Namespaces
	CompressData

	StdHexData

	StdPrismData

	StdPyrData

	StdQuadData

	StdSegData

	StdTetData

	StdTriData

Classes
class	AnalyticExpressionEvaluator
	This class defines evaluator of analytic (symbolic) mathematical expressions. Expressions are allowed to depend on a number of spatial-time variables and parameters. Pre-processing and evaluation stages are split. At evaluation stage one specifies values for each variable, resulting expression value is returned. Vectorized evaluator (evaluate expression at a set of points) is available. More...

class	Basis
	Represents a basis of a given type. More...

class	BasisKey
	Describes the specification for a Basis. More...

class	BLPoints

struct	CmdLineArg

class	Comm
	Base communications class. More...

class	CommMpi
	A global linear system. More...

class	CommSerial
	A global linear system. More...

struct	defOpLessCreator

class	Equation

struct	FieldDefinitions

class	FieldIO
	Class for operating on FLD files. More...

class	FourierPoints

class	FourierSingleModePoints

struct	func

struct	functions

struct	FunctionVariableDefinition

class	GaussPoints

class	Graph

class	GraphEdgeObject

class	GraphVertexObject

class	Kernel

struct	MeshCurvedInfo

struct	MeshCurvedPts

struct	MeshEdge

struct	MeshHex

class	MeshPartition

class	MeshPartitionMetis

class	MeshPartitionScotch

struct	MeshPrism

struct	MeshPyr

struct	MeshQuad

struct	MeshTet

struct	MeshTri

struct	MeshVertex

class	NekFactory
	Provides a generic Factory class. More...

class	NekFFTW

class	NekManager

class	NektarFFT

class	NodalPrismEvenlySpaced

class	NodalTetElec

class	NodalTetEvenlySpaced

class	NodalTriElec

class	NodalTriEvenlySpaced

class	NodalTriFekete

struct	none

class	Points
	Stores a set of points of datatype DataT, defined by a PointKey. More...

class	PointsKey
	Defines a specification for a set of points. More...

class	PolyEPoints

class	PtsField

class	PtsIO

class	PtsPoint

class	SessionReader
	Reads and parses information from a Nektar++ XML session file. More...

class	TimeIntegrationAdamsBashforthOrder2

class	TimeIntegrationAdamsBashforthOrder3

class	TimeIntegrationAdamsMoultonOrder2

class	TimeIntegrationBackwardEuler

class	TimeIntegrationBDFImplicitOrder1

class	TimeIntegrationBDFImplicitOrder2

class	TimeIntegrationClassicalRungeKutta4

class	TimeIntegrationCNAB

class	TimeIntegrationDIRKOrder2

class	TimeIntegrationDIRKOrder3

class	TimeIntegrationForwardEuler

class	TimeIntegrationIMEXdirk_1_1_1

class	TimeIntegrationIMEXdirk_1_2_1

class	TimeIntegrationIMEXdirk_1_2_2

class	TimeIntegrationIMEXdirk_2_2_2

class	TimeIntegrationIMEXdirk_2_3_2

class	TimeIntegrationIMEXdirk_2_3_3

class	TimeIntegrationIMEXdirk_3_4_3

class	TimeIntegrationIMEXdirk_4_4_3

class	TimeIntegrationIMEXGear

class	TimeIntegrationIMEXOrder1

class	TimeIntegrationIMEXOrder2

class	TimeIntegrationIMEXOrder3

class	TimeIntegrationMCNAB

class	TimeIntegrationMidpoint

class	TimeIntegrationRungeKutta2

class	TimeIntegrationRungeKutta2_ImprovedEuler

class	TimeIntegrationRungeKutta2_SSP

class	TimeIntegrationRungeKutta3_SSP

class	TimeIntegrationRungeKutta4

class	TimeIntegrationScheme

class	TimeIntegrationSchemeKey

class	TimeIntegrationSchemeOperators

class	TimeIntegrationSolution

class	TimeIntegrationWrapper

class	Transposition

Typedefs
typedef std::map< std::string, std::string >	FieldMetaDataMap

typedef boost::shared_ptr < FieldDefinitions >	FieldDefinitionsSharedPtr

typedef boost::shared_ptr < FieldIO >	FieldIOSharedPtr

typedef boost::shared_ptr < SessionReader >	SessionReaderSharedPtr

typedef std::map< int, std::vector< unsigned int > >	CompositeOrdering

typedef std::map< int, std::vector< unsigned int > >	BndRegionOrdering

typedef LibUtilities::NekFactory < std::string, MeshPartition, const SessionReaderSharedPtr & >	MeshPartitionFactory
	Datatype of the NekFactory used to instantiate classes derived from the EquationSystem class. More...

typedef boost::shared_ptr < MeshPartition >	MeshPartitionSharedPtr

typedef boost::unique_lock < boost::shared_mutex >	WriteLock

typedef boost::shared_lock < boost::shared_mutex >	ReadLock

typedef boost::shared_ptr < PtsField >	PtsFieldSharedPtr

typedef std::map< std::string, std::string >	PtsMetaDataMap

typedef boost::shared_ptr< PtsIO >	PtsIOSharedPtr

typedef std::map< std::string, std::string >	SolverInfoMap

typedef std::map< std::string, NekDouble >	ParameterMap

typedef std::map< std::string, std::string >	GeometricInfoMap

typedef std::map< std::string, std::string >	ExpressionMap

typedef std::vector< std::string >	VariableList

typedef std::map< std::string, std::string >	TagMap

typedef std::map< std::string, std::string >	FilterParams

typedef std::vector< std::pair < std::string, FilterParams > >	FilterMap

typedef std::map< std::string, CmdLineArg >	CmdLineArgMap

typedef std::map< std::string, int >	EnumMap

typedef std::map< std::string, EnumMap >	EnumMapList

typedef std::map< std::string, std::string >	GloSysInfoMap

typedef std::map< std::string, GloSysInfoMap >	GloSysSolnInfoList

typedef boost::shared_ptr < Equation >	EquationSharedPtr

typedef std::map< std::pair < std::string, int > , FunctionVariableDefinition >	FunctionVariableMap

typedef std::map< std::string, FunctionVariableMap >	FunctionMap

typedef boost::shared_ptr< Comm >	CommSharedPtr
	Pointer to a Communicator object. More...

typedef LibUtilities::NekFactory < std::string, Comm, int, char ** >	CommFactory
	Datatype of the NekFactory used to instantiate classes derived from the EquationSystem class. More...

typedef boost::shared_ptr < CommMpi >	CommMpiSharedPtr
	Pointer to a Communicator object. More...

typedef boost::shared_ptr < CommSerial >	CommSerialSharedPtr
	Pointer to a Communicator object. More...

typedef boost::shared_ptr < Transposition >	TranspositionSharedPtr

typedef boost::shared_ptr < NekFFTW >	NekFFTWSharedPtr

typedef boost::shared_ptr < NektarFFT >	NektarFFTSharedPtr

typedef LibUtilities::NekFactory < std::string, NektarFFT, int >	NektarFFTFactory
	Datatype of the NekFactory used to instantiate classes derived from the NektarFFT class. More...

typedef std::vector< BasisKey >	BasisKeyVector
	Name for a vector of BasisKeys. More...

typedef std::vector< BasisKey > ::iterator	BasisKeyVectorIter
	Name for an iterator over a BasisKeyVector. More...

typedef boost::shared_ptr< Basis >	BasisSharedPtr

typedef std::vector < BasisSharedPtr >	BasisVector

typedef std::vector < BasisSharedPtr >::iterator	BasisVectorIter

typedef Points< NekDouble >	PointsBaseType

typedef boost::shared_ptr < Points< NekDouble > >	PointsSharedPtr

typedef int	GraphVertexID

typedef NekManager< PointsKey, Points< NekDouble > , PointsKey::opLess >	PointsManagerT

typedef NekManager< BasisKey, Basis, BasisKey::opLess >	BasisManagerT

typedef std::vector< PointsKey >	PointsKeyVector

typedef NekDouble(*	PFD )()

typedef NekDouble(*	PFD1 )(NekDouble)

typedef NekDouble(*	PFD2 )(NekDouble, NekDouble)

typedef NekDouble(*	PFD3 )(NekDouble, NekDouble, NekDouble)

typedef NekDouble(*	PFD4 )(NekDouble, NekDouble, NekDouble, NekDouble)

typedef boost::shared_ptr< Kernel >	KernelSharedPtr

typedef boost::shared_ptr < TimeIntegrationScheme >	TimeIntegrationSchemeSharedPtr

typedef std::vector < TimeIntegrationSchemeSharedPtr >	TimeIntegrationSchemeVector

typedef std::vector < TimeIntegrationSchemeSharedPtr > ::iterator	TimeIntegrationSchemeVectorIter

typedef boost::shared_ptr < TimeIntegrationSolution >	TimeIntegrationSolutionSharedPtr

typedef std::vector < TimeIntegrationSolutionSharedPtr >	TimeIntegrationSolutionVector

typedef std::vector < TimeIntegrationSolutionSharedPtr > ::iterator	TimeIntegrationSolutionVectorIter

typedef NekManager < TimeIntegrationSchemeKey, TimeIntegrationScheme, TimeIntegrationSchemeKey::opLess >	TimeIntegrationSchemeManagerT

typedef NekFactory < std::string, TimeIntegrationWrapper >	TimeIntegrationWrapperFactory
	Datatype of the NekFactory used to instantiate classes derived from the EquationSystem class. More...

typedef boost::shared_ptr < TimeIntegrationWrapper >	TimeIntegrationWrapperSharedPtr

typedef boost::shared_ptr < TimeIntegrationIMEXOrder1 >	TimeIntegrationIMEXOrder1SharedPtr

Enumerations
enum	EndianType { eEndianUnknown, eEndianBig, eEndianLittle, eEndianBigWord, eEndianLittleWord }

enum	PtsType { ePtsFile, ePtsLine, ePtsPlane, ePtsBox, ePtsTriBlock, ePtsTetBlock }

enum	PtsInfo { eIsEquiSpacedData, ePtsPerElmtEdge }

enum	FunctionType { eFunctionTypeExpression, eFunctionTypeFile, eFunctionTypeTransientFile, eSIZE_FunctionType }

enum	ShapeType { eNoShapeType, ePoint, eSegment, eTriangle, eQuadrilateral, eTetrahedron, ePyramid, ePrism, eHexahedron, SIZE_ShapeType }

enum	ReduceOperator { ReduceSum, ReduceMax, ReduceMin }
	Type of operation to perform in AllReduce. More...

enum	TranspositionDir { eXYtoZ, eZtoXY, eXtoYZ, eYZtoX, eYZtoZY, eZYtoYZ, eXtoY, eYtoZ, eZtoX, eNoTrans }

enum	BasisType { eNoBasisType, eOrtho_A, eOrtho_B, eOrtho_C, eModified_A, eModified_B, eModified_C, eFourier, eGLL_Lagrange, eGauss_Lagrange, eLegendre, eChebyshev, eMonomial, eFourierSingleMode, eFourierHalfModeRe, eFourierHalfModeIm, SIZE_BasisType }

enum	PointsType { eNoPointsType, eGaussGaussLegendre, eGaussRadauMLegendre, eGaussRadauPLegendre, eGaussLobattoLegendre, eGaussGaussChebyshev, eGaussRadauMChebyshev, eGaussRadauPChebyshev, eGaussLobattoChebyshev, eGaussRadauMAlpha0Beta1, eGaussRadauMAlpha0Beta2, eGaussRadauMAlpha1Beta0, eGaussRadauMAlpha2Beta0, eGaussKronrodLegendre, eGaussRadauKronrodMLegendre, eGaussRadauKronrodMAlpha1Beta0, eGaussLobattoKronrodLegendre, ePolyEvenlySpaced, eFourierEvenlySpaced, eFourierSingleModeSpaced, eBoundaryLayerPoints, eBoundaryLayerPointsRev, eNodalTriElec, eNodalTriFekete, eNodalTriEvenlySpaced, eNodalTetEvenlySpaced, eNodalTetElec, eNodalPrismEvenlySpaced, SIZE_PointsType }

enum	TimeIntegrationMethod { eNoTimeIntegrationMethod, eAdamsBashforthOrder1, eAdamsBashforthOrder2, eAdamsBashforthOrder3, eAdamsMoultonOrder1, eAdamsMoultonOrder2, eBDFImplicitOrder1, eBDFImplicitOrder2, eClassicalRungeKutta4, eRungeKutta4, eRungeKutta3_SSP, eRungeKutta2_ImprovedEuler, eRungeKutta2_SSP, eForwardEuler, eBackwardEuler, eIMEXOrder1, eIMEXOrder2, eIMEXOrder3, eMidpoint, eRungeKutta2, eDIRKOrder2, eDIRKOrder3, eCNAB, eIMEXGear, eMCNAB, eIMEXdirk_1_1_1, eIMEXdirk_1_2_1, eIMEXdirk_1_2_2, eIMEXdirk_2_2_2, eIMEXdirk_2_3_2, eIMEXdirk_2_3_3, eIMEXdirk_3_4_3, eIMEXdirk_4_4_3, SIZE_TimeIntegrationMethod }

enum	TimeIntegrationSchemeType { eNoTimeIntegrationSchemeType, eExplicit, eDiagonallyImplicit, eIMEX, eImplicit }

Functions
EndianType	Endianness (void)

void	Write (const std::string &outFile, std::vector< FieldDefinitionsSharedPtr > &fielddefs, std::vector< std::vector< NekDouble > > &fielddata, const FieldMetaDataMap &fieldinfomap=NullFieldMetaDataMap)
	Write a field file in serial only. More...

void	Import (const std::string &infilename, std::vector< FieldDefinitionsSharedPtr > &fielddefs, std::vector< std::vector< NekDouble > > &fielddata=NullVectorNekDoubleVector, FieldMetaDataMap &fieldinfomap=NullFieldMetaDataMap, const Array< OneD, int > ElementiDs=NullInt1DArray)
	Imports an FLD file. More...

std::string	PortablePath (const boost::filesystem::path &path)
	create portable path on different platforms for boost::filesystem path More...

MeshPartitionFactory &	GetMeshPartitionFactory ()

void	PrintProgressbar (const int position, const int goal, const string message)
	Prints a progressbar. More...

void	Import (const string &inFile, PtsFieldSharedPtr &ptsField)

void	Write (const string &outFile, const PtsFieldSharedPtr &ptsField)

int	GetNumberOfCoefficients (ShapeType shape, std::vector< unsigned int > &modes, int offset)

int	GetNumberOfCoefficients (ShapeType shape, int na, int nb, int nc)

CommFactory &	GetCommFactory ()

NektarFFTFactory &	GetNektarFFTFactory ()

bool	operator< (const BasisKey &lhs, const BasisKey &rhs)

bool	operator> (const BasisKey &lhs, const BasisKey &rhs)

std::ostream &	operator<< (std::ostream &os, const BasisKey &rhs)

bool	operator== (const BasisKey &x, const BasisKey &y)

bool	operator== (const BasisKey *x, const BasisKey &y)

bool	operator== (const BasisKey &x, const BasisKey *y)

bool	operator!= (const BasisKey &x, const BasisKey &y)

bool	operator!= (const BasisKey *x, const BasisKey &y)

bool	operator!= (const BasisKey &x, const BasisKey *y)

static const BasisKey	NullBasisKey (eNoBasisType, 0, NullPointsKey)
	Defines a null basis with no type or points. More...

bool	operator== (const GraphVertexObject &x, const GraphVertexObject &y)

bool	operator!= (const GraphVertexObject &x, const GraphVertexObject &y)

void	Interp1D (const BasisKey &fbasis0, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, Array< OneD, NekDouble > &to)
	this function interpolates a 1D function evaluated at the quadrature points of the basis fbasis0 to the function values at the quadrature points of the basis tbasis0 More...

void	Interp1D (const PointsKey &fpoints0, const Array< OneD, const NekDouble > &from, const PointsKey &tpoints0, Array< OneD, NekDouble > &to)

void	Interp1D (const BasisKey &fbasis0, const NekDouble from, const BasisKey &tbasis0, NekDouble to)

void	Interp1D (const PointsKey &fpoints0, const NekDouble from, const PointsKey &tpoints0, NekDouble to)

void	Interp2D (const BasisKey &fbasis0, const BasisKey &fbasis1, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, Array< OneD, NekDouble > &to)
	this function interpolates a 2D function evaluated at the quadrature points of the 2D basis, constructed by fbasis0 and fbasis1, to the function values at the quadrature points of the 2D basis, constructed by tbasis0 and tbasis1 More...

void	Interp2D (const PointsKey &fpoints0, const PointsKey &fpoints1, const Array< OneD, const NekDouble > &from, const PointsKey &tpoints0, const PointsKey &tpoints1, Array< OneD, NekDouble > &to)

void	Interp2D (const PointsKey &fpoints0, const PointsKey &fpoints1, const NekDouble from, const PointsKey &tpoints0, const PointsKey &tpoints1, NekDouble to)

void	Interp3D (const BasisKey &fbasis0, const BasisKey &fbasis1, const BasisKey &fbasis2, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, const BasisKey &tbasis2, Array< OneD, NekDouble > &to)
	this function interpolates a 3D function evaluated at the quadrature points of the 3D basis, constructed by fbasis0, fbasis1, and fbasis2 to the function values at the quadrature points of the 3D basis, constructed by tbasis0, tbasis1, and tbasis2. More...

void	Interp3D (const PointsKey &fpoints0, const PointsKey &fpoints1, const PointsKey &fpoints2, const Array< OneD, const NekDouble > &from, const PointsKey &tpoints0, const PointsKey &tpoints1, const PointsKey &tpoints2, Array< OneD, NekDouble > &to)

void	Interp3D (const PointsKey &fpoints0, const PointsKey &fpoints1, const PointsKey &fpoints2, const NekDouble from, const PointsKey &tpoints0, const PointsKey &tpoints1, const PointsKey &tpoints2, NekDouble to)

void	InterpCoeff1D (const BasisKey &fbasis0, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, Array< OneD, NekDouble > &to)

void	InterpCoeff2D (const BasisKey &fbasis0, const BasisKey &fbasis1, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, Array< OneD, NekDouble > &to)

void	InterpCoeff2D (const BasisKey &fbasis0, const BasisKey &fbasis1, const NekDouble from, const BasisKey &tbasis0, const BasisKey &tbasis1, NekDouble to)

void	InterpCoeff3D (const BasisKey &fbasis0, const BasisKey &fbasis1, const BasisKey &fbasis2, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, const BasisKey &tbasis2, Array< OneD, NekDouble > &to)

void	InterpCoeff3D (const BasisKey &fbasis0, const BasisKey &fbasis1, const BasisKey &fbasis2, const NekDouble from, const BasisKey &tbasis0, const BasisKey &tbasis1, const BasisKey &tbasis2, NekDouble to)

PointsManagerT &	PointsManager (void)

BasisManagerT &	BasisManager (void)

template<typename T >
NekVector< T >	GetColumn (const NekMatrix< T > &matA, int n)

NekMatrix< NekDouble > &	SetColumn (NekMatrix< NekDouble > &matA, int n, const NekVector< NekDouble > &x)

NekVector< NekDouble >	GetE (int rows, int n)

NekMatrix< NekDouble >	Invert (const NekMatrix< NekDouble > &matA)

NekMatrix< NekDouble >	GetTranspose (const NekMatrix< NekDouble > &matA)

int	GetSize (const Array< OneD, const NekDouble > &x)

int	GetSize (const NekVector< NekDouble > &x)

NekVector< NekDouble >	ToVector (const Array< OneD, const NekDouble > &x)

Array< OneD, NekDouble >	ToArray (const NekVector< NekDouble > &x)

NekVector< NekDouble >	Hadamard (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekVector< NekDouble >	VectorPower (const NekVector< NekDouble > &x, NekDouble p)

std::string	MatrixToString (const NekMatrix< NekDouble > &A, int precision, NekDouble expSigFigs)

std::string	VectorToString (const NekVector< NekDouble > &v, int precision, NekDouble expSigFigs)

int	GetTriNumPoints (int degree)

int	GetDegree (int nBasisFunctions)

int	GetTetNumPoints (int degree)

int	GetTetDegree (int nBasisFunc)

NekDouble	MakeRound (NekDouble x)

NekVector< NekDouble >	MakeDubinerQuadratureSystem (int nBasisFunctions)

NekVector< NekDouble >	MakeTetQuadratureSystem (int nBasisFunctions)

NekVector< NekDouble >	JacobiPoly (int degree, const NekVector< NekDouble > &x, NekDouble alpha, NekDouble beta)

NekDouble	JacobiPoly (int degree, NekDouble x, NekDouble alpha, NekDouble beta)

NekVector< NekDouble >	LegendrePoly (int degree, const NekVector< NekDouble > &x)

NekVector< NekDouble >	DubinerPoly (int p, int q, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekVector< NekDouble >	TetrahedralBasis (int p, int q, int r, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetTetVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetTetVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, int degree)

NekMatrix< NekDouble >	GetVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

SharedNekMatrixPtr	MakeVmatrixOfTet (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

SharedNekMatrixPtr	MakeVmatrixOfDubinerPolynomial (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekVector< NekDouble >	MakeTetWeights (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekVector< NekDouble >	MakeQuadratureWeights (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekMatrix< NekDouble >	GetTetInterpolationMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi, const NekVector< NekDouble > &zi)

NekMatrix< NekDouble >	GetInterpolationMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi)

NekVector< NekDouble >	LegendrePolyDerivative (int degree, const NekVector< NekDouble > &x)

NekVector< NekDouble >	DubinerPolyXDerivative (int p, int q, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekVector< NekDouble >	TetXDerivative (int p, int q, int r, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetVandermondeForTetXDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetVandermondeForTetXDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

Points< NekDouble > ::MatrixSharedPtrType	GetTetXDerivativeMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi, const NekVector< NekDouble > &zi)

NekMatrix< NekDouble >	GetVandermondeForXDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, int degree)

NekMatrix< NekDouble >	GetVandermondeForXDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

Points< NekDouble > ::MatrixSharedPtrType	GetXDerivativeMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi)

NekVector< NekDouble >	JacobiPolyDerivative (int degree, const NekVector< NekDouble > &x, int alpha, int beta)

NekVector< NekDouble >	TetYDerivative (int p, int q, int r, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetVandermondeForTetYDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetVandermondeForTetYDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

Points< NekDouble > ::MatrixSharedPtrType	GetTetYDerivativeMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi, const NekVector< NekDouble > &zi)

NekVector< NekDouble >	TetZDerivative (int p, int q, int r, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetVandermondeForTetZDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetVandermondeForTetZDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

Points< NekDouble > ::MatrixSharedPtrType	GetTetZDerivativeMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi, const NekVector< NekDouble > &zi)

NekVector< NekDouble >	DubinerPolyYDerivative (int p, int q, const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekMatrix< NekDouble >	GetVandermondeForYDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, int degree)

Points< NekDouble > ::MatrixSharedPtrType	GetYDerivativeMatrix (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &xi, const NekVector< NekDouble > &yi)

NekMatrix< NekDouble >	GetVandermondeForYDerivative (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekMatrix< NekDouble >	GetMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, int degree)

NekMatrix< NekDouble >	GetMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekMatrix< NekDouble >	GetXDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, int degree)

NekMatrix< NekDouble >	GetXDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekMatrix< NekDouble >	GetTetXDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetTetXDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetTetYDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetTetYDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetTetZDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z, int degree)

NekMatrix< NekDouble >	GetTetZDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, const NekVector< NekDouble > &z)

NekMatrix< NekDouble >	GetYDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y, int degree)

NekMatrix< NekDouble >	GetYDerivativeOfMonomialVandermonde (const NekVector< NekDouble > &x, const NekVector< NekDouble > &y)

NekVector< NekDouble >	GetIntegralOfMonomialVandermonde (int degree)

void	PhysGalerkinProject1D (const BasisKey &fbasis0, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, Array< OneD, NekDouble > &to)

void	PhysGalerkinProject1D (const PointsKey &fpoints0, const Array< OneD, const NekDouble > &from, const PointsKey &tpoints0, Array< OneD, NekDouble > &to)

void	PhysGalerkinProject1D (const BasisKey &fbasis0, const NekDouble from, const BasisKey &tbasis0, NekDouble to)

void	PhysGalerkinProject1D (const PointsKey &fpoints0, const NekDouble from, const PointsKey &tpoints0, NekDouble to)

void	PhysGalerkinProject2D (const BasisKey &fbasis0, const BasisKey &fbasis1, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, Array< OneD, NekDouble > &to)

void	PhysGalerkinProject2D (const PointsKey &fpoints0, const PointsKey &fpoints1, const Array< OneD, const NekDouble > &from, const PointsKey &tpoints0, const PointsKey &tpoints1, Array< OneD, NekDouble > &to)

void	PhysGalerkinProject2D (const PointsKey &fpoints0, const PointsKey &fpoints1, const NekDouble from, const PointsKey &tpoints0, const PointsKey &tpoints1, NekDouble to)

void	PhysGalerkinProject3D (const BasisKey &fbasis0, const BasisKey &fbasis1, const BasisKey &fbasis2, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, const BasisKey &tbasis2, Array< OneD, NekDouble > &to)

void	PhysGalerkinProject3D (const PointsKey &fpoints0, const PointsKey &fpoints1, const PointsKey &fpoints2, const Array< OneD, const NekDouble > &from, const PointsKey &tpoints0, const PointsKey &tpoints1, const PointsKey &tpoints2, Array< OneD, NekDouble > &to)

void	PhysGalerkinProject3D (const PointsKey &fpoints0, const PointsKey &fpoints1, const PointsKey &fpoints2, const NekDouble from, const PointsKey &tpoints0, const PointsKey &tpoints1, const PointsKey &tpoints2, NekDouble to)

bool	operator== (const PointsKey &lhs, const PointsKey &rhs)

bool	operator< (const PointsKey &lhs, const PointsKey &rhs)

std::ostream &	operator<< (std::ostream &os, const PointsKey &rhs)

static const PointsKey	NullPointsKey (0, eNoPointsType)

NekDouble	sign (NekDouble arg)

NekDouble	awgn (NekDouble sigma)

static NekDouble	rad (NekDouble x, NekDouble y)

static NekDouble	ang (NekDouble x, NekDouble y)

TimeIntegrationSchemeManagerT &	TimeIntegrationSchemeManager (void)

bool	operator== (const TimeIntegrationSchemeKey &lhs, const TimeIntegrationSchemeKey &rhs)

bool	operator< (const TimeIntegrationSchemeKey &lhs, const TimeIntegrationSchemeKey &rhs)

std::ostream &	operator<< (std::ostream &os, const TimeIntegrationSchemeKey &rhs)

std::ostream &	operator<< (std::ostream &os, const TimeIntegrationSchemeSharedPtr &rhs)

std::ostream &	operator<< (std::ostream &os, const TimeIntegrationScheme &rhs)

static const TimeIntegrationSchemeKey	NullTimeIntegrationSchemeKey (eNoTimeIntegrationMethod)

TimeIntegrationWrapperFactory &	GetTimeIntegrationWrapperFactory ()

Variables
const std::string	EndianTypeMap []

static std::vector< NekDouble >	NullNekDoubleVector

static std::vector < LibUtilities::PointsType >	NullPointsTypeVector

static std::vector< unsigned int >	NullUnsignedIntVector

static FieldMetaDataMap	NullFieldMetaDataMap

static std::vector < std::vector< NekDouble > >	NullVectorNekDoubleVector

static map< PtsInfo, int >	NullPtsInfoMap

static PtsFieldSharedPtr	NullPtsField

static PtsMetaDataMap	NullPtsMetaDataMap

const char *const	FunctionTypeMap []

const char *const	ShapeTypeMap []

const unsigned int	ShapeTypeDimMap [SIZE_ShapeType]

static BasisSharedPtr	NullBasisSharedPtr

static Array< OneD, BasisSharedPtr >	NullBasisSharedPtr1DArray

const char *const	BasisTypeMap []

const std::string	kPointsTypeStr []

static const unsigned int	perm4_3d [4][4] = {{0,1,2,3},{3,0,1,2},{2,3,0,1},{1,2,3,0}}

static const unsigned int	perm6_3d [6][4] = {{0,1,2,3},{0,2,1,3},{0,2,3,1},{2,0,1,3},{2,0,3,1},{2,3,0,1}}

static const unsigned int	perm12A_3d [12][4]

static const unsigned int	perm12B_3d [12][4]

static const unsigned int	perm12C_3d [12][4]

static const unsigned int	perm24_3d [24][4]

const unsigned int	NodalTetElecAvailable = 10

static const unsigned int	NodalTetElecNPTS [NodalTetElecAvailable] = {1,2,3,5,6,9,11,15,18,23}

static const NekDouble	NodalTetElecData [][9]

static const unsigned int	perm3A_2d [3][3] = {{0,1,2},{2,0,1},{0,2,1}}

static const unsigned int	perm3B_2d [3][3] = {{0,1,2},{1,0,2},{1,2,0}}

static const unsigned int	perm6_2d [6][3]

const unsigned int	NodalTriElecAvailable = 16

static const unsigned int	NodalTriElecNPTS [NodalTriElecAvailable] = {1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30}

static const NekDouble	NodalTriElecData [][6]

static const unsigned int	perm3A_2d [3][3] = {{0,1,2},{2,0,1},{0,2,1}}

static const unsigned int	perm3B_2d [3][3] = {{0,1,2},{1,0,2},{1,2,0}}

static const unsigned int	perm3C_2d [3][3] = {{0,1,2},{2,0,1},{1,2,0}}

static const unsigned int	perm6_2d [6][3]

const unsigned int	NodalTriFeketeAvailable = 16

static const unsigned int	NodalTriFeketeNPTS [NodalTriFeketeAvailable] = {1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30}

static const NekDouble	NodalTriFeketeData [][6]

Nektar::LibUtilities::functions	functions_p

const char *const	TimeIntegrationMethodMap []

const char *const	TimeIntegrationSchemeTypeMap []

Typedef Documentation

typedef std::vector< BasisKey > Nektar::LibUtilities::BasisKeyVector

Name for a vector of BasisKeys.

Definition at line 69 of file FoundationsFwd.hpp.

typedef std::vector< BasisKey >::iterator Nektar::LibUtilities::BasisKeyVectorIter

Name for an iterator over a BasisKeyVector.

Definition at line 76 of file FoundationsFwd.hpp.

typedef NekManager<BasisKey, Basis, BasisKey::opLess> Nektar::LibUtilities::BasisManagerT

Definition at line 51 of file ManagerAccess.h.

typedef boost::shared_ptr<Basis> Nektar::LibUtilities::BasisSharedPtr

Definition at line 79 of file FoundationsFwd.hpp.

typedef std::vector< BasisSharedPtr > Nektar::LibUtilities::BasisVector

Definition at line 80 of file FoundationsFwd.hpp.

typedef std::vector< BasisSharedPtr >::iterator Nektar::LibUtilities::BasisVectorIter

Definition at line 81 of file FoundationsFwd.hpp.

typedef std::map< int, std::vector< unsigned int > > Nektar::LibUtilities::BndRegionOrdering

Definition at line 54 of file MeshPartition.h.

typedef std::map<std::string, CmdLineArg> Nektar::LibUtilities::CmdLineArgMap

Definition at line 75 of file SessionReader.h.

typedef LibUtilities::NekFactory< std::string, Comm, int, char** > Nektar::LibUtilities::CommFactory

Datatype of the NekFactory used to instantiate classes derived from the EquationSystem class.

Definition at line 60 of file Comm.h.

typedef boost::shared_ptr<CommMpi> Nektar::LibUtilities::CommMpiSharedPtr

Pointer to a Communicator object.

Definition at line 55 of file CommMpi.h.

typedef boost::shared_ptr<CommSerial> Nektar::LibUtilities::CommSerialSharedPtr

Pointer to a Communicator object.

Definition at line 49 of file CommSerial.h.

typedef boost::shared_ptr<Comm> Nektar::LibUtilities::CommSharedPtr

Pointer to a Communicator object.

Definition at line 53 of file Comm.h.

typedef std::map< int, std::vector< unsigned int > > Nektar::LibUtilities::CompositeOrdering

Definition at line 53 of file MeshPartition.h.

typedef std::map<std::string, int> Nektar::LibUtilities::EnumMap

Definition at line 77 of file SessionReader.h.

typedef std::map<std::string, EnumMap> Nektar::LibUtilities::EnumMapList

Definition at line 78 of file SessionReader.h.

typedef boost::shared_ptr<Equation> Nektar::LibUtilities::EquationSharedPtr

Definition at line 100 of file SessionReader.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::ExpressionMap

Definition at line 61 of file SessionReader.h.

typedef boost::shared_ptr<FieldDefinitions> Nektar::LibUtilities::FieldDefinitionsSharedPtr

Definition at line 118 of file FieldIO.h.

typedef boost::shared_ptr<FieldIO> Nektar::LibUtilities::FieldIOSharedPtr

Definition at line 225 of file FieldIO.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::FieldMetaDataMap

Definition at line 53 of file FieldIO.h.

typedef std::vector< std::pair<std::string, FilterParams> > Nektar::LibUtilities::FilterMap

Definition at line 66 of file SessionReader.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::FilterParams

Definition at line 64 of file SessionReader.h.

typedef std::map<std::string, FunctionVariableMap > Nektar::LibUtilities::FunctionMap

Definition at line 117 of file SessionReader.h.

typedef std::map<std::pair<std::string,int>, FunctionVariableDefinition> Nektar::LibUtilities::FunctionVariableMap

Definition at line 115 of file SessionReader.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::GeometricInfoMap

Definition at line 60 of file SessionReader.h.

typedef std::map< std::string, std::string > Nektar::LibUtilities::GloSysInfoMap

Definition at line 80 of file SessionReader.h.

typedef std::map< std::string, GloSysInfoMap > Nektar::LibUtilities::GloSysSolnInfoList

Definition at line 81 of file SessionReader.h.

typedef int Nektar::LibUtilities::GraphVertexID

Definition at line 85 of file FoundationsFwd.hpp.

typedef boost::shared_ptr<Kernel> Nektar::LibUtilities::KernelSharedPtr

Definition at line 215 of file kernel.h.

typedef LibUtilities::NekFactory< std::string, MeshPartition, const SessionReaderSharedPtr& > Nektar::LibUtilities::MeshPartitionFactory

Datatype of the NekFactory used to instantiate classes derived from the EquationSystem class.

Definition at line 58 of file MeshPartition.h.

typedef boost::shared_ptr<MeshPartition> Nektar::LibUtilities::MeshPartitionSharedPtr

Definition at line 235 of file MeshPartition.h.

typedef boost::shared_ptr<NekFFTW> Nektar::LibUtilities::NekFFTWSharedPtr

Definition at line 56 of file NekFFTW.h.

typedef LibUtilities::NekFactory< std::string, NektarFFT, int> Nektar::LibUtilities::NektarFFTFactory

Datatype of the NekFactory used to instantiate classes derived from the NektarFFT class.

Definition at line 63 of file NektarFFT.h.

typedef boost::shared_ptr<NektarFFT> Nektar::LibUtilities::NektarFFTSharedPtr

Definition at line 56 of file NektarFFT.h.

typedef std::map<std::string, NekDouble> Nektar::LibUtilities::ParameterMap

Definition at line 59 of file SessionReader.h.

typedef NekDouble(* Nektar::LibUtilities::PFD)()

Definition at line 74 of file AnalyticExpressionEvaluator.cpp.

typedef NekDouble(* Nektar::LibUtilities::PFD1)(NekDouble)

Definition at line 75 of file AnalyticExpressionEvaluator.cpp.

typedef NekDouble(* Nektar::LibUtilities::PFD2)(NekDouble, NekDouble)

Definition at line 76 of file AnalyticExpressionEvaluator.cpp.

typedef NekDouble(* Nektar::LibUtilities::PFD3)(NekDouble, NekDouble, NekDouble)

Definition at line 77 of file AnalyticExpressionEvaluator.cpp.

typedef NekDouble(* Nektar::LibUtilities::PFD4)(NekDouble, NekDouble, NekDouble, NekDouble)

Definition at line 78 of file AnalyticExpressionEvaluator.cpp.

typedef Points<NekDouble> Nektar::LibUtilities::PointsBaseType

Definition at line 83 of file FoundationsFwd.hpp.

typedef std::vector<PointsKey> Nektar::LibUtilities::PointsKeyVector

Definition at line 220 of file Points.h.

typedef NekManager<PointsKey, Points<NekDouble>, PointsKey::opLess> Nektar::LibUtilities::PointsManagerT

Definition at line 50 of file ManagerAccess.h.

typedef boost::shared_ptr<Points<NekDouble> > Nektar::LibUtilities::PointsSharedPtr

Definition at line 84 of file FoundationsFwd.hpp.

typedef boost::shared_ptr<PtsField> Nektar::LibUtilities::PtsFieldSharedPtr

Definition at line 262 of file PtsField.h.

typedef boost::shared_ptr<PtsIO> Nektar::LibUtilities::PtsIOSharedPtr

Definition at line 96 of file PtsIO.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::PtsMetaDataMap

Definition at line 61 of file PtsIO.h.

typedef boost::shared_lock< boost::shared_mutex > Nektar::LibUtilities::ReadLock

Definition at line 71 of file NekFactory.hpp.

typedef boost::shared_ptr< SessionReader > Nektar::LibUtilities::SessionReaderSharedPtr

Definition at line 51 of file MeshPartition.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::SolverInfoMap

Definition at line 58 of file SessionReader.h.

typedef std::map<std::string, std::string> Nektar::LibUtilities::TagMap

Definition at line 63 of file SessionReader.h.

typedef boost::shared_ptr<TimeIntegrationIMEXOrder1> Nektar::LibUtilities::TimeIntegrationIMEXOrder1SharedPtr

Definition at line 115 of file TimeIntegrationWrapper.h.

typedef NekManager<TimeIntegrationSchemeKey, TimeIntegrationScheme, TimeIntegrationSchemeKey::opLess> Nektar::LibUtilities::TimeIntegrationSchemeManagerT

Definition at line 354 of file TimeIntegrationScheme.h.

typedef boost::shared_ptr<TimeIntegrationScheme> Nektar::LibUtilities::TimeIntegrationSchemeSharedPtr

Definition at line 51 of file TimeIntegrationScheme.h.

typedef std::vector<TimeIntegrationSchemeSharedPtr> Nektar::LibUtilities::TimeIntegrationSchemeVector

Definition at line 55 of file TimeIntegrationScheme.h.

typedef std::vector<TimeIntegrationSchemeSharedPtr>::iterator Nektar::LibUtilities::TimeIntegrationSchemeVectorIter

Definition at line 56 of file TimeIntegrationScheme.h.

typedef boost::shared_ptr<TimeIntegrationSolution> Nektar::LibUtilities::TimeIntegrationSolutionSharedPtr

Definition at line 57 of file TimeIntegrationScheme.h.

typedef std::vector<TimeIntegrationSolutionSharedPtr> Nektar::LibUtilities::TimeIntegrationSolutionVector

Definition at line 58 of file TimeIntegrationScheme.h.

typedef std::vector<TimeIntegrationSolutionSharedPtr>::iterator Nektar::LibUtilities::TimeIntegrationSolutionVectorIter

Definition at line 59 of file TimeIntegrationScheme.h.

typedef NekFactory< std::string, TimeIntegrationWrapper > Nektar::LibUtilities::TimeIntegrationWrapperFactory

Datatype of the NekFactory used to instantiate classes derived from the EquationSystem class.

Definition at line 46 of file TimeIntegrationWrapper.h.

typedef boost::shared_ptr<TimeIntegrationWrapper> Nektar::LibUtilities::TimeIntegrationWrapperSharedPtr

Definition at line 57 of file TimeIntegrationWrapper.h.

typedef boost::shared_ptr<Transposition> Nektar::LibUtilities::TranspositionSharedPtr

Definition at line 171 of file Transposition.h.

typedef std::vector<std::string> Nektar::LibUtilities::VariableList

Definition at line 62 of file SessionReader.h.

typedef boost::unique_lock< boost::shared_mutex > Nektar::LibUtilities::WriteLock

Definition at line 70 of file NekFactory.hpp.

Enumeration Type Documentation

enum Nektar::LibUtilities::BasisType

Enumerator
eNoBasisType
eOrtho_A	Principle Orthogonal Functions $\widetilde{\psi}^a_p(z_i)$ .
eOrtho_B	Principle Orthogonal Functions $\widetilde{\psi}^b_{pq}(z_i)$ .
eOrtho_C	Principle Orthogonal Functions $\widetilde{\psi}^c_{pqr}(z_i)$ .
eModified_A	Principle Modified Functions $\phi^a_p(z_i)$ .
eModified_B	Principle Modified Functions $\phi^b_{pq}(z_i)$ .
eModified_C	Principle Modified Functions $\phi^c_{pqr}(z_i)$ .
eFourier	Fourier Expansion $\exp(i p\pi z_i)$ .
eGLL_Lagrange	Lagrange for SEM basis .
eGauss_Lagrange	Lagrange Polynomials using the Gauss points .
eLegendre	Legendre Polynomials $L_p(z_i) = P^{0,0}_p(z_i)$ . Same as Ortho_A.
eChebyshev	Chebyshev Polynomials $T_p(z_i) = P^{-1/2,-1/2}_p(z_i)$ .
eMonomial	Monomial polynomials $L_p(z_i) = z_i^{p}$ .
eFourierSingleMode	Fourier ModifiedExpansion with just the first mode $\exp(i \pi z_i)$ .
eFourierHalfModeRe	Fourier Modified expansions with just the real part of the first mode $Re[\exp(i \pi z_i)]$ .
eFourierHalfModeIm	Fourier Modified expansions with just the imaginary part of the first mode $Im[\exp(i \pi z_i)]$ .
SIZE_BasisType	Length of enum list.

Definition at line 43 of file BasisType.h.

         {
             eNoBasisType,
             eOrtho_A,           //!< Principle Orthogonal Functions \f$\widetilde{\psi}^a_p(z_i)\f$
             eOrtho_B,           //!< Principle Orthogonal Functions \f$\widetilde{\psi}^b_{pq}(z_i)\f$
             eOrtho_C,           //!< Principle Orthogonal Functions \f$\widetilde{\psi}^c_{pqr}(z_i)\f$
             eModified_A,        //!< Principle Modified Functions \f$ \phi^a_p(z_i) \f$
             eModified_B,        //!< Principle Modified Functions \f$ \phi^b_{pq}(z_i) \f$
             eModified_C,        //!< Principle Modified Functions \f$ \phi^c_{pqr}(z_i) \f$
             eFourier,           //!< Fourier Expansion \f$ \exp(i p\pi  z_i)\f$
             eGLL_Lagrange,      //!< Lagrange for SEM basis \f$ h_p(z_i) \f$
             eGauss_Lagrange,    //!< Lagrange Polynomials using the Gauss points \f$ h_p(z_i) \f$
             eLegendre,          //!< Legendre Polynomials \f$ L_p(z_i) = P^{0,0}_p(z_i)\f$. Same as Ortho_A
             eChebyshev,         //!< Chebyshev Polynomials \f$ T_p(z_i) = P^{-1/2,-1/2}_p(z_i)\f$
             eMonomial,          //!< Monomial polynomials \f$ L_p(z_i) = z_i^{p}\f$
             eFourierSingleMode, //!< Fourier ModifiedExpansion with just the first mode   \f$ \exp(i \pi  z_i)\f$
             eFourierHalfModeRe, //!< Fourier Modified expansions with just the real part of the first mode  \f$ Re[\exp(i \pi  z_i)]\f$    
             eFourierHalfModeIm, //!< Fourier Modified expansions with just the imaginary part of the first mode  \f$ Im[\exp(i \pi  z_i)]\f$    
             SIZE_BasisType      //!< Length of enum list
         };

enum Nektar::LibUtilities::EndianType

Enumerator
eEndianUnknown
eEndianBig
eEndianLittle
eEndianBigWord
eEndianLittleWord

Definition at line 60 of file CompressData.h.

     {
         eEndianUnknown,
         eEndianBig,
         eEndianLittle,
         eEndianBigWord,   /* Middle-endian, Honeywell 316 style */
         eEndianLittleWord /* Middle-endian, PDP-11 style */
     };

enum Nektar::LibUtilities::FunctionType

Enumerator
eFunctionTypeExpression
eFunctionTypeFile
eFunctionTypeTransientFile
eSIZE_FunctionType

Definition at line 86 of file SessionReader.h.

         {
             eFunctionTypeExpression,
             eFunctionTypeFile,
             eFunctionTypeTransientFile,
             eSIZE_FunctionType,
         };

enum Nektar::LibUtilities::PointsType

Enumerator
eNoPointsType
eGaussGaussLegendre	1D Gauss-Gauss-Legendre quadrature points
eGaussRadauMLegendre	1D Gauss-Radau-Legendre quadrature points, pinned at x=-1
eGaussRadauPLegendre	1D Gauss-Radau-Legendre quadrature points, pinned at x=1
eGaussLobattoLegendre	1D Gauss-Lobatto-Legendre quadrature points
eGaussGaussChebyshev	1D Gauss-Gauss-Chebyshev quadrature points
eGaussRadauMChebyshev	1D Gauss-Radau-Chebyshev quadrature points, pinned at x=-1
eGaussRadauPChebyshev	1D Gauss-Radau-Chebyshev quadrature points, pinned at x=1
eGaussLobattoChebyshev	1D Gauss-Lobatto-Legendre quadrature points
eGaussRadauMAlpha0Beta1	Gauss Radau pinned at x=-1, $\alpha = 0, \beta = 1$ .
eGaussRadauMAlpha0Beta2	Gauss Radau pinned at x=-1, $\alpha = 0, \beta = 2$ .
eGaussRadauMAlpha1Beta0	Gauss Radau pinned at x=-1, $\alpha = 1, \beta = 0$ .
eGaussRadauMAlpha2Beta0	Gauss Radau pinned at x=-1, $\alpha = 2, \beta = 0$ .
eGaussKronrodLegendre	1D Gauss-Kronrod-Legendre quadrature points
eGaussRadauKronrodMLegendre	1D Gauss-Radau-Kronrod-Legendre quadrature points, pinned at x=-1
eGaussRadauKronrodMAlpha1Beta0	1D Gauss-Radau-Kronrod-Legendre pinned at x=-1, $\alpha = 1, \beta = 0$
eGaussLobattoKronrodLegendre	1D Lobatto Kronrod quadrature points
ePolyEvenlySpaced	1D Evenly-spaced points using Lagrange polynomial
eFourierEvenlySpaced	1D Evenly-spaced points using Fourier Fit
eFourierSingleModeSpaced	1D Non Evenly-spaced points for Single Mode analysis
eBoundaryLayerPoints	1D power law distribution for boundary layer points
eBoundaryLayerPointsRev	1D power law distribution for boundary layer points
eNodalTriElec	2D Nodal Electrostatic Points on a Triangle
eNodalTriFekete	2D Nodal Fekete Points on a Triangle
eNodalTriEvenlySpaced	2D Evenly-spaced points on a Triangle
eNodalTetEvenlySpaced	3D Evenly-spaced points on a Tetrahedron
eNodalTetElec	3D Nodal Electrostatic Points on a Tetrahedron
eNodalPrismEvenlySpaced	3D Evenly-spaced points on a Prism
SIZE_PointsType	Length of enum list.

Definition at line 44 of file PointsType.h.

         {
             eNoPointsType,
             eGaussGaussLegendre,            //!<  1D Gauss-Gauss-Legendre quadrature points
             eGaussRadauMLegendre,           //!<  1D Gauss-Radau-Legendre quadrature points, pinned at x=-1
             eGaussRadauPLegendre,           //!<  1D Gauss-Radau-Legendre quadrature points, pinned at x=1
             eGaussLobattoLegendre,          //!<  1D Gauss-Lobatto-Legendre quadrature points
             eGaussGaussChebyshev,           //!<  1D Gauss-Gauss-Chebyshev quadrature points
             eGaussRadauMChebyshev,          //!<  1D Gauss-Radau-Chebyshev quadrature points, pinned at x=-1
             eGaussRadauPChebyshev,          //!<  1D Gauss-Radau-Chebyshev quadrature points, pinned at x=1
             eGaussLobattoChebyshev,         //!<  1D Gauss-Lobatto-Legendre quadrature points
             eGaussRadauMAlpha0Beta1,        //!<  Gauss Radau pinned at x=-1, \f$ \alpha =    0, \beta =    1 \f$
             eGaussRadauMAlpha0Beta2,        //!<  Gauss Radau pinned at x=-1, \f$ \alpha =    0, \beta =    2 \f$
             eGaussRadauMAlpha1Beta0,        //!<  Gauss Radau pinned at x=-1, \f$ \alpha =    1, \beta =    0 \f$
             eGaussRadauMAlpha2Beta0,        //!<  Gauss Radau pinned at x=-1, \f$ \alpha =    2, \beta =    0 \f$
             eGaussKronrodLegendre,          //!<  1D Gauss-Kronrod-Legendre quadrature points
             eGaussRadauKronrodMLegendre,    //!<  1D Gauss-Radau-Kronrod-Legendre quadrature points, pinned at x=-1
             eGaussRadauKronrodMAlpha1Beta0, //!<  1D Gauss-Radau-Kronrod-Legendre pinned at x=-1, \f$ \alpha =    1, \beta =    0 \f$
             eGaussLobattoKronrodLegendre,   //!<  1D Lobatto Kronrod quadrature points
             ePolyEvenlySpaced,              //!<  1D Evenly-spaced points using Lagrange polynomial
             eFourierEvenlySpaced,           //!<  1D Evenly-spaced points using Fourier Fit
             eFourierSingleModeSpaced,       //!<  1D Non Evenly-spaced points for Single Mode analysis
             eBoundaryLayerPoints,           //!<  1D power law distribution for boundary layer points
             eBoundaryLayerPointsRev,        //!<  1D power law distribution for boundary layer points
             eNodalTriElec,                  //!<  2D Nodal Electrostatic Points on a Triangle
             eNodalTriFekete,                //!<  2D Nodal Fekete Points on a Triangle
             eNodalTriEvenlySpaced,          //!<  2D Evenly-spaced points on a Triangle
             eNodalTetEvenlySpaced,          //!<  3D Evenly-spaced points on a Tetrahedron
             eNodalTetElec,                  //!<  3D Nodal Electrostatic Points on a Tetrahedron
             eNodalPrismEvenlySpaced,        //!<  3D Evenly-spaced points on a Prism
             SIZE_PointsType                 //!<  Length of enum list
         };

enum Nektar::LibUtilities::PtsInfo

Enumerator
eIsEquiSpacedData
ePtsPerElmtEdge

Definition at line 65 of file PtsField.h.

             {
     eIsEquiSpacedData,
     ePtsPerElmtEdge
 };

enum Nektar::LibUtilities::PtsType

Enumerator
ePtsFile
ePtsLine
ePtsPlane
ePtsBox
ePtsTriBlock
ePtsTetBlock

Definition at line 55 of file PtsField.h.

             {
     ePtsFile,
     ePtsLine,
     ePtsPlane,
     ePtsBox,
     ePtsTriBlock,
     ePtsTetBlock
 };

enum Nektar::LibUtilities::ReduceOperator

Type of operation to perform in AllReduce.

Enumerator
ReduceSum
ReduceMax
ReduceMin

Definition at line 65 of file Comm.h.

         {
             ReduceSum,
             ReduceMax,
             ReduceMin
         };

enum Nektar::LibUtilities::ShapeType

Enumerator
eNoShapeType
ePoint
eSegment
eTriangle
eQuadrilateral
eTetrahedron
ePyramid
ePrism
eHexahedron
SIZE_ShapeType

Definition at line 52 of file ShapeType.hpp.

         {
             eNoShapeType,
             ePoint,
             eSegment,
             eTriangle,
             eQuadrilateral,
             eTetrahedron,
             ePyramid,
             ePrism,
             eHexahedron,
             SIZE_ShapeType
         };

enum Nektar::LibUtilities::TimeIntegrationMethod

Enumerator
eNoTimeIntegrationMethod
eAdamsBashforthOrder1	Adams-Bashforth Forward multi-step scheme of order 1.
eAdamsBashforthOrder2	Adams-Bashforth Forward multi-step scheme of order 2.
eAdamsBashforthOrder3	Adams-Bashforth Forward multi-step scheme of order 3.
eAdamsMoultonOrder1	Adams-Moulton Forward multi-step scheme of order 1.
eAdamsMoultonOrder2	Adams-Moulton Forward multi-step scheme of order 2.
eBDFImplicitOrder1	BDF multi-step scheme of order 1 (implicit)
eBDFImplicitOrder2	BDF multi-step scheme of order 2 (implicit)
eClassicalRungeKutta4	Runge-Kutta multi-stage scheme 4th order explicit (old name)
eRungeKutta4	Classical RungeKutta4 method (new name for eClassicalRungeKutta4)
eRungeKutta3_SSP	Nonlinear SSP RungeKutta3 explicit.
eRungeKutta2_ImprovedEuler	Improved RungeKutta2 explicit (old name meaning Heun's method)
eRungeKutta2_SSP	Nonlinear SSP RungeKutta2 explicit (surrogate for eRungeKutta2_ImprovedEuler)
eForwardEuler	Forward Euler scheme.
eBackwardEuler	Backward Euler scheme.
eIMEXOrder1	IMEX 1st order scheme using Euler Backwards/Euler Forwards.
eIMEXOrder2	IMEX 2nd order scheme using Backward Different Formula & Extrapolation.
eIMEXOrder3	IMEX 3rd order scheme using Backward Different Formula & Extrapolation.
eMidpoint	midpoint method (old name)
eRungeKutta2	Classical RungeKutta2 method (new name for eMidpoint)
eDIRKOrder2	Diagonally Implicit Runge Kutta scheme of order 3.
eDIRKOrder3	Diagonally Implicit Runge Kutta scheme of order 3.
eCNAB	Crank-Nicolson/Adams-Bashforth Order 2 (CNAB)
eIMEXGear	IMEX Gear Order 2.
eMCNAB	Modified Crank-Nicolson/Adams-Bashforth Order 2 (MCNAB)
eIMEXdirk_1_1_1	Forward-Backward Euler IMEX DIRK(1,1,1)
eIMEXdirk_1_2_1	Forward-Backward Euler IMEX DIRK(1,2,1)
eIMEXdirk_1_2_2	Implicit-Explicit Midpoint IMEX DIRK(1,2,2)
eIMEXdirk_2_2_2	L-stable, two stage, second order IMEX DIRK(2,2,2)
eIMEXdirk_2_3_2	L-stable, three stage, third order IMEX DIRK(3,4,3)
eIMEXdirk_2_3_3	L-stable, two stage, third order IMEX DIRK(2,3,3)
eIMEXdirk_3_4_3	L-stable, three stage, third order IMEX DIRK(3,4,3)
eIMEXdirk_4_4_3	L-stable, four stage, third order IMEX DIRK(4,4,3)
SIZE_TimeIntegrationMethod	Length of enum list.

Definition at line 64 of file TimeIntegrationScheme.h.

         {
             eNoTimeIntegrationMethod,
             eAdamsBashforthOrder1,            //!< Adams-Bashforth Forward multi-step scheme of order 1
             eAdamsBashforthOrder2,            //!< Adams-Bashforth Forward multi-step scheme of order 2
             eAdamsBashforthOrder3,            //!< Adams-Bashforth Forward multi-step scheme of order 3
             eAdamsMoultonOrder1,              //!< Adams-Moulton Forward multi-step scheme of order 1
             eAdamsMoultonOrder2,              //!< Adams-Moulton Forward multi-step scheme of order 2
             eBDFImplicitOrder1,               //!< BDF multi-step scheme of order 1 (implicit)
             eBDFImplicitOrder2,               //!< BDF multi-step scheme of order 2 (implicit)
             eClassicalRungeKutta4,            //!< Runge-Kutta multi-stage scheme 4th order explicit (old name)
             eRungeKutta4,                     //!< Classical RungeKutta4 method (new name for eClassicalRungeKutta4)
             eRungeKutta3_SSP,                 //!< Nonlinear SSP RungeKutta3 explicit
             eRungeKutta2_ImprovedEuler,       //!< Improved RungeKutta2 explicit (old name meaning Heun's method)
             eRungeKutta2_SSP,                 //!< Nonlinear SSP RungeKutta2 explicit (surrogate for eRungeKutta2_ImprovedEuler)
             eForwardEuler,                    //!< Forward Euler scheme
             eBackwardEuler,                   //!< Backward Euler scheme
             eIMEXOrder1,                      //!< IMEX 1st order scheme using Euler Backwards/Euler Forwards
             eIMEXOrder2,                      //!< IMEX 2nd order scheme using Backward Different Formula & Extrapolation
             eIMEXOrder3,                      //!< IMEX 3rd order scheme using Backward Different Formula & Extrapolation
             eMidpoint,                        //!< midpoint method (old name)
             eRungeKutta2,                     //!< Classical RungeKutta2 method (new name for eMidpoint)
             eDIRKOrder2,                      //!< Diagonally Implicit Runge Kutta scheme of order 3
             eDIRKOrder3,                      //!< Diagonally Implicit Runge Kutta scheme of order 3
             eCNAB,                            //!< Crank-Nicolson/Adams-Bashforth Order 2 (CNAB)
             eIMEXGear,                        //!< IMEX Gear Order 2
             eMCNAB,                           //!< Modified Crank-Nicolson/Adams-Bashforth Order 2 (MCNAB)
             eIMEXdirk_1_1_1,                  //!< Forward-Backward Euler IMEX DIRK(1,1,1)
             eIMEXdirk_1_2_1,                  //!< Forward-Backward Euler IMEX DIRK(1,2,1)
             eIMEXdirk_1_2_2,                  //!< Implicit-Explicit Midpoint IMEX DIRK(1,2,2)
             eIMEXdirk_2_2_2,                  //!< L-stable, two stage, second order IMEX DIRK(2,2,2)
             eIMEXdirk_2_3_2,                  //!< L-stable, three stage, third order IMEX DIRK(3,4,3)
             eIMEXdirk_2_3_3,                  //!< L-stable, two stage, third order IMEX DIRK(2,3,3)
             eIMEXdirk_3_4_3,                  //!< L-stable, three stage, third order IMEX DIRK(3,4,3)
             eIMEXdirk_4_4_3,                  //!< L-stable, four stage, third order IMEX DIRK(4,4,3)
             SIZE_TimeIntegrationMethod        //!< Length of enum list
         };

enum Nektar::LibUtilities::TimeIntegrationSchemeType

Enumerator
eNoTimeIntegrationSchemeType
eExplicit	Formally explicit scheme.
eDiagonallyImplicit	Diagonally implicit scheme (e.g. the DIRK schemes)
eIMEX	Implicit Explicit General Linear Method.
eImplicit	Fully implicit scheme.

Definition at line 139 of file TimeIntegrationScheme.h.

         {
             eNoTimeIntegrationSchemeType,
             eExplicit,              //!< Formally explicit scheme
             eDiagonallyImplicit,    //!< Diagonally implicit scheme (e.g. the DIRK schemes)
             eIMEX,                  //!< Implicit Explicit General Linear Method
             eImplicit,              //!< Fully implicit scheme
         };

enum Nektar::LibUtilities::TranspositionDir

Enumerator
eXYtoZ
eZtoXY
eXtoYZ
eYZtoX
eYZtoZY
eZYtoYZ
eXtoY
eYtoZ
eZtoX
eNoTrans

Definition at line 49 of file Transposition.h.

         {
             eXYtoZ,
             eZtoXY,
             eXtoYZ,
             eYZtoX,
             eYZtoZY,
             eZYtoYZ,
             eXtoY,
             eYtoZ,
             eZtoX,
             eNoTrans
         };

Function Documentation

static NekDouble Nektar::LibUtilities::ang	(	NekDouble	x,
		NekDouble	y
	)

static

Definition at line 88 of file AnalyticExpressionEvaluator.hpp.

Referenced by Nektar::LibUtilities::AnalyticExpressionEvaluator::AnalyticExpressionEvaluator(), Nektar::LibUtilities::functions::functions(), Nektar::LibUtilities::AnalyticExpressionEvaluator::EvalAng::run_many(), and Nektar::LibUtilities::AnalyticExpressionEvaluator::EvalAng::run_once().

         {
             NekDouble theta = 0.;
             if ((x != 0.) || (y != 0.))
                 theta = atan2 (y,x);
             return theta;
         }

NekDouble Nektar::LibUtilities::awgn ( NekDouble sigma )

Definition at line 106 of file AnalyticExpressionEvaluator.cpp.

Referenced by Nektar::LibUtilities::functions::functions().

         {
             AnalyticExpressionEvaluator::RandomGeneratorType rng;
             boost::variate_generator<
                     AnalyticExpressionEvaluator::RandomGeneratorType&,
                     boost::normal_distribution<>
                 >  _normal(rng, boost::normal_distribution<>(0, sigma) );
             return _normal();
         }

BasisManagerT & Nektar::LibUtilities::BasisManager ( void )

Definition at line 97 of file ManagerAccess.cpp.

Referenced by Nektar::LibUtilities::Basis::CalculateInterpMatrix(), Nektar::MultiRegions::ExpListHomogeneous1D::ExpListHomogeneous1D(), Nektar::MultiRegions::ExpListHomogeneous2D::ExpListHomogeneous2D(), Nektar::LibUtilities::Basis::GenBasis(), InterpCoeff1D(), InterpCoeff2D(), InterpCoeff3D(), Nektar::MultiRegions::ExpListHomogeneous2D::SetPaddingBase(), Nektar::StdRegions::StdExpansion::StdExpansion(), Nektar::MultiRegions::DisContField1D::v_AddTraceIntegral(), and Nektar::StdRegions::StdQuadExp::v_GenMatrix().

         {
             return Loki::SingletonHolder<BasisManagerT>::Instance();
         }

NekVector< NekDouble > Nektar::LibUtilities::DubinerPoly	(	int	p,
		int	q,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 375 of file NodalUtil.cpp.

References GetSize(), JacobiPoly(), and LegendrePoly().

Referenced by GetVandermonde().

         {
             // Get the coordinate transform
             int size = GetSize(x);
             NekVector<NekDouble> eta_1(size);
     
             // Initialize the horizontal coordinate of the triangle (beta in Barycentric coordinates)
             for(int el=0; el<size; ++el)
             {
                 if( y[el] < 1.0 - 1e-16 )
                 {
                     eta_1[el] = 2.0*(1.0 + x[el]) / (1.0 - y[el]) - 1.0;
                 }
                 else
                 {
                     eta_1[el] = -1.0; // When y is close to 1, then we have a removeable singularity
                 }
             }
     
             // Initialize the vertical coordinate of the triangle (gamma in Barycentric coordinates)
             NekVector<NekDouble> eta_2 = y;
     
             // Orthogonal Dubiner polynomial
             int alpha = 2*p + 1; int beta = 0;
             NekVector<NekDouble> phi(size);
             NekVector<NekDouble> psi_a = LegendrePoly(p, eta_1);
             NekVector<NekDouble> upsilon = JacobiPoly(q, eta_2, alpha, beta);
             NekDouble w = sqrt((2.0 * p + 1.0) * (p + q + 1.0) / 2.0); // Normalizing Orthonormal weight
     
             for(int el=0; el<size; ++el)
             {
                 NekDouble zeta   = pow((1.0 - eta_2[el])/2.0, p);
                 NekDouble psi_b  = zeta * upsilon[el];
                 phi[el]          = w * psi_a[el] * psi_b;
             }
             return phi;
         }

NekVector< NekDouble > Nektar::LibUtilities::DubinerPolyXDerivative	(	int	p,
		int	q,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 664 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetRows(), GetSize(), JacobiPoly(), and LegendrePolyDerivative().

Referenced by GetVandermondeForXDerivative().

         {            
             // Get the coordinate transform
             int size = GetSize(y);
             NekVector<NekDouble> eta_1(size);
             NekVector<NekDouble> psi_x(x.GetRows());
             if(p>0)
             {
                     // Initialize the horizontal coordinate of the triangle (beta in Barycentric coordinates)
                 for(int el=0; el<size; ++el)
                 {
                     if(y[el] < 1.0 - 1e-16)
                     {
                         eta_1[el] = 2.0*(1.0 + x[el]) / (1.0 - y[el]) - 1.0;
                     }
                     else
                     {
                         eta_1[el] = -1.0; // When y is close to 1, then we have a removeable singularity
                     }
                 }
                 // Initialize the vertical coordinate of the triangle (gamma in Barycentric coordinates)
                 NekVector<NekDouble> eta_2 = y;
     
                 // Orthogonal Dubiner polynomial x-derivative
                 int alpha = 2*p + 1; int beta = 0;
                 NekVector<NekDouble> psi_a_x = LegendrePolyDerivative(p, eta_1);
                 NekVector<NekDouble> upsilon = JacobiPoly(q, eta_2, alpha, beta);
                 NekDouble w = sqrt((2.0*p + 1.0) * (p + q + 1.0) / 2.0); // Normalizing Orthonormal weight
     
                 for(int i=0; i<size; ++i)
                 {
                     NekDouble zeta = pow((1.0 -  eta_2[i])/2.0, (p-1.0));
                     NekDouble psi_b = zeta*upsilon[i];
                     psi_x[i] = w * psi_a_x[i] * psi_b;
                 }
             }
             else
             {
                 for(int i=0; i<int(x.GetRows()); ++i)
                 {
                     psi_x[i] = 0.0;
                 }
             }
     
             return psi_x;
         }

NekVector< NekDouble > Nektar::LibUtilities::DubinerPolyYDerivative	(	int	p,
		int	q,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 1217 of file NodalUtil.cpp.

References GetSize(), JacobiPoly(), JacobiPolyDerivative(), LegendrePoly(), and LegendrePolyDerivative().

Referenced by GetVandermondeForYDerivative().

         {
             // Get the coordinate transform
             int size = GetSize(y);
             NekVector<NekDouble> eta_1(size);
     
             // Initialize the horizontal coordinate of the triangle (beta in Barycentric coordinates)
             for(int el=0; el<size; ++el)
             {
                 if(y[el] < 1.0 - 1e-16)
                 {
                     eta_1[el] = 2.0*(1.0 + x[el]) / (1.0 - y[el]) - 1.0;
                 }
                  else
                  {
                     eta_1[el] = -1.0; // When y is close to 1, then we have a removeable singularity
                 }
             }
             // Initialize the vertical coordinate of the triangle (gamma in Barycentric coordinates)
             NekVector<NekDouble> eta_2 = y;
     
             // Orthogonal Dubiner y-polynomial
             int alpha = 2*p + 1; int beta = 0;
             
             NekVector<NekDouble> psi_a = LegendrePoly(p, eta_1);
             NekVector<NekDouble> psi_a_y = LegendrePolyDerivative(p, eta_1);
             NekVector<NekDouble> psi_b = JacobiPoly(q, eta_2, alpha, beta);
             NekVector<NekDouble> psi_b_y = JacobiPolyDerivative(q, eta_2, alpha, beta);
             NekVector<NekDouble> secondComponentOf_psi_b(size);
             NekVector<NekDouble> psi_y(size);
             
             NekVector<NekDouble> first_part_derivative(size);
 
             if(p > 0)
             {
                 for(int i=0; i<size; ++i)
                 {
                      
                      first_part_derivative[i] = (1.0 + eta_1[i])/2.0 * psi_a_y[i] * pow((1.0 - eta_2[i])/2.0, p-1.0) * psi_b[i];
                      secondComponentOf_psi_b[i] = -p/2.0 * pow(((1.0 - eta_2[i]) / 2.0), p - 1.0) * psi_b[i];
 
                 }                
             }
             else
             {
                 for(int i=0; i<size; ++i)
                 {
                     secondComponentOf_psi_b[i] = 0.0;
                     first_part_derivative[i] = 0.0;
                 }
             }
             for(int k=0; k<size; ++k)
             {
                      psi_y[k] = first_part_derivative[k] + psi_a[k] * ( pow((1.0 -  eta_2[k])/2.0, p) * psi_b_y[k] + secondComponentOf_psi_b[k] );
 
             }
             NekDouble w = sqrt((2.0*p + 1.0)*(p + q + 1.0)/2.0); // Normalizing Orthonormal weight
     
             return w * psi_y;
         }

EndianType Nektar::LibUtilities::Endianness ( void )

run time determination of endianness, returning an EndianType

Definition at line 60 of file CompressData.cpp.

References eEndianBig, eEndianBigWord, eEndianLittle, eEndianLittleWord, and eEndianUnknown.

Referenced by Nektar::LibUtilities::CompressData::GetCompressString().

     {
         union
         {
             boost::uint32_t value;
             boost::uint8_t  data[sizeof(boost::uint32_t)];
         } number;
 
         number.data[0] = 0x00;
         number.data[1] = 0x01;
         number.data[2] = 0x02;
         number.data[3] = 0x03;
 
         switch (number.value)
         {
         case UINT32_C(0x00010203): return eEndianBig;
         case UINT32_C(0x03020100): return eEndianLittle;
         case UINT32_C(0x02030001): return eEndianBigWord;
         case UINT32_C(0x01000302): return eEndianLittleWord;
         default:                   return eEndianUnknown;
         }
     }

template<typename T >

NekVector< T > Nektar::LibUtilities::GetColumn	(	const NekMatrix< T > &	matA,
		int	n
	)

Definition at line 52 of file NodalUtil.cpp.

         {
             NekVector<T> v(matA.GetRows());
             for( int i=0; i<matA.GetRows(); ++i )
             {
                 v[i] = matA(i,n);
             }
             return v;
         }

CommFactory & Nektar::LibUtilities::GetCommFactory ( )

Definition at line 64 of file Comm.cpp.

Referenced by Nektar::LibUtilities::SessionReader::CreateComm(), Import(), main(), Nektar::Utilities::InputFld::Process(), Nektar::Utilities::InputPts::Process(), and Write().

         {
             typedef Loki::SingletonHolder<CommFactory,
                 Loki::CreateUsingNew,
                 Loki::NoDestroy,
                 Loki::SingleThreaded> Type;
             return Type::Instance();
         }

int Nektar::LibUtilities::GetDegree ( int nBasisFunctions )

Definition at line 207 of file NodalUtil.cpp.

References ASSERTL1, GetTriNumPoints(), and MakeRound().

Referenced by GetInterpolationMatrix(), GetMonomialVandermonde(), GetVandermonde(), GetVandermondeForXDerivative(), GetVandermondeForYDerivative(), GetXDerivativeMatrix(), GetXDerivativeOfMonomialVandermonde(), GetYDerivativeMatrix(), and GetYDerivativeOfMonomialVandermonde().

         {
             int degree = int(MakeRound((-3.0 + sqrt(1.0 + 8.0*nBasisFunctions))/2.0));
 
             // TODO: Find out why ASSERTL0 and ASSERTL1 don't work
             ASSERTL1( GetTriNumPoints(degree) == nBasisFunctions, "The number of points defines an expansion of fractional degree, which is not supported." );
             return degree;
         }

NekVector< NekDouble > Nektar::LibUtilities::GetE	(	int	rows,
		int	n
	)

Definition at line 72 of file NodalUtil.cpp.

Referenced by Invert().

         {
             NekVector<NekDouble> e(rows, 0.0);
             e(n) = 1;
             return e;
         }

NekVector< NekDouble > Nektar::LibUtilities::GetIntegralOfMonomialVandermonde ( int degree )

Definition at line 1588 of file NodalUtil.cpp.

         {
             int cols = (degree + 1) * (degree + 2) / 2;
             NekVector<NekDouble>integralMVandermonde(cols, 0.0);
             
             for(int d=0, n=0; d <= degree; ++d)
             {
                 for(int p=0; p <= d; ++p, ++n)
                 {
                     int q = d - p;       
                     int sp = 1 - 2 * (p % 2);
                     int sq = 1 - 2 * (q % 2);
         
                     integralMVandermonde(n) = NekDouble(sp * (p+1) + sq * (q+1) + sp * sq * (p+q+2)) / ((p+1) * (q+1) * (p+q+2));
                 }
             }
             return integralMVandermonde;
         }        

NekMatrix< NekDouble > Nektar::LibUtilities::GetInterpolationMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi
	)

Definition at line 609 of file NodalUtil.cpp.

References GetDegree(), GetSize(), GetVandermonde(), and Invert().

Referenced by Nektar::LibUtilities::NodalTriElec::CalculateInterpMatrix(), Nektar::LibUtilities::NodalTriEvenlySpaced::CalculateInterpMatrix(), and Nektar::LibUtilities::NodalTriFekete::CalculateInterpMatrix().

         {
             int nNodes = GetSize(x);
             int degree = GetDegree(nNodes);
     
             NekMatrix<NekDouble> matS = GetVandermonde(x, y); // Square 'short' matrix
             NekMatrix<NekDouble> matT = GetVandermonde(xi, yi, degree); // Coefficient interpolation matrix (tall)
     
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
 
             // Get the interpolation matrix
             return matT*invertMatrix;
         }

MeshPartitionFactory & Nektar::LibUtilities::GetMeshPartitionFactory ( )

Definition at line 69 of file MeshPartition.cpp.

Referenced by Nektar::LibUtilities::SessionReader::PartitionMesh(), and Nektar::Utilities::OutputInfo::Process().

         {
             typedef Loki::SingletonHolder<MeshPartitionFactory,
                 Loki::CreateUsingNew,
                 Loki::NoDestroy,
                 Loki::SingleThreaded> Type;
             return Type::Instance();
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		int	degree
	)

Definition at line 1327 of file NodalUtil.cpp.

References GetSize().

Referenced by GetMonomialVandermonde().

         {
             int rows = GetSize(x);
             int cols = (degree + 1)*(degree + 2)/2;
             NekMatrix<NekDouble>matV(rows,cols, 0.0);
 
             for(int d=0, n=0; d <= degree; ++d)
             {
                 for(int p=0; p <= d; ++p, ++n)
                 {
                     int q = d - p;
                     
                     for(int i=0; i<rows; ++i)
                     {
                             matV(i, n) = pow(x[i], p) * pow(y[i], q);
                     }
                 }
             }
             return matV;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 1348 of file NodalUtil.cpp.

References GetSize().

         {            
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) * (degree + 3)/6;
 
             NekMatrix<NekDouble> matV(rows, cols, 0.0);
 
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
 
                         // Set n-th column of V to the monomial vector
                         for(int i=0; i<rows; ++i)
                         {
                             matV(i,n) = pow(x[i],p) * pow(y[i],q) * pow(z[i],r);
                         }
                     }
                 }
             }
             return matV;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1375 of file NodalUtil.cpp.

References GetMonomialVandermonde(), GetSize(), and GetTetDegree().

         {
             int rows = GetSize(x);
             int degree = GetTetDegree(rows);
             return GetMonomialVandermonde(x, y, z, degree);
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 1382 of file NodalUtil.cpp.

References GetDegree(), GetMonomialVandermonde(), and GetSize().

         {
             int rows = GetSize(x);
             int degree = GetDegree(rows);
             return GetMonomialVandermonde(x, y, degree);
         }

NektarFFTFactory & Nektar::LibUtilities::GetNektarFFTFactory ( )

Definition at line 69 of file NektarFFT.cpp.

Referenced by Nektar::LinearisedAdvection::DFT(), Nektar::AdjointAdvection::DFT(), Nektar::MultiRegions::ExpListHomogeneous1D::ExpListHomogeneous1D(), Nektar::MultiRegions::ExpListHomogeneous2D::ExpListHomogeneous2D(), and Nektar::ForcingMovingBody::InitialiseCableModel().

         {
             typedef Loki::SingletonHolder<NektarFFTFactory,
                 Loki::CreateUsingNew,
                 Loki::NoDestroy,
                 Loki::ClassLevelLockable> Type;
             return Type::Instance();
         }

int Nektar::LibUtilities::GetNumberOfCoefficients	(	ShapeType	shape,
		std::vector< unsigned int > &	modes,
		int	offset
	)

inline

Definition at line 312 of file ShapeType.hpp.

References ASSERTL0, eHexahedron, ePrism, ePyramid, eQuadrilateral, eSegment, eTetrahedron, eTriangle, Nektar::LibUtilities::StdTriData::getNumberOfCoefficients(), Nektar::LibUtilities::StdTetData::getNumberOfCoefficients(), Nektar::LibUtilities::StdPyrData::getNumberOfCoefficients(), and Nektar::LibUtilities::StdPrismData::getNumberOfCoefficients().

Referenced by Nektar::StdRegions::StdExpansion::PhysInterpToSimplexEquiSpaced(), Nektar::MultiRegions::ExpListHomogeneous1D::v_ExtractDataToCoeffs(), and Nektar::MultiRegions::ExpList::v_ExtractDataToCoeffs().

         {
             int returnval = 0; 
             switch(shape)
             {
             case eSegment:
                 returnval = modes[offset];
                 break;
             case eTriangle:
                 returnval = StdTriData::getNumberOfCoefficients(modes[offset],modes[offset+1]);
                 break;
             case eQuadrilateral:
                 returnval = modes[offset]*modes[offset+1];
                 break;
             case eTetrahedron:
                 returnval = StdTetData::getNumberOfCoefficients(modes[offset],modes[offset+1],modes[offset+2]);
                 break;
             case ePyramid:
                 returnval = StdPyrData::getNumberOfCoefficients(modes[offset],modes[offset+1],modes[offset+2]);
                 break;
             case ePrism:
                 returnval = StdPrismData::getNumberOfCoefficients(modes[offset],modes[offset+1],modes[offset+2]);
                 break;
             case eHexahedron:
                 returnval = modes[offset]*modes[offset+1]*modes[offset+2];
                 break;
             default:
                 ASSERTL0(false,"Unknown Shape Type");
                 break;
             }
 
             return returnval;
         }

int Nektar::LibUtilities::GetNumberOfCoefficients	(	ShapeType	shape,
		int	na,
		int	nb,
		int	nc
	)

inline

Definition at line 347 of file ShapeType.hpp.

References ASSERTL0, eHexahedron, ePrism, ePyramid, eQuadrilateral, eSegment, eTetrahedron, eTriangle, Nektar::LibUtilities::StdTriData::getNumberOfCoefficients(), Nektar::LibUtilities::StdTetData::getNumberOfCoefficients(), Nektar::LibUtilities::StdPyrData::getNumberOfCoefficients(), and Nektar::LibUtilities::StdPrismData::getNumberOfCoefficients().

         {
             int returnval = 0; 
             switch(shape)
             {
             case eSegment:
                 returnval = na;
                 break;
             case eTriangle:
                 returnval = StdTriData::getNumberOfCoefficients(na,nb);
                 break;
             case eQuadrilateral:
                 returnval = na*nb;
                 break;
             case eTetrahedron:
                 returnval = StdTetData::getNumberOfCoefficients(na,nb,nc);
                 break;
             case ePyramid:
                 returnval = StdPyrData::getNumberOfCoefficients(na,nb,nc);
                 break;
             case ePrism:
                 returnval = StdPrismData::getNumberOfCoefficients(na,nb,nc);
                 break;
             case eHexahedron:
                 returnval = na*nb*nc;
                 break;
             default:
                 ASSERTL0(false,"Unknown Shape Type");
                 break;
             }
 
             return returnval;
         }

int Nektar::LibUtilities::GetSize ( const Array< OneD, const NekDouble > & x )

Definition at line 111 of file NodalUtil.cpp.

Referenced by Nektar::NekMatrix< DataType, StandardMatrixTag >::CalculateIndex(), DubinerPoly(), DubinerPolyXDerivative(), DubinerPolyYDerivative(), GetInterpolationMatrix(), GetMonomialVandermonde(), GetTetInterpolationMatrix(), GetTetVandermonde(), GetTetXDerivativeMatrix(), GetTetXDerivativeOfMonomialVandermonde(), GetTetYDerivativeOfMonomialVandermonde(), GetTetZDerivativeMatrix(), GetTetZDerivativeOfMonomialVandermonde(), GetVandermonde(), GetVandermondeForTetXDerivative(), GetVandermondeForTetYDerivative(), GetVandermondeForTetZDerivative(), GetVandermondeForXDerivative(), GetVandermondeForYDerivative(), GetXDerivativeMatrix(), GetXDerivativeOfMonomialVandermonde(), GetYDerivativeMatrix(), GetYDerivativeOfMonomialVandermonde(), Hadamard(), JacobiPoly(), JacobiPolyDerivative(), LegendrePoly(), LegendrePolyDerivative(), Nektar::LibUtilities::SessionReader::PartitionMesh(), TetrahedralBasis(), TetXDerivative(), TetYDerivative(), TetZDerivative(), ToArray(), Nektar::StdRegions::ToVector(), and VectorPower().

         {
             return x.num_elements();
         }

int Nektar::LibUtilities::GetSize ( const NekVector< NekDouble > & x )

Definition at line 116 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetRows().

         {
             return x.GetRows();
         }

int Nektar::LibUtilities::GetTetDegree ( int nBasisFunc )

Definition at line 222 of file NodalUtil.cpp.

References ASSERTL1, GetTetNumPoints(), and MakeRound().

Referenced by GetMonomialVandermonde(), GetTetInterpolationMatrix(), GetTetVandermonde(), GetTetXDerivativeMatrix(), GetTetXDerivativeOfMonomialVandermonde(), GetTetYDerivativeOfMonomialVandermonde(), GetTetZDerivativeMatrix(), GetTetZDerivativeOfMonomialVandermonde(), GetVandermondeForTetXDerivative(), GetVandermondeForTetYDerivative(), and GetVandermondeForTetZDerivative().

         {
             NekDouble eq = pow( 81.0 * nBasisFunc + 3.0 * sqrt(-3.0 + 729.0 * nBasisFunc * nBasisFunc), 1.0/3.0);
             int degree = int(MakeRound(eq/3.0 + 1.0/eq - 1.0)) - 1;
 
             ASSERTL1( GetTetNumPoints(degree) == nBasisFunc, "The number of points defines an expansion of fractional degree, which is not supported." );
             return degree;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetInterpolationMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi,
		const NekVector< NekDouble > &	zi
	)

Definition at line 594 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), GetTetVandermonde(), and Invert().

Referenced by Nektar::LibUtilities::NodalTetElec::CalculateInterpMatrix(), and Nektar::LibUtilities::NodalTetEvenlySpaced::CalculateInterpMatrix().

         {
             int nNodes = GetSize(x);
             int degree = GetTetDegree(nNodes);
 
             NekMatrix<NekDouble> matS = GetTetVandermonde(x, y, z); // Square 'short' matrix
             NekMatrix<NekDouble> matT = GetTetVandermonde(xi, yi, zi, degree); // Coefficient interpolation matrix (tall)
 
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
 
             // Get the interpolation matrix
             return matT*invertMatrix;
         }

int Nektar::LibUtilities::GetTetNumPoints ( int degree )

Definition at line 216 of file NodalUtil.cpp.

Referenced by GetTetDegree().

         {
             return (degree+1) * (degree+2) * (degree+3) / 6;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 477 of file NodalUtil.cpp.

References GetSize(), and TetrahedralBasis().

Referenced by GetTetInterpolationMatrix(), GetTetVandermonde(), GetTetXDerivativeMatrix(), GetTetYDerivativeMatrix(), GetTetZDerivativeMatrix(), and MakeVmatrixOfTet().

         {
            //cout << "Begin  GetTetVandermonde" << endl;
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) * (degree + 3)/6;
             
             NekMatrix<NekDouble> matV(rows, cols, 0.0);
 
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         NekVector<NekDouble> columnVector = TetrahedralBasis(p, q, r, x, y, z);
 
                        //  cout << "degree = " << degree << ", (d,p,q,r) = (" << d << ", " << p << ", " << q << ", " << r << ")" << endl;
                         // Set n-th column of V to the TetrahedralBasis vector
                         for(int i=0; i<rows; ++i)
                         {
                             matV(i,n) = columnVector[i];
                         }
                     }
                 }
             }
             return matV;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 507 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetTetVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetTetDegree(rows);
             return GetTetVandermonde(x, y, z, degree);
         }

Points< NekDouble >::MatrixSharedPtrType Nektar::LibUtilities::GetTetXDerivativeMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi,
		const NekVector< NekDouble > &	zi
	)

Definition at line 806 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), GetTetVandermonde(), GetVandermondeForTetXDerivative(), and Invert().

Referenced by Nektar::LibUtilities::NodalTetElec::CalculateDerivMatrix(), and Nektar::LibUtilities::NodalTetEvenlySpaced::CalculateDerivMatrix().

         {
             int nNodes = GetSize(x);
             int degree = GetTetDegree(nNodes);
             NekMatrix<NekDouble> matS  = GetTetVandermonde(x, y, z); // Square 'short' matrix
             NekMatrix<NekDouble> matTx = GetVandermondeForTetXDerivative(xi, yi, zi, degree); // Tall matrix
     
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
     
             // Get the Derivation matrix    
             return Points<NekDouble>::MatrixSharedPtrType( new NekMatrix<NekDouble>(matTx*invertMatrix) );
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetXDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 1427 of file NodalUtil.cpp.

References GetSize().

Referenced by GetTetXDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) * (degree + 3) / 6;
             NekMatrix<NekDouble> matVx(rows, cols, 0.0);
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         if(p > 0)
                         {
                             // Set n-th column of V to the monomial vector
                             for(int i=0; i<rows; ++i)
                             {
                                 matVx(i,n) = p * pow(x[i],p-1.0) * pow(y[i],q) * pow(z[i],r);
                             }
                         }
                         else{
                             for(int j=0; j<rows; ++j)
                             {
                                 matVx(j, n) = 0.0;
                             }
                         }
                     }
                 }
             }
             return matVx;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetXDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1460 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetTetXDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetTetDegree(rows);
             return GetTetXDerivativeOfMonomialVandermonde(x, y, z, degree);
         }

Points< NekDouble >::MatrixSharedPtrType Nektar::LibUtilities::GetTetYDerivativeMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi,
		const NekVector< NekDouble > &	zi
	)

Definition at line 1047 of file NodalUtil.cpp.

References GetTetVandermonde(), GetVandermondeForTetYDerivative(), and Invert().

Referenced by Nektar::LibUtilities::NodalTetElec::CalculateDerivMatrix(), and Nektar::LibUtilities::NodalTetEvenlySpaced::CalculateDerivMatrix().

         {
             // int nNodes = GetSize(y);
             
             NekMatrix<NekDouble> matS  = GetTetVandermonde(x, y, z); // Square 'short' matrix
 
             NekMatrix<NekDouble> matTy = GetVandermondeForTetYDerivative(xi, yi, zi); // Tall matrix
 
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
             
             NekMatrix<NekDouble> makeDerivativeMatrix = matTy*invertMatrix;
 
             return Points<NekDouble>::MatrixSharedPtrType(new NekMatrix<NekDouble>(makeDerivativeMatrix));
 
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetYDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 1468 of file NodalUtil.cpp.

References GetSize().

Referenced by GetTetYDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) * (degree + 3) / 6;
             NekMatrix<NekDouble> matVy(rows, cols, 0.0);
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         if(q > 0)
                         {
                             // Set n-th column of V to the monomial vector
                             for(int i=0; i<rows; ++i)
                             {
                                 matVy(i,n) = q * pow(x[i],p) * pow(y[i],q-1.0) * pow(z[i],r);
                             }
                         }
                         else
                         {
                             for(int j=0; j<rows; ++j)
                             {
                                 matVy(j, n) = 0.0;
                             }
                         }
                     }
                 }
             }
             return matVy;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetYDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1502 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetTetYDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetTetDegree(rows);
             return GetTetYDerivativeOfMonomialVandermonde(x, y, z, degree);
         }

Points< NekDouble >::MatrixSharedPtrType Nektar::LibUtilities::GetTetZDerivativeMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi,
		const NekVector< NekDouble > &	zi
	)

Definition at line 1195 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), GetTetVandermonde(), GetVandermondeForTetZDerivative(), Invert(), and TetZDerivative().

Referenced by Nektar::LibUtilities::NodalTetElec::CalculateDerivMatrix(), and Nektar::LibUtilities::NodalTetEvenlySpaced::CalculateDerivMatrix().

         {
             int nNodes = GetSize(z);
             int degree = GetTetDegree(nNodes);
 
             NekMatrix<NekDouble> matS  = GetTetVandermonde(x, y, z); // Square 'short' matrix
 
             NekMatrix<NekDouble> matTz = GetVandermondeForTetZDerivative(xi, yi, zi, degree); // Tall matrix
 
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
 
             NekMatrix<NekDouble> makeDerivativeMatrix = matTz*invertMatrix;
 
             Points<NekDouble>::MatrixSharedPtrType TetZDerivative;
             TetZDerivative = Points<NekDouble>::MatrixSharedPtrType(new  NekMatrix<NekDouble>(makeDerivativeMatrix));
 
            return TetZDerivative;
 
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetZDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 1510 of file NodalUtil.cpp.

References GetSize().

Referenced by GetTetZDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) * (degree + 3) / 6;
             NekMatrix<NekDouble> matVz(rows, cols, 0.0);
              for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         if(r > 0)
                         {
                             // Set n-th column of V to the monomial vector
                             for(int i=0; i<rows; ++i)
                             {
                                 matVz(i,n) = r * pow(x[i],p) * pow(y[i],q) * pow(z[i],r-1.0);
                             }
                         }
                         else{
                             for(int j=0; j<rows; ++j)
                             {
                                 matVz(j, n) = 0.0;
                             }
                         }
                     }
                 }
             }
             return matVz;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTetZDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1543 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetTetZDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetTetDegree(rows);
             return GetTetZDerivativeOfMonomialVandermonde(x, y, z, degree);
         }

TimeIntegrationWrapperFactory & Nektar::LibUtilities::GetTimeIntegrationWrapperFactory ( )

Definition at line 42 of file TimeIntegrationWrapper.cpp.

Referenced by Nektar::UnsteadyAdvectionDiffusion::SetUpSubSteppingTimeIntegration(), Diffusion::TimeIntegrate(), Nektar::SolverUtils::UnsteadySystem::v_InitObject(), and Nektar::SubSteppingExtrapolate::v_SubSteppingTimeIntegration().

     {
         typedef Loki::SingletonHolder<TimeIntegrationWrapperFactory,
             Loki::CreateUsingNew,
             Loki::NoDestroy,
             Loki::SingleThreaded> Type;
         return Type::Instance();
     }

NekMatrix< NekDouble > Nektar::LibUtilities::GetTranspose ( const NekMatrix< NekDouble > & matA )

Definition at line 96 of file NodalUtil.cpp.

         {
             int rows = matA.GetRows(), columns = matA.GetColumns();
             NekMatrix<NekDouble> matX(rows,columns);
         
             for( int i=0; i<rows; ++i )
             {
                 for( int j=0; j<columns; ++j )
                 {
                     matX(j,i) = matA(i,j);
                 }
             }
             return matX;
         }

int Nektar::LibUtilities::GetTriNumPoints ( int degree )

Definition at line 202 of file NodalUtil.cpp.

Referenced by GetDegree().

         {
             return (degree+1) * (degree+2) / 2;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		int	degree
	)

Definition at line 515 of file NodalUtil.cpp.

References DubinerPoly(), and GetSize().

Referenced by GetInterpolationMatrix(), GetVandermonde(), GetXDerivativeMatrix(), GetYDerivativeMatrix(), and MakeVmatrixOfDubinerPolynomial().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) / 2;
             
             NekMatrix<NekDouble> matV(rows, cols, 0.0);
     
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p<=d; ++p, ++n)
                 {
                     int q = d - p;
                     NekVector<NekDouble> columnVector = DubinerPoly(p, q, x, y);
     
                     // Set n-th column of V to the DubinerPoly vector
                     for(int i=0; i<rows; ++i)
                     {
                             matV(i,n) = columnVector[i];
                     }
                 }
             }
     
             return matV;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 540 of file NodalUtil.cpp.

References GetDegree(), GetSize(), and GetVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetDegree(rows);
             return GetVandermonde( x, y, degree );
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForTetXDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 772 of file NodalUtil.cpp.

References GetSize(), and TetXDerivative().

Referenced by GetTetXDerivativeMatrix(), and GetVandermondeForTetXDerivative().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) * (degree + 3)/6;
             NekMatrix<NekDouble> matVx(rows, cols, 0.0);
             
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         NekVector<NekDouble> columnVector = TetXDerivative(p, q, r, x, y, z);
 
                         // Set n-th column of V to the TetrahedralBasis vector
                         for(int i=0; i<rows; ++i)
                         {
                             matVx(i,n) = columnVector[i];
                         }
                     }
                 }
             }
             return matVx;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForTetXDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 799 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetVandermondeForTetXDerivative().

         {
             int rows = GetSize(x);
             int degree = GetTetDegree(rows);
             return GetVandermondeForTetXDerivative(x, y, z, degree);
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForTetYDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 1013 of file NodalUtil.cpp.

References GetSize(), and TetYDerivative().

Referenced by GetTetYDerivativeMatrix(), and GetVandermondeForTetYDerivative().

                                                                                                         {
             int rows = GetSize(y);
             int cols = (degree + 1) * (degree + 2) * (degree + 3)/6;
             NekMatrix<NekDouble> matVy(rows, cols, 0.0);
             
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         NekVector<NekDouble> columnVector = TetYDerivative(p, q, r, x, y, z);
 
                         // Set n-th column of V to the TetrahedralBasis vector
                         for(int i=0; i<rows; ++i)
                         {
                             matVy(i,n) = columnVector[i];
                         }
                     }
                 }
             }
             return matVy;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForTetYDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1039 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetVandermondeForTetYDerivative().

         {
             int rows = GetSize(y);
             int degree = GetTetDegree(rows);
             return GetVandermondeForTetYDerivative(x, y, z, degree);
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForTetZDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z,
		int	degree
	)

Definition at line 1161 of file NodalUtil.cpp.

References GetSize(), and TetZDerivative().

Referenced by GetTetZDerivativeMatrix(), and GetVandermondeForTetZDerivative().

                                                                                                         {
             int rows = GetSize(z);
             int cols = (degree + 1) * (degree + 2) * (degree + 3)/6;
             NekMatrix<NekDouble> matVz(rows, cols, 0.0);
             
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p <= d; ++p)
                 {
                     for(int q=0; q <= d - p; ++q, ++n)
                     {
                         int r = d - p - q;
                         NekVector<NekDouble> columnVector = TetZDerivative(p, q, r, x, y, z);
 
                         // Set n-th column of V to the TetrahedralBasis vector
                         for(int i=0; i<rows; ++i)
                         {
                             matVz(i,n) = columnVector[i];
                         }
                     }
                 }
             }
             return matVz;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForTetZDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1187 of file NodalUtil.cpp.

References GetSize(), GetTetDegree(), and GetVandermondeForTetZDerivative().

         {
             int rows = GetSize(z);
             int degree = GetTetDegree(rows);
             return GetVandermondeForTetZDerivative(x, y, z, degree);
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForXDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		int	degree
	)

Definition at line 821 of file NodalUtil.cpp.

References DubinerPolyXDerivative(), and GetSize().

Referenced by GetVandermondeForXDerivative(), and GetXDerivativeMatrix().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2)/2;
             NekMatrix<NekDouble> matVx(rows, cols, 0.0);
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p<=d; ++p, ++n)
                 {
                     int q = d - p;
                     NekVector<NekDouble> columnVector = DubinerPolyXDerivative(p, q, x, y);
     
                     // Set n-th column of Vx to the DubinerPolyXDerivative vector
                     for(int i=0; i<rows; ++i)
                     {
                         matVx(i, n) = columnVector[i];
                     }
                 }
             }
             
             return matVx;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForXDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 845 of file NodalUtil.cpp.

References GetDegree(), GetSize(), and GetVandermondeForXDerivative().

         {
             int rows = GetSize(x);
             int degree = GetDegree(rows);
             return GetVandermondeForXDerivative(x, y, degree);
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForYDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		int	degree
	)

Definition at line 1280 of file NodalUtil.cpp.

References DubinerPolyYDerivative(), and GetSize().

Referenced by GetVandermondeForYDerivative(), and GetYDerivativeMatrix().

         {
             int rows = GetSize(y);
             int cols = (degree + 1) * (degree + 2)/2;
             NekMatrix<NekDouble> matVy(rows, cols, 0.0);
             
             for(int d=0, n=0; d<=degree; ++d)
             {
                 for(int p=0; p<=d; ++p, ++n)
                 {
                     int q = d - p;
                     NekVector<NekDouble> columnVector = DubinerPolyYDerivative(p, q, x, y);
     
                     for(int i=0; i<rows; ++i)
                     {
                         matVy(i, n) = columnVector[i];
                     }
                 }
             }
             return matVy;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetVandermondeForYDerivative	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 1320 of file NodalUtil.cpp.

References GetDegree(), GetSize(), and GetVandermondeForYDerivative().

         {
             int rows = GetSize(y);
             int degree = GetDegree(rows);
             return GetVandermondeForYDerivative(x, y, degree);
         }

Points< NekDouble >::MatrixSharedPtrType Nektar::LibUtilities::GetXDerivativeMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi
	)

Definition at line 852 of file NodalUtil.cpp.

References GetDegree(), GetSize(), GetVandermonde(), GetVandermondeForXDerivative(), and Invert().

Referenced by Nektar::LibUtilities::NodalTriElec::CalculateDerivMatrix(), Nektar::LibUtilities::NodalTriFekete::CalculateDerivMatrix(), and Nektar::LibUtilities::NodalTriEvenlySpaced::CalculateDerivMatrix().

         {
             int nNodes = GetSize(x);
             int degree = GetDegree(nNodes);
             NekMatrix<NekDouble> matS  = GetVandermonde(x, y); // Square 'short' matrix
             NekMatrix<NekDouble> matTx = GetVandermondeForXDerivative(xi, yi, degree); // Tall matrix
     
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
     
             // Get the Derivation matrix    
             return Points<NekDouble>::MatrixSharedPtrType( new NekMatrix<NekDouble>(matTx*invertMatrix) );
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetXDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		int	degree
	)

Definition at line 1389 of file NodalUtil.cpp.

References GetSize().

Referenced by GetXDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) / 2;
             NekMatrix<NekDouble> matVx(rows, cols, 0.0);
 
             for(int d=0, n=0; d <= degree; ++d)
             {
                 for(int p=0; p <= d; ++p, ++n)
                 {
                     int q = d - p;
 
                     if(p > 0)
                     {
                         for(int i=0; i<rows; ++i)
                         {
                             matVx(i, n) = p * pow(x[i], p-1.0) * pow(y[i],q);
                         }
                     }
                     else
                     {
                         for(int j=0; j<rows; ++j)
                         {
                             matVx(j, n) = 0.0;
                         }
                     }
                 }
             }
             return matVx;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetXDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 1420 of file NodalUtil.cpp.

References GetDegree(), GetSize(), and GetXDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetDegree(rows);
             return GetXDerivativeOfMonomialVandermonde(x, y, degree);
         }

Points< NekDouble >::MatrixSharedPtrType Nektar::LibUtilities::GetYDerivativeMatrix	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	xi,
		const NekVector< NekDouble > &	yi
	)

Definition at line 1303 of file NodalUtil.cpp.

References GetDegree(), GetSize(), GetVandermonde(), GetVandermondeForYDerivative(), and Invert().

Referenced by Nektar::LibUtilities::NodalTriElec::CalculateDerivMatrix(), Nektar::LibUtilities::NodalTriFekete::CalculateDerivMatrix(), and Nektar::LibUtilities::NodalTriEvenlySpaced::CalculateDerivMatrix().

         {
             int nNodes = GetSize(y);
             int degree = GetDegree(nNodes);
     
             NekMatrix<NekDouble> matS  = GetVandermonde(x, y); // Square 'short' matrix
             NekMatrix<NekDouble> matTy = GetVandermondeForYDerivative(xi, yi, degree); // Tall matrix
     
             NekMatrix<NekDouble> invertMatrix = Invert(matS);
 
 
             // Get the Derivation matrix
             return Points<NekDouble>::MatrixSharedPtrType( new NekMatrix<NekDouble>(matTy*invertMatrix) );
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetYDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		int	degree
	)

Definition at line 1551 of file NodalUtil.cpp.

References GetSize().

Referenced by GetYDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int cols = (degree + 1) * (degree + 2) / 2;
             NekMatrix<NekDouble> matVy(rows, cols, 0.0);
             
             for(int d=0, n=0; d <= degree; ++d)
             {
                 for(int p=0; p <= d; ++p, ++n)
                 {
                     int q = d - p;
                     if(q > 0)
                     {
                         for(int i=0; i<rows; ++i)
                         {
                             matVy(i, n) = q * pow(x[i], p) * pow(y[i], q-1.0);
                         }
                      }
                      else
                      {
                         for(int j=0; j<rows; ++j)
                         {
                             matVy(j, n) = 0.0;
                         }
                     }
                 }
             }
             return matVy;
         }

NekMatrix< NekDouble > Nektar::LibUtilities::GetYDerivativeOfMonomialVandermonde	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 1581 of file NodalUtil.cpp.

References GetDegree(), GetSize(), and GetYDerivativeOfMonomialVandermonde().

         {
             int rows = GetSize(x);
             int degree = GetDegree(rows);
             return GetYDerivativeOfMonomialVandermonde(x, y, degree);
         }

NekVector< NekDouble > Nektar::LibUtilities::Hadamard	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 131 of file NodalUtil.cpp.

References GetSize().

Referenced by LegendrePoly(), LegendrePolyDerivative(), TetYDerivative(), and TetZDerivative().

         {
             int size = GetSize(x);
             NekVector<NekDouble> z(size);
     
             for( int i=0; i<size; ++i )
             {
                 z[i] = x[i] * y[i];
             }
             return z;
         }

void Nektar::LibUtilities::Import	(	const string &	inFile,
		PtsFieldSharedPtr &	ptsField
	)

Definition at line 56 of file PtsIO.cpp.

References ASSERTL0, Nektar::LibUtilities::NekFactory< tKey, tBase, >::CreateInstance(), GetCommFactory(), and Nektar::LibUtilities::PtsIO::Import().

 {
 #ifdef NEKTAR_USE_MPI
     int size;
     int init;
     MPI_Initialized(&init);
 
     // If MPI has been initialised we can check the number of processes
     // and, if > 1, tell the user he should not be running this
     // function in parallel. If it is not initialised, we do not
     // initialise it here, and assume the user knows what they are
     // doing.
     if (init)
     {
         MPI_Comm_size(MPI_COMM_WORLD, &size);
         ASSERTL0(size == 1,
                  "This static function is not available in parallel. Please "
                  "instantiate a FieldIO object for parallel use.");
     }
 #endif
     CommSharedPtr c = GetCommFactory().CreateInstance("Serial", 0, 0);
     PtsIO p(c);
     p.Import(inFile, ptsField);
 }

void Nektar::LibUtilities::Import	(	const std::string &	infilename,
		std::vector< FieldDefinitionsSharedPtr > &	fielddefs,
		std::vector< std::vector< NekDouble > > &	fielddata,
		FieldMetaDataMap &	fieldinfomap,
		const Array< OneD, int >	ElementiDs
	)

Imports an FLD file.

This function allows for data to be imported from an FLD file when a session and/or communicator is not instantiated. Typically used in utilities which only operate in serial.

Definition at line 115 of file FieldIO.cpp.

References ASSERTL0, Nektar::LibUtilities::NekFactory< tKey, tBase, >::CreateInstance(), GetCommFactory(), and Nektar::LibUtilities::FieldIO::Import().

Referenced by GetStreakLocation(), Nektar::SolverUtils::EquationSystem::ImportFldToMultiDomains(), and main().

         {
 #ifdef NEKTAR_USE_MPI
             int size;
             int init;
             MPI_Initialized(&init);
 
             // If MPI has been initialised we can check the number of processes
             // and, if > 1, tell the user he should not be running this
             // function in parallel. If it is not initialised, we do not
             // initialise it here, and assume the user knows what they are
             // doing.
             if (init)
             {
                 MPI_Comm_size( MPI_COMM_WORLD, &size );
                 ASSERTL0(size == 1,
                      "This static function is not available in parallel. Please"
                      "instantiate a FieldIO object for parallel use.");
             }
 #endif
             CommSharedPtr c = GetCommFactory().CreateInstance("Serial", 0, 0);
             FieldIO f(c);
             f.Import(infilename, fielddefs, fielddata, fieldinfomap, ElementiDs);
         }

void Nektar::LibUtilities::Interp1D	(	const BasisKey &	fbasis0,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		Array< OneD, NekDouble > &	to
	)

this function interpolates a 1D function $f$ evaluated at the quadrature points of the basis fbasis0 to the function values at the quadrature points of the basis tbasis0

Given a function $ f$ evaluated at the Q quadrature points of the basis fbasis0, this routine calculates, using (Q-1)th order polynomial interpolation, the function values at the Q2 quadrature points of the basis tbasis0.

Parameters

fbasis0	the basis at which's quadrature points the function is given
from	the array containg the function evaluated at the quadrature points of fbasis0
tbasis0	the basis to which's quadrature points the function should be interpolated
to	the array containg the function evaluated at the quadrature points of tbasis0 (output of the function)

Definition at line 54 of file Interp.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey().

         {
             Interp1D(fbasis0.GetPointsKey(),from,tbasis0.GetPointsKey(),to);
         }

void Nektar::LibUtilities::Interp1D	(	const PointsKey &	fpoints0,
		const Array< OneD, const NekDouble > &	from,
		const PointsKey &	tpoints0,
		Array< OneD, NekDouble > &	to
	)

Definition at line 62 of file Interp.cpp.

References Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetNumPoints(), PointsManager(), and Vmath::Vcopy().

         {
             if(fpoints0 == tpoints0) //check to see if the same
             {
                 Vmath::Vcopy(fpoints0.GetNumPoints(),from,1,to,1);
             }
             else // interpolate
             {
                 DNekMatSharedPtr I0;
                 
                 I0 = PointsManager()[fpoints0]->GetI(tpoints0);
                 
                 NekVector<NekDouble> in(fpoints0.GetNumPoints(),from,eWrapper);
                 NekVector<NekDouble> out(tpoints0.GetNumPoints(),to,eWrapper);
                 
                 out  = (*I0)*in;
             }
         }

void Nektar::LibUtilities::Interp1D	(	const BasisKey &	fbasis0,
		const NekDouble *	from,
		const BasisKey &	tbasis0,
		NekDouble *	to
	)

Definition at line 84 of file Interp.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey(), and Interp1D().

         {
             Interp1D(fbasis0.GetPointsKey(),from,tbasis0.GetPointsKey(),to);
         }

void Nektar::LibUtilities::Interp1D	(	const PointsKey &	fpoints0,
		const NekDouble *	from,
		const PointsKey &	tpoints0,
		NekDouble *	to
	)

Definition at line 92 of file Interp.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), PointsManager(), and Vmath::Vcopy().

         {
             if(fpoints0 == tpoints0) //check to see if the same
             {
                 Vmath::Vcopy(fpoints0.GetNumPoints(),from,1,to,1);
             }
             else // interpolate
             {
                 
                 DNekMatSharedPtr I0;
                 
                 I0 = PointsManager()[fpoints0]
                     ->GetI(tpoints0);
                 
                 Blas::Dgemv('N', tpoints0.GetNumPoints(), fpoints0.GetNumPoints(), 
                             1.0, I0->GetPtr().get(), tpoints0.GetNumPoints(), 
                             from, 1, 0.0, to, 1);
             }
         }

void Nektar::LibUtilities::Interp2D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		Array< OneD, NekDouble > &	to
	)

this function interpolates a 2D function $f$ evaluated at the quadrature points of the 2D basis, constructed by fbasis0 and fbasis1, to the function values at the quadrature points of the 2D basis, constructed by tbasis0 and tbasis1

Given a function $ f$ evaluated at the Q quadrature points of the first expansion basis, this routine calculates, using (Q-1)th order polynomial interpolation, the function values at the Q2 quadrature points of the second basis.

Parameters

fbasis0	the basis at which's quadrature points the function is given
from	the array containg the function evaluated at the quadrature points of fbasis0
tbasis0	the basis to which's quadrature points the function should be interpolated
to	the array containg the function evaluated at the quadrature points of tbasis0 (output of the function)

Definition at line 116 of file Interp.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey().

Referenced by Nektar::Utilities::ProcessEquiSpacedOutput::GenOrthoModes(), Nektar::Utilities::ProcessQualityMetric::GetQ(), Nektar::SpatialDomains::GeomFactors::Interp(), Interp2D(), Nektar::SolverUtils::UpdateGeometry(), Nektar::LocalRegions::PyrExp::v_ComputeFaceNormal(), Nektar::LocalRegions::TetExp::v_ComputeFaceNormal(), Nektar::LocalRegions::PrismExp::v_ComputeFaceNormal(), Nektar::LocalRegions::HexExp::v_ComputeFaceNormal(), Nektar::LocalRegions::QuadExp::v_ExtractDataToCoeffs(), Nektar::SpatialDomains::QuadGeom::v_FillGeom(), Nektar::SpatialDomains::TriGeom::v_FillGeom(), Nektar::LocalRegions::Expansion::v_GetCoords(), Nektar::LocalRegions::Expansion3D::v_GetFacePhysVals(), Nektar::MultiRegions::ExpList2D::v_GetNormals(), and Nektar::MultiRegions::ExpList2D::v_PhysInterp1DScaled().

         {
             Interp2D(fbasis0.GetPointsKey(),fbasis1.GetPointsKey(),from.data(),
                      tbasis0.GetPointsKey(),tbasis1.GetPointsKey(),to.data());
         }

void Nektar::LibUtilities::Interp2D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const Array< OneD, const NekDouble > &	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		Array< OneD, NekDouble > &	to
	)

Definition at line 127 of file Interp.cpp.

References Interp2D().

         {
             Interp2D(fpoints0,fpoints1,from.data(),tpoints0,tpoints1,to.data());
         }

void Nektar::LibUtilities::Interp2D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const NekDouble *	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		NekDouble *	to
	)

Definition at line 137 of file Interp.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), PointsManager(), and Vmath::Vcopy().

         {
             // default interpolation
             if((fpoints0 == tpoints0)&&(fpoints1 == tpoints1))
             {
                 Vmath::Vcopy(tpoints0.GetNumPoints()*tpoints1.GetNumPoints(),
                              from,1,to,1);
                 return;
             }
 
             DNekMatSharedPtr I0,I1;
             Array<OneD, NekDouble> wsp(tpoints1.GetNumPoints()*fpoints0.GetNumPoints()); // fnp0*tnp1
 
             int fnp0 = fpoints0.GetNumPoints();
             int fnp1 = fpoints1.GetNumPoints();
             int tnp0 = tpoints0.GetNumPoints();
             int tnp1 = tpoints1.GetNumPoints();
 
             if(fpoints1 == tpoints1)
             {
                 Vmath::Vcopy(fnp0*tnp1,from,1,wsp.get(),1);
             }
             else
             {
                 I1 = PointsManager()[fpoints1]->GetI(tpoints1);
                 Blas::Dgemm('N', 'T', fnp0, tnp1, fnp1, 1.0, from, fnp0,
                              I1->GetPtr().get(), tnp1, 0.0,  wsp.get(), fnp0);     
             }
 
             if(fpoints0 == tpoints0)
             {
                 Vmath::Vcopy(tnp0*tnp1,wsp.get(),1,to,1);
             }
             else
             {
                 I0 = PointsManager()[fpoints0]->GetI(tpoints0);
                 Blas::Dgemm('N', 'N', tnp0, tnp1, fnp0, 1.0, I0->GetPtr().get(),
                             tnp0, wsp.get(), fnp0, 0.0, to, tnp0);     
             }
         }

void Nektar::LibUtilities::Interp3D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const BasisKey &	fbasis2,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		const BasisKey &	tbasis2,
		Array< OneD, NekDouble > &	to
	)

this function interpolates a 3D function $f$ evaluated at the quadrature points of the 3D basis, constructed by fbasis0, fbasis1, and fbasis2 to the function values at the quadrature points of the 3D basis, constructed by tbasis0, tbasis1, and tbasis2.

Given a function $ f$ evaluated at the Q quadrature points of the first expansion basis, this routine calculates, using (Q-1)th order polynomial interpolation, the function values at the Q2 quadrature points of the second basis, and the function values at the Q3 quadrature points of the third basis.

Parameters

fbasis0	the basis at which's quadrature points the function is given
from	the array containg the function evaluated at the quadrature points of fbasis0
tbasis0	the basis to which's quadrature points the function should be interpolated
to	the array containg the function evaluated at the quadrature points of tbasis0 (output of the function)

Definition at line 186 of file Interp.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey().

Referenced by Nektar::Utilities::ProcessQualityMetric::GetQ(), Nektar::SpatialDomains::GeomFactors::Interp(), Interp3D(), Nektar::LocalRegions::Expansion::v_GetCoords(), and Nektar::MultiRegions::ExpList3D::v_PhysInterp1DScaled().

         {
             Interp3D(fbasis0.GetPointsKey(),fbasis1.GetPointsKey(),
                      fbasis2.GetPointsKey(),from.data(),
                      tbasis0.GetPointsKey(),tbasis1.GetPointsKey(),
                      tbasis2.GetPointsKey(),to.data());
         }

void Nektar::LibUtilities::Interp3D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const PointsKey &	fpoints2,
		const Array< OneD, const NekDouble > &	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		const PointsKey &	tpoints2,
		Array< OneD, NekDouble > &	to
	)

Definition at line 202 of file Interp.cpp.

References Interp3D().

         {
             Interp3D(fpoints0,fpoints1,fpoints2,from.data(),
                      tpoints0,tpoints1,tpoints2,to.data());
         }

void Nektar::LibUtilities::Interp3D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const PointsKey &	fpoints2,
		const NekDouble *	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		const PointsKey &	tpoints2,
		NekDouble *	to
	)

Definition at line 215 of file Interp.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), and PointsManager().

         {
             int i;
             DNekMatSharedPtr I0, I1, I2;
             
             int fnp0 = fpoints0.GetNumPoints();
             int fnp1 = fpoints1.GetNumPoints();
             int fnp2 = fpoints2.GetNumPoints();
             int tnp0 = tpoints0.GetNumPoints();
             int tnp1 = tpoints1.GetNumPoints();
             int tnp2 = tpoints2.GetNumPoints();
             
             Array<OneD, NekDouble> wsp1(tnp0*tnp1*fnp2);
             Array<OneD, NekDouble> wsp2(tnp0*fnp1*fnp2);
             
             I0 = PointsManager()[fpoints0]->GetI(tpoints0);
             I1 = PointsManager()[fpoints1]->GetI(tpoints1);
             I2 = PointsManager()[fpoints2]->GetI(tpoints2);   
 
             Blas::Dgemm('N', 'N', tnp0, fnp1*fnp2, fnp0, 1.0, I0->GetPtr().get(),
                         tnp0, from, fnp0, 0.0, wsp2.get(), tnp0);
 
             for(i = 0; i < fnp2; i++)
             {
                 Blas::Dgemm('N', 'T', tnp0,  tnp1,  fnp1, 1.0, wsp2.get()+i*tnp0*fnp1, 
                             tnp0, I1->GetPtr().get(), tnp1, 0.0, wsp1.get()+i*tnp0*tnp1, tnp0);
             }
             
             Blas::Dgemm('N', 'T', tnp0*tnp1,  tnp2,  fnp2, 1.0, wsp1.get(), 
                         tnp0*tnp1, I2->GetPtr().get(), tnp2, 0.0, to, tnp0*tnp1);         
         }

void Nektar::LibUtilities::InterpCoeff1D	(	const BasisKey &	fbasis0,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		Array< OneD, NekDouble > &	to
	)

Definition at line 47 of file InterpCoeff.cpp.

References ASSERTL0, BasisManager(), Nektar::eWrapper, Nektar::LibUtilities::BasisKey::GetBasisType(), Nektar::LibUtilities::BasisKey::GetNumModes(), and Vmath::Vcopy().

Referenced by Nektar::LocalRegions::Expansion2D::v_AddEdgeNormBoundaryInt(), Nektar::StdRegions::StdSegExp::v_ReduceOrderCoeffs(), and Nektar::SolverUtils::FilterEnergy1D::v_Update().

         {
             ASSERTL0(fbasis0.GetNumModes() == tbasis0.GetNumModes(),
                      "Number of modes must be the same for "
                      "interpolating coefficients");
 
             // Check to see if the same basis
             if (fbasis0.GetBasisType() == tbasis0.GetBasisType())
             {
                 Vmath::Vcopy(fbasis0.GetNumModes(), from, 1, to, 1);
             }
             else
             {
                 // interpolate
                 DNekMatSharedPtr ftB = BasisManager()[fbasis0]->GetI(tbasis0);
         
                 NekVector<NekDouble> in (fbasis0.GetNumModes(), from, eWrapper);
                 NekVector<NekDouble> out(tbasis0.GetNumModes(), to,   eWrapper);
                 
                 out = (*ftB)*in;
             }
         }

void Nektar::LibUtilities::InterpCoeff2D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		Array< OneD, NekDouble > &	to
	)

Definition at line 73 of file InterpCoeff.cpp.

Referenced by Nektar::StdRegions::StdQuadExp::v_ReduceOrderCoeffs(), and Nektar::LocalRegions::QuadExp::v_ReduceOrderCoeffs().

         {
             InterpCoeff2D(fbasis0, fbasis1, from.data(),
                           tbasis0, tbasis1, to.  data());
         }

void Nektar::LibUtilities::InterpCoeff2D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const NekDouble *	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		NekDouble *	to
	)

Definition at line 84 of file InterpCoeff.cpp.

References BasisManager(), Nektar::LibUtilities::BasisKey::GetBasisType(), Nektar::LibUtilities::BasisKey::GetNumModes(), and Vmath::Vcopy().

         {
             const int fnm0 = fbasis0.GetNumModes();
             const int fnm1 = fbasis1.GetNumModes();
             const int tnm0 = tbasis0.GetNumModes();
             const int tnm1 = tbasis1.GetNumModes();
 
             Array<OneD, NekDouble> wsp(tnm1 * fnm0);
 
             if (fbasis1.GetBasisType() == tbasis1.GetBasisType())
             {
                 Vmath::Vcopy(fnm0*tnm1, from, 1, wsp.get(), 1);
             }
             else
             {
                 // interpolate
                 DNekMatSharedPtr ft1 = BasisManager()[fbasis1]->GetI(tbasis1);
 
                 Blas::Dgemm('N', 'T', fnm0, tnm1, fnm1, 1.0, from, fnm0,
                             ft1->GetPtr().get(), tnm1, 0.0,  wsp.get(), fnm0);
             }
 
             if (fbasis0.GetBasisType() == tbasis0.GetBasisType())
             {
                 Vmath::Vcopy(tnm0*tnm1, wsp.get(), 1, to, 1);
             }
             else
             {
                 // interpolate
                 DNekMatSharedPtr ft0 = BasisManager()[fbasis0]->GetI(tbasis0);
 
                 Blas::Dgemm('N', 'N', tnm0, tnm1, fnm0, 1.0, ft0->GetPtr().get(),
                             tnm0, wsp.get(), fnm0, 0.0, to, tnm0);
             }
         }

void Nektar::LibUtilities::InterpCoeff3D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const BasisKey &	fbasis2,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		const BasisKey &	tbasis2,
		Array< OneD, NekDouble > &	to
	)

Definition at line 125 of file InterpCoeff.cpp.

Referenced by Nektar::LocalRegions::HexExp::v_ReduceOrderCoeffs().

         {
             InterpCoeff3D(fbasis0, fbasis1, fbasis2, from.data(),
                           tbasis0, tbasis1, tbasis2, to.  data());
         }

void Nektar::LibUtilities::InterpCoeff3D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const BasisKey &	fbasis2,
		const NekDouble *	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		const BasisKey &	tbasis2,
		NekDouble *	to
	)

Definition at line 138 of file InterpCoeff.cpp.

References BasisManager(), and Nektar::LibUtilities::BasisKey::GetNumModes().

         {
             const int fnm0 = fbasis0.GetNumModes();
             const int fnm1 = fbasis1.GetNumModes();
             const int fnm2 = fbasis2.GetNumModes();
             const int tnm0 = tbasis0.GetNumModes();
             const int tnm1 = tbasis1.GetNumModes();
             const int tnm2 = tbasis2.GetNumModes();
 
             Array<OneD, NekDouble> wsp1(tnm0 * tnm1 * fnm2);
             Array<OneD, NekDouble> wsp2(tnm0 * fnm1 * fnm2);
 
             DNekMatSharedPtr ft0 = BasisManager()[fbasis0]->GetI(tbasis0);
             DNekMatSharedPtr ft1 = BasisManager()[fbasis1]->GetI(tbasis1);
             DNekMatSharedPtr ft2 = BasisManager()[fbasis2]->GetI(tbasis2);
 
             Blas::Dgemm('N', 'N', tnm0, fnm1*fnm2, fnm0, 1.0,
                         ft0->GetPtr().get(), tnm0, from, fnm0, 0.0,
                         wsp2.get(), tnm0);
 
             for (int i = 0; i < fnm2; i++)
             {
                 Blas::Dgemm('N', 'T', tnm0,  tnm1,  fnm1, 1.0,
                             wsp2.get()+i*tnm0*fnm1, tnm0, ft1->GetPtr().get(),
                             tnm1, 0.0, wsp1.get()+i*tnm0*tnm1, tnm0);
             }
 
             Blas::Dgemm('N', 'T', tnm0*tnm1, tnm2, fnm2, 1.0, wsp1.get(),
                         tnm0*tnm1, ft2->GetPtr().get(), tnm2,
                         0.0, to, tnm0*tnm1);
         }

NekMatrix< NekDouble > Nektar::LibUtilities::Invert ( const NekMatrix< NekDouble > & matA )

Definition at line 79 of file NodalUtil.cpp.

References GetE(), SetColumn(), and Nektar::LinearSystem::Solve().

Referenced by GetInterpolationMatrix(), GetTetInterpolationMatrix(), GetTetXDerivativeMatrix(), GetTetYDerivativeMatrix(), GetTetZDerivativeMatrix(), GetXDerivativeMatrix(), and GetYDerivativeMatrix().

         {
             int rows = matA.GetRows(), columns = matA.GetColumns();
             NekMatrix<NekDouble> matX(rows,columns);
     
             // The linear system solver
             LinearSystem matL( SharedNekMatrixPtr(new NekMatrix<NekDouble>(matA)) );
     
             // Solve each column for the identity matrix
             for( int j=0; j<columns; ++j )
             {
                 SetColumn( matX, j, matL.Solve( GetE(rows,j) ) );
             }
             
             return matX;
         }

NekVector< NekDouble > Nektar::LibUtilities::JacobiPoly	(	int	degree,
		const NekVector< NekDouble > &	x,
		NekDouble	alpha,
		NekDouble	beta
	)

Definition at line 253 of file NodalUtil.cpp.

References GetSize().

Referenced by DubinerPoly(), DubinerPolyXDerivative(), DubinerPolyYDerivative(), JacobiPoly(), JacobiPolyDerivative(), TetrahedralBasis(), TetXDerivative(), TetYDerivative(), and TetZDerivative().

         {
             int size = GetSize(x);
             NekVector<NekDouble> y(size);
             
             if(degree == 0)
             {
                 // Set y to ones
                 y = NekVector<NekDouble>(size, 1.0);
     
             }
             else if (degree == 1)
             {           
                 for(int el=0; el<size; ++el)
                 {
                     y[el] = 0.5*(alpha - beta + (alpha + beta + 2.0) * x[el]);
                 }
                 
             }
             else if (degree > 1)
             {           
                 NekDouble degm1 = degree - 1.0;
                 NekDouble tmp = 2.0 * degm1 + alpha + beta;
                 NekDouble a1 = 2.0 * (degm1 + 1.0) * (degm1 + alpha + beta + 1.0) * tmp;
                 NekDouble a2 = (tmp + 1.0) * (alpha * alpha - beta * beta);
                 NekDouble a3 = tmp * (tmp + 1.0) * (tmp + 2.0);
                 NekDouble a4 = 2.0 * (degm1 + alpha) * (degm1 + beta) * (tmp + 2.0);
     
                 // TODO: Make this efficient: Reuse the degree-2 for the degree-1 call.
                 // This can be done in linear time, but it is currently implemented to run in exponential time.
                 NekVector<NekDouble> z2 = JacobiPoly(degree-2, x, alpha, beta);
                 NekVector<NekDouble> z1 = JacobiPoly(degree-1, x, alpha, beta);
 
                 for (int el=0; el<size; ++el)
                 {
                     y[el] = ((a2 + a3 * x[el]) * z1[el] - a4 * z2[el])/a1;
                 }
                 
             }
             else
             {
                 cerr << "Bad degree" << endl;
             }
     
             return y;
         }

NekDouble Nektar::LibUtilities::JacobiPoly	(	int	degree,
		NekDouble	x,
		NekDouble	alpha,
		NekDouble	beta
	)

Definition at line 300 of file NodalUtil.cpp.

References JacobiPoly().

         {
             NekDouble y = 0.0;
             
             if(degree == 0)
             {
                 y = 1.0;
             }
             
             else if (degree == 1)
             {           
                 y = 0.5*(alpha - beta + (alpha + beta + 2.0) * x);
             }
             
             else if (degree > 1)
             {           
                 NekDouble degm1 = degree - 1.0;
                 NekDouble tmp = 2.0 * degm1 + alpha + beta;
                 NekDouble a1 = 2.0 * (degm1 + 1.0) * (degm1 + alpha + beta + 1.0) * tmp;
                 NekDouble a2 = (tmp + 1.0) * (alpha * alpha - beta * beta);
                 NekDouble a3 = tmp * (tmp + 1.0) * (tmp + 2.0);
                 NekDouble a4 = 2.0 * (degm1 + alpha) * (degm1 + beta) * (tmp + 2.0);
 
                 // TODO: Make this efficient: Reuse the degree-2 for the degree-1 call.
                 // This can be done in linear time, but it is currently implemented to run in exponential time.
                 NekDouble z2 = JacobiPoly(degree-2, x, alpha, beta);
                 NekDouble z1 = JacobiPoly(degree-1, x, alpha, beta);
 
                 y = ((a2 + a3 * x) * z1 - a4 * z2)/a1;
             }
             
             else
             {
                 cerr << "Bad degree" << endl;
             }
     
             return y;
         }

NekVector< NekDouble > Nektar::LibUtilities::JacobiPolyDerivative	(	int	degree,
		const NekVector< NekDouble > &	x,
		int	alpha,
		int	beta
	)

Definition at line 867 of file NodalUtil.cpp.

References GetSize(), and JacobiPoly().

Referenced by DubinerPolyYDerivative(), TetYDerivative(), and TetZDerivative().

         {
             int size = GetSize(x);
             NekVector<NekDouble> y(size);
     
             if(degree == 0)
             {
                 y = NekVector<NekDouble>(size, 0.0);
     
             }
              else
              {
                 y = 0.5 * (alpha + beta + degree + 1) * JacobiPoly(degree - 1, x, alpha + 1, beta + 1);
             }
             return y;
         }

NekVector< NekDouble > Nektar::LibUtilities::LegendrePoly	(	int	degree,
		const NekVector< NekDouble > &	x
	)

Definition at line 340 of file NodalUtil.cpp.

References GetSize(), and Hadamard().

Referenced by DubinerPoly(), DubinerPolyYDerivative(), TetrahedralBasis(), TetYDerivative(), and TetZDerivative().

         {
             int size = GetSize(x);
             NekVector<NekDouble> y(size);
             
             if(degree > 1)
             {
                 NekVector<NekDouble> a0(size, 1.0);
                 NekVector<NekDouble> a1 = x;
                 NekVector<NekDouble> a2(size);
     
                 for(int i=2; i<=degree; ++i)
                 {
                     NekDouble b = NekDouble(2.0*i-1.0)/i;
                     NekDouble c = NekDouble(i-1.0)/i;
     
                     // multiply each elements in matrix
                     a2 = b * Hadamard(a1, x)  -  c * a0;
                     a0 = a1;
                     a1 = a2;
                 }
                 y = a2;    
             }
             else if( degree == 1 )
             {
                 y = x;                
             }
             else
             {
                 y = NekVector<NekDouble>(size, 1.0);
             }
             return y;
         }

NekVector< NekDouble > Nektar::LibUtilities::LegendrePolyDerivative	(	int	degree,
		const NekVector< NekDouble > &	x
	)

Definition at line 624 of file NodalUtil.cpp.

References GetSize(), and Hadamard().

Referenced by DubinerPolyXDerivative(), DubinerPolyYDerivative(), TetXDerivative(), TetYDerivative(), and TetZDerivative().

         {
             int size = GetSize(x);
             NekVector<NekDouble> y(size), b3(size), a2(size);
             
             if(degree >= 3)
             {
                 NekVector<NekDouble> b0(size, 0.0), b1(size, 1.0), b2 = 3.0 * x;
                 NekVector<NekDouble> a0(size, 1.0), a1 = x;
     
                 for(int n=3; n<=degree; ++n)
                 {
                     a2 = ((2.0*n - 3.0)/(n - 1.0)) * Hadamard(x, a1) - (n - 2.0)/(n - 1.0) * a0;
                     a0 = a1;
                     a1 = a2;
     
                     b3 = (2.0*n - 1.0)/n * (Hadamard(b2, x) + a2) - (n - 1.0)/n * b1;
                     b1 = b2;
                     b2 = b3;
                 }
                 y = b3;
                 
             }
             else if(degree == 2)
             {
                 y = 3.0 * x;                
             }
             else if(degree == 1)
             {
                 y = NekVector<NekDouble>(size, 1.0);
                 
             }
             else
             {
                 y = NekVector<NekDouble>(size, 0.0);
             }
             return y;
         }

NekVector< NekDouble > Nektar::LibUtilities::MakeDubinerQuadratureSystem ( int nBasisFunctions )

Definition at line 236 of file NodalUtil.cpp.

Referenced by MakeQuadratureWeights().

         {
             // Make the vector of integrals: note that each modal basis function integrates to zero except for the 0th degree
             NekVector<NekDouble> g(nBasisFunctions, 0.0);
             g(0) = sqrt(2.0);
     
             return g;
         }

NekVector< NekDouble > Nektar::LibUtilities::MakeQuadratureWeights	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 579 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetRows(), MakeDubinerQuadratureSystem(), MakeVmatrixOfDubinerPolynomial(), and Nektar::LinearSystem::SolveTranspose().

Referenced by Nektar::LibUtilities::NodalTriElec::CalculateWeights(), Nektar::LibUtilities::NodalTriFekete::CalculateWeights(), and Nektar::LibUtilities::NodalTriEvenlySpaced::CalculateWeights().

         {
     
             NekVector<NekDouble> g = MakeDubinerQuadratureSystem(x.GetRows());
             
             SharedNekMatrixPtr   matV =  MakeVmatrixOfDubinerPolynomial( x, y);
 
             // Initialize the linear system solver
             LinearSystem matL(matV);
 
             // Deduce the quadrature weights
             return matL.SolveTranspose(g);
     
         }

NekDouble Nektar::LibUtilities::MakeRound ( NekDouble x )

Definition at line 231 of file NodalUtil.cpp.

Referenced by GetDegree(), GetTetDegree(), MatrixToString(), and VectorToString().

         {
             return floor(x + 0.5);
         }

NekVector< NekDouble > Nektar::LibUtilities::MakeTetQuadratureSystem ( int nBasisFunctions )

Definition at line 245 of file NodalUtil.cpp.

Referenced by MakeTetWeights().

         {
             NekVector<NekDouble> g(nBasisFunctions, 0.0);
             g(0) = 1.0;
             return g;
         }

NekVector< NekDouble > Nektar::LibUtilities::MakeTetWeights	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 562 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetRows(), MakeTetQuadratureSystem(), MakeVmatrixOfTet(), and Nektar::LinearSystem::SolveTranspose().

Referenced by Nektar::LibUtilities::NodalTetElec::CalculateWeights(), and Nektar::LibUtilities::NodalTetEvenlySpaced::CalculateWeights().

         {
 
             NekVector<NekDouble> g = MakeTetQuadratureSystem(x.GetRows());
           
             SharedNekMatrixPtr matV = MakeVmatrixOfTet(x, y, z);
 
             // Initialize the linear system solver
             LinearSystem matL(matV);
 
 
             // Deduce the quadrature weights
             NekVector<NekDouble> w = matL.SolveTranspose(g);
             
             return w;
         }

SharedNekMatrixPtr Nektar::LibUtilities::MakeVmatrixOfDubinerPolynomial	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y
	)

Definition at line 554 of file NodalUtil.cpp.

References GetVandermonde().

Referenced by MakeQuadratureWeights().

         {
             // Construct the Vandermonde matrix of DubinerPolynomials
             SharedNekMatrixPtr vandermonde(new NekMatrix<NekDouble>( GetVandermonde(x, y) ));
     
             return vandermonde;
         }

SharedNekMatrixPtr Nektar::LibUtilities::MakeVmatrixOfTet	(	const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 547 of file NodalUtil.cpp.

References GetTetVandermonde().

Referenced by MakeTetWeights().

         {
             // Construct the Vandermonde matrix of Tetrahedron
             SharedNekMatrixPtr vMat(new NekMatrix<NekDouble>( GetTetVandermonde(x, y, z)));
             return vMat;
         }

std::string Nektar::LibUtilities::MatrixToString	(	const NekMatrix< NekDouble > &	A,
		int	precision,
		NekDouble	expSigFigs
	)

Definition at line 157 of file NodalUtil.cpp.

References MakeRound().

         {
             stringstream s;
             s << setprecision(precision);
             int M = int(A.GetRows()), N = int(A.GetColumns());
             
             for(int i=0; i<M; ++i )
             {
                 for(int j=0; j<N; ++j)
                 {
                     NekDouble a = MakeRound(expSigFigs * A(i, j)) / expSigFigs;
                     s << setw(7) << right << a;
                     if( j < N-1 )
                     {
                         s << ", ";
                     }
                 }
                 if( i < M-1 )
                 {
                     s << "\n";
                 }
             }
             return s.str();
         }

static const BasisKey Nektar::LibUtilities::NullBasisKey	(	eNoBasisType	,
		0	,
		NullPointsKey
	)

static

Defines a null basis with no type or points.

Referenced by Nektar::StdRegions::EvaluateQuadFaceBasisKey(), Nektar::StdRegions::EvaluateTriFaceBasisKey(), Nektar::MultiRegions::ExpListHomogeneous1D::ExpListHomogeneous1D(), Nektar::MultiRegions::ExpListHomogeneous2D::ExpListHomogeneous2D(), Nektar::SpatialDomains::MeshGraph2D::GetEdgeBasisKey(), Nektar::SpatialDomains::MeshGraph3D::GetFaceBasisKey(), Nektar::StdRegions::StdExpansion::StdExpansion(), Nektar::StdRegions::StdTriExp::v_DetEdgeBasisKey(), Nektar::StdRegions::StdExpansion::v_DetEdgeBasisKey(), Nektar::StdRegions::StdPrismExp::v_DetFaceBasisKey(), Nektar::StdRegions::StdTetExp::v_DetFaceBasisKey(), Nektar::StdRegions::StdPyrExp::v_DetFaceBasisKey(), and Nektar::StdRegions::StdExpansion::v_DetFaceBasisKey().

static const PointsKey Nektar::LibUtilities::NullPointsKey	(	0	,
		eNoPointsType
	)

static

Referenced by Nektar::StdRegions::StdExpansion::v_GetFacePointsKey(), and Nektar::StdRegions::StdExpansion::v_GetNodalPointsKey().

static const TimeIntegrationSchemeKey Nektar::LibUtilities::NullTimeIntegrationSchemeKey ( eNoTimeIntegrationMethod )

static

bool Nektar::LibUtilities::operator!=	(	const GraphVertexObject &	x,
		const GraphVertexObject &	y
	)

Definition at line 76 of file Graph.cpp.

References Nektar::LibUtilities::GraphVertexObject::m_id.

         {
             return (x.m_id != y.m_id);
         }

bool Nektar::LibUtilities::operator!=	(	const BasisKey &	x,
		const BasisKey &	y
	)

Definition at line 723 of file Basis.cpp.

         {
             return (!(x == y));
         }

bool Nektar::LibUtilities::operator!=	(	const BasisKey *	x,
		const BasisKey &	y
	)

Definition at line 729 of file Basis.cpp.

         {
             return (!(*x == y));
         }

bool Nektar::LibUtilities::operator!=	(	const BasisKey &	x,
		const BasisKey *	y
	)

Definition at line 735 of file Basis.cpp.

         {
             return (!(x == *y));
         }

bool Nektar::LibUtilities::operator<	(	const BasisKey &	lhs,
		const BasisKey &	rhs
	)

Definition at line 49 of file Basis.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey(), Nektar::LibUtilities::BasisKey::m_basistype, and Nektar::LibUtilities::BasisKey::m_nummodes.

         {
             PointsKey lhsPointsKey = lhs.GetPointsKey();
             PointsKey rhsPointsKey = rhs.GetPointsKey();
 
             if (lhsPointsKey  < rhsPointsKey)
             {
                 return true;
             }
             if (lhsPointsKey != rhsPointsKey)
             {
                 return false;
             }
 
             if (lhs.m_nummodes < rhs.m_nummodes)
             {
                 return true;
             }
             if (lhs.m_nummodes > rhs.m_nummodes)
             {
                 return false;
             }
 
             return (lhs.m_basistype < rhs.m_basistype);
         }

bool Nektar::LibUtilities::operator<	(	const PointsKey &	lhs,
		const PointsKey &	rhs
	)

Definition at line 55 of file Points.cpp.

References Nektar::LibUtilities::PointsKey::m_factor, Nektar::LibUtilities::PointsKey::m_numpoints, and Nektar::LibUtilities::PointsKey::m_pointstype.

         {
             if (lhs.m_pointstype < rhs.m_pointstype)
             {
                 return true;
             }
 
             if (lhs.m_pointstype > rhs.m_pointstype)
             {
                 return false;
             }
 
             if (lhs.m_numpoints < rhs.m_numpoints)
             {
                 return true;
             }
             
             if (lhs.m_numpoints > rhs.m_numpoints)
             {
                 return false;
             }
             
             if(lhs.m_factor < rhs.m_factor)
             {
                 return true;
             }
             
             if(lhs.m_factor > rhs.m_factor)
             {
                 return true;
             }
 
             return false;
         }

bool Nektar::LibUtilities::operator<	(	const TimeIntegrationSchemeKey &	lhs,
		const TimeIntegrationSchemeKey &	rhs
	)

Definition at line 58 of file TimeIntegrationScheme.cpp.

References Nektar::LibUtilities::TimeIntegrationSchemeKey::m_method.

         {
             return (lhs.m_method < rhs.m_method);
         }

std::ostream & Nektar::LibUtilities::operator<<	(	std::ostream &	os,
		const TimeIntegrationSchemeKey &	rhs
	)

Definition at line 68 of file TimeIntegrationScheme.cpp.

References Nektar::LibUtilities::TimeIntegrationSchemeKey::GetIntegrationMethod(), and TimeIntegrationMethodMap.

         {
             os << "Time Integration Scheme: " << TimeIntegrationMethodMap[rhs.GetIntegrationMethod()] << endl;
 
             return os;
         }

std::ostream & Nektar::LibUtilities::operator<<	(	std::ostream &	os,
		const BasisKey &	rhs
	)

Definition at line 85 of file Basis.cpp.

References BasisTypeMap, Nektar::LibUtilities::BasisKey::GetBasisType(), Nektar::LibUtilities::BasisKey::GetNumModes(), and Nektar::LibUtilities::BasisKey::GetPointsKey().

Referenced by operator<<().

         {
             os << "NumModes: " << rhs.GetNumModes() << " BasisType: " << BasisTypeMap[rhs.GetBasisType()];
             os << " " << rhs.GetPointsKey() << std::endl;
 
             return os;
         }

std::ostream & Nektar::LibUtilities::operator<<	(	std::ostream &	os,
		const PointsKey &	rhs
	)

Definition at line 95 of file Points.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetPointsType(), and kPointsTypeStr.

         {
             os << "NumPoints: " << rhs.GetNumPoints() << " PointsType: " << kPointsTypeStr[rhs.GetPointsType()] << std::endl;
 
             return os;
         }

std::ostream & Nektar::LibUtilities::operator<<	(	std::ostream &	os,
		const TimeIntegrationSchemeSharedPtr &	rhs
	)

Definition at line 1779 of file TimeIntegrationScheme.cpp.

References operator<<().

         {
             return operator<<(os,*rhs);
         }

std::ostream & Nektar::LibUtilities::operator<<	(	std::ostream &	os,
		const TimeIntegrationScheme &	rhs
	)

Definition at line 1784 of file TimeIntegrationScheme.cpp.

         {
             int i,j;
             int r = rhs.GetNsteps();
             int s = rhs.GetNstages();
             TimeIntegrationSchemeType type = rhs.GetIntegrationSchemeType();
 
             int oswidth = 9;
             int osprecision = 6;
 
             os << "Time Integration Scheme: " << TimeIntegrationMethodMap[rhs.GetIntegrationMethod()] << endl;
             os << "- number of steps:  " << r << endl;
             os << "- number of stages: " << s << endl;
             os << "- type of scheme:   " << TimeIntegrationSchemeTypeMap[rhs.GetIntegrationSchemeType()] << endl;
             os << "General linear method tableau: " << endl;
 
             for(i = 0; i < s; i++)
             {
                 for(j = 0; j < s; j++)
                 {
                     os.width(oswidth);
                     os.precision(osprecision);
                     os << right << rhs.A(i,j) << " ";
                 }
                 if(type == eIMEX)
                 {
                     os << " '"; 
                     for(j = 0; j < s; j++)
                     {
                         os.width(oswidth);
                         os.precision(osprecision);
                         os << right << rhs.A_IMEX(i,j) << " ";
                     }
                 }
                 os << " |"; 
 
                 for(j = 0; j < r; j++)
                 {
                     os.width(oswidth);
                     os.precision(osprecision);
                     os << right << rhs.U(i,j);
                 }
                 os << endl;
             }
             int imexflag = (type == eIMEX)?2:1;
             for(int i = 0; i < (r+imexflag*s)*(oswidth+1)+imexflag*2-1; i++)
             {
                 os << "-";
             }
             os << endl;
             for(i = 0; i < r; i++)
             {
                 for(j = 0; j < s; j++)
                 {
                     os.width(oswidth);
                     os.precision(osprecision);
                     os << right << rhs.B(i,j) << " ";
                 }
                 if(type == eIMEX)
                 {
                     os << " '"; 
                     for(j = 0; j < s; j++)
                     {
                         os.width(oswidth);
                         os.precision(osprecision);
                         os << right << rhs.B_IMEX(i,j) << " ";
                     }
                 }
                 os << " |"; 
 
                 for(j = 0; j < r; j++)
                 {
                     os.width(oswidth);
                     os.precision(osprecision);
                     os << right << rhs.V(i,j);
                 }
                 os << endl;
             }
             return os;
         }

bool Nektar::LibUtilities::operator==	(	const PointsKey &	lhs,
		const PointsKey &	rhs
	)

Definition at line 49 of file Points.cpp.

References Nektar::LibUtilities::PointsKey::m_numpoints, and Nektar::LibUtilities::PointsKey::m_pointstype.

         {
             return (lhs.m_numpoints == rhs.m_numpoints &&
                     lhs.m_pointstype == rhs.m_pointstype);
         }

bool Nektar::LibUtilities::operator==	(	const TimeIntegrationSchemeKey &	lhs,
		const TimeIntegrationSchemeKey &	rhs
	)

Definition at line 53 of file TimeIntegrationScheme.cpp.

References Nektar::LibUtilities::TimeIntegrationSchemeKey::m_method.

         {
             return (lhs.m_method == rhs.m_method);
         }

bool Nektar::LibUtilities::operator==	(	const GraphVertexObject &	x,
		const GraphVertexObject &	y
	)

Definition at line 71 of file Graph.cpp.

References Nektar::LibUtilities::GraphVertexObject::m_id.

         {
             return (x.m_id == y.m_id);
         }

bool Nektar::LibUtilities::operator==	(	const BasisKey &	x,
		const BasisKey &	y
	)

Definition at line 703 of file Basis.cpp.

References Nektar::LibUtilities::BasisKey::GetNumModes(), Nektar::LibUtilities::BasisKey::GetPointsKey(), and Nektar::LibUtilities::BasisKey::m_basistype.

         {
             return (x.GetPointsKey() == y.GetPointsKey() &&
                 x.m_basistype == y.m_basistype &&
                 x.GetNumModes() == y.GetNumModes());
         }

bool Nektar::LibUtilities::operator==	(	const BasisKey *	x,
		const BasisKey &	y
	)

Definition at line 711 of file Basis.cpp.

         {
             return (*x == y);
         }

bool Nektar::LibUtilities::operator==	(	const BasisKey &	x,
		const BasisKey *	y
	)

Definition at line 717 of file Basis.cpp.

         {
             return (x == *y);
         }

bool Nektar::LibUtilities::operator>	(	const BasisKey &	lhs,
		const BasisKey &	rhs
	)

Definition at line 75 of file Basis.cpp.

         {
             return (rhs < lhs);
         }

void Nektar::LibUtilities::PhysGalerkinProject1D	(	const BasisKey &	fbasis0,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		Array< OneD, NekDouble > &	to
	)

Definition at line 53 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey().

Referenced by PhysGalerkinProject1D().

         {
             PhysGalerkinProject1D(fbasis0.GetPointsKey(),from,tbasis0.GetPointsKey(),to);
         }

void Nektar::LibUtilities::PhysGalerkinProject1D	(	const PointsKey &	fpoints0,
		const Array< OneD, const NekDouble > &	from,
		const PointsKey &	tpoints0,
		Array< OneD, NekDouble > &	to
	)

Definition at line 61 of file PhysGalerkinProject.cpp.

References Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetNumPoints(), PointsManager(), and Vmath::Vcopy().

         {
             if(fpoints0 == tpoints0) //check to see if the same
             {
                 Vmath::Vcopy(fpoints0.GetNumPoints(),from,1,to,1);
             }
             else // interpolate
             {
                 DNekMatSharedPtr GP0;
                 
                 GP0 = PointsManager()[tpoints0]->GetGalerkinProjection(fpoints0);
                 
                 NekVector<NekDouble> in(fpoints0.GetNumPoints(),from,eWrapper);
                 NekVector<NekDouble> out(tpoints0.GetNumPoints(),to,eWrapper);
                 
                 GP0->Transpose();
                 out  = (*GP0)*in;
             }
         }

void Nektar::LibUtilities::PhysGalerkinProject1D	(	const BasisKey &	fbasis0,
		const NekDouble *	from,
		const BasisKey &	tbasis0,
		NekDouble *	to
	)

Definition at line 84 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey(), and PhysGalerkinProject1D().

         {
             PhysGalerkinProject1D(fbasis0.GetPointsKey(),from,tbasis0.GetPointsKey(),to);
         }

void Nektar::LibUtilities::PhysGalerkinProject1D	(	const PointsKey &	fpoints0,
		const NekDouble *	from,
		const PointsKey &	tpoints0,
		NekDouble *	to
	)

Definition at line 92 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), PointsManager(), and Vmath::Vcopy().

         {
             if(fpoints0 == tpoints0) //check to see if the same
             {
                 Vmath::Vcopy(fpoints0.GetNumPoints(),from,1,to,1);
             }
             else // interpolate
             {
                 
                 DNekMatSharedPtr GP0;
                 
                 GP0 = PointsManager()[tpoints0]
                     ->GetGalerkinProjection(fpoints0);
                 
                 Blas::Dgemv('T', tpoints0.GetNumPoints(), fpoints0.GetNumPoints(), 
                             1.0, GP0->GetPtr().get(), tpoints0.GetNumPoints(), 
                             from, 1, 0.0, to, 1);
             }
         }

void Nektar::LibUtilities::PhysGalerkinProject2D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		Array< OneD, NekDouble > &	to
	)

Definition at line 116 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey().

Referenced by PhysGalerkinProject2D(), and Nektar::MultiRegions::ExpList2D::v_PhysGalerkinProjection1DScaled().

         {
             PhysGalerkinProject2D(fbasis0.GetPointsKey(),fbasis1.GetPointsKey(),from.data(),
                      tbasis0.GetPointsKey(),tbasis1.GetPointsKey(),to.data());
         }

void Nektar::LibUtilities::PhysGalerkinProject2D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const Array< OneD, const NekDouble > &	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		Array< OneD, NekDouble > &	to
	)

Definition at line 127 of file PhysGalerkinProject.cpp.

References PhysGalerkinProject2D().

         {
             PhysGalerkinProject2D(fpoints0,fpoints1,from.data(),tpoints0,tpoints1,to.data());
         }

void Nektar::LibUtilities::PhysGalerkinProject2D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const NekDouble *	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		NekDouble *	to
	)

Definition at line 137 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), PointsManager(), and Vmath::Vcopy().

         {
             DNekMatSharedPtr GP0,GP1;
             Array<OneD, NekDouble> wsp(tpoints1.GetNumPoints()*fpoints0.GetNumPoints()); // fnp0*tnp1
 
             int fnp0 = fpoints0.GetNumPoints();
             int fnp1 = fpoints1.GetNumPoints();
             int tnp0 = tpoints0.GetNumPoints();
             int tnp1 = tpoints1.GetNumPoints();
 
             if(fpoints1 == tpoints1)
             {
                 Vmath::Vcopy(fnp0*tnp1,from,1,wsp.get(),1);
             }
             else
             {
                 GP1 = PointsManager()[tpoints1]->GetGalerkinProjection(fpoints1);
                 Blas::Dgemm('N', 'T', fnp0, tnp1, fnp1, 1.0, from, fnp0,
                              GP1->GetPtr().get(), tnp1, 0.0,  wsp.get(), fnp0);     
             }
 
             if(fpoints0 == tpoints0)
             {
                 Vmath::Vcopy(tnp0*tnp1,wsp.get(),1,to,1);
             }
             else
             {
                 GP0 = PointsManager()[tpoints0]->GetGalerkinProjection(fpoints0);
                 Blas::Dgemm('N', 'N', tnp0, tnp1, fnp0, 1.0, 
                             GP0->GetPtr().get(),
                             tnp0, wsp.get(), fnp0, 0.0, to, tnp0);     
             }
         }

void Nektar::LibUtilities::PhysGalerkinProject3D	(	const BasisKey &	fbasis0,
		const BasisKey &	fbasis1,
		const BasisKey &	fbasis2,
		const Array< OneD, const NekDouble > &	from,
		const BasisKey &	tbasis0,
		const BasisKey &	tbasis1,
		const BasisKey &	tbasis2,
		Array< OneD, NekDouble > &	to
	)

Definition at line 178 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::BasisKey::GetPointsKey().

Referenced by PhysGalerkinProject3D(), and Nektar::MultiRegions::ExpList3D::v_PhysGalerkinProjection1DScaled().

         {
             PhysGalerkinProject3D(fbasis0.GetPointsKey(),
                                   fbasis1.GetPointsKey(),
                                   fbasis2.GetPointsKey(),
                                   from.data(),
                                   tbasis0.GetPointsKey(),
                                   tbasis1.GetPointsKey(),
                                   tbasis2.GetPointsKey(),
                                   to.data());
         }

void Nektar::LibUtilities::PhysGalerkinProject3D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const PointsKey &	fpoints2,
		const Array< OneD, const NekDouble > &	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		const PointsKey &	tpoints2,
		Array< OneD, NekDouble > &	to
	)

Definition at line 197 of file PhysGalerkinProject.cpp.

References PhysGalerkinProject3D().

         {
             PhysGalerkinProject3D(fpoints0,fpoints1,fpoints2,from.data(),
                                   tpoints0,tpoints1,tpoints2,to.data());
         }

void Nektar::LibUtilities::PhysGalerkinProject3D	(	const PointsKey &	fpoints0,
		const PointsKey &	fpoints1,
		const PointsKey &	fpoints2,
		const NekDouble *	from,
		const PointsKey &	tpoints0,
		const PointsKey &	tpoints1,
		const PointsKey &	tpoints2,
		NekDouble *	to
	)

Definition at line 210 of file PhysGalerkinProject.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), and PointsManager().

         {
             DNekMatSharedPtr GP0,GP1,GP2;
 
             int fnp0 = fpoints0.GetNumPoints();
             int fnp1 = fpoints1.GetNumPoints();
             int fnp2 = fpoints2.GetNumPoints();
             int tnp0 = tpoints0.GetNumPoints();
             int tnp1 = tpoints1.GetNumPoints();
             int tnp2 = tpoints2.GetNumPoints();
 
             Array<OneD, NekDouble> wsp1(fnp0*tnp1*tnp2);
             Array<OneD, NekDouble> wsp2(fnp0*fnp1*tnp2);
 
             GP2 = PointsManager()[tpoints2]->GetGalerkinProjection(fpoints2);
             Blas::Dgemm('N', 'T', fnp0*fnp1, tnp2, fnp2, 1.0, from, fnp0*fnp1,
                         GP2->GetPtr().get(), tnp2, 0.0,  wsp2.get(), fnp0*fnp1);
 
             GP1 = PointsManager()[tpoints1]->GetGalerkinProjection(fpoints1);
             for(int i = 0; i < tnp2; i++)
             {
                 Blas::Dgemm('N', 'T', fnp0,  tnp1,   fnp1, 1.0,
                             wsp2.get()+i*fnp0*fnp1,
                             fnp0, GP1->GetPtr().get(),tnp1, 0.0,
                             wsp1.get()+i*fnp0*tnp1,
                             fnp0);
             }
 
             GP0 = PointsManager()[tpoints0]->GetGalerkinProjection(fpoints0);
             Blas::Dgemm('N', 'N', tnp0, tnp1*tnp2, fnp0, 1.0,
                         GP0->GetPtr().get(), tnp0, wsp1.get(), fnp0, 0.0,
                         to, tnp0);
         }

PointsManagerT & Nektar::LibUtilities::PointsManager ( void )

Definition at line 92 of file ManagerAccess.cpp.

         {
             return Loki::SingletonHolder<PointsManagerT>::Instance();
         }

std::string Nektar::LibUtilities::PortablePath ( const boost::filesystem::path & path )

create portable path on different platforms for boost::filesystem path

Definition at line 41 of file FileSystem.cpp.

         {
             fs::path temp = path;
 #if BOOST_VERSION > 104200
             temp.make_preferred();
             return temp.string();
 #else
             return temp.file_string();
 #endif
         }

void Nektar::LibUtilities::PrintProgressbar	(	const int	position,
		const int	goal,
		const string	message
	)

inline

Prints a progressbar.

Parameters

position	State of the current process
goal	Goal of the current process
message	Short Description of the current process

This function plots a simple progressbar to the console or log file to visualize the current state of an ongoing process. Make sure you minimize calling this routine. Ideally, this should be called only when the percentage is increased by an integer.

Definition at line 69 of file Progressbar.hpp.

References ISTTY.

Referenced by Nektar::Utilities::Iso::globalcondense(), Nektar::NekMeshUtils::SurfaceMesh::HOSurf(), Nektar::NekMeshUtils::SurfaceMesh::Mesh(), Nektar::Utilities::ProcessInterpPointDataToFld::PrintProgressbar(), Nektar::SolverUtils::EquationSystem::PrintProgressbar(), and Nektar::Utilities::Iso::separate_regions().

 {
     std::cout.unsetf ( std::ios::floatfield );
     if (ISTTY)
     {
         // carriage return
         cout << "\r";
 
         cout << message << ": ";
         float progress = position / float(goal);
         cout << setw(3) << ceil(100 * progress) << "% [";
         for (int j = 0; j < ceil(progress * 49); j++)
         {
             cout << "=";
         }
         for (int j = ceil(progress * 49); j < 49; j++)
         {
             cout << " ";
         }
         cout << "]" << flush;
     }
     else
     {
         // print only every 2 percent
         if (int(ceil(double(100 * position / goal))) % 2 ==  0)
         {
             cout << "." <<  flush;
         }
     }
 }

static NekDouble Nektar::LibUtilities::rad	(	NekDouble	x,
		NekDouble	y
	)

static

Definition at line 80 of file AnalyticExpressionEvaluator.hpp.

Referenced by Nektar::LibUtilities::AnalyticExpressionEvaluator::AnalyticExpressionEvaluator(), Nektar::LibUtilities::functions::functions(), Nektar::LibUtilities::AnalyticExpressionEvaluator::EvalRad::run_many(), and Nektar::LibUtilities::AnalyticExpressionEvaluator::EvalRad::run_once().

         {
             if (x != 0. || y != 0.)
                 return sqrt (x*x + y*y);
             else
                 return 0.;
         }

NekMatrix< NekDouble > & Nektar::LibUtilities::SetColumn	(	NekMatrix< NekDouble > &	matA,
		int	n,
		const NekVector< NekDouble > &	x
	)

Definition at line 62 of file NodalUtil.cpp.

Referenced by Invert().

         {
             for( int i=0; i<int(matA.GetRows()); ++i )
             {
                 matA(i,n) = x[i];
             }
             return matA;
         }

NekDouble Nektar::LibUtilities::sign ( NekDouble arg )

Definition at line 97 of file AnalyticExpressionEvaluator.cpp.

Referenced by Nektar::LibUtilities::AnalyticExpressionEvaluator::AnalyticExpressionEvaluator().

         {
             return (arg > 0.0) - (arg < 0.0);
         }

NekVector< NekDouble > Nektar::LibUtilities::TetrahedralBasis	(	int	p,
		int	q,
		int	r,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 415 of file NodalUtil.cpp.

References GetSize(), JacobiPoly(), and LegendrePoly().

Referenced by GetTetVandermonde().

         {
             // Get the coordinate transform
             int size = GetSize(x);
             NekVector<NekDouble> eta_1(size), eta_2(size);
   
             // Initialize the horizontal coordinate of the Tetrahedral 
             for(int el=0; el<size; ++el)
             {
                 if( z[el] < -y[el] - numeric_limits<NekDouble>::epsilon() )
                 {
                     eta_1[el] = 2.0*(1.0 + x[el])/(-y[el]-z[el]) - 1.0;
                 }
                 else
                 {
                     eta_1[el] = -1.0;
                 }
             }
 
              // Initialize the  coordinate of the Tetrahedral 
             for(int el=0; el<size; ++el)
             {
                 if( z[el] < 1.0 - numeric_limits<NekDouble>::epsilon())
                 {
                     eta_2[el] = 2.0*(1.0 + y[el]) / (1.0 - z[el]) - 1.0;
                 }
                 else
                 {
                     eta_2[el] = -1.0;  // When z is close to 1, then we have a removeable singularity
                     eta_1[el] = -1.0;  // When z is close to 1, then we have a removeable singularity
                 }
             }
             
             // Initialize the vertical coordinate of the Tetrahedral 
             NekVector<NekDouble> eta_3 = z;
 
             // Orthogonal basis polynomial
             int alpha = 2*p + 1; int beta = 0;
             int alpha_r = 2*p + 2*q + 2; int beta_r = 0;
             NekVector<NekDouble> phi(size);
             NekVector<NekDouble> psi_a    = LegendrePoly(p,eta_1);
             NekVector<NekDouble> psi_bpq  = JacobiPoly(q, eta_2, alpha, beta);
             NekVector<NekDouble> psi_cpqr = JacobiPoly(r, eta_3, alpha_r, beta_r);
             NekDouble w = 1.0;
 
             for(int el=0; el<size; ++el)
             {
                 NekDouble zeta_1 = pow((1.0 - eta_2[el])/2.0, p);                
                 NekDouble zeta_2 = pow((1.0 - eta_3[el])/2.0, p+q);
                 
                 NekDouble psi_b = zeta_1 * psi_bpq[el];
                 NekDouble psi_c = zeta_2 * psi_cpqr[el];
 
                 phi[el]         = w * psi_a[el] * psi_b * psi_c;
 
             }
                
             return phi;
 
         }

NekVector< NekDouble > Nektar::LibUtilities::TetXDerivative	(	int	p,
		int	q,
		int	r,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 711 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetRows(), GetSize(), JacobiPoly(), and LegendrePolyDerivative().

Referenced by GetVandermondeForTetXDerivative().

         {
             // Get the coordinate transform
             int size = GetSize(y);
             NekVector<NekDouble> eta_1(size), eta_2(size);
             NekVector<NekDouble> psi_x(x.GetRows());
             if(p > 0){
                 // Initialize the horizontal coordinate of the Tetrahedral (beta in Barycentric coordinate)
                 for(int el=0; el<size; ++el)
                 {
                     if( y[el] < -z[el] - numeric_limits<NekDouble>::epsilon())
                     {
                         eta_1[el] = 2.0*(1.0 + x[el])/(-y[el]-z[el]) - 1.0;
                     } else
                     {
                         eta_1[el] = -1.0;
                     }
                 }
                 
                     // Initialize the  coordinate of the Tetrahedral (gamma in Barycentric coordinate)
                 for(int el=0; el<size; ++el)
                 {
                     if( z[el] < 1.0 - numeric_limits<NekDouble>::epsilon())
                     {
                         eta_2[el] = 2.0*(1.0 + y[el]) / (1.0 - z[el]) - 1.0;
                     }
                     else
                     {
                         eta_2[el] = -1.0;  // When z is close to 1, then we have a removeable singularity
                     }
                 }
                 // Initialize the vertical coordinate of the Tetrahedral (delta in Barycentric coordinate)
                 NekVector<NekDouble> eta_3 = z;
                             
                 // Orthogonal basis polynomial x-derivative
                 int alpha = 2*p + 1; int beta = 0;
                 int alpha_r = 2*p + 2*q + 2; int beta_r = 0;
                 NekVector<NekDouble> psi_a_x    = LegendrePolyDerivative(p,eta_1);
                 NekVector<NekDouble> psi_bpq  = JacobiPoly(q, eta_2, alpha, beta);
                 NekVector<NekDouble> psi_cpqr = JacobiPoly(r, eta_3, alpha_r, beta_r);
 
                 for(int el=0; el<size; ++el)
                 {
                     NekDouble jacobi_b =  pow((1.0-eta_2[el])/2.0, p-1.0);
                     NekDouble jacobi_c =  pow((1.0-eta_3[el])/2.0,p+q-1.0);
                     NekDouble psi_b = jacobi_b * psi_bpq[el];
                     NekDouble psi_c = jacobi_c * psi_cpqr[el];
                     psi_x[el] = psi_a_x[el] * psi_b * psi_c;
                 }
             }
             else
             {
                 for(int el=0; el<int(x.GetRows()); ++el)
                 {
                     psi_x[el] = 0.0;
                 }
             }
             return psi_x;
         }

NekVector< NekDouble > Nektar::LibUtilities::TetYDerivative	(	int	p,
		int	q,
		int	r,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 886 of file NodalUtil.cpp.

References GetSize(), Hadamard(), JacobiPoly(), JacobiPolyDerivative(), LegendrePoly(), LegendrePolyDerivative(), and VectorPower().

Referenced by GetVandermondeForTetYDerivative().

          {
             // Get the coordinate transform
             int size = GetSize(y);
             NekVector<NekDouble> eta_1(size), eta_2(size);
             NekVector<NekDouble> eta_1_dy(size), eta_2_dy(size);
     
             // Initialize the collapsed horizontal coordinate of the Tetrahedral
             for(int el=0; el<size; ++el)
             {
                 if( y[el] < -z[el] - numeric_limits<NekDouble>::epsilon())
                 {
                     eta_1[el]       = 2.0*(1.0 + x[el])/(-y[el]-z[el]) - 1.0;
                     eta_1_dy[el]    = 2.0*(1.0 + x[el])/((y[el]+z[el])*(y[el]+z[el]));
                 }
                 else
                 {
                     eta_1[el]       = -1.0;
                     eta_1_dy[el]    =  0.0; // No change in the squeeze direction
                 }
             }
     
             // Initialize the collapsed depth coordinate of the Tetrahedral
             for(int el=0; el<size; ++el)
             {
                 if( z[el] < 1.0 - numeric_limits<NekDouble>::epsilon())
                 {
                     eta_2[el]       = 2.0*(1.0 + y[el]) / (1.0 - z[el]) - 1.0;
                     eta_2_dy[el]    = 2.0/(1.0 - z[el]);
                 }
                 else
                 {
                         // When z is close to 1, then we have a removeable singularity
                     eta_2[el]       = -1.0;
                     eta_2_dy[el]    =  0.0; // No change in the squeeze direction
                 }
             }
             // Initialize the collapsed vertical coordinate of the Tetrahedral
             NekVector<NekDouble> eta_3 = z;
     
             // Orthogonal basis expansion polynomials and their y-derivatives for the tetrahedron
             // phi(vec xi) = psi_a(eta_1(xi)) * psi_b(eta_2(xi)) * psi_c(eta_3(xi))
             int alpha_b = 2*p + 1; int beta_b = 0;
             int alpha_c = 2*p + 2*q + 2; int beta_c = 0;
             NekVector<NekDouble> ones( size, 1.0 );
     
             NekVector<NekDouble> jacobi_b   = VectorPower( (ones - eta_2)/2.0, p );
             NekVector<NekDouble> jacobi_c   = VectorPower( (ones - eta_3)/2.0, p+q );
     
             NekVector<NekDouble> J_q        = JacobiPoly(q, eta_2, alpha_b, beta_b);
             NekVector<NekDouble> J_r        = JacobiPoly(r, eta_3, alpha_c, beta_c);
     
             NekVector<NekDouble> psi_a      = LegendrePoly(p, eta_1);
             NekVector<NekDouble> LD         = LegendrePolyDerivative(p, eta_1);
             NekVector<NekDouble> JD         = JacobiPolyDerivative(q, eta_2, alpha_b, beta_b);
             NekVector<NekDouble> psi_b      = Hadamard( J_q, jacobi_b );
             NekVector<NekDouble> psi_c      = Hadamard( J_r, jacobi_c );
     
             // Compute the partials wrt y (psi_c_dy = 0)
             NekVector<NekDouble> secondComponentOfPsi_b_dy( size, 0.0 );
 
             if(p > 0)
             {
                 for(int i=0; i<size; ++i)
                 {
                     NekDouble jacobi_b_dy = -p / 2.0 * pow( (1.0 - eta_2[i])/2.0, p-1.0 );
                     secondComponentOfPsi_b_dy[i] = J_q[i] * jacobi_b_dy;
                 }
             }
              else
             {
                 for(int i=0; i<size; ++i)
                 {
                     secondComponentOfPsi_b_dy[i] = 0.0;
                 }
             }
 
             NekVector<NekDouble> psi_a_dy   = Hadamard( LegendrePolyDerivative(p, eta_1), eta_1_dy );
             NekVector<NekDouble> psi_b_dy   = Hadamard( Hadamard( JacobiPolyDerivative(q, eta_2, alpha_b, beta_b), jacobi_b)
                                               + secondComponentOfPsi_b_dy, eta_2_dy );
 
             NekVector<NekDouble> psi_dy(size);
             for(int k=0; k<size; ++k)
             {
                 psi_dy[k] = (psi_a_dy[k]*psi_b[k]*psi_c[k])  +  (psi_a[k]*psi_b_dy[k]*psi_c[k]);
             }
 
             // Fix singularity at z=1
             for(int k=0; k<size; ++k)
             {
                 if( z[k] >= 1.0 - numeric_limits<NekDouble>::epsilon() )
                 {
                     if( p + q > 0 )
                     {
                         psi_dy[k] = ((2.0*p+q+2.0)*JacobiPoly(q, eta_2[k], alpha_b, 1) - (p+q+2.0)*J_q[k]) *
                         psi_a[k] * pow( (1.0-eta_3[k])/2.0, p+q-1 ) / 2.0 * ((p+q+r+3.0)*J_r[k] - (2.0*p+2.0*q+r+3.0)*JacobiPoly(r, eta_3[k], alpha_c, 1));
                     }
                     else
                     {
                         psi_dy[k] = 0.0;
                     }
                 }
             }
 
 //             cout << "(p,q,r) = (" << p << ", " << q << ", " << r << ")" << endl;
 // 
 //             cout << "psi_a    = " << VectorToString(psi_a) << endl;
 //             cout << "psi_b    = " << VectorToString(psi_b) << endl;
 //             cout << "psi_c    = " << VectorToString(psi_c) << endl;
 //             cout << "psi_a_dy = " << VectorToString(psi_a_dy) << endl;
 //             cout << "psi_b_dy = " << VectorToString(psi_b_dy) << endl;
 //             cout << "(psi_a_dy*psi_b*psi_c)          = " << VectorToString(Hadamard(Hadamard(psi_a_dy,psi_b), psi_c)) << endl;
 //             cout << "(psi_a*jacobi_b*psi_b_dy*psi_c) = " << VectorToString(Hadamard(Hadamard(psi_a,jacobi_b),Hadamard(psi_b_dy,psi_c))) << endl;
 //             cout << "secondComponentOfPsi_b_dy = " << VectorToString(secondComponentOfPsi_b_dy) << endl;
 //             
 //             cout << "psi_dy   = " << VectorToString(psi_dy) << endl;
 // // //            cout << "jacobi_c = " << VectorToString(jacobi_c) << endl;
 // // //             cout << "eta_3 = " << VectorToString(eta_3) << endl;
 // // //             cout << "ones - eta_3 = " << VectorToString(ones - eta_3) << endl;
 // // //             cout << "(ones - eta_3)/2.0 = " << VectorToString((ones - eta_3)/2.0) << endl;
 
 
             return psi_dy;
         }

NekVector< NekDouble > Nektar::LibUtilities::TetZDerivative	(	int	p,
		int	q,
		int	r,
		const NekVector< NekDouble > &	x,
		const NekVector< NekDouble > &	y,
		const NekVector< NekDouble > &	z
	)

Definition at line 1064 of file NodalUtil.cpp.

References GetSize(), Hadamard(), JacobiPoly(), JacobiPolyDerivative(), LegendrePoly(), LegendrePolyDerivative(), and VectorPower().

Referenced by GetTetZDerivativeMatrix(), and GetVandermondeForTetZDerivative().

          {
             int size = GetSize(z);
             NekVector<NekDouble> eta_1(size), eta_2(size);
             NekVector<NekDouble> eta_1_dz(size), eta_2_dz(size);
             
              // Initialize the collapsed horizontal coordinate of the Tetrahedral 
             for(int el=0; el<size; ++el)
             {
                 if( y[el] < -z[el] - numeric_limits<NekDouble>::epsilon())
                 {
                     eta_1[el]       = 2.0*(1.0 + x[el]) / (-y[el]-z[el]) - 1.0;
                     eta_1_dz[el]    = 2.0*(1.0 + x[el]) / ((y[el]+z[el])*(y[el]+z[el]));
                 }
                 else
                 {
                     eta_1[el]       = -1.0;
                     eta_1_dz[el]    =  0.0; // No change in the squeeze direction
                 }
             }
 
             // Initialize the collapsed depth coordinate of the Tetrahedral
             for(int el=0; el<size; ++el)
             {
                 if( z[el] < 1.0 - numeric_limits<NekDouble>::epsilon())
                 {
                     eta_2[el]       = 2.0*(1.0 + y[el]) / (1.0 - z[el])  -  1.0;
                     eta_2_dz[el]    = 2.0*(1.0 + y[el]) / ((1.0 - z[el])*(1.0 - z[el]));
                 }
                 else
                 {    // When z is close to 1, then we have a removeable singularity
                     eta_2[el]       = -1.0;
                     eta_2_dz[el]    =  0.0; // No change in the squeeze direction
                 }
             }
 
 
             // Initialize the collapsed vertical coordinate of the Tetrahedral 
             NekVector<NekDouble> eta_3 = z;
             NekVector<NekDouble> eta_3_dz(size, 1.0);
 
             
             // Orthogonal basis expansion polynomials and their z-derivatives for the tetrahedron
             // phi(vec xi) = psi_a(eta_1(xi)) * psi_b(eta_2(xi)) * psi_c(eta_3(xi))
             int alpha_b = 2*p + 1; int beta_b = 0;
             int alpha_c = 2*p + 2*q + 2; int beta_c = 0;
             NekVector<NekDouble> ones( size, 1.0 );
 
             NekVector<NekDouble> jacobi_b   = VectorPower( (ones - eta_2)/2.0, p );
             NekVector<NekDouble> jacobi_c   = VectorPower( (ones - eta_3)/2.0, p+q );
             
             NekVector<NekDouble> J_q        = JacobiPoly(q, eta_2, alpha_b, beta_b);
             NekVector<NekDouble> J_r        = JacobiPoly(r, eta_3, alpha_c, beta_c);
             
             NekVector<NekDouble> psi_a      = LegendrePoly(p, eta_1);
             NekVector<NekDouble> psi_b      = Hadamard( J_q, jacobi_b );
             NekVector<NekDouble> psi_c      = Hadamard( J_r, jacobi_c );
 
                         
             // Compute the partials wrt y and z (psi_c_dy = 0)
             NekVector<NekDouble> secondComponentOfPsi_b_dz( size, 0.0 );            
             NekVector<NekDouble> secondComponentOfPsi_c_dz( size, 0.0 );
             if(p > 0)
             {
                 for(int i=0; i<size; ++i)
                 {
                     NekDouble jacobi_b_dz = -p / 2.0 * pow( (1.0 - eta_2[i])/2.0, p-1.0 );
                     secondComponentOfPsi_b_dz[i] = J_q[i] * jacobi_b_dz;
                 }
             }
             
             if(p + q > 0)
             {
                 for(int i=0; i<size; ++i)
                 {
                     NekDouble jacobi_c_dz = -(p+q)/2.0*pow( (1.0 - eta_3[i])/2.0, p+q-1.0);
                     secondComponentOfPsi_c_dz[i] = J_r[i] * jacobi_c_dz;
                 }
             }
             
             NekVector<NekDouble> psi_a_dz   = Hadamard( LegendrePolyDerivative(p, eta_1), eta_1_dz );
             NekVector<NekDouble> psi_b_dz   = Hadamard( Hadamard(JacobiPolyDerivative(q, eta_2, alpha_b, beta_b), jacobi_b)
                                               + secondComponentOfPsi_b_dz, eta_2_dz );
             NekVector<NekDouble> psi_c_dz   = Hadamard( Hadamard(JacobiPolyDerivative(r, eta_3, alpha_c, beta_c), jacobi_c)
                                               + secondComponentOfPsi_c_dz, eta_3_dz );
 
             NekVector<NekDouble> psi_dz(size);
             
             for(int k=0; k<size; ++k)
             {
                psi_dz[k] = psi_a_dz[k] * psi_b[k] * psi_c[k]  +  psi_a[k] * psi_b_dz[k] * psi_c[k]  +  psi_a[k] * psi_b[k] * psi_c_dz[k];
             }
             
             return psi_dz;                                                                    
         }

TimeIntegrationSchemeManagerT & Nektar::LibUtilities::TimeIntegrationSchemeManager ( void )

Definition at line 45 of file TimeIntegrationScheme.cpp.

References Nektar::LibUtilities::TimeIntegrationScheme::Create(), and Nektar::LibUtilities::NekManager< KeyType, ValueT, opLessCreator >::RegisterGlobalCreator().

         {
             TimeIntegrationSchemeManagerT& m = Loki::SingletonHolder<TimeIntegrationSchemeManagerT>::Instance();
             m.RegisterGlobalCreator(TimeIntegrationScheme::Create);
             return m;
         }

Array< OneD, NekDouble > Nektar::LibUtilities::ToArray ( const NekVector< NekDouble > & x )

Definition at line 126 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetPtr(), and GetSize().

         {
             return Array<OneD, NekDouble>( GetSize(x), x.GetPtr() );
         }

NekVector< NekDouble > Nektar::LibUtilities::ToVector ( const Array< OneD, const NekDouble > & x )

Definition at line 121 of file NodalUtil.cpp.

References GetSize().

         {
             return NekVector<NekDouble>( GetSize(x), x.data() );
         }

NekVector< NekDouble > Nektar::LibUtilities::VectorPower	(	const NekVector< NekDouble > &	x,
		NekDouble	p
	)

Definition at line 143 of file NodalUtil.cpp.

References GetSize().

Referenced by TetYDerivative(), and TetZDerivative().

         {
             int size = GetSize(x);
             NekVector<NekDouble> z(size);
     
             for( int i=0; i<size; ++i )
             {
                 z[i] = pow( x[i], p );
             }
             
             return z;
         }

std::string Nektar::LibUtilities::VectorToString	(	const NekVector< NekDouble > &	v,
		int	precision,
		NekDouble	expSigFigs
	)

Definition at line 183 of file NodalUtil.cpp.

References Nektar::NekVector< DataType >::GetRows(), and MakeRound().

         {
             stringstream s;
             s << setprecision(precision) << "[ ";
             int N = int(v.GetRows());
             for(int j=0; j<N; ++j )
             {
                 NekDouble x = MakeRound(expSigFigs * v(j)) / expSigFigs;
                 s << setw(7) << right << x;
                 if( j < N-1 )
                 {
                     s << ", ";
                 }
             }
             s << " ]";
             return s.str();
         }

void Nektar::LibUtilities::Write	(	const std::string &	outFile,
		std::vector< FieldDefinitionsSharedPtr > &	fielddefs,
		std::vector< std::vector< NekDouble > > &	fielddata,
		const FieldMetaDataMap &	fieldinfomap
	)

Write a field file in serial only.

This function allows for data to be written to an FLD file when a session and/or communicator is not instantiated. Typically used in utilities which do not take XML input and operate in serial only.

Definition at line 81 of file FieldIO.cpp.

References ASSERTL0, Nektar::LibUtilities::NekFactory< tKey, tBase, >::CreateInstance(), GetCommFactory(), and Nektar::LibUtilities::FieldIO::Write().

Referenced by CalcNonLinearForcing(), main(), WriteBcs(), WriteFld(), and Nektar::PulseWaveSystem::WriteVessels().

         {
 #ifdef NEKTAR_USE_MPI
             int size;
             int init;
             MPI_Initialized(&init);
 
             // If MPI has been initialised we can check the number of processes
             // and, if > 1, tell the user he should not be running this
             // function in parallel. If it is not initialised, we do not
             // initialise it here, and assume the user knows what they are
             // doing.
             if (init)
             {
                 MPI_Comm_size( MPI_COMM_WORLD, &size );
                 ASSERTL0(size == 1,
                      "This static function is not available in parallel. Please"
                      "instantiate a FieldIO object for parallel use.");
             }
 #endif
             CommSharedPtr c = GetCommFactory().CreateInstance("Serial", 0, 0);
             FieldIO f(c);
             f.Write(outFile, fielddefs, fielddata, fieldinfomap);
         }

void Nektar::LibUtilities::Write	(	const string &	outFile,
		const PtsFieldSharedPtr &	ptsField
	)

Definition at line 81 of file PtsIO.cpp.

References ASSERTL0, Nektar::LibUtilities::NekFactory< tKey, tBase, >::CreateInstance(), GetCommFactory(), and Nektar::LibUtilities::PtsIO::Write().

 {
 #ifdef NEKTAR_USE_MPI
     int size;
     int init;
     MPI_Initialized(&init);
 
     // If MPI has been initialised we can check the number of processes
     // and, if > 1, tell the user he should not be running this
     // function in parallel. If it is not initialised, we do not
     // initialise it here, and assume the user knows what they are
     // doing.
     if (init)
     {
         MPI_Comm_size(MPI_COMM_WORLD, &size);
         ASSERTL0(size == 1,
                  "This static function is not available in parallel. Please "
                  "instantiate a FieldIO object for parallel use.");
     }
 #endif
     CommSharedPtr c = GetCommFactory().CreateInstance("Serial", 0, 0);
     PtsIO p(c);
     p.Write(outFile, ptsField);
 }

Variable Documentation

const char* const Nektar::LibUtilities::BasisTypeMap[]

Initial value:

= 
        {
            "NoBasisType",
            "Ortho_A",
            "Ortho_B",
            "Ortho_C",
            "Modified_A",
            "Modified_B",
            "Modified_C",
            "Fourier",
            "GLL_Lagrange",
            "Gauss_Lagrange",
            "Legendre",
            "Chebyshev",
            "Monomial",
            "FourierSingleMode",
            "FourierHalfModeRe",
            "FourierHalfModeIm"
        }

Definition at line 47 of file Foundations.hpp.

Referenced by Nektar::LibUtilities::FieldIO::ImportFieldDefs(), operator<<(), Nektar::SpatialDomains::MeshGraph::ReadExpansions(), Nektar::SolverUtils::DriverAdaptive::ReplaceExpansion(), and Nektar::LibUtilities::FieldIO::Write().

const std::string Nektar::LibUtilities::EndianTypeMap[]

Initial value:

=
    {
        "UnknownEndian",
        "BigEndian",
        "LittleEndian",
        "BigWordEndian",
        "LittleWordEndian"
    }

Definition at line 69 of file CompressData.h.

Referenced by Nektar::LibUtilities::CompressData::GetCompressString().

Nektar::LibUtilities::functions Nektar::LibUtilities::functions_p

static

Referenced by Nektar::LibUtilities::AnalyticExpressionEvaluator::AnalyticExpression::definition< ScannerT >::definition().

const char* const Nektar::LibUtilities::FunctionTypeMap[]

Initial value:

=
        {
            "No Function type",
            "Expression",
            "File"
        }

Definition at line 93 of file SessionReader.h.

const std::string Nektar::LibUtilities::kPointsTypeStr[]

Definition at line 69 of file Foundations.hpp.

Referenced by Nektar::LibUtilities::FieldIO::ImportFieldDefs(), operator<<(), Nektar::LibUtilities::MeshPartition::OutputPartition(), Nektar::SpatialDomains::MeshGraph::ReadCurves(), Nektar::SpatialDomains::MeshGraph::ReadExpansions(), Nektar::LibUtilities::MeshPartition::ReadGeometry(), Nektar::SpatialDomains::MeshGraph::WriteGeometry(), and Nektar::Utilities::OutputNekpp::WriteXmlCurves().

const unsigned int Nektar::LibUtilities::NodalTetElecAvailable = 10

Definition at line 23 of file NodalTetElecData.h.

const NekDouble Nektar::LibUtilities::NodalTetElecData[][9]

static

Definition at line 25 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::NodalTetElecNPTS[NodalTetElecAvailable] = {1,2,3,5,6,9,11,15,18,23}

static

Definition at line 24 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::NodalTriElecAvailable = 16

Definition at line 10 of file NodalTriElecData.h.

const NekDouble Nektar::LibUtilities::NodalTriElecData[][6]

static

Definition at line 12 of file NodalTriElecData.h.

Referenced by Nektar::LibUtilities::NodalTriElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::NodalTriElecNPTS[NodalTriElecAvailable] = {1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30}

static

Definition at line 11 of file NodalTriElecData.h.

Referenced by Nektar::LibUtilities::NodalTriElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::NodalTriFeketeAvailable = 16

Definition at line 10 of file NodalTriFeketeData.h.

const NekDouble Nektar::LibUtilities::NodalTriFeketeData[][6]

static

Definition at line 12 of file NodalTriFeketeData.h.

Referenced by Nektar::LibUtilities::NodalTriFekete::CalculatePoints().

const unsigned int Nektar::LibUtilities::NodalTriFeketeNPTS[NodalTriFeketeAvailable] = {1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30}

static

Definition at line 11 of file NodalTriFeketeData.h.

Referenced by Nektar::LibUtilities::NodalTriFekete::CalculatePoints().

BasisSharedPtr Nektar::LibUtilities::NullBasisSharedPtr

static

Definition at line 358 of file Basis.h.

Referenced by Nektar::MultiRegions::ExpList::v_GetHomogeneousBasis().

Array<OneD, BasisSharedPtr> Nektar::LibUtilities::NullBasisSharedPtr1DArray

static

Definition at line 359 of file Basis.h.

FieldMetaDataMap Nektar::LibUtilities::NullFieldMetaDataMap

static

Definition at line 54 of file FieldIO.h.

Referenced by Nektar::LibUtilities::FieldIO::AddInfoTag(), Nektar::SolverUtils::UnsteadySystem::CheckForRestartTime(), Nektar::SolverUtils::EquationSystem::EvaluateFunction(), Nektar::LinearisedAdvection::ImportFldBase(), Nektar::AdjointAdvection::ImportFldBase(), Nektar::Utilities::ProcessInterpPoints::Process(), Nektar::Utilities::ProcessInterpField::Process(), Nektar::Utilities::ProcessMultiShear::Process(), Nektar::Utilities::ProcessAddFld::Process(), and Nektar::Utilities::ProcessInnerProduct::Process().

std::vector<NekDouble> Nektar::LibUtilities::NullNekDoubleVector

static

Definition at line 49 of file FieldIO.h.

std::vector<LibUtilities::PointsType> Nektar::LibUtilities::NullPointsTypeVector

static

Definition at line 50 of file FieldIO.h.

PtsFieldSharedPtr Nektar::LibUtilities::NullPtsField

static

Definition at line 263 of file PtsField.h.

Referenced by Nektar::Utilities::OutputVtk::Process(), Nektar::Utilities::ProcessInterpPoints::Process(), Nektar::Utilities::ProcessPointDataToFld::Process(), Nektar::Utilities::ProcessInterpPointDataToFld::Process(), and Nektar::Utilities::OutputTecplot::Process().

map<PtsInfo,int> Nektar::LibUtilities::NullPtsInfoMap

static

Definition at line 71 of file PtsField.h.

Referenced by Nektar::LibUtilities::PtsIO::ImportFieldData().

PtsMetaDataMap Nektar::LibUtilities::NullPtsMetaDataMap

static

Definition at line 62 of file PtsIO.h.

std::vector<unsigned int> Nektar::LibUtilities::NullUnsignedIntVector

static

Definition at line 51 of file FieldIO.h.

Referenced by Nektar::MultiRegions::ExpListHomogeneous2D::v_GetFieldDefinitions().

std::vector<std::vector<NekDouble> > Nektar::LibUtilities::NullVectorNekDoubleVector

static

Initial value:

=

boost::assign::list_of(NullNekDoubleVector)

Nektar::LibUtilities::NullNekDoubleVector

static std::vector< NekDouble > NullNekDoubleVector

Definition: FieldIO.h:49

Definition at line 55 of file FieldIO.h.

Referenced by Nektar::LibUtilities::FieldIO::Import().

const unsigned int Nektar::LibUtilities::perm12A_3d[12][4]

static

Initial value:

= {{0,1,2,3},{0,1,3,2},{0,2,1,3},{0,2,3,1},{0,3,1,2},{0,3,2,1},

{2,0,1,3},{2,0,3,1},{2,3,0,1},{3,0,1,2},{3,0,2,1},{3,2,0,1}}

Definition at line 9 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm12B_3d[12][4]

static

Initial value:

= {{0,1,2,3},{0,2,1,3},{0,2,3,1},{1,0,2,3},{1,2,0,3},{1,2,3,0},

{2,0,1,3},{2,0,3,1},{2,1,0,3},{2,1,3,0},{2,3,0,1},{2,3,1,0}}

Definition at line 11 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm12C_3d[12][4]

static

Initial value:

= {{0,1,2,3},{0,1,3,2},{0,3,1,2},{1,0,2,3},{1,0,3,2},{1,2,0,3},

{1,2,3,0},{1,3,0,2},{1,3,2,0},{3,0,1,2},{3,1,0,2},{3,1,2,0}}

Definition at line 13 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm24_3d[24][4]

static

Initial value:

= {
            {0,1,2,3},{0,1,3,2},{0,2,1,3},{0,2,3,1},{0,3,1,2},{0,3,2,1},
            {1,0,2,3},{1,0,3,2},{1,2,0,3},{1,2,3,0},{1,3,0,2},{1,3,2,0},
            {2,0,1,3},{2,0,3,1},{2,1,0,3},{2,1,3,0},{2,3,0,1},{2,3,1,0},
            {3,0,1,2},{3,0,2,1},{3,1,0,2},{3,1,2,0},{3,2,0,1},{3,2,1,0}
        }

Definition at line 16 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm3A_2d[3][3] = {{0,1,2},{2,0,1},{0,2,1}}

static

Definition at line 5 of file NodalTriFeketeData.h.

const unsigned int Nektar::LibUtilities::perm3A_2d[3][3] = {{0,1,2},{2,0,1},{0,2,1}}

static

Definition at line 6 of file NodalTriElecData.h.

Referenced by Nektar::LibUtilities::NodalTriElec::CalculatePoints(), and Nektar::LibUtilities::NodalTriFekete::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm3B_2d[3][3] = {{0,1,2},{1,0,2},{1,2,0}}

static

Definition at line 6 of file NodalTriFeketeData.h.

const unsigned int Nektar::LibUtilities::perm3B_2d[3][3] = {{0,1,2},{1,0,2},{1,2,0}}

static

Definition at line 7 of file NodalTriElecData.h.

Referenced by Nektar::LibUtilities::NodalTriElec::CalculatePoints(), and Nektar::LibUtilities::NodalTriFekete::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm3C_2d[3][3] = {{0,1,2},{2,0,1},{1,2,0}}

static

Definition at line 7 of file NodalTriFeketeData.h.

const unsigned int Nektar::LibUtilities::perm4_3d[4][4] = {{0,1,2,3},{3,0,1,2},{2,3,0,1},{1,2,3,0}}

static

Definition at line 6 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm6_2d[6][3]

static

Initial value:

= {{0,1,2},{1,0,2},{2,0,1},

{2,1,0},{0,2,1},{1,2,0}}

Definition at line 8 of file NodalTriFeketeData.h.

const unsigned int Nektar::LibUtilities::perm6_2d[6][3]

static

Initial value:

= {{0,1,2},{1,0,2},{2,0,1},

{2,1,0},{0,2,1},{1,2,0}}

Definition at line 8 of file NodalTriElecData.h.

Referenced by Nektar::LibUtilities::NodalTriElec::CalculatePoints(), and Nektar::LibUtilities::NodalTriFekete::CalculatePoints().

const unsigned int Nektar::LibUtilities::perm6_3d[6][4] = {{0,1,2,3},{0,2,1,3},{0,2,3,1},{2,0,1,3},{2,0,3,1},{2,3,0,1}}

static

Definition at line 7 of file NodalTetElecData.h.

Referenced by Nektar::LibUtilities::NodalTetElec::CalculatePoints().

const unsigned int Nektar::LibUtilities::ShapeTypeDimMap[SIZE_ShapeType]

Initial value:

Definition at line 81 of file ShapeType.hpp.

Referenced by Nektar::StdRegions::operator<(), Nektar::StdRegions::operator<<(), and Nektar::StdRegions::operator==().

const char* const Nektar::LibUtilities::ShapeTypeMap[]

Initial value:

=
        {
            "NoGeomShapeType",
            "Point",
            "Segment",
            "Triangle",
            "Quadrilateral",
            "Tetrahedron",
            "Pyramid",
            "Prism",
            "Hexahedron"
        }

Definition at line 66 of file ShapeType.hpp.

Referenced by Nektar::LibUtilities::FieldIO::ImportFieldDefs(), Nektar::MultiRegions::operator<<(), Nektar::StdRegions::operator<<(), Nektar::Utilities::InputGmsh::Process(), Nektar::Utilities::InputXml::Process(), Nektar::Utilities::ProcessJac::Process(), Nektar::SolverUtils::DriverAdaptive::ReplaceExpansion(), and Nektar::LibUtilities::FieldIO::Write().

const char* const Nektar::LibUtilities::TimeIntegrationMethodMap[]

Definition at line 102 of file TimeIntegrationScheme.h.

Referenced by operator<<(), Nektar::SolverUtils::UnsteadySystem::v_GenerateSummary(), and Nektar::VelocityCorrectionScheme::v_GenerateSummary().

const char* const Nektar::LibUtilities::TimeIntegrationSchemeTypeMap[]

Initial value:

= 
        {
            "NoTimeIntegrationSchemeType",
            "Explicit",
            "DiagonallyImplicit",
            "IMEX",
            "Implicit"
        }

Definition at line 148 of file TimeIntegrationScheme.h.

Referenced by operator<<().

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