o i]7@sDddlZddlZddlmZeejZddZ ddZ dd Z dS) N)get_arrays_tolc s|rmt|ts Jt|tjr|jdksJt|s Jt|tjr,|j|jks.Jt|tjr:|j|jks 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. cs | S)N)xcurvr_/home/kim/smarthome/.venv/lib/python3.10/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.py[s z!cauchy_geometry..皙?) isinstancefloatnpndarrayndiminspect signaturebindshapeboolrallisfiniteminimummaximum _cauchy_geomabslinalgnorm) constgradr xlxudeltadebugtolZstep1Zq_val1Zstep2Zq_val2steprrr cauchy_geometry s<:     r'c"Cs|rt|ts Jt|tjr|jdksJt||s Jt|tjr3|jdkr3|jd|j ks5Jt|tjrA|j|jksCJt|tjrO|j|jksQJt|tsXJt|t s_Jt ||}t ||ksmJt || kswJt |r|dksJt|d}t|d}t|} |} tjj|dd} |tj k|jt |k@} |tj k|jt|k@} |tjk|jt|k@}|tjk|jt |k@}tt|| j| |j| }tj|dtj d}tt||jd}tt|| j| |j| }tj|dtjd}tt||jd}tt||j||j|}tj|dtj d}tt||jd}tt||j||j|}tj|dtjd}tt||jd}t|jdD]>}| |t|krt|| |d}nqrtt||||d}tt||||d}||dd|f}||dd|f}|dkr|t |ks|dkr|t |krt| |d}ntj}|dkr|t|ks|dkr|t|krt| |d}ntj }t||}t| |}|||d|d |}|||d|d |}||krH|||d|d |} t| t|krH|}| }||krh|||d|d |}!t|!t|krh|}|!}t|t|krt|t| krt||dd|f||} |} qrt|t|krt|t| krt||dd|f||} |} qr|rt || ksJt | |ksJtj| d |ksJ| S) 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. rrrr)axis)r(initialN?@r )r rrrrrrrrsizerrrrrr zeros_likerrinfTTINYZ atleast_2dZ broadcast_tomaxZ atleast_1drangeminrclip)"rr r Zxptr!r"r#r$r%r&q_vals_normZi_xl_posZi_xl_negZi_xu_posZi_xu_negZ alpha_xl_posZ alpha_xl_negZ alpha_xu_negZ alpha_xu_poskalpha_trZ alpha_bd_posZ alpha_bd_neg grad_step curv_stepZalpha_quad_posZalpha_quad_negZ alpha_posZ alpha_negZ q_val_posZ q_val_negZq_val_quad_posZq_val_quad_negrrr spider_geometryjs<             $$r;cCs|dk|dk@}|dk|dk@}t|} ||| |<||| |<tj| |kr||B} tj|| } t|d| | | | } | tt| krWt| | d} nn3| || | | <| | |k@}| | |k@}t|swt|swn||| |<||| |<| ||B@} q.|| }|dkrtj| }|t|krt||d}nd}|| }|t |krt| |d}ntj }|tj k| t|k@}|tj k| t|k@}tj ||| |tj d}tj ||| |tj d}t ||}t |||}t || ||}|||d|d|}nt|}|}|rBt ||ks+Jt ||ks5Jtj|d|ksBJ||fS)zM Same as `bound_constrained_cauchy_step` without the absolute value. rTr+)r)r*r ) rr-rrsqrtr0rr1anyr.r3r4r)rr r r!r"r#r$Zfixed_xlZfixed_xuZ cauchy_stepZworkingZg_normZ delta_reducedmur9r6r8r:Z alpha_quadZi_xlZi_xuZalpha_xlZalpha_xuZalpha_bdalphar&r5rrr r8sb             r) rnumpyrutilsrZfinforZtinyr0r'r;rrrrr s  _ O