Driver class for sparse QR decomposition. More...

#include <driver.hh>

Inheritance diagram for sparseqr::Driver:

Collaboration diagram for sparseqr::Driver:

Public Member Functions
	Driver (const concepts::SparseMatrix< Real > &A)
	Constructor.
concepts::TrivExtendRestrict < Real > *	extension ()
	Returns the extension from the last n-r to n degrees of freedom.
void	operator() (const concepts::Vector< Real > &fncY, concepts::Vector< Real > &fncX)
virtual void	operator() (const concepts::Function< Real > &fncY, concepts::Function< Real > &fncX)
concepts::Permutation< Real > *	Pcol ()
	Returns .
concepts::Permutation< Real > *	Prow ()
	Returns .
sparseqr::GivensRotations< Real > *	Q ()
	Returns .
sparseqr::GivensRotations< Real > *	Qt ()
	Returns $Q^\top$ .
int	rank ()
	Returns the rank of the matrix.
concepts::TrivExtendRestrict < Real > *	restriction ()
	Returns the restriction from n to the last n-r degrees of freedom.
virtual	~Driver ()
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Types
typedef Cmplxtype< Real >::type	c_type
	Real type of data type.
typedef Realtype< Real >::type	r_type
	Real type of data type.
typedef Real	type
	Type of data, e.g. matrix entries.
Private Member Functions
void	compute_ ()
virtual const uint	dimX () const
	Returns the size of the image space of the operator (number of rows of the corresponding matrix)
virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix)
virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`.
virtual void	operator() (const Function< r_type > &fncY, Function< Real > &fncX)
	Application operator for real function `fncY`.
Private Attributes
const concepts::SparseMatrix < Real > &	A_
bool	computed_
uint	dimX_
	Dimension of image space and the source space.
uint	dimY_
std::auto_ptr < concepts::TrivExtendRestrict < Real > >	ext_
std::auto_ptr < concepts::Permutation< Real > >	Pcol_
concepts::Array< int >	pcol_
concepts::Array< int >	prow_
std::auto_ptr < concepts::Permutation< Real > >	Prow_
sparseqr::Qmatrix	q_
std::auto_ptr < sparseqr::GivensRotations < Real > >	Q_
std::auto_ptr< QR >	qr_
std::auto_ptr < sparseqr::GivensRotations < Real > >	Qt_
int	rank_
std::auto_ptr < concepts::TrivExtendRestrict < Real > >	restr_

Detailed Description

Driver class for sparse QR decomposition.

Performs a QR factorization on a sparse mxn matrix A, m>=n, such that

$P_r \cdot Q^\top \cdot A \cdot P_c^\top = \begin{pmatrix} R \\ 0 \end{pmatrix}$

the different matrices can be asked for individually. At the same time, this class can act as a linear solver using the QR decomposition of the matrix.

Author:: Philipp Frauenfelder, 2004

Test:

test::DriverTest

test::DeepCompositionsTest

Definition at line 32 of file driver.hh.

Member Typedef Documentation

typedef Cmplxtype<Real >::type concepts::Operator< Real >::c_type [inherited]

Real type of data type.

Reimplemented in concepts::VecOperator< Real >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< Real >, concepts::Permutation< Real >, and concepts::SparseMatrix< Real >.

Definition at line 47 of file compositions.hh.

typedef Realtype<Real >::type concepts::Operator< Real >::r_type [inherited]

Real type of data type.

Reimplemented in concepts::VecOperator< Real >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< Real >, concepts::Permutation< Real >, and concepts::SparseMatrix< Real >.

Definition at line 45 of file compositions.hh.

typedef Real concepts::Operator< Real >::type [inherited]

Type of data, e.g. matrix entries.

Definition at line 43 of file compositions.hh.

Constructor & Destructor Documentation

sparseqr::Driver::Driver ( const concepts::SparseMatrix< Real > & A ) [inline]

Constructor.

The constructor does not compute or copy anything, just initialises local variables.

Parameters:

A	Matrix to decompose

Definition at line 39 of file driver.hh.

virtual sparseqr::Driver::~Driver ( ) [virtual]

Member Function Documentation

void sparseqr::Driver::compute_ ( ) [private]

virtual const uint concepts::Operator< Real >::dimX ( ) const [inline, virtual, inherited]

Returns the size of the image space of the operator (number of rows of the corresponding matrix)

Examples:: hpFEM2d-simple.cc, and hpFEM2d.cc.

Definition at line 87 of file compositions.hh.

virtual const uint concepts::Operator< Real >::dimY ( ) const [inline, virtual, inherited]

Returns the size of the source space of the operator (number of columns of the corresponding matrix)

Definition at line 92 of file compositions.hh.

concepts::TrivExtendRestrict<Real>* sparseqr::Driver::extension ( )

Returns the extension from the last n-r to n degrees of freedom.

virtual std::ostream& sparseqr::Driver::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::Operator< Real >.

void sparseqr::Driver::operator()	(	const concepts::Vector< Real > &	fncY,
		concepts::Vector< Real > &	fncX
	)

virtual void sparseqr::Driver::operator()	(	const concepts::Function< Real > &	fncY,
		concepts::Function< Real > &	fncX
	)		`[virtual]`

virtual void concepts::Operator< Real >::operator()	(	const Function< c_type > &	fncY,
		Function< c_type > &	fncX
	)		`[virtual, inherited]`

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the function fncY is splitted into real and imaginary part and the application operator for real functions is called for each. Then the result is combined.

If in a derived class the operator() for complex Operator's is not implemented, a exception is thrown from here.

Reimplemented in concepts::VecOperator< Real >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< Real >, concepts::Permutation< Real >, and concepts::SparseMatrix< Real >.

virtual void concepts::Operator< Real >::operator()	(	const Function< r_type > &	fncY,
		Function< Real > &	fncX
	)		`[virtual, inherited]`

Application operator for real function fncY.

Computes fncX = A(fncY) where A is this operator.

fncX becomes the type of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the function fncY is transformed to a complex function and then the application operator for complex functions is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

Reimplemented in concepts::VecOperator< Real >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< Real >, concepts::Permutation< Real >, and concepts::SparseMatrix< Real >.

concepts::Permutation<Real>* sparseqr::Driver::Pcol ( )

Returns $P_c$ .

concepts::Permutation<Real>* sparseqr::Driver::Prow ( )

Returns $P_r$ .

sparseqr::GivensRotations<Real>* sparseqr::Driver::Q ( )

Returns $Q$ .

sparseqr::GivensRotations<Real>* sparseqr::Driver::Qt ( )

Returns $Q^\top$ .

int sparseqr::Driver::rank ( ) [inline]

Returns the rank of the matrix.