bool with shape of x True means that a trust-region bound is taken as a corresponding bound in the intersection region. )npmaximumminimumequal) r tr_boundslbub lb_centered ub_centeredlb_totalub_totalorig_lorig_utr_ltr_us &&&& r!find_intersectionr>Osw&K&Kzz+z2Hzz+1H XXh ,F XXh ,F 88Hj )D 88H (D vt 99r#c\WWg4wrrr\P!V\R7p\ WV 4'dWR3#\ \P!V4V)W4wpp\ W4^V4^,)V,pVV, p\ VVW4wppRVV^8V ,&^VV^8V ,&\P!V^8V ,V^8V ,,4pVVV,,VV3#)aFind dogleg step in a rectangular region. Returns ------- step : ndarray, shape (n,) Computed dogleg step. bound_hits : ndarray of int, shape (n,) Each component shows whether a corresponding variable hits the initial bound after the step is taken: * 0 - a variable doesn't hit the bound. * -1 - lower bound is hit. * 1 - upper bound is hit. tr_hit : bool Whether the step hit the boundary of the trust-region. r(F)r>r/ zeros_likeintr r rany)r newton_stepgabr3r4r5r8r9r:r;r<r= bound_hits to_bounds_ cauchy_step step_diff step_sizehitstr_hits&&&&&&&& r! dogleg_steprQls 6G b62Hq,J11--%bmmA&6HOLIq)q)V !V4pR\P!V^,4,p\VVV4wppMR\P!VV4,p\ VV4p\ V \4;'dV R8HpV'd\V4wppM T ^V , pp\VV,\PR7pV^8XdRp\P!V\R7pRV\P!W%4&^V\P!W&4&Tp\P!V4pV fVP^d,p Rp ^p!Rp"Rp#V^8Xd \!4VV,^8p$V$(p%VV%,p&VP4p'^VV$&\V\PR7p(V(V 8d^p V^8Xd\#V!VVV#V"V(4V fVV 8XdEMVV%,p)VV%,p*VV%,p+VV%,p,V R8Xd4VR V%3,p-\%V-V)RR 7^,p.\'V-V&V&)4wp/p0MUV R 8XdO\)V4p1\+V1VV$4p2\-V2V3/VB^,V%,)p.V.V,,p.\'V1VV)4wp/p0Rp#V#^8:EdiVV 8EdaVV,,p3\/V)X.V&X/X0V3V*V+4wp4p5p6VP1R 4V4VV%&V R8Xd\3X-V&V44)p7MV R 8Xd\3X1VV4)p7\P4!VV,WV4p8V!V84p9V^, p\VV,\PR7p:\P6!\P8!V944'g R V:,pKV e V !V9RR7p;MR\P!V9V94,p;VV;, p#\;VV#X7V:V64wpp<\V4p"\=V#VV"\V4VX;V>R&\AVV>4'gEKmRp V f^p \?VVVVV'V(VVVV R7 #)Ng?jac)ordg?r@Texact:NNN)rcondrgg?) cost_only)rfunnitnfevcost) rr\rYrTgrad optimality active_maskr[njevstatusrAg)!rr/sumrdotr isinstancestrrrinfrBrCr2 empty_likesizerrrr rr-rrQfillr clipallisfiniter rrr)?rYrTx0f0J0r4r5ftolxtolgtolmax_nfevx_scale loss_function tr_solver tr_optionsverbosecallbackff_truer[Jr`rhor\rF jac_scalescale scale_invDeltaon_boundrsteptermination_status iteration step_normactual_reductionrfree_setg_freeg_fullg_normrlb_freeub_free scale_freeJ_freerErGrHrlsmr_opr3 step_free on_bound_freerPpredicted_reductionx_newf_new step_h_normcost_newratiomaskintermediate_results?&&&&&&&&&&&&&&&&& r!dogboxrsE A VVXF D A D ARVVCF^#-aC81RVVAq\!QA7C(==W-=I,Q/y"AKy iRVV ,E z}}Rs+H!#HRXXb !"HRXXb  A == D77S=II!| \A% ;8* aRVV$ D=!"  a< %it=M&/ 9  )TX-= 8X,X,8_   q({^F"5a8K&ffvg>DAq & "1%C$C ;G9j9!DhAdGq=DhAdGAVVXFDAA AID(#A&5aC@1Q"A#4Q #B yI Q   "0 #6 *2  '(-&("!  $F64d;M OOr#)N)__doc__numpyr/ numpy.linalgrrscipy.sparse.linalgrrrscipy.optimizerscipy._lib._utilrcommonr r r r r rrrrrrrr-r>rQrr#r!rsL)T$FF)67777O*::(CVBOr#