Main class for parallel PEXSI. More...

#include <ppexsi.hpp>

Public Member Functions
	PPEXSIData (MPI_Comm comm, Int numProcRow, Int numProcCol, Int outputFileIndex)

void	LoadRealMatrix (Int nrows, Int nnz, Int nnzLocal, Int numColLocal, Int colptrLocal, Int rowindLocal, Real HnzvalLocal, Int isSIdentity, Real SnzvalLocal, Int solver, Int verbosity)

void	LoadComplexMatrix (Int nrows, Int nnz, Int nnzLocal, Int numColLocal, Int colptrLocal, Int rowindLocal, Complex HnzvalLocal, Int isSIdentity, Complex SnzvalLocal, Int solver, Int verbosity)

void	SymbolicFactorizeRealSymmetricMatrix (Int solver, std::string ColPerm, Int numProcSymbFact, Int verbosity)
	Symbolically factorize the loaded matrices for real arithmetic factorization and selected inversion. More...

void	SymbolicFactorizeRealUnsymmetricMatrix (Int solver, std::string ColPerm, std::string RowPerm, Int numProcSymbFact, Int Transpose, double *AnzvalLocal, Int verbosity)
	Symbolically factorize the loaded matrices for real arithmetic factorization and selected inversion. More...

void	SymbolicFactorizeComplexSymmetricMatrix (Int solver, std::string ColPerm, Int numProcSymbFact, Int verbosity)
	Symbolically factorize the loaded matrices for complex arithmetic factorization and selected inversion. More...

void	SymbolicFactorizeComplexUnsymmetricMatrix (Int solver, std::string ColPerm, std::string RowPerm, Int numProcSymbFact, Int Transpose, double *AnzvalLocal, Int verbosity)
	Symbolically factorize the loaded matrices for complex arithmetic factorization and selected inversion. More...

void	SelInvRealSymmetricMatrix (Int solver, double AnzvalLocal, Int verbosity, double AinvnzvalLocal)

void	SelInvRealUnsymmetricMatrix (Int solver, double AnzvalLocal, Int verbosity, double AinvnzvalLocal)

void	SelInvComplexSymmetricMatrix (Int solver, double AnzvalLocal, Int verbosity, double AinvnzvalLocal)

void	SelInvComplexUnsymmetricMatrix (Int solver, double AnzvalLocal, Int verbosity, double AinvnzvalLocal)

void	CalculateNegativeInertiaReal (const std::vector< Real > &shiftVec, std::vector< Real > &inertiaVec, Int solver, Int verbosity)
	Compute the negative inertia (the number of eigenvalues below a shift) for real symmetric matrices. The factorization uses real arithemetic factorization routine. More...

void	CalculateNegativeInertiaComplex (const std::vector< Real > &shiftVec, std::vector< Real > &inertiaVec, Int solver, Int verbosity)
	Compute the negative inertia (the number of eigenvalues below a shift) for complex Hermitian matrices. Currently this is performed with LU factorization without row permutation. More...

void	CalculateFermiOperatorReal (Int numPole, Real temperature, Real gap, Real deltaE, Real mu, Real numElectronExact, Real numElectronTolerance, Int solver, Int verbosity, Real &numElectron, Real &numElectronDrvMu)
	Compute the Fermi operator for a given chemical potential for real symmetric matrices. More...

void	CalculateFermiOperatorComplex (Int numPole, Real temperature, Real gap, Real deltaE, Real mu, Real numElectronExact, Real numElectronTolerance, Int solver, Int verbosity, Real &numElectron, Real &numElectronDrvMu)
	Compute the Fermi operator for a given chemical potential for complex Hermitian matrices. More...

void	DFTDriver (Real numElectronExact, Real temperature, Real gap, Real deltaE, Int numPole, Int isInertiaCount, Int maxPEXSIIter, Real muMin0, Real muMax0, Real mu0, Real muInertiaTolerance, Real muInertiaExpansion, Real muPEXSISafeGuard, Real numElectronPEXSITolerance, Int matrixType, Int isSymbolicFactorize, Int solver, Int ordering, Int numProcSymbFact, Int verbosity, Real &muPEXSI, Real &numElectronPEXSI, Real &muMinInertia, Real &muMaxInertia, Int &numTotalInertiaIter, Int &numTotalPEXSIIter)
	Main driver for solving KSDFT.

void	CalculateFermiOperatorReal2 (Int numPole, Real temperature, Real gap, Real deltaE, Real numElectronExact, Real numElectronTolerance, Real muMinPEXSI, Real muMaxPEXSI, Int solver, Int verbosity, Real &mu, Real &numElectron, bool &isPEXSIConverged)
	Compute the Fermi operator and derivied quantities. More...

void	DFTDriver2 (Real numElectronExact, Real temperature, Real gap, Real deltaE, Int numPole, Int isInertiaCount, Real muMin0, Real muMax0, Real mu0, Real muInertiaTolerance, Real muInertiaExpansion, Real numElectronPEXSITolerance, Int matrixType, Int isSymbolicFactorize, Int solver, Int ordering, Int numProcSymbFact, Int verbosity, Real &muPEXSI, Real &numElectronPEXSI, Real &muMinInertia, Real &muMaxInertia, Int &numTotalInertiaIter)
	Updated main driver for DFT. This reuses the pole expansion and only performs one PEXSI iteration per SCF step.

const GridType *	GridPole () const

const DistSparseMatrix< Real > &	RhoRealMat () const
	Density matrix. More...

const DistSparseMatrix< Complex > &	RhoComplexMat () const

const DistSparseMatrix< Real > &	EnergyDensityRealMat () const
	Energy density matrix. More...

const DistSparseMatrix< Complex > &	EnergyDensityComplexMat () const

const DistSparseMatrix< Real > &	FreeEnergyDensityRealMat () const
	Total Helmholtz free energy matrix (band energy part only). More...

const DistSparseMatrix< Complex > &	FreeEnergyDensityComplexMat () const

Real	TotalEnergyH () const

Real	TotalEnergyS () const

Real	TotalFreeEnergy () const

Detailed Description

Main class for parallel PEXSI.

Member Function Documentation

void PEXSI::PPEXSIData::CalculateFermiOperatorComplex	(	Int	numPole,
		Real	temperature,
		Real	gap,
		Real	deltaE,
		Real	mu,
		Real	numElectronExact,
		Real	numElectronTolerance,
		Int	solver,
		Int	verbosity,
		Real &	numElectron,
		Real &	numElectronDrvMu
	)

Compute the Fermi operator for a given chemical potential for complex Hermitian matrices.

This routine also computes the single particle density matrix, the Helmholtz free energy density matrix, and the energy density matrix (for computing the Pulay force) simultaneously. These matrices can be called later via member functions DensityMatrix, FreeEnergyDensityMatrix, EnergyDensityMatrix.

Parameters

[in]	numPole	Number of poles for the pole expansion
[in]	temperature	Temperature
[in]	gap	Band gap
[in]	deltaE	Upperbound of the spectrum width
[in]	mu	Initial guess of chemical potential.
[in]	numElectronExact	Exact number of electrons.
[in]	numElectronTolerance	Tolerance for the number of electrons. This is just used to discard some poles in the pole expansion.
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.
[out]	numElectron	The number of electron calculated at mu.
[out]	numElectronDrvMu	The derivative of the number of electron calculated with respect to the chemical potential at mu.

void PEXSI::PPEXSIData::CalculateFermiOperatorReal	(	Int	numPole,
		Real	temperature,
		Real	gap,
		Real	deltaE,
		Real	mu,
		Real	numElectronExact,
		Real	numElectronTolerance,
		Int	solver,
		Int	verbosity,
		Real &	numElectron,
		Real &	numElectronDrvMu
	)

Compute the Fermi operator for a given chemical potential for real symmetric matrices.

This routine also computes the single particle density matrix, the Helmholtz free energy density matrix, and the energy density matrix (for computing the Pulay force) simultaneously. These matrices can be called later via member functions DensityMatrix, FreeEnergyDensityMatrix, EnergyDensityMatrix.

Parameters

[in]	numPole	Number of poles for the pole expansion
[in]	temperature	Temperature
[in]	gap	Band gap
[in]	deltaE	Upperbound of the spectrum width
[in]	mu	Initial guess of chemical potential.
[in]	numElectronExact	Exact number of electrons.
[in]	numElectronTolerance	Tolerance for the number of electrons. This is just used to discard some poles in the pole expansion.
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.
[out]	numElectron	The number of electron calculated at mu.
[out]	numElectronDrvMu	The derivative of the number of electron calculated with respect to the chemical potential at mu.

void PEXSI::PPEXSIData::CalculateFermiOperatorReal2	(	Int	numPole,
		Real	temperature,
		Real	gap,
		Real	deltaE,
		Real	numElectronExact,
		Real	numElectronTolerance,
		Real	muMinPEXSI,
		Real	muMaxPEXSI,
		Int	solver,
		Int	verbosity,
		Real &	mu,
		Real &	numElectron,
		bool &	isPEXSIConverged
	)

Compute the Fermi operator and derivied quantities.

This routine also updates the chemical potential mu by reusing Green's functions but with updated contour.

This routine also computes the single particle density matrix, the Helmholtz free energy density matrix, and the energy density matrix (for computing the Pulay force) simultaneously. These matrices can be called later via member functions DensityMatrix, FreeEnergyDensityMatrix, EnergyDensityMatrix.

Parameters

[in]	numPole	Number of poles for the pole expansion
[in]	temperature	Temperature
[in]	gap	Band gap
[in]	deltaE	Upperbound of the spectrum width
[in]	numElectronExact	Exact number of electrons.
[in]	numElectronTolerance	Tolerance for the number of electrons. This is just used to discard some poles in the pole expansion.
[in]	muMinPEXSI	Minimum of the interval for searching mu.
[in]	muMaxPEXSI	Maximum of the interval for searching mu.
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.
[in,out]	mu	Initial guess of chemical potential. On return it gives the updated chemical potential within the range of [muMinPEXSI, muMaxPEXSI]
[out]	numElectron	The number of electron calculated at mu.
[out]	isConverged	Whether the update strategy for finding the chemical potential has converged.

void PEXSI::PPEXSIData::CalculateNegativeInertiaComplex	(	const std::vector< Real > &	shiftVec,
		std::vector< Real > &	inertiaVec,
		Int	solver,
		Int	verbosity
	)

Compute the negative inertia (the number of eigenvalues below a shift) for complex Hermitian matrices. Currently this is performed with LU factorization without row permutation.

This subroutine computes the negative inertia of the matrix

I = H - shift * S

where I is the same as the number of eigenvalues lambda for

H x = lambda S x

with lambda < shift according to the Sylvester's law of inertia.

Parameters

[in]	shiftVec	Shift vectors.
[out]	inertiaVec	Negative inertia count, the same size as shiftVec.
[in]	HMat	Hamiltonian matrix saved in distributed compressed sparse column format. See DistSparseMatrix.
[in]	SMat	Overlap matrix saved in distributed compressed sparse column format. See DistSparseMatrix.

Note: If SMat.size == 0, SMat is treated as an identity matrix.

Parameters

[in]

verbosity

The level of output information.

= 0 : No output.
= 1 : Basic output (default)
= 2 : Detailed output.

void PEXSI::PPEXSIData::CalculateNegativeInertiaReal	(	const std::vector< Real > &	shiftVec,
		std::vector< Real > &	inertiaVec,
		Int	solver,
		Int	verbosity
	)

Compute the negative inertia (the number of eigenvalues below a shift) for real symmetric matrices. The factorization uses real arithemetic factorization routine.

This subroutine computes the negative inertia of the matrix

I = H - shift * S

where I is the same as the number of eigenvalues lambda for

H x = lambda S x

with lambda < shift according to the Sylvester's law of inertia.

Parameters

[in]	shiftVec	Shift vectors.
[out]	inertiaVec	Negative inertia count, the same size as shiftVec.
[in]	HMat	Hamiltonian matrix saved in distributed compressed sparse column format. See DistSparseMatrix.
[in]	SMat	Overlap matrix saved in distributed compressed sparse column format. See DistSparseMatrix.

Note: If SMat.size == 0, SMat is treated as an identity matrix.

Parameters

[in]

verbosity

The level of output information.

= 0 : No output.
= 1 : Basic output (default)
= 2 : Detailed output.

const DistSparseMatrix<Real>& PEXSI::PPEXSIData::EnergyDensityRealMat ( ) const

inline

Energy density matrix.

Can be used to estimate the total band energy via Tr[EDM*S] or the force, including the Hellman-Feynman force and the Pulay force.

const DistSparseMatrix<Real>& PEXSI::PPEXSIData::FreeEnergyDensityRealMat ( ) const

inline

Total Helmholtz free energy matrix (band energy part only).

The Helmholtz free energy is computed by Tr[rho_f*H].

For more information see Alavi, A., Kohanoff, J., Parrinello, M., & Frenkel, D. (1994). Ab initio molecular dynamics with excited electrons. Physical review letters, 73(19), 2599–2602.

const DistSparseMatrix<Real>& PEXSI::PPEXSIData::RhoRealMat ( ) const

inline

Density matrix.

Can be used to estimate the number of electrons by Tr[DM*S] or the band energy via Tr[DM*H]

void PEXSI::PPEXSIData::SymbolicFactorizeComplexSymmetricMatrix	(	Int	solver,
		std::string	ColPerm,
		Int	numProcSymbFact,
		Int	verbosity
	)

Symbolically factorize the loaded matrices for complex arithmetic factorization and selected inversion.

The symbolic information is saved internally at luComplexMat_ or sympackComplexMat_ and PMComplexMat_.

Parameters

[in]	solver	Solver used: SuperLU_DIST or symPACK
[in]	ColPerm	Permutation method used by the solver
[in]	numProcSymbFact	Number of processors used for parallel symbolic factorization and PARMETIS/PT-SCOTCH.
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.

void PEXSI::PPEXSIData::SymbolicFactorizeComplexUnsymmetricMatrix	(	Int	solver,
		std::string	ColPerm,
		std::string	RowPerm,
		Int	numProcSymbFact,
		Int	Transpose,
		double *	AnzvalLocal,
		Int	verbosity
	)

Symbolically factorize the loaded matrices for complex arithmetic factorization and selected inversion.

The symbolic information is saved internally at luComplexMat_ and PMComplexUnsymMat_.

Parameters

[in]	solver	Solver used: SuperLU_DIST
[in]	ColPerm	Permutation method used for SuperLU_DIST
[in]	RowPerm	Row Permutation method used for SuperLU_DIST
[in]	numProcSymbFact	Number of processors used for parallel symbolic factorization and PARMETIS/PT-SCOTCH.
[in]	Transpose	TODO
[in]	AnzvalLocal	non zero values for row permutation
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.

void PEXSI::PPEXSIData::SymbolicFactorizeRealSymmetricMatrix	(	Int	solver,
		std::string	ColPerm,
		Int	numProcSymbFact,
		Int	verbosity
	)

Symbolically factorize the loaded matrices for real arithmetic factorization and selected inversion.

The symbolic information is saved internally at luRealMat_ or sympackRealMat_ and PMRealMat_.

Parameters

[in]	solver	Solver used: SuperLU_DIST or symPACK
[in]	ColPerm	Permutation method used by the solver
[in]	numProcSymbFact	Number of processors used for parallel symbolic factorization and PARMETIS/PT-SCOTCH.
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.

void PEXSI::PPEXSIData::SymbolicFactorizeRealUnsymmetricMatrix	(	Int	solver,
		std::string	ColPerm,
		std::string	RowPerm,
		Int	numProcSymbFact,
		Int	Transpose,
		double *	AnzvalLocal,
		Int	verbosity
	)

Symbolically factorize the loaded matrices for real arithmetic factorization and selected inversion.

The symbolic information is saved internally at luRealMat_ and PMRealMat_.

Parameters

[in]	solver	Solver used: SuperLU_DIST
[in]	ColPerm	Permutation method used for SuperLU_DIST
[in]	RowPerm	Row Permutation method used for SuperLU_DIST
[in]	numProcSymbFact	Number of processors used for parallel symbolic factorization and PARMETIS/PT-SCOTCH.
[in]	Transpose	TODO
[in]	AnzvalLocal	non zero values for row permutation
[in]	verbosity	The level of output information. = 0 : No output. = 1 : Basic output (default) = 2 : Detailed output.

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

Public Member Functions

Detailed Description

Member Function Documentation