Class implementing sparse matrix stored in skyline form. More...

#include <skyline.h>

Inheritance diagram for oofem::Skyline:

Collaboration diagram for oofem::Skyline:

Public Member Functions
	Skyline (int n)
	Constructor. More...

	Skyline ()
	Constructor. More...

virtual	~Skyline ()
	Destructor. More...

virtual SparseMtrx *	GiveCopy () const
	Returns a newly allocated copy of receiver. More...

virtual void	times (const FloatArray &x, FloatArray &answer) const
	Evaluates $y = A \cdot x$ . More...

virtual void	timesT (const FloatArray &x, FloatArray &answer) const
	Evaluates $y = A^{\mathrm{T}} \cdot x$ . More...

virtual void	times (double x)
	Multiplies receiver by scalar value. More...

virtual void	add (double x, SparseMtrx &m)
	Adds x * m. More...

virtual int	buildInternalStructure (EngngModel *, int, const UnknownNumberingScheme &)
	Builds internal structure of receiver. More...

virtual SparseMtrx *	giveSubMatrix (const IntArray &rows, const IntArray &cols)

int	setInternalStructure (IntArray &a)
	Allocates and builds internal structure according to given array holding addresses of diagonal members values (adr). More...

virtual int	assemble (const IntArray &loc, const FloatMatrix &mat)
	Assembles sparse matrix from contribution of local elements. More...

virtual int	assemble (const IntArray &rloc, const IntArray &cloc, const FloatMatrix &mat)
	Assembles sparse matrix from contribution of local elements. More...

virtual bool	canBeFactorized () const
	Determines, whether receiver can be factorized. More...

virtual SparseMtrx *	factorized ()
	Returns the receiver factorized. More...

virtual FloatArray *	backSubstitutionWith (FloatArray &) const
	Computes the solution of linear system $A\cdot x = y$ where A is receiver. More...

virtual void	zero ()
	Zeroes the receiver. More...

void	rbmodes (FloatMatrix &r, int &nse, IntArray &se, double limit, int tc)
	Splits the receiver to LDLT form, and computes the rigid body motions. More...

void	ldl_feti_sky (FloatArray &x, FloatArray &y, int nse, double limit, IntArray &se)
	Solves the singular system of equations, the receiver should be factorized using rbmodes service. More...

virtual double &	at (int, int)
	Returns coefficient at position (i,j). More...

virtual double	at (int i, int j) const
	Returns coefficient at position (i,j). More...

virtual bool	isAllocatedAt (int i, int j) const
	Returns 0 if the memory is not allocated at position (i,j). More...

int	giveNumberOfNonZeros () const

virtual void	toFloatMatrix (FloatMatrix &answer) const
	Converts receiving sparse matrix to a dense float matrix. More...

virtual void	printYourself () const
	Prints receiver to stdout. More...

virtual void	writeToFile (const char *fname) const
	Helpful for debugging, writes the matrix to given file. More...

int	giveAllocatedSize ()

virtual SparseMtrxType	giveType () const
	Sparse matrix type identification. More...

virtual bool	isAsymmetric () const
	Returns true if asymmetric. More...

virtual const char *	giveClassName () const

Public Member Functions inherited from oofem::SparseMtrx
	SparseMtrx (int n, int m)
	Constructor, creates (n,m) sparse matrix. More...

	SparseMtrx ()
	Constructor. More...

virtual	~SparseMtrx ()
	Destructor. More...

SparseMtrxVersionType	giveVersion ()
	Return receiver version. More...

void	checkBounds (int i, int j) const
	Checks size of receiver towards requested bounds. More...

int	giveNumberOfRows () const
	Returns number of rows of receiver. More...

int	giveNumberOfColumns () const
	Returns number of columns of receiver. More...

bool	isSquare () const
	Returns nonzero if receiver is square matrix. More...

bool	isNotEmpty () const
	Tests for empty matrix. More...

virtual void	times (const FloatMatrix &B, FloatMatrix &answer) const
	Evaluates $C = A^{\mathrm{T}} \cdot B$ . More...

virtual void	timesT (const FloatMatrix &B, FloatMatrix &answer) const
	Evaluates $C = A^{\mathrm{T}} \cdot B$ . More...

virtual void	addDiagonal (double x, FloatArray &m)
	Adds x * m (treats m as a diagonal matrix, stored as an array) More...

virtual int	buildInternalStructure (EngngModel *eModel, int n, int m, const IntArray &I, const IntArray &J)
	Builds internal structure of receiver based on I and J. More...

virtual int	buildInternalStructure (EngngModel *eModel, int di, const UnknownNumberingScheme &r_s, const UnknownNumberingScheme &c_s)
	Build internal structure of receiver. More...

virtual int	assembleBegin ()
	Starts assembling the elements. More...

virtual int	assembleEnd ()
	Returns when assemble is completed. More...

virtual double	computeNorm () const
	Returns the norm of receiver. More...

virtual void	printStatistics () const
	Prints the receiver statistics (one-line) to stdout. More...

std::string	errorInfo (const char *func) const
	Error printing helper. More...

FloatArray	operator* (const FloatArray &x) const
	IML compatibility, $A \cdot x$ . More...

FloatArray	trans_mult (const FloatArray &x) const
	IML compatibility, $A^{\mathrm{T}} \cdot x$ . More...

Protected Member Functions
	Skyline (int, int, double *, const IntArray &)

Protected Attributes
int	nwk
	Total number of nonzero coefficients stored. More...

IntArray	adr
	Integer array holding addresses of diagonal members. More...

double *	mtrx
	Vector of stored coefficients. More...

int	isFactorized
	Flag indicating whether factorized. More...

Protected Attributes inherited from oofem::SparseMtrx
int	nRows
	Number of rows. More...

int	nColumns
	Number of columns. More...

SparseMtrxVersionType	version
	Allows to track if receiver changes. More...

Additional Inherited Members
Public Types inherited from oofem::SparseMtrx
typedef long	SparseMtrxVersionType

Detailed Description

Class implementing sparse matrix stored in skyline form.

This class assumes symmetric form of matrix to be stored, i.e., only upper half part is therefore stored. Coefficients are stored in one dimensional float array, containing for each column the values from the diagonal to the last nonzero entry. This requires to remember the addresses of diagonal members in such array (adr attribute)

Attribute 'isFactorized' is True if the skyline is already in U(T).D.U factorized form, else it is False. Attribute adr is array of diagonal members, it's size is size+1 (adr[0]=neni, adr[1]=1) Attribute mtrx is double pointer to skyline stored in a array form (but we start from index 1)

Tasks:

building its internal storage structure (method 'buildInternalStructure')
store and localize local matrices (method 'localize')
performing standard operations : multiplication by array (method 'times')
possible factorization and backSubstitution (recognized by nonzero result of canBeFactorized) (methods 'factorize' and 'backSubstitution')
setting all coefficients to zero (method 'zero')

See also: SparseMtrx class

Definition at line 68 of file skyline.h.

Constructor & Destructor Documentation

oofem::Skyline::Skyline ( int n )

Constructor.

Before any operation an internal profile must be built.

See also: builInternalStructure

Definition at line 62 of file skyline.C.

References isFactorized, mtrx, and nwk.

oofem::Skyline::Skyline ( )

Constructor.

Before any operation an internal profile must be built.

See also: builInternalStructure

Definition at line 73 of file skyline.C.

References isFactorized, mtrx, and nwk.

Referenced by GiveCopy(), and giveSubMatrix().

oofem::Skyline::~Skyline ( )

virtual

Destructor.

Definition at line 83 of file skyline.C.

References oofem::SparseMtrx::giveNumberOfRows(), and mtrx.

oofem::Skyline::Skyline	(	int	neq,
		int	nwk1,
		double *	mtrx1,
		const IntArray &	adr1
	)

protected

Definition at line 704 of file skyline.C.

References adr, isFactorized, mtrx, and nwk.

Member Function Documentation

void oofem::Skyline::add	(	double	x,
		SparseMtrx &	m
	)

virtual

Adds x * m.

Parameters

x	Value to multiply m by.
m	Matrix to add (should of the same matrix type).

Reimplemented from oofem::SparseMtrx.

Definition at line 633 of file skyline.C.

References mtrx, nwk, and oofem::SparseMtrx::version.

int oofem::Skyline::assemble	(	const IntArray &	loc,
		const FloatMatrix &	mat
	)

virtual

Assembles sparse matrix from contribution of local elements.

This method for each element adds its contribution to itself. Mapping between local element contribution and its global position is given by local code numbers of element.

Parameters

loc	Location array. The values corresponding to zero loc array value are not assembled.
mat	Contribution to be assembled using loc array.

Returns: Zero iff successful.

Implements oofem::SparseMtrx.

Definition at line 224 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::FloatMatrix::at(), oofem::FloatMatrix::giveNumberOfRows(), oofem::IntArray::giveSize(), mtrx, OOFEM_ERROR, and oofem::SparseMtrx::version.

int oofem::Skyline::assemble	(	const IntArray &	rloc,
		const IntArray &	cloc,
		const FloatMatrix &	mat
	)

virtual

Assembles sparse matrix from contribution of local elements.

This method for each element adds its contribution to itself. Mapping between local element contribution and its global position is given by row and column local code numbers.

Parameters

rloc	Row location array. The values corresponding to zero loc array value are not assembled.
cloc	Column location array. The values corresponding to zero loc array value are not assembled.
mat	Contribution to be assembled using rloc and cloc arrays. The rloc position determines the row, the cloc position determines the corresponding column.

Returns: Zero iff successful.

Implements oofem::SparseMtrx.

Definition at line 266 of file skyline.C.

References oofem::IntArray::at(), at(), oofem::FloatMatrix::at(), oofem::FloatMatrix::giveNumberOfColumns(), oofem::FloatMatrix::giveNumberOfRows(), and oofem::SparseMtrx::version.

double & oofem::Skyline::at	(	int	i,
		int	j
	)

virtual

Returns coefficient at position (i,j).

Implements oofem::SparseMtrx.

Definition at line 93 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::SparseMtrx::giveNumberOfRows(), mtrx, OOFEM_ERROR, and oofem::SparseMtrx::version.

Referenced by assemble(), and giveSubMatrix().

double oofem::Skyline::at	(	int	i,
		int	j
	)		const

virtual

Returns coefficient at position (i,j).

Implements oofem::SparseMtrx.

Definition at line 134 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::SparseMtrx::giveNumberOfRows(), mtrx, and OOFEM_ERROR.

FloatArray * oofem::Skyline::backSubstitutionWith ( FloatArray & y ) const

virtual

Computes the solution of linear system $A\cdot x = y$ where A is receiver.

Solution vector x overwrites the right hand side vector y. Receiver must be in factorized form.

Parameters

y	Right hand side on input, solution on output.

Returns: Pointer to y array.

Reimplemented from oofem::SparseMtrx.

Definition at line 289 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::SparseMtrx::giveNumberOfRows(), and mtrx.

int oofem::Skyline::buildInternalStructure	(	EngngModel *	eModel,
		int	di,
		const UnknownNumberingScheme &	s
	)

virtual

Builds internal structure of receiver.

This method determines the internal profile of sparse matrix, allocates necessary space for storing nonzero coefficients and initializes receiver. In general, the profile of sparse matrix is determined using one (or more) loop over local code numbers of elements. This method must be called before any operation, like assembly, zeroing, or multiplication.

Parameters

eModel	Pointer to corresponding engineering model.
di	Domain index specify which domain to use.
s	Determines unknown numbering scheme.

Returns: Zero iff successful.

Implements oofem::SparseMtrx.

Definition at line 362 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::IntArray::clear(), oofem::Domain::giveBcs(), oofem::ContactManager::giveContactDefinition(), oofem::ContactDefinition::giveContactElement(), oofem::Domain::giveContactManager(), oofem::EngngModel::giveDomain(), oofem::Domain::giveElements(), oofem::ContactElement::giveLocationArray(), oofem::ActiveBoundaryCondition::giveLocationArrays(), oofem::ContactManager::giveNumberOfContactDefinitions(), oofem::EngngModel::giveNumberOfDomainEquations(), oofem::ContactDefinition::giveNumbertOfContactElements(), oofem::UnknownNumberingScheme::giveRequiredNumberOfDomainEquation(), oofem::Domain::hasContactManager(), oofem::UnknownNumberingScheme::isDefault(), oofem::min(), mtrx, oofem::SparseMtrx::nColumns, oofem::SparseMtrx::nRows, nwk, OOFEM_ERROR, oofem::IntArray::resize(), and oofem::SparseMtrx::version.

virtual bool oofem::Skyline::canBeFactorized ( ) const

inlinevirtual

Determines, whether receiver can be factorized.

Implements oofem::SparseMtrx.

Definition at line 115 of file skyline.h.

SparseMtrx * oofem::Skyline::factorized ( )

virtual

Returns the receiver factorized.

$L^{\mathrm{T}} \cdot D \cdot L$ form is used.

Returns: pointer to the receiver

Reimplemented from oofem::SparseMtrx.

Definition at line 499 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::Timer::getUtime(), oofem::SparseMtrx::giveNumberOfRows(), isFactorized, mtrx, nwk, OOFEM_LOG_DEBUG, oofem::Timer::startTimer(), and oofem::Timer::stopTimer().

int oofem::Skyline::giveAllocatedSize ( )

inline

Definition at line 153 of file skyline.h.

virtual const char* oofem::Skyline::giveClassName ( ) const

inlinevirtual

Implements oofem::SparseMtrx.

Definition at line 158 of file skyline.h.

SparseMtrx * oofem::Skyline::GiveCopy ( ) const

virtual

Returns a newly allocated copy of receiver.

Programmer must take care about proper deallocation of allocated space.

Returns: Newly allocated copy of receiver.

Reimplemented from oofem::SparseMtrx.

Definition at line 682 of file skyline.C.

References adr, oofem::SparseMtrx::giveNumberOfRows(), mtrx, nwk, OOFEM_ERROR, and Skyline().

int oofem::Skyline::giveNumberOfNonZeros ( ) const

inline

Definition at line 148 of file skyline.h.

Referenced by giveSubMatrix().

SparseMtrx * oofem::Skyline::giveSubMatrix	(	const IntArray &	rows,
		const IntArray &	cols
	)

virtual

Reimplemented from oofem::SparseMtrx.

Definition at line 720 of file skyline.C.

References oofem::IntArray::at(), at(), giveNumberOfNonZeros(), oofem::IntArray::giveSize(), isAllocatedAt(), OOFEM_ERROR, and Skyline().

virtual SparseMtrxType oofem::Skyline::giveType ( ) const

inlinevirtual

Sparse matrix type identification.

Implements oofem::SparseMtrx.

Definition at line 155 of file skyline.h.

References oofem::SMT_Skyline.

bool oofem::Skyline::isAllocatedAt	(	int	i,
		int	j
	)		const

virtual

Returns 0 if the memory is not allocated at position (i,j).

Reimplemented from oofem::SparseMtrx.

Definition at line 174 of file skyline.C.

References adr, and oofem::IntArray::at().

Referenced by giveSubMatrix().

virtual bool oofem::Skyline::isAsymmetric ( ) const

inlinevirtual

Returns true if asymmetric.

Implements oofem::SparseMtrx.

Definition at line 156 of file skyline.h.

void oofem::Skyline::ldl_feti_sky	(	FloatArray &	x,
		FloatArray &	y,
		int	nse,
		double	limit,
		IntArray &	se
	)

Solves the singular system of equations, the receiver should be factorized using rbmodes service.

Parameters

x	solution vector
y	right hand side
nse	number of rigid body motions
limit	determines the linear dependence or independence
se	indexes of singular equations

Definition at line 932 of file skyline.C.

References adr, oofem::IntArray::at(), oofem::FloatArray::at(), oofem::SparseMtrx::giveNumberOfRows(), and mtrx.

Referenced by oofem::FETISolver::solve().

void oofem::Skyline::printYourself ( ) const

virtual

Prints receiver to stdout.

Reimplemented from oofem::SparseMtrx.

Definition at line 644 of file skyline.C.

References oofem::FloatMatrix::printYourself(), and toFloatMatrix().

void oofem::Skyline::rbmodes	(	FloatMatrix &	r,
		int &	nse,
		IntArray &	se,
		double	limit,
		int	tc
	)

Splits the receiver to LDLT form, and computes the rigid body motions.

Parameters

r	matrix containing the rigid body motions base vectors.
nse	number of rigid body motions
se	array containing indexes of singular eqs.
limit	determines linear dependence or independence
tc	type of calculation = 1 = Decomposition to LDL form = 2 = ? konstruovani baze prostoru ? Ker A = 3 = Decomposition to LDL form and ? konstruovani baze prostoru ? Ker A