Basis descriptor. More...

#include <spxbasis.h>

Public Types

enum	Status { P_ON_LOWER = -4, P_ON_UPPER = -2, P_FREE = -1, P_FIXED = P_ON_UPPER + P_ON_LOWER, D_FREE = 1, D_ON_UPPER = 2, D_ON_LOWER = 4, D_ON_BOTH = D_ON_LOWER + D_ON_UPPER, D_UNDEFINED = 8 }
	Status of a variable. More...

Public Member Functions

int	nCols () const
	returns number of columns.

int	nRows () const
	returns number of rows.

int	dim () const
	returns dimension.

int	coDim () const
	returns codimension.

Status &	rowStatus (int i)

Status	rowStatus (int i) const
	returns status of row `i`.

const Status *	rowStatus (void) const
	returns the array of row Statuses.

Status &	colStatus (int i)

Status	colStatus (int i) const
	returns status of column `i`.

const Status *	colStatus (void) const
	returns the array of column Statuses.

Status &	status (int i)

Status	status (int i) const
	returns status of variable `i`.

const Status *	status (void) const
	returns the array of variable Statuses.

Status &	coStatus (int i)

Status	coStatus (int i) const
	returns status of covariable `i`.

const Status *	coStatus (void) const
	returns the array of covariable Statuses.

void	reSize (int rowDim, int colDim)
	resets dimensions.


void	dump () const
	Prints out status.

bool	isConsistent () const
	consistency check.


	Desc ()
	default constructor

	Desc (const SPxSolver &base)

	Desc (const Desc &old)
	copy constructor

Desc &	operator= (const Desc &rhs)
	assignment operator

Private Attributes

DataArray< Status >	rowstat
	status of rows.

DataArray< Status >	colstat
	status of columns.

DataArray< Status > *	stat
	basis' status.

DataArray< Status > *	costat
	cobasis' status.

Friends
class	SPxBasis

std::ostream &	operator<< (std::ostream &os, const Status &stat)

Detailed Description

Basis descriptor.

Definition at line 98 of file spxbasis.h.

Member Enumeration Documentation

enum Status

Status of a variable.

    A basis is described by assigning a Status to all of the LP
    variables and covariables. This assignment is maintained by the
    basis #Desc%riptor.

    Variables and covariables may have a primal or dual Status. The
    first type specifies that a variable is set on a primal bound, while
    the latter type indicates a dual variable to be set on a bound.
    If a row variable has a primal status, say #P_ON_UPPER, this means
    that the upper bound of the inequality is set to be tight. Hence,
    in this case the upper bound must not be infinity.

    Equivalently, if the status of a variable is dual, say #D_ON_UPPER,
    it means that the dual variable corresponding to the upper bound
    inequality of this variable is set to 0.

    For a column basis, primal #Status%es correspond to nonbasic
    variables, while dual ones are basic. This is reversed for a row
    basis. We will now reveal in more detail the significance of
    variable #Status%es.

    <b>Primal Variables</b>

    Consider a range inequality \form#36 or bounds on
    a variable \form#37. The following table reveals
    what is implied if the corresponding variable or covariable is
    assigned to a primal #Status:

$\begin{array}{lcl} l_c \le x_c \le u_c & \mbox{Status}(x_i) & l_r \le a^T x \le u_r \\ \hline x_c = u_c < \infty & \mbox{P\_ON\_UPPER} & a^T x = u_r < \infty \\ x_c = l_c > -\infty & \mbox{P\_ON\_LOWER} & a^T x = l_r > -\infty \\ -\infty < l_c = x_c = u_c < \infty & \mbox{P\_FIXED} & -\infty < l_r = a^T x = u_r < \infty \\ -\infty = l_i < x_i=0 < u_i = \infty & \mbox{P\_FREE} & -\infty = l_r < a^T x = 0 < u_r = \infty \\ \end{array}$

    Note that to determine whether a variable with #Status stat is set to
    its upper bound, one can compute the test (-stat | -#P_ON_UPPER).
    This will yield true even if the variable is fixed, i.e., sitting on
    both bounds at the same time.

    <b>Dual Variables</b>

    In principle for implementing the Simplex algorithm it would suffice
    to use only one dual #Status. However, for performance reasons it
    is advisable to introduce various dual status types, reflecting
    the structure of the bounds. Given an upper bound \form#39 and a lower
    bound \form#40 of a constraint or variable, the following table 
    indicates the setting of the dual Status of this variable.

$\begin{array}{cl} l \le ... \le u & \mbox{Status} \\ \hline -\infty < l \ne u < \infty & \mbox{D\_ON\_BOTH} \\ -\infty < l \ne u = \infty & \mbox{D\_ON\_UPPER} \\ -\infty = l \ne u < \infty & \mbox{D\_ON\_LOWER} \\ -\infty < l = u < \infty & \mbox{D\_FREE} \\ -\infty = l \ne u = \infty & \mbox{D\_UNDEFINED} \\ \end{array}$

    Note that unbounded primal variables are reflected by an #D_UNDEFINED
    dual variable, since no dual variables exist for them. To facilitate
    the assignment of dual #Status%es, class SPxBasis provides methods
    #dualStatus(), #dualColStatus() and #dualRowStatus)().

Enumerator
P_ON_LOWER	primal variable is set to its lower bound
P_ON_UPPER	primal variable is set to its upper bound
P_FREE	primal variable is left free, but unset
P_FIXED	primal variable is fixed to both bounds
D_FREE	dual variable is left free, but unset
D_ON_UPPER	dual variable is set to its upper bound
D_ON_LOWER	dual variable is set to its lower bound
D_ON_BOTH	dual variable has two bounds
D_UNDEFINED	primal or dual variable has no status