Direct sparse solver for unsymmetric matrices. More...

#include <superLU.hh>

Inheritance diagram for concepts::SuperLU< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type. More...

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. More...

typedef F	type
	Type of data, e.g. matrix entries. More...

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) More...

virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix) More...

uint	iterations () const

void	operator() ()
	Application method without second argument. Used for parallel solvers. More...

virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`. More...

virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator for real function `fncY`. More...

void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_() More...

void	operator() (const Matrix< r_type > &mX, Matrix< F > &mY)
	Application method to real matrices. Calls function apply() More...

virtual void	operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)
	Application operator for complex function `fncY`. More...

virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
	Application operator for real vector `fncY`. More...

virtual void	show_messages ()

	SuperLU (const Operator< F > &A, enum order ispec=COLAMD)
	Constructor. More...

virtual	~SuperLU ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const

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

uint	dimY_

Private Member Functions
virtual void	apply_ ()
	Intrinsic application method without argument. More...

virtual void	apply_ (const Vector< F > &fncY, Vector< F > &fncX)
	Intrinsic application method, i.e. More...

Private Attributes
void *	A_
	The matrix of the operator in a special sparse notation. More...

bool	factorized_
	Flag if the matrix is factorized. More...

enum order	ispec_
	Ordering option for the call to `get_perm_c` of SuperLU. More...

void *	L_
	L and U matrices of the factorization. More...

uint	n_
	Dimension of the matrix. More...

int *	perm_c_

int *	perm_r_
	Row and column permutation vectors. More...

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 . 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.

Enumerator
NATURAL
MMD_PROD
MMD_SUM
COLAMD

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

◆ ~SuperLU()

template<class F >

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

virtual

Member Function Documentation

◆ apply_() [1/2]

template<class F >

virtual void concepts::SuperLU< F >::apply_ ( )

privatevirtual

Intrinsic application method without argument.

Implements concepts::VecOperator< F >.

◆ apply_() [2/2]

template<class F >

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

privatevirtual

Intrinsic application method, i.e.

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

Implements concepts::VecOperator< F >.

◆ 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)

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)

Definition at line 98 of file compositions.hh.

◆ info()

template<class F >

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

protectedvirtual

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()() [1/7]

template<class F >

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

virtualinherited

Application method without second argument. Used for parallel solvers.

Reimplemented from concepts::Operator< F >.

◆ operator()() [2/7]

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()() [3/7]

template<class F >

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

◆ operator()() [4/7]

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_()

◆ operator()() [5/7]

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()

◆ operator()() [6/7]

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()() [7/7]

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::Newton< F >, concepts::MumpsOverlap< F >, and concepts::Mumps< F >.

Definition at line 100 of file compositions.hh.

Member Data Documentation

◆ A_

template<class F >

void* concepts::SuperLU< F >::A_

private

The matrix of the operator in a special sparse notation.

Definition at line 95 of file superLU.hh.

◆ 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.

◆ factorized_

template<class F >

bool concepts::SuperLU< F >::factorized_

private

Flag if the matrix is factorized.

Definition at line 101 of file superLU.hh.

◆ ispec_

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.

◆ L_

template<class F >

void* concepts::SuperLU< F >::L_

private

L and U matrices of the factorization.

Definition at line 106 of file superLU.hh.

◆ n_

template<class F >

uint concepts::SuperLU< F >::n_

private

Dimension of the matrix.

Definition at line 98 of file superLU.hh.

◆ perm_c_

template<class F >

int * concepts::SuperLU< F >::perm_c_

private

Definition at line 108 of file superLU.hh.

◆ perm_r_

template<class F >

int* concepts::SuperLU< F >::perm_r_

private

Row and column permutation vectors.

Definition at line 108 of file superLU.hh.

◆ U_

template<class F >

void * concepts::SuperLU< F >::U_

private

Definition at line 106 of file superLU.hh.

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

operator/superLU.hh

concepts::SuperLU< F > Class Template ReferenceLinear Solvers

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

◆ c_type

◆ r_type

◆ type

Member Enumeration Documentation

◆ order

Constructor & Destructor Documentation

◆ SuperLU()

◆ ~SuperLU()

Member Function Documentation

◆ apply_() [1/2]

◆ apply_() [2/2]

◆ dimX()

◆ dimY()

◆ info()

◆ iterations()

◆ operator()() [1/7]

◆ operator()() [2/7]

◆ operator()() [3/7]

◆ operator()() [4/7]

◆ operator()() [5/7]

◆ operator()() [6/7]

◆ operator()() [7/7]

◆ show_messages()

Member Data Documentation

◆ A_

◆ dimX_

◆ dimY_

◆ factorized_

◆ ispec_

◆ L_

◆ n_

◆ perm_c_

◆ perm_r_

◆ U_

concepts::SuperLU< F > Class Template Reference
Linear Solvers

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