^Mh-dZddlZddlmZmZddlmZmZm Z ddl m Z ddl m Z mZmZmZmZmZmZmZmZmZmZmZdZd Zd Zd ZdS) 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) 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_nonlinearclj\}}fd}fd}t||f||tS)zCompute LinearOperator to use in LSMR by dogbox algorithm. `active_set` mask is used to excluded active variables from computations of matrix-vector products. c|}d|<|zSNr)ravelcopymatvec)xx_freeJop active_setds Z/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/optimize/_lsq/dogbox.pyrzlsmr_operator..matvec@s:!!zzz!a%   cB|z}d|<|Sr)rmatvec)rrrrr s r!r$zlsmr_operator..rmatvecEs%  A * r")rr$dtype)shaperfloat)rr rmnrr$s``` r! lsmr_operatorr+8su 9DAq!!!!!!!  1a& N N NNr"c&||z }||z }tj|| }tj||}tj||}tj||} tj|| } tj||} |||| | | fS)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<Msq&Kq&Kz+ z22Hz+y11H Xh , ,F Xh , ,F 8Hyj ) )D 8Hi ( (D XvvtT 99r"ct||||\}} } } } } tj|t}t ||| r||dfSt tj|| || \}}t ||d|d |z}||z }t |||| \}}d||dk| z<d||dk| z<tj|dk| z|dk| zz}|||zz||fS)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&Frr )r<r- zeros_likeintr r rany)r newton_stepgabr1r2r3r6r7r8r9r:r; bound_hits to_bounds_ cauchy_step step_diff step_sizehitstr_hits r! dogleg_steprOjs/ 6G 9b"662Hhdq,,,Jh11.J--%bmA&6&6HhOOLIq)Aq)<r?dTexact)rcondrggg?) cost_only) rcostfunrQgrad optimality active_masknfevnjevstatus) rr-sumrdotr isinstancestrrrinfr@rAr0 empty_likesizerrrrrr+rrOfillr clipallisfiniter rr)=rYrQx0f0J0r2r3ftolxtolgtolmax_nfevx_scale loss_function tr_solver tr_optionsverboseff_truer]Jr^rhorXrD jac_scalescale scale_invDeltaon_boundrsteptermination_status iteration step_normactual_reductionrfree_setg_freeg_fullg_normrlb_freeub_free scale_freeJ_freerCrErFrlsmr_opr1 step_free on_bound_freerNpredicted_reductionx_newf_new step_h_normcost_newratiomasks= r!dogboxrs A VVXXF D A D mARVCF^^#-aC8811RVAq\\!QA7C((=W-=I0,Q//yy"AKy iRV , , ,E zz}Rs+++H!#HRXb"  !"HRXb"   A =  D7S=II!||   A\A% ;8* aRV$$$ D==!"  a<< %it=M&/ 9 9 9  )TX-=-= 8X,X,8_    qqq({^F"555a8K&ffvg>>DAqq & "1%%C$C ;;G99j99!DhAdGq=DhAdGAVVXXFDAq A AID(#mA&&5aC@@1Q""A C#4Q #B#B yI Q CAF!  $F64d;M O O OOr")__doc__numpyr- numpy.linalgrrscipy.sparse.linalgrrrscipy.optimizercommonr r r r rrrrrrrrr+r<rOrr"r!rsI))T$$$$$$$$FFFFFFFFFF))))))7777777777777777777777777777OOO*::::(C(C(CVvOvOvOvOvOr"