+ /i]7l^RIt^RIt^RIHt]P !]4PtRt Rt Rt R#)N)get_arrays_tolc aV'Ed\V\4'gQh\V\P4'dVP^8XgQh\ P !S4PV4'gQh\V\P4'dVPVP8XgQh\V\P4'dVPVP8XgQh\V\4'gQh\V\4'gQh\W44p\P!W78*4'gQh\P!WG)84'gQh\P!V4'dVR8gQh\P!VR4p\P!VR4p\WSW4WV4wr\V)V)V3RlVVVV4wr\!V 4\!V 48dTMT p V'dn\P!W<8*4'gQh\P!W8*4'gQh\P"P%V 4RV,8gQhV #)ao Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region. This function solves approximately .. math:: \max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ \lVert s \rVert \le \Delta, \end{array} \right. by maximizing the objective function along the constrained Cauchy direction. Parameters ---------- const : float Constant :math:`c` as shown above. grad : `numpy.ndarray`, shape (n,) Gradient :math:`g` as shown above. curv : callable Curvature of :math:`H` along any vector. ``curv(s) -> float`` returns :math:`s^{\mathsf{T}} H s`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Notes ----- This function is described as the first alternative in Section 6.5 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. 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. c<S!V4)#)N)xcurvs&c/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.py!cauchy_geometry..[s 47(皙?) isinstancefloatnpndarrayndiminspect signaturebindshapeboolrallisfiniteminimummaximum _cauchy_geomabslinalgnorm) constgradr xlxudeltadebugtolstep1q_val1step2q_val2steps &&f&&&& r cauchy_geometryr- st u%''''$ ++ Q>>  &++D1111"bjj))bhh$**.DDD"bjj))bhh$**.DDD%''''%&&&&R$vvbi    vvbDj!!!!{{5!!eck11 B B B B !dBEIME      MEK3v;.5ED vvbj!!!!vvdj!!!!yy~~d#cEk111 Kr cvV'Ed\V\4'gQh\V\P4'dVP^8XgQh\ P !V4PV4'gQh\V\P4'd4VP^8Xd#VP^,VP8XgQh\V\P4'dVPVP8XgQh\V\P4'dVPVP8XgQh\V\4'gQh\V\4'gQh\WE4p\P!WH8*4'gQh\P!WX)84'gQh\P!V4'dVR8gQh\P!VR4p\P!VR4p\P !V4p Tp \P"P%V^R7p V\P&)8VP(\*)V,8,p V\P&)8VP(\*V,8,p V\P&8VP(\*V,8,pV\P&8VP(\*)V,8,p\P,!\P.!WLP4V ,VP(V ,, 4p\P0!V^\P&)R7p\P.!\P2!V4VP^,4p\P,!\P.!WMP4V ,VP(V ,, 4p\P0!V^\P&R7p\P.!\P2!V4VP^,4p\P,!\P.!W_P4V,VP(V,, 4p\P0!V^\P&)R7p\P.!\P2!V4VP^,4p\P,!\P.!W^P4V,VP(V,, 4p\P0!V^\P&R7p\P.!\P2!V4VP^,4p\5VP^,4EF$pV V,\*V,8d\1WkV,, R4pMK9\1\7VV,VV,4R4p\7\1VV,VV,4R4pWRV3,,pV!VRV3,4pVR8dV\*)V,8gVR8:d)V\*)V,8d\1V)V, R4pM\P&pVR8dV\*V,8gVR8:d(V\*V,8d\7V)V, R4pM\P&)p\7VV4p\1V)V4pVVV,,RVR,,V,,pVVV,,RVR,,V,,pVV8dJVVV,,RVR,,V,,p \9V 4\9V48dTpT pVV8dJVVV,,RVR,,V,,p!\9V!4\9V48dTpT!p\9V4\9V48dF\9V4\9V 48d-\P:!VVRV3,,WE4p Tp EK\9V4\9V48gEK\9V4\9V 48gEK\P:!VVRV3,,WE4p Tp EK' V'dn\P!WI8*4'gQh\P!W8*4'gQh\P"P%V 4RV,8gQhV #)a Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region. This function solves approximately .. math:: \max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ \lVert s \rVert \le \Delta, \end{array} \right. by maximizing the objective function along given straight lines. Parameters ---------- const : float Constant :math:`c` as shown above. grad : `numpy.ndarray`, shape (n,) Gradient :math:`g` as shown above. curv : callable Curvature of :math:`H` along any vector. ``curv(s) -> float`` returns :math:`s^{\mathsf{T}} H s`. xpt : `numpy.ndarray`, shape (n, npt) Points defining the straight lines. The straight lines considered are the ones passing through the origin and the points in `xpt`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Notes ----- This function is described as the second alternative in Section 6.5 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. 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. r)axis)r/initial:NNN?@r)rrrrrrrrrsizerrrrrr zeros_likerr infTTINY atleast_2d broadcast_tomax atleast_1drangeminrclip)"r!r"r xptr#r$r%r&r'r,q_vals_normi_xl_posi_xl_negi_xu_posi_xu_neg alpha_xl_pos alpha_xl_neg alpha_xu_neg alpha_xu_poskalpha_tr alpha_bd_pos alpha_bd_neg grad_step curv_stepalpha_quad_posalpha_quad_neg alpha_pos alpha_neg q_val_pos q_val_negq_val_quad_posq_val_quad_negs"&&&&&&&& r spider_geometryrXjsx u%''''$ ++ Q>>  &++D1111 sBJJ ' 'A  !  )  *"bjj))bhh$**.DDD"bjj))bhh$**.DDD%''''%&&&&R$vvbi    vvbDj!!!!{{5!!eck11 B B B B == D E YY^^Ca^ (FbffW $!34HbffW !23HRVV r 12HRVV  23H== NN+H5hGL66,Q@L??2==#> ! ML== NN+H5hGL66,Q?L??2==#> ! ML== NN+H5hGL66,Q@L??2==#> ! ML== NN+H5hGL66,Q?L??2==#> ! ML 399Q<  !9te| #5!9,c2H 3|A Q@#F 3|A Q@#F q!t9$ QTO  TEI--CTEI-- )i!7=NVVN  D9,,CD9,, )i!7=N ffWN,/  <0 I ) )C)S.,@9,L L  I ) )C)S.,@9,L L  I % 9,-++i78  >"S^3* * I % 9,-++i78  >"S^3* * y>S^ +IU0K779s1a4y0"9DE ^c)n ,Y#e*1L779s1a4y0"9DEU!X vvbj!!!!vvdj!!!!yy~~d#cEk111 Kr cVR8VR8,pVR8VR8,p\P!V4p W7,W&WH,W&\PPV 4V8EdWx,p \PPW,4p \P!VR,W(,W(,,, 4p V \ \ V 4,8d\W, R4p MMWV ,,W&WV8,pWV8,p\P!V4'g\P!V4'gM'W7,W&WH,W&WV,(,p EKW,pVR8Ed\PPV 4pV\ V,8d\W_, R4pMRpV!V 4pV\ )V,8d\V)V, R4pM\PpV\P)8V \ V,8,pV\P8V \ V,8,p\P!VV,V V,, \PR7p\P!VV,V V,, \PR7p\VV4p\VVV4p\P!VV ,W44pVVV,,RVR,,V,,pM\P!V4pTpV'dp\P!VV8*4'gQh\P!VV8*4'gQh\PPV4RV,8gQhVV3#)zE Same as `bound_constrained_cauchy_step` without the absolute value. rr2)r0r1r) rr4rr sqrtr7rr:anyr5r=r>r)r!r"r r#r$r%r&fixed_xlfixed_xu cauchy_stepworkingg_norm delta_reducedmurNrArKrO alpha_quadi_xli_xualpha_xlalpha_xualpha_bdalphar,r@s&&&&&&& r rr8s STCZ(HSTCZ(H--%KLKLK yy~~k"U*%YY^^DM2FGGs [2[5JJJMs=111/5#%W #5K "23H"23H66(##BFF8,<,<$&LK !$&LK !X"5 66G"IC , D5L 5>3/HH% uy( (iZ)3S9JJbffW tby!89RVV dRi 7866"T([%66G66"T([%66Gx*Hj(3wwu{*B3 ))C%*,rns7" xx\~K\Kr