Contains linear algebra functions used in the implementation of an eigen solver. More...

Namespaces
namespace	internal
	Contains internal functions used in linearAlgebraOperations.

Functions
void	inverse (double *A, int N)
	Compute inverse of serial matrix using LAPACK LU factorization.

void	inverse (std::complex< double > *A, int N)
	Compute inverse of serial matrix using LAPACK LU factorization.

template<typename T, dftfe::utils::MemorySpace memorySpace>
std::pair< double, double >	generalisedLanczosLowerUpperBoundEigenSpectrum (const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< memorySpace > > &BLASWrapperPtr, operatorDFTClass< memorySpace > &operatorMatrix, dftfe::linearAlgebra::MultiVector< T, memorySpace > &X, dftfe::linearAlgebra::MultiVector< T, memorySpace > &Y, dftfe::linearAlgebra::MultiVector< T, memorySpace > &Z, dftfe::linearAlgebra::MultiVector< T, memorySpace > &tempVec, const dftParameters &dftParams)
	Calculates an estimate of lower and upper bounds of a matrix using k-step Generalised Lanczos method. Algo is present in PAW PRB paper.

template<typename T, dftfe::utils::MemorySpace memorySpace>
void	chebyshevFilter (operatorDFTClass< memorySpace > &operatorMatrix, dftfe::linearAlgebra::MultiVector< T, memorySpace > &X, dftfe::linearAlgebra::MultiVector< T, memorySpace > &Y, const unsigned int m, const double a, const double b, const double a0)
	Apply Chebyshev filter to a given subspace.

template<typename T1, typename T2, dftfe::utils::MemorySpace memorySpace>
void	reformulatedChebyshevFilter (const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< memorySpace > > &BLASWrapperPtr, operatorDFTClass< memorySpace > &operatorMatrix, dftfe::linearAlgebra::MultiVector< T1, memorySpace > &X, dftfe::linearAlgebra::MultiVector< T1, memorySpace > &Y, dftfe::linearAlgebra::MultiVector< T2, memorySpace > &Residual, dftfe::linearAlgebra::MultiVector< T2, memorySpace > &ResidualNew, std::vector< double > eigenvalues, const unsigned int m, const double a, const double b, const double a0, const bool approxOverlapMatrix)
	Apply Residual based Chebyshev filter to a given subspace.

template<typename T>
void	gramSchmidtOrthogonalization (T *X, const unsigned int numberComponents, const unsigned int numberDofs, const MPI_Comm &mpiComm)
	Orthogonalize given subspace using GramSchmidt orthogonalization.

unsigned int	lowdenOrthogonalization (std::vector< dataTypes::number > &X, const unsigned int numberComponents, const MPI_Comm &mpiComm, const dftParameters &dftParams)
	Orthogonalize given subspace using Lowden orthogonalization for double data-type (serial version using LAPACK)

template<typename T>
unsigned int	pseudoGramSchmidtOrthogonalization (elpaScalaManager &elpaScala, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, T *X, const unsigned int numberComponents, const unsigned int numberDofs, const MPI_Comm &mpiCommParent, const MPI_Comm &interBandGroupComm, const MPI_Comm &mpiCommDomain, const bool useMixedPrec, const dftParameters &dftParams)
	Orthogonalize given subspace using Pseudo-Gram-Schmidt orthogonalization (serial version using LAPACK, parallel version using ScaLAPACK)

template<typename T>
void	rayleighRitzGEP (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, elpaScalaManager &elpaScala, T *X, const unsigned int numberComponents, const unsigned int numberDofs, const MPI_Comm &mpiCommParent, const MPI_Comm &interBandGroupComm, const MPI_Comm &mpiCommDomain, std::vector< double > &eigenValues, const bool useMixedPrec, const dftParameters &dftParams)
	Compute Rayleigh-Ritz projection (serial version using LAPACK, parallel version using ScaLAPACK)

template<typename T>
void	rayleighRitz (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, elpaScalaManager &elpaScala, T *X, const unsigned int numberComponents, const unsigned int numberDofs, const MPI_Comm &mpiCommParent, const MPI_Comm &interBandGroupComm, const MPI_Comm &mpiCommDomain, std::vector< double > &eigenValues, const dftParameters &dftParams, const bool doCommAfterBandParal=true)
	Compute Rayleigh-Ritz projection (serial version using LAPACK, parallel version using ScaLAPACK)

template<typename T>
void	computeEigenResidualNorm (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, T *X, const std::vector< double > &eigenValues, const unsigned int numberComponents, const unsigned int numberDofs, const MPI_Comm &mpiCommParent, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, std::vector< double > &residualNorm, const dftParameters &dftParams)
	Compute residual norm associated with eigenValue problem of the given operator.

template<typename T>
void	densityMatrixEigenBasisFirstOrderResponse (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, T *X, const unsigned int N, const unsigned int numberLocalDofs, const MPI_Comm &mpiCommParent, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const std::vector< double > &eigenValues, const double fermiEnergy, std::vector< double > &densityMatDerFermiEnergy, elpaScalaManager &elpaScala, const dftParameters &dftParams)
	Compute first order response in density matrix with respect to perturbation in the Hamiltonian. Perturbation is computed in the eigenbasis.

void	XtHX (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int numberComponents, const unsigned int numberLocalDofs, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, std::vector< dataTypes::number > &ProjHam)
	Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}HConjXConj.

void	XtHX (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int numberComponents, const unsigned int numberLocalDofs, const std::shared_ptr< const dftfe::ProcessGrid > &processGrid, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, dftfe::ScaLAPACKMatrix< dataTypes::number > &projHamPar, const bool onlyHPrimePartForFirstOrderDensityMatResponse=false)
	Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}HConjXConj.

void	XtOX (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int numberComponents, const unsigned int numberLocalDofs, const std::shared_ptr< const dftfe::ProcessGrid > &processGrid, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, dftfe::ScaLAPACKMatrix< dataTypes::number > &projOverlapPar)
	Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}HConjXConj.

void	XtHXMixedPrec (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int totalNumberComponents, const unsigned int singlePrecComponents, const unsigned int numberLocalDofs, const std::shared_ptr< const dftfe::ProcessGrid > &processGrid, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, dftfe::ScaLAPACKMatrix< dataTypes::number > &projHamPar, const bool onlyHPrimePartForFirstOrderDensityMatResponse=false)
	Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}HConjXConj.

void	XtOXMixedPrec (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int totalNumberComponents, const unsigned int singlePrecComponents, const unsigned int numberLocalDofs, const std::shared_ptr< const dftfe::ProcessGrid > &processGrid, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, dftfe::ScaLAPACKMatrix< dataTypes::number > &projOverlapPar)
	Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}HConjXConj.

void	XtHXXtOX (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int numberComponents, const unsigned int numberLocalDofs, const std::shared_ptr< const dftfe::ProcessGrid > &processGrid, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, dftfe::ScaLAPACKMatrix< dataTypes::number > &projHamPar, dftfe::ScaLAPACKMatrix< dataTypes::number > &projOverlapPar, const bool onlyHPrimePartForFirstOrderDensityMatResponse=false)
	Computes the projection of Hamiltonian and Overlap with only a single extraction. Single extraction will be beneficial in full M, PAW cases.

void	XtHXXtOXMixedPrec (operatorDFTClass< dftfe::utils::MemorySpace::HOST > &operatorMatrix, const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &BLASWrapperPtr, const dataTypes::number *X, const unsigned int totalNumberComponents, const unsigned int singlePrecComponents, const unsigned int numberLocalDofs, const std::shared_ptr< const dftfe::ProcessGrid > &processGrid, const MPI_Comm &mpiCommDomain, const MPI_Comm &interBandGroupComm, const dftParameters &dftParams, dftfe::ScaLAPACKMatrix< dataTypes::number > &projHamPar, dftfe::ScaLAPACKMatrix< dataTypes::number > &projOverlapPar, const bool onlyHPrimePartForFirstOrderDensityMatResponse=false)
	Computes the projection of Hamiltonian and Overlap with only a single extraction with mixed precision. Single extraction will be beneficial in full M, PAW cases. THe projected Hamiltonain has full precision along blocks of diagonal and for states greater than Ncore THe projected Overlap will be of full precision along the diagonal.

Detailed Description

Contains linear algebra functions used in the implementation of an eigen solver.

Author: Phani Motamarri, Sambit Das

Function Documentation

◆ chebyshevFilter()

template<typename T, dftfe::utils::MemorySpace memorySpace>

void dftfe::linearAlgebraOperations::chebyshevFilter	(	operatorDFTClass< memorySpace > &	operatorMatrix,
		dftfe::linearAlgebra::MultiVector< T, memorySpace > &	X,
		dftfe::linearAlgebra::MultiVector< T, memorySpace > &	Y,
		const unsigned int	m,
		const double	a,
		const double	b,
		const double	a0 )

Apply Chebyshev filter to a given subspace.

Parameters

[in]	operatorMatrix	An object which has access to the given matrix
[in,out]	X	Given subspace as a dealii array representing multiple fields as a flattened array. In-place update of the given subspace.
[in]	numberComponents	Number of multiple-fields
[in]	m	Chebyshev polynomial degree
[in]	a	lower bound of unwanted spectrum
[in]	b	upper bound of unwanted spectrum
[in]	a0	lower bound of wanted spectrum

◆ computeEigenResidualNorm()

template<typename T>

void dftfe::linearAlgebraOperations::computeEigenResidualNorm	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		T *	X,
		const std::vector< double > &	eigenValues,
		const unsigned int	numberComponents,
		const unsigned int	numberDofs,
		const MPI_Comm &	mpiCommParent,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		std::vector< double > &	residualNorm,
		const dftParameters &	dftParams )

Compute residual norm associated with eigenValue problem of the given operator.

Parameters

[in]	operatorMatrix	An object which has access to the given matrix
[in]	X	Given subspace as STL vector of dealii vectors
[in]	eigenValues	eigenValues of the operator
[in]	mpiCommParent	parent mpi communicator
[in]	mpiCommDomain	domain decomposition communicator
[out]	residualNorms	of the eigen Value problem

◆ densityMatrixEigenBasisFirstOrderResponse()

template<typename T>

void dftfe::linearAlgebraOperations::densityMatrixEigenBasisFirstOrderResponse	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		T *	X,
		const unsigned int	N,
		const unsigned int	numberLocalDofs,
		const MPI_Comm &	mpiCommParent,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const std::vector< double > &	eigenValues,
		const double	fermiEnergy,
		std::vector< double > &	densityMatDerFermiEnergy,
		elpaScalaManager &	elpaScala,
		const dftParameters &	dftParams )

Compute first order response in density matrix with respect to perturbation in the Hamiltonian. Perturbation is computed in the eigenbasis.

◆ generalisedLanczosLowerUpperBoundEigenSpectrum()

template<typename T, dftfe::utils::MemorySpace memorySpace>

std::pair< double, double > dftfe::linearAlgebraOperations::generalisedLanczosLowerUpperBoundEigenSpectrum	(	const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< memorySpace > > &	BLASWrapperPtr,
		operatorDFTClass< memorySpace > &	operatorMatrix,
		dftfe::linearAlgebra::MultiVector< T, memorySpace > &	X,
		dftfe::linearAlgebra::MultiVector< T, memorySpace > &	Y,
		dftfe::linearAlgebra::MultiVector< T, memorySpace > &	Z,
		dftfe::linearAlgebra::MultiVector< T, memorySpace > &	tempVec,
		const dftParameters &	dftParams )

Calculates an estimate of lower and upper bounds of a matrix using k-step Generalised Lanczos method. Algo is present in PAW PRB paper.

Parameters

operatorMatrix	An object which has access to the given matrix
vect	A dummy vector

Returns: std::pair<double,double> An estimate of the lower and upper bound of the given matrix

◆ gramSchmidtOrthogonalization()

template<typename T>

void dftfe::linearAlgebraOperations::gramSchmidtOrthogonalization	(	T *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberDofs,
		const MPI_Comm &	mpiComm )

Orthogonalize given subspace using GramSchmidt orthogonalization.

Parameters

[in,out]	X	Given subspace as flattened array of multi-vectors. In-place update of the given subspace
[in]	numberComponents	Number of multiple-fields
[in]	mpiComm	global communicator

◆ inverse() [1/2]

void dftfe::linearAlgebraOperations::inverse	(	double *	A,
		int	N )

Compute inverse of serial matrix using LAPACK LU factorization.

◆ inverse() [2/2]

void dftfe::linearAlgebraOperations::inverse	(	std::complex< double > *	A,
		int	N )

Compute inverse of serial matrix using LAPACK LU factorization.

◆ lowdenOrthogonalization()

unsigned int dftfe::linearAlgebraOperations::lowdenOrthogonalization	(	std::vector< dataTypes::number > &	X,
		const unsigned int	numberComponents,
		const MPI_Comm &	mpiComm,
		const dftParameters &	dftParams )

Orthogonalize given subspace using Lowden orthogonalization for double data-type (serial version using LAPACK)

Parameters

[in,out]	X	Given subspace as flattened array of multi-vectors. In-place update of the given subspace
[in]	numberComponents	Number of multiple-fields
[in]	mpiComm	global communicator

Returns: flag indicating success/failure. 1 for failure, 0 for success

◆ pseudoGramSchmidtOrthogonalization()

template<typename T>

unsigned int dftfe::linearAlgebraOperations::pseudoGramSchmidtOrthogonalization	(	elpaScalaManager &	elpaScala,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		T *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberDofs,
		const MPI_Comm &	mpiCommParent,
		const MPI_Comm &	interBandGroupComm,
		const MPI_Comm &	mpiCommDomain,
		const bool	useMixedPrec,
		const dftParameters &	dftParams )

Orthogonalize given subspace using Pseudo-Gram-Schmidt orthogonalization (serial version using LAPACK, parallel version using ScaLAPACK)

Parameters

[in,out]	X	Given subspace as flattened array of multi-vectors. In-place update of the given subspace
[in]	numberComponents	Number of multiple-fields
[in]	mpiCommParent	parent communicator
[in]	interBandGroupComm	interpool communicator for parallelization over band groups
[in]	mpiComm	domain decomposition communicator

Returns: flag indicating success/failure. 1 for failure, 0 for success

◆ rayleighRitz()

template<typename T>

void dftfe::linearAlgebraOperations::rayleighRitz	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		elpaScalaManager &	elpaScala,
		T *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberDofs,
		const MPI_Comm &	mpiCommParent,
		const MPI_Comm &	interBandGroupComm,
		const MPI_Comm &	mpiCommDomain,
		std::vector< double > &	eigenValues,
		const dftParameters &	dftParams,
		const bool	doCommAfterBandParal = true )

Compute Rayleigh-Ritz projection (serial version using LAPACK, parallel version using ScaLAPACK)

Parameters

[in]	operatorMatrix	An object which has access to the given matrix
[in,out]	X	Given subspace as flattened array of multi-vectors. In-place rotated subspace
[in]	numberComponents	Number of vectors
[in]	mpiCommParent	parent mpi communicator
[in]	interBandGroupComm	interpool communicator for parallelization over band groups
[in]	mpiCommDomain	domain decomposition communicator
[out]	eigenValues	of the Projected Hamiltonian

◆ rayleighRitzGEP()

template<typename T>

void dftfe::linearAlgebraOperations::rayleighRitzGEP	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		elpaScalaManager &	elpaScala,
		T *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberDofs,
		const MPI_Comm &	mpiCommParent,
		const MPI_Comm &	interBandGroupComm,
		const MPI_Comm &	mpiCommDomain,
		std::vector< double > &	eigenValues,
		const bool	useMixedPrec,
		const dftParameters &	dftParams )

Compute Rayleigh-Ritz projection (serial version using LAPACK, parallel version using ScaLAPACK)

Parameters

[in]	operatorMatrix	An object which has access to the given matrix
[in,out]	X	Given subspace as flattened array of multi-vectors. In-place rotated subspace
[in]	numberComponents	Number of vectors
[in]	mpiCommDomain	parent communicator
[in]	interBandGroupComm	interpool communicator for parallelization over band groups
[in]	mpiCommDomain	domain decomposition communicator
[out]	eigenValues	of the Projected Hamiltonian

◆ reformulatedChebyshevFilter()

template<typename T1, typename T2, dftfe::utils::MemorySpace memorySpace>

void dftfe::linearAlgebraOperations::reformulatedChebyshevFilter	(	const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< memorySpace > > &	BLASWrapperPtr,
		operatorDFTClass< memorySpace > &	operatorMatrix,
		dftfe::linearAlgebra::MultiVector< T1, memorySpace > &	X,
		dftfe::linearAlgebra::MultiVector< T1, memorySpace > &	Y,
		dftfe::linearAlgebra::MultiVector< T2, memorySpace > &	Residual,
		dftfe::linearAlgebra::MultiVector< T2, memorySpace > &	ResidualNew,
		std::vector< double >	eigenvalues,
		const unsigned int	m,
		const double	a,
		const double	b,
		const double	a0,
		const bool	approxOverlapMatrix )

Apply Residual based Chebyshev filter to a given subspace.

Parameters

[in]	operatorMatrix	An object which has access to the given matrix
[in,out]	X	Given subspace as a dealii array representing multiple fields as a flattened array. In-place update of the given subspace.
[in]	eigenvalues	estimate of eigenvalues, usually the eigenvalues from previous pass
[in]	m	Chebyshev polynomial degree
[in]	a	lower bound of unwanted spectrum
[in]	b	upper bound of unwanted spectrum
[in]	a0	lower bound of wanted spectrum
[in]	approxOverlapMatrix	to use approximate overlap matrix while computing initial residual

◆ XtHX() [1/2]

void dftfe::linearAlgebraOperations::XtHX	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberLocalDofs,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		std::vector< dataTypes::number > &	ProjHam )

Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}*HConj*XConj.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
numberComponents	number of wavefunctions associated with a given node
ProjMatrix	projected small matrix

◆ XtHX() [2/2]

void dftfe::linearAlgebraOperations::XtHX	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberLocalDofs,
		const std::shared_ptr< const dftfe::ProcessGrid > &	processGrid,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projHamPar,
		const bool	onlyHPrimePartForFirstOrderDensityMatResponse = false )

Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}*HConj*XConj.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
numberComponents	number of wavefunctions associated with a given node
processGrid	two-dimensional processor grid corresponding to the parallel projHamPar
projHamPar	parallel ScaLAPACKMatrix which stores the computed projection of the operation into the given subspace

◆ XtHXMixedPrec()

void dftfe::linearAlgebraOperations::XtHXMixedPrec	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	totalNumberComponents,
		const unsigned int	singlePrecComponents,
		const unsigned int	numberLocalDofs,
		const std::shared_ptr< const dftfe::ProcessGrid > &	processGrid,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projHamPar,
		const bool	onlyHPrimePartForFirstOrderDensityMatResponse = false )

Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}*HConj*XConj.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
totalNumberComponents	number of wavefunctions associated with a given node
singlePrecComponents	number of wavecfuntions starting from the first for which the project Hamiltionian block will be computed in single procession. However the cross blocks will still be computed in double precision.
processGrid	two-dimensional processor grid corresponding to the parallel projHamPar
projHamPar	parallel ScaLAPACKMatrix which stores the computed projection of the operation into the given subspace

◆ XtHXXtOX()

void dftfe::linearAlgebraOperations::XtHXXtOX	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberLocalDofs,
		const std::shared_ptr< const dftfe::ProcessGrid > &	processGrid,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projHamPar,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projOverlapPar,
		const bool	onlyHPrimePartForFirstOrderDensityMatResponse = false )

Computes the projection of Hamiltonian and Overlap with only a single extraction. Single extraction will be beneficial in full M, PAW cases.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
numberComponents	number of wavefunctions associated with a given node
numberLocalDofs	number of DOFs owned in the current procesor
processGrid	two-dimensional processor grid corresponding to the parallel projHamPar
projHamPar	parallel ScaLAPACKMatrix which stores the computed projection of the Hamiltonian into the given subspace
projOverlapPar	parallel ScaLAPACKMatrix which stores the computed projection of the Overlap into the given subspace

◆ XtHXXtOXMixedPrec()

void dftfe::linearAlgebraOperations::XtHXXtOXMixedPrec	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	totalNumberComponents,
		const unsigned int	singlePrecComponents,
		const unsigned int	numberLocalDofs,
		const std::shared_ptr< const dftfe::ProcessGrid > &	processGrid,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projHamPar,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projOverlapPar,
		const bool	onlyHPrimePartForFirstOrderDensityMatResponse = false )

Computes the projection of Hamiltonian and Overlap with only a single extraction with mixed precision. Single extraction will be beneficial in full M, PAW cases. THe projected Hamiltonain has full precision along blocks of diagonal and for states greater than Ncore THe projected Overlap will be of full precision along the diagonal.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
numberComponents	number of wavefunctions associated with a given node
numberLocalDofs	number of DOFs owned in the current procesor
processGrid	two-dimensional processor grid corresponding to the parallel projHamPar
projHamPar	parallel ScaLAPACKMatrix which stores the computed projection of the Hamiltonian into the given subspace
projOverlapPar	parallel ScaLAPACKMatrix which stores the computed projection of the Overlap into the given subspace

◆ XtOX()

void dftfe::linearAlgebraOperations::XtOX	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	numberComponents,
		const unsigned int	numberLocalDofs,
		const std::shared_ptr< const dftfe::ProcessGrid > &	processGrid,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projOverlapPar )

Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}*HConj*XConj.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
numberComponents	number of wavefunctions associated with a given node
processGrid	two-dimensional processor grid corresponding to the parallel projHamPar
projHamPar	parallel ScaLAPACKMatrix which stores the computed projection of the operation into the given subspace

◆ XtOXMixedPrec()

void dftfe::linearAlgebraOperations::XtOXMixedPrec	(	operatorDFTClass< dftfe::utils::MemorySpace::HOST > &	operatorMatrix,
		const std::shared_ptr< dftfe::linearAlgebra::BLASWrapper< dftfe::utils::MemorySpace::HOST > > &	BLASWrapperPtr,
		const dataTypes::number *	X,
		const unsigned int	totalNumberComponents,
		const unsigned int	singlePrecComponents,
		const unsigned int	numberLocalDofs,
		const std::shared_ptr< const dftfe::ProcessGrid > &	processGrid,
		const MPI_Comm &	mpiCommDomain,
		const MPI_Comm &	interBandGroupComm,
		const dftParameters &	dftParams,
		dftfe::ScaLAPACKMatrix< dataTypes::number > &	projOverlapPar )

Compute projection of the operator into a subspace spanned by a given orthogonal basis HProjConj=X^{T}*HConj*XConj.

Parameters

X	Vector of Vectors containing multi-wavefunction fields
totalNumberComponents	number of wavefunctions associated with a given node
singlePrecComponents	number of wavecfuntions starting from the first for which the project Hamiltionian block will be computed in single procession. However the cross blocks will still be computed in double precision.
processGrid	two-dimensional processor grid corresponding to the parallel projHamPar
projHamPar	parallel ScaLAPACKMatrix which stores the computed projection of the operation into the given subspace

Namespaces

Functions

Detailed Description

Function Documentation

◆ chebyshevFilter()

◆ computeEigenResidualNorm()

◆ densityMatrixEigenBasisFirstOrderResponse()

◆ generalisedLanczosLowerUpperBoundEigenSpectrum()

◆ gramSchmidtOrthogonalization()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ lowdenOrthogonalization()

◆ pseudoGramSchmidtOrthogonalization()

◆ rayleighRitz()

◆ rayleighRitzGEP()

◆ reformulatedChebyshevFilter()

◆ XtHX() [1/2]

◆ XtHX() [2/2]

◆ XtHXMixedPrec()

◆ XtHXXtOX()

◆ XtHXXtOXMixedPrec()

◆ XtOX()

◆ XtOXMixedPrec()