Sparse Linear Solver virtual base class.Class SLinSolver provides a class for solving sparse linear systems with a matrix \(A\) and arbitrary right-hand side vectors. For doing so, the matrix must be first loaded to an SLinSolver object as an array of pointers to the column SVectors of this matrix. More...

#include <dsvectorbase.h>

Public Types
Types
enum	Status { OK = 0, INSTABLE = 1, SINGULAR = 2, UNLOADED = 4, ERROR = 8 }
	status flags of the SLinSolver class. More...

Public Member Functions
Miscellaneous
virtual const char *	getName () const =0
	returns the name of the SLinSolver. More...

virtual Status	status () const =0
	returns the Status of the SLinSolver. More...

virtual void	clear ()=0
	unloads any matrix. More...

virtual int	memory () const =0
	returns current memory consumption. More...

virtual int	dim () const =0
	returns dimension of loaded matrix. More...

virtual Status	load (const SVectorBase< R > *vec[], int dim)=0
	loads `dim` column vectors `vec` into the solver. More...

virtual R	stability () const =0
	returns a stability number (0: singularity, 1: perfect stability). More...

virtual R	matrixMetric (int type=0) const =0
	return estimate for the condition number based on the diagonal of U More...

virtual std::string	statistics () const =0
	returns statistical information in form of a string. More...

virtual Status	change (int idx, const SVectorBase< R > &subst, const SSVectorBase< R > *eta=0)=0
	Substitute column `idx` with `subst`. More...

virtual bool	isConsistent () const =0
	consistency check. More...

virtual int	getFactorCount () const =0
	get number of factorizations More...

Solving linear systems
For solving linear systems with an SLinSolver object, it must have previously been loaded with the matrix to use. Two types of systems can be solved \(A x = b\) and \(x^T A = b^T\). Method names related to the first and second type are solveRight() and solveLeft(), respectively. The methods receive their right hand-side vector \(b\) as a `const` parameter, that will hence be unchanged after termination. Some methods are available with two parameters for right hand-side vectors. Then two system are solved in one method invocation. This should generally be faster than solving two systems seperately. The result vector(s) are allways given as the first parameter(s). Two types of result vectors are supported, VectorBase<R> and SSVectorBase<R> .
virtual void	solveRight (VectorBase< R > &x, const VectorBase< R > &b)=0
	Solves \(Ax=b\). More...

virtual void	solveRight (SSVectorBase< R > &x, const SSVectorBase< R > &b)=0
	Solves \(Ax=b\). More...

virtual void	solveRight (SSVectorBase< R > &x, const SVectorBase< R > &b)=0

virtual void	solveRight4update (SSVectorBase< R > &x, const SVectorBase< R > &b)=0
	Solves \(Ax=b\). Possibly sets up internal data structures suitable for an optimized subsequent change() call with \(b\) as entering column. More...

virtual void	solve2right4update (SSVectorBase< R > &x, VectorBase< R > &y, const SVectorBase< R > &b, SSVectorBase< R > &d)=0
	Solves \(Ax=b\) and \(Ay=d\). More...

virtual void	solve2right4update (SSVectorBase< R > &x, SSVectorBase< R > &y, const SVectorBase< R > &b, SSVectorBase< R > &d)=0
	sparse version of solving two systems of equations More...

virtual void	solve3right4update (SSVectorBase< R > &x, VectorBase< R > &y, VectorBase< R > &z, const SVectorBase< R > &b, SSVectorBase< R > &d, SSVectorBase< R > &e)=0
	Solves \(Ax=b\), \(Ay=d\) and \(Az=e\). More...

virtual void	solve3right4update (SSVectorBase< R > &x, SSVectorBase< R > &y, SSVectorBase< R > &z, const SVectorBase< R > &b, SSVectorBase< R > &d, SSVectorBase< R > &e)=0
	sparse version of solving three systems of equations More...

virtual void	solveLeft (VectorBase< R > &x, const VectorBase< R > &b)=0
	solves \(x^TA=b^T\). More...

virtual void	solveLeft (SSVectorBase< R > &x, const SSVectorBase< R > &b)=0

virtual void	solveLeft (SSVectorBase< R > &x, const SVectorBase< R > &b)=0
	sparse version of solving one system of equations with transposed basis matrix More...

virtual void	solveLeft (SSVectorBase< R > &x, VectorBase< R > &two, const SVectorBase< R > &b, SSVectorBase< R > &rhs2)=0
	solves \(x^TA=b^T\) and \(x^TA=rhs2^T\) internally using \(rhs2\). More...

virtual void	solveLeft (SSVectorBase< R > &x, SSVectorBase< R > &two, const SVectorBase< R > &b, SSVectorBase< R > &rhs2)=0
	sparse version of solving two systems of equations with transposed basis matrix More...

virtual void	solveLeft (SSVectorBase< R > &x, VectorBase< R > &y, VectorBase< R > &z, const SVectorBase< R > &b, SSVectorBase< R > &d, SSVectorBase< R > &e)=0
	solves \(x^TA=b^T\), \(y^TA=d^T\) and \(z^TA=e^T\) More...

virtual void	solveLeft (SSVectorBase< R > &x, SSVectorBase< R > &y, SSVectorBase< R > &z, const SVectorBase< R > &b, SSVectorBase< R > &d, SSVectorBase< R > &e)=0
	sparse version of solving three systems of equations with transposed basis matrix More...

Constructors / Destructors
	SLinSolver ()
	default constructor More...

virtual	~SLinSolver ()
	destructor More...

virtual SLinSolver< R > *	clone () const =0
	clone function for polymorphism More...

Public Attributes
SPxOut *	spxout
	message handler More...

Detailed Description

template<class R>
class soplex::SLinSolver< R >

Sparse Linear Solver virtual base class.

Class SLinSolver provides a class for solving sparse linear systems with a matrix \(A\) and arbitrary right-hand side vectors. For doing so, the matrix must be first loaded to an SLinSolver object as an array of pointers to the column SVectors of this matrix.

Definition at line 30 of file dsvectorbase.h.

Member Enumeration Documentation

◆ Status

enum Status

status flags of the SLinSolver class.

Enumerator
OK	The SLinSolver is ready for solving linear systems with the loaded matrix
INSTABLE	The loaded matrix allows only for instable solutions to be computed
SINGULAR	The loaded matrix is singular.
UNLOADED	No matrix has yet been loaded.
ERROR	An error has occurred.

Definition at line 51 of file slinsolver.h.

Constructor & Destructor Documentation

◆ SLinSolver()

SLinSolver ( )

default constructor

Definition at line 203 of file slinsolver.h.

◆ ~SLinSolver()

virtual ~SLinSolver ( )

virtual

destructor

Definition at line 207 of file slinsolver.h.

References SLinSolver< R >::clone().

Member Function Documentation

◆ change()

virtual Status change	(	int	idx,
		const SVectorBase< R > &	subst,
		const SSVectorBase< R > *	eta = `0`
	)

pure virtual

Substitute column idx with subst.

The change method is used to modify the loaded matrix by substituting column idx with the new vector subst. One may also pass the optional parameter eta to the solution of solveRight() if readily availabble. This may improve on the performance of the update.

Implemented in SLUFactor< R >.

◆ clear()

virtual void clear ( )

pure virtual

unloads any matrix.

Implemented in SLUFactor< R >.

◆ clone()

virtual SLinSolver<R>* clone ( ) const

pure virtual

clone function for polymorphism

Implemented in SLUFactor< R >.

Referenced by SLinSolver< R >::~SLinSolver().

◆ dim()

virtual int dim ( ) const

pure virtual

returns dimension of loaded matrix.

Implemented in SLUFactor< R >.

◆ getFactorCount()

virtual int getFactorCount ( ) const

pure virtual

get number of factorizations

Implemented in SLUFactor< R >.

◆ getName()

virtual const char* getName ( ) const

pure virtual

returns the name of the SLinSolver.

Implemented in SLUFactor< R >.

◆ isConsistent()

virtual bool isConsistent ( ) const

pure virtual

consistency check.

Implemented in SLUFactor< R >.

◆ load()

virtual Status load	(	const SVectorBase< R > *	vec[],
		int	dim
	)

pure virtual

loads dim column vectors vec into the solver.

Initializes SLinSolver for the solution of linear systems with the matrix consisting of dim column vectors given in vec.

Implemented in SLUFactor< R >.

◆ matrixMetric()

virtual R matrixMetric ( int type = 0 ) const

pure virtual

return estimate for the condition number based on the diagonal of U

Implemented in SLUFactor< R >.

◆ memory()

virtual int memory ( ) const

pure virtual

returns current memory consumption.

Implemented in SLUFactor< R >.

◆ solve2right4update() [1/2]

virtual void solve2right4update	(	SSVectorBase< R > &	x,
		VectorBase< R > &	y,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	d
	)

pure virtual

Solves \(Ax=b\) and \(Ay=d\).

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::solve4update().

◆ solve2right4update() [2/2]

virtual void solve2right4update	(	SSVectorBase< R > &	x,
		SSVectorBase< R > &	y,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	d
	)

pure virtual

sparse version of solving two systems of equations

Implemented in SLUFactor< R >.

◆ solve3right4update() [1/2]

virtual void solve3right4update	(	SSVectorBase< R > &	x,
		VectorBase< R > &	y,
		VectorBase< R > &	z,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	d,
		SSVectorBase< R > &	e
	)

pure virtual

Solves \(Ax=b\), \(Ay=d\) and \(Az=e\).

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::solve4update().

◆ solve3right4update() [2/2]

virtual void solve3right4update	(	SSVectorBase< R > &	x,
		SSVectorBase< R > &	y,
		SSVectorBase< R > &	z,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	d,
		SSVectorBase< R > &	e
	)

pure virtual

sparse version of solving three systems of equations

Implemented in SLUFactor< R >.

◆ solveLeft() [1/7]

virtual void solveLeft	(	VectorBase< R > &	x,
		const VectorBase< R > &	b
	)

pure virtual

solves \(x^TA=b^T\).

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::coSolve().

◆ solveLeft() [2/7]

virtual void solveLeft	(	SSVectorBase< R > &	x,
		const SSVectorBase< R > &	b
	)

pure virtual

Implemented in SLUFactor< R >.

◆ solveLeft() [3/7]

virtual void solveLeft	(	SSVectorBase< R > &	x,
		const SVectorBase< R > &	b
	)

pure virtual

sparse version of solving one system of equations with transposed basis matrix

Implemented in SLUFactor< R >.

◆ solveLeft() [4/7]

virtual void solveLeft	(	SSVectorBase< R > &	x,
		VectorBase< R > &	two,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	rhs2
	)

pure virtual

solves \(x^TA=b^T\) and \(x^TA=rhs2^T\) internally using \(rhs2\).

Implemented in SLUFactor< R >.

◆ solveLeft() [5/7]

virtual void solveLeft	(	SSVectorBase< R > &	x,
		SSVectorBase< R > &	two,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	rhs2
	)

pure virtual

sparse version of solving two systems of equations with transposed basis matrix

Implemented in SLUFactor< R >.

◆ solveLeft() [6/7]

virtual void solveLeft	(	SSVectorBase< R > &	x,
		VectorBase< R > &	y,
		VectorBase< R > &	z,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	d,
		SSVectorBase< R > &	e
	)

pure virtual

solves \(x^TA=b^T\), \(y^TA=d^T\) and \(z^TA=e^T\)

Implemented in SLUFactor< R >.

◆ solveLeft() [7/7]

virtual void solveLeft	(	SSVectorBase< R > &	x,
		SSVectorBase< R > &	y,
		SSVectorBase< R > &	z,
		const SVectorBase< R > &	b,
		SSVectorBase< R > &	d,
		SSVectorBase< R > &	e
	)

pure virtual

sparse version of solving three systems of equations with transposed basis matrix

Implemented in SLUFactor< R >.

◆ solveRight() [1/3]

virtual void solveRight	(	VectorBase< R > &	x,
		const VectorBase< R > &	b
	)

pure virtual

Solves \(Ax=b\).

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::solve().

◆ solveRight() [2/3]

virtual void solveRight	(	SSVectorBase< R > &	x,
		const SSVectorBase< R > &	b
	)

pure virtual

Solves \(Ax=b\).

Implemented in SLUFactor< R >.

◆ solveRight() [3/3]

virtual void solveRight	(	SSVectorBase< R > &	x,
		const SVectorBase< R > &	b
	)

pure virtual

Implemented in SLUFactor< R >.

◆ solveRight4update()

virtual void solveRight4update	(	SSVectorBase< R > &	x,
		const SVectorBase< R > &	b
	)

pure virtual

Solves \(Ax=b\). Possibly sets up internal data structures suitable for an optimized subsequent change() call with \(b\) as entering column.

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::solve4update().

◆ stability()

virtual R stability ( ) const

pure virtual

returns a stability number (0: singularity, 1: perfect stability).

Returns a stability parameter between 0 and 1, where 0 indicates singularity, while 1 indicates perfect stability.

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::stability().

◆ statistics()

virtual std::string statistics ( ) const

pure virtual

returns statistical information in form of a string.

Implemented in SLUFactor< R >.

Referenced by SPxBasisBase< R >::statistics().

◆ status()

virtual Status status ( ) const

pure virtual

returns the Status of the SLinSolver.

Implemented in SLUFactor< R >.

Member Data Documentation

◆ spxout

SPxOut* spxout

message handler

Definition at line 214 of file slinsolver.h.

SoPlex

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<class R> class soplex::SLinSolver< R >

Member Enumeration Documentation

◆ Status

Constructor & Destructor Documentation

◆ SLinSolver()

◆ ~SLinSolver()

Member Function Documentation

◆ change()

◆ clear()

◆ clone()

◆ dim()

◆ getFactorCount()

◆ getName()

◆ isConsistent()

◆ load()

◆ matrixMetric()

◆ memory()

◆ solve2right4update() [1/2]

◆ solve2right4update() [2/2]

◆ solve3right4update() [1/2]

◆ solve3right4update() [2/2]

◆ solveLeft() [1/7]

◆ solveLeft() [2/7]

◆ solveLeft() [3/7]

◆ solveLeft() [4/7]

◆ solveLeft() [5/7]

◆ solveLeft() [6/7]

◆ solveLeft() [7/7]

◆ solveRight() [1/3]

◆ solveRight() [2/3]

◆ solveRight() [3/3]

◆ solveRight4update()

◆ stability()

◆ statistics()

◆ status()

Member Data Documentation

◆ spxout

template<class R>
class soplex::SLinSolver< R >