Namespaces
namespace	blasLapack

namespace	CGLinearSolverInternal

namespace	LanczosExtremeEigenSolverInternal

namespace	OrthonormalizationFunctionsInternal

Classes
class	ChebyshevFilteredEigenSolver
	A derived class of OperatorContext to encapsulate the action of a discrete operator on vectors, matrices, etc. More...

struct	EigenSolverError

class	EigenSolverErrorMsg

class	IdentityOperatorContext
	Abstract class to encapsulate the action of a discrete operator on vectors, matrices, etc. More...

class	JacobiPreconditioner
	A class to encapsulate the Jacobi preconditioner in a linear or non-linear solve. More...

class	LanczosExtremeEigenSolver
	A derived class of OperatorContext to encapsulate the action of a discrete operator on vectors, matrices, etc. More...

struct	LapackError

class	LapackErrorMsg
	A class to map Error to a message. More...

class	LinAlgOpContext

class	LinearAlgebraProfiler

class	LinearSolverDefaults

struct	LinearSolverError

class	LinearSolverErrorMsg
	A class to map Error to a message. More...

class	LinearSolverImpl
	Abstract class that implements the LinearSolver algorithm. For example, the derived classes of it, such as CGLinearSolver, GMRESLinearSolver implement the Conjugate-Gradient (CG) and Generalized Minimum Residual (GMRES) Krylov subspace based approches, respectively, to solve a linear system of equations. More...

class	MultiPassLowdinDefaults

class	MultiVector
	An class template to encapsulate a MultiVector. A MultiVector is a collection of $N$ vectors belonging to the same finite-dimensional vector space, where usual notion of vector size denotes the dimension of the vector space. Note that this in the mathematical sense and not in the sense of an multi-dimensional array.The MultiVector is stored contiguously with the vector index being the fastest index, or in other words a matrix of size $M \times N$ in row major format with $M $ denoting the dimension of the vector space (size of individual vector). More...

struct	NewtonRaphsonError

class	NewtonRaphsonErrorMsg

class	NewtonRaphsonSolver
	A class that implements the Newton-Raphson solver to find root of a function. More...

class	NewtonRaphsonSolverFunction

class	OperatorContext
	Abstract class to encapsulate the action of a discrete operator on vectors, matrices, etc. More...

struct	OrthonormalizationError

class	OrthonormalizationErrorMsg

class	OrthonormalizationFunctions

class	Preconditioner
	Abstract class to encapsulate a preconditioner. More...

class	PreconditionerJacobi
	Class to encapsulate the Jacobi preconditioner. More...

class	PreconditionerNone
	Class to encapsulate the NONE preconditioner. Just takes in a vector and returns it. More...

class	PrintControlDefaults

class	RayleighRitzEigenSolver
	A derived class of OperatorContext to encapsulate the action of a discrete operator on vectors, matrices, etc. More...

class	Vector
	A class that encapsulates a vector. This is a vector in the mathematical sense and not in the sense of an array or STL container. This class handles both serial and distributed vector in a unfied way. There are different constructors provided for the serial and distributed case. More...

class	VectorAttributes

Enumerations
enum class	LinearSolverType { CG , CG }

enum class	PreconditionerType { NONE , JACOBI }

enum class	NonLinearSolverType { CG , LBFGS }

enum class	ParallelPrintType { NONE , ROOT_ONLY , ALL }

enum class	LapackErrorCode { SUCCESS , FAILED_DENSE_MATRIX_INVERSE , FAILED_TRIA_MATRIX_INVERSE , FAILED_CHOLESKY_FACTORIZATION , FAILED_REAL_TRIDIAGONAL_EIGENPROBLEM , FAILED_STANDARD_EIGENPROBLEM , FAILED_GENERALIZED_EIGENPROBLEM , FAILED_LINEAR_SYSTEM_SOLVE , OTHER_ERROR }

enum class	LinearSolverErrorCode { SUCCESS , FAILED_TO_CONVERGE , RESIDUAL_DIVERGENCE , DIVISON_BY_ZERO , OTHER_ERROR }

enum class	EigenSolverErrorCode { SUCCESS , LAPACK_ERROR , LANCZOS_BETA_ZERO , LANCZOS_SUBSPACE_INSUFFICIENT , CHFSI_ORTHONORMALIZATION_ERROR , CHFSI_RAYLEIGH_RITZ_ERROR , KS_MAX_PASS_ERROR , KS_CHFSI_ERROR , KS_LANCZOS_ERROR , KS_NEWTON_RAPHSON_ERROR , OTHER_ERROR }

enum class	OrthonormalizationErrorCode { SUCCESS , LAPACK_ERROR , NON_ORTHONORMALIZABLE_MULTIVECTOR , MAX_PASS_EXCEEDED }

enum class	NewtonRaphsonErrorCode { SUCCESS , FORCE_TOLERANCE_ERR , FAILED_TO_CONVERGE , OTHER_ERROR }

enum class	LinearSolverType { CG , CG }

enum class	PCType { NONE , JACOBI }

enum class	LinearSolverReturnType { SUCCESS , FAILURE , MAX_ITER_REACHED , INDEFINITE_PC , NAN_RES }

Functions
	CGLinearSolver (const size_type maxIter, const double absoluteTol, const double relativeTol, const double divergenceTol, LinearAlgebraProfiler profiler=LinearAlgebraProfiler())
	A class that implements the Conjugate-Gradient (CG) based Krylov subspace algorithm to solve a linear system of (i.e., solve for \( \mathbf{Ax}=\mathbf{b}$\f). @see <em>An Introduction to the Conjugate Gradient Method Without the Agonizing Pain</em>, Jonathan Richard Shewchuk (<a href="https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf">Painless Conjugate-Gradient</a>) @see <em> Numerical Linear Algebra </em>, Trefethen, Lloyd N., and David Bau III., Vol. 50. Siam, 1997. @tparam ValueTypeOperator The datatype (float, double, complex<double>, etc.) for the operator (e.g. Matrix) associated with the linear solve @tparam ValueTypeOperand The datatype (float, double, complex<double>, etc.) of the vector, matrices, etc. on which the operator will act @tparam memorySpace The meory space (HOST, DEVICE, HOST_PINNED, etc.) in which the data of the operator and its operands reside / template <typename ValueTypeOperator, typename ValueTypeOperand, utils::MemorySpace memorySpace> class CGLinearSolver : public LinearSolverImpl<ValueTypeOperator, ValueTypeOperand, memorySpace> { public: /* @brief Constructor @param[in] maxIter Maximum number of iterations to allow the solver to iterate. Generally, this determines the maximum size of the Krylov subspace that will be used. @param[in] absoluteTol Convergence tolerane on the absolute \) L_2 $\f norm of the residual (i.e., on $\|\|\mathbf{Ax}-\mathbf{b}\|\|$\f) @param[in] relativeTol Convergence tolerane on the relative L2 norm of the residual (i.e., on $\|\|\mathbf{Ax}-\mathbf{b}\|\|/\|\|\mathbf{b}\|\|$\f) More...

	~CGLinearSolver ()=default
	Default Destructor. More...

LinearSolverError	solve (LinearSolverFunction< ValueTypeOperator, ValueTypeOperand, memorySpace > &linearSolverFunction) override
	Function that initiates the linear solve. More...

template<typename ValueTypeOperator , typename ValueTypeOperand , utils::MemorySpace memorySpace>
void	ChebyshevFilter (const OperatorContext< ValueTypeOperator, ValueTypeOperand, memorySpace > &A, const OperatorContext< ValueTypeOperator, ValueTypeOperand, memorySpace > &BInv, MultiVector< ValueTypeOperand, memorySpace > &eigenSubspaceGuess, const size_type polynomialDegree, const double wantedSpectrumLowerBound, const double wantedSpectrumUpperBound, const double unWantedSpectrumUpperBound, MultiVector< blasLapack::scalar_type< ValueTypeOperator, ValueTypeOperand >, memorySpace > &filteredSubspace)
	A class to get chebyshevFiletered subspace "filteredSubspace" from original subspace "eigenSubspaceGuess". Note both of these vectors have to be apriori allocated and both will change after the function is called. More...

template<typename ValueType , dftefe::utils::MemorySpace memorySpace>
void	swap (MultiVector< ValueType, memorySpace > &X, MultiVector< ValueType, memorySpace > &Y)
	Swaps the data of u with this multivector. More...

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>
void	add (blasLapack::scalar_type< ValueType1, ValueType2 > a, const MultiVector< ValueType1, memorySpace > &u, blasLapack::scalar_type< ValueType1, ValueType2 > b, const MultiVector< ValueType2, memorySpace > &v, MultiVector< blasLapack::scalar_type< ValueType1, ValueType2 >, memorySpace > &w)
	Perform $ w = au + bv $. More...

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>
void	add (const std::vector< blasLapack::scalar_type< ValueType1, ValueType2 > > &a, const MultiVector< ValueType1, memorySpace > &u, const std::vector< blasLapack::scalar_type< ValueType1, ValueType2 > > &b, const MultiVector< ValueType2, memorySpace > &v, MultiVector< blasLapack::scalar_type< ValueType1, ValueType2 >, memorySpace > &w)
	Perform $ w = au + bv $. More...

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>
void	dot (const MultiVector< ValueType1, memorySpace > &u, const MultiVector< ValueType2, memorySpace > &v, blasLapack::scalar_type< ValueType1, ValueType2 > *dotProds, const blasLapack::ScalarOp &opU, const blasLapack::ScalarOp &opV)

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>
void	dot (const MultiVector< ValueType1, memorySpace > &u, const MultiVector< ValueType2, memorySpace > &v, std::vector< blasLapack::scalar_type< ValueType1, ValueType2 > > &dotProds, const blasLapack::ScalarOp &opU, const blasLapack::ScalarOp &opV)

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>
void	dot (const Vector< ValueType1, memorySpace > &u, const Vector< ValueType2, memorySpace > &v, blasLapack::scalar_type< ValueType1, ValueType2 > &dotProd, const blasLapack::ScalarOp &opU, const blasLapack::ScalarOp &opV)

Variables
LinearAlgebraProfiler	d_profiler

size_type	d_maxIter

double	d_absoluteTol

double	d_relativeTol

double	d_divergenceTol

Enumeration Type Documentation

◆ EigenSolverErrorCode

enum class dftefe::linearAlgebra::EigenSolverErrorCode

strong

Enumerator
SUCCESS
LAPACK_ERROR
LANCZOS_BETA_ZERO
LANCZOS_SUBSPACE_INSUFFICIENT
CHFSI_ORTHONORMALIZATION_ERROR
CHFSI_RAYLEIGH_RITZ_ERROR
KS_MAX_PASS_ERROR
KS_CHFSI_ERROR
KS_LANCZOS_ERROR
KS_NEWTON_RAPHSON_ERROR
OTHER_ERROR

◆ LapackErrorCode

enum class dftefe::linearAlgebra::LapackErrorCode

strong

Enumerator
SUCCESS
FAILED_DENSE_MATRIX_INVERSE
FAILED_TRIA_MATRIX_INVERSE
FAILED_CHOLESKY_FACTORIZATION
FAILED_REAL_TRIDIAGONAL_EIGENPROBLEM
FAILED_STANDARD_EIGENPROBLEM
FAILED_GENERALIZED_EIGENPROBLEM
FAILED_LINEAR_SYSTEM_SOLVE
OTHER_ERROR

◆ LinearSolverErrorCode

enum class dftefe::linearAlgebra::LinearSolverErrorCode

strong

Enumerator
SUCCESS
FAILED_TO_CONVERGE
RESIDUAL_DIVERGENCE
DIVISON_BY_ZERO
OTHER_ERROR

◆ LinearSolverReturnType

enum class dftefe::linearAlgebra::LinearSolverReturnType

strong

Enumerator
SUCCESS
FAILURE
MAX_ITER_REACHED
INDEFINITE_PC
NAN_RES

◆ LinearSolverType [1/2]

enum class dftefe::linearAlgebra::LinearSolverType

strong

Enumerator
CG
CG

◆ LinearSolverType [2/2]

enum class dftefe::linearAlgebra::LinearSolverType

strong

Enumerator
CG
CG

◆ NewtonRaphsonErrorCode

enum class dftefe::linearAlgebra::NewtonRaphsonErrorCode

strong

Enumerator
SUCCESS
FORCE_TOLERANCE_ERR
FAILED_TO_CONVERGE
OTHER_ERROR

◆ NonLinearSolverType

enum class dftefe::linearAlgebra::NonLinearSolverType

strong

Enumerator
CG
LBFGS

◆ OrthonormalizationErrorCode

enum class dftefe::linearAlgebra::OrthonormalizationErrorCode

strong

Enumerator
SUCCESS
LAPACK_ERROR
NON_ORTHONORMALIZABLE_MULTIVECTOR
MAX_PASS_EXCEEDED

◆ ParallelPrintType

enum class dftefe::linearAlgebra::ParallelPrintType

strong

Enumerator
NONE
ROOT_ONLY
ALL

◆ PCType

enum class dftefe::linearAlgebra::PCType

strong

Enumerator
NONE
JACOBI

◆ PreconditionerType

enum class dftefe::linearAlgebra::PreconditionerType

strong

Enumerator
NONE
JACOBI

Function Documentation

◆ add() [1/2]

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::add	(	blasLapack::scalar_type< ValueType1, ValueType2 >	a,
		const MultiVector< ValueType1, memorySpace > &	u,
		blasLapack::scalar_type< ValueType1, ValueType2 >	b,
		const MultiVector< ValueType2, memorySpace > &	v,
		MultiVector< blasLapack::scalar_type< ValueType1, ValueType2 >, memorySpace > &	w
	)

Perform $ w = au + bv $.

Parameters

[in]	a	scalar
[in]	u	first MultiVector on the right
[in]	b	scalar
[in]	v	second MultiVector on the right
[out]	w	resulting MultiVector

Template Parameters

ValueType1	DataType (double, float, complex<double>, etc.) of u vector
ValueType2	DataType (double, float, complex<double>, etc.) of v vector
memorySpace	defines the MemorySpace (i.e., HOST or DEVICE) in which the vector must reside.

Note: The datatype of the scalars a, b, and the resultant MultiVector w is decided through a union of ValueType1 and ValueType2 (e.g., union of double and complex<double> is complex<double>)

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◆ add() [2/2]

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::add	(	const std::vector< blasLapack::scalar_type< ValueType1, ValueType2 > > &	a,
		const MultiVector< ValueType1, memorySpace > &	u,
		const std::vector< blasLapack::scalar_type< ValueType1, ValueType2 > > &	b,
		const MultiVector< ValueType2, memorySpace > &	v,
		MultiVector< blasLapack::scalar_type< ValueType1, ValueType2 >, memorySpace > &	w
	)

Perform $ w = au + bv $.

Parameters

[in]	a	vector
[in]	u	first MultiVector on the right
[in]	b	vector
[in]	v	second MultiVector on the right
[out]	w	resulting MultiVector

Template Parameters

ValueType1	DataType (double, float, complex<double>, etc.) of u vector
ValueType2	DataType (double, float, complex<double>, etc.) of v vector
memorySpace	defines the MemorySpace (i.e., HOST or DEVICE) in which the vector must reside.

Note: The datatype of the scalars a, b, and the resultant MultiVector w is decided through a union of ValueType1 and ValueType2 (e.g., union of double and complex<double> is complex<double>)

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◆ CGLinearSolver()

dftefe::linearAlgebra::CGLinearSolver	(	const size_type	maxIter,
		const double	absoluteTol,
		const double	relativeTol,
		const double	divergenceTol,
		LinearAlgebraProfiler	profiler = `LinearAlgebraProfiler()`
	)

A class that implements the Conjugate-Gradient (CG) based Krylov subspace algorithm to solve a linear system of (i.e., solve for \( \mathbf{Ax}=\mathbf{b}$\f). @see <em>An Introduction to the Conjugate Gradient Method Without the Agonizing Pain</em>, Jonathan Richard Shewchuk (<a href="https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf">Painless Conjugate-Gradient</a>) @see <em> Numerical Linear Algebra </em>, Trefethen, Lloyd N., and David Bau III., Vol. 50. Siam, 1997. @tparam ValueTypeOperator The datatype (float, double, complex<double>, etc.) for the operator (e.g. Matrix) associated with the linear solve @tparam ValueTypeOperand The datatype (float, double, complex<double>, etc.) of the vector, matrices, etc. on which the operator will act @tparam memorySpace The meory space (HOST, DEVICE, HOST_PINNED, etc.) in which the data of the operator and its operands reside */ template <typename ValueTypeOperator, typename ValueTypeOperand, utils::MemorySpace memorySpace> class CGLinearSolver : public LinearSolverImpl<ValueTypeOperator, ValueTypeOperand, memorySpace> { public: /** @brief Constructor @param[in] maxIter Maximum number of iterations to allow the solver to iterate. Generally, this determines the maximum size of the Krylov subspace that will be used. @param[in] absoluteTol Convergence tolerane on the absolute \) L_2 $\f norm of the residual (i.e., on $||\mathbf{Ax}-\mathbf{b}||$\f) @param[in] relativeTol Convergence tolerane on the relative L2 norm of the residual (i.e., on $||\mathbf{Ax}-\mathbf{b}||/||\mathbf{b}||$\f)

Parameters

[in] divergenceTol Tolerance to abort the linear solver if the L2 norm of the residual exceeds it (i.e., if $||\mathbf{Ax}-\mathbf{b}|| > divergenceTol$\f) @note Convergence is achieved if $||\mathbf{Ax}-\mathbf{b}|| < max(absoluteTol, relativeTol*||\mathbf{b}||)$\f

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◆ ChebyshevFilter()

template<typename ValueTypeOperator , typename ValueTypeOperand , utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::ChebyshevFilter	(	const OperatorContext< ValueTypeOperator, ValueTypeOperand, memorySpace > &	A,
		const OperatorContext< ValueTypeOperator, ValueTypeOperand, memorySpace > &	BInv,
		MultiVector< ValueTypeOperand, memorySpace > &	eigenSubspaceGuess,
		const size_type	polynomialDegree,
		const double	wantedSpectrumLowerBound,
		const double	wantedSpectrumUpperBound,
		const double	unWantedSpectrumUpperBound,
		MultiVector< blasLapack::scalar_type< ValueTypeOperator, ValueTypeOperand >, memorySpace > &	filteredSubspace
	)

A class to get chebyshevFiletered subspace "filteredSubspace" from original subspace "eigenSubspaceGuess". Note both of these vectors have to be apriori allocated and both will change after the function is called.

Template Parameters

ValueTypeOperator	The datatype (float, double, complex<double>, etc.) for the underlying operator
ValueTypeOperand	The datatype (float, double, complex<double>, etc.) of the vector, matrices, etc. on which the operator will act
memorySpace	The meory space (HOST, DEVICE, HOST_PINNED, etc.) in which the data of the operator and its operands reside

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◆ dot() [1/3]

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::dot	(	const MultiVector< ValueType1, memorySpace > &	u,
		const MultiVector< ValueType2, memorySpace > &	v,
		blasLapack::scalar_type< ValueType1, ValueType2 > *	dotProds,
		const blasLapack::ScalarOp &	opU,
		const blasLapack::ScalarOp &	opV
	)

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◆ dot() [2/3]

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::dot	(	const MultiVector< ValueType1, memorySpace > &	u,
		const MultiVector< ValueType2, memorySpace > &	v,
		std::vector< blasLapack::scalar_type< ValueType1, ValueType2 > > &	dotProds,
		const blasLapack::ScalarOp &	opU,
		const blasLapack::ScalarOp &	opV
	)

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◆ dot() [3/3]

template<typename ValueType1 , typename ValueType2 , utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::dot	(	const Vector< ValueType1, memorySpace > &	u,
		const Vector< ValueType2, memorySpace > &	v,
		blasLapack::scalar_type< ValueType1, ValueType2 > &	dotProd,
		const blasLapack::ScalarOp &	opU,
		const blasLapack::ScalarOp &	opV
	)

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◆ solve()

LinearSolverError dftefe::linearAlgebra::solve ( LinearSolverFunction< ValueTypeOperator, ValueTypeOperand, memorySpace > & linearSolverFunction )

override

Function that initiates the linear solve.

Parameters

[in] linearSolverFunction Reference to a LinearSolverFunction object that encapsulates the discrete partial differential equation that is being solved as a linear solve. Typically, the linearSolverFunction provides the right hand side vector (i.e., $\mathbf{b}$\f) and the handle to the action of the discrete operator on a Vector. It also stores the final solution $\mathbf{x}$\f

◆ swap()

template<typename ValueType , dftefe::utils::MemorySpace memorySpace>

void dftefe::linearAlgebra::swap	(	MultiVector< ValueType, memorySpace > &	X,
		MultiVector< ValueType, memorySpace > &	Y
	)

Swaps the data of u with this multivector.

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◆ ~CGLinearSolver()

dftefe::linearAlgebra::~CGLinearSolver ( )

default

Default Destructor.

Variable Documentation

◆ d_absoluteTol

double dftefe::linearAlgebra::d_absoluteTol

private

◆ d_divergenceTol

double dftefe::linearAlgebra::d_divergenceTol

private

◆ d_maxIter

size_type dftefe::linearAlgebra::d_maxIter

private

◆ d_profiler

LinearAlgebraProfiler dftefe::linearAlgebra::d_profiler

private

◆ d_relativeTol

double dftefe::linearAlgebra::d_relativeTol

private

Namespaces

Classes

Enumerations

Functions

Variables

Enumeration Type Documentation

◆ EigenSolverErrorCode

◆ LapackErrorCode

◆ LinearSolverErrorCode

◆ LinearSolverReturnType

◆ LinearSolverType [1/2]

◆ LinearSolverType [2/2]

◆ NewtonRaphsonErrorCode

◆ NonLinearSolverType

◆ OrthonormalizationErrorCode

◆ ParallelPrintType

◆ PCType

◆ PreconditionerType

Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ CGLinearSolver()

◆ ChebyshevFilter()

◆ dot() [1/3]

◆ dot() [2/3]

◆ dot() [3/3]

◆ solve()

◆ swap()

◆ ~CGLinearSolver()

Variable Documentation

◆ d_absoluteTol

◆ d_divergenceTol

◆ d_maxIter

◆ d_profiler

◆ d_relativeTol