Simplex basis.Consider the linear program as provided from class SPxLP:

$\begin{array}{rl} \hbox{max} & c^T x \\ \hbox{s.t.} & l_r \le Ax \le u_r \\ & l_c \le x \le u_c \end{array}$

where $c, l_c, u_c, x \in {\bf R}^n$ , $l_r, u_r \in {\bf R}^m$ and $A \in {\bf R}^{m \times n}$ . Solving this LP with the simplex algorithm requires the definition of a basis. Such can be defined as a set of column vectors or a set of row vectors building a nonsingular matrix. We will refer to the first case as the columnwise representation and the latter case will be called the rowwise representation. In both cases, a basis is a set of vectors forming a nonsigular matrix. The dimension of the vectors is refered to as the basis' dimension, whereas the number of vectors belonging to the LP is called the basis' codimension. More...

#include <spxbasis.h>

Inheritance diagram for SPxBasis:

[legend]

Classes
class	Desc
	Basis descriptor. More...

Public Types
enum	SPxStatus { NO_PROBLEM = -2, SINGULAR = -1, REGULAR = 0, DUAL = 1, PRIMAL = 2, OPTIMAL = 3, UNBOUNDED = 4, INFEASIBLE = 5 }
	basis status. More...

Public Member Functions
Status and Descriptor related Methods
SPxStatus	status () const
	returns current SPxStatus. More...

void	setStatus (SPxStatus stat)
	sets basis SPxStatus to `stat`. More...

void	setMaxUpdates (int maxUp)
	change maximum number of iterations until a refactorization is performed More...

int	getMaxUpdates () const
	returns maximum number of updates before a refactorization is performed More...

const Desc &	desc () const

Desc &	desc ()
	returns current basis Descriptor. More...

Desc::Status	dualColStatus (int i) const
	dual Status for the `i'th` column variable of the loaded LP. More...

Desc::Status	dualStatus (const SPxColId &id) const
	dual Status for the column variable with ID `id` of the loaded LP. More...

Desc::Status	dualRowStatus (int i) const
	dual Status for the `i'th` row variable of the loaded LP. More...

Desc::Status	dualStatus (const SPxRowId &id) const
	dual Status for the row variable with ID `id` of the loaded LP. More...

Desc::Status	dualStatus (const SPxId &id) const
	dual Status for the variable with ID `id` of the loaded LP. More...

Inquiry Methods
SPxId &	baseId (int i)

SPxId	baseId (int i) const
	returns the Id of the `i'th` basis vector. More...

const SVector &	baseVec (int i) const
	returns the `i'th` basic vector. More...

SPxId	lastEntered () const
	returns SPxId of last vector included to the basis. More...

SPxId	lastLeft () const
	returns SPxId of last vector that left the basis. More...

int	lastIndex () const
	returns index in basis where last update was done. More...

int	lastUpdate () const
	returns number of basis changes since last refactorization. More...

int	iteration () const
	returns number of basis changes since last load(). More...

SPxSolver *	solver () const
	returns loaded solver. More...

Linear Algebra
Vector &	multBaseWith (Vector &x) const
	Basis-vector product. More...

void	multBaseWith (SSVector &x, SSVector &result) const
	Basis-vector product. More...

Vector &	multWithBase (Vector &x) const
	Vector-basis product. More...

void	multWithBase (SSVector &x, SSVector &result) const
	Vector-basis product. More...

Real	condition (int maxiters=10, Real tolerance=1e-6)

Real	getEstimatedCondition ()

Real	getExactCondition ()

Real	stability () const
	returns the stability of the basis matrix. More...

void	solve (Vector &x, const Vector &rhs)

void	solve (SSVector &x, const SVector &rhs)

void	solve4update (SSVector &x, const SVector &rhs)
	solves linear system with basis matrix. More...

void	solve4update (SSVector &x, Vector &y, const SVector &rhsx, SSVector &rhsy)
	solves two systems in one call. More...

void	solve4update (SSVector &x, SSVector &y, const SVector &rhsx, SSVector &rhsy)
	solves two systems in one call using only sparse data structures More...

void	solve4update (SSVector &x, Vector &y, Vector &y2, const SVector &rhsx, SSVector &rhsy, SSVector &rhsy2)
	solves three systems in one call. More...

void	solve4update (SSVector &x, SSVector &y, SSVector &y2, const SVector &rhsx, SSVector &rhsy, SSVector &rhsy2)
	solves three systems in one call using only sparse data structures More...

void	coSolve (Vector &x, const Vector &rhs)
	Cosolves linear system with basis matrix. More...

void	coSolve (SSVector &x, const SVector &rhs)
	Sparse version of coSolve. More...

void	coSolve (SSVector &x, Vector &y, const SVector &rhsx, SSVector &rhsy)
	solves two systems in one call. More...

void	coSolve (SSVector &x, SSVector &y, const SVector &rhsx, SSVector &rhsy)
	Sparse version of solving two systems in one call. More...

void	coSolve (SSVector &x, Vector &y, Vector &z, const SVector &rhsx, SSVector &rhsy, SSVector &rhsz)
	solves three systems in one call. May be improved by using just one pass through the basis. More...

void	coSolve (SSVector &x, SSVector &y, SSVector &z, const SVector &rhsx, SSVector &rhsy, SSVector &rhsz)
	Sparse version of solving three systems in one call. More...

Modification notification.
These methods must be called after the loaded LP has been modified.
void	addedRows (int n)
	inform SPxBasis, that `n` new rows had been added. More...

void	removedRow (int i)
	inform SPxBasis that row `i` had been removed. More...

void	removedRows (const int perm[])
	inform SPxBasis that rows in `perm` with negative entry were removed. More...

void	addedCols (int n)
	inform SPxBasis that `n` new columns had been added. More...

void	removedCol (int i)
	inform SPxBasis that column `i` had been removed. More...

void	removedCols (const int perm[])
	inform SPxBasis that columns in `perm` with negative entry were removed. More...

void	changedRow (int)
	inform SPxBasis that a row had been changed. More...

void	changedCol (int)
	inform SPxBasis that a column had been changed. More...

void	changedElement (int, int)
	inform SPxBasis that a matrix entry had been changed. More...

Miscellaneous
virtual void	change (int i, SPxId &id, const SVector enterVec, const SSVector eta=0)
	performs basis update. More...

virtual bool	readBasis (std::istream &in, const NameSet rowNames, const NameSet colNames)

virtual void	writeBasis (std::ostream &os, const NameSet rownames, const NameSet colnames, const bool cpxFormat=false) const

virtual void	printMatrix () const

void	printMatrixMTX (int number)

virtual bool	isDescValid (const Desc &ds)
	checks if a Descriptor is valid for the current LP w.r.t. its bounds More...

virtual void	loadDesc (const Desc &)
	sets up basis. More...

virtual void	loadSolver (SLinSolver *solver, const bool destroy=false)
	sets up linear solver to use. More...

virtual void	load (SPxSolver *lp)
	loads the LP `lp` to the basis. More...

virtual void	unLoad ()
	unloads the LP from the basis. More...

void	invalidate ()
	invalidates actual basis. More...

void	restoreInitialBasis ()
	Restores initial basis. More...

void	dump ()
	output basis entries. More...

bool	isConsistent () const
	consistency check. More...

Real	getTotalUpdateTime () const
	time spent in updates More...

int	getTotalUpdateCount () const
	number of updates performed More...

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

void	setOutstream (SPxOut &newOutstream)

Constructors / Destructors
	SPxBasis (Timer::TYPE ttype=Timer::USER_TIME)
	default constructor. More...

	SPxBasis (const SPxBasis &old)
	copy constructor More...

SPxBasis &	operator= (const SPxBasis &rhs)
	assignment operator More...

virtual	~SPxBasis ()
	destructor. More...

Protected Member Functions
Protected helpers
void	loadMatrixVecs ()
	loads matrix according to the SPxIds stored in theBaseId. More...

void	reDim ()
	resizes internal arrays. More...

virtual void	factorize ()
	factorizes the basis matrix. More...

void	setRep ()
	sets descriptor representation according to loaded LP. More...

Protected Attributes

SPxSolver *	theLP
	the LP More...

DataArray< SPxId >	theBaseId
	SPxIds of basic vectors. More...

DataArray< const SVector * >	matrix
	pointers to the vectors of the basis matrix. More...

bool	matrixIsSetup
	`true` iff the pointers in matrix are set up correctly. More...

SLinSolver *	factor

bool	factorized
	`true` iff factor = matrix $^{-1}$ . More...

int	maxUpdates
	number of updates before refactorization. More...

Real	nonzeroFactor
	allowed increase of nonzeros before refactorization. More...

Real	fillFactor
	allowed increase in realtive fill before refactorization More...

int	iterCount
	number of calls to change() since last manipulation More...

int	updateCount
	number of calls to change() since last factorize() More...

int	totalUpdateCount
	number of updates More...

int	nzCount
	number of nonzeros in basis matrix More...

int	lastMem
	memory needed after last fresh factorization More...

Real	lastFill
	fill ratio that occured during last factorization More...

int	lastNzCount
	number of nonzeros in basis matrix after last fresh factorization More...

Timer *	theTime
	time spent in updates More...

Timer::TYPE	timerType
	type of timer (user or wallclock) More...

SPxId	lastin
	lastEntered(): variable entered the base last More...

SPxId	lastout
	lastLeft(): variable left the base last More...

int	lastidx
	lastIndex(): basis index where last update was done More...

Real	minStab
	minimum stability More...

Private Attributes

SPxStatus	thestatus
	current status of the basis. More...

Desc	thedesc
	the basis' Descriptor More...

bool	freeSlinSolver
	true iff factor should be freed inside of this object More...

SPxOut *	spxout
	message handler More...

Detailed Description

Simplex basis.

Consider the linear program as provided from class SPxLP:

$\begin{array}{rl} \hbox{max} & c^T x \\ \hbox{s.t.} & l_r \le Ax \le u_r \\ & l_c \le x \le u_c \end{array}$

where $c, l_c, u_c, x \in {\bf R}^n$ , $l_r, u_r \in {\bf R}^m$ and $A \in {\bf R}^{m \times n}$ . Solving this LP with the simplex algorithm requires the definition of a basis. Such can be defined as a set of column vectors or a set of row vectors building a nonsingular matrix. We will refer to the first case as the columnwise representation and the latter case will be called the rowwise representation. In both cases, a basis is a set of vectors forming a nonsigular matrix. The dimension of the vectors is refered to as the basis' dimension, whereas the number of vectors belonging to the LP is called the basis' codimension.

Class SPxBasis is designed to represent a generic simplex basis, suitable for both representations. At any time the representation can be changed by calling method setRep().

Class SPxBasis provides methods for solving linear systems with the basis matrix. However, SPxBasis does not provide a linear solver by its own. Instead, a SLinSolver object must be loaded to a SPxBasis which will be called for solving linear systems.

Definition at line 82 of file spxbasis.h.

Member Enumeration Documentation

enum SPxStatus

basis status.

Each SPxBasis is assigned a status flag, which can take on of the above values.

Enumerator
NO_PROBLEM	No Problem has been loaded to the basis.
SINGULAR	Basis is singular.
REGULAR	Basis is not known to be dual nor primal feasible.
DUAL	Basis is dual feasible.
PRIMAL	Basis is primal feasible.
OPTIMAL	Basis is optimal, i.e. dual and primal feasible.
UNBOUNDED	LP has been proven to be primal unbounded.
INFEASIBLE	LP has been proven to be primal infeasible.

Definition at line 90 of file spxbasis.h.

Constructor & Destructor Documentation

SPxBasis ( Timer::TYPE ttype = Timer::USER_TIME )

default constructor.

Definition at line 1142 of file spxbasis.cpp.

References TimerFactory::createTimer(), SPxBasis::theTime, and SPxBasis::timerType.

SPxBasis ( const SPxBasis & old )

copy constructor

Warning: Do not change the LP object. Only pointer to that object is copied. Hint: no problem, we use this function for copy constructor of SPxSolver

Definition at line 1175 of file spxbasis.cpp.

References SLinSolver::clone(), SPxBasis::factor, SPxBasis::freeSlinSolver, and SPxBasis::isConsistent().

~SPxBasis ( )

virtual

destructor.

Definition at line 1209 of file spxbasis.cpp.

References SPxBasis::factor, SPxBasis::freeSlinSolver, soplex::spx_free(), and SPxBasis::theTime.

Referenced by SPxBasis::setOutstream().

Member Function Documentation

void addedCols ( int n )

inform SPxBasis that n new columns had been added.

Definition at line 255 of file spxchangebasis.cpp.

References SPxBasis::baseId(), SPxBasis::Desc::colStatus(), SPxSolver::COLUMN, SPxBasis::DUAL, SPxBasis::factorized, SPxBasis::INFEASIBLE, SPxBasis::loadMatrixVecs(), SPxBasis::matrixIsSetup, MSG_ERROR, SPxLPBase< R >::nCols(), SPxBasis::NO_PROBLEM, SPxBasis::OPTIMAL, SPxBasis::PRIMAL, soplex::primalColStatus(), SPxBasis::reDim(), SPxBasis::REGULAR, SPxSolver::rep(), SPxSolver::ROW, SPxBasis::setStatus(), SPxBasis::SINGULAR, SPxBasis::status(), SPxBasis::thedesc, SPxBasis::theLP, and SPxBasis::UNBOUNDED.

Referenced by SPxSolver::addedCols(), SPxSolver::addedRows(), and SPxBasis::coSolve().

void addedRows ( int n )

inform SPxBasis, that n new rows had been added.

Definition at line 59 of file spxchangebasis.cpp.

References SPxBasis::baseId(), SPxSolver::COLUMN, SPxBasis::DUAL, SPxBasis::dualRowStatus(), SPxBasis::factorized, SPxBasis::INFEASIBLE, SPxBasis::loadMatrixVecs(), SPxBasis::matrixIsSetup, MSG_ERROR, SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxBasis::OPTIMAL, SPxBasis::PRIMAL, SPxBasis::reDim(), SPxBasis::REGULAR, SPxSolver::rep(), SPxSolver::ROW, SPxBasis::Desc::rowStatus(), SPxBasis::setStatus(), SPxBasis::SINGULAR, SPxBasis::status(), SPxBasis::thedesc, SPxBasis::theLP, and SPxBasis::UNBOUNDED.

Referenced by SPxSolver::addedRows(), and SPxBasis::coSolve().

SPxId& baseId ( int i )

Definition at line 497 of file spxbasis.h.

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxSolver::computeDualfarkas4Row(), SPxSolver::computeEnterCoPrhs(), SPxSolver::computeEnterCoPrhs4Col(), SPxSolver::computeEnterCoPrhs4Row(), SPxSolver::computeLeaveCoPrhs(), SPxSolver::computeLeaveCoPrhs4Col(), SPxSolver::computeLeaveCoPrhs4Row(), SPxWeightPR::computeLeavePenalty(), SPxSolver::computePrimalray4Col(), SPxSolver::enter(), SPxBoundFlippingRT::flipAndUpdate(), SoPlex::getBasisInd(), SoPlex::getBasisInverseColReal(), SoPlex::getBasisInverseRowReal(), SoPlex::getBasisInverseTimesVecReal(), SPxBoundFlippingRT::getData(), SPxSolver::getDual(), SPxSolver::getEnterVals2(), SPxSolver::getLeaveVals(), SPxSolver::getPrimal(), SPxSolver::getRedCost(), SPxSolver::getSlacks(), SPxSolver::leave(), SPxBasis::loadMatrixVecs(), SPxFastRT::maxReLeave(), SPxFastRT::minReLeave(), SPxSolver::perturbMax(), SPxSolver::perturbMin(), SPxBasis::removedCol(), SPxBasis::removedRow(), SPxBasis::restoreInitialBasis(), SPxFastRT::selectLeave(), SPxBoundFlippingRT::selectLeave(), SPxSolver::setDual(), SPxSolver::setEnterBound4Col(), SPxSolver::setEnterBound4Row(), SPxSolver::setEnterBounds(), SPxSolver::setLeaveBound4Col(), SPxSolver::setLeaveBound4Row(), SPxSolver::setLeaveBounds(), SPxSolver::setPrimal(), SPxSolver::setRedCost(), SPxSolver::setSlacks(), SPxSteepPR::setupWeights(), SPxSolver::solve(), and SPxSolver::unShift().

SPxId baseId ( int i ) const

returns the Id of the i'th basis vector.

Definition at line 502 of file spxbasis.h.

const SVector& baseVec ( int i ) const

returns the i'th basic vector.

Definition at line 508 of file spxbasis.h.

Referenced by SPxSolver::enter(), SPxSolver::leave(), and SPxBasis::printMatrixMTX().

void change	(	int	i,
		SPxId &	id,
		const SVector *	enterVec,
		const SSVector *	eta = `0`
	)

virtual

performs basis update.

Changes the i 'th vector of the basis with the vector associated to id. This includes:

updating the factorization, or recomputing it from scratch by calling factorize(),
resetting lastEntered(),
resetting lastIndex(),
resetting lastLeft(),
resetting lastUpdate(),
resetting iterations().

The basis descriptor is not modified, since factor() cannot know about how to set up the status of the involved variables correctly.

A vector enterVec may be passed for a fast ETA update of the LU factorization associated to the basis. It must be initialized with the solution vector $x$ of the right linear system $Bx = b$ with the entering vector as right-hand side vector $b$ , where $B$ denotes the basis matrix. This can be computed using method solve(). When using FAST updates, a vector eta may be passed for improved performance. It must be initialized by a call to factor->solveRightUpdate() as described in SLinSolver. The implementation hidden behind FAST updates depends on the SLinSolver implementation class.

Definition at line 715 of file spxbasis.cpp.

References SLinSolver::change(), SPxBasis::factor, SPxBasis::factorize(), SPxBasis::factorized, SPxBasis::iterCount, SPxBasis::lastFill, SPxBasis::lastidx, SPxBasis::lastin, SPxBasis::lastNzCount, SPxBasis::lastout, SPxBasis::matrix, SPxBasis::matrixIsSetup, SPxBasis::maxUpdates, SLinSolver::memory(), SPxBasis::minStab, MSG_INFO3, SPxBasis::nonzeroFactor, SPxBasis::nzCount, SLinSolver::OK, SPxBasis::REGULAR, SVectorBase< R >::size(), SPxBasis::spxout, SLinSolver::stability(), Timer::start(), SLinSolver::status(), SPxBasis::status(), Timer::stop(), SPxBasis::theBaseId, SPxBasis::theTime, SPxBasis::totalUpdateCount, and SPxBasis::updateCount.

Referenced by SPxBasis::coSolve(), SPxSolver::enter(), and SPxSolver::leave().

void changedCol ( int )

inform SPxBasis that a column had been changed.

Todo:: is this correctly implemented?

Definition at line 474 of file spxchangebasis.cpp.

References SPxBasis::invalidate(), and SPxBasis::restoreInitialBasis().

Referenced by SPxSolver::changeCol(), and SPxBasis::coSolve().

void changedElement	(	int	,
		int
	)

inform SPxBasis that a matrix entry had been changed.

Todo:: is this correctly implemented?

Definition at line 482 of file spxchangebasis.cpp.

References SPxBasis::invalidate(), and SPxBasis::restoreInitialBasis().

Referenced by SPxSolver::changeElement(), and SPxBasis::coSolve().

void changedRow ( int )

inform SPxBasis that a row had been changed.

Todo:: Implement changedRow(), changedCol(), changedElement() in a more clever way. For instance, the basis won't be singular (but maybe infeasible) if the change doesn't affect the basis rows/columns.

The following methods (changedRow(), changedCol(), changedElement()) radically change the current basis to the original (slack) basis also present after loading the LP. The reason is that through the changes, the current basis may become singular. Going back to the initial basis is quite inefficient, but correct.

Todo:: is this correctly implemented?

Definition at line 466 of file spxchangebasis.cpp.

References SPxBasis::invalidate(), and SPxBasis::restoreInitialBasis().

Referenced by SPxSolver::changeRow(), and SPxBasis::coSolve().

Real condition	(	int	maxiters = `10`,
		Real	tolerance = `1e-6`
	)

Definition at line 978 of file spxbasis.cpp.

References SSVectorBase< R >::add(), SPxBasis::factor, SSVectorBase< R >::length(), SPxBasis::matrix, SPxBasis::matrixIsSetup, SPxBasis::multBaseWith(), SPxBasis::multWithBase(), SPxBasis::REGULAR, SSVectorBase< R >::setValue(), SLinSolver::solveLeft(), SLinSolver::solveRight(), soplex::spxAbs(), SPxBasis::status(), and SPxBasis::thedesc.

Referenced by SPxBasis::getEstimatedCondition(), SPxBasis::getExactCondition(), and SPxBasis::solver().

void coSolve	(	Vector &	x,
		const Vector &	rhs
	)

Cosolves linear system with basis matrix.

Depending on the representation, for a SPxBasis B, B.coSolve(x) computes

$x \leftarrow rhs^TB^{-1}$ in the columnwise case and
$x \leftarrow B^{-1}rhs$ in the rowwise case.

Both can be seen uniformly as solving a linear system with the basis matrix B and a right handside vector x aligned the same way as the covectors of B.

Definition at line 678 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveLeft().

Referenced by SPxSolver::addedRows(), SPxSolver::enter(), SPxSolver::factorize(), SoPlex::getBasisInverseColReal(), SoPlex::getBasisInverseRowReal(), SoPlex::getBasisInverseTimesVecReal(), SPxSolver::init(), SPxSteepPR::isConsistent(), SPxSolver::leave(), SPxSolver::reinitializeVecs(), SPxSteepPR::selectLeave(), SPxSteepPR::setupWeights(), SPxSolver::terminate(), and SPxSolver::testVecs().

void coSolve	(	SSVector &	x,
		const SVector &	rhs
	)

Sparse version of coSolve.

Definition at line 685 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveLeft().

void coSolve	(	SSVector &	x,
		Vector &	y,
		const SVector &	rhsx,
		SSVector &	rhsy
	)

solves two systems in one call.

Definition at line 692 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveLeft().

void coSolve	(	SSVector &	x,
		SSVector &	y,
		const SVector &	rhsx,
		SSVector &	rhsy
	)

Sparse version of solving two systems in one call.

Definition at line 699 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveLeft().

void coSolve	(	SSVector &	x,
		Vector &	y,
		Vector &	z,
		const SVector &	rhsx,
		SSVector &	rhsy,
		SSVector &	rhsz
	)

solves three systems in one call. May be improved by using just one pass through the basis.

Definition at line 706 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveLeft().

void coSolve	(	SSVector &	x,
		SSVector &	y,
		SSVector &	z,
		const SVector &	rhsx,
		SSVector &	rhsy,
		SSVector &	rhsz
	)

Sparse version of solving three systems in one call.

Definition at line 713 of file spxbasis.h.

References SPxBasis::addedCols(), SPxBasis::addedRows(), SPxBasis::change(), SPxBasis::changedCol(), SPxBasis::changedElement(), SPxBasis::changedRow(), SPxBasis::factorize(), SPxBasis::isDescValid(), SPxBasis::load(), SPxBasis::loadDesc(), SPxBasis::loadSolver(), SPxBasis::printMatrix(), SPxBasis::printMatrixMTX(), SPxBasis::readBasis(), SPxBasis::removedCol(), SPxBasis::removedCols(), SPxBasis::removedRow(), SPxBasis::removedRows(), SLinSolver::solveLeft(), SPxBasis::solver(), and SPxBasis::writeBasis().

const Desc& desc ( ) const

Definition at line 457 of file spxbasis.h.

References SPxBasis::thedesc.

Desc& desc ( )

returns current basis Descriptor.

Definition at line 462 of file spxbasis.h.

References SPxBasis::dualColStatus(), SPxBasis::dualRowStatus(), SPxBasis::dualStatus(), and SPxBasis::thedesc.

SPxBasis::Desc::Status dualColStatus ( int i ) const

dual Status for the i'th column variable of the loaded LP.

Definition at line 69 of file spxbasis.cpp.

References SPxBasis::Desc::D_FREE, SPxBasis::Desc::D_ON_BOTH, SPxBasis::Desc::D_ON_LOWER, SPxBasis::Desc::D_ON_UPPER, SPxBasis::Desc::D_UNDEFINED, soplex::infinity, and SPxBasis::theLP.

Referenced by SPxSolver::changeLowerStatus(), SPxSolver::changeUpperStatus(), SPxBasis::desc(), SPxBasis::dualStatus(), SPxSolver::getEnterVals2(), SPxSolver::getLeaveVals(), SPxSolver::getLeaveVals2(), SPxBasis::isConsistent(), SPxBasis::isDescValid(), SPxBasis::loadDesc(), SPxBasis::readBasis(), SPxSolver::setDualRowBounds(), soplex::setDualStatus(), and SPxSolver::varStatusToBasisStatusCol().

SPxBasis::Desc::Status dualRowStatus ( int i ) const

dual Status for the i'th row variable of the loaded LP.

Definition at line 46 of file spxbasis.cpp.

References SPxBasis::Desc::D_FREE, SPxBasis::Desc::D_ON_BOTH, SPxBasis::Desc::D_ON_LOWER, SPxBasis::Desc::D_ON_UPPER, SPxBasis::Desc::D_UNDEFINED, soplex::infinity, SPxLPBase< R >::lhs(), SPxLPBase< R >::rhs(), and SPxBasis::theLP.

Referenced by SPxBasis::addedRows(), SPxSolver::changeLhsStatus(), SPxSolver::changeRhsStatus(), SPxBasis::desc(), SPxBasis::dualStatus(), SPxSolver::getEnterVals2(), SPxSolver::getLeaveVals(), SPxSolver::getLeaveVals2(), SPxBasis::isConsistent(), SPxBasis::isDescValid(), SPxBasis::loadDesc(), SPxBasis::readBasis(), SPxBasis::restoreInitialBasis(), SPxSolver::setDualRowBounds(), soplex::setDualStatus(), and SPxSolver::varStatusToBasisStatusRow().

SPxBasis::Desc::Status dualStatus ( const SPxColId & id ) const

dual Status for the column variable with ID id of the loaded LP.

Definition at line 34 of file spxbasis.cpp.

References SPxBasis::dualColStatus(), and SPxBasis::theLP.

Referenced by SPxBasis::desc(), SPxBasis::dualStatus(), SPxBoundFlippingRT::getData(), SPxFastRT::maxReLeave(), SPxFastRT::minReLeave(), SPxSolver::perturbMax(), and SPxSolver::perturbMin().

SPxBasis::Desc::Status dualStatus ( const SPxRowId & id ) const

dual Status for the row variable with ID id of the loaded LP.

Definition at line 40 of file spxbasis.cpp.

References SPxBasis::dualRowStatus(), and SPxBasis::theLP.

Desc::Status dualStatus ( const SPxId & id ) const

dual Status for the variable with ID id of the loaded LP.

It is automatically detected, whether the id is one of a row or a column variable, and the correct row or column status is returned.

Definition at line 484 of file spxbasis.h.

References SPxBasis::dualStatus().

void dump ( )

output basis entries.

Definition at line 1051 of file spxbasis.cpp.

References SPxBasis::Desc::colStatus(), SPxSolver::dim(), SPxSolver::isBasic(), SPxBasis::matrix, SPxLPBase< R >::nCols(), SPxBasis::Desc::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxBasis::Desc::nRows(), SPxLPBase< R >::number(), SPxBasis::Desc::rowStatus(), SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

void factorize ( )

protectedvirtual

factorizes the basis matrix.

Reimplemented in SPxSolver.

Definition at line 845 of file spxbasis.cpp.

References SPxBasis::factor, SPxBasis::factorized, SPxBasis::fillFactor, SPxBasis::lastFill, SPxBasis::lastMem, SPxBasis::lastNzCount, SLinSolver::load(), SPxBasis::loadDesc(), SPxBasis::matrix, SPxBasis::matrixIsSetup, SLinSolver::memory(), SPxBasis::minStab, MSG_ERROR, SPxBasis::nonzeroFactor, SPxBasis::nzCount, SLinSolver::OK, SPxBasis::REGULAR, SPxBasis::setStatus(), SLinSolver::SINGULAR, SPxBasis::SINGULAR, SLinSolver::stability(), SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::updateCount.

Referenced by SPxBasis::change(), SPxBasis::coSolve(), SPxSolver::factorize(), SPxSolver::init(), SPxBasis::setOutstream(), SPxBasis::solve(), and SPxBasis::solve4update().

Real getEstimatedCondition ( )

Definition at line 588 of file spxbasis.h.

References SPxBasis::condition().

Referenced by SoPlex::getEstimatedCondition().

Real getExactCondition ( )

Definition at line 594 of file spxbasis.h.

References SPxBasis::condition().

Referenced by SoPlex::getExactCondition().

int getMaxUpdates ( ) const

returns maximum number of updates before a refactorization is performed

Definition at line 451 of file spxbasis.h.

References SPxBasis::maxUpdates.

Referenced by SPxSolver::writeState().

int getTotalUpdateCount ( ) const

number of updates performed

Definition at line 853 of file spxbasis.h.

References SPxBasis::totalUpdateCount.

Referenced by SPxBasis::statistics().

Real getTotalUpdateTime ( ) const

time spent in updates

Definition at line 848 of file spxbasis.h.

References Timer::time().

Referenced by SPxBasis::statistics().

void invalidate ( )

invalidates actual basis.

This method makes the basis matrix and vectors invalid. The basis will be reinitialized if needed.

Todo:: is this correctly implemented?

Definition at line 398 of file spxchangebasis.cpp.

References SPxBasis::factorized, SPxBasis::matrixIsSetup, MSG_INFO3, and SPxBasis::spxout.

Referenced by SPxBasis::changedCol(), SPxBasis::changedElement(), SPxBasis::changedRow(), SPxBasis::setStatus(), and SPxBasis::unLoad().

bool isConsistent ( ) const

consistency check.

Definition at line 1094 of file spxbasis.cpp.

References SPxBasis::Desc::colStatus(), SPxSolver::dim(), SPxBasis::dualColStatus(), SPxBasis::dualRowStatus(), SPxBasis::factor, SLinSolver::isConsistent(), SPxBasis::Desc::isConsistent(), SPxBasis::matrix, MSGinconsistent, SPxLPBase< R >::nCols(), SPxBasis::Desc::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxBasis::Desc::nRows(), SPxBasis::Desc::rowStatus(), SPxBasis::status(), SPxBasis::theBaseId, SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxSolver::isConsistent(), SPxBasis::operator=(), and SPxBasis::SPxBasis().

bool isDescValid ( const Desc & ds )

virtual

checks if a Descriptor is valid for the current LP w.r.t. its bounds

Definition at line 111 of file spxbasis.cpp.

References SPxBasis::Desc::colstat, SPxBasis::dualColStatus(), SPxBasis::dualRowStatus(), soplex::infinity, MSG_DEBUG, SPxLPBase< R >::nCols(), SPxBasis::Desc::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxBasis::Desc::nRows(), SPxBasis::Desc::P_FIXED, SPxBasis::Desc::P_ON_LOWER, SPxBasis::Desc::P_ON_UPPER, SPxBasis::Desc::rowstat, SPxBasis::status(), and SPxBasis::theLP.

Referenced by SPxBasis::coSolve(), SPxBasis::loadDesc(), and SoPlexLegacy::solve().

int iteration ( ) const

returns number of basis changes since last load().

Definition at line 539 of file spxbasis.h.

References SPxBasis::iterCount.

Referenced by SPxSteepPR::entered4(), SPxSolver::factorize(), SoPlexLegacy::iteration(), SPxSolver::leave(), SPxSteepPR::left4(), SPxSolver::perturbMaxEnter(), SPxSolver::perturbMaxLeave(), SPxSolver::perturbMinEnter(), SPxSolver::perturbMinLeave(), SPxSolver::printDisplayLine(), SPxFastRT::selectEnter(), SPxBoundFlippingRT::selectEnter(), SPxFastRT::selectLeave(), SPxBoundFlippingRT::selectLeave(), SPxSolver::solve(), SPxSolver::terminate(), SPxSolver::testVecs(), and SPxSolver::updateNonbasicValue().

SPxId lastEntered ( ) const

returns SPxId of last vector included to the basis.

Definition at line 515 of file spxbasis.h.

References SPxBasis::lastin.

Referenced by SPxSolver::solve().

int lastIndex ( ) const

returns index in basis where last update was done.

Definition at line 527 of file spxbasis.h.

References SPxBasis::lastidx.

Referenced by SPxSolver::solve().

SPxId lastLeft ( ) const

returns SPxId of last vector that left the basis.

Definition at line 521 of file spxbasis.h.

References SPxBasis::lastout.

Referenced by SPxSolver::solve().

int lastUpdate ( ) const

returns number of basis changes since last refactorization.

Definition at line 533 of file spxbasis.h.

References SPxBasis::updateCount.

Referenced by SPxSolver::enter(), SPxSolver::leave(), SPxSolver::qualRedCostViolation(), SPxDevexPR::selectEnterX(), SPxSteepPR::selectEnterX(), SPxDevexPR::selectLeave(), SPxSteepPR::selectLeave(), and SPxSolver::solve().

void load ( SPxSolver * lp )

virtual

loads the LP lp to the basis.

This involves resetting all counters to 0 and setting up a regular default basis consisting of slacks, artificial variables or bounds.

Definition at line 305 of file spxbasis.cpp.

References SPxBasis::loadDesc(), SPxBasis::restoreInitialBasis(), SPxBasis::setOutstream(), SPxBasis::setRep(), SPxSolver::spxout, SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::coSolve(), SPxSolver::init(), SPxSolver::loadBasis(), SPxSolver::loadLP(), SPxBasis::readBasis(), SPxSolver::setBasis(), SPxSolver::setType(), and SPxSolver::solve().

void loadDesc ( const Desc & ds )

virtual

sets up basis.

Loads a Descriptor to the basis and sets up the basis matrix and all vectors accordingly. The Descriptor must have the same number of rows and columns as the currently loaded LP.

Definition at line 188 of file spxbasis.cpp.

References SLinSolver::clear(), SPxBasis::Desc::colStatus(), SPxSolver::dim(), SPxBasis::dualColStatus(), SPxBasis::dualRowStatus(), SPxBasis::factor, SPxBasis::factorized, soplex::infinity, SPxSolver::isBasic(), SPxBasis::isDescValid(), SPxBasis::iterCount, SPxBasis::lastidx, SPxBasis::lastin, SPxBasis::lastout, SPxBasis::matrix, SPxBasis::matrixIsSetup, MSG_INFO3, SPxLPBase< R >::nCols(), SPxBasis::Desc::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxBasis::Desc::nRows(), SPxBasis::nzCount, SPxBasis::Desc::P_FIXED, SPxBasis::Desc::P_FREE, SPxBasis::Desc::P_ON_LOWER, SPxBasis::Desc::P_ON_UPPER, SPxBasis::restoreInitialBasis(), SPxBasis::Desc::rowStatus(), SPxBasis::setRep(), SPxBasis::spxout, SPxBasis::status(), SPxBasis::theBaseId, SPxBasis::thedesc, SPxBasis::theLP, SPxBasis::updateCount, and SPxSolver::vector().

Referenced by SPxBasis::coSolve(), SPxBasis::factorize(), SPxSolver::init(), SPxSolver::initRep(), SPxBasis::load(), SPxSolver::loadBasis(), and SPxBasis::readBasis().

void loadMatrixVecs ( )

protected

loads matrix according to the SPxIds stored in theBaseId.

This method must be called whenever there is a chance, that the vector pointers may have changed due to manipulations of the LP.

Definition at line 91 of file spxbasis.cpp.

References SPxBasis::baseId(), SLinSolver::clear(), SPxSolver::dim(), SPxBasis::factor, SPxBasis::factorized, SPxBasis::matrix, SPxBasis::matrixIsSetup, MSG_INFO3, SPxBasis::nzCount, SPxBasis::spxout, SPxBasis::theLP, and SPxSolver::vector().

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxBasis::restoreInitialBasis(), and SPxBasis::setOutstream().

void loadSolver	(	SLinSolver *	solver,
		const bool	destroy = `false`
	)

virtual

sets up linear solver to use.

If destroy is true, solver will be freed inside this object, e.g. in the destructor.

Definition at line 319 of file spxbasis.cpp.

References SLinSolver::clear(), SPxBasis::factor, SPxBasis::factorized, SPxBasis::freeSlinSolver, MSG_INFO3, SPxBasis::setOutstream(), SLinSolver::spxout, and SPxBasis::spxout.

Referenced by SPxBasis::coSolve(), and SPxSolver::setSolver().

Vector & multBaseWith ( Vector & x ) const

Basis-vector product.

Depending on the representation, for an SPxBasis B, B.multBaseWith(x) computes

$x \leftarrow Bx$ in the columnwise case, and
$x \leftarrow x^TB$ in the rowwise case.

Both can be seen uniformly as multiplying the basis matrix B with a vector x aligned the same way as the vectors of B.

Definition at line 931 of file spxbasis.cpp.

References VectorBase< R >::clear(), VectorBase< R >::dim(), SPxSolver::dim(), SPxBasis::matrix, SPxBasis::matrixIsSetup, VectorBase< R >::multAdd(), SPxBasis::SINGULAR, SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::condition(), SPxSolver::enter(), SPxSolver::factorize(), SPxSolver::leave(), SPxBasis::solver(), and SPxSolver::testVecs().

void multBaseWith	(	SSVector &	x,
		SSVector &	result
	)		const

Basis-vector product.

Definition at line 954 of file spxbasis.cpp.

References SSVectorBase< R >::clear(), SSVectorBase< R >::dim(), SPxSolver::dim(), SPxBasis::matrix, SPxBasis::matrixIsSetup, SSVectorBase< R >::multAdd(), SPxBasis::SINGULAR, SSVectorBase< R >::size(), SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

Vector & multWithBase ( Vector & x ) const

Vector-basis product.

Depending on the representation, for a SPxBasis B, B.multWithBase(x) computes

$x \leftarrow x^TB$ in the columnwise case and
$x \leftarrow Bx$ in the rowwise case.

Both can be seen uniformly as multiplying the basis matrix B with a vector x aligned the same way as the covectors of B.

Definition at line 894 of file spxbasis.cpp.

References VectorBase< R >::dim(), SPxSolver::dim(), SPxBasis::matrix, SPxBasis::matrixIsSetup, SPxBasis::SINGULAR, SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::condition(), SPxSolver::factorize(), SPxBasis::solver(), and SPxSolver::testVecs().

void multWithBase	(	SSVector &	x,
		SSVector &	result
	)		const

Vector-basis product.

Definition at line 913 of file spxbasis.cpp.

References SSVectorBase< R >::dim(), SPxSolver::dim(), SPxBasis::matrix, SPxBasis::matrixIsSetup, SSVectorBase< R >::setValue(), SPxBasis::SINGULAR, SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

SPxBasis & operator= ( const SPxBasis & rhs )

assignment operator

Warning: Note that we do not create a deep copy of the corresponding SPxSolver object. Only the reference to that object is copied.

Definition at line 1227 of file spxbasis.cpp.

References SLinSolver::clone(), SPxBasis::factor, SPxBasis::factorized, SPxBasis::fillFactor, SPxBasis::freeSlinSolver, SPxBasis::isConsistent(), SPxBasis::iterCount, SPxBasis::lastFill, SPxBasis::lastidx, SPxBasis::lastin, SPxBasis::lastNzCount, SPxBasis::lastout, SPxBasis::matrix, SPxBasis::matrixIsSetup, SPxBasis::maxUpdates, SPxBasis::minStab, SPxBasis::nonzeroFactor, SPxBasis::nzCount, SPxBasis::theBaseId, SPxBasis::thedesc, SPxBasis::theLP, and SPxBasis::thestatus.

Referenced by SPxSolver::operator=().

void printMatrix ( ) const

virtual

Definition at line 673 of file spxbasis.cpp.

References SPxBasis::matrix, and SPxBasis::matrixIsSetup.

Referenced by SPxBasis::coSolve().

void printMatrixMTX ( int number )

Prints current basis matrix to a file using the MatrixMarket format: row col value The filename is basis/basis[number].mtx where number is a parameter.

Definition at line 684 of file spxbasis.cpp.

References SPxBasis::baseVec(), SVectorBase< R >::index(), SPxBasis::matrix, SPxBasis::nzCount, REAL_FORMAT, SVectorBase< R >::size(), and SVectorBase< R >::value().

Referenced by SPxBasis::coSolve().

bool readBasis	(	std::istream &	is,
		const NameSet *	rowNames,
		const NameSet *	colNames
	)

virtual

Load basis from in in MPS format. If rowNames and colNames are NULL, default names are used for the constraints and variables.

The specification is taken from the

ILOG CPLEX 7.0 Reference Manual, Appendix E, Page 543.

This routine should read valid BAS format files.

Returns: true if the file was read correctly.

Here is a very brief outline of the format:

The format is in a form similar to an MPS file. The basic assumption is that all (column) variables are nonbasic at their lower bound and all row (variables) are basic; only the differences to this rule are given. Each data line contains an indicator, a variable name and possibly a row/constraint name. The following meaning applies with respect to the indicators:

XU: the variable is basic, the row is nonbasic at its upper bound
XL: the variable is basic, the row is nonbasic at its lower bound
UL: the variable is nonbasic and at its upper bound
LL: the variable is nonbasic and at its lower bound

The CPLEX format contains an additional indicator 'BS', but this is unsupported here.

Nonbasic variables without lower bound have the following default status for SoPlex:

at their upper bound if finite,
at zero if free.

Definition at line 372 of file spxbasis.cpp.

References NameSet::add(), SPxSolver::colId(), SPxBasis::Desc::colstat, SPxBasis::dualColStatus(), SPxBasis::dualRowStatus(), SPxBasis::Desc::dump(), MPSInput::ENDATA, LPRowBase< R >::EQUAL, MPSInput::field0(), MPSInput::field1(), MPSInput::field2(), MPSInput::field3(), LPRowBase< R >::GREATER_EQUAL, MPSInput::hasError(), soplex::infinity, LPRowBase< R >::LESS_EQUAL, SPxBasis::load(), SPxBasis::loadDesc(), MSG_DEBUG, SPxLPBase< R >::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), NameSet::number(), SPxBasis::Desc::P_FIXED, SPxBasis::Desc::P_FREE, SPxBasis::Desc::P_ON_LOWER, SPxBasis::Desc::P_ON_UPPER, MPSInput::readLine(), SPxBasis::REGULAR, NameSet::reMax(), SPxSolver::rowId(), SPxBasis::Desc::rowstat, MPSInput::section(), MPSInput::setSection(), SPxBasis::setStatus(), soplex::spx_alloc(), soplex::spx_free(), SPxBasis::status(), MPSInput::syntaxError(), SPxBasis::thedesc, SPxBasis::theLP, and NameSet::~NameSet().

Referenced by SPxBasis::coSolve(), and SPxSolver::readBasisFile().

void reDim ( )

protected

resizes internal arrays.

When a new LP is loaded, the basis matrix and vectors become invalid and possibly also of the wrong dimension. Hence, after loading an LP, reDim() is called to reset all arrays etc. accoriding to the dimensions of the loaded LP.

Definition at line 26 of file spxchangebasis.cpp.

References SPxSolver::dim(), SPxBasis::factorized, SPxBasis::matrix, SPxBasis::matrixIsSetup, MSG_DEBUG, MSG_INFO3, SPxLPBase< R >::nCols(), SPxLPBase< R >::nRows(), SPxBasis::Desc::reSize(), SPxBasis::spxout, SPxBasis::theBaseId, SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxSolver::clear(), SPxBasis::removedCol(), SPxBasis::removedCols(), SPxBasis::removedRow(), SPxBasis::removedRows(), SPxBasis::setOutstream(), and SPxBasis::setRep().

void removedCol ( int i )

inform SPxBasis that column i had been removed.

Definition at line 314 of file spxchangebasis.cpp.

References SPxBasis::baseId(), SPxBasis::Desc::colStatus(), SPxSolver::COLUMN, SPxSolver::dim(), SPxBasis::factorized, SPxSolver::isBasic(), SPxBasis::matrix, SPxBasis::matrixIsSetup, SPxLPBase< R >::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::number(), SPxBasis::reDim(), SPxSolver::rep(), SPxSolver::ROW, SPxBasis::setStatus(), SPxBasis::status(), SPxBasis::thedesc, SPxBasis::theLP, and SPxSolver::vector().

Referenced by SPxBasis::coSolve(), and SPxSolver::doRemoveCol().

void removedCols ( const int perm[] )

inform SPxBasis that columns in perm with negative entry were removed.

Definition at line 352 of file spxchangebasis.cpp.

References SPxBasis::Desc::colStatus(), SPxSolver::COLUMN, SPxBasis::factorized, SPxSolver::isBasic(), SPxBasis::matrixIsSetup, SPxBasis::Desc::nCols(), SPxBasis::NO_PROBLEM, SPxBasis::reDim(), SPxSolver::rep(), SPxSolver::ROW, SPxBasis::setStatus(), SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::coSolve(), and SPxSolver::doRemoveCols().

void removedRow ( int i )

inform SPxBasis that row i had been removed.

Definition at line 119 of file spxchangebasis.cpp.

References SPxBasis::baseId(), SPxSolver::COLUMN, SPxSolver::dim(), SPxBasis::factorized, SPxSolver::isBasic(), SPxBasis::matrix, SPxBasis::matrixIsSetup, MSG_DEBUG, SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxLPBase< R >::number(), SPxBasis::reDim(), SPxSolver::rep(), SPxSolver::ROW, SPxBasis::Desc::rowStatus(), SPxBasis::setStatus(), SPxBasis::status(), SPxBasis::thedesc, SPxBasis::theLP, and SPxSolver::vector().

Referenced by SPxBasis::coSolve(), and SPxSolver::doRemoveRow().

void removedRows ( const int perm[] )

inform SPxBasis that rows in perm with negative entry were removed.

Definition at line 165 of file spxchangebasis.cpp.

References SPxSolver::COLUMN, SPxBasis::factorized, SPxSolver::isBasic(), SPxBasis::matrixIsSetup, MSG_DEBUG, SPxBasis::NO_PROBLEM, SPxBasis::Desc::nRows(), SPxBasis::reDim(), SPxSolver::rep(), SPxSolver::ROW, SPxBasis::Desc::rowStatus(), SPxBasis::setStatus(), SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::coSolve(), and SPxSolver::doRemoveRows().

void restoreInitialBasis ( )

Restores initial basis.

This method changes the basis to that present just after loading the LP (see addedRows() and addedCols()). This may be necessary if a row or a column is changed, since then the current basis may become singular.

Create the initial slack basis descriptor and set up the basis matrix accordingly. This code has been adapted from SPxBasis::addedRows() and SPxBasis::addedCols().

Definition at line 415 of file spxchangebasis.cpp.

References SPxBasis::baseId(), SPxBasis::Desc::colStatus(), SPxSolver::COLUMN, SPxBasis::dualRowStatus(), SPxBasis::factorized, SPxBasis::loadMatrixVecs(), SPxBasis::matrixIsSetup, SPxLPBase< R >::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), soplex::primalColStatus(), SPxBasis::REGULAR, SPxSolver::rep(), SPxSolver::ROW, SPxBasis::Desc::rowStatus(), SPxBasis::setStatus(), SPxBasis::status(), SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxBasis::changedCol(), SPxBasis::changedElement(), SPxBasis::changedRow(), SPxBasis::load(), SPxBasis::loadDesc(), and SPxBasis::unLoad().

void setMaxUpdates ( int maxUp )

change maximum number of iterations until a refactorization is performed

Definition at line 444 of file spxbasis.h.

Referenced by SoPlex::setIntParam().

void setOutstream ( SPxOut & newOutstream )

Definition at line 872 of file spxbasis.h.

References SPxBasis::factorize(), SPxBasis::loadMatrixVecs(), SPxBasis::Desc::operator<<, SPxBasis::Desc::operator=(), SPxBasis::reDim(), SPxBasis::setRep(), SPxBasis::Desc::SPxBasis, SPxBasis::Desc::status(), Timer::USER_TIME, and SPxBasis::~SPxBasis().

Referenced by SPxBasis::load(), and SPxBasis::loadSolver().

void setRep ( )

protected

sets descriptor representation according to loaded LP.

Definition at line 286 of file spxbasis.cpp.

References SPxBasis::Desc::colstat, SPxBasis::Desc::costat, SPxBasis::minStab, SPxBasis::reDim(), SPxSolver::rep(), SPxSolver::ROW, SPxBasis::Desc::rowstat, SPxBasis::Desc::stat, SPxBasis::thedesc, and SPxBasis::theLP.

Referenced by SPxSolver::initRep(), SPxBasis::load(), SPxBasis::loadDesc(), and SPxBasis::setOutstream().

void setStatus ( SPxStatus stat )

sets basis SPxStatus to stat.

Definition at line 425 of file spxbasis.h.

References SPxBasis::invalidate(), MSG_DEBUG, and SPxBasis::NO_PROBLEM.

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxBasis::factorize(), SPxBasis::readBasis(), SPxBasis::removedCol(), SPxBasis::removedCols(), SPxBasis::removedRow(), SPxBasis::removedRows(), SPxBasis::restoreInitialBasis(), and SPxBasis::unLoad().

void solve	(	Vector &	x,
		const Vector &	rhs
	)

Definition at line 605 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveRight().

Referenced by SPxSolver::addedRows(), SPxSolver::factorize(), SoPlex::getBasisInverseColReal(), SoPlex::getBasisInverseRowReal(), SoPlex::getBasisInverseTimesVecReal(), SPxSolver::init(), SPxSolver::leave(), SPxSolver::reinitializeVecs(), SPxSolver::terminate(), and SPxSolver::testVecs().

void solve	(	SSVector &	x,
		const SVector &	rhs
	)

Definition at line 612 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveRight().

void solve4update	(	SSVector &	x,
		const SVector &	rhs
	)

solves linear system with basis matrix.

Depending on the representation, for a SPxBasis B, B.solve(x) computes

$x \leftarrow B^{-1}rhs$ in the columnwise case and
$x \leftarrow rhs^TB^{-1}$ in the rowwise case.

Both can be seen uniformly as solving a linear system with the basis matrix B and a right handside vector x aligned the same way as the vectors of B.

Definition at line 628 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solveRight4update().

Referenced by SPxSolver::enter(), SPxSolver::leave(), and SPxSteepPR::selectEnter().

void solve4update	(	SSVector &	x,
		Vector &	y,
		const SVector &	rhsx,
		SSVector &	rhsy
	)

solves two systems in one call.

Definition at line 635 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solve2right4update().

void solve4update	(	SSVector &	x,
		SSVector &	y,
		const SVector &	rhsx,
		SSVector &	rhsy
	)

solves two systems in one call using only sparse data structures

Definition at line 642 of file spxbasis.h.

References SPxBasis::factorize(), and SLinSolver::solve2right4update().

void solve4update	(	SSVector &	x,
		Vector &	y,
		Vector &	y2,
		const SVector &	rhsx,
		SSVector &	rhsy,
		SSVector &	rhsy2
	)

solves three systems in one call.

Definition at line 649 of file spxbasis.h.

References SPxBasis::factorize(), SSVectorBase< R >::isSetup(), and SLinSolver::solve3right4update().

void solve4update	(	SSVector &	x,
		SSVector &	y,
		SSVector &	y2,
		const SVector &	rhsx,
		SSVector &	rhsy,
		SSVector &	rhsy2
	)

solves three systems in one call using only sparse data structures

Definition at line 659 of file spxbasis.h.

References SPxBasis::factorize(), SSVectorBase< R >::isSetup(), and SLinSolver::solve3right4update().

SPxSolver* solver ( ) const

returns loaded solver.

Definition at line 544 of file spxbasis.h.

References SPxBasis::condition(), SPxBasis::multBaseWith(), SPxBasis::multWithBase(), and SPxBasis::theLP.

Referenced by SPxBasis::coSolve(), and SPxSolver::init().

Real stability ( ) const

returns the stability of the basis matrix.

Definition at line 600 of file spxbasis.h.

References SLinSolver::stability().

Referenced by SPxFastRT::selectLeave().

std::string statistics ( ) const

returns statistical information in form of a string.

Definition at line 859 of file spxbasis.h.

References SPxBasis::getTotalUpdateCount(), SPxBasis::getTotalUpdateTime(), and SLinSolver::statistics().

SPxStatus status ( void ) const

returns current SPxStatus.

Definition at line 419 of file spxbasis.h.

References SPxBasis::thestatus.

virtual void unLoad ( )

virtual

unloads the LP from the basis.

Definition at line 822 of file spxbasis.h.

References SPxBasis::Desc::dump(), SPxBasis::invalidate(), SPxBasis::Desc::isConsistent(), SPxBasis::NO_PROBLEM, SPxBasis::restoreInitialBasis(), and SPxBasis::setStatus().

Referenced by SPxSolver::loadLP(), SPxSolver::read(), and SPxSolver::reLoad().

void writeBasis	(	std::ostream &	os,
		const NameSet *	rownames,
		const NameSet *	colnames,
		const bool	cpxFormat = `false`
	)		const

virtual

Write basis to os in MPS format. If rowNames and colNames are NULL, default names are used for the constraints and variables.

Definition at line 589 of file spxbasis.cpp.

References SPxBasis::Desc::colStatus(), SPxBasis::Desc::dump(), soplex::getColName(), soplex::getRowName(), soplex::infinity, SPxLPBase< R >::lower(), MSG_DEBUG, SPxLPBase< R >::nCols(), SPxBasis::NO_PROBLEM, SPxLPBase< R >::nRows(), SPxBasis::Desc::P_FIXED, SPxBasis::Desc::P_FREE, SPxBasis::Desc::P_ON_LOWER, SPxBasis::Desc::P_ON_UPPER, LPRowBase< R >::RANGE, SPxBasis::Desc::rowStatus(), SPxBasis::status(), SPxBasis::thedesc, SPxBasis::theLP, and SPxLPBase< R >::upper().

Referenced by SPxBasis::coSolve(), and SPxSolver::writeBasisFile().

Member Data Documentation

SLinSolver* factor

protected

Definition at line 355 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::condition(), SPxBasis::factorize(), SPxBasis::isConsistent(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::loadSolver(), SPxBasis::operator=(), SPxBasis::SPxBasis(), and SPxBasis::~SPxBasis().

bool factorized

protected

true iff factor = matrix $^{-1}$ .

Definition at line 357 of file spxbasis.h.

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxBasis::change(), SPxBasis::factorize(), SPxSolver::init(), SPxBasis::invalidate(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::loadSolver(), SPxBasis::operator=(), SPxBasis::reDim(), SPxBasis::removedCol(), SPxBasis::removedCols(), SPxBasis::removedRow(), SPxBasis::removedRows(), SPxBasis::restoreInitialBasis(), and SPxSolver::setType().

Real fillFactor

protected

allowed increase in realtive fill before refactorization

When the real relative fill is bigger than fillFactor times lastFill the Basis will be refactorized.

Definition at line 379 of file spxbasis.h.

Referenced by SPxBasis::factorize(), and SPxBasis::operator=().

bool freeSlinSolver

private

true iff factor should be freed inside of this object

Definition at line 408 of file spxbasis.h.

Referenced by SPxBasis::loadSolver(), SPxBasis::operator=(), SPxBasis::SPxBasis(), and SPxBasis::~SPxBasis().

int iterCount

protected

number of calls to change() since last manipulation

Definition at line 384 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::iteration(), SPxBasis::loadDesc(), SPxBasis::operator=(), SPxSolver::solve(), and SPxSolver::testBounds().

Real lastFill

protected

fill ratio that occured during last factorization

Definition at line 389 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::factorize(), and SPxBasis::operator=().

int lastidx

protected

lastIndex(): basis index where last update was done

Definition at line 397 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::lastIndex(), SPxBasis::loadDesc(), and SPxBasis::operator=().

SPxId lastin

protected

lastEntered(): variable entered the base last

Definition at line 395 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::lastEntered(), SPxBasis::loadDesc(), and SPxBasis::operator=().

int lastMem

protected

memory needed after last fresh factorization

Definition at line 388 of file spxbasis.h.

Referenced by SPxBasis::factorize().

int lastNzCount

protected

number of nonzeros in basis matrix after last fresh factorization

Definition at line 390 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::factorize(), and SPxBasis::operator=().

SPxId lastout

protected

lastLeft(): variable left the base last

Definition at line 396 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::lastLeft(), SPxBasis::loadDesc(), and SPxBasis::operator=().

DataArray< const SVector* > matrix

protected

pointers to the vectors of the basis matrix.

Definition at line 347 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::condition(), SPxBasis::dump(), SPxBasis::factorize(), SPxBasis::isConsistent(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::multBaseWith(), SPxBasis::multWithBase(), SPxBasis::operator=(), SPxBasis::printMatrix(), SPxBasis::printMatrixMTX(), SPxBasis::reDim(), SPxBasis::removedCol(), and SPxBasis::removedRow().

bool matrixIsSetup

protected

true iff the pointers in matrix are set up correctly.

Definition at line 349 of file spxbasis.h.

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxBasis::change(), SPxBasis::condition(), SPxBasis::factorize(), SPxSolver::init(), SPxBasis::invalidate(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::multBaseWith(), SPxBasis::multWithBase(), SPxBasis::operator=(), SPxBasis::printMatrix(), SPxBasis::reDim(), SPxBasis::removedCol(), SPxBasis::removedCols(), SPxBasis::removedRow(), SPxBasis::removedRows(), SPxBasis::restoreInitialBasis(), SPxSolver::setType(), and SPxSolver::solve().

int maxUpdates

protected

number of updates before refactorization.

When a vector of the basis matrix is exchanged by a call to method change(), the LU factorization of the matrix is updated accordingly. However, after atmost maxUpdates updates of the factorization, it is recomputed in order to regain numerical stability and reduce fill in.

Definition at line 366 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::getMaxUpdates(), and SPxBasis::operator=().

Real minStab

protected

minimum stability

Definition at line 398 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::factorize(), SPxBasis::operator=(), and SPxBasis::setRep().

Real nonzeroFactor

protected

allowed increase of nonzeros before refactorization.

When the number of nonzeros in LU factorization exceeds nonzeroFactor times the number of nonzeros in B, the basis matrix is refactorized.

Definition at line 373 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::factorize(), and SPxBasis::operator=().

int nzCount

protected

number of nonzeros in basis matrix

Definition at line 387 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::factorize(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::operator=(), and SPxBasis::printMatrixMTX().

SPxOut* spxout

private

message handler

Definition at line 409 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::invalidate(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::loadSolver(), and SPxBasis::reDim().

DataArray< SPxId > theBaseId

protected

SPxIds of basic vectors.

Definition at line 345 of file spxbasis.h.

Referenced by SPxBasis::change(), SPxBasis::isConsistent(), SPxBasis::loadDesc(), SPxBasis::operator=(), and SPxBasis::reDim().

Desc thedesc

private

SPxSolver* theLP

protected

the LP

For storing the basis matrix we keep two arrays: Array theBaseId contains the SPxIds of the basis vectors, and matrix the pointers to the vectors themselfes. Method loadMatrixVecs() serves for loading matrix according to the SPxIds stored in theBaseId. This method must be called whenever the vector pointers may have changed due to manipulations of the LP.

Definition at line 343 of file spxbasis.h.

Referenced by SPxBasis::addedCols(), SPxBasis::addedRows(), SPxSolver::clear(), SPxBasis::dualColStatus(), SPxBasis::dualRowStatus(), SPxBasis::dualStatus(), SPxBasis::dump(), SPxBasis::isConsistent(), SPxBasis::isDescValid(), SPxBasis::load(), SPxBasis::loadDesc(), SPxBasis::loadMatrixVecs(), SPxBasis::multBaseWith(), SPxBasis::multWithBase(), SPxBasis::operator=(), SPxSolver::operator=(), SPxSolver::read(), SPxBasis::readBasis(), SPxBasis::reDim(), SPxSolver::reLoad(), SPxBasis::removedCol(), SPxBasis::removedCols(), SPxBasis::removedRow(), SPxBasis::removedRows(), SPxBasis::restoreInitialBasis(), SPxBasis::setRep(), SPxBasis::solver(), SPxSolver::SPxSolver(), and SPxBasis::writeBasis().