risb.optimize.solver_newton module¶

Abstract base class for quasi-Newton methods.

class risb.optimize.solver_newton.NewtonSolver(history_size=6, n_restart=inf)[source]¶

Bases: ABC

Base class for quasi-Newton methods to find the root of a function.

Parameters:

history_size (int, optional) – Maximum size of subspace.
n_restart (int, optional) – Fully reset subspace after this many iterations.

Notes

update_x() must be defined in the inherited class.

error¶

History of error vector of x.

g_x¶

History of fixed point function with x as the input.

Iteration counter for solver.

solve(fun, x0, args=(), tol=1e-12, maxiter=1000, options=None)[source]¶

Find the root of a function. It is called similarly to :func:scipy.optimize.root.

Parameters:

fun (callable) – The function to find the root of. It must be callable as fun(x, *args).
x0 (numpy.ndarray) – Initial guess of the parameters. This does not neccessarily have to be flattened, but it usually is.
args (tuple, optional) – Additional arguments to pass to fun.
tol (float, optional) – The tolerance. When the 2-norm difference of the return of fun is less than this, the solver stops.
maxiter (int, optional) – Maximum number of iterations.
options (dict, optional) – keyword arguments to pass to update_x().

Returns:

Root of fun.

Return type:

numpy.ndarray

success¶

Whether the solver converged to within tolerance.

abstract update_x(**kwargs)[source]¶

Return a single iteration for the new guess for x.

Parameters:: **kwargs (dict) – Keyword arguments specific to the solver implementation.
Returns:: New guess for x to add to history.
Return type:: numpy.ndarray

History of guesses to the root problem.