o Eb%@sFdZddlZddlZddlmZmZgZd ddZ Gdd d eZ dS) z"Dog-leg trust-region optimization.N)_minimize_trust_regionBaseQuadraticSubproblemcKs<|durtdt|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)argsjachessZ subproblem) ValueErrorcallablerDoglegSubproblem)ZfunZx0rrrZtrust_region_optionsrrD/usr/lib/python3/dist-packages/scipy/optimize/_trustregion_dogleg.py_minimize_dogleg sr c@s(eZdZdZddZddZddZdS) 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)Z _cauchy_pointrZhesspnpdot)selfgZBgrrr 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)Z _newton_pointrrscipylinalgZ cho_factorZ cho_solve)rrBZcho_inforrr newton_point3s  zDoglegSubproblem.newton_pointc Cs|}tj||krd}||fS|}tj|}||kr,|||}d}||fS|||||\}}||||}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)rrrZnormrZget_boundaries_intersections) rZ trust_radiusZp_bestZ hits_boundaryZp_uZp_u_normZ p_boundary_tbrrr solve>s "   zDoglegSubproblem.solveN)__name__ __module__ __qualname____doc__rrrrrrr r &s  r )rNN) rZnumpyrZ scipy.linalgrZ _trustregionrr__all__r r rrrr s