concepts::SuperLU< F > Class Template Reference

#include <superLU.hh>

Inheritance diagram for concepts::SuperLU< F >:

Public Types
enum	order { NATURAL = 0 , MMD_PROD = 1 , MMD_SUM = 2 , COLAMD = 3 }
	Column ordering options for call to get_perm_c of SuperLU. More...
typedef Realtype< F >::type	r_type
	Real type of data type.
typedef Cmplxtype< F >::type	c_type
	Real type of data type.
typedef F	type
	Type of data, e.g. matrix entries.

Public Member Functions
	SuperLU (const Operator< F > &A, enum order ispec=COLAMD)
uint	iterations () const
virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
virtual void	operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)
void	operator() (const Matrix< r_type > &mX, Matrix< F > &mY)
	Application method to real matrices. Calls function apply()
void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_()
void	operator() ()
	Application method without second argument. Used for parallel solvers.
virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
virtual const uint	dimX () const
virtual const uint	dimY () const
virtual void	show_messages ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Protected Attributes
uint	dimX_
	Dimension of image space and the source space.
uint	dimY_

Detailed Description

template<class F>
class concepts::SuperLU< F >

Direct sparse solver for unsymmetric matrices.

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices.

SuperLU offers different ordering options for a column permutation . Experiments with a 584 by 584 matrix from a Maxwell problem showed the following behaviour for the different parameters:

NATURAL	Use natural column ordering. Factor time = 1.01 Factor flops = 1.207525e+08 Mflops = 119.56 Solve time = 0.01 Solve flops = 6.571840e+05 Mflops = 65.72
MMD_PROD	Use minimum degree ordering on A'*A. Factor time = 0.22 Factor flops = 2.542033e+07 Mflops = 115.55 Solve time = 0.01 Solve flops = 3.422840e+05 Mflops = 34.23
MMD_SUM	Use minimum degree ordering on A'+A. Factor time = 0.37 Factor flops = 4.331220e+07 Mflops = 117.06 Solve time = 0.01 Solve flops = 4.200160e+05 Mflops = 42.00
COLAMD	.. Use approximate minimum degree column ordering. Factor time = 0.19 Factor flops = 2.458012e+07 Mflops = 129.37 Solve time = 0.01 Solve flops = 3.401680e+05 Mflops = 34.02

That is why the default value for the ordering option is set to COLAMD (see documentation of the constructor).

Author

Andreas Rueegg, David Hoch, Philipp Frauenfelder, Manuel Walser

See also

Homepage of SuperLU

James W. Demmel, John R. Gilbert, and Xiaoye S. Li. SuperLU Users' Guide. Technical Report LBNL-44289, Lawrence Berkely National Lab, 2003.

Examples

BGT_0.cc, elasticity2D_tutorial.cc, exactDtN.cc, hpFEM2d.cc, and inhomDirichletBCsLagrange.cc.

Definition at line 70 of file superLU.hh.

Member Typedef Documentation

c_type

template<class F >

typedef Cmplxtype<F>::type concepts::VecOperator< F >::c_type

inherited

Real type of data type.

Definition at line 120 of file compositions.hh.

r_type

template<class F >

typedef Realtype<F>::type concepts::VecOperator< F >::r_type

inherited

Real type of data type.

Definition at line 118 of file compositions.hh.

type

template<class F >

typedef F concepts::Operator< F >::type

inherited

Type of data, e.g. matrix entries.

Definition at line 45 of file compositions.hh.

Member Enumeration Documentation

order

template<class F >

enum concepts::SuperLU::order

Column ordering options for call to get_perm_c of SuperLU.

Definition at line 73 of file superLU.hh.

Constructor & Destructor Documentation

SuperLU()

template<class F >

concepts::SuperLU< F >::SuperLU	(	const Operator< F > &	A,
		enum order	ispec = COLAMD
	)

Constructor.

Parameters

A	Operator which should be inverted. Everything which is needed from A is copied in the constructor
ispec	Ordering option for the call to get_perm_c of SuperLU

Member Function Documentation

dimX()

template<class F >

virtual const uint concepts::Operator< F >::dimX ( ) const

inlinevirtualinherited

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

Examples

hpFEM2d-simple.cc, hpFEM2d.cc, and matfileTutorial.cc.

Definition at line 93 of file compositions.hh.

dimY()

template<class F >

virtual const uint concepts::Operator< F >::dimY ( ) const

inlinevirtualinherited

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

Examples

matfileTutorial.cc.

Definition at line 98 of file compositions.hh.

info()

template<class F >

virtual std::ostream & concepts::SuperLU< F >::info ( std::ostream &  os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::VecOperator< F >.

iterations()

template<class F >

uint concepts::SuperLU< F >::iterations ( ) const

inline

Definition at line 90 of file superLU.hh.

operator()() [1/5]

template<class F >

void concepts::VecOperator< F >::operator() ( )

virtualinherited

Application method without second argument. Used for parallel solvers.

Reimplemented from concepts::Operator< F >.

operator()() [2/5]

template<class F >

virtual void concepts::VecOperator< F >::operator() ( const Function< c_type > &  fncY, Function< c_type > &  fncX  )

virtualinherited

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 from concepts::Operator< F >.

operator()() [3/5]

template<class F >

virtual void concepts::Operator< F >::operator() ( const Function< r_type > &  fncY, Function< F > &  fncX  )

virtualinherited

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 aglowav::C2W< F >, aglowav2::C2W< F >, aglowav::W2C< F >, aglowav2::W2C< F >, aglowav::C2_tl2< F >, aglowav::C2tl2< F >, aglowav::CGt2< F >, aglowav::ComposeN< F >, aglowav2::Operator00< F >, bem::D< F >, bem::D_1< F >, concepts::TrivExtendRestrict< F >, sparseqr::GivensRotations< F >, vectorial::BlockOperator< F >, concepts::TrivExtendRestrict< Real >, sparseqr::GivensRotations< Real >, concepts::AfterIteration< F >, concepts::Compose< F, H >, concepts::DDSolver< F, G >, concepts::Multiple< F >, concepts::LiCoI< F >, concepts::LiCo< F >, concepts::DenseMatrix< F >, concepts::DiagonalMatrix< F >, concepts::Permutation< F >, concepts::Matrix< F >, concepts::Matrix< F::type >, and concepts::DiagonalSolver< F >.

operator()() [4/5]

template<class F >

virtual void concepts::VecOperator< F >::operator() ( const Vector< c_type > &  fncY, Vector< c_type > &  fncX  )

virtualinherited

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 vector fncY is splitted into real and imaginary part and the application operator for real vectors is called for each. Then the result is combined

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

operator()() [5/5]

template<class F >

virtual void concepts::VecOperator< F >::operator() ( const Vector< r_type > &  fncY, Vector< F > &  fncX  )

virtualinherited

Application operator for real vector fncY.

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

Type of fncX becomes that 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 vector fncY is transformed to a complex vector and then the application for complex vectors is called.

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

show_messages()

template<class F >

virtual void concepts::Operator< F >::show_messages ( )

inlinevirtualinherited

Reimplemented in concepts::MumpsOverlap< F >.

Definition at line 100 of file compositions.hh.

Member Data Documentation

dimX_

template<class F >

uint concepts::Operator< F >::dimX_

protectedinherited

Dimension of image space and the source space.

Definition at line 104 of file compositions.hh.

dimY_

template<class F >

uint concepts::Operator< F >::dimY_

protectedinherited

Definition at line 104 of file compositions.hh.

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

• operator/superLU.hh