Documentation

template<typename D>
class mpqc::math::DavidsonDiag< D >

Davidson Algorithm.

Solves eigen value problem H x = e x for the lowest n eigenpairs

it starts with orthogonal guess vector B {b1, b2, ... bn} the eigen vector is a linear combination of B extrapolate() will update the vector B and store new x

Template Parameters

D

array type D::element_type must be defined and D must provide the following stand-alone functions:

D copy(const D&)
element_type inner_product(const D& a, const D& b)
void scale(D& y , element_type a)
void axpy(D&y , element_tye a, const D& z)
void zero(D& x)
element_type norm2(const D& x)

Public Types
using	element_type = typename TA::detail::numeric_type< D >::type

using	result_type = EigenVector< element_type >

using	value_type = std::vector< D >

Public Member Functions
	DavidsonDiag (unsigned int n_roots, bool symmetric=true, unsigned int n_guess=2, unsigned int max_n_guess=4, double vector_threshold=1.0e-5)

virtual	~DavidsonDiag ()

template<typename Operator >
EigenVector< element_type >	solve (value_type &guess, Operator &&op, const DavidsonDiagPred< D > *const pred, double convergence, std::size_t max_iter)

virtual value_type &	eigen_vector ()

std::tuple< EigenVector< element_type >, EigenVector< element_type > >	extrapolate (value_type &HB, value_type &B, const DavidsonDiagPred< D > *const pred)

void	reset ()
	clean the cached values More...

Protected Attributes
unsigned int	n_roots_

bool	symmetric_

unsigned int	n_guess_

unsigned int	max_n_guess_

double	vector_threshold_

std::deque< value_type >	eigen_vector_

value_type	HB_

value_type	B_

RowMatrix< element_type >	subspace_

Member Typedef Documentation

◆ element_type

template<typename D >

using mpqc::math::DavidsonDiag< D >::element_type = typename TA::detail::numeric_type<D>::type

◆ result_type

template<typename D >

using mpqc::math::DavidsonDiag< D >::result_type = EigenVector<element_type>

◆ value_type

template<typename D >

using mpqc::math::DavidsonDiag< D >::value_type = std::vector<D>

Constructor & Destructor Documentation

◆ DavidsonDiag()

template<typename D >

mpqc::math::DavidsonDiag< D >::DavidsonDiag	(	unsigned int	n_roots,
		bool	symmetric = `true`,
		unsigned int	n_guess = `2`,
		unsigned int	max_n_guess = `4`,
		double	vector_threshold = `1.0e-5`
	)

inline

Parameters

n_roots	number of lowest roots to solve
symmetric	if matrix is symmetric
n_guess	number of eigen vector per root at subspace collapse, default is 2
max_n_guess	max number of guess vector per root, default is 4
vector_threshold	threshold for the norm of new guess vector in gram schmidt orthonormalization

◆ ~DavidsonDiag()

template<typename D >

virtual mpqc::math::DavidsonDiag< D >::~DavidsonDiag ( )

inlinevirtual

Member Function Documentation

◆ eigen_vector()

template<typename D >

virtual value_type& mpqc::math::DavidsonDiag< D >::eigen_vector ( )

inlinevirtual

Returns: return current eigen vector in Davidson

Reimplemented in mpqc::math::SingleStateDavidsonDiag< D >.

◆ extrapolate()

template<typename D >

std::tuple<EigenVector<element_type>, EigenVector<element_type> > mpqc::math::DavidsonDiag< D >::extrapolate	(	value_type &	HB,
		value_type &	B,
		const DavidsonDiagPred< D > *const	pred
	)

inline

Parameters

HB	product with A and guess vector
B	guess vector
pred	preconditioner, which inherit from DavidsonDiagPred

Returns: B updated guess vector; updated eigen values, norm of residual

◆ reset()

template<typename D >

void mpqc::math::DavidsonDiag< D >::reset ( )

inline

clean the cached values

◆ solve()

template<typename D >

template<typename Operator >

EigenVector<element_type> mpqc::math::DavidsonDiag< D >::solve	(	value_type &	guess,
		Operator &&	op,
		const DavidsonDiagPred< D > *const	pred,
		double	convergence,
		std::size_t	max_iter
	)

inline

Template Parameters

Operator operator that computes the product of H*B

Parameters

guess	initial guess vector
op	op(B) should compute HB
pred	preconditioner, which inherit from DavidsonDiagPred
convergence	convergence threshold
max_iter	max number of iteration allowed

Returns

protected

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

mpqc/math/linalg/davidson_diag.h

Documentation

template<typename D> class mpqc::math::DavidsonDiag< D >

Public Types

Public Member Functions

Protected Attributes

Member Typedef Documentation

◆ element_type

◆ result_type

◆ value_type

Constructor & Destructor Documentation

◆ DavidsonDiag()

◆ ~DavidsonDiag()

Member Function Documentation

◆ eigen_vector()

◆ extrapolate()

◆ reset()

◆ solve()

Member Data Documentation

◆ B_

◆ eigen_vector_

◆ HB_

◆ max_n_guess_

◆ n_guess_

◆ n_roots_

◆ subspace_

◆ symmetric_

◆ vector_threshold_

template<typename D>
class mpqc::math::DavidsonDiag< D >