ExternalField::AndersonHistory

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Anderson mixing history of a fixed-point iteration x -> G(x) on spinors, as used by the mixed-state solvers.

Holds the map outputs \( g_k = G(x_k) \), the residuals \( r_k = g_k - x_k \) and their Gram matrix, and a scalar carried with each entry (an amplitude linear in the state, mixed with the same coefficients; zero if unused). The Gram matrix is kept incrementally: a new entry costs one inner product per kept entry, not a rebuild of the whole matrix. At most depth entries are kept: the oldest is dropped when the history is full, and (see anderson_coefficients) while the Gram matrix is ill-conditioned.

#include <Anderson.hpp>

Public Member Functions
	AndersonHistory (std::size_t depth)
void	push (DiracSpinor g, DiracSpinor r, double r2, double k=0.0)
	Adds the entry (g, r), with |r|^2 = r2 (which the caller has from its convergence test) and the carried scalar k; drops the oldest entry if the history is full.
void	mix (DiracSpinor *x, double *k=nullptr)
	The Anderson extrapolation over the kept entries, x = sum_k c_k g_k and (if k is non-null) k = sum_k c_k k_k, with the coefficients of anderson_coefficients; entries that had to be dropped for conditioning are dropped from the history too.
std::size_t	size () const
	Number of kept entries.

Member Function Documentation

push()

void ExternalField::AndersonHistory::push	(	DiracSpinor	g,
		DiracSpinor	r,
		double	r2,
		double	k = 0.0
	)

Adds the entry (g, r), with |r|^2 = r2 (which the caller has from its convergence test) and the carried scalar k; drops the oldest entry if the history is full.

mix()

void ExternalField::AndersonHistory::mix	(	DiracSpinor *	x,
		double *	k = nullptr
	)

The Anderson extrapolation over the kept entries, x = sum_k c_k g_k and (if k is non-null) k = sum_k c_k k_k, with the coefficients of anderson_coefficients; entries that had to be dropped for conditioning are dropped from the history too.

If no entry is usable (the coefficients could not be solved for), x is the plain step: the latest map output, and the history is cleared.

size()

std::size_t ExternalField::AndersonHistory::size ( ) const

inline

Number of kept entries.

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The documentation for this class was generated from the following files:

• ExternalField/Anderson.hpp
• ExternalField/Anderson.cpp