o `^h%ã@sFdZddlZddlZddlmZmZgZd dd„Z Gdd „d eƒZ dS) z"Dog-leg trust-region optimization.éNé)Ú_minimize_trust_regionÚBaseQuadraticSubproblem©cKs<|durtdƒ‚t|ƒstdƒ‚t||f|||tdœ|¤ŽS)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)ÚargsÚjacÚhessÚ subproblem)Ú ValueErrorÚcallablerÚDoglegSubproblem)ÚfunÚx0rrrÚtrust_region_optionsrrú`/home/air/shanriGPT/back/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_dogleg.pyÚ_minimize_dogleg sÿþrc@s(eZdZdZdd„Zdd„Zdd„ZdS) r z0Quadratic subproblem solved by the dogleg methodcCs@|jdur|j}| |¡}t ||¡t ||¡ ||_|jS)zV The Cauchy point is minimal along the direction of steepest descent. N)Ú _cauchy_pointrÚhesspÚnpÚdot)ÚselfÚgÚBgrrrÚ cauchy_point)s   zDoglegSubproblem.cauchy_pointcCs:|jdur|j}|j}tj |¡}tj ||¡ |_|jS)zS The Newton point is a global minimum of the approximate function. N)Ú _newton_pointrrÚscipyÚlinalgÚ cho_factorÚ cho_solve)rrÚBÚcho_inforrrÚ newton_point3s  zDoglegSubproblem.newton_pointc CsŠ| ¡}tj |¡|krd}||fS| ¡}tj |¡}||kr,|||}d}||fS| ||||¡\}}||||}d}||fS)aŒ 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!rrÚnormrÚget_boundaries_intersections) rÚ trust_radiusÚp_bestÚ hits_boundaryÚp_uÚp_u_normÚ p_boundaryÚ_ÚtbrrrÚsolve>s "   ÿzDoglegSubproblem.solveN)Ú__name__Ú __module__Ú __qualname__Ú__doc__rr!r,rrrrr &s  r )rNN) r0ÚnumpyrÚ scipy.linalgrÚ _trustregionrrÚ__all__rr rrrrÚs