o  h@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_indexnpzeros m_linear_ub _lm_linear_ub m_linear_eq _lm_linear_eqm_nonlinear_ub_lm_nonlinear_ubm_nonlinear_eq_lm_nonlinear_eqset_multipliersx_bestrRHOBEG _resolution resolution_radius)selfpboptions constantsr,O/var/www/vscode/kcb/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-r0L z TrustRegion.ncCr/)z Number of linear inequality constraints. Returns ------- int Number of linear inequality constraints. )rrr1r,r,r-rXr2zTrustRegion.m_linear_ubcCr/)z Number of linear equality constraints. Returns ------- int Number of linear equality constraints. )rrr1r,r,r-rdr2zTrustRegion.m_linear_eqcCr/)z Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rrr1r,r,r-rpr2zTrustRegion.m_nonlinear_ubcCr/)z Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rr r1r,r,r-r |r2zTrustRegion.m_nonlinear_eqcC|jS)zv Trust-region radius. Returns ------- float Trust-region radius. )r'r1r,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'r4rrDECREASE_RADIUS_THRESHOLDr&)r(r4r,r,r-r4s   cCr3)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%r1r,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. Nr7)r(r&r,r,r-r&s cCr3)zr Penalty parameter. Returns ------- float Penalty parameter. )rr1r,r,r-rr5zTrustRegion.penaltycCr3)z Models of the objective function and constraints. Returns ------- `cobyqa.models.Models` Models of the objective function and constraints. )rr1r,r,r-modelsr5zTrustRegion.modelscCr3)z Index of the best interpolation point. Returns ------- int Index of the best interpolation point. )rr1r,r,r- best_indexr5zTrustRegion.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. )r8 interpolationpointr9r1r,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`. )r8fun_valr9r1r,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)r8cub_valr9r1r,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)r8ceq_valr9r1r,r,r-ceq_best rAzTrustRegion.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`. )r8funrrlineara_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`. ) r8fun_gradrrrErFrrHrcub_gradr!ceq_gradrLr,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)r8fun_hessrrcub_hessr r!ceq_hess)r(hessr,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`. )r8 fun_hess_prodr cub_hess_prodr! ceq_hess_prodr(vr,r,r-lag_model_hess_prodTs zTrustRegion.lag_model_hess_prodcCrX)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`. )r8fun_curvrcub_curvr!ceq_curvr\r,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?)r8rOr#r^r(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`. )r8rJr#rPrcr,r,r-sqp_cub zTrustRegion.sqp_cubcCrf)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`. )r8rKr#rQrcr,r,r-sqp_ceqrhzTrustRegion.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?rB)rrr violationr count_nonzerolinalgnorm)r(rMr<r?rBm_valc_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. ) rblockrrErFr8rPrGrJrHrQrIrK)r(rMaubbubaeqbeqr,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) unconstrainedzbound-constraineddebugz;The tangential step does not respect the bound constraints.zz/TrustRegion.get_geometry_step..Nrcrrrrrr,r-rr)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.rwrxz?The geometry step does not respect the trust-region constraint.))rrr9rsqueezeeyer8nptrr:gradr#rr|r}r~rr4 determinantsxptnewaxisr absrrvrr Trlrmr0TINYrrqrmincliprrrr)r(k_newr* coord_vecg_lagr}r~rdsigmarstep_alt sigma_altrrrsrtrutol_bdtol_ubfree_xlfree_xufree_ubn_actq g_lag_projnorm_g_lag_projcbdrJrK maxcv_valrr,rr-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.rwrxzNThe second-order correction step does not respect the trust-region constraint.)rvr#rr|r}r~rrlrmr rrrrrrrr) r(rdr*rrrsrtrur}r~r4soc_steprr,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) rpr#r=r@rCr8rJrKrergrirr) r(rdr<r?rB merit_old merit_newmerit_model_oldmerit_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?)rvr#rrrlrmrqrrerrrr!rrr9rrrPENALTY_INCREASE_THRESHOLDPENALTY_INCREASE_FACTORr) r(rdrrrsrtru viol_diffsqp_val thresholdbest_index_saver,r,r-increase_penaltyysV       zTrustRegion.increase_penaltycCst|j||_|dS)z1 Decrease the penalty parameter. N)rr_get_low_penaltyrr1r,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)r9rpr#r8r<r?rBrmaxcvEPSrr0rrranger:r;r) r(r9m_bestr_bestrkx_valrnr_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. Nryraxisrg@r)rsumr8r:rr9rrrrrrLOW_RADIUS_FACTORr4r&argmaxrr)r(x_newdist_sqrweightsk_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) rrlrmrr LOW_RATIOr4DECREASE_RADIUS_FACTOR HIGH_RATIOrrINCREASE_RADIUS_FACTORINCREASE_RADIUS_THRESHOLD)r(rdratios_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) rrLARGE_RESOLUTION_THRESHOLDrRHOENDr&DECREASE_RESOLUTION_FACTORMODERATE_RESOLUTION_THRESHOLDrrrrr'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)r8 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. rrNbvls)r|method)rrErFrGr@r|r}r~rrkrr rr0r_r8rPrHrQrOfullshapeinfrrrMrrrr!)r(rMincl_linear_ubincl_nonlinear_ubincl_xlincl_xurrm_xlm_xuidentityc_jacrxl_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)rc_r8r:x_baserrrrrErFrGr?rHrIrqrBnanminnanmaxrrTHRESHOLD_RATIO_CONSTRAINTSrr<minimumrrr) r(r_val_ubr_val_eqrc_minc_maxindicesf_minf_max c_min_negc_diffrr,r,r-rsX      zTrustRegion._get_low_penalty)NNNr),__name__ __module__ __qualname____doc__r.propertyr0rrrr r4setterr&rr8r9r#r=r@rCrNrRrWr^rbrergrirprvrrrrrrrrrrrr"rr,r,r,r-rsv0                   .t208 *7 ! Kr)rnumpyrscipy.optimizerr8rrsettingsrr subsolversrr r r r subsolvers.optimr utilsrfinfofloattinyrepsrrr,r,r,r-s