Direct sparse solver for unsymmetric matrices. More...

#include <superLU.hh>

Inheritance diagram for concepts::SuperLU< F >:

Collaboration diagram for concepts::SuperLU< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type.
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 F	type
	Type of data, e.g. matrix entries.
Public Member Functions
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)
uint	iterations () const
void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_()
virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`.
virtual void	operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)
	Application operator for complex function `fncY`.
void	operator() (const Matrix< r_type > &mX, Matrix< F > &mY)
	Application method to real matrices. Calls function apply()
virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator for real function `fncY`.
virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
	Application operator for real vector `fncY`.
	SuperLU (const Operator< F > &A, enum order ispec=COLAMD)
	Constructor.
virtual	~SuperLU ()
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_
Private Member Functions
virtual void	apply_ (const Vector< F > &fncY, Vector< F > &fncX)
	Intrinsic application method, i.e.
Private Attributes
void *	A_
	The matrix of the operator in a special sparse notation.
bool	factorized_
	Flag if the matrix is factorized.
enum order	ispec_
	Ordering option for the call to `get_perm_c` of SuperLU.
void *	L_
	L and U matrices of the factorization.
uint	n_
	Dimension of the matrix.
int *	perm_c_
int *	perm_r_
	Row and column permutation vectors.
void *	U_

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 $ P_c $ . 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, exactDtN.cc, hpFEM2d.cc, and inhomDirichletBCsLagrange.cc.

Definition at line 68 of file superLU.hh.

Member Typedef Documentation

template<class F>

typedef Cmplxtype<F>::type concepts::VecOperator< F >::c_type [inherited]

Real type of data type.

Reimplemented from concepts::Operator< F >.

Definition at line 112 of file compositions.hh.

template<class F>

typedef Realtype<F>::type concepts::VecOperator< F >::r_type [inherited]

Real type of data type.

Reimplemented from concepts::Operator< F >.

Definition at line 110 of file compositions.hh.

template<class F>

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

Type of data, e.g. matrix entries.

Reimplemented in concepts::AfterIteration< F >, and concepts::SubMatrixN< F >.

Definition at line 43 of file compositions.hh.

Member Enumeration Documentation

template<class F>

enum concepts::SuperLU::order

Column ordering options for call to get_perm_c of SuperLU.

Enumerator:

NATURAL
MMD_PROD
MMD_SUM
COLAMD

Definition at line 71 of file superLU.hh.

Constructor & Destructor Documentation

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

template<class F>

virtual concepts::SuperLU< F >::~SuperLU ( ) [virtual]

Member Function Documentation

template<class F>

virtual void concepts::SuperLU< F >::apply_	(	const Vector< F > &	fncY,
		Vector< F > &	fncX
	)		`[private, virtual]`

Intrinsic application method, i.e.

real Operator and real Vector or complex Operator and real Vector.

Implements concepts::VecOperator< F >.

template<class F>

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

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

Definition at line 87 of file compositions.hh.

template<class F>

virtual const uint concepts::Operator< F >::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.

template<class F>

virtual std::ostream& concepts::SuperLU< F >::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::VecOperator< F >.

template<class F>

uint concepts::SuperLU< F >::iterations ( ) const [inline]

Definition at line 88 of file superLU.hh.

template<class F>

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

template<class F>

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

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.

template<class F>

virtual void concepts::VecOperator< F >::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 from concepts::Operator< F >.

template<class F>

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

template<class F>

void concepts::VecOperator< F >::operator()	(	const Matrix< c_type > &	mX,
		Matrix< c_type > &	mY
	)		`[inherited]`

Application method to complex matrices. Calls apply_()

template<class F>

void concepts::VecOperator< F >::operator()	(	const Matrix< r_type > &	mX,
		Matrix< F > &	mY
	)		`[inherited]`

Application method to real matrices. Calls function apply()

Member Data Documentation

template<class F>

void* concepts::SuperLU< F >::A_ [private]

The matrix of the operator in a special sparse notation.

Definition at line 93 of file superLU.hh.

template<class F>

uint concepts::Operator< F >::dimX_ [protected, inherited]

Dimension of image space and the source space.

Definition at line 96 of file compositions.hh.

template<class F>

uint concepts::Operator< F >::dimY_ [protected, inherited]

Definition at line 96 of file compositions.hh.

template<class F>

bool concepts::SuperLU< F >::factorized_ [private]

Flag if the matrix is factorized.

Definition at line 99 of file superLU.hh.

template<class F>

enum order concepts::SuperLU< F >::ispec_ [private]

Ordering option for the call to get_perm_c of SuperLU.

Definition at line 101 of file superLU.hh.

template<class F>

void* concepts::SuperLU< F >::L_ [private]

L and U matrices of the factorization.

Definition at line 104 of file superLU.hh.

template<class F>

uint concepts::SuperLU< F >::n_ [private]

Dimension of the matrix.

Definition at line 96 of file superLU.hh.

template<class F>

int * concepts::SuperLU< F >::perm_c_ [private]

Definition at line 106 of file superLU.hh.

template<class F>

int* concepts::SuperLU< F >::perm_r_ [private]

Row and column permutation vectors.

Definition at line 106 of file superLU.hh.

template<class F>

void * concepts::SuperLU< F >::U_ [private]

Definition at line 104 of file superLU.hh.

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

operator/superLU.hh

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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