This class computes the orthogonalizing transform for a basis set. More...

#include <chemistry/qc/basis/orthog.h>

Inheritance diagram for sc::OverlapOrthog:

Public Types
enum	OrthogMethod { Symmetric =1, Canonical =2, GramSchmidt =3 }
	An enum for the types of orthogonalization.

Public Member Functions
	OverlapOrthog (OrthogMethod method, const RefSymmSCMatrix &overlap, const Ref< SCMatrixKit > &result_kit, double lindep_tolerance, int debug=0)

	OverlapOrthog (StateIn &)

void	save_data_state (StateOut &)
	Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them. More...

void	reinit (OrthogMethod method, const RefSymmSCMatrix &overlap, const Ref< SCMatrixKit > &result_kit, double lindep_tolerance, int debug=0)

double	min_orthog_res () const

double	max_orthog_res () const

Ref< OverlapOrthog >	copy () const

OrthogMethod	orthog_method () const
	Returns the orthogonalization method.

double	lindep_tol () const
	Returns the tolerance for linear dependencies.

RefSCMatrix	basis_to_orthog_basis ()
	Returns a matrix which does the requested transform from a basis to an orthogonal basis. More...

RefSCMatrix	basis_to_orthog_basis_inverse ()
	Returns the inverse of the transformation returned by basis_to_orthog_basis() . More...

RefSymmSCMatrix	overlap_inverse ()
	Return an $S^{-1}$.

RefSCDimension	dim ()

RefSCDimension	orthog_dim ()

int	nlindep ()
	Returns the number of linearly dependent functions eliminated from the orthogonal basis.

Public Member Functions inherited from sc::SavableState
SavableState &	operator= (const SavableState &)

void	save_state (StateOut &)
	Save the state of the object as specified by the StateOut object. More...

void	save_object_state (StateOut &)
	This can be used for saving state when the exact type of the object is known for both the save and the restore. More...

virtual void	save_vbase_state (StateOut &)
	Save the virtual bases for the object. More...

Public Member Functions inherited from sc::DescribedClass
	DescribedClass (const DescribedClass &)

DescribedClass &	operator= (const DescribedClass &)

ClassDesc *	class_desc () const MPQC__NOEXCEPT
	This returns the unique pointer to the ClassDesc corresponding to the given type_info object. More...

const char *	class_name () const
	Return the name of the object's exact type.

int	class_version () const
	Return the version of the class.

virtual void	print (std::ostream &=ExEnv::out0()) const
	Print the object.

Ref< DescribedClass >	ref ()
	Return this object wrapped up in a Ref smart pointer. More...

Public Member Functions inherited from sc::RefCount
size_t	identifier () const
	Return the unique identifier for this object that can be compared for different objects of different types. More...

int	lock_ptr () const
	Lock this object.

int	unlock_ptr () const
	Unlock this object.

void	use_locks (bool inVal)
	start and stop using locks on this object

refcount_t	nreference () const
	Return the reference count.

refcount_t	reference ()
	Increment the reference count and return the new count.

refcount_t	dereference ()
	Decrement the reference count and return the new count.

int	managed () const

void	unmanage ()
	Turn off the reference counting mechanism for this object. More...

Static Public Member Functions
static OrthogMethod	default_orthog_method ()
	default is to use Symmetric orthogonalization

static double	default_lindep_tol ()
	default orthog threshold is 1e-8

Static Public Member Functions inherited from sc::SavableState
static void	save_state (SavableState *s, StateOut &)

static SavableState *	restore_state (StateIn &si)
	Restores objects saved with save_state. More...

static SavableState *	key_restore_state (StateIn &si, const char *keyword)
	Like restore_state, but keyword is used to override values while restoring.

static SavableState *	dir_restore_state (StateIn &si, const char objectname, const char keyword=0)

Additional Inherited Members
Protected Member Functions inherited from sc::SavableState
	SavableState (const SavableState &)

	SavableState (StateIn &)
	Each derived class StateIn CTOR handles the restore corresponding to calling save_object_state, save_vbase_state, and save_data_state listed above. More...

Protected Member Functions inherited from sc::RefCount
	RefCount (const RefCount &)

RefCount &	operator= (const RefCount &)

Detailed Description

This class computes the orthogonalizing transform for a basis set.

Constructor & Destructor Documentation

◆ OverlapOrthog()

sc::OverlapOrthog::OverlapOrthog	(	OrthogMethod	method,
		const RefSymmSCMatrix &	overlap,
		const Ref< SCMatrixKit > &	result_kit,
		double	lindep_tolerance,
		int	debug = `0`
	)

Parameters

lindep_tolerance If non-negative, this specifies the degree of linear dependence tolerated in the result. The precise definition is method-dependent. For symmetric/canonical methods this specifies the condition number of the truncated metric. If negative and method is symmetric/canonical, std::floor(-lindep_tolerance) specifies the number of linearly-dependent basis functions to be removed.

Member Function Documentation

◆ basis_to_orthog_basis()

RefSCMatrix sc::OverlapOrthog::basis_to_orthog_basis ( )

Returns a matrix which does the requested transform from a basis to an orthogonal basis.

The row dimension is the orthogonal basis dimension and the column dimension is the given basis dimension.

This matrix can be used to transform operators from the given basis to the orthogonal basis and to transform functions from the orthogonal basis to the given basis. An operator in the orthogonal basis is obtained by $ X O_bas X^T$ , where $X$ is the return value of this function and $ O_bas $ is the operator in the given basis. A function in the given basis is obtained by $ X^T F_obas $ , where $ F_obas $ is the function in the orthogonal basis.

◆ basis_to_orthog_basis_inverse()

RefSCMatrix sc::OverlapOrthog::basis_to_orthog_basis_inverse ( )

Returns the inverse of the transformation returned by basis_to_orthog_basis() .

The column dimension is the orthogonal basis dimension and the row dimension is the given basis dimension.

This matrix can be used to transform operators from the orthogonal basis to the given basis and to transform functions from the orthogonal basis to the given basis. An operator in the given basis is obtained by $X O_obas X^T$ , where $X$ is the return value of this function and $ O_obas $ is the operator in the orthogonal basis. A function in the orthogonal basis is obtained by $ X^T F_bas $ , where $ F_bas $ is the function in the given basis.