occ::qm::CoulombMetric Class Reference

Factorization of a density-fitting Coulomb metric V = (P|Q). More...

#include <coulomb_metric.h>

Public Member Functions
void	compute (const Mat &V, double lindep=1e-12)
	Factorize V. lindep is relative to the largest eigenvalue.
bool	uses_cholesky () const
Eigen::Index	num_discarded () const
bool	initialized () const
template<typename Derived >
Mat	solve (const Eigen::MatrixBase< Derived > &b) const
	V^-1 b.
template<typename Derived >
Mat	half_inverse_apply (const Eigen::MatrixBase< Derived > &b) const
	L^-1 b, where L L^T = V (or its eigen equivalent U diag(w)^-1/2): the half-inverse that turns 3-centre integrals into DF B tensors.

Detailed Description

Factorization of a density-fitting Coulomb metric V = (P|Q).

Cholesky whenever V is numerically positive definite, otherwise a symmetric eigendecomposition with the near-null space discarded. Two situations need the second path, and both otherwise fail badly:

• an auxiliary basis that is close to linearly dependent for the given geometry (Eigen's LLT then reports failure, and solving with the failed factorization returns garbage);
• the long-range metric (P|erf(omega r)/r|Q) of a range-separated hybrid, whose attenuated kernel damps the high-exponent auxiliary functions so hard that a JK-fitting basis is near-singular under it.

Member Function Documentation

compute()

void occ::qm::CoulombMetric::compute	(	const Mat &	V,
		double	lindep = 1e-12
	)

Factorize V. lindep is relative to the largest eigenvalue.

half_inverse_apply()

template<typename Derived >

Mat occ::qm::CoulombMetric::half_inverse_apply ( const Eigen::MatrixBase< Derived > &  b ) const

inline

L^-1 b, where L L^T = V (or its eigen equivalent U diag(w)^-1/2): the half-inverse that turns 3-centre integrals into DF B tensors.

Has fewer rows than naux when the eigen path drops vectors.

initialized()

bool occ::qm::CoulombMetric::initialized ( ) const

inline

num_discarded()

Eigen::Index occ::qm::CoulombMetric::num_discarded ( ) const

inline

solve()

template<typename Derived >

Mat occ::qm::CoulombMetric::solve ( const Eigen::MatrixBase< Derived > &  b ) const

inline

V^-1 b.

uses_cholesky()

bool occ::qm::CoulombMetric::uses_cholesky ( ) const

inline

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

• /home/runner/work/occ/occ/include/occ/qm/coulomb_metric.h