package scipy

Interface for implementing Hessian update strategies.

Many optimization methods make use of Hessian (or inverse Hessian) approximations, such as the quasi-Newton methods BFGS, SR1, L-BFGS. Some of these approximations, however, do not actually need to store the entire matrix or can compute the internal matrix product with a given vector in a very efficiently manner. This class serves as an abstract interface between the optimization algorithm and the quasi-Newton update strategies, giving freedom of implementation to store and update the internal matrix as efficiently as possible. Different choices of initialization and update procedure will result in different quasi-Newton strategies.

Four methods should be implemented in derived classes: ``initialize``, ``update``, ``dot`` and ``get_matrix``.

Notes ----- Any instance of a class that implements this interface, can be accepted by the method ``minimize`` and used by the compatible solvers to approximate the Hessian (or inverse Hessian) used by the optimization algorithms.

Compute the product of the internal matrix with the given vector.

Parameters ---------- p : array_like 1-d array representing a vector.

Returns ------- Hp : array 1-d represents the result of multiplying the approximation matrix by vector p.

Return current internal matrix.

Returns ------- H : ndarray, shape (n, n) Dense matrix containing either the Hessian or its inverse (depending on how 'approx_type' is defined).

Initialize internal matrix.

Allocate internal memory for storing and updating the Hessian or its inverse.

Parameters ---------- n : int Problem dimension. approx_type : 'hess', 'inv_hess' Selects either the Hessian or the inverse Hessian. When set to 'hess' the Hessian will be stored and updated. When set to 'inv_hess' its inverse will be used instead.

Update internal matrix.

Update Hessian matrix or its inverse (depending on how 'approx_type' is defined) using information about the last evaluated points.

Parameters ---------- delta_x : ndarray The difference between two points the gradient function have been evaluated at: ``delta_x = x2 - x1``. delta_grad : ndarray The difference between the gradients: ``delta_grad = grad(x2) - grad(x1)``.

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.