__init__(self, func, jacobian, hessian=None, spring_constants=0.1, distance_function=None, step_finder='gradient-descent', logger=None, **opts): 

LLM Docstring

Initialize a nudged-elastic-band (NEB) step finder with spring couplings between neighbouring images.

• func: Callable

  the per-image objective

• jacobian: Callable

  the per-image gradient

• hessian: Callable | None

  the per-image Hessian

• spring_constants: float | np.ndarray

  spring constant(s) between images

• distance_function: Callable | None

  optional custom inter-image distance

• step_finder: str

  the base per-image method

• logger: object | None

  optional logger

• opts: Any

  extra options for the base step finder

get_dist(self, p1, p2): 

LLM Docstring

Return the Euclidean distance between two image geometries.

• p1: np.ndarray

  the first geometry

• p2: np.ndarray

  the second geometry

• :returns: np.ndarray

  the distance

get_tangent(self, guess, mask, cur, prev, next): 

LLM Docstring

Compute the (normalized) NEB path tangent at an image, using the energy-weighted tangent scheme based on the neighbouring image energies.

• guess: np.ndarray

  the full chain

• mask: np.ndarray

  active-member indices

• cur: int

  current image index

• prev: int

  previous image index

• next: int

  next image index

• :returns: np.ndarray

  the unit path tangent

adjust_jacobian(self, jac, guess, mask, cur, prev, next): 

LLM Docstring

Project the tangential component out of the per-image gradient (the NEB nudging), caching the current path tangent.

• jac: np.ndarray

  the base gradient

• guess: np.ndarray

  the full chain

• mask: np.ndarray

  active-member indices

• cur: int

  current image index

• prev: int | None

  previous image index

• next: int | None

  next image index

• :returns: np.ndarray

  the nudged gradient

climbing_node_step(self, guess, mask, gradient_modifer=None, projector=None): 

LLM Docstring

Take a climbing-image step: invert the tangential force component so the image climbs toward the saddle along the path.

• guess: np.ndarray

  the climbing-image parameters

• mask: np.ndarray

  active-member indices

• gradient_modifer: Callable | None

  optional gradient transformation

• projector: np.ndarray | None

  optional projector

• :returns: tuple

  (step, gradient)

image_pairwise_contribution(self, guess, mask, cur, prev, next, order=0): 

LLM Docstring

Compute the NEB spring contribution to the objective/gradient/Hessian from the difference of the distances to the two neighbouring images.

• guess: np.ndarray

  the full chain

• mask: np.ndarray

  active-member indices

• cur: int

  current image index

• prev: int | None

  previous image index

• next: int | None

  next image index

• order: int

  derivative order (0=value, 1=gradient, 2=Hessian)

• :returns: np.ndarray | int

  the spring contribution