o i@sddlZddlZddlmZddlmZmZddlm Z m Z ddl m Z m Z mZmZmZddlmZddlmZeejZeejZGd d d ZdS) N) lsq_linear)Models Quadratic)Options Constants)cauchy_geometryspider_geometrynormal_byrd_omojokuntangential_byrd_omojokun$constrained_tangential_byrd_omojokun)qr_tangential_byrd_omojokun)get_arrays_tolc@seZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ e j ddZ eddZ e j ddZ eddZeddZeddZeddZeddZeddZed d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/Zd0d1ZdQd3d4Zd5d6Zd7d8Zd9d:Z d;d<Z!d=d>Z"d?d@Z#dAdBZ$dCdDZ%dRdEdFZ&dGdHZ'dIdJZ(dKdLZ)dMdNZ*dOdPZ+d2S)S TrustRegionz! Trust-region framework. cCsd|_||_t|j||j|_||_d|_|t |j |_ t |j |_ t |j|_t |j|_||j|tj|_|j|_dS)a  Initialize the trust-region framework. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to solve. options : dict Options of the solver. constants : dict Constants of the solver. Raises ------ `cobyqa.utils.MaxEvalError` If the maximum number of evaluations is reached. `cobyqa.utils.TargetSuccess` If a nearly feasible point has been found with an objective function value below the target. `cobyqa.utils.FeasibleSuccess` If a feasible point has been found for a feasibility problem. `numpy.linalg.LinAlgError` If the initial interpolation system is ill-defined. rN)_penalty_pbrpenalty_models _constants _best_indexset_best_indexnpZzeros m_linear_ub _lm_linear_ub m_linear_eq _lm_linear_eqm_nonlinear_ub_lm_nonlinear_ubm_nonlinear_eq_lm_nonlinear_eqset_multipliersx_bestrZRHOBEG _resolution resolution_radius)selfZpboptions constantsr)U/home/kim/smarthome/.venv/lib/python3.10/site-packages/scipy/_lib/cobyqa/framework.py__init__s   zTrustRegion.__init__cC|jjS)zt Number of variables. Returns ------- int Number of variables. )rnr&r)r)r*r-L z TrustRegion.ncCr,)z Number of linear inequality constraints. Returns ------- int Number of linear inequality constraints. )rrr.r)r)r*rXr/zTrustRegion.m_linear_ubcCr,)z Number of linear equality constraints. Returns ------- int Number of linear equality constraints. )rrr.r)r)r*rdr/zTrustRegion.m_linear_eqcCr,)z Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rrr.r)r)r*rpr/zTrustRegion.m_nonlinear_ubcCr,)z Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rrr.r)r)r*r|r/zTrustRegion.m_nonlinear_eqcC|jS)zv Trust-region radius. Returns ------- float Trust-region radius. )r%r.r)r)r*radius zTrustRegion.radiuscCs.||_|j|jtj|jkr|j|_dSdS)z Set the trust-region radius. Parameters ---------- radius : float New trust-region radius. N)r%r1rrZDECREASE_RADIUS_THRESHOLDr$)r&r1r)r)r*r1s   cCr0)z Resolution of the trust-region framework. The resolution is a lower bound on the trust-region radius. Returns ------- float Resolution of the trust-region framework. r#r.r)r)r*r$s zTrustRegion.resolutioncCs ||_dS)z Set the resolution of the trust-region framework. Parameters ---------- resolution : float New resolution of the trust-region framework. Nr3)r&r$r)r)r*r$s cCr0)zr Penalty parameter. Returns ------- float Penalty parameter. )rr.r)r)r*rr2zTrustRegion.penaltycCr0)z Models of the objective function and constraints. Returns ------- `cobyqa.models.Models` Models of the objective function and constraints. )rr.r)r)r*modelsr2zTrustRegion.modelscCr0)z Index of the best interpolation point. Returns ------- int Index of the best interpolation point. )rr.r)r)r* best_indexr2zTrustRegion.best_indexcCs|jj|jS)z Best interpolation point. Its value is interpreted as relative to the origin, not the base point. Returns ------- `numpy.ndarray` Best interpolation point. )r4 interpolationpointr5r.r)r)r*r"s zTrustRegion.x_bestcCs|jj|jS)z Value of the objective function at `x_best`. Returns ------- float Value of the objective function at `x_best`. )r4fun_valr5r.r)r)r*fun_bests zTrustRegion.fun_bestcC|jj|jddfS)z Values of the nonlinear inequality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Values of the nonlinear inequality constraints at `x_best`. N)r4cub_valr5r.r)r)r*cub_best zTrustRegion.cub_bestcCr:)z Values of the nonlinear equality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_best`. N)r4ceq_valr5r.r)r)r*ceq_best r=zTrustRegion.ceq_bestcCsl|j||j|jjj||jjj|j|jjj||jjj |j |j ||j |j |S)a/ Evaluate the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrangian model is evaluated. Returns ------- float Value of the Lagrangian model at `x`. )r4Zfunrrlineara_ubb_ubra_eqb_eqrcubr ceqr&xr)r)r* lag_models zTrustRegion.lag_modelcCsP|j||j|jjj|j|jjj|j|j ||j |j |S)ah Evaluate the gradient of the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the gradient of the Lagrangian model is evaluated. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the Lagrangian model at `x`. ) r4fun_gradrrr@rArrCrcub_gradr ceq_gradrGr)r)r*lag_model_grad.s zTrustRegion.lag_model_gradcCsJ|j}|jdkr||j|j7}|jdkr#||j|j7}|S)z Evaluate the Hessian matrix of the Lagrangian model at a given point. Returns ------- `numpy.ndarray`, shape (n, n) Hessian matrix of the Lagrangian model at `x`. r)r4Zfun_hessrrZcub_hessrr Zceq_hess)r&Zhessr)r)r*lag_model_hessDs  zTrustRegion.lag_model_hesscC0|j||j|j||j|j|S)a Evaluate the right product of the Hessian matrix of the Lagrangian model with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the Lagrangian model is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the Lagrangian model with `v`. )r4Z fun_hess_prodrZ cub_hess_prodr Z ceq_hess_prodr&vr)r)r*lag_model_hess_prodTs zTrustRegion.lag_model_hess_prodcCrO)ar Evaluate the curvature of the Lagrangian model along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the Lagrangian model is evaluated. Returns ------- float Curvature of the Lagrangian model along `v`. )r4Zfun_curvrZcub_curvr Zceq_curvrPr)r)r*lag_model_curvks zTrustRegion.lag_model_curvcCs ||j|jd||S)a} Evaluate the objective function of the SQP subproblem. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the objective function of the SQP subproblem is evaluated. Returns ------- float Value of the objective function of the SQP subproblem along `step`. g?)r4rJr"rRr&stepr)r)r*sqp_funs   zTrustRegion.sqp_funcC |j|j|j|j|S)a Evaluate the linearization of the nonlinear inequality constraints. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the linearization of the nonlinear inequality constraints is evaluated. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Value of the linearization of the nonlinear inequality constraints along `step`. )r4rEr"rKrTr)r)r*sqp_cub zTrustRegion.sqp_cubcCrW)a Evaluate the linearization of the nonlinear equality constraints. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the linearization of the nonlinear equality constraints is evaluated. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Value of the linearization of the nonlinear equality constraints along `step`. )r4rFr"rLrTr)r)r*sqp_ceqrYzTrustRegion.sqp_ceqNcCsp|dus |dus |dur|||j\}}}|}|jdkr6|jj|||d}t|r6||jtj|7}|S)av Evaluate the merit function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the merit function is evaluated. fun_val : float, optional Value of the objective function at `x`. If not provided, the objective function is evaluated at `x`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Values of the nonlinear inequality constraints. If not provided, the nonlinear inequality constraints are evaluated at `x`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Values of the nonlinear equality constraints. If not provided, the nonlinear equality constraints are evaluated at `x`. Returns ------- float Value of the merit function at `x`. Nr)r;r>)rrrZ violationr count_nonzerolinalgnorm)r&rHr8r;r>m_valZc_valr)r)r*merits  zTrustRegion.meritcCst|jjjg|j|gg}t|jjj|jjj||j| g}t|jjj g|j |gg}t|jjj |jjj ||j | g}||||fS)a; Get the linearizations of the constraints at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the linearizations of the constraints are evaluated. Returns ------- `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub, n) Left-hand side matrix of the linearized inequality constraints. `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub,) Right-hand side vector of the linearized inequality constraints. `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq, n) Left-hand side matrix of the linearized equality constraints. `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq,) Right-hand side vector of the linearized equality constraints. ) rblockrr@rAr4rKrBrErCrLrDrF)r&rHaubbubaeqbeqr)r)r*get_constraint_linearizationss*       z)TrustRegion.get_constraint_linearizationsc Cs||j\}}}}|jjj|j}|jjj|j}|jtj|j }t ||||||||t j fi|j} |t j rjt ||} t| | |ksRt|| | krYtdtdtj| d|krjtdtdt|j d| | }|| 8}|| 8}t||| d}|j|j|| } |jjdvrt| |j||||t j fi|j} nt| |j|||||||df i|j} |t j rt ||} t| | |kst|| | krtd tdtj| | dtd|j krtd td| | fS) aK Get the trust-region step. The trust-region step is computed by solving the derivative-free trust-region SQP subproblem using a Byrd-Omojokun composite-step approach. For more details, see Section 5.2.3 of [1]_. Parameters ---------- options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Normal step. `numpy.ndarray`, shape (n,) Tangential step. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. z6the normal step does not respect the bound constraint.皙?z=the normal step does not respect the trust-region constraint.@r)Z unconstrainedzbound-constraineddebugz;The tangential step does not respect the bound constraints.zz/TrustRegion.get_geometry_step..Nrcrxryrzr|r}r)r*r~r)zlinearly constrainedznonlinearly constrainedcss|] }tj|ddVqdS)rinitialN)rmax).0arrayr)r)r* s  z0TrustRegion.get_geometry_step..r$@g{Gz?g?z9The geometry step does not respect the bound constraints.rfrgz?The geometry step does not respect the trust-region constraint.))rrmr5rZsqueezeeyer4nptrr6Zgradr"rrjrkrlrr1 determinantsxptnewaxisr absrtrerr Tr\r]r-TINYr{r`rminZcliprnrorprq)r&Zk_newr'Z coord_vecZg_lagrkrlrUsigmarZstep_altZ sigma_altrarbrcrdZtol_bdZtol_ubZfree_xlZfree_xuZfree_ubZn_actqZ g_lag_projZnorm_g_lag_projZcbdrErFZ maxcv_valrur)r}r*get_geometry_steps    (     . 0  &    (zTrustRegion.get_geometry_stepc Cs||j\}}}}|jjj|j}|jjj|j}tj|} t ||||||| |t j fi|j } |t j rgt ||} t| | |ksOt|| | krVtdtdtj| d| krgtdtd| S)aQ Get the second-order correction step. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Second-order correction step. zHThe second-order correction step does not respect the bound constraints.rfrgzNThe second-order correction step does not respect the trust-region constraint.)rer"rrjrkrlrr\r]r rrmrrrnrorprq) r&rUr'rarbrcrdrkrlr1Zsoc_steprur)r)r* get_second_order_correction_steps>   $z,TrustRegion.get_second_order_correction_stepc Cs||j|j|j|j}||j||||}||jd|j|j|j|j}||j|||| || |}t ||t t ||krV||t ||SdS)a: Get the reduction ratio. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. fun_val : float Objective function value at the trial point. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Nonlinear inequality constraint values at the trial point. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Nonlinear equality constraint values at the trial point. Returns ------- float Reduction ratio. r) r_r"r9r<r?r4rErFrVrXrZrr) r&rUr8r;r>Z merit_oldZ merit_newZmerit_model_oldZmerit_model_newr)r)r*get_reduction_ratioIs4  zTrustRegion.get_reduction_ratioc Cs||j\}}}}ttjttd| |gtjttd||||||gd}||}tjt|j |j |j |j g}t |tt |kr[t|||}|j} |j|jtj|kryt|jtj|d|_|| |jkS)z Increase the penalty parameter. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. r?)rer"rrr\r]r`rsrVrrrr rrr5rrrZPENALTY_INCREASE_THRESHOLDZPENALTY_INCREASE_FACTORr) r&rUrarbrcrdZ viol_diffZsqp_val thresholdZbest_index_saver)r)r*increase_penaltyysV       zTrustRegion.increase_penaltycCst|j||_|dS)z1 Decrease the penalty parameter. N)rr_get_low_penaltyrr.r)r)r*decrease_penaltys zTrustRegion.decrease_penaltyc Cs^|j}||j|jj||jj|ddf|jj|ddf}|j|j|jj|ddf|jj|ddf}dt t |jj |jj t t |d}t|jj D]V}||jkr|jj|}|||jj||jj|ddf|jj|ddf}|j||jj|ddf|jj|ddf}||ks|||kr||kr|}|}|}qS||_dS)z2 Set the index of the best point. Nrr)r5r_r"r4r8r;r>rZmaxcvEPSrr-rrranger6r7r) r&r5Zm_bestZr_bestrukZx_valr^r_valr)r)r*rsP     zTrustRegion.set_best_indexcCstj|jjj|jjjdd|jtjfddd}|dur#d}|}n"|j|}td|t |j t j |j |jdd}d||j<t|t|}|t||fS)a Get the index of the interpolation point to remove. If `x_new` is not provided, the index returned should be used during the geometry-improvement phase. Otherwise, the index returned is the best index for included `x_new` in the interpolation set. Parameters ---------- x_new : `numpy.ndarray`, shape (n,), optional New point to be included in the interpolation set. Returns ------- int Index of the interpolation point to remove. float Distance between `x_best` and the removed point. Raises ------ `numpy.linalg.LinAlgError` If the computation of a determinant fails. NrhrZaxisrg@r)rsumr4r6rr5rrrsrrrZLOW_RADIUS_FACTORr1r$Zargmaxrrr)r&Zx_newZdist_sqrweightsZk_maxr)r)r*get_index_to_removes>    zTrustRegion.get_index_to_removecCstj|}||jtjkr|j|jtj9_dS||jtjkr2t |jtj|j||_dSt |jtj |jt |jtj|j|jtj ||_dS)z Update the trust-region radius. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. ratio : float Reduction ratio. N) rr\r]rrZ LOW_RATIOr1DECREASE_RADIUS_FACTORZ HIGH_RATIOrrZINCREASE_RADIUS_FACTORZINCREASE_RADIUS_THRESHOLD)r&rUratioZs_normr)r)r* update_radiuss.       zTrustRegion.update_radiuscCs|jtj|tj|jkr|j|jtj9_n!|jtj|tj|jkr5t |j|tj|_n|tj|_t |jtj |j |j|_ dS)z Enhance the resolution of the trust-region framework. Parameters ---------- options : dict Options of the solver. N) rrZLARGE_RESOLUTION_THRESHOLDrZRHOENDr$ZDECREASE_RESOLUTION_FACTORZMODERATE_RESOLUTION_THRESHOLDrrrrrr%r&r'r)r)r*enhance_resolution9s*     zTrustRegion.enhance_resolutioncCs|jt|j|dS)z Shift the base point to `x_best`. Parameters ---------- options : dict Options of the solver. N)r4 shift_x_basercopyr"rr)r)r*rZs zTrustRegion.shift_x_basec Cs|jjj||jjjk}|jdk}|jjj|k}|jjj|k}t |}t |}t |}t |} |||j |j dkrt |jj } tj| |ddf | |ddf|jjj|ddf|j|||jjj|j|f} |j|} t| jdtj } d| d|| ||<t| j| | tjfdd}|j|| || ||j|<d|j|<|j|| ||| |||j|<d|j|<|j|| |||| |||j |jdd<|j|| |||j d|jdd<dSdS)aI Set the Lagrange multipliers. This method computes and set the Lagrange multipliers of the linear and nonlinear constraints to be the QP multipliers. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrange multipliers are computed. rrNZbvls)rjmethod)rr@rArBr<rjrkrlrr[rrrr-Zr_r4rKrCrLrJfullshapeinfrrrHrrrr )r&rHZincl_linear_ubZincl_nonlinear_ubZincl_xlZincl_xurrZm_xlZm_xuidentityZc_jacrvZxl_lmresr)r)r*r!es            zTrustRegion.set_multipliersc Csttj|jjjtjddf|jjjj|jj j j|jj j tjddf|jj f}|jjjtjddf|jjjj|jj j j|jj jtjddf}t|| |jj|jj g}t||g}tj|dd}tj|dd}||jtj|k}t|rt|jj}t|jj}td||} t||| } | t||kr||| } | Stj} | Sd} | S)Nrrr)rZc_r4r6Zx_baserrrrr@rArBr;rCrDr`r>ZnanminZnanmaxrrZTHRESHOLD_RATIO_CONSTRAINTSrnr8minimumrrr) r&Zr_val_ubZr_val_eqrZc_minZc_maxindicesZf_minZf_maxZ c_min_negZc_diffrr)r)r*rsX      zTrustRegion._get_low_penalty)NNNry),__name__ __module__ __qualname____doc__r+propertyr-rrrrr1setterr$rr4r5r"r9r<r?rIrMrNrRrSrVrXrZr_rerwrrrrrrrrrrr!rr)r)r)r*rsv0                   .t208 *7 ! Kr)ronumpyrZscipy.optimizerr4rrsettingsrrZ subsolversrr r r r Zsubsolvers.optimr utilsrZfinfofloatZtinyrepsrrr)r)r)r*s