U Gv f%ã@sFdZddlZddlZddlmZmZgZd dd„Z Gdd „d eƒZ dS) z"Dog-leg trust-region optimization.éNé)Ú_minimize_trust_regionÚBaseQuadraticSubproblem©cKs<|dkrtdƒ‚t|ƒs tdƒ‚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)ÚargsÚjacÚhessZ subproblem)Ú ValueErrorÚcallablerÚDoglegSubproblem)ZfunZx0rrrZtrust_region_optionsrrúF/tmp/pip-unpacked-wheel-96ln3f52/scipy/optimize/_trustregion_dogleg.pyÚ_minimize_dogleg sÿþr c@s(eZdZdZdd„Zdd„Zdd„ZdS) r z0Quadratic subproblem solved by the dogleg methodcCs@|jdkr:|j}| |¡}t ||¡t ||¡ ||_|jS)zV The Cauchy point is minimal along the direction of steepest descent. N)Z _cauchy_pointrZhesspÚnpÚdot)ÚselfÚgZBgrrr Ú cauchy_point)s    zDoglegSubproblem.cauchy_pointcCs:|jdkr4|j}|j}tj |¡}tj ||¡ |_|jS)zS The Newton point is a global minimum of the approximate function. N)Z _newton_pointrrÚscipyÚlinalgZ cho_factorZ cho_solve)rrÚBZcho_inforrr Ú newton_point3s   zDoglegSubproblem.newton_pointc CsŠ| ¡}tj |¡|kr$d}||fS| ¡}tj |¡}||krX|||}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)rrrZnormrZget_boundaries_intersections) rZ trust_radiusZp_bestZ hits_boundaryZp_uZp_u_normZ p_boundaryÚ_Útbrrr Úsolve>s "   ÿzDoglegSubproblem.solveN)Ú__name__Ú __module__Ú __qualname__Ú__doc__rrrrrrr r &s  r )rNN) rZnumpyrZ scipy.linalgrZ _trustregionrrÚ__all__r r rrrr Ús