Collaboration diagram for mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >:

Documentation

template<typename Tile, typename Policy, typename Gradient, typename Mat>
class mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >

Implements non-linear conjugate gradient for a given gradient expression.

Public Member Functions
virtual	~NonLinearConjGradient ()=default

	NonLinearConjGradient (const KeyVal &kv)

double	inner_product (Mat const &bra_mat, Mat const &ket_mat) const

std::vector< Mat >	rotate_W (const int nkpts, double mu, std::vector< Mat > const &Hn, std::vector< Mat > const &Wn) const

int	find_max_idx (Eigen::VectorXd const &list, double const max_value) const

Eigen::VectorXd	fit_data (Eigen::VectorXd const &mu_list, Eigen::VectorXd const &P_list) const

void	evaluate_P_on_range (Eigen::VectorXd &mu_list, Eigen::VectorXd &P_list, const double lower_bound, const double upper_bound, const int p, const int nkpts, Eigen::Vector3i const &nk, std::vector< Mat > const &Hn, std::vector< Mat > const &Wn, std::vector< std::vector< Mat >> const &Q_list) const

double	get_upper_bound (double const &lower_bound, double const &upper_bound, Eigen::VectorXd &mu_list, Eigen::VectorXd &P_list, const int p, const double P_initial, Eigen::Vector3i const &nk, std::vector< Mat > const &Hn, std::vector< Mat > const &Wn, std::vector< std::vector< Mat >> const &Q_list, const int nkpts) const

double	solve_root (const double &lower_bound, double &upper_bound, const int p, const double P_initial, const int nkpts, Eigen::Vector3i const &nk, std::vector< Mat > const &Hn, std::vector< Mat > const &Wn, std::vector< std::vector< Mat >> const &Q_list) const

std::vector< Mat >	update_W_fit_functional (const int nkpts, const int p, double const &lower_bound, double &upper_bound, double &P_initial, Eigen::Vector3i const &nk, std::vector< Mat > const &Hn, std::vector< Mat > const &Wn, std::vector< std::vector< Mat >> const &Q_list) const

std::vector< Mat >	compute (std::vector< Mat > const &C, std::vector< Mat > &C_rotated, Eigen::Vector3i const &nk, int64_t nocc, size_t ncols_of_C_to_skip=0) const final

Public Member Functions inherited from mpqc::lcao::zOrbitalLocalizer< Tile, Policy, Mat >
virtual	~zOrbitalLocalizer ()=default

Protected Member Functions
void	init (std::shared_ptr< detail::zOrbitalLocalizationGradient< Mat >> gradient)

	NonLinearConjGradient (int max_iter, double target_precision)

Protected Attributes
std::shared_ptr< WavefunctionWorld >	wfn_world_

std::shared_ptr< lcao::pbc::gaussian::AOFactory< TileD, Policy > >	ao_factory_

double	convergence_threshold_

size_t	max_iter_

std::string	update_factor_

std::string	initial_W_

std::shared_ptr< detail::zOrbitalLocalizationGradient< Mat > >	gradient_

Constructor & Destructor Documentation

◆ ~NonLinearConjGradient()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

virtual mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::~NonLinearConjGradient ( )

virtualdefault

◆ NonLinearConjGradient() [1/2]

template<typename Tile , typename Policy , typename Gradient , typename Mat >

mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::NonLinearConjGradient ( const KeyVal & kv )

inlineexplicit

KeyVal constructor for NonLinearConjGradient

Parameters

kv

the KeyVal object; it will be queried for the following keywords:

Keyword	Type	Default	Description
`wfn_world`	class	none	the WavefunctionWorld
`convergence_threshold`	double	1e-8	the non-linear conjugate gradient solver is converged when the norm of the gradient falls below this value
`max_iter`	int	50	the maximum number of iterations
`update_factor`	string	sdsa	the means of forming gamma

◆ NonLinearConjGradient() [2/2]

template<typename Tile , typename Policy , typename Gradient , typename Mat >

mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::NonLinearConjGradient	(	int	max_iter,
		double	target_precision
	)

inlineprotected

Member Function Documentation

◆ compute()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::vector<Mat> mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::compute	(	std::vector< Mat > const &	C,
		std::vector< Mat > &	C_rotated,
		Eigen::Vector3i const &	nk,
		int64_t	nocc,
		size_t	ncols_of_C_to_skip = `0`
	)		const

inlinefinalvirtual

Parameters

	C	input LCAOs
[in]	ncols_of_C_to_skip	the number of columns of C to keep non-localized, presumably because they are already localized

Returns: transformation matrix U that converts C to localized LCAOs, i.e.
Cao("mu,k") * U("k,i")

computes the AO coefficients of localized MOs from the AO coefficients of input MOs";

Step 1: Get the maximum of all omega_k

Step 2: Determine the order q of the cost function

Step 3: Determine the value of Tmu = 2 pi / (q * max_omega)

Step 1: Get the maximum of all omega_k

Step 2: Determine the order q of the cost function

Step 3: Determine the value of Tmu = 2 pi / (q * max_omega)

Implements mpqc::lcao::zOrbitalLocalizer< Tile, Policy, Mat >.

◆ evaluate_P_on_range()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

void mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::evaluate_P_on_range	(	Eigen::VectorXd &	mu_list,
		Eigen::VectorXd &	P_list,
		const double	lower_bound,
		const double	upper_bound,
		const int	p,
		const int	nkpts,
		Eigen::Vector3i const &	nk,
		std::vector< Mat > const &	Hn,
		std::vector< Mat > const &	Wn,
		std::vector< std::vector< Mat >> const &	Q_list
	)		const

inline

Step 5: Evaluate R(mu) at each mu_i

Step 6: For each R(mu), evaluate the PM functional

◆ find_max_idx()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

int mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::find_max_idx	(	Eigen::VectorXd const &	list,
		double const	max_value
	)		const

inline

Given an Eigen::VectorXd of items and the max item in that vector, find the index of the max item

◆ fit_data()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

Eigen::VectorXd mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::fit_data	(	Eigen::VectorXd const &	mu_list,
		Eigen::VectorXd const &	P_list
	)		const

inline

◆ get_upper_bound()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

double mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::get_upper_bound	(	double const &	lower_bound,
		double const &	upper_bound,
		Eigen::VectorXd &	mu_list,
		Eigen::VectorXd &	P_list,
		const int	p,
		const double	P_initial,
		Eigen::Vector3i const &	nk,
		std::vector< Mat > const &	Hn,
		std::vector< Mat > const &	Wn,
		std::vector< std::vector< Mat >> const &	Q_list,
		const int	nkpts
	)		const

inline

◆ init()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

void mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::init ( std::shared_ptr< detail::zOrbitalLocalizationGradient< Mat >> gradient )

inlineprotected

◆ inner_product()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

double mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::inner_product	(	Mat const &	bra_mat,
		Mat const &	ket_mat
	)		const

inline

◆ rotate_W()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::vector<Mat> mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::rotate_W	(	const int	nkpts,
		double	mu,
		std::vector< Mat > const &	Hn,
		std::vector< Mat > const &	Wn
	)		const

inline

I believe that this is the correct one to use Given an appropriate double mu and vector of matrices Hn, generate the rotated W matrices Rotate each W with the same mu but a different H

◆ solve_root()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

double mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::solve_root	(	const double &	lower_bound,
		double &	upper_bound,
		const int	p,
		const double	P_initial,
		const int	nkpts,
		Eigen::Vector3i const &	nk,
		std::vector< Mat > const &	Hn,
		std::vector< Mat > const &	Wn,
		std::vector< std::vector< Mat >> const &	Q_list
	)		const

inline

◆ update_W_fit_functional()

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::vector<Mat> mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::update_W_fit_functional	(	const int	nkpts,
		const int	p,
		double const &	lower_bound,
		double &	upper_bound,
		double &	P_initial,
		Eigen::Vector3i const &	nk,
		std::vector< Mat > const &	Hn,
		std::vector< Mat > const &	Wn,
		std::vector< std::vector< Mat >> const &	Q_list
	)		const

inline

Compute the optimal step size, \mu_{opt} and update W by fitting the P(mu) values and then finding the roots of the first derivative of this function

Parameters

[in]	nkpts	the number of k points
[in]	p	the order of the polynomial
[in]	Hn	the current iteration's search descent direction: one matrix for each k point
[in]	Wn	the current iteration's estimate of the orbital transformation matrix: one matrix for each k point

Returns: mu_n a vector containing the current optimal step size for each k point

Member Data Documentation

◆ ao_factory_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::shared_ptr<lcao::pbc::gaussian::AOFactory<TileD, Policy> > mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::ao_factory_

protected

◆ convergence_threshold_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

double mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::convergence_threshold_

protected

◆ gradient_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::shared_ptr<detail::zOrbitalLocalizationGradient<Mat> > mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::gradient_

protected

◆ initial_W_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::string mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::initial_W_

protected

◆ max_iter_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

size_t mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::max_iter_

protected

◆ update_factor_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::string mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::update_factor_

protected

◆ wfn_world_

template<typename Tile , typename Policy , typename Gradient , typename Mat >

std::shared_ptr<WavefunctionWorld> mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >::wfn_world_

protected

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

mpqc/chemistry/qc/lcao/scf/pbc/zorbital_localization.h

Documentation

template<typename Tile, typename Policy, typename Gradient, typename Mat> class mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ ~NonLinearConjGradient()

◆ NonLinearConjGradient() [1/2]

◆ NonLinearConjGradient() [2/2]

Member Function Documentation

◆ compute()

◆ evaluate_P_on_range()

◆ find_max_idx()

◆ fit_data()

◆ get_upper_bound()

◆ init()

◆ inner_product()

◆ rotate_W()

◆ solve_root()

◆ update_W_fit_functional()

Member Data Documentation

◆ ao_factory_

◆ convergence_threshold_

◆ gradient_

◆ initial_W_

◆ max_iter_

◆ update_factor_

◆ wfn_world_

template<typename Tile, typename Policy, typename Gradient, typename Mat>
class mpqc::lcao::pbc::NonLinearConjGradient< Tile, Policy, Gradient, Mat >