^Mh%RdZddlZddlZddlmZmZgZd dZ GddeZ dS) z"Dog-leg trust-region optimization.N)_minimize_trust_regionBaseQuadraticSubproblemc |tdt|stdt||f|||td|S)a  Minimization of scalar function of one or more variables using the dog-leg trust-region algorithm. Options ------- initial_trust_radius : float Initial trust-region radius. max_trust_radius : float Maximum value of the trust-region radius. No steps that are longer than this value will be proposed. eta : float Trust region related acceptance stringency for proposed steps. gtol : float Gradient norm must be less than `gtol` before successful termination. Nz,Jacobian is required for dogleg minimizationz+Hessian is required for dogleg minimization)argsjachess subproblem) ValueErrorcallablerDoglegSubproblem)funx0rr r trust_region_optionss b/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/optimize/_trustregion_dogleg.py_minimize_doglegr sg( {GHHH D>>HFGGG !#r :#D-= : :$8 : ::c$eZdZdZdZdZdZdS)rz0Quadratic subproblem solved by the dogleg methodc|jP|j}||}tj||tj||z |z|_|jS)zV The Cauchy point is minimal along the direction of steepest descent. ) _cauchy_pointr hesspnpdot)selfgBgs r cauchy_pointzDoglegSubproblem.cauchy_point)sU   %AAB#%6!Q<<"&B--#?!@1!DD !!rc|jS|j}|j}tj|}tj|| |_|jS)zS The Newton point is a global minimum of the approximate function. ) _newton_pointr r scipylinalg cho_factor cho_solve)rrBcho_infos r newton_pointzDoglegSubproblem.newton_point3sV   %A A|..q11H"',"8"81"E"E!ED !!rcf|}tj||krd}||fS|}tj|}||kr|||z z}d}||fS||||z |\}}||||z zz}d}||fS)a Minimize a function using the dog-leg trust-region algorithm. This algorithm requires function values and first and second derivatives. It also performs a costly Hessian decomposition for most iterations, and the Hessian is required to be positive definite. Parameters ---------- trust_radius : float We are allowed to wander only this far away from the origin. Returns ------- p : ndarray The proposed step. hits_boundary : bool True if the proposed step is on the boundary of the trust region. Notes ----- The Hessian is required to be positive definite. References ---------- .. [1] Jorge Nocedal and Stephen Wright, Numerical Optimization, second edition, Springer-Verlag, 2006, page 73. FT)r'r!r"normrget_boundaries_intersections) r trust_radiusp_best hits_boundaryp_up_u_norm p_boundary_tbs rsolvezDoglegSubproblem.solve>sD""$$ <  V $ $| 3 3!M=( (!!<$$S)) | # # x 78J M}, ,11#v|2>@@22#..  =((rN)__name__ __module__ __qualname____doc__rr'r3rrrrr&sG::""" " " "<)<)<)<)<)rr)rNN) r7numpyr scipy.linalgr! _trustregionrr__all__rrrrrr<s((KKKKKKKK :::::T)T)T)T)T).T)T)T)T)T)r