soplex.cpp

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the class library                   */
/*       SoPlex --- the Sequential object-oriented simPlex.                  */
/*                                                                           */
/*    Copyright (C) 1996-2019 Konrad-Zuse-Zentrum                            */
/*                            fuer Informationstechnik Berlin                */
/*                                                                           */
/*  SoPlex is distributed under the terms of the ZIB Academic Licence.       */
/*                                                                           */
/*  You should have received a copy of the ZIB Academic License              */
/*  along with SoPlex; see the file COPYING. If not email to soplex@zib.de.  */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file  soplex.cpp
 * @brief Preconfigured SoPlex LP solver
 */

#include <assert.h>
#include "limits.h"
#include <iostream>

#ifndef _MSC_VER
#include <strings.h>
#endif

#include "soplex.h"
#include "soplex/spxfileio.h"
#include "soplex/statistics.h"
#include "soplex/mpsinput.h"

/// maximum length of lines in settings file
#define SET_MAX_LINE_LEN 500
/// default setting for LU refactorization interval
#define DEFAULT_REFACTOR_INTERVAL 200

#ifdef _MSC_VER
#define strncasecmp _strnicmp
#endif

namespace soplex
{
SoPlex::Settings::BoolParam::BoolParam()
{
   // should lifting be used to reduce range of nonzero matrix coefficients?
   name[SoPlex::LIFTING] = "lifting";
   description[SoPlex::LIFTING] =
      "should lifting be used to reduce range of nonzero matrix coefficients?";
   defaultValue[SoPlex::LIFTING] = false;

   // should LP be transformed to equality form before a rational solve?
   name[SoPlex::EQTRANS] = "eqtrans";
   description[SoPlex::EQTRANS] = "should LP be transformed to equality form before a rational solve?";
   defaultValue[SoPlex::EQTRANS] = false;

   // should dual infeasibility be tested in order to try to return a dual solution even if primal infeasible?
   name[SoPlex::TESTDUALINF] = "testdualinf";
   description[SoPlex::TESTDUALINF] =
      "should dual infeasibility be tested in order to try to return a dual solution even if primal infeasible?";
   defaultValue[SoPlex::TESTDUALINF] = false;

   // should a rational factorization be performed after iterative refinement?
   name[SoPlex::RATFAC] = "ratfac";
   description[SoPlex::RATFAC] =
      "should a rational factorization be performed after iterative refinement?";
   defaultValue[SoPlex::RATFAC] = true;

   // should the decomposition based dual simplex be used to solve the LP? Setting this to true forces the solve mode to
   // SOLVEMODE_REAL and the basis representation to REPRESENTATION_ROW
   name[SoPlex::USEDECOMPDUALSIMPLEX] = "decompositiondualsimplex";
   description[SoPlex::USEDECOMPDUALSIMPLEX] =
      "should the decomposition based dual simplex be used to solve the LP?";
   defaultValue[SoPlex::USEDECOMPDUALSIMPLEX] = false;

   // should the degeneracy be computed for each basis?
   name[SoPlex::COMPUTEDEGEN] = "computedegen";
   description[SoPlex::COMPUTEDEGEN] = "should the degeneracy be computed for each basis?";
   defaultValue[SoPlex::COMPUTEDEGEN] = false;

   // should the dual of the complementary problem be used in the decomposition simplex?
   name[SoPlex::USECOMPDUAL] = "usecompdual";
   description[SoPlex::USECOMPDUAL] =
      "should the dual of the complementary problem be used in the decomposition simplex?";
   defaultValue[SoPlex::USECOMPDUAL] = false;

   /// should row and bound violations be computed explicitly in the update of reduced problem in the decomposition
   // simplex
   name[SoPlex::EXPLICITVIOL] = "explicitviol";
   description[SoPlex::EXPLICITVIOL] =
      "Should violations of the original problem be explicitly computed in the decomposition simplex?";
   defaultValue[SoPlex::EXPLICITVIOL] = false;

   // should cycling solutions be accepted during iterative refinement?
   name[SoPlex::ACCEPTCYCLING] = "acceptcycling";
   description[SoPlex::ACCEPTCYCLING] =
      "should cycling solutions be accepted during iterative refinement?";
   defaultValue[SoPlex::ACCEPTCYCLING] = false;

   // apply rational reconstruction after each iterative refinement?
   name[SoPlex::RATREC] = "ratrec";
   description[SoPlex::RATREC] = "apply rational reconstruction after each iterative refinement?";
   defaultValue[SoPlex::RATREC] = true;

   // round scaling factors for iterative refinement to powers of two?
   name[SoPlex::POWERSCALING] = "powerscaling";
   description[SoPlex::POWERSCALING] =
      "round scaling factors for iterative refinement to powers of two?";
   defaultValue[SoPlex::POWERSCALING] = true;

   // continue iterative refinement with exact basic solution if not optimal?
   name[SoPlex::RATFACJUMP] = "ratfacjump";
   description[SoPlex::RATFACJUMP] =
      "continue iterative refinement with exact basic solution if not optimal?";
   defaultValue[SoPlex::RATFACJUMP] = false;

   // use bound flipping also for row representation?
   name[SoPlex::ROWBOUNDFLIPS] = "rowboundflips";
   description[SoPlex::ROWBOUNDFLIPS] = "use bound flipping also for row representation?";
   defaultValue[SoPlex::ROWBOUNDFLIPS] = false;

   // use persistent scaling?
   name[SoPlex::PERSISTENTSCALING] = "persistentscaling";
   description[SoPlex::PERSISTENTSCALING] = "should persistent scaling be used?";
   defaultValue[SoPlex::PERSISTENTSCALING] = true;

   // perturb the entire problem or only the relevant bounds of s single pivot?
   name[SoPlex::FULLPERTURBATION] = "fullperturbation";
   description[SoPlex::FULLPERTURBATION] = "should perturbation be applied to the entire problem?";
   defaultValue[SoPlex::FULLPERTURBATION] = false;

   /// re-optimize the original problem to get a proof of infeasibility/unboundedness?
   name[SoPlex::ENSURERAY] = "ensureray";
   description[SoPlex::ENSURERAY] =
      "re-optimize the original problem to get a proof (ray) of infeasibility/unboundedness?";
   defaultValue[SoPlex::ENSURERAY] = false;
}

SoPlex::Settings::IntParam::IntParam()
{
   // objective sense
   name[SoPlex::OBJSENSE] = "objsense";
   description[SoPlex::OBJSENSE] = "objective sense (-1 - minimize, +1 - maximize)";
   lower[SoPlex::OBJSENSE] = -1;
   upper[SoPlex::OBJSENSE] = 1;
   defaultValue[SoPlex::OBJSENSE] = SoPlex::OBJSENSE_MAXIMIZE;

   // type of computational form, i.e., column or row representation
   name[SoPlex::REPRESENTATION] = "representation";
   description[SoPlex::REPRESENTATION] =
      "type of computational form (0 - auto, 1 - column representation, 2 - row representation)";
   lower[SoPlex::REPRESENTATION] = 0;
   upper[SoPlex::REPRESENTATION] = 2;
   defaultValue[SoPlex::REPRESENTATION] = SoPlex::REPRESENTATION_AUTO;

   // type of algorithm, i.e., primal or dual
   name[SoPlex::ALGORITHM] = "algorithm";
   description[SoPlex::ALGORITHM] = "type of algorithm (0 - primal, 1 - dual)";
   lower[SoPlex::ALGORITHM] = 0;
   upper[SoPlex::ALGORITHM] = 1;
   defaultValue[SoPlex::ALGORITHM] = SoPlex::ALGORITHM_DUAL;

   // type of LU update
   name[SoPlex::FACTOR_UPDATE_TYPE] = "factor_update_type";
   description[SoPlex::FACTOR_UPDATE_TYPE] =
      "type of LU update (0 - eta update, 1 - Forrest-Tomlin update)";
   lower[SoPlex::FACTOR_UPDATE_TYPE] = 0;
   upper[SoPlex::FACTOR_UPDATE_TYPE] = 1;
   defaultValue[SoPlex::FACTOR_UPDATE_TYPE] = SoPlex::FACTOR_UPDATE_TYPE_FT;

   // maximum number of updates without fresh factorization
   name[SoPlex::FACTOR_UPDATE_MAX] = "factor_update_max";
   description[SoPlex::FACTOR_UPDATE_MAX] =
      "maximum number of LU updates without fresh factorization (0 - auto)";
   lower[SoPlex::FACTOR_UPDATE_MAX] = 0;
   upper[SoPlex::FACTOR_UPDATE_MAX] = INT_MAX;
   defaultValue[SoPlex::FACTOR_UPDATE_MAX] = 0;

   // iteration limit (-1 if unlimited)
   name[SoPlex::ITERLIMIT] = "iterlimit";
   description[SoPlex::ITERLIMIT] = "iteration limit (-1 - no limit)";
   lower[SoPlex::ITERLIMIT] = -1;
   upper[SoPlex::ITERLIMIT] = INT_MAX;
   defaultValue[SoPlex::ITERLIMIT] = -1;

   // refinement limit (-1 if unlimited)
   name[SoPlex::REFLIMIT] = "reflimit";
   description[SoPlex::REFLIMIT] = "refinement limit (-1 - no limit)";
   lower[SoPlex::REFLIMIT] = -1;
   upper[SoPlex::REFLIMIT] = INT_MAX;
   defaultValue[SoPlex::REFLIMIT] = -1;

   // stalling refinement limit (-1 if unlimited)
   name[SoPlex::STALLREFLIMIT] = "stallreflimit";
   description[SoPlex::STALLREFLIMIT] = "stalling refinement limit (-1 - no limit)";
   lower[SoPlex::STALLREFLIMIT] = -1;
   upper[SoPlex::STALLREFLIMIT] = INT_MAX;
   defaultValue[SoPlex::STALLREFLIMIT] = -1;

   // display frequency
   name[SoPlex::DISPLAYFREQ] = "displayfreq";
   description[SoPlex::DISPLAYFREQ] = "display frequency";
   lower[SoPlex::DISPLAYFREQ] = 1;
   upper[SoPlex::DISPLAYFREQ] = INT_MAX;
   defaultValue[SoPlex::DISPLAYFREQ] = 200;

   // verbosity level
   name[SoPlex::VERBOSITY] = "verbosity";
   description[SoPlex::VERBOSITY] =
      "verbosity level (0 - error, 1 - warning, 2 - debug, 3 - normal, 4 - high, 5 - full)";
   lower[SoPlex::VERBOSITY] = 0;
   upper[SoPlex::VERBOSITY] = 5;
   defaultValue[SoPlex::VERBOSITY] = SoPlex::VERBOSITY_NORMAL;
   //_intParamDefault[SoPlex::VERBOSITY] = SoPlex::VERBOSITY_FULL;

   // type of simplifier
   name[SoPlex::SIMPLIFIER] = "simplifier";
   description[SoPlex::SIMPLIFIER] = "simplifier (0 - off, 1 - auto)";
   lower[SoPlex::SIMPLIFIER] = 0;
   upper[SoPlex::SIMPLIFIER] = 1;
   defaultValue[SoPlex::SIMPLIFIER] = SoPlex::SIMPLIFIER_AUTO;

   // type of scaler
   name[SoPlex::SCALER] = "scaler";
   description[SoPlex::SCALER] =
      "scaling (0 - off, 1 - uni-equilibrium, 2 - bi-equilibrium, 3 - geometric, 4 - iterated geometric, 5 - least squares, 6 - geometric-equilibrium)";
   lower[SoPlex::SCALER] = 0;
   upper[SoPlex::SCALER] = 6;
   defaultValue[SoPlex::SCALER] = SoPlex::SCALER_BIEQUI;

   // type of starter used to create crash basis
   name[SoPlex::STARTER] = "starter";
   description[SoPlex::STARTER] =
      "crash basis generated when starting from scratch (0 - none, 1 - weight, 2 - sum, 3 - vector)";
   lower[SoPlex::STARTER] = 0;
   upper[SoPlex::STARTER] = 3;
   defaultValue[SoPlex::STARTER] = SoPlex::STARTER_OFF;

   // type of pricer
   name[SoPlex::PRICER] = "pricer";
   description[SoPlex::PRICER] =
      "pricing method (0 - auto, 1 - dantzig, 2 - parmult, 3 - devex, 4 - quicksteep, 5 - steep)";
   lower[SoPlex::PRICER] = 0;
   upper[SoPlex::PRICER] = 5;
   defaultValue[SoPlex::PRICER] = SoPlex::PRICER_AUTO;

   // type of ratio test
   name[SoPlex::RATIOTESTER] = "ratiotester";
   description[SoPlex::RATIOTESTER] =
      "method for ratio test (0 - textbook, 1 - harris, 2 - fast, 3 - boundflipping)";
   lower[SoPlex::RATIOTESTER] = 0;
   upper[SoPlex::RATIOTESTER] = 3;
   defaultValue[SoPlex::RATIOTESTER] = SoPlex::RATIOTESTER_BOUNDFLIPPING;

   // mode for synchronizing real and rational LP
   name[SoPlex::SYNCMODE] = "syncmode";
   description[SoPlex::SYNCMODE] =
      "mode for synchronizing real and rational LP (0 - store only real LP, 1 - auto, 2 - manual)";
   lower[SoPlex::SYNCMODE] = 0;
   upper[SoPlex::SYNCMODE] = 2;
   defaultValue[SoPlex::SYNCMODE] = SoPlex::SYNCMODE_ONLYREAL;

   // mode for reading LP files
   name[SoPlex::READMODE] = "readmode";
   description[SoPlex::READMODE] = "mode for reading LP files (0 - floating-point, 1 - rational)";
   lower[SoPlex::READMODE] = 0;
   upper[SoPlex::READMODE] = 1;
   defaultValue[SoPlex::READMODE] = SoPlex::READMODE_REAL;

   // mode for iterative refinement strategy
   name[SoPlex::SOLVEMODE] = "solvemode";
   description[SoPlex::SOLVEMODE] =
      "mode for iterative refinement strategy (0 - floating-point solve, 1 - auto, 2 - exact rational solve)";
   lower[SoPlex::SOLVEMODE] = 0;
   upper[SoPlex::SOLVEMODE] = 2;
   defaultValue[SoPlex::SOLVEMODE] = SoPlex::SOLVEMODE_AUTO;

   // mode for iterative refinement strategy
   name[SoPlex::CHECKMODE] = "checkmode";
   description[SoPlex::CHECKMODE] =
      "mode for a posteriori feasibility checks (0 - floating-point check, 1 - auto, 2 - exact rational check)";
   lower[SoPlex::CHECKMODE] = 0;
   upper[SoPlex::CHECKMODE] = 2;
   defaultValue[SoPlex::CHECKMODE] = SoPlex::CHECKMODE_AUTO;

   // type of timing
   name[SoPlex::TIMER] = "timer";
   description[SoPlex::TIMER] =
      "type of timer (1 - cputime, aka. usertime, 2 - wallclock time, 0 - no timing)";
   lower[SoPlex::TIMER] = 0;
   upper[SoPlex::TIMER] = 2;
   defaultValue[SoPlex::TIMER] = SoPlex::TIMER_CPU;

   // mode for hyper sparse pricing
   name[SoPlex::HYPER_PRICING] = "hyperpricing";
   description[SoPlex::HYPER_PRICING] =
      "mode for hyper sparse pricing (0 - off, 1 - auto, 2 - always)";
   lower[SoPlex::HYPER_PRICING] = 0;
   upper[SoPlex::HYPER_PRICING] = 2;
   defaultValue[SoPlex::HYPER_PRICING] = SoPlex::HYPER_PRICING_AUTO;

   // minimum number of stalling refinements since last pivot to trigger rational factorization
   name[SoPlex::RATFAC_MINSTALLS] = "ratfac_minstalls";
   description[SoPlex::RATFAC_MINSTALLS] =
      "minimum number of stalling refinements since last pivot to trigger rational factorization";
   lower[SoPlex::RATFAC_MINSTALLS] = 0;
   upper[SoPlex::RATFAC_MINSTALLS] = INT_MAX;
   defaultValue[SoPlex::RATFAC_MINSTALLS] = 2;

   // maximum number of conjugate gradient iterations in least square scaling
   name[SoPlex::LEASTSQ_MAXROUNDS] = "leastsq_maxrounds";
   description[SoPlex::LEASTSQ_MAXROUNDS] =
      "maximum number of conjugate gradient iterations in least square scaling";
   lower[SoPlex::LEASTSQ_MAXROUNDS] = 0;
   upper[SoPlex::LEASTSQ_MAXROUNDS] = INT_MAX;
   defaultValue[SoPlex::LEASTSQ_MAXROUNDS] = 50;

   // mode for solution polishing
   name[SoPlex::SOLUTION_POLISHING] = "solution_polishing";
   description[SoPlex::SOLUTION_POLISHING] =
      "mode for solution polishing (0 - off, 1 - max basic slack, 2 - min basic slack)";
   lower[SoPlex::SOLUTION_POLISHING] = 0;
   upper[SoPlex::SOLUTION_POLISHING] = 2;
   defaultValue[SoPlex::SOLUTION_POLISHING] = SoPlex::POLISHING_OFF;

   // the number of iterations before the decomposition simplex initialisation is terminated.
   name[SoPlex::DECOMP_ITERLIMIT] = "decomp_iterlimit";
   description[SoPlex::DECOMP_ITERLIMIT] =
      "the number of iterations before the decomposition simplex initialisation solve is terminated";
   lower[SoPlex::DECOMP_ITERLIMIT] = 1;
   upper[SoPlex::DECOMP_ITERLIMIT] = INT_MAX;
   defaultValue[SoPlex::DECOMP_ITERLIMIT] = 100;

   // maximum number of violated rows added in each iteration of the decomposition simplex
   name[SoPlex::DECOMP_MAXADDEDROWS] = "decomp_maxaddedrows";
   description[SoPlex::DECOMP_MAXADDEDROWS] =
      "maximum number of rows that are added to the reduced problem when using the decomposition based simplex";
   lower[SoPlex::DECOMP_MAXADDEDROWS] = 1;
   upper[SoPlex::DECOMP_MAXADDEDROWS] = INT_MAX;
   defaultValue[SoPlex::DECOMP_MAXADDEDROWS] = 500;

   // maximum number of violated rows added in each iteration of the decomposition simplex
   name[SoPlex::DECOMP_DISPLAYFREQ] = "decomp_displayfreq";
   description[SoPlex::DECOMP_DISPLAYFREQ] =
      "the frequency that the decomposition based simplex status output is displayed.";
   lower[SoPlex::DECOMP_DISPLAYFREQ] = 1;
   upper[SoPlex::DECOMP_DISPLAYFREQ] = INT_MAX;
   defaultValue[SoPlex::DECOMP_DISPLAYFREQ] = 50;

   // the verbosity of the decomposition based simplex
   name[SoPlex::DECOMP_VERBOSITY] = "decomp_verbosity";
   description[SoPlex::DECOMP_VERBOSITY] =
      "the verbosity of decomposition based simplex (0 - error, 1 - warning, 2 - debug, 3 - normal, 4 - high, 5 - full).";
   lower[SoPlex::DECOMP_VERBOSITY] = 1;
   upper[SoPlex::DECOMP_VERBOSITY] = 5;
   defaultValue[SoPlex::DECOMP_VERBOSITY] = VERBOSITY_ERROR;

   // printing condition number during the solve
   name[SoPlex::PRINTCONDITION] = "printcondition";
   description[SoPlex::PRINTCONDITION] =
      "print condition number during the solve (0 - off, 1 - ratio estimate , 2 - sum estimate, 3 - product estimate, 4 - exact)";
   lower[SoPlex::PRINTCONDITION] = 0;
   upper[SoPlex::PRINTCONDITION] = 4;
   defaultValue[SoPlex::PRINTCONDITION] = 0;
}

SoPlex::Settings::RealParam::RealParam()
{
   // primal feasibility tolerance
   name[SoPlex::FEASTOL] = "feastol";
   description[SoPlex::FEASTOL] = "primal feasibility tolerance";
   lower[SoPlex::FEASTOL] = 0.0;
   upper[SoPlex::FEASTOL] = 1.0;
   defaultValue[SoPlex::FEASTOL] = 1e-6;

   // dual feasibility tolerance
   name[SoPlex::OPTTOL] = "opttol";
   description[SoPlex::OPTTOL] = "dual feasibility tolerance";
   lower[SoPlex::OPTTOL] = 0.0;
   upper[SoPlex::OPTTOL] = 1.0;
   defaultValue[SoPlex::OPTTOL] = 1e-6;

   ///@todo define suitable values depending on Real type
   // general zero tolerance
   name[SoPlex::EPSILON_ZERO] = "epsilon_zero";
   description[SoPlex::EPSILON_ZERO] = "general zero tolerance";
   lower[SoPlex::EPSILON_ZERO] = 0.0;
   upper[SoPlex::EPSILON_ZERO] = 1.0;
   defaultValue[SoPlex::EPSILON_ZERO] = DEFAULT_EPS_ZERO;

   ///@todo define suitable values depending on Real type
   // zero tolerance used in factorization
   name[SoPlex::EPSILON_FACTORIZATION] = "epsilon_factorization";
   description[SoPlex::EPSILON_FACTORIZATION] = "zero tolerance used in factorization";
   lower[SoPlex::EPSILON_FACTORIZATION] = 0.0;
   upper[SoPlex::EPSILON_FACTORIZATION] = 1.0;
   defaultValue[SoPlex::EPSILON_FACTORIZATION] = DEFAULT_EPS_FACTOR;

   ///@todo define suitable values depending on Real type
   // zero tolerance used in update of the factorization
   name[SoPlex::EPSILON_UPDATE] = "epsilon_update";
   description[SoPlex::EPSILON_UPDATE] = "zero tolerance used in update of the factorization";
   lower[SoPlex::EPSILON_UPDATE] = 0.0;
   upper[SoPlex::EPSILON_UPDATE] = 1.0;
   defaultValue[SoPlex::EPSILON_UPDATE] = DEFAULT_EPS_UPDATE;

   ///@todo define suitable values depending on Real type
   // pivot zero tolerance used in factorization
   name[SoPlex::EPSILON_PIVOT] = "epsilon_pivot";
   description[SoPlex::EPSILON_PIVOT] = "pivot zero tolerance used in factorization";
   lower[SoPlex::EPSILON_PIVOT] = 0.0;
   upper[SoPlex::EPSILON_PIVOT] = 1.0;
   defaultValue[SoPlex::EPSILON_PIVOT] = DEFAULT_EPS_PIVOT;

   ///@todo define suitable values depending on Real type
   // infinity threshold
   name[SoPlex::INFTY] = "infty";
   description[SoPlex::INFTY] = "infinity threshold";
   lower[SoPlex::INFTY] = 1e10;
   upper[SoPlex::INFTY] = 1e100;
   defaultValue[SoPlex::INFTY] = DEFAULT_INFINITY;

   // time limit in seconds (INFTY if unlimited)
   name[SoPlex::TIMELIMIT] = "timelimit";
   description[SoPlex::TIMELIMIT] = "time limit in seconds";
   lower[SoPlex::TIMELIMIT] = 0.0;
   upper[SoPlex::TIMELIMIT] = DEFAULT_INFINITY;
   defaultValue[SoPlex::TIMELIMIT] = DEFAULT_INFINITY;

   // lower limit on objective value
   name[SoPlex::OBJLIMIT_LOWER] = "objlimit_lower";
   description[SoPlex::OBJLIMIT_LOWER] = "lower limit on objective value";
   lower[SoPlex::OBJLIMIT_LOWER] = -DEFAULT_INFINITY;
   upper[SoPlex::OBJLIMIT_LOWER] = DEFAULT_INFINITY;
   defaultValue[SoPlex::OBJLIMIT_LOWER] = -DEFAULT_INFINITY;

   // upper limit on objective value
   name[SoPlex::OBJLIMIT_UPPER] = "objlimit_upper";
   description[SoPlex::OBJLIMIT_UPPER] = "upper limit on objective value";
   lower[SoPlex::OBJLIMIT_UPPER] = -DEFAULT_INFINITY;
   upper[SoPlex::OBJLIMIT_UPPER] = DEFAULT_INFINITY;
   defaultValue[SoPlex::OBJLIMIT_UPPER] = DEFAULT_INFINITY;

   // working tolerance for feasibility in floating-point solver during iterative refinement
   name[SoPlex::FPFEASTOL] = "fpfeastol";
   description[SoPlex::FPFEASTOL] =
      "working tolerance for feasibility in floating-point solver during iterative refinement";
   lower[SoPlex::FPFEASTOL] = 1e-12;
   upper[SoPlex::FPFEASTOL] = 1.0;
   defaultValue[SoPlex::FPFEASTOL] = 1e-9;

   // working tolerance for optimality in floating-point solver during iterative refinement
   name[SoPlex::FPOPTTOL] = "fpopttol";
   description[SoPlex::FPOPTTOL] =
      "working tolerance for optimality in floating-point solver during iterative refinement";
   lower[SoPlex::FPOPTTOL] = 1e-12;
   upper[SoPlex::FPOPTTOL] = 1.0;
   defaultValue[SoPlex::FPOPTTOL] = 1e-9;

   // maximum increase of scaling factors between refinements
   name[SoPlex::MAXSCALEINCR] = "maxscaleincr";
   description[SoPlex::MAXSCALEINCR] = "maximum increase of scaling factors between refinements";
   lower[SoPlex::MAXSCALEINCR] = 1.0;
   upper[SoPlex::MAXSCALEINCR] = DEFAULT_INFINITY;
   defaultValue[SoPlex::MAXSCALEINCR] = 1e25;

   // lower threshold in lifting (nonzero matrix coefficients with smaller absolute value will be reformulated)
   name[SoPlex::LIFTMINVAL] = "liftminval";
   description[SoPlex::LIFTMINVAL] =
      "lower threshold in lifting (nonzero matrix coefficients with smaller absolute value will be reformulated)";
   lower[SoPlex::LIFTMINVAL] = 0.0;
   upper[SoPlex::LIFTMINVAL] = 0.1;
   defaultValue[SoPlex::LIFTMINVAL] = 0.000976562; // = 1/1024

   // upper threshold in lifting (nonzero matrix coefficients with larger absolute value will be reformulated)
   name[SoPlex::LIFTMAXVAL] = "liftmaxval";
   description[SoPlex::LIFTMAXVAL] =
      "lower threshold in lifting (nonzero matrix coefficients with smaller absolute value will be reformulated)";
   lower[SoPlex::LIFTMAXVAL] = 10.0;
   upper[SoPlex::LIFTMAXVAL] = DEFAULT_INFINITY;
   defaultValue[SoPlex::LIFTMAXVAL] = 1024.0;

   // threshold for using sparse pricing (no. of violations need to be smaller than threshold * dimension of problem)
   name[SoPlex::SPARSITY_THRESHOLD] = "sparsity_threshold";
   description[SoPlex::SPARSITY_THRESHOLD] =
      "sparse pricing threshold (#violations < dimension * SPARSITY_THRESHOLD activates sparse pricing)";
   lower[SoPlex::SPARSITY_THRESHOLD] = 0.0;
   upper[SoPlex::SPARSITY_THRESHOLD] = 1.0;
   defaultValue[SoPlex::SPARSITY_THRESHOLD] = 0.6;

   // threshold on number of rows vs. number of columns for switching from column to row representations in auto mode
   name[SoPlex::REPRESENTATION_SWITCH] = "representation_switch";
   description[SoPlex::REPRESENTATION_SWITCH] =
      "threshold on number of rows vs. number of columns for switching from column to row representations in auto mode";
   lower[SoPlex::REPRESENTATION_SWITCH] = 0.0;
   upper[SoPlex::REPRESENTATION_SWITCH] = DEFAULT_INFINITY;
   defaultValue[SoPlex::REPRESENTATION_SWITCH] = 1.2;

   // geometric frequency at which to apply rational reconstruction
   name[SoPlex::RATREC_FREQ] = "ratrec_freq";
   description[SoPlex::RATREC_FREQ] = "geometric frequency at which to apply rational reconstruction";
   lower[SoPlex::RATREC_FREQ] = 1.0;
   upper[SoPlex::RATREC_FREQ] = DEFAULT_INFINITY;
   defaultValue[SoPlex::RATREC_FREQ] = 1.2;

   // minimal reduction (sum of removed rows/cols) to continue simplification
   name[SoPlex::MINRED] = "minred";
   description[SoPlex::MINRED] =
      "minimal reduction (sum of removed rows/cols) to continue simplification";
   lower[SoPlex::MINRED] = 0.0;
   upper[SoPlex::MINRED] = 1.0;
   defaultValue[SoPlex::MINRED] = 1e-4;

   // refactor threshold for nonzeros in last factorized basis matrix compared to updated basis matrix
   name[SoPlex::REFAC_BASIS_NNZ] = "refac_basis_nnz";
   description[SoPlex::REFAC_BASIS_NNZ] =
      "refactor threshold for nonzeros in last factorized basis matrix compared to updated basis matrix";
   lower[SoPlex::REFAC_BASIS_NNZ] = 1.0;
   upper[SoPlex::REFAC_BASIS_NNZ] = 100.0;
   defaultValue[SoPlex::REFAC_BASIS_NNZ] = 10.0;

   // refactor threshold for fill-in in current factor update compared to fill-in in last factorization
   name[SoPlex::REFAC_UPDATE_FILL] = "refac_update_fill";
   description[SoPlex::REFAC_UPDATE_FILL] =
      "refactor threshold for fill-in in current factor update compared to fill-in in last factorization";
   lower[SoPlex::REFAC_UPDATE_FILL] = 1.0;
   upper[SoPlex::REFAC_UPDATE_FILL] = 100.0;
   defaultValue[SoPlex::REFAC_UPDATE_FILL] = 5.0;

   // refactor threshold for memory growth in factorization since last refactorization
   name[SoPlex::REFAC_MEM_FACTOR] = "refac_mem_factor";
   description[SoPlex::REFAC_MEM_FACTOR] =
      "refactor threshold for memory growth in factorization since last refactorization";
   lower[SoPlex::REFAC_MEM_FACTOR] = 1.0;
   upper[SoPlex::REFAC_MEM_FACTOR] = 10.0;
   defaultValue[SoPlex::REFAC_MEM_FACTOR] = 1.5;

   // accuracy of conjugate gradient method in least squares scaling (higher value leads to more iterations)
   name[SoPlex::LEASTSQ_ACRCY] = "leastsq_acrcy";
   description[SoPlex::LEASTSQ_ACRCY] =
      "accuracy of conjugate gradient method in least squares scaling (higher value leads to more iterations)";
   lower[SoPlex::LEASTSQ_ACRCY] = 1.0;
   upper[SoPlex::LEASTSQ_ACRCY] = DEFAULT_INFINITY;
   defaultValue[SoPlex::LEASTSQ_ACRCY] = 1000.0;

   // objective offset
   name[SoPlex::OBJ_OFFSET] = "obj_offset";
   description[SoPlex::OBJ_OFFSET] = "objective offset to be used";
   lower[SoPlex::OBJ_OFFSET] = -DEFAULT_INFINITY;
   upper[SoPlex::OBJ_OFFSET] = DEFAULT_INFINITY;
   defaultValue[SoPlex::OBJ_OFFSET] = 0.0;
}

#ifdef SOPLEX_WITH_RATIONALPARAM
SoPlex::Settings::RationalParam::RationalParam() {}
#endif

SoPlex::Settings::Settings()
{
   for(int i = 0; i < SoPlex::BOOLPARAM_COUNT; i++)
      _boolParamValues[i] = boolParam.defaultValue[i];

   for(int i = 0; i < SoPlex::INTPARAM_COUNT; i++)
      _intParamValues[i] = intParam.defaultValue[i];

   for(int i = 0; i < SoPlex::REALPARAM_COUNT; i++)
      _realParamValues[i] = realParam.defaultValue[i];

#ifdef SOPLEX_WITH_RATIONALPARAM

   for(int i = 0; i < SoPlex::RATIONALPARAM_COUNT; i++)
      _rationalParamValues[i] = rationalParam.defaultValue[i];

#endif
}

SoPlex::Settings::Settings(const Settings& settings)
{
   *this = settings;
}

SoPlex::Settings& SoPlex::Settings::operator=(const Settings& settings)
{
   for(int i = 0; i < SoPlex::BOOLPARAM_COUNT; i++)
      _boolParamValues[i] = settings._boolParamValues[i];

   for(int i = 0; i < SoPlex::INTPARAM_COUNT; i++)
      _intParamValues[i] = settings._intParamValues[i];

   for(int i = 0; i < SoPlex::REALPARAM_COUNT; i++)
      _realParamValues[i] = settings._realParamValues[i];

#ifdef SOPLEX_WITH_RATIONALPARAM

   for(int i = 0; i < SoPlex::RATIONALPARAM_COUNT; i++)
      _rationalParamValues[i] = settings._rationalParamValues[i];

#endif

   return *this;
}

SoPlex::Settings::BoolParam SoPlex::Settings::boolParam;
SoPlex::Settings::IntParam SoPlex::Settings::intParam;
SoPlex::Settings::RealParam SoPlex::Settings::realParam;
#ifdef SOPLEX_WITH_RATIONALPARAM
SoPlex::Settings::RationalParam SoPlex::Settings::rationalParam;
#endif

/// default constructor
SoPlex::SoPlex()
   : _statistics(0)
   , _currentSettings(0)
   , _scalerUniequi(false)
   , _scalerBiequi(true)
   , _scalerGeo1(false, 1)
   , _scalerGeo8(false, 8)
   , _scalerGeoequi(true)
   , _scalerLeastsq()
   , _simplifier(0)
   , _scaler(0)
   , _starter(0)
   , _rationalLP(0)
   , _unitMatrixRational(0)
   , _status(SPxSolver::UNKNOWN)
   , _hasBasis(false)
   , _hasSolReal(false)
   , _hasSolRational(false)
   , _rationalPosone(1)
   , _rationalNegone(-1)
   , _rationalZero(0)
{
   // transfer message handler
   _solver.setOutstream(spxout);
   _scalerUniequi.setOutstream(spxout);
   _scalerBiequi.setOutstream(spxout);
   _scalerGeo1.setOutstream(spxout);
   _scalerGeo8.setOutstream(spxout);
   _scalerGeoequi.setOutstream(spxout);
   _scalerLeastsq.setOutstream(spxout);

   // give lu factorization to solver
   _solver.setBasisSolver(&_slufactor);

   // the real LP is initially stored in the solver; the rational LP is constructed, when the parameter SYNCMODE is
   // initialized in setSettings() below
   _realLP = &_solver;
   _isRealLPLoaded = true;
   _isRealLPScaled = false;
   _applyPolishing = false;
   _optimizeCalls = 0;
   _unscaleCalls = 0;
   _realLP->setOutstream(spxout);
   _currentProb = DECOMP_ORIG;

   // initialize statistics
   spx_alloc(_statistics);
   _statistics = new(_statistics) Statistics();

   // initialize parameter settings to default
   spx_alloc(_currentSettings);
   _currentSettings = new(_currentSettings) Settings();
   setSettings(*_currentSettings, true);

   _lastSolveMode = intParam(SoPlex::SOLVEMODE);

   assert(_isConsistent());
}



/// assignment operator
SoPlex& SoPlex::operator=(const SoPlex& rhs)
{
   if(this != &rhs)
   {
      // copy message handler
      spxout = rhs.spxout;

      // copy statistics
      *_statistics = *(rhs._statistics);

      // copy settings
      *_currentSettings = *(rhs._currentSettings);

      // copy solver components
      _solver = rhs._solver;
      _slufactor = rhs._slufactor;
      _simplifierMainSM = rhs._simplifierMainSM;
      _scalerUniequi = rhs._scalerUniequi;
      _scalerBiequi = rhs._scalerBiequi;
      _scalerGeo1 = rhs._scalerGeo1;
      _scalerGeo8 = rhs._scalerGeo8;
      _scalerGeoequi = rhs._scalerGeoequi;
      _scalerLeastsq = rhs._scalerLeastsq;
      _starterWeight = rhs._starterWeight;
      _starterSum = rhs._starterSum;
      _starterVector = rhs._starterVector;
      _pricerAuto = rhs._pricerAuto;
      _pricerDantzig = rhs._pricerDantzig;
      _pricerParMult = rhs._pricerParMult;
      _pricerDevex = rhs._pricerDevex;
      _pricerQuickSteep = rhs._pricerQuickSteep;
      _pricerSteep = rhs._pricerSteep;
      _ratiotesterTextbook = rhs._ratiotesterTextbook;
      _ratiotesterHarris = rhs._ratiotesterHarris;
      _ratiotesterFast = rhs._ratiotesterFast;
      _ratiotesterBoundFlipping = rhs._ratiotesterBoundFlipping;

      // copy solution data
      _status = rhs._status;
      _lastSolveMode = rhs._lastSolveMode;
      _basisStatusRows = rhs._basisStatusRows;
      _basisStatusCols = rhs._basisStatusCols;

      if(rhs._hasSolReal)
         _solReal = rhs._solReal;

      if(rhs._hasSolRational)
         _solRational = rhs._solRational;

      // set message handlers in members
      _solver.setOutstream(spxout);
      _scalerUniequi.setOutstream(spxout);
      _scalerBiequi.setOutstream(spxout);
      _scalerGeo1.setOutstream(spxout);
      _scalerGeo8.setOutstream(spxout);
      _scalerGeoequi.setOutstream(spxout);
      _scalerLeastsq.setOutstream(spxout);

      // transfer the lu solver
      _solver.setBasisSolver(&_slufactor);

      // initialize pointers for simplifier, scaler, and starter
      setIntParam(SoPlex::SIMPLIFIER, intParam(SoPlex::SIMPLIFIER), true);
      setIntParam(SoPlex::SCALER, intParam(SoPlex::SCALER), true);
      setIntParam(SoPlex::STARTER, intParam(SoPlex::STARTER), true);

      // copy real LP if different from the LP in the solver
      if(rhs._realLP != &(rhs._solver))
      {
         _realLP = 0;
         spx_alloc(_realLP);
         _realLP = new(_realLP) SPxLPReal(*(rhs._realLP));
      }
      else
         _realLP = &_solver;

      // copy rational LP
      if(rhs._rationalLP == 0)
      {
         assert(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL);
         _rationalLP = 0;
      }
      else
      {
         assert(intParam(SoPlex::SYNCMODE) != SYNCMODE_ONLYREAL);
         _rationalLP = 0;
         spx_alloc(_rationalLP);
         _rationalLP = new(_rationalLP) SPxLPRational(*rhs._rationalLP);
      }

      // copy rational factorization
      if(rhs._rationalLUSolver.status() == SLinSolverRational::OK)
         _rationalLUSolver = rhs._rationalLUSolver;

      // copy boolean flags
      _isRealLPLoaded = rhs._isRealLPLoaded;
      _isRealLPScaled = rhs._isRealLPScaled;
      _hasSolReal = rhs._hasSolReal;
      _hasSolRational = rhs._hasSolRational;
      _hasBasis = rhs._hasBasis;
      _applyPolishing = rhs._applyPolishing;

      // rational constants do not need to be assigned
      _rationalPosone = 1;
      _rationalNegone = -1;
      _rationalZero = 0;
   }

   assert(_isConsistent());

   return *this;
}



/// copy constructor
///@todo improve performance by implementing a separate copy constructor
SoPlex::SoPlex(const SoPlex& rhs)
{
   // allocate memory as in default constructor
   _statistics = 0;
   spx_alloc(_statistics);
   _statistics = new(_statistics) Statistics();

   _currentSettings = 0;
   spx_alloc(_currentSettings);
   _currentSettings = new(_currentSettings) Settings();

   // call assignment operator
   *this = rhs;
}



/// destructor
SoPlex::~SoPlex()
{
   assert(_isConsistent());

   // free settings
   _currentSettings->~Settings();
   spx_free(_currentSettings);

   // free statistics
   _statistics->~Statistics();
   spx_free(_statistics);

   // free real LP if different from the LP in the solver
   assert(_realLP != 0);

   if(_realLP != &_solver)
   {
      _realLP->~SPxLPReal();
      spx_free(_realLP);
   }

   // free rational LP
   if(_rationalLP != 0)
   {
      _rationalLP->~SPxLPRational();
      spx_free(_rationalLP);
   }

   // free unit vectors
   for(int i = 0; i < _unitMatrixRational.size(); i++)
   {
      if(_unitMatrixRational[i] != 0)
      {
         _unitMatrixRational[i]->~UnitVectorRational();
         spx_free(_unitMatrixRational[i]);
      }
   }
}



/// returns number of rows
int SoPlex::numRowsReal() const
{
   assert(_realLP != 0);
   return _realLP->nRows();
}



/// returns number of columns
int SoPlex::numColsReal() const
{
   assert(_realLP != 0);
   return _realLP->nCols();
}



/// returns number of nonzeros
int SoPlex::numNonzerosReal() const
{
   assert(_realLP != 0);
   return _realLP->nNzos();
}



/// returns smallest non-zero element in absolute value
Real SoPlex::minAbsNonzeroReal() const
{
   assert(_realLP != 0);
   return _realLP->minAbsNzo();
}



/// returns biggest non-zero element in absolute value
Real SoPlex::maxAbsNonzeroReal() const
{
   assert(_realLP != 0);
   return _realLP->maxAbsNzo();
}



/// returns (unscaled) coefficient
Real SoPlex::coefReal(int row, int col) const
{
   if(_realLP->isScaled())
   {
      assert(_scaler);
      return _scaler->getCoefUnscaled(*_realLP, row, col);
   }
   else
      return colVectorRealInternal(col)[row];
}



/// returns vector of row \p i, ignoring scaling
const SVectorReal& SoPlex::rowVectorRealInternal(int i) const
{
   assert(_realLP != 0);
   return _realLP->rowVector(i);
}



/// gets vector of row \p i
void SoPlex::getRowVectorReal(int i, DSVectorReal& row) const
{
   assert(_realLP);

   if(_realLP->isScaled())
   {
      assert(_scaler);
      row.setMax(_realLP->rowVector(i).size());
      _scaler->getRowUnscaled(*_realLP, i, row);
   }
   else
      row = _realLP->rowVector(i);
}



/// returns right-hand side vector, ignoring scaling
const VectorReal& SoPlex::rhsRealInternal() const
{
   assert(_realLP != 0);
   return _realLP->rhs();
}



/// gets right-hand side vector
void SoPlex::getRhsReal(DVectorReal& rhs) const
{
   assert(_realLP);
   _realLP->getRhsUnscaled(rhs);
}



/// returns right-hand side of row \p i
Real SoPlex::rhsReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->rhsUnscaled(i);
}



/// returns left-hand side vector, ignoring scaling
const VectorReal& SoPlex::lhsRealInternal() const
{
   assert(_realLP != 0);
   return _realLP->lhs();
}



/// gets left-hand side vector
void SoPlex::getLhsReal(DVectorReal& lhs) const
{
   assert(_realLP);
   _realLP->getLhsUnscaled(lhs);
}



/// returns left-hand side of row \p i
Real SoPlex::lhsReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->lhsUnscaled(i);
}



/// returns inequality type of row \p i
LPRowReal::Type SoPlex::rowTypeReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->rowType(i);
}



/// returns vector of col \p i, ignoring scaling
const SVectorReal& SoPlex::colVectorRealInternal(int i) const
{
   assert(_realLP != 0);
   return _realLP->colVector(i);
}



/// gets vector of col \p i
void SoPlex::getColVectorReal(int i, DSVectorReal& col) const
{
   assert(_realLP);
   _realLP->getColVectorUnscaled(i, col);
}



/// returns upper bound vector
const VectorReal& SoPlex::upperRealInternal() const
{
   assert(_realLP != 0);
   return _realLP->upper();
}



/// returns upper bound of column \p i
Real SoPlex::upperReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->upperUnscaled(i);
}



/// gets upper bound vector
void SoPlex::getUpperReal(DVectorReal& upper) const
{
   assert(_realLP != 0);
   return _realLP->getUpperUnscaled(upper);
}



/// returns lower bound vector
const VectorReal& SoPlex::lowerRealInternal() const
{
   assert(_realLP != 0);
   return _realLP->lower();
}



/// returns lower bound of column \p i
Real SoPlex::lowerReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->lowerUnscaled(i);
}



/// gets lower bound vector
void SoPlex::getLowerReal(DVectorReal& lower) const
{
   assert(_realLP != 0);
   return _realLP->getLowerUnscaled(lower);
}




/// gets objective function vector
void SoPlex::getObjReal(VectorReal& obj) const
{
   assert(_realLP != 0);
   _realLP->getObjUnscaled(obj);
}



/// returns objective value of column \p i
Real SoPlex::objReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->objUnscaled(i);
}



/// returns objective function vector after transformation to a maximization problem; since this is how it is stored
/// internally, this is generally faster
const VectorReal& SoPlex::maxObjRealInternal() const
{
   assert(_realLP != 0);
   return _realLP->maxObj();
}



/// returns objective value of column \p i after transformation to a maximization problem; since this is how it is
/// stored internally, this is generally faster
Real SoPlex::maxObjReal(int i) const
{
   assert(_realLP != 0);
   return _realLP->maxObjUnscaled(i);
}



/// gets number of available dual norms
void SoPlex::getNdualNorms(int& nnormsRow, int& nnormsCol) const
{
   _solver.getNdualNorms(nnormsRow, nnormsCol);
}



/// gets steepest edge norms and returns false if they are not available
bool SoPlex::getDualNorms(int& nnormsRow, int& nnormsCol, Real* norms) const
{
   return _solver.getDualNorms(nnormsRow, nnormsCol, norms);
}



/// sets steepest edge norms and returns false if that's not possible
bool SoPlex::setDualNorms(int nnormsRow, int nnormsCol, Real* norms)
{
   return _solver.setDualNorms(nnormsRow, nnormsCol, norms);
}



/// pass integrality information about the variables to the solver
void SoPlex::setIntegralityInformation(int ncols, int* intInfo)
{
   assert(ncols == _solver.nCols() || (ncols == 0 && intInfo == NULL));
   _solver.setIntegralityInformation(ncols, intInfo);
}



/// returns number of rows
int SoPlex::numRowsRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->nRows();
}



/// returns number of columns
int SoPlex::numColsRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->nCols();
}



/// returns number of nonzeros
int SoPlex::numNonzerosRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->nNzos();
}



/// returns smallest non-zero element in absolute value
Rational SoPlex::minAbsNonzeroRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->minAbsNzo();
}



/// returns biggest non-zero element in absolute value
Rational SoPlex::maxAbsNonzeroRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->maxAbsNzo();
}



/// gets row \p i
void SoPlex::getRowRational(int i, LPRowRational& lprow) const
{
   assert(_rationalLP != 0);
   _rationalLP->getRow(i, lprow);
}



/// gets rows \p start, ..., \p end.
void SoPlex::getRowsRational(int start, int end, LPRowSetRational& lprowset) const
{
   assert(_rationalLP != 0);
   _rationalLP->getRows(start, end, lprowset);
}



/// returns vector of row \p i
const SVectorRational& SoPlex::rowVectorRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->rowVector(i);
}



/// returns right-hand side vector
const VectorRational& SoPlex::rhsRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->rhs();
}



/// returns right-hand side of row \p i
const Rational& SoPlex::rhsRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->rhs(i);
}



/// returns left-hand side vector
const VectorRational& SoPlex::lhsRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->lhs();
}



/// returns left-hand side of row \p i
const Rational& SoPlex::lhsRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->lhs(i);
}



/// returns inequality type of row \p i
LPRowRational::Type SoPlex::rowTypeRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->rowType(i);
}



/// gets column \p i
void SoPlex::getColRational(int i, LPColRational& lpcol) const
{
   assert(_rationalLP != 0);
   return _rationalLP->getCol(i, lpcol);
}



/// gets columns \p start, ..., \p end
void SoPlex::getColsRational(int start, int end, LPColSetRational& lpcolset) const
{
   assert(_rationalLP != 0);
   return _rationalLP->getCols(start, end, lpcolset);
}



/// returns vector of column \p i
const SVectorRational& SoPlex::colVectorRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->colVector(i);
}



/// returns upper bound vector
const VectorRational& SoPlex::upperRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->upper();
}



/// returns upper bound of column \p i
const Rational& SoPlex::upperRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->upper(i);
}



/// returns lower bound vector
const VectorRational& SoPlex::lowerRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->lower();
}



/// returns lower bound of column \p i
const Rational& SoPlex::lowerRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->lower(i);
}



/// gets objective function vector
void SoPlex::getObjRational(VectorRational& obj) const
{
   assert(_rationalLP != 0);
   _rationalLP->getObj(obj);
}



/// gets objective value of column \p i
void SoPlex::getObjRational(int i, Rational& obj) const
{
   obj = maxObjRational(i);

   if(intParam(SoPlex::OBJSENSE) == SoPlex::OBJSENSE_MINIMIZE)
      obj *= -1;
}



/// returns objective value of column \p i
Rational SoPlex::objRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->obj(i);
}



/// returns objective function vector after transformation to a maximization problem; since this is how it is stored
/// internally, this is generally faster
const VectorRational& SoPlex::maxObjRational() const
{
   assert(_rationalLP != 0);
   return _rationalLP->maxObj();
}



/// returns objective value of column \p i after transformation to a maximization problem; since this is how it is
/// stored internally, this is generally faster
const Rational& SoPlex::maxObjRational(int i) const
{
   assert(_rationalLP != 0);
   return _rationalLP->maxObj(i);
}



/// adds a single row
void SoPlex::addRowReal(const LPRowReal& lprow)
{
   assert(_realLP != 0);

   _addRowReal(lprow);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->addRow(lprow);
      _completeRangeTypesRational();
   }

   _invalidateSolution();
}



/// adds multiple rows
void SoPlex::addRowsReal(const LPRowSetReal& lprowset)
{
   assert(_realLP != 0);

   _addRowsReal(lprowset);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->addRows(lprowset);
      _completeRangeTypesRational();
   }

   _invalidateSolution();
}



/// adds a single column
void SoPlex::addColReal(const LPColReal& lpcol)
{
   assert(_realLP != 0);

   _addColReal(lpcol);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->addCol(lpcol);
      _completeRangeTypesRational();
   }

   _invalidateSolution();
}



/// adds multiple columns
void SoPlex::addColsReal(const LPColSetReal& lpcolset)
{
   assert(_realLP != 0);

   _addColsReal(lpcolset);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->addCols(lpcolset);
      _completeRangeTypesRational();
   }

   _invalidateSolution();
}



/// replaces row \p i with \p lprow
void SoPlex::changeRowReal(int i, const LPRowReal& lprow)
{
   assert(_realLP != 0);

   _changeRowReal(i, lprow);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeRow(i, lprow);
      _rowTypes[i] = _rangeTypeReal(lprow.lhs(), lprow.rhs());
      _completeRangeTypesRational();
   }

   _invalidateSolution();
}



/// changes left-hand side vector for constraints to \p lhs
void SoPlex::changeLhsReal(const VectorReal& lhs)
{
   assert(_realLP != 0);

   _changeLhsReal(lhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeLhs(DVectorRational(lhs));

      for(int i = 0; i < numRowsRational(); i++)
         _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));
   }

   _invalidateSolution();
}



/// changes left-hand side of row \p i to \p lhs
void SoPlex::changeLhsReal(int i, const Real& lhs)
{
   assert(_realLP != 0);

   _changeLhsReal(i, lhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeLhs(i, lhs);
      _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));
   }

   _invalidateSolution();
}



/// changes right-hand side vector to \p rhs
void SoPlex::changeRhsReal(const VectorReal& rhs)
{
   assert(_realLP != 0);

   _changeRhsReal(rhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeRhs(DVectorRational(rhs));

      for(int i = 0; i < numRowsRational(); i++)
         _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));
   }

   _invalidateSolution();
}



/// changes right-hand side of row \p i to \p rhs
void SoPlex::changeRhsReal(int i, const Real& rhs)
{
   assert(_realLP != 0);

   _changeRhsReal(i, rhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeRhs(i, rhs);
      _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));
   }

   _invalidateSolution();
}



/// changes left- and right-hand side vectors
void SoPlex::changeRangeReal(const VectorReal& lhs, const VectorReal& rhs)
{
   assert(_realLP != 0);

   _changeRangeReal(lhs, rhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeRange(DVectorRational(lhs), DVectorRational(rhs));

      for(int i = 0; i < numRowsRational(); i++)
         _rowTypes[i] = _rangeTypeReal(lhs[i], rhs[i]);
   }

   _invalidateSolution();
}



/// changes left- and right-hand side of row \p i
void SoPlex::changeRangeReal(int i, const Real& lhs, const Real& rhs)
{
   assert(_realLP != 0);

   _changeRangeReal(i, lhs, rhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeRange(i, lhs, rhs);
      _rowTypes[i] = _rangeTypeReal(lhs, rhs);
   }

   _invalidateSolution();
}



/// replaces column \p i with \p lpcol
void SoPlex::changeColReal(int i, const LPColReal& lpcol)
{
   assert(_realLP != 0);

   _changeColReal(i, lpcol);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeCol(i, lpcol);
      _colTypes[i] = _rangeTypeReal(lpcol.lower(), lpcol.upper());
      _completeRangeTypesRational();
   }

   _invalidateSolution();
}



/// changes vector of lower bounds to \p lower
void SoPlex::changeLowerReal(const VectorReal& lower)
{
   assert(_realLP != 0);

   _changeLowerReal(lower);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeLower(DVectorRational(lower));

      for(int i = 0; i < numColsRational(); i++)
         _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));
   }


   _invalidateSolution();
}



/// changes lower bound of column i to \p lower
void SoPlex::changeLowerReal(int i, const Real& lower)
{
   assert(_realLP != 0);

   _changeLowerReal(i, lower);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeLower(i, lower);
      _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));
   }

   _invalidateSolution();
}



/// changes vector of upper bounds to \p upper
void SoPlex::changeUpperReal(const VectorReal& upper)
{
   assert(_realLP != 0);

   _changeUpperReal(upper);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeUpper(DVectorRational(upper));

      for(int i = 0; i < numColsRational(); i++)
         _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));
   }

   _invalidateSolution();
}



/// changes \p i 'th upper bound to \p upper
void SoPlex::changeUpperReal(int i, const Real& upper)
{
   assert(_realLP != 0);

   _changeUpperReal(i, upper);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeUpper(i, upper);
      _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));
   }

   _invalidateSolution();
}



/// changes vectors of column bounds to \p lower and \p upper
void SoPlex::changeBoundsReal(const VectorReal& lower, const VectorReal& upper)
{
   assert(_realLP != 0);

   _changeBoundsReal(lower, upper);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeBounds(DVectorRational(lower), DVectorRational(upper));

      for(int i = 0; i < numColsRational(); i++)
         _colTypes[i] = _rangeTypeReal(lower[i], upper[i]);
   }

   _invalidateSolution();
}



/// changes bounds of column \p i to \p lower and \p upper
void SoPlex::changeBoundsReal(int i, const Real& lower, const Real& upper)
{
   assert(_realLP != 0);

   _changeBoundsReal(i, lower, upper);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->changeBounds(i, lower, upper);
      _colTypes[i] = _rangeTypeReal(lower, upper);
   }

   _invalidateSolution();
}



/// changes objective function vector to \p obj
void SoPlex::changeObjReal(const VectorReal& obj)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeObj(obj, scale);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _rationalLP->changeObj(DVectorRational(obj));

   _invalidateSolution();
}



/// changes objective coefficient of column i to \p obj
void SoPlex::changeObjReal(int i, const Real& obj)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeObj(i, obj, scale);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _rationalLP->changeObj(i, obj);

   _invalidateSolution();
}



/// changes matrix entry in row \p i and column \p j to \p val
void SoPlex::changeElementReal(int i, int j, const Real& val)
{
   assert(_realLP != 0);

   _changeElementReal(i, j, val);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _rationalLP->changeElement(i, j, val);

   _invalidateSolution();
}



/// removes row \p i
void SoPlex::removeRowReal(int i)
{
   assert(_realLP != 0);

   _removeRowReal(i);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->removeRow(i);

      // only swap elements if not the last one was removed
      if(i < _rationalLP->nRows())
      {
         _rowTypes[i] = _rowTypes[_rationalLP->nRows()];
         assert(_rowTypes[i] == _rangeTypeRational(lhsRational(i), rhsRational(i)));
      }

      _rowTypes.reSize(_rationalLP->nRows());
   }

   _invalidateSolution();
}



/// removes all rows with an index \p i such that \p perm[i] < 0; upon completion, \p perm[i] >= 0 indicates the
/// new index where row \p i has been moved to; note that \p perm must point to an array of size at least
/// #numRowsReal()
void SoPlex::removeRowsReal(int perm[])
{
   assert(_realLP != 0);

   const int oldsize = numRowsReal();
   _removeRowsReal(perm);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->removeRows(perm);

      for(int i = 0; i < oldsize; i++)
      {
         if(perm[i] >= 0)
            _rowTypes[perm[i]] = _rowTypes[i];
      }

      _rowTypes.reSize(_rationalLP->nRows());

      for(int i = 0; i < numRowsRational(); i++)
      {
         assert(_rowTypes[i] == _rangeTypeRational(lhsRational(i), rhsRational(i)));
      }
   }

   _invalidateSolution();
}



/// remove all rows with indices in array \p idx of size \p n; an array \p perm of size #numRowsReal() may be passed
/// as buffer memory
void SoPlex::removeRowsReal(int idx[], int n, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numRowsReal());
      _idxToPerm(idx, n, p.get_ptr(), numRowsReal());
      SoPlex::removeRowsReal(p.get_ptr());
   }
   else
   {
      _idxToPerm(idx, n, perm, numRowsReal());
      SoPlex::removeRowsReal(perm);
   }
}



/// removes rows \p start to \p end including both; an array \p perm of size #numRowsReal() may be passed as buffer
/// memory
void SoPlex::removeRowRangeReal(int start, int end, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numRowsReal());
      _rangeToPerm(start, end, p.get_ptr(), numRowsReal());
      SoPlex::removeRowsReal(p.get_ptr());
   }
   else
   {
      _rangeToPerm(start, end, perm, numRowsReal());
      SoPlex::removeRowsReal(perm);
   }
}



/// removes column i
void SoPlex::removeColReal(int i)
{
   assert(_realLP != 0);

   _removeColReal(i);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->removeCol(i);

      // only swap elements if not the last one was removed
      if(i < _rationalLP->nCols())
      {
         _colTypes[i] = _colTypes[_rationalLP->nCols()];
         assert(_colTypes[i] == _rangeTypeRational(lowerRational(i), upperRational(i)));
      }

      _colTypes.reSize(_rationalLP->nCols());
   }

   _invalidateSolution();
}



/// removes all columns with an index \p i such that \p perm[i] < 0; upon completion, \p perm[i] >= 0 indicates the
/// new index where column \p i has been moved to; note that \p perm must point to an array of size at least
/// #numColsReal()
void SoPlex::removeColsReal(int perm[])
{
   assert(_realLP != 0);

   const int oldsize = numColsReal();
   _removeColsReal(perm);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->removeCols(perm);

      for(int i = 0; i < oldsize; i++)
      {
         if(perm[i] >= 0)
            _colTypes[perm[i]] = _colTypes[i];
      }

      _colTypes.reSize(_rationalLP->nCols());

      for(int i = 0; i < numColsRational(); i++)
      {
         assert(_colTypes[i] == _rangeTypeRational(lowerRational(i), upperRational(i)));
      }
   }

   _invalidateSolution();
}



/// remove all columns with indices in array \p idx of size \p n; an array \p perm of size #numColsReal() may be
/// passed as buffer memory
void SoPlex::removeColsReal(int idx[], int n, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numColsReal());
      _idxToPerm(idx, n, p.get_ptr(), numColsReal());
      SoPlex::removeColsReal(p.get_ptr());
   }
   else
   {
      _idxToPerm(idx, n, perm, numColsReal());
      SoPlex::removeColsReal(perm);
   }
}



/// removes columns \p start to \p end including both; an array \p perm of size #numColsReal() may be passed as
/// buffer memory
void SoPlex::removeColRangeReal(int start, int end, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numColsReal());
      _rangeToPerm(start, end, p.get_ptr(), numColsReal());
      SoPlex::removeColsReal(p.get_ptr());
   }
   else
   {
      _rangeToPerm(start, end, perm, numColsReal());
      SoPlex::removeColsReal(perm);
   }
}



/// clears the LP
void SoPlex::clearLPReal()
{
   assert(_realLP != 0);

   _realLP->clear();
   _hasBasis = false;
   _rationalLUSolver.clear();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _rationalLP->clear();
      _rowTypes.clear();
      _colTypes.clear();
   }

   _invalidateSolution();
}



/// synchronizes real LP with rational LP, i.e., copies (rounded) rational LP into real LP, if sync mode is manual
void SoPlex::syncLPReal()
{
   assert(_isConsistent());

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_MANUAL)
      _syncLPReal();
}



/// adds a single row
void SoPlex::addRowRational(const LPRowRational& lprow)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addRow(lprow);
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _addRowReal(lprow);

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// adds a single row
void SoPlex::addRowRational(const mpq_t* lhs, const mpq_t* rowValues, const int* rowIndices,
                            const int rowSize, const mpq_t* rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addRow(lhs, rowValues, rowIndices, rowSize, rhs);
   _completeRangeTypesRational();

   int i = numRowsRational() - 1;

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _addRowReal(Real(lhsRational(i)), DSVectorReal(_rationalLP->rowVector(i)), Real(rhsRational(i)));

   _invalidateSolution();
}



/// adds a set of rows
void SoPlex::addRowsRational(const mpq_t* lhs, const mpq_t* rowValues, const int* rowIndices,
                             const int* rowStarts, const int* rowLengths, const int numRows, const int numValues,
                             const mpq_t* rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addRows(lhs, rowValues, rowIndices, rowStarts, rowLengths, numRows, numValues, rhs);
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      LPRowSetReal lprowset;

      for(int i = numRowsRational() - numRows; i < numRowsRational(); i++)
         lprowset.add(Real(lhsRational(i)), DSVectorReal(_rationalLP->rowVector(i)), Real(rhsRational(i)));

      _addRowsReal(lprowset);
   }

   _invalidateSolution();
}
#endif



/// adds multiple rows
void SoPlex::addRowsRational(const LPRowSetRational& lprowset)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addRows(lprowset);
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _addRowsReal(lprowset);

   _invalidateSolution();
}



/// adds a single column
void SoPlex::addColRational(const LPColRational& lpcol)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addCol(lpcol);
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _addColReal(lpcol);

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// adds a single column
void SoPlex::addColRational(const mpq_t* obj, const mpq_t* lower, const mpq_t* colValues,
                            const int* colIndices, const int colSize, const mpq_t* upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addCol(obj, lower, colValues, colIndices, colSize, upper);
   int i = numColsRational() - 1;
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _addColReal(Real(maxObjRational(i)) * (intParam(SoPlex::OBJSENSE) == SoPlex::OBJSENSE_MAXIMIZE ?
                                             1.0 : -1.0),
                  Real(lowerRational(i)), DSVectorReal(_rationalLP->colVector(i)), Real(upperRational(i)));

   _invalidateSolution();
}



/// adds a set of columns
void SoPlex::addColsRational(const mpq_t* obj, const mpq_t* lower, const mpq_t* colValues,
                             const int* colIndices, const int* colStarts, const int* colLengths, const int numCols,
                             const int numValues, const mpq_t* upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addCols(obj, lower, colValues, colIndices, colStarts, colLengths, numCols, numValues,
                        upper);
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      LPColSetReal lpcolset;

      for(int i = numColsRational() - numCols; i < numColsRational(); i++)
         lpcolset.add(Real(maxObjRational(i)) * (intParam(SoPlex::OBJSENSE) == SoPlex::OBJSENSE_MAXIMIZE ?
                                                 1.0 : -1.0),
                      Real(lowerRational(i)), DSVectorReal(_rationalLP->colVector(i)), Real(upperRational(i)));

      _addColsReal(lpcolset);
   }

   _invalidateSolution();
}
#endif



/// adds multiple columns
void SoPlex::addColsRational(const LPColSetRational& lpcolset)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->addCols(lpcolset);
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _addColsReal(lpcolset);

   _invalidateSolution();
}



/// replaces row \p i with \p lprow
void SoPlex::changeRowRational(int i, const LPRowRational& lprow)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeRow(i, lprow);
   _rowTypes[i] = _rangeTypeRational(lprow.lhs(), lprow.rhs());
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRowReal(i, lprow);

   _invalidateSolution();
}



/// changes left-hand side vector for constraints to \p lhs
void SoPlex::changeLhsRational(const VectorRational& lhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeLhs(lhs);

   for(int i = 0; i < numRowsRational(); i++)
      _rowTypes[i] = _rangeTypeRational(lhs[i], _rationalLP->rhs(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeLhsReal(DVectorReal(lhs));

   _invalidateSolution();
}



/// changes left-hand side of row \p i to \p lhs
void SoPlex::changeLhsRational(int i, const Rational& lhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeLhs(i, lhs);
   _rowTypes[i] = _rangeTypeRational(lhs, _rationalLP->rhs(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeLhsReal(i, Real(lhs));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes left-hand side of row \p i to \p lhs
void SoPlex::changeLhsRational(int i, const mpq_t* lhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeLhs(i, lhs);
   _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeLhsReal(i, Real(lhsRational(i)));

   _invalidateSolution();
}
#endif



/// changes right-hand side vector to \p rhs
void SoPlex::changeRhsRational(const VectorRational& rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeRhs(rhs);

   for(int i = 0; i < numRowsRational(); i++)
      _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), rhs[i]);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRhsReal(DVectorReal(rhs));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes right-hand side vector to \p rhs
void SoPlex::changeRhsRational(const mpq_t* rhs, int rhsSize)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   for(int i = 0; i < rhsSize; i++)
   {
      _rationalLP->changeRhs(i, rhs[i]);
      _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));
   }

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRhsReal(DVectorReal(rhsRational()));

   _invalidateSolution();
}
#endif



/// changes right-hand side of row \p i to \p rhs
void SoPlex::changeRhsRational(int i, const Rational& rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeRhs(i, rhs);
   _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), rhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRhsReal(i, Real(rhs));

   _invalidateSolution();
}



/// changes left- and right-hand side vectors
void SoPlex::changeRangeRational(const VectorRational& lhs, const VectorRational& rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeRange(lhs, rhs);

   for(int i = 0; i < numRowsRational(); i++)
      _rowTypes[i] = _rangeTypeRational(lhs[i], rhs[i]);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRangeReal(DVectorReal(lhs), DVectorReal(rhs));

   _invalidateSolution();
}



/// changes left- and right-hand side of row \p i
void SoPlex::changeRangeRational(int i, const Rational& lhs, const Rational& rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeRange(i, lhs, rhs);
   _rowTypes[i] = _rangeTypeRational(lhs, rhs);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRangeReal(i, Real(lhs), Real(rhs));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes left-hand side of row \p i to \p lhs
void SoPlex::changeRangeRational(int i, const mpq_t* lhs, const mpq_t* rhs)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeRange(i, lhs, rhs);
   _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeRangeReal(i, Real(lhsRational(i)), Real(rhsRational(i)));

   _invalidateSolution();
}
#endif



/// replaces column \p i with \p lpcol
void SoPlex::changeColRational(int i, const LPColRational& lpcol)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeCol(i, lpcol);
   _colTypes[i] = _rangeTypeRational(lpcol.lower(), lpcol.upper());
   _completeRangeTypesRational();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeColReal(i, lpcol);

   _invalidateSolution();
}



/// changes vector of lower bounds to \p lower
void SoPlex::changeLowerRational(const VectorRational& lower)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeLower(lower);

   for(int i = 0; i < numColsRational(); i++)
      _colTypes[i] = _rangeTypeRational(lower[i], _rationalLP->upper(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeLowerReal(DVectorReal(lower));

   _invalidateSolution();
}



/// changes lower bound of column i to \p lower
void SoPlex::changeLowerRational(int i, const Rational& lower)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeLower(i, lower);
   _colTypes[i] = _rangeTypeRational(lower, _rationalLP->upper(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeLowerReal(i, Real(lower));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes lower bound of column i to \p lower
void SoPlex::changeLowerRational(int i, const mpq_t* lower)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeLower(i, lower);
   _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeLowerReal(i, Real(lowerRational(i)));

   _invalidateSolution();
}
#endif



/// changes vector of upper bounds to \p upper
void SoPlex::changeUpperRational(const VectorRational& upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeUpper(upper);

   for(int i = 0; i < numColsRational(); i++)
      _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), upper[i]);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeUpperReal(DVectorReal(upper));

   _invalidateSolution();
}



/// changes \p i 'th upper bound to \p upper
void SoPlex::changeUpperRational(int i, const Rational& upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeUpper(i, upper);
   _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), upper);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeUpperReal(i, Real(upper));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes upper bound of column i to \p upper
void SoPlex::changeUpperRational(int i, const mpq_t* upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeUpper(i, upper);
   _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeUpperReal(i, Real(upperRational(i)));

   _invalidateSolution();
}
#endif



/// changes vectors of column bounds to \p lower and \p upper
void SoPlex::changeBoundsRational(const VectorRational& lower, const VectorRational& upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeBounds(lower, upper);

   for(int i = 0; i < numColsRational(); i++)
      _colTypes[i] = _rangeTypeRational(lower[i], upper[i]);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeBoundsReal(DVectorReal(lower), DVectorReal(upper));

   _invalidateSolution();
}



/// changes bounds of column \p i to \p lower and \p upper
void SoPlex::changeBoundsRational(int i, const Rational& lower, const Rational& upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeBounds(i, lower, upper);
   _colTypes[i] = _rangeTypeRational(lower, upper);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeBoundsReal(i, Real(lower), Real(upper));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes bounds of column \p i to \p lower and \p upper
void SoPlex::changeBoundsRational(int i, const mpq_t* lower, const mpq_t* upper)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeBounds(i, lower, upper);
   _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeBoundsReal(i, Real(lowerRational(i)), Real(upperRational(i)));

   _invalidateSolution();
}
#endif



/// changes objective function vector to \p obj
void SoPlex::changeObjRational(const VectorRational& obj)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeObj(obj);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _realLP->changeObj(DVectorReal(obj));

   _invalidateSolution();
}



/// changes objective coefficient of column i to \p obj
void SoPlex::changeObjRational(int i, const Rational& obj)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeObj(i, obj);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _realLP->changeObj(i, Real(obj));

   _invalidateSolution();
}



#ifdef SOPLEX_WITH_GMP
/// changes objective coefficient of column i to \p obj
void SoPlex::changeObjRational(int i, const mpq_t* obj)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeObj(i, obj);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _realLP->changeObj(i, Real(objRational(i)));

   _invalidateSolution();
}
#endif



/// changes matrix entry in row \p i and column \p j to \p val
void SoPlex::changeElementRational(int i, int j, const Rational& val)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeElement(i, j, val);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeElementReal(i, j, Real(val));

   _invalidateSolution();
}


#ifdef SOPLEX_WITH_GMP
/// changes matrix entry in row \p i and column \p j to \p val
void SoPlex::changeElementRational(int i, int j, const mpq_t* val)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->changeElement(i, j, val);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _changeElementReal(i, j, mpq_get_d(*val));

   _invalidateSolution();
}
#endif


/// removes row \p i
void SoPlex::removeRowRational(int i)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->removeRow(i);

   // only swap elements if not the last one was removed
   if(i < _rationalLP->nRows())
   {
      _rowTypes[i] = _rowTypes[_rationalLP->nRows()];
      assert(_rowTypes[i] == _rangeTypeRational(lhsRational(i), rhsRational(i)));
   }

   _rowTypes.reSize(_rationalLP->nRows());

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _removeRowReal(i);

   _invalidateSolution();
}



/// removes all rows with an index \p i such that \p perm[i] < 0; upon completion, \p perm[i] >= 0 indicates the new
/// index where row \p i has been moved to; note that \p perm must point to an array of size at least
/// #numRowsRational()
void SoPlex::removeRowsRational(int perm[])
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   const int oldsize = numRowsRational();
   _rationalLP->removeRows(perm);

   for(int i = 0; i < oldsize; i++)
   {
      if(perm[i] >= 0)
         _rowTypes[perm[i]] = _rowTypes[i];
   }

   _rowTypes.reSize(_rationalLP->nRows());

   for(int i = 0; i < numRowsRational(); i++)
   {
      assert(_rowTypes[i] == _rangeTypeRational(lhsRational(i), rhsRational(i)));
   }


   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _removeRowsReal(perm);

   _invalidateSolution();
}



/// remove all rows with indices in array \p idx of size \p n; an array \p perm of size #numRowsRational() may be
/// passed as buffer memory
void SoPlex::removeRowsRational(int idx[], int n, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numRowsRational());
      _idxToPerm(idx, n, p.get_ptr(), numRowsRational());
      SoPlex::removeRowsRational(p.get_ptr());
   }
   else
   {
      _idxToPerm(idx, n, perm, numRowsRational());
      SoPlex::removeRowsRational(perm);
   }
}



/// removes rows \p start to \p end including both; an array \p perm of size #numRowsRational() may be passed as
/// buffer memory
void SoPlex::removeRowRangeRational(int start, int end, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numRowsRational());
      _rangeToPerm(start, end, p.get_ptr(), numRowsRational());
      SoPlex::removeRowsRational(p.get_ptr());
   }
   else
   {
      _rangeToPerm(start, end, perm, numRowsRational());
      SoPlex::removeRowsRational(perm);
   }
}



/// removes column i
void SoPlex::removeColRational(int i)
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->removeCol(i);

   // only swap elements if not the last one was removed
   if(i < _rationalLP->nCols())
   {
      _colTypes[i] = _colTypes[_rationalLP->nCols()];
      assert(_colTypes[i] == _rangeTypeRational(lowerRational(i), upperRational(i)));
   }

   _colTypes.reSize(_rationalLP->nCols());

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _removeColReal(i);

   _invalidateSolution();
}



/// removes all columns with an index \p i such that \p perm[i] < 0; upon completion, \p perm[i] >= 0 indicates the
/// new index where column \p i has been moved to; note that \p perm must point to an array of size at least
/// #numColsRational()
void SoPlex::removeColsRational(int perm[])
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   const int oldsize = numColsRational();
   _rationalLP->removeCols(perm);

   for(int i = 0; i < oldsize; i++)
   {
      if(perm[i] >= 0)
         _colTypes[perm[i]] = _colTypes[i];
   }

   _colTypes.reSize(_rationalLP->nCols());

   for(int i = 0; i < numColsRational(); i++)
   {
      assert(_colTypes[i] == _rangeTypeRational(lowerRational(i), upperRational(i)));
   }

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
      _removeColsReal(perm);

   _invalidateSolution();
}



/// remove all columns with indices in array \p idx of size \p n; an array \p perm of size #numColsRational() may be
/// passed as buffer memory
void SoPlex::removeColsRational(int idx[], int n, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numColsRational());
      _idxToPerm(idx, n, p.get_ptr(), numColsRational());
      SoPlex::removeColsRational(p.get_ptr());
   }
   else
   {
      _idxToPerm(idx, n, perm, numColsRational());
      SoPlex::removeColsRational(perm);
   }
}



/// removes columns \p start to \p end including both; an array \p perm of size #numColsRational() may be passed as
/// buffer memory
void SoPlex::removeColRangeRational(int start, int end, int perm[])
{
   if(perm == 0)
   {
      DataArray< int > p(numColsRational());
      _rangeToPerm(start, end, p.get_ptr(), numColsRational());
      SoPlex::removeColsRational(p.get_ptr());
   }
   else
   {
      _rangeToPerm(start, end, perm, numColsRational());
      SoPlex::removeColsRational(perm);
   }
}



/// clears the LP
void SoPlex::clearLPRational()
{
   assert(_rationalLP != 0);

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return;

   _rationalLP->clear();
   _rationalLUSolver.clear();
   _rowTypes.clear();
   _colTypes.clear();

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
   {
      _realLP->clear();
      _hasBasis = false;
   }

   _invalidateSolution();
}



/// synchronizes rational LP with real LP, i.e., copies real LP to rational LP, if sync mode is manual
void SoPlex::syncLPRational()
{
   assert(_isConsistent());

   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_MANUAL)
      _syncLPRational();
}



/// solves the LP
SPxSolver::Status SoPlex::optimize()
{
   assert(_isConsistent());

   // clear statistics
   _statistics->clearSolvingData();

   // the solution is no longer valid
   _invalidateSolution();

   // if the decomposition based dual simplex flag is set to true
   if(boolParam(SoPlex::USEDECOMPDUALSIMPLEX))
   {
      setIntParam(SoPlex::SOLVEMODE, SOLVEMODE_REAL);
      setIntParam(SoPlex::REPRESENTATION, REPRESENTATION_ROW);
      setIntParam(SoPlex::ALGORITHM, ALGORITHM_DUAL);
      //setBoolParam(SoPlex::PERSISTENTSCALING, false);

      _solver.setComputeDegenFlag(boolParam(COMPUTEDEGEN));

      _solveDecompositionDualSimplex();
   }
   // decide whether to solve the rational LP with iterative refinement or call the standard floating-point solver
   else if(intParam(SoPlex::SOLVEMODE) == SOLVEMODE_REAL
           || (intParam(SoPlex::SOLVEMODE) == SOLVEMODE_AUTO
               && GE(realParam(SoPlex::FEASTOL), 1e-9) && GE(realParam(SoPlex::OPTTOL), 1e-9)))
   {
      // ensure that tolerances are reasonable for the floating-point solver
      if(realParam(SoPlex::FEASTOL) < _currentSettings->realParam.lower[SoPlex::FPFEASTOL])
      {
         MSG_WARNING(spxout, spxout << "Cannot call floating-point solver with feasibility tolerance below "
                     << _currentSettings->realParam.lower[SoPlex::FPFEASTOL] << " - relaxing tolerance\n");
         _solver.setFeastol(_currentSettings->realParam.lower[SoPlex::FPFEASTOL]);
      }
      else
         _solver.setFeastol(realParam(SoPlex::FEASTOL));

      if(realParam(SoPlex::OPTTOL) < _currentSettings->realParam.lower[SoPlex::FPOPTTOL])
      {
         MSG_WARNING(spxout, spxout << "Cannot call floating-point solver with optimality tolerance below "
                     << _currentSettings->realParam.lower[SoPlex::FPOPTTOL] << " - relaxing tolerance\n");
         _solver.setOpttol(_currentSettings->realParam.lower[SoPlex::FPOPTTOL]);
      }
      else
         _solver.setOpttol(realParam(SoPlex::OPTTOL));

      _solver.setComputeDegenFlag(boolParam(COMPUTEDEGEN));

      _optimizeReal();
#ifdef SOPLEX_DEBUG // this check will remove scaling of the realLP
      _checkBasisScaling();
#endif
   }
   else if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
   {
      _syncLPRational();
      _optimizeRational();
   }
   else if(intParam(SoPlex::SYNCMODE) == SYNCMODE_MANUAL)
   {
#ifdef ENABLE_ADDITIONAL_CHECKS
      assert(areLPsInSync(true, true, false));
#else
      assert(areLPsInSync(true, false, false));
#endif

      _optimizeRational();

#ifdef ENABLE_ADDITIONAL_CHECKS
      assert(areLPsInSync(true, true, false));
#else
      assert(areLPsInSync(true, false, false));
#endif
   }
   else
   {
#ifdef ENABLE_ADDITIONAL_CHECKS
      assert(areLPsInSync(true, true, false));
#else
      assert(areLPsInSync(true, false, false));
#endif

      _optimizeRational();
   }

   MSG_INFO1(spxout, spxout << "\n";
             printShortStatistics(spxout.getStream(SPxOut::INFO1));
             spxout << "\n");


   return status();
}



/// returns the current solver status
SPxSolver::Status SoPlex::status() const
{
   return _status;
}



/// is stored primal solution feasible?
bool SoPlex::isPrimalFeasible() const
{
   return (_hasSolReal && _solReal.isPrimalFeasible()) || (_hasSolRational
          && _solRational.isPrimalFeasible());
}



/// is a primal feasible solution available?
bool SoPlex::hasPrimal() const
{
   return _hasSolReal || _hasSolRational;
}



/// is a primal unbounded ray available?
bool SoPlex::hasPrimalRay() const
{
   return (_hasSolReal && _solReal.hasPrimalRay()) || (_hasSolRational && _solRational.hasPrimalRay());
}



/// is stored dual solution feasible?
bool SoPlex::isDualFeasible() const
{
   return (_hasSolReal && _solReal.isDualFeasible()) || (_hasSolRational
          && _solRational.isDualFeasible());
}



/// is a dual feasible solution available?
bool SoPlex::hasDual() const
{
   return _hasSolReal || _hasSolRational;
}



/// is Farkas proof of infeasibility available?
bool SoPlex::hasDualFarkas() const
{
   return (_hasSolReal && _solReal.hasDualFarkas()) || (_hasSolRational
          && _solRational.hasDualFarkas());
}



/// returns the objective value if a primal or dual solution is available
Real SoPlex::objValueReal()
{
   assert(OBJSENSE_MAXIMIZE == 1);
   assert(OBJSENSE_MINIMIZE == -1);

   if(status() == SPxSolver::UNBOUNDED)
      return realParam(SoPlex::INFTY) * intParam(SoPlex::OBJSENSE);
   else if(status() == SPxSolver::INFEASIBLE)
      return -realParam(SoPlex::INFTY) * intParam(SoPlex::OBJSENSE);
   else if(hasPrimal() || hasDual())
   {
      _syncRealSolution();
      return _solReal._objVal;
   }
   else
      return 0.0;
}



/// gets the primal solution vector if available; returns true on success
bool SoPlex::getPrimalReal(VectorReal& vector)
{
   if(hasPrimal() && vector.dim() >= numColsReal())
   {
      _syncRealSolution();
      _solReal.getPrimal(vector);
      return true;
   }
   else
      return false;
}



/// gets the vector of slack values if available; returns true on success
bool SoPlex::getSlacksReal(VectorReal& vector)
{
   if(hasPrimal() && vector.dim() >= numRowsReal())
   {
      _syncRealSolution();
      _solReal.getSlacks(vector);
      return true;
   }
   else
      return false;
}



/// gets the primal ray if available; returns true on success
bool SoPlex::getPrimalRayReal(VectorReal& vector)
{
   if(hasPrimalRay() && vector.dim() >= numColsReal())
   {
      _syncRealSolution();
      _solReal.getPrimalRay(vector);
      return true;
   }
   else
      return false;
}



/// gets the dual solution vector if available; returns true on success
bool SoPlex::getDualReal(VectorReal& vector)
{
   if(hasDual() && vector.dim() >= numRowsReal())
   {
      _syncRealSolution();
      _solReal.getDual(vector);
      return true;
   }
   else
      return false;
}



/// gets the vector of reduced cost values if available; returns true on success
bool SoPlex::getRedCostReal(VectorReal& vector)
{
   if(hasDual() && vector.dim() >= numColsReal())
   {
      _syncRealSolution();
      _solReal.getRedCost(vector);
      return true;
   }
   else
      return false;
}



/// gets the Farkas proof if available; returns true on success
bool SoPlex::getDualFarkasReal(VectorReal& vector)
{
   if(hasDualFarkas() && vector.dim() >= numRowsReal())
   {
      _syncRealSolution();
      _solReal.getDualFarkas(vector);
      return true;
   }
   else
      return false;
}



/// gets violation of bounds; returns true on success
bool SoPlex::getBoundViolationReal(Real& maxviol, Real& sumviol)
{
   if(!isPrimalFeasible())
      return false;

   _syncRealSolution();
   VectorReal& primal = _solReal._primal;
   assert(primal.dim() == numColsReal());

   maxviol = 0.0;
   sumviol = 0.0;

   for(int i = numColsReal() - 1; i >= 0; i--)
   {
      Real lower = _realLP->lowerUnscaled(i);
      Real upper = _realLP->upperUnscaled(i);
      Real viol = lower - primal[i];

      if(viol > 0.0)
      {
         sumviol += viol;

         if(viol > maxviol)
            maxviol = viol;
      }

      viol = primal[i] - upper;

      if(viol > 0.0)
      {
         sumviol += viol;

         if(viol > maxviol)
            maxviol = viol;
      }
   }

   return true;
}



/// gets violation of constraints; returns true on success
bool SoPlex::getRowViolationReal(Real& maxviol, Real& sumviol)
{
   if(!isPrimalFeasible())
      return false;

   _syncRealSolution();
   VectorReal& primal = _solReal._primal;
   assert(primal.dim() == numColsReal());

   DVectorReal activity(numRowsReal());
   _realLP->computePrimalActivity(primal, activity, true);
   maxviol = 0.0;
   sumviol = 0.0;

   for(int i = numRowsReal() - 1; i >= 0; i--)
   {
      Real lhs = _realLP->lhsUnscaled(i);
      Real rhs = _realLP->rhsUnscaled(i);

      Real viol = lhs - activity[i];

      if(viol > 0.0)
      {
         sumviol += viol;

         if(viol > maxviol)
            maxviol = viol;
      }

      viol = activity[i] - rhs;

      if(viol > 0.0)
      {
         sumviol += viol;

         if(viol > maxviol)
            maxviol = viol;
      }
   }

   return true;
}



/// gets violation of reduced costs; returns true on success
bool SoPlex::getRedCostViolationReal(Real& maxviol, Real& sumviol)
{
   if(!isDualFeasible() || !hasBasis())
      return false;

   _syncRealSolution();
   VectorReal& redcost = _solReal._redCost;
   assert(redcost.dim() == numColsReal());

   maxviol = 0.0;
   sumviol = 0.0;

   for(int c = numColsReal() - 1; c >= 0; c--)
   {
      SPxSolver::VarStatus colStatus = basisColStatus(c);

      if(intParam(SoPlex::OBJSENSE) == OBJSENSE_MINIMIZE)
      {
         if(colStatus != SPxSolver::ON_UPPER && colStatus != SPxSolver::FIXED && redcost[c] < 0.0)
         {
            sumviol += -redcost[c];

            if(redcost[c] < -maxviol)
               maxviol = -redcost[c];
         }

         if(colStatus != SPxSolver::ON_LOWER && colStatus != SPxSolver::FIXED && redcost[c] > 0.0)
         {
            sumviol += redcost[c];

            if(redcost[c] > maxviol)
               maxviol = redcost[c];
         }
      }
      else
      {
         if(colStatus != SPxSolver::ON_UPPER && colStatus != SPxSolver::FIXED && redcost[c] > 0.0)
         {
            sumviol += redcost[c];

            if(redcost[c] > maxviol)
               maxviol = redcost[c];
         }

         if(colStatus != SPxSolver::ON_LOWER && colStatus != SPxSolver::FIXED && redcost[c] < 0.0)
         {
            sumviol += -redcost[c];

            if(redcost[c] < -maxviol)
               maxviol = -redcost[c];
         }
      }
   }

   return true;
}



/// gets violation of dual multipliers; returns true on success
bool SoPlex::getDualViolationReal(Real& maxviol, Real& sumviol)
{
   if(!isDualFeasible() || !hasBasis())
      return false;

   _syncRealSolution();
   VectorReal& dual = _solReal._dual;
   assert(dual.dim() == numRowsReal());

   maxviol = 0.0;
   sumviol = 0.0;

   for(int r = numRowsReal() - 1; r >= 0; r--)
   {
      SPxSolver::VarStatus rowStatus = basisRowStatus(r);

      if(intParam(SoPlex::OBJSENSE) == OBJSENSE_MINIMIZE)
      {
         if(rowStatus != SPxSolver::ON_UPPER && rowStatus != SPxSolver::FIXED && dual[r] < 0.0)
         {
            sumviol += -dual[r];

            if(dual[r] < -maxviol)
               maxviol = -dual[r];
         }

         if(rowStatus != SPxSolver::ON_LOWER && rowStatus != SPxSolver::FIXED && dual[r] > 0.0)
         {
            sumviol += dual[r];

            if(dual[r] > maxviol)
               maxviol = dual[r];
         }
      }
      else
      {
         if(rowStatus != SPxSolver::ON_UPPER && rowStatus != SPxSolver::FIXED && dual[r] > 0.0)
         {
            sumviol += dual[r];

            if(dual[r] > maxviol)
               maxviol = dual[r];
         }

         if(rowStatus != SPxSolver::ON_LOWER && rowStatus != SPxSolver::FIXED && dual[r] < 0.0)
         {
            sumviol += -dual[r];

            if(dual[r] < -maxviol)
               maxviol = -dual[r];
         }
      }
   }

   return true;
}



/// returns the objective value if a primal or dual solution is available
Rational SoPlex::objValueRational()
{
   assert(OBJSENSE_MAXIMIZE == 1);
   assert(OBJSENSE_MINIMIZE == -1);

   if(status() == SPxSolver::UNBOUNDED)
   {
      if(intParam(SoPlex::OBJSENSE) == OBJSENSE_MAXIMIZE)
         return _rationalPosInfty;
      else
         return _rationalNegInfty;
   }
   else if(status() == SPxSolver::INFEASIBLE)
   {
      if(intParam(SoPlex::OBJSENSE) == OBJSENSE_MAXIMIZE)
         return _rationalNegInfty;
      else
         return _rationalPosInfty;
   }
   else if(hasPrimal() || hasDual())
   {
      _syncRationalSolution();
      return _solRational._objVal;
   }
   else
      return _rationalZero;
}



/// gets the primal solution vector if available; returns true on success
bool SoPlex::getPrimalRational(VectorRational& vector)
{
   if(_rationalLP != 0 && hasPrimal() && vector.dim() >= numColsRational())
   {
      _syncRationalSolution();
      _solRational.getPrimal(vector);
      return true;
   }
   else
      return false;
}



/// gets the vector of slack values if available; returns true on success
bool SoPlex::getSlacksRational(VectorRational& vector)
{
   if(_rationalLP != 0 && hasPrimal() && vector.dim() >= numRowsRational())
   {
      _syncRationalSolution();
      _solRational.getSlacks(vector);
      return true;
   }
   else
      return false;
}



/// gets the primal ray if LP is unbounded; returns true on success
bool SoPlex::getPrimalRayRational(VectorRational& vector)
{
   if(_rationalLP != 0 && hasPrimalRay() && vector.dim() >= numColsRational())
   {
      _syncRationalSolution();
      _solRational.getPrimalRay(vector);
      return true;
   }
   else
      return false;
}



/// gets the dual solution vector if available; returns true on success
bool SoPlex::getDualRational(VectorRational& vector)
{
   if(_rationalLP != 0 && hasDual() && vector.dim() >= numRowsRational())
   {
      _syncRationalSolution();
      _solRational.getDual(vector);
      return true;
   }
   else
      return false;
}



/// gets the vector of reduced cost values if available; returns true on success
bool SoPlex::getRedCostRational(VectorRational& vector)
{
   if(_rationalLP != 0 && hasDual() && vector.dim() >= numColsRational())
   {
      _syncRationalSolution();
      _solRational.getRedCost(vector);
      return true;
   }
   else
      return false;
}



/// gets the Farkas proof if LP is infeasible; returns true on success
bool SoPlex::getDualFarkasRational(VectorRational& vector)
{
   if(_rationalLP != 0 && hasDualFarkas() && vector.dim() >= numRowsRational())
   {
      _syncRationalSolution();
      _solRational.getDualFarkas(vector);
      return true;
   }
   else
      return false;
}



/// gets violation of bounds; returns true on success
bool SoPlex::getBoundViolationRational(Rational& maxviol, Rational& sumviol)
{
   if(!isPrimalFeasible())
      return false;

   // if we have to synchronize, we do not measure time, because this would affect the solving statistics
   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      _syncLPRational(false);

   _syncRationalSolution();
   VectorRational& primal = _solRational._primal;
   assert(primal.dim() == numColsRational());

   maxviol = 0;
   sumviol = 0;

   for(int i = numColsRational() - 1; i >= 0; i--)
   {
      Rational viol = lowerRational(i) - primal[i];

      if(viol > 0)
      {
         sumviol += viol;

         if(viol > maxviol)
         {
            maxviol = viol;
            MSG_DEBUG(std::cout << "increased bound violation for column " << i << ": " << rationalToString(
                         viol)
                      << " lower: " << rationalToString(lowerRational(i))
                      << ", primal: " << rationalToString(primal[i]) << "\n");
         }
      }

      viol = primal[i] - upperRational(i);

      if(viol > 0)
      {
         sumviol += viol;

         if(viol > maxviol)
         {
            maxviol = viol;
            MSG_DEBUG(std::cout << "increased bound violation for column " << i << ": " << rationalToString(
                         viol)
                      << " upper: " << rationalToString(upperRational(i))
                      << ", primal: " << rationalToString(primal[i]) << "\n");
         }
      }
   }

   return true;
}



/// gets violation of constraints; returns true on success
bool SoPlex::getRowViolationRational(Rational& maxviol, Rational& sumviol)
{
   if(!isPrimalFeasible())
      return false;

   // if we have to synchronize, we do not measure time, because this would affect the solving statistics
   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      _syncLPRational(false);

   _syncRationalSolution();
   VectorRational& primal = _solRational._primal;
   assert(primal.dim() == numColsRational());

   DVectorRational activity(numRowsRational());
   _rationalLP->computePrimalActivity(primal, activity);
   maxviol = 0;
   sumviol = 0;

   for(int i = numRowsRational() - 1; i >= 0; i--)
   {
      Rational viol = lhsRational(i) - activity[i];

      if(viol > 0)
      {
         sumviol += viol;

         if(viol > maxviol)
         {
            maxviol = viol;
            MSG_DEBUG(std::cout << "increased constraint violation for row " << i << ": " << rationalToString(
                         viol)
                      << " lhs: " << rationalToString(lhsRational(i))
                      << ", activity: " << rationalToString(activity[i]) << "\n");
         }
      }

      viol = activity[i] - rhsRational(i);

      if(viol > 0)
      {
         sumviol += viol;

         if(viol > maxviol)
         {
            maxviol = viol;
            MSG_DEBUG(std::cout << "increased constraint violation for row " << i << ": " << rationalToString(
                         viol)
                      << " rhs: " << rationalToString(rhsRational(i))
                      << ", activity: " << rationalToString(activity[i]) << "\n");
         }
      }
   }

   return true;
}



/// gets violation of reduced costs; returns true on success
bool SoPlex::getRedCostViolationRational(Rational& maxviol, Rational& sumviol)
{
   if(!isPrimalFeasible() || !isDualFeasible())
      return false;

   // if we have to synchronize, we do not measure time, because this would affect the solving statistics
   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      _syncLPRational(false);

   _syncRationalSolution();
   VectorRational& redcost = _solRational._redCost;
   assert(redcost.dim() == numColsRational());

   maxviol = 0;
   sumviol = 0;

   for(int c = numColsReal() - 1; c >= 0; c--)
   {
      assert(!_hasBasis || basisColStatus(c) != SPxSolver::UNDEFINED);

      if(_colTypes[c] == RANGETYPE_FIXED)
      {
         assert(lowerRational(c) == upperRational(c));
         continue;
      }

      assert(!_hasBasis || basisColStatus(c) != SPxSolver::ON_LOWER
             || _solRational._primal[c] == lowerRational(c));
      assert(!_hasBasis || basisColStatus(c) != SPxSolver::ON_UPPER
             || _solRational._primal[c] == upperRational(c));
      assert(!_hasBasis || basisColStatus(c) != SPxSolver::FIXED
             || _solRational._primal[c] == lowerRational(c));
      assert(!_hasBasis || basisColStatus(c) != SPxSolver::FIXED
             || _solRational._primal[c] == upperRational(c));

      if(intParam(SoPlex::OBJSENSE) == OBJSENSE_MINIMIZE)
      {
         if(_solRational._primal[c] != upperRational(c) && redcost[c] < 0)
         {
            sumviol += -redcost[c];

            if(redcost[c] < -maxviol)
            {
               MSG_DEBUG(std::cout << "increased reduced cost violation for column " << c <<
                         " not on upper bound: " << rationalToString(-redcost[c]) << "\n");
               maxviol = -redcost[c];
            }
         }

         if(_solRational._primal[c] != lowerRational(c) && redcost[c] > 0)
         {
            sumviol += redcost[c];

            if(redcost[c] > maxviol)
            {
               MSG_DEBUG(std::cout << "increased reduced cost violation for column " << c <<
                         " not on lower bound: " << rationalToString(redcost[c]) << "\n");
               maxviol = redcost[c];
            }
         }
      }
      else
      {
         if(_solRational._primal[c] != upperRational(c) && redcost[c] > 0)
         {
            sumviol += redcost[c];

            if(redcost[c] > maxviol)
            {
               MSG_DEBUG(std::cout << "increased reduced cost violation for column " << c <<
                         " not on upper bound: " << rationalToString(redcost[c]) << "\n");
               maxviol = redcost[c];
            }
         }

         if(_solRational._primal[c] != lowerRational(c) && redcost[c] < 0)
         {
            sumviol += -redcost[c];

            if(redcost[c] < -maxviol)
            {
               MSG_DEBUG(std::cout << "increased reduced cost violation for column " << c <<
                         " not on lower bound: " << rationalToString(-redcost[c]) << "\n");
               maxviol = -redcost[c];
            }
         }
      }
   }

   return true;
}



/// gets violation of dual multipliers; returns true on success
bool SoPlex::getDualViolationRational(Rational& maxviol, Rational& sumviol)
{
   if(!isDualFeasible() || !isPrimalFeasible())
      return false;

   // if we have to synchronize, we do not measure time, because this would affect the solving statistics
   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      _syncLPRational(false);

   _syncRationalSolution();
   VectorRational& dual = _solRational._dual;
   assert(dual.dim() == numRowsRational());

   maxviol = 0;
   sumviol = 0;

   for(int r = numRowsReal() - 1; r >= 0; r--)
   {
      assert(!_hasBasis || basisRowStatus(r) != SPxSolver::UNDEFINED);

      if(_rowTypes[r] == RANGETYPE_FIXED)
      {
         assert(lhsRational(r) == rhsRational(r));
         continue;
      }

      assert(!_hasBasis || basisRowStatus(r) != SPxSolver::ON_LOWER
             || _solRational._slacks[r] <= lhsRational(r) + _rationalFeastol);
      assert(!_hasBasis || basisRowStatus(r) != SPxSolver::ON_UPPER
             || _solRational._slacks[r] >= rhsRational(r) - _rationalFeastol);
      assert(!_hasBasis || basisRowStatus(r) != SPxSolver::FIXED
             || _solRational._slacks[r] <= lhsRational(r) + _rationalFeastol);
      assert(!_hasBasis || basisRowStatus(r) != SPxSolver::FIXED
             || _solRational._slacks[r] >= rhsRational(r) - _rationalFeastol);

      if(intParam(SoPlex::OBJSENSE) == OBJSENSE_MINIMIZE)
      {
         if(_solRational._slacks[r] < rhsRational(r) - _rationalFeastol && dual[r] < 0)
         {
            sumviol += -dual[r];

            if(dual[r] < -maxviol)
            {
               MSG_DEBUG(std::cout << "increased dual violation for row " << r << " not on upper bound: " <<
                         rationalToString(-dual[r])
                         << " (slack = " << rationalToString(_solRational._slacks[r])
                         << ", status = " << basisRowStatus(r)
                         << ", lhs = " << rationalToString(lhsRational(r))
                         << ", rhs = " << rationalToString(rhsRational(r)) << ")\n");
               maxviol = -dual[r];
            }
         }

         if(_solRational._slacks[r] > lhsRational(r) + _rationalFeastol && dual[r] > 0)
         {
            sumviol += dual[r];

            if(dual[r] > maxviol)
            {
               MSG_DEBUG(std::cout << "increased dual violation for row " << r << " not on lower bound: " <<
                         rationalToString(dual[r])
                         << " (slack = " << rationalToString(_solRational._slacks[r])
                         << ", status = " << basisRowStatus(r)
                         << ", lhs = " << rationalToString(lhsRational(r))
                         << ", rhs = " << rationalToString(rhsRational(r)) << ")\n");
               maxviol = dual[r];
            }
         }
      }
      else
      {
         if(_solRational._slacks[r] < rhsRational(r) - _rationalFeastol && dual[r] > 0)
         {
            sumviol += dual[r];

            if(dual[r] > maxviol)
            {
               MSG_DEBUG(std::cout << "increased dual violation for row " << r << " not on upper bound: " <<
                         rationalToString(dual[r])
                         << " (slack = " << rationalToString(_solRational._slacks[r])
                         << ", status = " << basisRowStatus(r)
                         << ", lhs = " << rationalToString(lhsRational(r))
                         << ", rhs = " << rationalToString(rhsRational(r)) << ")\n");
               maxviol = dual[r];
            }
         }

         if(_solRational._slacks[r] > lhsRational(r) + _rationalFeastol && dual[r] < 0)
         {
            sumviol += -dual[r];

            if(dual[r] < -maxviol)
            {
               MSG_DEBUG(std::cout << "increased dual violation for row " << r << " not on lower bound: " <<
                         rationalToString(-dual[r])
                         << " (slack = " << rationalToString(_solRational._slacks[r])
                         << ", status = " << basisRowStatus(r)
                         << ", lhs = " << rationalToString(lhsRational(r))
                         << ", rhs = " << rationalToString(rhsRational(r)) << ")\n");
               maxviol = -dual[r];
            }
         }
      }
   }

   return true;
}



#ifdef SOPLEX_WITH_GMP
/// gets the primal solution vector if available; returns true on success
bool SoPlex::getPrimalRational(mpq_t* vector, const int size)
{
   assert(size >= numColsRational());

   if(hasPrimal())
   {
      _syncRationalSolution();

      for(int i = 0; i < numColsRational(); i++)
         mpq_set(vector[i], _solRational._primal[i].getMpqRef());

      return true;
   }
   else
      return false;
}


/// gets the vector of slack values if available; returns true on success
bool SoPlex::getSlacksRational(mpq_t* vector, const int size)
{
   assert(size >= numRowsRational());

   if(hasPrimal())
   {
      _syncRationalSolution();

      for(int i = 0; i < numRowsRational(); i++)
         mpq_set(vector[i], _solRational._slacks[i].getMpqRef());

      return true;
   }
   else
      return false;
}



/// gets the primal ray if LP is unbounded; returns true on success
bool SoPlex::getPrimalRayRational(mpq_t* vector, const int size)
{
   assert(size >= numColsRational());

   if(hasPrimalRay())
   {
      _syncRationalSolution();

      for(int i = 0; i < numColsRational(); i++)
         mpq_set(vector[i], _solRational._primalRay[i].getMpqRef());

      return true;
   }
   else
      return false;
}



/// gets the dual solution vector if available; returns true on success
bool SoPlex::getDualRational(mpq_t* vector, const int size)
{
   assert(size >= numRowsRational());

   if(hasDual())
   {
      _syncRationalSolution();

      for(int i = 0; i < numRowsRational(); i++)
         mpq_set(vector[i], _solRational._dual[i].getMpqRef());

      return true;
   }
   else
      return false;
}



/// gets the vector of reduced cost values if available; returns true on success
bool SoPlex::getRedCostRational(mpq_t* vector, const int size)
{
   assert(size >= numColsRational());

   if(hasDual())
   {
      _syncRationalSolution();

      for(int i = 0; i < numColsRational(); i++)
         mpq_set(vector[i], _solRational._redCost[i].getMpqRef());

      return true;
   }
   else
      return false;
}



/// gets the Farkas proof if LP is infeasible; returns true on success
bool SoPlex::getDualFarkasRational(mpq_t* vector, const int size)
{
   assert(size >= numRowsRational());

   if(hasDualFarkas())
   {
      _syncRationalSolution();

      for(int i = 0; i < numRowsRational(); i++)
         mpq_set(vector[i], _solRational._dualFarkas[i].getMpqRef());

      return true;
   }
   else
      return false;
}
#endif



/// get size of primal solution
int SoPlex::totalSizePrimalRational(const int base)
{
   if(hasPrimal() || hasPrimalRay())
   {
      _syncRationalSolution();
      return _solRational.totalSizePrimal(base);
   }
   else
      return 0;
}



/// get size of dual solution
int SoPlex::totalSizeDualRational(const int base)
{
   if(hasDual() || hasDualFarkas())
   {
      _syncRationalSolution();
      return _solRational.totalSizeDual(base);
   }
   else
      return 0;
}



/// get size of least common multiple of denominators in primal solution
int SoPlex::dlcmSizePrimalRational(const int base)
{
   if(hasPrimal() || hasPrimalRay())
   {
      _syncRationalSolution();
      return _solRational.dlcmSizePrimal(base);
   }
   else
      return 0;
}



/// get size of least common multiple of denominators in dual solution
int SoPlex::dlcmSizeDualRational(const int base)
{
   if(hasDual() || hasDualFarkas())
   {
      _syncRationalSolution();
      return _solRational.dlcmSizeDual(base);
   }
   else
      return 0;
}



/// get size of largest denominator in primal solution
int SoPlex::dmaxSizePrimalRational(const int base)
{
   if(hasPrimal() || hasPrimalRay())
   {
      _syncRationalSolution();
      return _solRational.dmaxSizePrimal(base);
   }
   else
      return 0;
}



/// get size of largest denominator in dual solution
int SoPlex::dmaxSizeDualRational(const int base)
{
   if(hasDual() || hasDualFarkas())
   {
      _syncRationalSolution();
      return _solRational.dmaxSizeDual(base);
   }
   else
      return 0;
}



/// is an advanced starting basis available?
bool SoPlex::hasBasis() const
{
   return _hasBasis;
}



/// returns the current basis status
SPxBasis::SPxStatus SoPlex::basisStatus() const
{
   if(!hasBasis())
      return SPxBasis::NO_PROBLEM;
   else if(status() == SPxSolver::OPTIMAL || status() == SPxSolver::OPTIMAL_UNSCALED_VIOLATIONS)
      return SPxBasis::OPTIMAL;
   else if(status() == SPxSolver::UNBOUNDED)
      return SPxBasis::UNBOUNDED;
   else if(status() == SPxSolver::INFEASIBLE)
      return SPxBasis::INFEASIBLE;
   else if(hasPrimal())
      return SPxBasis::PRIMAL;
   else if(hasDual())
      return SPxBasis::DUAL;
   else
      return SPxBasis::REGULAR;
}



/// returns basis status for a single row
SPxSolver::VarStatus SoPlex::basisRowStatus(int row) const
{
   assert(row >= 0);
   assert(row < numRowsReal());

   // if no basis is available, return slack basis; if index is out of range, return basic status as for a newly
   // added row
   if(!hasBasis() || row < 0 || row >= numRowsReal())
      return SPxSolver::BASIC;
   // if the real LP is loaded, ask solver
   else if(_isRealLPLoaded)
   {
      return _solver.getBasisRowStatus(row);
   }
   // if the real LP is not loaded, the basis is stored in the basis arrays of this class
   else
   {
      assert(row < _basisStatusRows.size());
      return _basisStatusRows[row];
   }
}



/// returns basis status for a single column
SPxSolver::VarStatus SoPlex::basisColStatus(int col) const
{
   assert(col >= 0);
   assert(col < numColsReal());

   // if index is out of range, return nonbasic status as for a newly added unbounded column
   if(col < 0 || col >= numColsReal())
   {
      return SPxSolver::ZERO;
   }
   // if no basis is available, return slack basis
   else if(!hasBasis())
   {
      if(lowerReal(col) > -realParam(SoPlex::INFTY))
         return SPxSolver::ON_LOWER;
      else if(upperReal(col) < realParam(SoPlex::INFTY))
         return SPxSolver::ON_UPPER;
      else
         return SPxSolver::ZERO;
   }
   // if the real LP is loaded, ask solver
   else if(_isRealLPLoaded)
   {
      return _solver.getBasisColStatus(col);
   }
   // if the real LP is not loaded, the basis is stored in the basis arrays of this class
   else
   {
      assert(col < _basisStatusCols.size());
      return _basisStatusCols[col];
   }
}



/// gets current basis
void SoPlex::getBasis(SPxSolver::VarStatus rows[], SPxSolver::VarStatus cols[]) const
{
   // if no basis is available, return slack basis
   if(!hasBasis())
   {
      for(int i = numRowsReal() - 1; i >= 0; i--)
         rows[i] = SPxSolver::BASIC;

      for(int i = numColsReal() - 1; i >= 0; i--)
      {
         if(lowerReal(i) > -realParam(SoPlex::INFTY))
            cols[i] = SPxSolver::ON_LOWER;
         else if(upperReal(i) < realParam(SoPlex::INFTY))
            cols[i] = SPxSolver::ON_UPPER;
         else
            cols[i] = SPxSolver::ZERO;
      }
   }
   // if the real LP is loaded, ask solver
   else if(_isRealLPLoaded)
   {
      (void)_solver.getBasis(rows, cols);
   }
   // if the real LP is not loaded, the basis is stored in the basis arrays of this class
   else
   {
      assert(numRowsReal() == _basisStatusRows.size());
      assert(numColsReal() == _basisStatusCols.size());

      for(int i = numRowsReal() - 1; i >= 0; i--)
         rows[i] = _basisStatusRows[i];

      for(int i = numColsReal() - 1; i >= 0; i--)
         cols[i] = _basisStatusCols[i];
   }
}



/// returns the indices of the basic columns and rows; basic column n gives value n, basic row m gives value -1-m
void SoPlex::getBasisInd(int* bind) const
{
   // if no basis is available, return slack basis
   if(!hasBasis())
   {
      for(int i = 0; i < numRowsReal(); ++i)
         bind[i] = -1 - i;
   }
   // if the real LP is not loaded, the basis is stored in the basis arrays of this class
   else if(!_isRealLPLoaded)
   {
      int k = 0;

      assert(numRowsReal() == _basisStatusRows.size());
      assert(numColsReal() == _basisStatusCols.size());

      for(int i = 0; i < numRowsReal(); ++i)
      {
         if(_basisStatusRows[i] == SPxSolver::BASIC)
         {
            bind[k] = -1 - i;
            k++;
         }
      }

      for(int j = 0; j < numColsReal(); ++j)
      {
         if(_basisStatusCols[j] == SPxSolver::BASIC)
         {
            bind[k] = j;
            k++;
         }
      }

      assert(k == numRowsReal());
   }
   // if the real LP is loaded, the basis is stored in the solver and we need to distinguish between column and row
   // representation; ask the solver itself which representation it has, since the REPRESENTATION parameter of this
   // class might be set to automatic
   else if(_solver.rep() == SPxSolver::COLUMN)
   {
      for(int i = 0; i < numRowsReal(); ++i)
      {
         SPxId id = _solver.basis().baseId(i);
         bind[i] = (id.isSPxColId() ? _solver.number(id) : - 1 - _solver.number(id));
      }
   }
   // for row representation, return the complement of the row basis; for this, we need to loop through all rows and columns
   else
   {
      assert(_solver.rep() == SPxSolver::ROW);

      int k = 0;

      for(int i = 0; i < numRowsReal(); ++i)
      {
         if(!_solver.isRowBasic(i))
         {
            bind[k] = -1 - i;
            k++;
         }
      }

      for(int j = 0; j < numColsReal(); ++j)
      {
         if(!_solver.isColBasic(j))
         {
            bind[k] = j;
            k++;
         }
      }

      assert(k == numRowsReal());
   }
}


/// compute condition number estimate based on the diagonal of the LU factorization; returns true on success
/// type = 0: max/min ratio
/// type = 1: trace of U (sum of diagonal elements)
/// type = 2: product of diagonal elements
bool SoPlex::getFastCondition(Real& condition, int type)
{
   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   if(_solver.basis().status() == SPxBasis::NO_PROBLEM)
      return false;

   condition = _solver.basis().getFastCondition(type);

   return true;
}

/// computes an estimated condition number for the current basis matrix using the power method; returns true on success
bool SoPlex::getEstimatedCondition(Real& condition)
{
   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   if(_solver.basis().status() == SPxBasis::NO_PROBLEM)
      return false;

   condition = _solver.basis().getEstimatedCondition();

   return true;
}

/// computes the exact condition number for the current basis matrix using the power method; returns true on success
bool SoPlex::getExactCondition(Real& condition)
{
   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   if(_solver.basis().status() == SPxBasis::NO_PROBLEM)
      return false;

   condition = _solver.basis().getExactCondition();

   return true;
}

/// computes row r of basis inverse; returns true on success
bool SoPlex::getBasisInverseRowReal(int r, Real* coef, int* inds, int* ninds, bool unscale)
{
   assert(r >= 0);
   assert(r < numRowsReal());
   assert(coef != 0);

   if(!hasBasis() || r < 0 || r >= numRowsReal())
      return false;

   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   // we need to distinguish between column and row representation; ask the solver itself which representation it
   // has, since the REPRESENTATION parameter of this class might be set to automatic
   if(_solver.rep() == SPxSolver::COLUMN)
   {
      int idx;
      SSVectorReal x(numRowsReal());

      try
      {
         /* unscaling required? */
         if(unscale && _solver.isScaled())
         {
            /* for information on the unscaling procedure see spxscaler.h */

            int scaleExp;
            DSVector rhs(_solver.unitVector(r));

            if(_solver.basis().baseId(r).isSPxColId())
               scaleExp = _scaler->getColScaleExp(_solver.number(_solver.basis().baseId(r)));
            else
               scaleExp = - _scaler->getRowScaleExp(_solver.number(_solver.basis().baseId(r)));

            rhs *= spxLdexp(1.0, scaleExp);

            _solver.basis().coSolve(x, rhs);
            x.setup();
            int size = x.size();

            for(int i = 0; i < size; i++)
            {
               scaleExp = _scaler->getRowScaleExp(x.index(i));
               x.scaleValue(x.index(i), scaleExp);
            }
         }
         else
         {
            _solver.basis().coSolve(x, _solver.unitVector(r));
         }
      }
      catch(const SPxException& E)
      {
         MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                   "> while computing basis inverse row.\n");
         return false;
      }

      // copy sparse data to dense result vector based on coef array
      if(ninds != 0 && inds != 0)
      {
         // during solving SoPlex may have destroyed the sparsity structure so we need to restore it
         x.setup();
         *ninds = x.size();

         for(int i = 0; i < *ninds; ++i)
         {
            idx = x.index(i);
            coef[idx] = x[idx];
            // set sparsity pattern of coef array
            inds[i] = idx;
         }
      }
      else
      {
         VectorReal y(numRowsReal(), coef);
         y = x;

         if(ninds != NULL)
            *ninds = -1;
      }
   }
   else
   {
      assert(_solver.rep() == SPxSolver::ROW);

      // @todo should rhs be a reference?
      DSVector rhs(numColsReal());
      SSVector y(numColsReal());
      int* bind = 0;
      int index;

      // get ordering of column basis matrix
      spx_alloc(bind, numRowsReal());
      getBasisInd(bind);

      // get vector corresponding to requested index r
      index = bind[r];

      // r corresponds to a row vector
      if(index < 0)
      {
         // transform index to actual row index
         index = -index - 1;

         // should be a valid row index and in the column basis matrix, i.e., not basic w.r.t. row representation
         assert(index >= 0);
         assert(index < numRowsReal());
         assert(!_solver.isRowBasic(index));

         // get row vector
         rhs = _solver.rowVector(index);
         rhs *= -1.0;

         if(unscale && _solver.isScaled())
         {
            for(int i = 0; i < rhs.size(); ++i)
               rhs.value(i) = spxLdexp(rhs.value(i), -_scaler->getRowScaleExp(index));
         }
      }
      // r corresponds to a column vector
      else
      {
         // should be a valid column index and in the column basis matrix, i.e., not basic w.r.t. row representation
         assert(index < numColsReal());
         assert(!_solver.isColBasic(index));

         // get unit vector
         rhs = UnitVectorReal(index);

         if(unscale && _solver.isScaled())
            rhs *= spxLdexp(1.0, _scaler->getColScaleExp(index));
      }

      // solve system "y B = rhs", where B is the row basis matrix
      try
      {
         _solver.basis().solve(y, rhs);
      }
      catch(const SPxException& E)
      {
         MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                   "> while computing basis inverse row.\n");
         return false;
      }

      // initialize result vector x as zero
      memset(coef, 0, (unsigned int)numRowsReal() * sizeof(Real));

      // add nonzero entries
      for(int i = 0; i < numColsReal(); ++i)
      {
         SPxId id = _solver.basis().baseId(i);

         if(id.isSPxRowId())
         {
            assert(_solver.number(id) >= 0);
            assert(_solver.number(id) < numRowsReal());
            assert(bind[r] >= 0 || _solver.number(id) != index);

            int rowindex = _solver.number(id);
            coef[rowindex] = y[i];

            if(unscale && _solver.isScaled())
               coef[rowindex] = spxLdexp(y[i], _scaler->getRowScaleExp(rowindex));
         }
      }

      // if r corresponds to a row vector, we have to add a 1 at position r
      if(bind[r] < 0)
      {
         assert(coef[index] == 0.0);
         coef[index] = 1.0;
      }

      // @todo implement returning of sparsity information like in column wise case
      if(ninds != NULL)
         *ninds = -1;

      // free memory
      spx_free(bind);
   }

   return true;
}



/// computes column c of basis inverse; returns true on success
/// @todo does not work correctly for the row representation
bool SoPlex::getBasisInverseColReal(int c, Real* coef, int* inds, int* ninds, bool unscale)
{
   assert(c >= 0);
   assert(c < numRowsReal());
   assert(coef != 0);

   if(!hasBasis() || c < 0 || c >= numRowsReal())
      return false;

   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   // we need to distinguish between column and row representation; ask the solver itself which representation it
   // has, since the REPRESENTATION parameter of this class might be set to automatic
   if(_solver.rep() == SPxSolver::COLUMN)
   {
      int idx;
      SSVectorReal x(numRowsReal());

      try
      {
         /* unscaling required? */
         if(unscale && _solver.isScaled())
         {
            /* for information on the unscaling procedure see spxscaler.h */

            int scaleExp = _scaler->getRowScaleExp(c);
            DSVector rhs(_solver.unitVector(c));
            rhs *= spxLdexp(1.0, scaleExp);

            _solver.basis().solve(x, rhs);

            x.setup();
            int size = x.size();

            for(int i = 0; i < size; i++)
            {
               if(_solver.basis().baseId(x.index(i)).isSPxColId())
               {
                  idx = _solver.number(_solver.basis().baseId(x.index(i)));
                  scaleExp = _scaler->getColScaleExp(idx);
                  x.scaleValue(x.index(i), scaleExp);
               }
               else
               {
                  idx = _solver.number(_solver.basis().baseId(x.index(i)));
                  scaleExp = - _scaler->getRowScaleExp(idx);
                  x.scaleValue(x.index(i), scaleExp);
               }
            }
         }
         else
         {
            _solver.basis().solve(x, _solver.unitVector(c));
         }
      }
      catch(const SPxException& E)
      {
         MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                   "> while computing basis inverse row.\n");
         return false;
      }

      // copy sparse data to dense result vector based on coef array
      if(ninds != 0 && inds != 0)
      {
         // SoPlex may have destroyed the sparsity structure so we need to restore it
         x.setup();
         *ninds = x.size();

         for(int i = 0; i < *ninds; ++i)
         {
            idx = x.index(i);
            coef[idx] = x[idx];
            // set sparsity pattern of coef array
            inds[i] = idx;
         }
      }
      else
      {
         VectorReal y(numRowsReal(), coef);
         y = x;

         if(ninds != 0)
            *ninds = -1;
      }
   }
   else
   {
      assert(_solver.rep() == SPxSolver::ROW);

      // @todo should rhs be a reference?
      DSVectorReal rhs(numColsReal());
      SSVectorReal y(numColsReal());
      int* bind = 0;
      int index;

      // get ordering of column basis matrix
      spx_alloc(bind, numRowsReal());
      getBasisInd(bind);

      // get vector corresponding to requested index c
      index = bind[c];

      // c corresponds to a row vector
      if(index < 0)
      {
         // transform index to actual row index
         index = -index - 1;

         // should be a valid row index and in the column basis matrix, i.e., not basic w.r.t. row representation
         assert(index >= 0);
         assert(index < numRowsReal());
         assert(!_solver.isRowBasic(index));

         // get row vector
         rhs = _solver.rowVector(index);
         rhs *= -1.0;
      }
      // c corresponds to a column vector
      else
      {
         // should be a valid column index and in the column basis matrix, i.e., not basic w.r.t. row representation
         assert(index < numColsReal());
         assert(!_solver.isColBasic(index));

         // get unit vector
         rhs = UnitVectorReal(index);
      }

      // solve system "y B = rhs", where B is the row basis matrix
      try
      {
         /* unscaling required? */
         if(unscale && _solver.isScaled())
         {
            int size = rhs.size();
            int scaleExp;

            for(int i = 0; i < size; i++)
            {
               scaleExp = _scaler->getColScaleExp(i);
               rhs.value(i) *= spxLdexp(1.0, scaleExp);
            }

            _solver.basis().coSolve(y, rhs);

            int rowIdx;
            size = y.size();

            for(int i = 0; i < size; i++)
            {
               assert(_solver.basis().baseId(y.index(i)).isSPxRowId());
               rowIdx = _solver.basis().baseId(y.index(i)).getIdx();
               scaleExp = _scaler->getRowScaleExp(rowIdx);
               y.setValue(i, y.value(i) * spxLdexp(1.0, scaleExp));
            }
         }
         else
         {
            _solver.basis().coSolve(y, rhs);
         }
      }
      catch(const SPxException& E)
      {
         MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                   "> while computing basis inverse row.\n");
         return false;
      }

      // initialize result vector x as zero
      memset(coef, 0, (unsigned int)numRowsReal() * sizeof(Real));

      // add nonzero entries
      for(int i = 0; i < numColsReal(); ++i)
      {
         SPxId id = _solver.basis().baseId(i);

         if(id.isSPxRowId())
         {
            assert(_solver.number(id) >= 0);
            assert(_solver.number(id) < numRowsReal());
            assert(bind[c] >= 0 || _solver.number(id) != index);

            coef[_solver.number(id)] = y[i];
         }
      }

      // if c corresponds to a row vector, we have to add a 1 at position c
      if(bind[c] < 0)
      {
         assert(coef[index] == 0.0);
         coef[index] = 1.0;
      }

      // @todo implement returning of sparsity information like in column wise case
      if(ninds != NULL)
         *ninds = -1;

      // free memory
      spx_free(bind);
   }

   return true;
}



/// computes dense solution of basis matrix B * sol = rhs; returns true on success
bool SoPlex::getBasisInverseTimesVecReal(Real* rhs, Real* sol, bool unscale)
{
   VectorReal v(numRowsReal(), rhs);
   VectorReal x(numRowsReal(), sol);

   if(!hasBasis())
      return false;

   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   // we need to distinguish between column and row representation; ask the solver itself which representation it
   // has, since the REPRESENTATION parameter of this class might be set to automatic; in the column case we can use
   // the existing factorization
   if(_solver.rep() == SPxSolver::COLUMN)
   {
      // solve system "x = B^-1 * v"
      try
      {
         /* unscaling required? */
         if(unscale && _solver.isScaled())
         {
            /* for information on the unscaling procedure see spxscaler.h */
            int scaleExp;
            int idx;

            for(int i = 0; i < v.dim(); ++i)
            {
               if(isNotZero(v[i]))
               {
                  scaleExp = _scaler->getRowScaleExp(i);
                  v[i] = spxLdexp(v[i], scaleExp);
               }
            }

            _solver.basis().solve(x, v);

            for(int i = 0; i < x.dim(); i++)
            {
               if(isNotZero(x[i]))
               {
                  idx = _solver.number(_solver.basis().baseId(i));

                  if(_solver.basis().baseId(i).isSPxColId())
                     scaleExp = _scaler->getColScaleExp(idx);
                  else
                     scaleExp = - _scaler->getRowScaleExp(idx);

                  x[i] = spxLdexp(x[i], scaleExp);
               }
            }
         }
         else
         {
            _solver.basis().solve(x, v);
         }
      }
      catch(const SPxException& E)
      {
         MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                   "> while solving with basis matrix.\n");
         return false;
      }
   }
   else
   {
      assert(_solver.rep() == SPxSolver::ROW);

      DSVectorReal rowrhs(numColsReal());
      SSVectorReal y(numColsReal());
      int* bind = 0;

      bool adaptScaling = unscale && _realLP->isScaled();
      int scaleExp;
      int idx;

      // get ordering of column basis matrix
      spx_alloc(bind, numRowsReal());
      getBasisInd(bind);

      // fill right-hand side for row-based system
      for(int i = 0; i < numColsReal(); ++i)
      {
         SPxId id = _solver.basis().baseId(i);

         if(id.isSPxRowId())
         {
            assert(_solver.number(id) >= 0);
            assert(_solver.number(id) < numRowsReal());

            if(adaptScaling)
            {
               idx = _solver.number(id);
               scaleExp = _scaler->getRowScaleExp(idx);
               rowrhs.add(i, spxLdexp(v[idx], scaleExp));
            }
            else
               rowrhs.add(i, v[_solver.number(id)]);
         }
         else
         {
            assert(rowrhs[i] == 0.0);
         }
      }

      // solve system "B y = rowrhs", where B is the row basis matrix
      try
      {
         _solver.basis().coSolve(y, rowrhs);
      }
      catch(const SPxException& E)
      {
         MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                   "> while solving with basis matrix.\n");
         return false;
      }

      // fill result w.r.t. order given by bind
      for(int i = 0; i < numRowsReal(); ++i)
      {
         int index;

         index = bind[i];

         if(index < 0)
         {
            index = -index - 1;

            // should be a valid row index and in the column basis matrix, i.e., not basic w.r.t. row representation
            assert(index >= 0);
            assert(index < numRowsReal());
            assert(!_solver.isRowBasic(index));

            x[i] = v[index] - (rowVectorRealInternal(index) * Vector(numColsReal(), y.get_ptr()));

            if(adaptScaling)
            {
               scaleExp = -_scaler->getRowScaleExp(index);
               x[i] = spxLdexp(x[i], scaleExp);
            }
         }
         else
         {
            // should be a valid column index and in the column basis matrix, i.e., not basic w.r.t. row representation
            assert(index >= 0);
            assert(index < numColsReal());
            assert(!_solver.isColBasic(index));

            if(adaptScaling)
            {
               scaleExp = _scaler->getColScaleExp(index);
               x[i] = spxLdexp(y[index], scaleExp);
            }
            else
               x[i] = y[index];
         }
      }

      // free memory
      spx_free(bind);
   }

   return true;
}



/// multiply with basis matrix; B * vec (inplace)
bool SoPlex::multBasis(Real* vec, bool unscale)
{
   if(!hasBasis())
      return false;

   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   if(_solver.rep() == SPxSolver::COLUMN)
   {
      int basisdim = numRowsReal();

      // create Vector from input values
      Vector x(basisdim, vec);

      if(unscale && _solver.isScaled())
      {
         /* for information on the unscaling procedure see spxscaler.h */

         int scaleExp;

         for(int i = 0; i < basisdim; ++i)
         {
            if(isNotZero(vec[i]))
            {
               if(_solver.basis().baseId(i).isSPxColId())
                  scaleExp = - _scaler->getColScaleExp(_solver.number(_solver.basis().baseId(i)));
               else
                  scaleExp = _scaler->getRowScaleExp(_solver.number(_solver.basis().baseId(i)));

               vec[i] = spxLdexp(vec[i], scaleExp);
            }
         }

         _solver.basis().multBaseWith(x);

         for(int i = 0; i < basisdim; ++i)
         {
            scaleExp = _scaler->getRowScaleExp(i);
            vec[i] = spxLdexp(vec[i], -scaleExp);
         }
      }
      else
         _solver.basis().multBaseWith(x);
   }
   else
   {
      int colbasisdim = numRowsReal();

      DSVector y(colbasisdim);

      y.clear();

      // create Vector from input values
      Vector x(colbasisdim, vec);

      int* bind = 0;
      int index;

      // get ordering of column basis matrix
      spx_alloc(bind, colbasisdim);
      getBasisInd(bind);

      // temporarily create the column basis and multiply every column with x
      for(int i = 0; i < colbasisdim; ++i)
      {
         if(isNotZero(x[i]))
         {
            // get vector corresponding to requested index i
            index = bind[i];

            // r corresponds to a row vector
            if(index < 0)
            {
               // transform index to actual row index
               index = -index - 1;

               // should be a valid row index and in the column basis matrix, i.e., not basic w.r.t. row representation
               assert(index >= 0);
               assert(index < numRowsReal());
               assert(!_solver.isRowBasic(index));

               y.add(x[i] * UnitVectorReal(index));
            }
            // r corresponds to a column vector
            else
            {
               // should be a valid column index and in the column basis matrix, i.e., not basic w.r.t. row representation
               assert(index < numColsReal());
               assert(!_solver.isColBasic(index));

               if(unscale && _solver.isScaled())
               {
                  DSVector col;
                  _solver.getColVectorUnscaled(index, col);
                  y.add(x[i] * col);
               }

               y.add(x[i] * _solver.colVector(index));
            }
         }
      }

      spx_free(bind);
      x = y;
   }

   return true;
}



/// multiply with transpose of basis matrix; vec * B^T (inplace)
bool SoPlex::multBasisTranspose(Real* vec, bool unscale)
{
   if(!hasBasis())
      return false;

   _ensureRealLPLoaded();

   if(!_isRealLPLoaded)
      return false;

   if(_solver.rep() == SPxSolver::COLUMN)
   {
      int basisdim = numRowsReal();

      // create Vector from input values
      Vector x(basisdim, vec);

      if(unscale && _solver.isScaled())
      {
         /* for information on the unscaling procedure see spxscaler.h */

         int scaleExp;

         for(int i = 0; i < basisdim; ++i)
         {
            if(isNotZero(vec[i]))
            {
               scaleExp = - _scaler->getRowScaleExp(i);
               vec[i] = spxLdexp(vec[i], scaleExp);
            }
         }

         _solver.basis().multWithBase(x);

         for(int i = 0; i < basisdim; ++i)
         {
            if(isNotZero(vec[i]))
            {
               if(_solver.basis().baseId(i).isSPxColId())
                  scaleExp = - _scaler->getColScaleExp(_solver.number(_solver.basis().baseId(i)));
               else
                  scaleExp = _scaler->getRowScaleExp(_solver.number(_solver.basis().baseId(i)));

               vec[i] = spxLdexp(vec[i], scaleExp);
            }
         }
      }
      else
         _solver.basis().multWithBase(x);
   }
   else
   {
      int colbasisdim = numRowsReal();

      DSVector y(colbasisdim);

      // create Vector from input values
      Vector x(colbasisdim, vec);

      int* bind = 0;
      int index;

      // get ordering of column basis matrix
      spx_alloc(bind, colbasisdim);
      getBasisInd(bind);

      // temporarily create the column basis and multiply every column with x
      for(int i = 0; i < colbasisdim; ++i)
      {
         // get vector corresponding to requested index i
         index = bind[i];

         // r corresponds to a row vector
         if(index < 0)
         {
            // transform index to actual row index
            index = -index - 1;

            // should be a valid row index and in the column basis matrix, i.e., not basic w.r.t. row representation
            assert(index >= 0);
            assert(index < numRowsReal());
            assert(!_solver.isRowBasic(index));

            y.add(i, x * UnitVectorReal(index));
         }
         // r corresponds to a column vector
         else
         {
            // should be a valid column index and in the column basis matrix, i.e., not basic w.r.t. row representation
            assert(index < numColsReal());
            assert(!_solver.isColBasic(index));

            if(unscale && _solver.isScaled())
            {
               DSVector col;
               _solver.getColVectorUnscaled(index, col);
               y.add(i, x * col);
            }
            else
               y.add(i, x * _solver.colVector(index));
         }
      }

      spx_free(bind);
      x = y;
   }

   return true;
}



/// compute rational basis inverse; returns true on success
bool SoPlex::computeBasisInverseRational()
{
   if(!hasBasis())
   {
      _rationalLUSolver.clear();
      assert(_rationalLUSolver.status() == SLinSolverRational::UNLOADED);
      return false;
   }

   if(_rationalLUSolver.status() == SLinSolverRational::UNLOADED
         || _rationalLUSolver.status() == SLinSolverRational::TIME)
   {
      _rationalLUSolverBind.reSize(numRowsRational());
      getBasisInd(_rationalLUSolverBind.get_ptr());
      _computeBasisInverseRational();
   }

   if(_rationalLUSolver.status() == SLinSolverRational::OK)
      return true;

   return false;
}



/// gets an array of indices for the columns of the rational basis matrix; bind[i] >= 0 means that the i-th column of
/// the basis matrix contains variable bind[i]; bind[i] < 0 means that the i-th column of the basis matrix contains
/// the slack variable for row -bind[i]-1; performs rational factorization if not available; returns true on success
bool SoPlex::getBasisIndRational(DataArray<int>& bind)
{
   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      computeBasisInverseRational();

   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      return false;

   bind = _rationalLUSolverBind;
   assert(bind.size() == numRowsRational());
   return true;
}



/// computes row r of basis inverse; performs rational factorization if not available; returns true on success
bool SoPlex::getBasisInverseRowRational(const int r, SSVectorRational& vec)
{
   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      computeBasisInverseRational();

   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      return false;

   try
   {
      vec.reDim(numRowsRational());
      _rationalLUSolver.solveLeft(vec, *_unitVectorRational(r));
   }
   catch(const SPxException& E)
   {
      MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                "> while computing rational basis inverse row.\n");
      return false;
   }

   return true;
}



/// computes column c of basis inverse; performs rational factorization if not available; returns true on success
bool SoPlex::getBasisInverseColRational(const int c, SSVectorRational& vec)
{
   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      computeBasisInverseRational();

   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      return false;

   try
   {
      vec.reDim(numRowsRational());
      _rationalLUSolver.solveRight(vec, *_unitVectorRational(c));
   }
   catch(const SPxException& E)
   {
      MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                "> while computing rational basis inverse column.\n");
      return false;
   }

   return true;
}



/// computes solution of basis matrix B * sol = rhs; performs rational factorization if not available; returns true
/// on success
bool SoPlex::getBasisInverseTimesVecRational(const SVectorRational& rhs, SSVectorRational& sol)
{
   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      computeBasisInverseRational();

   if(_rationalLUSolver.status() != SLinSolverRational::OK)
      return false;

   try
   {
      sol.reDim(numRowsRational());
      _rationalLUSolver.solveRight(sol, rhs);
   }
   catch(const SPxException& E)
   {
      MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() <<
                "> during right solve with rational basis inverse.\n");
      return false;
   }

   return true;
}



/// sets starting basis via arrays of statuses
void SoPlex::setBasis(const SPxSolver::VarStatus rows[], const SPxSolver::VarStatus cols[])
{
   _rationalLUSolver.clear();

   if(_isRealLPLoaded)
   {
      assert(numRowsReal() == _solver.nRows());
      assert(numColsReal() == _solver.nCols());

      _solver.setBasis(rows, cols);
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else
   {
      _basisStatusRows.reSize(numRowsReal());
      _basisStatusCols.reSize(numColsReal());

      for(int i = numRowsReal() - 1; i >= 0; i--)
         _basisStatusRows[i] = rows[i];

      for(int j = numColsReal() - 1; j >= 0; j--)
         _basisStatusCols[j] = cols[j];

      _hasBasis = true;
   }
}



/// clears starting basis
void SoPlex::clearBasis()
{
   _solver.reLoad();
   _status = _solver.status();
   _hasBasis = false;
   _rationalLUSolver.clear();
}



/// number of iterations since last call to solve
int SoPlex::numIterations() const
{
   return _statistics->iterations;
}



/// time spent in last call to solve
Real SoPlex::solveTime() const
{
   return _statistics->solvingTime->time();
}



/// statistical information in form of a string
std::string SoPlex::statisticString() const
{
   std::stringstream s;
   s  << "Factorizations     : " << std::setw(10) << _statistics->luFactorizationsReal << std::endl
      << "  Time spent       : " << std::setw(10) << std::fixed << std::setprecision(
         2) << _statistics->luFactorizationTimeReal << std::endl
      << "Solves             : " << std::setw(10) << _statistics->luSolvesReal << std::endl
      << "  Time spent       : " << std::setw(10) << _statistics->luSolveTimeReal << std::endl
      << "Solution time      : " << std::setw(10) << std::fixed << std::setprecision(
         2) << solveTime() << std::endl
      << "Iterations         : " << std::setw(10) << numIterations() << std::endl;

   return s.str();
}



/// name of starter
const char* SoPlex::getStarterName()
{
   if(_starter)
      return _starter->getName();
   else
      return "none";
}



/// name of simplifier
const char* SoPlex::getSimplifierName()
{
   if(_simplifier)
      return _simplifier->getName();
   else
      return "none";
}



/// name of scaling method after simplifier
const char* SoPlex::getScalerName()
{
   if(_scaler)
      return _scaler->getName();
   else
      return "none";
}



/// name of currently loaded pricer
const char* SoPlex::getPricerName()
{
   return _solver.pricer()->getName();
}



/// name of currently loaded ratiotester
const char* SoPlex::getRatiotesterName()
{
   return _solver.ratiotester()->getName();
}



/// reads LP file in LP or MPS format according to READMODE parameter; gets row names, column names, and
/// integer variables if desired; returns true on success
bool SoPlex::readFile(const char* filename, NameSet* rowNames, NameSet* colNames, DIdxSet* intVars)
{
   bool success = false;

   if(intParam(SoPlex::READMODE) == READMODE_REAL)
      success = _readFileReal(filename, rowNames, colNames, intVars);
   else
      success = _readFileRational(filename, rowNames, colNames, intVars);

   // storing the row and column names for use in the DBDS print basis methods
   _rowNames = rowNames;
   _colNames = colNames;

   return success;
}

/// writes real LP to file; LP or MPS format is chosen from the extension in \p filename; if \p rowNames and \p
/// colNames are \c NULL, default names are used; if \p intVars is not \c NULL, the variables contained in it are
/// marked as integer; returns true on success
bool SoPlex::writeFileReal(const char* filename, const NameSet* rowNames, const NameSet* colNames,
                           const DIdxSet* intVars, const bool unscale) const
{
   ///@todo implement return value
   if(unscale && _realLP->isScaled())
   {
      MSG_INFO3(spxout, spxout << "copy LP to write unscaled original problem" << std::endl;)
      SPxLPReal* origLP;
      origLP = 0;
      spx_alloc(origLP);
      origLP = new(origLP) SPxLPReal(*_realLP);
      origLP->unscaleLP();
      origLP->writeFile(filename, rowNames, colNames, intVars);
      origLP->~SPxLPReal();
      spx_free(origLP);
   }
   else
      _realLP->writeFile(filename, rowNames, colNames, intVars);

   return true;
}



/// writes rational LP to file; LP or MPS format is chosen from the extension in \p filename; if \p rowNames and \p
/// colNames are \c NULL, default names are used; if \p intVars is not \c NULL, the variables contained in it are
/// marked as integer; returns true on success
bool SoPlex::writeFileRational(const char* filename, const NameSet* rowNames,
                               const NameSet* colNames, const DIdxSet* intVars) const
{
   if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      return false;
   else
   {
      assert(_rationalLP != 0);
      _rationalLP->writeFile(filename, rowNames, colNames, intVars);

      ///@todo implement return value
      return true;
   }
}



/// writes the dual of the real LP to file; LP or MPS format is chosen from the extension in \p filename;
/// if \p rowNames and \p colNames are \c NULL, default names are used; if \p intVars is not \c NULL,
/// the variables contained in it are marked as integer; returns true on success
bool SoPlex::writeDualFileReal(const char* filename, const NameSet* rowNames,
                               const NameSet* colNames, const DIdxSet* intVars) const
{
   SPxLPReal dualLP;
   _realLP->buildDualProblem(dualLP);
   dualLP.setOutstream(spxout);

   // swap colnames and rownames
   dualLP.writeFile(filename, colNames, rowNames);
   return true;
}



/// reads basis information from \p filename and returns true on success; if \p rowNames and \p colNames are \c NULL,
/// default names are assumed; returns true on success
bool SoPlex::readBasisFile(const char* filename, const NameSet* rowNames, const NameSet* colNames)
{
   clearBasis();

#if 1
   assert(filename != 0);
   assert(_realLP != 0);

   // start timing
   _statistics->readingTime->start();

   // read
   if(!_isRealLPLoaded)
   {
      assert(_realLP != &_solver);

      _solver.loadLP(*_realLP);
      _realLP->~SPxLPReal();
      spx_free(_realLP);
      _realLP = &_solver;
      _isRealLPLoaded = true;
   }

   _hasBasis = _solver.readBasisFile(filename, rowNames, colNames);
   assert(_hasBasis == (_solver.basis().status() > SPxBasis::NO_PROBLEM));

   // stop timing
   _statistics->readingTime->stop();

   return _hasBasis;
#else
   // this is alternative code for reading bases without the SPxSolver class
   assert(filename != 0);

   // start timing
   _statistics->readingTime->start();

   // read
   spxifstream file(filename);

   if(!file)
      return false;

   // get problem size
   int numRows = numRowsReal();
   int numCols = numColsReal();

   // prepare column names
   const NameSet* colNamesPtr = colNames;
   NameSet* tmpColNames = 0;

   if(colNames == 0)
   {
      std::stringstream name;

      spx_alloc(tmpColNames);
      tmpColNames = new(tmpColNames) NameSet();
      tmpColNames->reMax(numCols);

      for(int j = 0; j < numCols; ++j)
      {
         name << "x" << j;
         tmpColNames->add(name.str().c_str());
      }

      colNamesPtr = tmpColNames;
   }

   // prepare row names
   const NameSet* rowNamesPtr = rowNames;
   NameSet* tmpRowNames = 0;

   if(rowNamesPtr == 0)
   {
      std::stringstream name;

      spx_alloc(tmpRowNames);
      tmpRowNames = new(tmpRowNames) NameSet();
      tmpRowNames->reMax(numRows);

      for(int i = 0; i < numRows; ++i)
      {
         name << "C" << i;
         tmpRowNames->add(name.str().c_str());
      }

      rowNamesPtr = tmpRowNames;
   }

   // initialize with default slack basis
   _basisStatusRows.reSize(numRows);
   _basisStatusCols.reSize(numCols);

   for(int i = 0; i < numRows; i++)
      _basisStatusRows[i] = SPxSolver::BASIC;

   for(int i = 0; i < numCols; i++)
   {
      if(lowerRealInternal(i) == upperRealInternal(i))
         _basisStatusCols[i] = SPxSolver::FIXED;
      else if(lowerRealInternal(i) <= double(-realParam(SoPlex::INFTY))
              && upperRealInternal(i) >= double(realParam(SoPlex::INFTY)))
         _basisStatusCols[i] = SPxSolver::ZERO;
      else if(lowerRealInternal(i) <= double(-realParam(SoPlex::INFTY)))
         _basisStatusCols[i] = SPxSolver::ON_UPPER;
      else
         _basisStatusCols[i] = SPxSolver::ON_LOWER;
   }

   // read basis
   MPSInput mps(file);

   if(mps.readLine() && (mps.field0() != 0) && !strcmp(mps.field0(), "NAME"))
   {
      while(mps.readLine())
      {
         int c = -1;
         int r = -1;

         if(mps.field0() != 0 && !strcmp(mps.field0(), "ENDATA"))
         {
            mps.setSection(MPSInput::ENDATA);
            break;
         }

         if(mps.field1() == 0 || mps.field2() == 0)
            break;

         if((c = colNamesPtr->number(mps.field2())) < 0)
            break;

         if(*mps.field1() == 'X')
         {
            if(mps.field3() == 0 || (r = rowNamesPtr->number(mps.field3())) < 0)
               break;
         }

         if(!strcmp(mps.field1(), "XU"))
         {
            _basisStatusCols[c] = SPxSolver::BASIC;

            if(_rowTypes[r] == SoPlex::RANGETYPE_LOWER)
               _basisStatusRows[r] = SPxSolver::ON_LOWER;
            else if(_rowTypes[r] == SoPlex::RANGETYPE_FIXED)
               _basisStatusRows[r] = SPxSolver::FIXED;
            else
               _basisStatusRows[r] = SPxSolver::ON_UPPER;
         }
         else if(!strcmp(mps.field1(), "XL"))
         {
            _basisStatusCols[c] = SPxSolver::BASIC;

            if(_rowTypes[r] == SoPlex::RANGETYPE_UPPER)
               _basisStatusRows[r] = SPxSolver::ON_UPPER;
            else if(_rowTypes[r] == SoPlex::RANGETYPE_FIXED)
               _basisStatusRows[r] = SPxSolver::FIXED;
            else
               _basisStatusRows[r] = SPxSolver::ON_LOWER;
         }
         else if(!strcmp(mps.field1(), "UL"))
         {
            _basisStatusCols[c] = SPxSolver::ON_UPPER;
         }
         else if(!strcmp(mps.field1(), "LL"))
         {
            _basisStatusCols[c] = SPxSolver::ON_LOWER;
         }
         else
         {
            mps.syntaxError();
            break;
         }
      }
   }

   if(rowNames == 0)
   {
      tmpRowNames->~NameSet();
      spx_free(tmpRowNames);
   }

   if(colNames == 0)
   {
      tmpColNames->~NameSet();
      spx_free(tmpColNames);
   }

   _hasBasis = !mps.hasError();

   // stop timing
   _statistics->readingTime->stop();

   return _hasBasis;
#endif
}



/// writes basis information to \p filename; if \p rowNames and \p colNames are \c NULL, default names are used;
/// returns true on success
bool SoPlex::writeBasisFile(const char* filename, const NameSet* rowNames, const NameSet* colNames,
                            const bool cpxFormat) const
{
   assert(filename != 0);

   if(_isRealLPLoaded)
      return _solver.writeBasisFile(filename, rowNames, colNames, cpxFormat);
   else
   {
      std::ofstream file(filename);

      if(!file.good())
         return false;

      file.setf(std::ios::left);
      file << "NAME  " << filename << "\n";

      // do not write basis if there is none
      if(!_hasBasis)
      {
         file << "ENDATA\n";
         return true;
      }

      // start writing
      int numRows = _basisStatusRows.size();
      int numCols = _basisStatusCols.size();
      int row = 0;

      for(int col = 0; col < numCols; col++)
      {
         assert(_basisStatusCols[col] != SPxSolver::UNDEFINED);

         if(_basisStatusCols[col] == SPxSolver::BASIC)
         {
            // find nonbasic row
            for(; row < numRows; row++)
            {
               assert(_basisStatusRows[row] != SPxSolver::UNDEFINED);

               if(_basisStatusRows[row] != SPxSolver::BASIC)
                  break;
            }

            assert(row != numRows);

            if(_basisStatusRows[row] == SPxSolver::ON_UPPER && (!cpxFormat
                  || _rowTypes[row] == SoPlex::RANGETYPE_BOXED))
               file << " XU ";
            else
               file << " XL ";

            file << std::setw(8);

            if(colNames != 0 && colNames->has(col))
               file << (*colNames)[col];
            else
               file << "x" << col;

            file << "       ";

            if(rowNames != 0 && rowNames->has(row))
               file << (*rowNames)[row];
            else
               file << "C" << row;

            file << "\n";
            row++;
         }
         else
         {
            if(_basisStatusCols[col] == SPxSolver::ON_UPPER)
            {
               file << " UL ";

               file << std::setw(8);

               if(colNames != 0 && colNames->has(col))
                  file << (*colNames)[col];
               else
                  file << "x" << col;

               file << "\n";
            }
         }
      }

      file << "ENDATA\n";

#ifndef NDEBUG

      // check that the remaining rows are basic
      for(; row < numRows; row++)
      {
         assert(_basisStatusRows[row] == SPxSolver::BASIC);
      }

#endif

      return true;
   }
}



/// writes internal LP, basis information, and parameter settings; if \p rowNames and \p colNames are \c NULL,
/// default names are used
void SoPlex::writeStateReal(const char* filename, const NameSet* rowNames, const NameSet* colNames,
                            const bool cpxFormat) const
{
   std::string ofname;

   // write parameter settings
   ofname = std::string(filename) + ".set";
   saveSettingsFile(ofname.c_str());

   // write problem in MPS/LP format
   ofname = std::string(filename) + ((cpxFormat) ? ".lp" : ".mps");
   writeFileReal(ofname.c_str(), rowNames, colNames, 0);

   // write basis
   ofname = std::string(filename) + ".bas";
   writeBasisFile(ofname.c_str(), rowNames, colNames, cpxFormat);
}



/// writes internal LP, basis information, and parameter settings; if \p rowNames and \p colNames are \c NULL,
/// default names are used
void SoPlex::writeStateRational(const char* filename, const NameSet* rowNames,
                                const NameSet* colNames, const bool cpxFormat) const
{
   std::string ofname;

   // write parameter settings
   ofname = std::string(filename) + ".set";
   saveSettingsFile(ofname.c_str());

   // write problem in MPS/LP format
   ofname = std::string(filename) + ((cpxFormat) ? ".lp" : ".mps");
   writeFileRational(ofname.c_str(), rowNames, colNames, 0);

   // write basis
   ofname = std::string(filename) + ".bas";
   writeBasisFile(ofname.c_str(), rowNames, colNames, cpxFormat);
}



/// returns boolean parameter value
bool SoPlex::boolParam(const BoolParam param) const
{
   assert(param >= 0);
   assert(param < SoPlex::BOOLPARAM_COUNT);
   return _currentSettings->_boolParamValues[param];
}



/// returns integer parameter value
int SoPlex::intParam(const IntParam param) const
{
   assert(param >= 0);
   assert(param < INTPARAM_COUNT);
   return _currentSettings->_intParamValues[param];
}



/// returns real parameter value
Real SoPlex::realParam(const RealParam param) const
{
   assert(param >= 0);
   assert(param < REALPARAM_COUNT);
   return _currentSettings->_realParamValues[param];
}



#ifdef SOPLEX_WITH_RATIONALPARAM
/// returns rational parameter value
Rational SoPlex::rationalParam(const RationalParam param) const
{
   assert(param >= 0);
   assert(param < RATIONALPARAM_COUNT);
   return _currentSettings->_rationalParamValues[param];
}
#endif



/// returns current parameter settings
const SoPlex::Settings& SoPlex::settings() const
{
   return *_currentSettings;
}



/// sets boolean parameter value; returns true on success
bool SoPlex::setBoolParam(const BoolParam param, const bool value, const bool init)
{
   assert(param >= 0);
   assert(param < SoPlex::BOOLPARAM_COUNT);
   assert(init || _isConsistent());

   if(!init && value == boolParam(param))
      return true;

   switch(param)
   {
   case LIFTING:
      break;

   case EQTRANS:
      break;

   case TESTDUALINF:
      break;

   case RATFAC:
      break;

   case USEDECOMPDUALSIMPLEX:
      break;

   case COMPUTEDEGEN:
      break;

   case USECOMPDUAL:
      break;

   case EXPLICITVIOL:
      break;

   case ACCEPTCYCLING:
      break;

   case RATREC:
      break;

   case POWERSCALING:
      break;

   case RATFACJUMP:
      break;

   case ROWBOUNDFLIPS:
      _ratiotesterBoundFlipping.useBoundFlipsRow(value);
      break;

   case PERSISTENTSCALING:
      break;

   case FULLPERTURBATION:
      _solver.useFullPerturbation(value);
      break;

   case ENSURERAY:
      break;

   default:
      return false;
   }

   _currentSettings->_boolParamValues[param] = value;
   return true;
}



/// sets integer parameter value; returns true on success
bool SoPlex::setIntParam(const IntParam param, const int value, const bool init)
{
   assert(param >= 0);
   assert(param < INTPARAM_COUNT);
   assert(init || _isConsistent());

   if(!init && value == intParam(param))
      return true;

   // check for a valid parameter value wrt bounds
   if(value < _currentSettings->intParam.lower[param]
         || value > _currentSettings->intParam.upper[param])
      return false;

   switch(param)
   {
   // objective sense
   case SoPlex::OBJSENSE:
      if(value != SoPlex::OBJSENSE_MAXIMIZE && value != SoPlex::OBJSENSE_MINIMIZE)
         return false;

      _realLP->changeSense(value == SoPlex::OBJSENSE_MAXIMIZE ? SPxLPReal::MAXIMIZE :
                           SPxLPReal::MINIMIZE);

      if(_rationalLP != 0)
         _rationalLP->changeSense(value == SoPlex::OBJSENSE_MAXIMIZE ? SPxLPRational::MAXIMIZE :
                                  SPxLPRational::MINIMIZE);

      _invalidateSolution();
      break;

   // type of computational form, i.e., column or row representation
   case SoPlex::REPRESENTATION:
      if(value != SoPlex::REPRESENTATION_COLUMN && value != SoPlex::REPRESENTATION_ROW
            && value != SoPlex::REPRESENTATION_AUTO)
         return false;

      break;

   // type of algorithm, i.e., primal or dual
   case SoPlex::ALGORITHM:
      // decide upon entering/leaving at solve time depending on representation
      break;

   // type of LU update
   case SoPlex::FACTOR_UPDATE_TYPE:
      if(value != SoPlex::FACTOR_UPDATE_TYPE_ETA && value != SoPlex::FACTOR_UPDATE_TYPE_FT)
         return false;

      _slufactor.setUtype(value == SoPlex::FACTOR_UPDATE_TYPE_ETA ? SLUFactor::ETA :
                          SLUFactor::FOREST_TOMLIN);
      break;

   // maximum number of updates before fresh factorization
   case SoPlex::FACTOR_UPDATE_MAX:
      if(value == 0)
         _solver.basis().setMaxUpdates(DEFAULT_REFACTOR_INTERVAL);
      else
         _solver.basis().setMaxUpdates(value);

      break;

   // iteration limit (-1 if unlimited)
   case SoPlex::ITERLIMIT:
      break;

   // refinement limit (-1 if unlimited)
   case SoPlex::REFLIMIT:
      break;

   // stalling refinement limit (-1 if unlimited)
   case SoPlex::STALLREFLIMIT:
      break;

   // display frequency
   case SoPlex::DISPLAYFREQ:
      _solver.setDisplayFreq(value);
      break;

   // verbosity level
   case SoPlex::VERBOSITY:
      switch(value)
      {
      case 0:
         spxout.setVerbosity(SPxOut::ERROR);
         break;

      case 1:
         spxout.setVerbosity(SPxOut::WARNING);
         break;

      case 2:
         spxout.setVerbosity(SPxOut::DEBUG);
         break;

      case 3:
         spxout.setVerbosity(SPxOut::INFO1);
         break;

      case 4:
         spxout.setVerbosity(SPxOut::INFO2);
         break;

      case 5:
         spxout.setVerbosity(SPxOut::INFO3);
         break;
      }

      break;

   // type of simplifier
   case SoPlex::SIMPLIFIER:
      switch(value)
      {
      case SIMPLIFIER_OFF:
         _simplifier = 0;
         break;

      case SIMPLIFIER_AUTO:
         _simplifier = &_simplifierMainSM;
         assert(_simplifier != 0);
         break;

      default:
         return false;
      }

      break;

   // type of scaler
   case SoPlex::SCALER:
      switch(value)
      {
      case SCALER_OFF:
         _scaler = 0;
         break;

      case SCALER_UNIEQUI:
         _scaler = &_scalerUniequi;
         break;

      case SCALER_BIEQUI:
         _scaler = &_scalerBiequi;
         break;

      case SCALER_GEO1:
         _scaler = &_scalerGeo1;
         break;

      case SCALER_GEO8:
         _scaler = &_scalerGeo8;
         break;

      case SCALER_LEASTSQ:
         _scaler = &_scalerLeastsq;
         break;

      case SCALER_GEOEQUI:
         _scaler = &_scalerGeoequi;
         break;

      default:
         return false;
      }

      break;

   // type of starter used to create crash basis
   case SoPlex::STARTER:
      switch(value)
      {
      case STARTER_OFF:
         _starter = 0;
         break;

      case STARTER_WEIGHT:
         _starter = &_starterWeight;
         break;

      case STARTER_SUM:
         _starter = &_starterSum;
         break;

      case STARTER_VECTOR:
         _starter = &_starterVector;
         break;

      default:
         return false;
      }

      break;

   // type of pricer
   case SoPlex::PRICER:
      switch(value)
      {
      case PRICER_AUTO:
         _solver.setPricer(&_pricerAuto);
         break;

      case PRICER_DANTZIG:
         _solver.setPricer(&_pricerDantzig);
         break;

      case PRICER_PARMULT:
         _solver.setPricer(&_pricerParMult);
         break;

      case PRICER_DEVEX:
         _solver.setPricer(&_pricerDevex);
         break;

      case PRICER_QUICKSTEEP:
         _solver.setPricer(&_pricerQuickSteep);
         break;

      case PRICER_STEEP:
         _solver.setPricer(&_pricerSteep);
         break;

      default:
         return false;
      }

      break;

   // mode for synchronizing real and rational LP
   case SoPlex::SYNCMODE:
      switch(value)
      {
      case SYNCMODE_ONLYREAL:
         if(_rationalLP != 0)
         {
            _rationalLP->~SPxLPRational();
            spx_free(_rationalLP);
         }

         break;

      case SYNCMODE_AUTO:
         if(intParam(param) == SYNCMODE_ONLYREAL)
            _syncLPRational();

         break;

      case SYNCMODE_MANUAL:
         _ensureRationalLP();
         break;

      default:
         return false;
      }

      break;

   // mode for reading LP files; nothing to do but change the value if valid
   case SoPlex::READMODE:
      switch(value)
      {
      case READMODE_REAL:
      case READMODE_RATIONAL:
         break;

      default:
         return false;
      }

      break;

   // mode for iterative refinement strategy; nothing to do but change the value if valid
   case SoPlex::SOLVEMODE:
      switch(value)
      {
      case SOLVEMODE_REAL:
      case SOLVEMODE_AUTO:
      case SOLVEMODE_RATIONAL:
         break;

      default:
         return false;
      }

      break;

   // mode for a posteriori feasibility checks; nothing to do but change the value if valid
   case SoPlex::CHECKMODE:
      switch(value)
      {
      case CHECKMODE_REAL:
      case CHECKMODE_AUTO:
      case CHECKMODE_RATIONAL:
         break;

      default:
         return false;
      }

      break;

   // type of ratio test
   case SoPlex::RATIOTESTER:
      switch(value)
      {
      case RATIOTESTER_TEXTBOOK:
         _solver.setTester(&_ratiotesterTextbook);
         break;

      case RATIOTESTER_HARRIS:
         _solver.setTester(&_ratiotesterHarris);
         break;

      case RATIOTESTER_FAST:
         _solver.setTester(&_ratiotesterFast);
         break;

      case RATIOTESTER_BOUNDFLIPPING:
         _solver.setTester(&_ratiotesterBoundFlipping);
         break;

      default:
         return false;
      }

      break;

   // type of timer
   case SoPlex::TIMER:
      switch(value)
      {
      case TIMER_OFF:
         _solver.setTiming(Timer::OFF);
         break;

      case TIMER_CPU:
         _solver.setTiming(Timer::USER_TIME);
         break;

      case TIMER_WALLCLOCK:
         _solver.setTiming(Timer::WALLCLOCK_TIME);
         break;

      default:
         return false;
      }

      break;

   // mode of hyper pricing
   case SoPlex::HYPER_PRICING:
      switch(value)
      {
      case HYPER_PRICING_OFF:
      case HYPER_PRICING_AUTO:
      case HYPER_PRICING_ON:
         break;

      default:
         return false;
      }

      break;

   // minimum number of stalling refinements since last pivot to trigger rational factorization
   case SoPlex::RATFAC_MINSTALLS:
      break;

   // maximum number of conjugate gradient iterations in least square scaling
   case SoPlex::LEASTSQ_MAXROUNDS:
      if(_scaler)
         _scaler->setIntParam(value);

      break;

   // mode of solution polishing
   case SoPlex::SOLUTION_POLISHING:
      switch(value)
      {
      case POLISHING_OFF:
         _solver.setSolutionPolishing(SPxSolver::POLISH_OFF);
         break;

      case POLISHING_INTEGRALITY:
         _solver.setSolutionPolishing(SPxSolver::POLISH_INTEGRALITY);
         break;

      case POLISHING_FRACTIONALITY:
         _solver.setSolutionPolishing(SPxSolver::POLISH_FRACTIONALITY);
         break;

      default:
         return false;
      }

      break;

   // the decomposition based simplex parameter settings
   case DECOMP_ITERLIMIT:
      break;

   case DECOMP_MAXADDEDROWS:
      break;

   case DECOMP_DISPLAYFREQ:
      break;

   case DECOMP_VERBOSITY:
      break;

   // printing of condition n
   case PRINTCONDITION:
      _solver.setConditionInformation(value);
      break;

   default:
      return false;
   }

   _currentSettings->_intParamValues[param] = value;
   return true;
}



/// sets real parameter value; returns true on success
bool SoPlex::setRealParam(const RealParam param, const Real value, const bool init)
{
   assert(param >= 0);
   assert(param < REALPARAM_COUNT);
   assert(init || _isConsistent());

   if(!init && value == realParam(param))
      return true;

   if(value < _currentSettings->realParam.lower[param]
         || value > _currentSettings->realParam.upper[param])
      return false;

   // required to set a different feastol or opttol
   Real tmp_value = value;

   switch(param)
   {
   // primal feasibility tolerance; passed to the floating point solver only when calling solve()
   case SoPlex::FEASTOL:
#ifndef SOPLEX_WITH_GMP
      if(value < DEFAULT_EPS_PIVOT)
      {
         MSG_WARNING(spxout, spxout << "Cannot set feasibility tolerance to small value " << value <<
                     " without GMP - using " << DEFAULT_EPS_PIVOT << ".\n");
         tmp_value = DEFAULT_EPS_PIVOT;
         _rationalFeastol = DEFAULT_EPS_PIVOT;
         break;
      }

#endif
      _rationalFeastol = value;
      break;

   // dual feasibility tolerance; passed to the floating point solver only when calling solve()
   case SoPlex::OPTTOL:
#ifndef SOPLEX_WITH_GMP
      if(value < DEFAULT_EPS_PIVOT)
      {
         MSG_WARNING(spxout, spxout << "Cannot set optimality tolerance to small value " << value <<
                     " without GMP - using " << DEFAULT_EPS_PIVOT << ".\n");
         tmp_value = DEFAULT_EPS_PIVOT;
         _rationalOpttol = DEFAULT_EPS_PIVOT;
         break;
      }

#endif
      _rationalOpttol = value;
      break;

   // general zero tolerance
   case SoPlex::EPSILON_ZERO:
      Param::setEpsilon(value);
      break;

   // zero tolerance used in factorization
   case SoPlex::EPSILON_FACTORIZATION:
      Param::setEpsilonFactorization(value);
      break;

   // zero tolerance used in update of the factorization
   case SoPlex::EPSILON_UPDATE:
      Param::setEpsilonUpdate(value);
      break;

   // pivot zero tolerance used in factorization (declare numerical singularity for small LU pivots)
   case SoPlex::EPSILON_PIVOT:
      Param::setEpsilonPivot(value);
      break;

   // infinity threshold
   case SoPlex::INFTY:
      _rationalPosInfty = value;
      _rationalNegInfty = -value;

      if(intParam(SoPlex::SYNCMODE) != SYNCMODE_ONLYREAL)
         _recomputeRangeTypesRational();

      break;

   // time limit in seconds (INFTY if unlimited)
   case SoPlex::TIMELIMIT:
      break;

   // lower limit on objective value is set in solveReal()
   case SoPlex::OBJLIMIT_LOWER:
      break;

   // upper limit on objective value is set in solveReal()
   case SoPlex::OBJLIMIT_UPPER:
      break;

   // working tolerance for feasibility in floating-point solver
   case SoPlex::FPFEASTOL:
      break;

   // working tolerance for optimality in floating-point solver
   case SoPlex::FPOPTTOL:
      break;

   // maximum increase of scaling factors between refinements
   case SoPlex::MAXSCALEINCR:
      _rationalMaxscaleincr = value;
      break;

   // lower threshold in lifting (nonzero matrix coefficients with smaller absolute value will be reformulated)
   case SoPlex::LIFTMINVAL:
      break;

   // upper threshold in lifting (nonzero matrix coefficients with larger absolute value will be reformulated)
   case SoPlex::LIFTMAXVAL:
      break;

   // threshold for sparse pricing
   case SoPlex::SPARSITY_THRESHOLD:
      break;

   // threshold on number of rows vs. number of columns for switching from column to row representations in auto mode
   case SoPlex::REPRESENTATION_SWITCH:
      break;

   // geometric frequency at which to apply rational reconstruction
   case SoPlex::RATREC_FREQ:
      break;

   // minimal reduction (sum of removed rows/cols) to continue simplification
   case SoPlex::MINRED:
      break;

   case SoPlex::REFAC_BASIS_NNZ:
      break;

   case SoPlex::REFAC_UPDATE_FILL:
      break;

   case SoPlex::REFAC_MEM_FACTOR:
      break;

   // accuracy of conjugate gradient method in least squares scaling (higher value leads to more iterations)
   case SoPlex::LEASTSQ_ACRCY:
      if(_scaler)
         _scaler->setRealParam(value);

      break;

   // objective offset
   case SoPlex::OBJ_OFFSET:
      if(_realLP)
         _realLP->changeObjOffset(value);

      if(_rationalLP)
         _rationalLP->changeObjOffset(value);

      break;

   default:
      return false;
   }

   _currentSettings->_realParamValues[param] = tmp_value;
   return true;
}



#ifdef SOPLEX_WITH_RATIONALPARAM
/// sets rational parameter value; returns true on success
bool SoPlex::setRationalParam(const RationalParam param, const Rational value, const bool init)
{
   assert(param >= 0);
   assert(param < RATIONALPARAM_COUNT);
   assert(init || _isConsistent());

   if(!init && value == rationalParam(param))
      return true;

   if(value < _currentSettings->rationalParam.lower[param]
         || value > _currentSettings->rationalParam.upper[param])
      return false;

   switch(param)
   {
   default:
      // currently, there are no rational-valued parameters
      return false;
   }

   _currentSettings->_rationalParamValues[param] = value;
   return true;
}
#endif



/// sets parameter settings; returns true on success
bool SoPlex::setSettings(const Settings& newSettings, const bool init)
{
   assert(init || _isConsistent());

   bool success = true;

   *_currentSettings = newSettings;

   for(int i = 0; i < SoPlex::BOOLPARAM_COUNT; i++)
      success &= setBoolParam((BoolParam)i, _currentSettings->_boolParamValues[i], init);

   for(int i = 0; i < SoPlex::INTPARAM_COUNT; i++)
      success &= setIntParam((IntParam)i, _currentSettings->_intParamValues[i], init);

   for(int i = 0; i < SoPlex::REALPARAM_COUNT; i++)
      success &= setRealParam((RealParam)i, _currentSettings->_realParamValues[i], init);

#ifdef SOPLEX_WITH_RATIONALPARAM

   for(int i = 0; i < SoPlex::RATIONALPARAM_COUNT; i++)
      success &= setRationalParam((RationalParam)i, _currentSettings->_rationalParamValues[i], init);

#endif

   assert(_isConsistent());

   return success;
}

/// resets default parameter settings
void SoPlex::resetSettings(const bool quiet, const bool init)
{
   for(int i = 0; i < SoPlex::BOOLPARAM_COUNT; i++)
      setBoolParam((BoolParam)i, _currentSettings->boolParam.defaultValue[i], init);

   for(int i = 0; i < SoPlex::INTPARAM_COUNT; i++)
      setIntParam((IntParam)i, _currentSettings->intParam.defaultValue[i], init);

   for(int i = 0; i < SoPlex::REALPARAM_COUNT; i++)
      setRealParam((RealParam)i, _currentSettings->realParam.defaultValue[i], init);

#ifdef SOPLEX_WITH_RATIONALPARAM

   for(int i = 0; i < SoPlex::RATIONALPARAM_COUNT; i++)
      success &= setRationalParam((RationalParam)i, _currentSettings->rationalParam.defaultValue[i],
                                  init);

#endif
}


/// print non-default parameter values
void SoPlex::printUserSettings()
{
   bool printedValue = false;

   SPxOut::setFixed(spxout.getCurrentStream());

   for(int i = 0; i < SoPlex::BOOLPARAM_COUNT; i++)
   {
      if(_currentSettings->_boolParamValues[i] == _currentSettings->boolParam.defaultValue[i])
         continue;

      spxout << "bool:" << _currentSettings->boolParam.name[i] << " = " <<
             (_currentSettings->_boolParamValues[i] ? "true\n" : "false\n");
      printedValue = true;
   }

   for(int i = 0; i < SoPlex::INTPARAM_COUNT; i++)
   {
      if(_currentSettings->_intParamValues[i] == _currentSettings->intParam.defaultValue[i])
         continue;

      spxout << "int:" << _currentSettings->intParam.name[i] << " = " <<
             _currentSettings->_intParamValues[i] << "\n";
      printedValue = true;
   }

   SPxOut::setScientific(spxout.getCurrentStream());

   for(int i = 0; i < SoPlex::REALPARAM_COUNT; i++)
   {
      if(_currentSettings->_realParamValues[i] == _currentSettings->realParam.defaultValue[i])
         continue;

      spxout << "real:" << _currentSettings->realParam.name[i] << " = " <<
             _currentSettings->_realParamValues[i] << "\n";
      printedValue = true;
   }

#ifdef SOPLEX_WITH_RATIONALPARAM

   for(int i = 0; i < SoPlex::RATIONALPARAM_COUNT; i++)
   {
      if(_currentSettings->_rationalParamValues[i] == _currentSettings->rationalParam.defaultValue[i])
         continue;

      spxout << "rational:" << _currentSettings->rationalParam.name[i] << " = " <<
             _currentSettings->_rationalParamValues[i] << "\n";
      printedValue = true;
   }

#endif

   if(_solver.random.getSeed() != DEFAULT_RANDOM_SEED)
   {
      spxout << "uint:random_seed = " << _solver.random.getSeed() << "\n";
      printedValue = true;
   }

   if(printedValue)
      spxout << std::endl;
}



/// writes settings file; returns true on success
bool SoPlex::saveSettingsFile(const char* filename, const bool onlyChanged) const
{
   assert(filename != 0);

   std::ofstream file(filename);
   SPxOut::setScientific(file, 16);

   if(!file.good())
      return false;

   file.setf(std::ios::left);

   SPxOut::setFixed(file);

   file << "# SoPlex version " << SOPLEX_VERSION / 100 << "." << (SOPLEX_VERSION / 10) % 10 << "." <<
        SOPLEX_VERSION % 10;
#if SOPLEX_SUBVERSION > 0
   file << "." << SOPLEX_SUBVERSION;
#endif
   file << "\n";

   for(int i = 0; i < SoPlex::BOOLPARAM_COUNT; i++)
   {
      if(onlyChanged
            && _currentSettings->_boolParamValues[i] == _currentSettings->boolParam.defaultValue[i])
         continue;

      file << "\n";
      file << "# " << _currentSettings->boolParam.description[i] << "\n";
      file << "# range {true, false}, default " << (_currentSettings->boolParam.defaultValue[i] ?
            "true\n" : "false\n");
      file << "bool:" << _currentSettings->boolParam.name[i] << " = " <<
           (_currentSettings->_boolParamValues[i] ? "true\n" : "false\n");
   }

   for(int i = 0; i < SoPlex::INTPARAM_COUNT; i++)
   {
      if(onlyChanged
            && _currentSettings->_intParamValues[i] == _currentSettings->intParam.defaultValue[i])
         continue;

      file << "\n";
      file << "# " << _currentSettings->intParam.description[i] << "\n";
      file << "# range [" << _currentSettings->intParam.lower[i] << "," <<
           _currentSettings->intParam.upper[i]
           << "], default " << _currentSettings->intParam.defaultValue[i] << "\n";
      file << "int:" << _currentSettings->intParam.name[i] << " = " <<
           _currentSettings->_intParamValues[i] << "\n";
   }

   SPxOut::setScientific(file);

   for(int i = 0; i < SoPlex::REALPARAM_COUNT; i++)
   {
      if(onlyChanged
            && _currentSettings->_realParamValues[i] == _currentSettings->realParam.defaultValue[i])
         continue;

      file << "\n";
      file << "# " << _currentSettings->realParam.description[i] << "\n";
      file << "# range [" << _currentSettings->realParam.lower[i] << "," <<
           _currentSettings->realParam.upper[i]
           << "], default " << _currentSettings->realParam.defaultValue[i] << "\n";
      file << "real:" << _currentSettings->realParam.name[i] << " = " <<
           _currentSettings->_realParamValues[i] << "\n";
   }

#ifdef SOPLEX_WITH_RATIONALPARAM

   for(int i = 0; i < SoPlex::RATIONALPARAM_COUNT; i++)
   {
      if(onlyChanged
            && _currentSettings->_rationalParamValues[i] == _currentSettings->rationalParam.defaultValue[i])
         continue;

      file << "\n";
      file << "# " << _currentSettings->rationalParam.description[i] << "\n";
      file << "# range [" << _currentSettings->rationalParam.lower[i] << "," <<
           _currentSettings->rationalParam.upper[i]
           << "], default " << _currentSettings->rationalParam.defaultValue[i] << "\n";
      file << "rational:" << _currentSettings->rationalParam.name[i] << " = " <<
           _currentSettings->_rationalParamValues[i] << "\n";
   }

#endif

   if(!onlyChanged || _solver.random.getSeed() != DEFAULT_RANDOM_SEED)
   {
      file << "\n";
      file << "# initial random seed used for perturbation\n";
      file << "# range [0, " << UINT_MAX << "], default " << DEFAULT_RANDOM_SEED << "\n";
      file << "uint:random_seed = " << _solver.random.getSeed() << "\n";
   }

   return true;
}



/// reads settings file; returns true on success
bool SoPlex::loadSettingsFile(const char* filename)
{
   assert(filename != 0);

   // start timing
   _statistics->readingTime->start();

   MSG_INFO1(spxout, spxout << "Loading settings file <" << filename << "> . . .\n");

   // open file
   spxifstream file(filename);

   if(!file)
   {
      MSG_INFO1(spxout, spxout << "Error opening settings file.\n");
      return false;
   }

   // read file
   char line[SET_MAX_LINE_LEN];
   int lineNumber = 0;
   bool readError = false;
   bool parseError = false;

   while(!readError && !parseError)
   {
      lineNumber++;
      readError = !file.getline(line, sizeof(line));

      if(!readError)
         parseError = !_parseSettingsLine(line, lineNumber);
   }

   readError = readError && !file.eof();

   if(readError && strlen(line) == SET_MAX_LINE_LEN - 1)
   {
      MSG_INFO1(spxout, spxout << "Error reading settings file: line " << lineNumber <<
                " in settings file exceeds " << SET_MAX_LINE_LEN - 2 << " characters.\n");
   }
   else if(readError)
   {
      MSG_INFO1(spxout, spxout << "Error reading settings file: line " << lineNumber << ".\n");
   }

   // stop timing
   _statistics->readingTime->stop();

   return !readError;
}

/// parses one setting string and returns true on success
bool SoPlex::parseSettingsString(char* string)
{
   assert(string != 0);

   if(string == 0)
      return false;

   char parseString[SET_MAX_LINE_LEN];
   spxSnprintf(parseString, SET_MAX_LINE_LEN - 1, "%s", string);

   char* line = parseString;

   // find the start of the parameter type
   while(*line == ' ' || *line == '\t' || *line == '\r')
      line++;

   if(*line == '\0' || *line == '\n' || *line == '#')
      return true;

   char* paramTypeString = line;

   // find the end of the parameter type
   while(*line != ' ' && *line != '\t' && *line != '\r' && *line != '\n' && *line != '#'
         && *line != '\0' && *line != ':')
      line++;

   if(*line == ':')
   {
      *line = '\0';
      line++;
   }
   else
   {
      *line = '\0';
      line++;

      // search for the ':' char in the line
      while(*line == ' ' || *line == '\t' || *line == '\r')
         line++;

      if(*line != ':')
      {
         MSG_INFO1(spxout, spxout <<
                   "Error parsing setting string: no ':' separating parameter type and name.\n");
         return false;
      }

      line++;
   }

   // find the start of the parameter name
   while(*line == ' ' || *line == '\t' || *line == '\r')
      line++;

   if(*line == '\0' || *line == '\n' || *line == '#')
   {
      MSG_INFO1(spxout, spxout << "Error parsing setting string: no parameter name.\n");
      return false;
   }

   char* paramName = line;

   // find the end of the parameter name
   while(*line != ' ' && *line != '\t' && *line != '\r' && *line != '\n' && *line != '#'
         && *line != '\0' && *line != '=')
      line++;

   if(*line == '=')
   {
      *line = '\0';
      line++;
   }
   else
   {
      *line = '\0';
      line++;

      // search for the '=' char in the line
      while(*line == ' ' || *line == '\t' || *line == '\r')
         line++;

      if(*line != '=')
      {
         MSG_INFO1(spxout, spxout << "Error parsing setting string: no '=' after parameter name.\n");
         return false;
      }

      line++;
   }

   // find the start of the parameter value string
   while(*line == ' ' || *line == '\t' || *line == '\r')
      line++;

   if(*line == '\0' || *line == '\n' || *line == '#')
   {
      MSG_INFO1(spxout, spxout << "Error parsing setting string: no parameter value.\n");
      return false;
   }

   char* paramValueString = line;

   // find the end of the parameter value string
   while(*line != ' ' && *line != '\t' && *line != '\r' && *line != '\n' && *line != '#'
         && *line != '\0')
      line++;

   if(*line != '\0')
   {
      // check, if the rest of the line is clean
      *line = '\0';
      line++;

      while(*line == ' ' || *line == '\t' || *line == '\r')
         line++;

      if(*line != '\0' && *line != '\n' && *line != '#')
      {
         MSG_INFO1(spxout, spxout << "Error parsing setting string: additional character '" << *line <<
                   "' after parameter value.\n");
         return false;
      }
   }

   // check whether we have a bool parameter
   if(strncmp(paramTypeString, "bool", 4) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::BOOLPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing setting string: unknown parameter name <" << paramName <<
                      ">.\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->boolParam.name[param].c_str(), SET_MAX_LINE_LEN) == 0)
         {
            if(strncasecmp(paramValueString, "true", 4) == 0
                  || strncasecmp(paramValueString, "TRUE", 4) == 0
                  || strncasecmp(paramValueString, "t", 4) == 0
                  || strncasecmp(paramValueString, "T", 4) == 0
                  || strtol(paramValueString, NULL, 4) == 1)
            {
               setBoolParam((SoPlex::BoolParam)param, true);
               break;
            }
            else if(strncasecmp(paramValueString, "false", 5) == 0
                    || strncasecmp(paramValueString, "FALSE", 5) == 0
                    || strncasecmp(paramValueString, "f", 5) == 0
                    || strncasecmp(paramValueString, "F", 5) == 0
                    || strtol(paramValueString, NULL, 5) == 0)
            {
               setBoolParam((SoPlex::BoolParam)param, false);
               break;
            }
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing setting string: invalid value <" << paramValueString <<
                         "> for bool parameter <" << paramName << ">.\n");
               return false;
            }
         }
      }

      return true;
   }

   // check whether we have an integer parameter
   if(strncmp(paramTypeString, "int", 3) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::INTPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing setting string: unknown parameter name <" << paramName <<
                      ">.\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->intParam.name[param].c_str(), SET_MAX_LINE_LEN) == 0)
         {
            int value;
            value = std::stoi(paramValueString);

            if(setIntParam((SoPlex::IntParam)param, value, false))
               break;
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing setting string: invalid value <" << paramValueString <<
                         "> for int parameter <" << paramName << ">.\n");
               return false;
            }
         }
      }

      return true;
   }

   // check whether we have a real parameter
   if(strncmp(paramTypeString, "real", 4) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::REALPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing setting string: unknown parameter name <" << paramName <<
                      ">.\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->realParam.name[param].c_str(), SET_MAX_LINE_LEN) == 0)
         {
            Real value;
#ifdef WITH_LONG_DOUBLE
            value = std::stold(paramValueString);
#else
#ifdef WITH_FLOAT
            value = std::stof(paramValueString);
#else
            value = std::stod(paramValueString);
#endif
#endif

            if(setRealParam((SoPlex::RealParam)param, value))
               break;
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing setting string: invalid value <" << paramValueString <<
                         "> for real parameter <" << paramName << ">.\n");
               return false;
            }
         }
      }

      return true;
   }

#ifdef SOPLEX_WITH_RATIONALPARAM

   // check whether we have a rational parameter
   if(strncmp(paramTypeString, "rational", 8) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::RATIONALPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing setting string: unknown parameter name <" << paramName <<
                      ">.\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->rationalParam.name[param].c_str(),
                         SET_MAX_LINE_LEN) == 0)
         {
            Rational value;

            if(readStringRational(paramValueString, value)
                  && setRationalParam((SoPlex::RationalParam)param, value))
               break;
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing setting string: invalid value <" << paramValueString <<
                         "> for rational parameter <" << paramName << ">.\n");
               return false;
            }
         }
      }

      return true;
   }

#endif

   // check whether we have the random seed
   if(strncmp(paramTypeString, "uint", 4) == 0)
   {
      if(strncmp(paramName, "random_seed", 11) == 0)
      {
         unsigned int value;
         unsigned long parseval;

         parseval = std::stoul(paramValueString);

         if(parseval > UINT_MAX)
         {
            value = UINT_MAX;
            MSG_WARNING(spxout, spxout << "Converting number greater than UINT_MAX to uint.\n");
         }
         else
            value = (unsigned int) parseval;

         setRandomSeed(value);
         return true;
      }

      MSG_INFO1(spxout, spxout << "Error parsing setting string for uint parameter <random_seed>.\n");
      return false;
   }

   MSG_INFO1(spxout, spxout << "Error parsing setting string: invalid parameter type <" <<
             paramTypeString << "> for parameter <" << paramName << ">.\n");

   return false;
}




/// prints solution statistics
void SoPlex::printSolutionStatistics(std::ostream& os)
{
   SPxOut::setScientific(os);

   if(_lastSolveMode == SOLVEMODE_REAL)
   {
      os << "Solution (real)     : \n"
         << "  Objective value   : " << objValueReal() << "\n";
   }
   else if(_lastSolveMode == SOLVEMODE_RATIONAL)
   {
      os << "Solution (rational) : \n"
         << "  Objective value   : " << rationalToString(objValueRational()) << "\n";
      os << "Size (base 2/10)    : \n"
         << "  Total primal      : " << totalSizePrimalRational() << " / " << totalSizePrimalRational(
            10) << "\n"
         << "  Total dual        : " << totalSizeDualRational() << " / " << totalSizeDualRational(10) << "\n"
         << "  DLCM primal       : " << dlcmSizePrimalRational() << " / " << dlcmSizePrimalRational(
            10) << "\n"
         << "  DLCM dual         : " << dlcmSizeDualRational() << " / " << dlcmSizeDualRational(10) << "\n"
         << "  DMAX primal       : " << dmaxSizePrimalRational() << " / " << dmaxSizePrimalRational(
            10) << "\n"
         << "  DMAX dual         : " << dmaxSizeDualRational() << " / " << dmaxSizeDualRational(10) << "\n";
   }
   else
   {
      os << "Solution            : \n"
         << "  Objective value   : -\n";
   }

   if(intParam(SoPlex::CHECKMODE) == CHECKMODE_RATIONAL
         || (intParam(SoPlex::CHECKMODE) == CHECKMODE_AUTO
             && intParam(SoPlex::READMODE) == READMODE_RATIONAL))
   {
      Rational maxviol;
      Rational sumviol;

      os << "Violation (rational): \n";

      if(getBoundViolationRational(maxviol, sumviol))
         os << "  Max/sum bound     : " << rationalToString(maxviol) << " / " << rationalToString(
               sumviol) << "\n";
      else
         os << "  Max/sum bound     : - / -\n";

      if(getRowViolationRational(maxviol, sumviol))
         os << "  Max/sum row       : " << rationalToString(maxviol) << " / " << rationalToString(
               sumviol) << "\n";
      else
         os << "  Max/sum row       : - / -\n";

      if(getRedCostViolationRational(maxviol, sumviol))
         os << "  Max/sum redcost   : " << rationalToString(maxviol) << " / " << rationalToString(
               sumviol) << "\n";
      else
         os << "  Max/sum redcost   : - / -\n";

      if(getDualViolationRational(maxviol, sumviol))
         os << "  Max/sum dual      : " << rationalToString(maxviol) << " / " << rationalToString(
               sumviol) << "\n";
      else
         os << "  Max/sum dual      : - / -\n";
   }
   else
   {
      Real maxviol;
      Real sumviol;

      os << "Violations (real)   : \n";

      if(getBoundViolationReal(maxviol, sumviol))
         os << "  Max/sum bound     : " << maxviol << " / " << sumviol << "\n";
      else
         os << "  Max/sum bound     : - / -\n";

      if(getRowViolationReal(maxviol, sumviol))
         os << "  Max/sum row       : " << maxviol << " / " << sumviol << "\n";
      else
         os << "  Max/sum row       : - / -\n";

      if(getRedCostViolationReal(maxviol, sumviol))
         os << "  Max/sum redcost   : " << maxviol << " / " << sumviol << "\n";
      else
         os << "  Max/sum redcost   : - / -\n";

      if(getDualViolationReal(maxviol, sumviol))
         os << "  Max/sum dual      : " << maxviol << " / " << sumviol << "\n";
      else
         os << "  Max/sum dual      : - / -\n";
   }
}


/// prints statistics on solving process
void SoPlex::printSolvingStatistics(std::ostream& os)
{
   assert(_statistics != 0);
   _statistics->print(os);
}



/// prints short statistics
void SoPlex::printShortStatistics(std::ostream& os)
{
   printStatus(os, _status);
   SPxOut::setFixed(os, 2);
   os << "Solving time (sec)  : " << _statistics->solvingTime->time() << "\n"
      << "Iterations          : " << _statistics->iterations << "\n";
   SPxOut::setScientific(os);
   os << "Objective value     : " << objValueReal() << "\n";
}



/// prints complete statistics
void SoPlex::printStatistics(std::ostream& os)
{
   SPxOut::setFixed(os, 2);

   printStatus(os, _status);

   os << "Original problem    : \n";

   if(boolParam(SoPlex::USEDECOMPDUALSIMPLEX))
      printOriginalProblemStatistics(os);
   else
   {
      if(intParam(SoPlex::READMODE) == READMODE_REAL)
         _realLP->printProblemStatistics(os);
      else
         _rationalLP->printProblemStatistics(os);
   }

   os << "Objective sense     : " << (intParam(SoPlex::OBJSENSE) == SoPlex::OBJSENSE_MINIMIZE ?
                                      "minimize\n" : "maximize\n");
   printSolutionStatistics(os);
   printSolvingStatistics(os);
}

/// prints status
void SoPlex::printStatus(std::ostream& os, SPxSolver::Status stat)
{
   os << "SoPlex status       : ";

   switch(stat)
   {
   case SPxSolver::ERROR:
      os << "error [unspecified]";
      break;

   case SPxSolver::NO_RATIOTESTER:
      os << "error [no ratiotester loaded]";
      break;

   case SPxSolver::NO_PRICER:
      os << "error [no pricer loaded]";
      break;

   case SPxSolver::NO_SOLVER:
      os << "error [no linear solver loaded]";
      break;

   case SPxSolver::NOT_INIT:
      os << "error [not initialized]";
      break;

   case SPxSolver::ABORT_CYCLING:
      os << "solving aborted [cycling]";
      break;

   case SPxSolver::ABORT_TIME:
      os << "solving aborted [time limit reached]";
      break;

   case SPxSolver::ABORT_ITER:
      os << "solving aborted [iteration limit reached]";
      break;

   case SPxSolver::ABORT_VALUE:
      os << "solving aborted [objective limit reached]";
      break;

   case SPxSolver::NO_PROBLEM:
      os << "no problem loaded";
      break;

   case SPxSolver::REGULAR:
      os << "basis is regular";
      break;

   case SPxSolver::SINGULAR:
      os << "basis is singular";
      break;

   case SPxSolver::OPTIMAL:
      os << "problem is solved [optimal]";
      break;

   case SPxSolver::UNBOUNDED:
      os << "problem is solved [unbounded]";
      break;

   case SPxSolver::INFEASIBLE:
      os << "problem is solved [infeasible]";
      break;

   case SPxSolver::INForUNBD:
      os << "problem is solved [infeasible or unbounded]";
      break;

   case SPxSolver::OPTIMAL_UNSCALED_VIOLATIONS:
      os << "problem is solved [optimal with unscaled violations]";
      break;

   default:
   case SPxSolver::UNKNOWN:
      os << "unknown";
      break;
   }

   os << "\n";
}



/// prints version and compilation options
void SoPlex::printVersion() const
{
   // do not use preprocessor directives within the MSG_INFO1 macro
#if (SOPLEX_SUBVERSION > 0)
   MSG_INFO1(spxout, spxout << "SoPlex version " << SOPLEX_VERSION / 100
             << "." << (SOPLEX_VERSION % 100) / 10
             << "." << SOPLEX_VERSION % 10
             << "." << SOPLEX_SUBVERSION);
#else
   MSG_INFO1(spxout, spxout << "SoPlex version " << SOPLEX_VERSION / 100
             << "." << (SOPLEX_VERSION % 100) / 10
             << "." << SOPLEX_VERSION % 10);
#endif

#ifndef NDEBUG
   MSG_INFO1(spxout, spxout << " [mode: debug]");
#else
   MSG_INFO1(spxout, spxout << " [mode: optimized]");
#endif

   MSG_INFO1(spxout, spxout << " [precision: " << (int)sizeof(Real) << " byte]");

#ifdef SOPLEX_WITH_GMP
#ifdef mpir_version
   MSG_INFO1(spxout, spxout << " [rational: MPIR " << mpir_version << "]");
#else
   MSG_INFO1(spxout, spxout << " [rational: GMP " << gmp_version << "]");
#endif
#else
   MSG_INFO1(spxout, spxout << " [rational: long double]");
#endif

   MSG_INFO1(spxout, spxout << " [githash: " << getGitHash() << "]\n");
}



/// checks if real LP and rational LP are in sync; dimensions will always be compared,
/// vector and matrix values only if the respective parameter is set to true.
/// If quiet is set to true the function will only display which vectors are different.
bool SoPlex::areLPsInSync(const bool checkVecVals, const bool checkMatVals, const bool quiet) const
{
   bool result = true;
   bool nRowsMatch = true;
   bool nColsMatch = true;
   bool rhsDimMatch = true;
   bool lhsDimMatch = true;
   bool maxObjDimMatch = true;
   bool upperDimMatch = true;
   bool lowerDimMatch = true;

   // compare number of Rows
   if(_realLP->nRows() != _rationalLP->nRows())
   {
      MSG_INFO1(spxout, spxout <<
                "The number of Rows in the Real LP does not match the one in the Rational LP."
                << " Real LP: " << _realLP->nRows() << "  Rational LP: " << _rationalLP->nRows() << std::endl);
      result = false;
      nRowsMatch = false;
   }

   // compare number of Columns
   if(_realLP->nCols() != _rationalLP->nCols())
   {
      MSG_INFO1(spxout, spxout <<
                "The number of Columns in the Real LP does not match the one in the Rational LP."
                << " Real LP: " << _realLP->nCols() << "  Rational LP: " << _rationalLP->nCols() << std::endl);
      result = false;
      nColsMatch = false;
   }

   // compare number of nonZeros
   if(_realLP->nNzos() != _rationalLP->nNzos())
   {
      MSG_INFO1(spxout, spxout <<
                "The number of nonZeros in the Real LP does not match the one in the Rational LP."
                << " Real LP: " << _realLP->nNzos() << "  Rational LP: " << _rationalLP->nNzos() << std::endl);
      result = false;
   }

   // compare the dimensions of the right hand side vectors
   if(_realLP->rhs().dim() != _rationalLP->rhs().dim())
   {
      MSG_INFO1(spxout, spxout <<
                "The dimension of the right hand side vector of the Real LP does not match the one of the Rational LP."
                << " Real LP: " << _realLP->rhs().dim() << "  Rational LP: " << _rationalLP->rhs().dim() <<
                std::endl);
      result = false;
      rhsDimMatch = false;

   }

   // compare the dimensions of the left hand side vectors
   if(_realLP->lhs().dim() != _rationalLP->lhs().dim())
   {
      MSG_INFO1(spxout, spxout <<
                "The dimension of the left hand side vector of the Real LP does not match the one of the Rational LP."
                << " Real LP: " << _realLP->lhs().dim() << "  Rational LP: " << _rationalLP->lhs().dim() <<
                std::endl);
      result = false;
      lhsDimMatch = false;
   }

   // compare the dimensions of the objective function vectors
   if(_realLP->maxObj().dim() != _rationalLP->maxObj().dim())
   {
      MSG_INFO1(spxout, spxout <<
                "The dimension of the objective function vector of the Real LP does not match the one of the Rational LP."
                << " Real LP: " << _realLP->maxObj().dim() << "  Rational LP: " << _rationalLP->maxObj().dim() <<
                std::endl);
      result = false;
      maxObjDimMatch = false;
   }

   // compare the sense
   if((int)_realLP->spxSense() != (int)_rationalLP->spxSense())
   {
      MSG_INFO1(spxout, spxout <<
                "The objective function sense of the Real LP does not match the one of the Rational LP."
                << " Real LP: " << (_realLP->spxSense() == SPxLPReal::MINIMIZE ? "MIN" : "MAX")
                << "  Rational LP: " << (_rationalLP->spxSense() == SPxLPRational::MINIMIZE ? "MIN" : "MAX") <<
                std::endl);
      result = false;
   }

   // compare the dimensions of upper bound vectors
   if(_realLP->upper().dim() != _rationalLP->upper().dim())
   {
      MSG_INFO1(spxout, spxout <<
                "The dimension of the upper bound vector of the Real LP does not match the one of the Rational LP."
                << " Real LP: " << _realLP->upper().dim() << "  Rational LP: " << _rationalLP->upper().dim() <<
                std::endl);
      result = false;
      upperDimMatch = false;
   }

   // compare the dimensions of the objective function vectors
   if(_realLP->lower().dim() != _rationalLP->lower().dim())
   {
      MSG_INFO1(spxout, spxout <<
                "The dimension of the lower bound vector of the Real LP does not match the one of the Rational LP."
                << " Real LP: " << _realLP->lower().dim() << "  Rational LP: " << _rationalLP->lower().dim() <<
                std::endl);
      result = false;
      lowerDimMatch = false;
   }

   // compares the values of the rhs, lhs, maxObj, upper, lower vectors
   if(checkVecVals)
   {
      bool rhsValMatch = true;
      bool lhsValMatch = true;
      bool maxObjValMatch = true;
      bool upperValMatch = true;
      bool lowerValMatch = true;

      // compares the values of the right hand side vectors
      if(rhsDimMatch)
      {
         for(int i = 0; i < _realLP->rhs().dim(); i++)
         {
            if((GE(_realLP->rhs()[i], realParam(SoPlex::INFTY)) != (_rationalLP->rhs()[i] >= _rationalPosInfty))
                  || (LT(_realLP->rhs()[i], realParam(SoPlex::INFTY)) && _rationalLP->rhs()[i] < _rationalPosInfty
                      && !_rationalLP->rhs()[i].isAdjacentTo((double)_realLP->rhs()[i])))
            {
               if(!quiet)
               {
                  MSG_INFO1(spxout, spxout << "Entries number " << i << " of the right hand side vectors don't match."
                            << " Real LP: " << _realLP->rhs()[i] << "  Rational LP: " << _rationalLP->rhs()[i] << std::endl);
               }

               rhsValMatch = false;
               result = false;
            }
         }

         if(!rhsValMatch && quiet)
         {
            MSG_INFO1(spxout, spxout << "The values of the right hand side vectors don't match." << std::endl);
         }
      }

      // compares the values of the left hand side vectors
      if(lhsDimMatch)
      {
         for(int i = 0; i < _realLP->lhs().dim(); i++)
         {
            if((LE(_realLP->lhs()[i], -realParam(SoPlex::INFTY)) != (_rationalLP->lhs()[i] <=
                  _rationalNegInfty))
                  || (GT(_realLP->lhs()[i], -realParam(SoPlex::INFTY)) && _rationalLP->lhs()[i] > _rationalNegInfty
                      && !_rationalLP->lhs()[i].isAdjacentTo((double)_realLP->lhs()[i])))
            {
               if(!quiet)
               {
                  MSG_INFO1(spxout, spxout << "Entries number " << i << " of the left hand side vectors don't match."
                            << " Real LP: " << _realLP->lhs()[i] << "  Rational LP: " << _rationalLP->lhs()[i] << std::endl);
               }

               lhsValMatch = false;
               result = false;
            }
         }

         if(!lhsValMatch && quiet)
         {
            MSG_INFO1(spxout, spxout << "The values of the left hand side vectors don't match." << std::endl);
         }
      }

      // compares the values of the objective function vectors
      if(maxObjDimMatch)
      {
         for(int i = 0; i < _realLP->maxObj().dim(); i++)
         {
            if(!_rationalLP->maxObj()[i].isAdjacentTo((double)_realLP->maxObj()[i]))
            {
               if(!quiet)
               {
                  MSG_INFO1(spxout, spxout << "Entries number " << i <<
                            " of the objective function vectors don't match."
                            << " Real LP: " << _realLP->maxObj()[i] << "  Rational LP: " << _rationalLP->maxObj()[i] <<
                            std::endl);
               }

               maxObjValMatch = false;
               result = false;
            }
         }

         if(!maxObjValMatch && quiet)
         {
            MSG_INFO1(spxout, spxout << "The values of the objective function vectors don't match." <<
                      std::endl);
         }
      }

      // compares the values of the upper bound vectors
      if(upperDimMatch)
      {
         for(int i = 0; i < _realLP->upper().dim(); i++)
         {
            if((GE(_realLP->upper()[i], realParam(SoPlex::INFTY)) != (_rationalLP->upper()[i] >=
                  _rationalPosInfty))
                  || (LT(_realLP->upper()[i], realParam(SoPlex::INFTY)) && _rationalLP->upper()[i] < _rationalPosInfty
                      && !_rationalLP->upper()[i].isAdjacentTo((double)_realLP->upper()[i])))
            {
               if(!quiet)
               {
                  MSG_INFO1(spxout, spxout << "Entries number " << i << " of the upper bound vectors don't match."
                            << " Real LP: " << _realLP->upper()[i] << "  Rational LP: " << _rationalLP->upper()[i] <<
                            std::endl);
               }

               upperValMatch = false;
               result = false;
            }
         }

         if(!upperValMatch && quiet)
         {
            MSG_INFO1(spxout, spxout << "The values of the upper bound vectors don't match." << std::endl);
         }
      }

      // compares the values of the lower bound vectors
      if(lowerDimMatch)
      {
         for(int i = 0; i < _realLP->lower().dim(); i++)
         {
            if((LE(_realLP->lower()[i], -realParam(SoPlex::INFTY)) != (_rationalLP->lower()[i] <=
                  _rationalNegInfty))
                  || (GT(_realLP->lower()[i], -realParam(SoPlex::INFTY))
                      && _rationalLP->lower()[i] > _rationalNegInfty
                      && !_rationalLP->lower()[i].isAdjacentTo((double)_realLP->lower()[i])))
            {
               if(!quiet)
               {
                  MSG_INFO1(spxout, spxout << "Entries number " << i << " of the lower bound vectors don't match."
                            << " Real LP: " << _realLP->lower()[i] << "  Rational LP: " << _rationalLP->lower()[i] <<
                            std::endl);
               }

               lowerValMatch = false;
               result = false;
            }
         }

         if(!lowerValMatch && quiet)
         {
            MSG_INFO1(spxout, spxout << "The values of the lower bound vectors don't match." << std::endl);
         }
      }
   }

   // compare the values of the matrix
   if(checkMatVals && nRowsMatch && nColsMatch)
   {
      bool matrixValMatch = true;

      for(int i = 0; i < _realLP->nCols() ; i++)
      {
         for(int j = 0; j < _realLP->nRows() ; j++)
         {
            if(!_rationalLP->colVector(i)[j].isAdjacentTo((double)_realLP->colVector(i)[j]))
            {
               if(!quiet)
               {
                  MSG_INFO1(spxout, spxout << "Entries number " << j << " of column number " << i << " don't match."
                            << " Real LP: " << _realLP->colVector(i)[j] << "  Rational LP: " << _rationalLP->colVector(
                               i)[j] << std::endl);
               }

               matrixValMatch = false;
               result = false;
            }
         }
      }

      if(!matrixValMatch && quiet)
      {
         MSG_INFO1(spxout, spxout << "The values of the matrices don't match." << std::endl);
      }
   }

   return result;
}



/// set the random seed of the solver instance
void SoPlex::setRandomSeed(unsigned int seed)
{
   _solver.random.setSeed(seed);
}



/// returns the current random seed of the solver instance or the one stored in the settings
unsigned int SoPlex::randomSeed() const
{
   return _solver.random.getSeed();
}



/// extends sparse vector to hold newmax entries if and only if it holds no more free entries
void SoPlex::_ensureDSVectorRationalMemory(DSVectorRational& vec, const int newmax) const
{
   assert(newmax > vec.size());

   if(vec.size() >= vec.max())
      vec.setMax(newmax);
}



/// creates a permutation for removing rows/columns from an array of indices
void SoPlex::_idxToPerm(int* idx, int idxSize, int* perm, int permSize) const
{
   assert(idx != 0);
   assert(idxSize >= 0);
   assert(perm != 0);
   assert(permSize >= 0);

   for(int i = 0; i < permSize; i++)
      perm[i] = i;

   for(int i = 0; i < idxSize; i++)
   {
      assert(idx[i] >= 0);
      assert(idx[i] < permSize);
      perm[idx[i]] = -1;
   }
}



/// creates a permutation for removing rows/columns from a range of indices
void SoPlex::_rangeToPerm(int start, int end, int* perm, int permSize) const
{
   assert(perm != 0);
   assert(permSize >= 0);

   for(int i = 0; i < permSize; i++)
      perm[i] = (i < start || i > end) ? i : -1;
}



/// checks consistency
bool SoPlex::_isConsistent() const
{
   assert(_statistics != 0);
   assert(_currentSettings != 0);

   assert(_realLP != 0);
   assert(_rationalLP != 0 || intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL);

   assert(_realLP != &_solver || _isRealLPLoaded);
   assert(_realLP == &_solver || !_isRealLPLoaded);

   assert(!_hasBasis || _isRealLPLoaded || _basisStatusRows.size() == numRowsReal());
   assert(!_hasBasis || _isRealLPLoaded || _basisStatusCols.size() == numColsReal());
   assert(_rationalLUSolver.status() == SLinSolverRational::UNLOADED || _hasBasis);
   assert(_rationalLUSolver.status() == SLinSolverRational::UNLOADED
          || _rationalLUSolver.dim() == _rationalLUSolverBind.size());
   assert(_rationalLUSolver.status() == SLinSolverRational::UNLOADED
          || _rationalLUSolver.dim() == numRowsRational());

   assert(_rationalLP == 0 || _colTypes.size() == numColsRational());
   assert(_rationalLP == 0 || _rowTypes.size() == numRowsRational());

   return true;
}



/// should solving process be stopped?
bool SoPlex::_isSolveStopped(bool& stoppedTime, bool& stoppedIter) const
{
   assert(_statistics != 0);

   stoppedTime = (realParam(TIMELIMIT) < realParam(INFTY)
                  && _statistics->solvingTime->time() >= realParam(TIMELIMIT));
   stoppedIter = (intParam(ITERLIMIT) >= 0 && _statistics->iterations >= intParam(ITERLIMIT))
                 || (intParam(REFLIMIT) >= 0 && _statistics->refinements >= intParam(REFLIMIT))
                 || (intParam(STALLREFLIMIT) >= 0 && _statistics->stallRefinements >= intParam(STALLREFLIMIT));

   return stoppedTime || stoppedIter;
}



/// determines RangeType from real bounds
SoPlex::RangeType SoPlex::_rangeTypeReal(const Real& lower, const Real& upper) const
{
   assert(lower <= upper);

   if(lower <= -infinity)
   {
      if(upper >= infinity)
         return RANGETYPE_FREE;
      else
         return RANGETYPE_UPPER;
   }
   else
   {
      if(upper >= infinity)
         return RANGETYPE_LOWER;
      else if(lower == upper)
         return RANGETYPE_FIXED;
      else
         return RANGETYPE_BOXED;
   }
}



/// determines RangeType from rational bounds
SoPlex::RangeType SoPlex::_rangeTypeRational(const Rational& lower, const Rational& upper) const
{
   assert(lower <= upper);

   if(lower <= _rationalNegInfty)
   {
      if(upper >= _rationalPosInfty)
         return RANGETYPE_FREE;
      else
         return RANGETYPE_UPPER;
   }
   else
   {
      if(upper >= _rationalPosInfty)
         return RANGETYPE_LOWER;
      else if(lower == upper)
         return RANGETYPE_FIXED;
      else
         return RANGETYPE_BOXED;
   }
}



/// switches RANGETYPE_LOWER to RANGETYPE_UPPER and vice versa
SoPlex::RangeType SoPlex::_switchRangeType(const SoPlex::RangeType& rangeType) const
{
   if(rangeType == RANGETYPE_LOWER)
      return RANGETYPE_UPPER;
   else if(rangeType == RANGETYPE_UPPER)
      return RANGETYPE_LOWER;
   else
      return rangeType;
}



/// checks whether RangeType corresponds to finite lower bound
bool SoPlex::_lowerFinite(const RangeType& rangeType) const
{
   return (rangeType == RANGETYPE_LOWER || rangeType == RANGETYPE_BOXED
           || rangeType == RANGETYPE_FIXED);
}



/// checks whether RangeType corresponds to finite upper bound
bool SoPlex::_upperFinite(const RangeType& rangeType) const
{
   return (rangeType == RANGETYPE_UPPER || rangeType == RANGETYPE_BOXED
           || rangeType == RANGETYPE_FIXED);
}



/// adds a single row to the real LP and adjusts basis
void SoPlex::_addRowReal(const LPRowReal& lprow)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->addRow(lprow, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
      _basisStatusRows.append(SPxSolver::BASIC);

   _rationalLUSolver.clear();
}



/// adds a single row to the real LP and adjusts basis
void SoPlex::_addRowReal(Real lhs, const SVectorReal& lprow, Real rhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->addRow(lhs, lprow, rhs, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
      _basisStatusRows.append(SPxSolver::BASIC);

   _rationalLUSolver.clear();
}



/// adds multiple rows to the real LP and adjusts basis
void SoPlex::_addRowsReal(const LPRowSetReal& lprowset)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->addRows(lprowset, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
      _basisStatusRows.append(lprowset.num(), SPxSolver::BASIC);

   _rationalLUSolver.clear();
}


/// adds a single column to the real LP and adjusts basis
void SoPlex::_addColReal(const LPColReal& lpcol)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->addCol(lpcol, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
   {
      if(lpcol.lower() > -realParam(SoPlex::INFTY))
         _basisStatusCols.append(SPxSolver::ON_LOWER);
      else if(lpcol.upper() < realParam(SoPlex::INFTY))
         _basisStatusCols.append(SPxSolver::ON_UPPER);
      else
         _basisStatusCols.append(SPxSolver::ZERO);
   }

   _rationalLUSolver.clear();
}



/// adds a single column to the real LP and adjusts basis
void SoPlex::_addColReal(Real obj, Real lower, const SVectorReal& lpcol, Real upper)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->addCol(obj, lower, lpcol, upper, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
      _basisStatusRows.append(SPxSolver::BASIC);

   _rationalLUSolver.clear();
}



/// adds multiple columns to the real LP and adjusts basis
void SoPlex::_addColsReal(const LPColSetReal& lpcolset)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->addCols(lpcolset, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
   {
      for(int i = 0; i < lpcolset.num(); i++)
      {
         if(lpcolset.lower(i) > -realParam(SoPlex::INFTY))
            _basisStatusCols.append(SPxSolver::ON_LOWER);
         else if(lpcolset.upper(i) < realParam(SoPlex::INFTY))
            _basisStatusCols.append(SPxSolver::ON_UPPER);
         else
            _basisStatusCols.append(SPxSolver::ZERO);
      }
   }

   _rationalLUSolver.clear();
}


/// replaces row \p i with \p lprow and adjusts basis
void SoPlex::_changeRowReal(int i, const LPRowReal& lprow)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeRow(i, lprow, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
   {
      if(_basisStatusRows[i] != SPxSolver::BASIC)
         _hasBasis = false;
      else if(_basisStatusRows[i] == SPxSolver::ON_LOWER && lprow.lhs() <= -realParam(SoPlex::INFTY))
         _basisStatusRows[i] = (lprow.rhs() < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER :
                               SPxSolver::ZERO;
      else if(_basisStatusRows[i] == SPxSolver::ON_UPPER && lprow.rhs() >= realParam(SoPlex::INFTY))
         _basisStatusRows[i] = (lprow.lhs() > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                               SPxSolver::ZERO;
   }

   _rationalLUSolver.clear();
}



/// changes left-hand side vector for constraints to \p lhs and adjusts basis
void SoPlex::_changeLhsReal(const VectorReal& lhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeLhs(lhs, scale);

   if(_isRealLPLoaded)
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   else if(_hasBasis)
   {
      for(int i = numRowsReal() - 1; i >= 0; i--)
      {
         if(_basisStatusRows[i] == SPxSolver::ON_LOWER && lhs[i] <= -realParam(SoPlex::INFTY))
            _basisStatusRows[i] = (rhsReal(i) < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER :
                                  SPxSolver::ZERO;
      }
   }
}



/// changes left-hand side of row \p i to \p lhs and adjusts basis
void SoPlex::_changeLhsReal(int i, const Real& lhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeLhs(i, lhs, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis && _basisStatusRows[i] == SPxSolver::ON_LOWER && lhs <= -realParam(SoPlex::INFTY))
      _basisStatusRows[i] = (rhsReal(i) < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER :
                            SPxSolver::ZERO;

}



/// changes right-hand side vector to \p rhs and adjusts basis
void SoPlex::_changeRhsReal(const VectorReal& rhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeRhs(rhs, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numRowsReal() - 1; i >= 0; i--)
      {
         if(_basisStatusRows[i] == SPxSolver::ON_UPPER && rhs[i] >= realParam(SoPlex::INFTY))
            _basisStatusRows[i] = (lhsReal(i) > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                                  SPxSolver::ZERO;
      }
   }
}



/// changes right-hand side of row \p i to \p rhs and adjusts basis
void SoPlex::_changeRhsReal(int i, const Real& rhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeRhs(i, rhs, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis && _basisStatusRows[i] == SPxSolver::ON_UPPER && rhs >= realParam(SoPlex::INFTY))
      _basisStatusRows[i] = (lhsReal(i) > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                            SPxSolver::ZERO;
}



/// changes left- and right-hand side vectors and adjusts basis
void SoPlex::_changeRangeReal(const VectorReal& lhs, const VectorReal& rhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeRange(lhs, rhs, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numRowsReal() - 1; i >= 0; i--)
      {
         if(_basisStatusRows[i] == SPxSolver::ON_LOWER && lhs[i] <= -realParam(SoPlex::INFTY))
            _basisStatusRows[i] = (rhs[i] < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER : SPxSolver::ZERO;
         else if(_basisStatusRows[i] == SPxSolver::ON_UPPER && rhs[i] >= realParam(SoPlex::INFTY))
            _basisStatusRows[i] = (lhs[i] > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER : SPxSolver::ZERO;
      }
   }
}



/// changes left- and right-hand side of row \p i and adjusts basis
void SoPlex::_changeRangeReal(int i, const Real& lhs, const Real& rhs)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeRange(i, lhs, rhs, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      if(_basisStatusRows[i] == SPxSolver::ON_LOWER && lhs <= -realParam(SoPlex::INFTY))
         _basisStatusRows[i] = (rhs < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER : SPxSolver::ZERO;
      else if(_basisStatusRows[i] == SPxSolver::ON_UPPER && rhs >= realParam(SoPlex::INFTY))
         _basisStatusRows[i] = (lhs > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER : SPxSolver::ZERO;
   }
}



/// replaces column \p i with \p lpcol and adjusts basis
void SoPlex::_changeColReal(int i, const LPColReal& lpcol)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeCol(i, lpcol, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      if(_basisStatusCols[i] == SPxSolver::BASIC)
         _hasBasis = false;
      else if(_basisStatusCols[i] == SPxSolver::ON_LOWER && lpcol.lower() <= -realParam(SoPlex::INFTY))
         _basisStatusCols[i] = (lpcol.upper() < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER :
                               SPxSolver::ZERO;
      else if(_basisStatusCols[i] == SPxSolver::ON_UPPER && lpcol.upper() >= realParam(SoPlex::INFTY))
         _basisStatusCols[i] = (lpcol.lower() > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                               SPxSolver::ZERO;
   }

   _rationalLUSolver.clear();
}



/// changes vector of lower bounds to \p lower and adjusts basis
void SoPlex::_changeLowerReal(const VectorReal& lower)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeLower(lower, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numColsReal() - 1; i >= 0; i--)
      {
         if(_basisStatusCols[i] == SPxSolver::ON_LOWER && lower[i] <= -realParam(SoPlex::INFTY))
            _basisStatusCols[i] = (upperReal(i) < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER :
                                  SPxSolver::ZERO;
      }
   }
}



/// changes lower bound of column i to \p lower and adjusts basis
void SoPlex::_changeLowerReal(int i, const Real& lower)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeLower(i, lower, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis && _basisStatusCols[i] == SPxSolver::ON_LOWER
           && lower <= -realParam(SoPlex::INFTY))
      _basisStatusCols[i] = (upperReal(i) < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER :
                            SPxSolver::ZERO;
}



/// changes vector of upper bounds to \p upper and adjusts basis
void SoPlex::_changeUpperReal(const VectorReal& upper)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeUpper(upper, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numColsReal() - 1; i >= 0; i--)
      {
         if(_basisStatusCols[i] == SPxSolver::ON_UPPER && upper[i] >= realParam(SoPlex::INFTY))
            _basisStatusCols[i] = (lowerReal(i) > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                                  SPxSolver::ZERO;
      }
   }
}



/// changes \p i 'th upper bound to \p upper and adjusts basis
void SoPlex::_changeUpperReal(int i, const Real& upper)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeUpper(i, upper, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis &&  _basisStatusCols[i] == SPxSolver::ON_UPPER
           && upper >= realParam(SoPlex::INFTY))
      _basisStatusCols[i] = (lowerReal(i) > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                            SPxSolver::ZERO;
}



/// changes vectors of column bounds to \p lower and \p upper and adjusts basis
void SoPlex::_changeBoundsReal(const VectorReal& lower, const VectorReal& upper)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeBounds(lower, upper, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numColsReal() - 1; i >= 0; i--)
      {
         if(_basisStatusCols[i] == SPxSolver::ON_LOWER && lower[i] <= -realParam(SoPlex::INFTY))
            _basisStatusCols[i] = (upper[i] < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER : SPxSolver::ZERO;
         else if(_basisStatusCols[i] == SPxSolver::ON_UPPER && upper[i] >= realParam(SoPlex::INFTY))
            _basisStatusCols[i] = (lower[i] > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER :
                                  SPxSolver::ZERO;
      }
   }
}



/// changes bounds of column \p i to \p lower and \p upper and adjusts basis
void SoPlex::_changeBoundsReal(int i, const Real& lower, const Real& upper)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeBounds(i, lower, upper, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      if(_basisStatusCols[i] == SPxSolver::ON_LOWER && lower <= -realParam(SoPlex::INFTY))
         _basisStatusCols[i] = (upper < realParam(SoPlex::INFTY)) ? SPxSolver::ON_UPPER : SPxSolver::ZERO;
      else if(_basisStatusCols[i] == SPxSolver::ON_UPPER && upper >= realParam(SoPlex::INFTY))
         _basisStatusCols[i] = (lower > -realParam(SoPlex::INFTY)) ? SPxSolver::ON_LOWER : SPxSolver::ZERO;
   }
}



/// changes matrix entry in row \p i and column \p j to \p val and adjusts basis
void SoPlex::_changeElementReal(int i, int j, const Real& val)
{
   assert(_realLP != 0);

   bool scale = _realLP->isScaled();
   _realLP->changeElement(i, j, val, scale);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      if(_basisStatusRows[i] != SPxSolver::BASIC && _basisStatusCols[i] == SPxSolver::BASIC)
         _hasBasis = false;
   }

   _rationalLUSolver.clear();
}



/// removes row \p i and adjusts basis
void SoPlex::_removeRowReal(int i)
{
   assert(_realLP != 0);

   _realLP->removeRow(i);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      if(_basisStatusRows[i] != SPxSolver::BASIC)
         _hasBasis = false;
      else
      {
         _basisStatusRows[i] = _basisStatusRows[_basisStatusRows.size() - 1];
         _basisStatusRows.removeLast();
      }
   }

   _rationalLUSolver.clear();
}



/// removes all rows with an index \p i such that \p perm[i] < 0; upon completion, \p perm[i] >= 0 indicates the
/// new index where row \p i has been moved to; note that \p perm must point to an array of size at least
/// #numRowsReal()
void SoPlex::_removeRowsReal(int perm[])
{
   assert(_realLP != 0);

   _realLP->removeRows(perm);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numRowsReal() - 1; i >= 0 && _hasBasis; i--)
      {
         if(perm[i] < 0 && _basisStatusRows[i] != SPxSolver::BASIC)
            _hasBasis = false;
         else if(perm[i] >= 0 && perm[i] != i)
         {
            assert(perm[i] < numRowsReal());
            assert(perm[perm[i]] < 0);

            _basisStatusRows[perm[i]] = _basisStatusRows[i];
         }
      }

      if(_hasBasis)
         _basisStatusRows.reSize(numRowsReal());
   }

   _rationalLUSolver.clear();
}



/// removes column i
void SoPlex::_removeColReal(int i)
{
   assert(_realLP != 0);

   _realLP->removeCol(i);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      if(_basisStatusCols[i] == SPxSolver::BASIC)
         _hasBasis = false;
      else
      {
         _basisStatusCols[i] = _basisStatusCols[_basisStatusCols.size() - 1];
         _basisStatusCols.removeLast();
      }
   }

   _rationalLUSolver.clear();
}



/// removes all columns with an index \p i such that \p perm[i] < 0; upon completion, \p perm[i] >= 0 indicates the
/// new index where column \p i has been moved to; note that \p perm must point to an array of size at least
/// #numColsReal()
void SoPlex::_removeColsReal(int perm[])
{
   assert(_realLP != 0);

   _realLP->removeCols(perm);

   if(_isRealLPLoaded)
   {
      _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
   }
   else if(_hasBasis)
   {
      for(int i = numColsReal() - 1; i >= 0 && _hasBasis; i--)
      {
         if(perm[i] < 0 && _basisStatusCols[i] == SPxSolver::BASIC)
            _hasBasis = false;
         else if(perm[i] >= 0 && perm[i] != i)
         {
            assert(perm[i] < numColsReal());
            assert(perm[perm[i]] < 0);

            _basisStatusCols[perm[i]] = _basisStatusCols[i];
         }
      }

      if(_hasBasis)
         _basisStatusCols.reSize(numColsReal());
   }

   _rationalLUSolver.clear();
}



/// invalidates solution
void SoPlex::_invalidateSolution()
{
   ///@todo maybe this should be done individually at the places when this method is called
   _status = SPxSolver::UNKNOWN;

   _solReal.invalidate();
   _hasSolReal = false;

   _solRational.invalidate();
   _hasSolRational = false;
}



/// enables simplifier and scaler
void SoPlex::_enableSimplifierAndScaler()
{
   // type of simplifier
   switch(intParam(SoPlex::SIMPLIFIER))
   {
   case SIMPLIFIER_OFF:
      _simplifier = 0;
      break;

   case SIMPLIFIER_AUTO:
      _simplifier = &_simplifierMainSM;
      assert(_simplifier != 0);
      _simplifier->setMinReduction(realParam(MINRED));
      break;

   default:
      break;
   }

   // type of scaler
   switch(intParam(SoPlex::SCALER))
   {
   case SCALER_OFF:
      _scaler = 0;
      break;

   case SCALER_UNIEQUI:
      _scaler = &_scalerUniequi;
      break;

   case SCALER_BIEQUI:
      _scaler = &_scalerBiequi;
      break;

   case SCALER_GEO1:
      _scaler = &_scalerGeo1;
      break;

   case SCALER_GEO8:
      _scaler = &_scalerGeo8;
      break;

   case SCALER_LEASTSQ:
      _scaler = &_scalerLeastsq;
      break;

   case SCALER_GEOEQUI:
      _scaler = &_scalerGeoequi;
      break;

   default:
      break;
   }
}



/// disables simplifier and scaler
void SoPlex::_disableSimplifierAndScaler()
{
   _simplifier = 0;

   // preserve scaler when persistent scaling is used
   if(!_isRealLPScaled)
      _scaler = 0;
   else
      assert(boolParam(SoPlex::PERSISTENTSCALING));
}



/// ensures that the rational LP is available; performs no sync
void SoPlex::_ensureRationalLP()
{
   if(_rationalLP == 0)
   {
      spx_alloc(_rationalLP);
      _rationalLP = new(_rationalLP) SPxLPRational();
      _rationalLP->setOutstream(spxout);
   }
}



/// ensures that the real LP and the basis are loaded in the solver; performs no sync
void SoPlex::_ensureRealLPLoaded()
{
   if(!_isRealLPLoaded)
   {
      assert(_realLP != &_solver);

      _solver.loadLP(*_realLP);
      _realLP->~SPxLPReal();
      spx_free(_realLP);
      _realLP = &_solver;
      _isRealLPLoaded = true;

      if(_hasBasis)
      {
         ///@todo this should not fail even if the basis is invalid (wrong dimension or wrong number of basic
         ///      entries); fix either in SPxSolver or in SPxBasis
         assert(_basisStatusRows.size() == numRowsReal());
         assert(_basisStatusCols.size() == numColsReal());
         _solver.setBasis(_basisStatusRows.get_const_ptr(), _basisStatusCols.get_const_ptr());
         _hasBasis = (_solver.basis().status() > SPxBasis::NO_PROBLEM);
      }
   }
}



/// call floating-point solver and update statistics on iterations etc.
void SoPlex::_solveRealLPAndRecordStatistics()
{
   bool _hadBasis = _hasBasis;

   // set time and iteration limit
   if(intParam(SoPlex::ITERLIMIT) < realParam(SoPlex::INFTY))
      _solver.setTerminationIter(intParam(SoPlex::ITERLIMIT) - _statistics->iterations);
   else
      _solver.setTerminationIter(-1);

   if(realParam(SoPlex::TIMELIMIT) < realParam(SoPlex::INFTY))
      _solver.setTerminationTime(realParam(SoPlex::TIMELIMIT) - _statistics->solvingTime->time());
   else
      _solver.setTerminationTime(realParam(SoPlex::INFTY));

   // ensure that tolerances are not too small
   if(_solver.feastol() < 1e-12)
      _solver.setFeastol(1e-12);

   if(_solver.opttol() < 1e-12)
      _solver.setOpttol(1e-12);

   // set correct representation
   if((intParam(SoPlex::REPRESENTATION) == SoPlex::REPRESENTATION_COLUMN
         || (intParam(SoPlex::REPRESENTATION) == SoPlex::REPRESENTATION_AUTO
             && (_solver.nCols() + 1) * realParam(SoPlex::REPRESENTATION_SWITCH) >= (_solver.nRows() + 1)))
         && _solver.rep() != SPxSolver::COLUMN)
   {
      _solver.setRep(SPxSolver::COLUMN);
   }
   else if((intParam(SoPlex::REPRESENTATION) == SoPlex::REPRESENTATION_ROW
            || (intParam(SoPlex::REPRESENTATION) == SoPlex::REPRESENTATION_AUTO
                && (_solver.nCols() + 1) * realParam(SoPlex::REPRESENTATION_SWITCH) < (_solver.nRows() + 1)))
           && _solver.rep() != SPxSolver::ROW)
   {
      _solver.setRep(SPxSolver::ROW);
   }

   // set correct type
   if(((intParam(ALGORITHM) == SoPlex::ALGORITHM_PRIMAL && _solver.rep() == SPxSolver::COLUMN)
         || (intParam(ALGORITHM) == SoPlex::ALGORITHM_DUAL && _solver.rep() == SPxSolver::ROW))
         && _solver.type() != SPxSolver::ENTER)
   {
      _solver.setType(SPxSolver::ENTER);
   }
   else if(((intParam(ALGORITHM) == SoPlex::ALGORITHM_DUAL && _solver.rep() == SPxSolver::COLUMN)
            || (intParam(ALGORITHM) == SoPlex::ALGORITHM_PRIMAL && _solver.rep() == SPxSolver::ROW))
           && _solver.type() != SPxSolver::LEAVE)
   {
      _solver.setType(SPxSolver::LEAVE);
   }

   // set pricing modes
   _solver.setSparsePricingFactor(realParam(SoPlex::SPARSITY_THRESHOLD));

   if((intParam(SoPlex::HYPER_PRICING) == SoPlex::HYPER_PRICING_ON)
         || ((intParam(SoPlex::HYPER_PRICING) == SoPlex::HYPER_PRICING_AUTO)
             && (_solver.nRows() + _solver.nCols() > HYPERPRICINGTHRESHOLD)))
      _solver.hyperPricing(true);
   else if(intParam(SoPlex::HYPER_PRICING) == SoPlex::HYPER_PRICING_OFF)
      _solver.hyperPricing(false);

   _solver.setNonzeroFactor(realParam(SoPlex::REFAC_BASIS_NNZ));
   _solver.setFillFactor(realParam(SoPlex::REFAC_UPDATE_FILL));
   _solver.setMemFactor(realParam(SoPlex::REFAC_MEM_FACTOR));

   // call floating-point solver and catch exceptions
   _statistics->simplexTime->start();

   try
   {
      _solver.solve();
   }
   catch(const SPxException& E)
   {
      MSG_INFO1(spxout, spxout << "Caught exception <" << E.what() << "> while solving real LP.\n");
      _status = SPxSolver::ERROR;
   }
   catch(...)
   {
      MSG_INFO1(spxout, spxout << "Caught unknown exception while solving real LP.\n");
      _status = SPxSolver::ERROR;
   }

   _statistics->simplexTime->stop();

   // invalidate rational factorization of basis if pivots have been performed
   if(_solver.iterations() > 0)
      _rationalLUSolver.clear();

   // record statistics
   _statistics->iterations += _solver.iterations();
   _statistics->iterationsPrimal += _solver.primalIterations();
   _statistics->iterationsFromBasis += _hadBasis ? _solver.iterations() : 0;
   _statistics->iterationsPolish += _solver.polishIterations();
   _statistics->boundflips += _solver.boundFlips();
   _statistics->luFactorizationTimeReal += _slufactor.getFactorTime();
   _statistics->luSolveTimeReal += _slufactor.getSolveTime();
   _statistics->luFactorizationsReal += _slufactor.getFactorCount();
   _statistics->luSolvesReal += _slufactor.getSolveCount();
   _slufactor.resetCounters();

   _statistics->degenPivotsPrimal += _solver.primalDegeneratePivots();
   _statistics->degenPivotsDual += _solver.dualDegeneratePivots();
   _statistics->sumDualDegen += _solver.sumDualDegeneracy();
   _statistics->sumPrimalDegen += _solver.sumPrimalDegeneracy();
}



/// reads real LP in LP or MPS format from file and returns true on success; gets row names, column names, and
/// integer variables if desired
bool SoPlex::_readFileReal(const char* filename, NameSet* rowNames, NameSet* colNames,
                           DIdxSet* intVars)
{
   assert(_realLP != 0);

   // clear statistics
   _statistics->clearAllData();

   // update status
   clearBasis();
   _invalidateSolution();
   _status = SPxSolver::UNKNOWN;

   // start timing
   _statistics->readingTime->start();

   // read
   bool success = _realLP->readFile(filename, rowNames, colNames, intVars);

   // stop timing
   _statistics->readingTime->stop();

   if(success)
   {
      setIntParam(SoPlex::OBJSENSE, (_realLP->spxSense() == SPxLPReal::MAXIMIZE ?
                                     SoPlex::OBJSENSE_MAXIMIZE : SoPlex::OBJSENSE_MINIMIZE), true);
      _realLP->changeObjOffset(realParam(SoPlex::OBJ_OFFSET));

      // if sync mode is auto, we have to copy the (rounded) real LP to the rational LP; this is counted to sync time
      // and not to reading time
      if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
         _syncLPRational();
   }
   else
      clearLPReal();

   return success;
}



/// reads rational LP in LP or MPS format from file and returns true on success; gets row names, column names, and
/// integer variables if desired
bool SoPlex::_readFileRational(const char* filename, NameSet* rowNames, NameSet* colNames,
                               DIdxSet* intVars)
{
   // clear statistics
   _statistics->clearAllData();

   // start timing
   _statistics->readingTime->start();

   // update status
   clearBasis();
   _invalidateSolution();
   _status = SPxSolver::UNKNOWN;

   // read
   _ensureRationalLP();
   bool success = _rationalLP->readFile(filename, rowNames, colNames, intVars);

   // stop timing
   _statistics->readingTime->stop();

   if(success)
   {
      setIntParam(SoPlex::OBJSENSE, (_rationalLP->spxSense() == SPxLPRational::MAXIMIZE ?
                                     SoPlex::OBJSENSE_MAXIMIZE : SoPlex::OBJSENSE_MINIMIZE), true);
      _rationalLP->changeObjOffset(realParam(SoPlex::OBJ_OFFSET));
      _recomputeRangeTypesRational();

      // if sync mode is auto, we have to copy the (rounded) real LP to the rational LP; this is counted to sync time
      // and not to reading time
      if(intParam(SoPlex::SYNCMODE) == SYNCMODE_AUTO)
         _syncLPReal();
      // if a rational LP file is read, but only the (rounded) real LP should be kept, we have to free the rational LP
      else if(intParam(SoPlex::SYNCMODE) == SYNCMODE_ONLYREAL)
      {
         _syncLPReal();
         _rationalLP->~SPxLPRational();
         spx_free(_rationalLP);
      }
   }
   else
      clearLPRational();

   return success;
}



/// completes range type arrays after adding columns and/or rows
void SoPlex::_completeRangeTypesRational()
{
   // we use one method for bot columns and rows, because during column/row addition, rows/columns can be added
   // implicitly
   for(int i = _colTypes.size(); i < numColsRational(); i++)
      _colTypes.append(_rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i)));

   for(int i = _rowTypes.size(); i < numRowsRational(); i++)
      _rowTypes.append(_rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i)));
}



/// recomputes range types from scratch using real LP
void SoPlex::_recomputeRangeTypesReal()
{
   _rowTypes.reSize(numRowsReal());

   for(int i = 0; i < numRowsReal(); i++)
      _rowTypes[i] = _rangeTypeReal(_realLP->lhs(i), _realLP->rhs(i));

   _colTypes.reSize(numColsReal());

   for(int i = 0; i < numColsReal(); i++)
      _colTypes[i] = _rangeTypeReal(_realLP->lower(i), _realLP->upper(i));
}



/// recomputes range types from scratch using rational LP
void SoPlex::_recomputeRangeTypesRational()
{
   _rowTypes.reSize(numRowsRational());

   for(int i = 0; i < numRowsRational(); i++)
      _rowTypes[i] = _rangeTypeRational(_rationalLP->lhs(i), _rationalLP->rhs(i));

   _colTypes.reSize(numColsRational());

   for(int i = 0; i < numColsRational(); i++)
      _colTypes[i] = _rangeTypeRational(_rationalLP->lower(i), _rationalLP->upper(i));
}



/// synchronizes real LP with rational LP, i.e., copies (rounded) rational LP into real LP, without looking at the sync mode
void SoPlex::_syncLPReal(bool time)
{
   // start timing
   if(time)
      _statistics->syncTime->start();

   // copy LP
   if(_isRealLPLoaded)
      _solver.loadLP((SPxLPReal)(*_rationalLP));
   else
      *_realLP = *_rationalLP;

   ///@todo try loading old basis
   _hasBasis = false;
   _rationalLUSolver.clear();

   // stop timing
   if(time)
      _statistics->syncTime->stop();
}



/// synchronizes rational LP with real LP, i.e., copies real LP to rational LP, without looking at the sync mode
void SoPlex::_syncLPRational(bool time)
{
   // start timing
   if(time)
      _statistics->syncTime->start();

   // copy LP
   _ensureRationalLP();
   *_rationalLP = *_realLP;
   _recomputeRangeTypesRational();

   // stop timing
   if(time)
      _statistics->syncTime->stop();
}



/// synchronizes rational solution with real solution, i.e., copies (rounded) rational solution to real solution
void SoPlex::_syncRealSolution()
{
   if(_hasSolRational && !_hasSolReal)
   {
      _solReal = _solRational;
      _hasSolReal = true;
   }
}



/// synchronizes real solution with rational solution, i.e., copies real solution to rational solution
void SoPlex::_syncRationalSolution()
{
   if(_hasSolReal && !_hasSolRational)
   {
      _solRational = _solReal;
      _hasSolRational = true;
   }
}



/// returns pointer to a constant unit vector available until destruction of the SoPlex class
const UnitVectorRational* SoPlex::_unitVectorRational(const int i)
{
   assert(i >= 0);

   if(i < 0)
      return 0;
   else if(i >= _unitMatrixRational.size())
      _unitMatrixRational.append(i + 1 - _unitMatrixRational.size(), (UnitVectorRational*)0);

   assert(i < _unitMatrixRational.size());

   if(_unitMatrixRational[i] == 0)
   {
      spx_alloc(_unitMatrixRational[i]);
      new(_unitMatrixRational[i]) UnitVectorRational(i);
   }

   assert(_unitMatrixRational[i] != 0);

   return _unitMatrixRational[i];
}



/// parses one line in a settings file and returns true on success; note that the string is modified
bool SoPlex::_parseSettingsLine(char* line, const int lineNumber)
{
   assert(line != 0);

   // find the start of the parameter type
   while(*line == ' ' || *line == '\t' || *line == '\r')
      line++;

   if(*line == '\0' || *line == '\n' || *line == '#')
      return true;

   char* paramTypeString = line;

   // find the end of the parameter type
   while(*line != ' ' && *line != '\t' && *line != '\r' && *line != '\n' && *line != '#'
         && *line != '\0' && *line != ':')
      line++;

   if(*line == ':')
   {
      *line = '\0';
      line++;
   }
   else
   {
      *line = '\0';
      line++;

      // search for the ':' char in the line
      while(*line == ' ' || *line == '\t' || *line == '\r')
         line++;

      if(*line != ':')
      {
         MSG_INFO1(spxout, spxout <<
                   "Error parsing settings file: no ':' separating parameter type and name in line " << lineNumber <<
                   ".\n");
         return false;
      }

      line++;
   }

   // find the start of the parameter name
   while(*line == ' ' || *line == '\t' || *line == '\r')
      line++;

   if(*line == '\0' || *line == '\n' || *line == '#')
   {
      MSG_INFO1(spxout, spxout << "Error parsing settings file: no parameter name in line " << lineNumber
                << ".\n");
      return false;
   }

   char* paramName = line;

   // find the end of the parameter name
   while(*line != ' ' && *line != '\t' && *line != '\r' && *line != '\n' && *line != '#'
         && *line != '\0' && *line != '=')
      line++;

   if(*line == '=')
   {
      *line = '\0';
      line++;
   }
   else
   {
      *line = '\0';
      line++;

      // search for the '=' char in the line
      while(*line == ' ' || *line == '\t' || *line == '\r')
         line++;

      if(*line != '=')
      {
         MSG_INFO1(spxout, spxout << "Error parsing settings file: no '=' after parameter name in line " <<
                   lineNumber << ".\n");
         return false;
      }

      line++;
   }

   // find the start of the parameter value string
   while(*line == ' ' || *line == '\t' || *line == '\r')
      line++;

   if(*line == '\0' || *line == '\n' || *line == '#')
   {
      MSG_INFO1(spxout, spxout << "Error parsing settings file: no parameter value in line " << lineNumber
                << ".\n");
      return false;
   }

   char* paramValueString = line;

   // find the end of the parameter value string
   while(*line != ' ' && *line != '\t' && *line != '\r' && *line != '\n' && *line != '#'
         && *line != '\0')
      line++;

   if(*line != '\0')
   {
      // check, if the rest of the line is clean
      *line = '\0';
      line++;

      while(*line == ' ' || *line == '\t' || *line == '\r')
         line++;

      if(*line != '\0' && *line != '\n' && *line != '#')
      {
         MSG_INFO1(spxout, spxout << "Error parsing settings file: additional character '" << *line <<
                   "' after parameter value in line " << lineNumber << ".\n");
         return false;
      }
   }

   // check whether we have a bool parameter
   if(strncmp(paramTypeString, "bool", 4) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::BOOLPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing settings file: unknown parameter name <" << paramName <<
                      "> in line " << lineNumber << ".\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->boolParam.name[param].c_str(), SET_MAX_LINE_LEN) == 0)
         {
            if(strncasecmp(paramValueString, "true", 4) == 0
                  || strncasecmp(paramValueString, "TRUE", 4) == 0
                  || strncasecmp(paramValueString, "t", 4) == 0
                  || strncasecmp(paramValueString, "T", 4) == 0
                  || strtol(paramValueString, NULL, 4) == 1)
            {
               setBoolParam((SoPlex::BoolParam)param, true);
               break;
            }
            else if(strncasecmp(paramValueString, "false", 5) == 0
                    || strncasecmp(paramValueString, "FALSE", 5) == 0
                    || strncasecmp(paramValueString, "f", 5) == 0
                    || strncasecmp(paramValueString, "F", 5) == 0
                    || strtol(paramValueString, NULL, 5) == 0)
            {
               setBoolParam((SoPlex::BoolParam)param, false);
               break;
            }
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing settings file: invalid value <" << paramValueString <<
                         "> for bool parameter <" << paramName << "> in line " << lineNumber << ".\n");
               return false;
            }
         }
      }

      return true;
   }

   // check whether we have an integer parameter
   if(strncmp(paramTypeString, "int", 3) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::INTPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing settings file: unknown parameter name <" << paramName <<
                      "> in line " << lineNumber << ".\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->intParam.name[param].c_str(), SET_MAX_LINE_LEN) == 0)
         {
            int value;
            value = std::stoi(paramValueString);

            if(setIntParam((SoPlex::IntParam)param, value, false))
               break;
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing settings file: invalid value <" << paramValueString <<
                         "> for int parameter <" << paramName << "> in line " << lineNumber << ".\n");
               return false;
            }
         }
      }

      return true;
   }

   // check whether we have a real parameter
   if(strncmp(paramTypeString, "real", 4) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::REALPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing settings file: unknown parameter name <" << paramName <<
                      "> in line " << lineNumber << ".\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->realParam.name[param].c_str(), SET_MAX_LINE_LEN) == 0)
         {
            Real value;

#ifdef WITH_LONG_DOUBLE
            value = std::stold(paramValueString);
#else
#ifdef WITH_FLOAT
            value = std::stof(paramValueString);
#else
            value = std::stod(paramValueString);
#endif
#endif

            if(setRealParam((SoPlex::RealParam)param, value))
               break;
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing settings file: invalid value <" << paramValueString <<
                         "> for real parameter <" << paramName << "> in line " << lineNumber << ".\n");
               return false;
            }
         }
      }

      return true;
   }

#ifdef SOPLEX_WITH_RATIONALPARAM

   // check whether we have a rational parameter
   if(strncmp(paramTypeString, "rational", 8) == 0)
   {
      for(int param = 0; ; param++)
      {
         if(param >= SoPlex::RATIONALPARAM_COUNT)
         {
            MSG_INFO1(spxout, spxout << "Error parsing settings file: unknown parameter name <" << paramName <<
                      "> in line " << lineNumber << ".\n");
            return false;
         }
         else if(strncmp(paramName, _currentSettings->rationalParam.name[param].c_str(),
                         SET_MAX_LINE_LEN) == 0)
         {
            Rational value;

            if(readStringRational(paramValueString, value)
                  && setRationalParam((SoPlex::RationalParam)param, value))
               break;
            else
            {
               MSG_INFO1(spxout, spxout << "Error parsing settings file: invalid value <" << paramValueString <<
                         "> for rational parameter <" << paramName << "> in line " << lineNumber << ".\n");
               return false;
            }
         }
      }

      return true;
   }

#endif

   // check whether we have the random seed
   if(strncmp(paramTypeString, "uint", 4) == 0)
   {
      if(strncmp(paramName, "random_seed", 11) == 0)
      {
         unsigned int value;
         unsigned long parseval;

         parseval = std::stoul(paramValueString);

         if(parseval > UINT_MAX)
         {
            value = UINT_MAX;
            MSG_WARNING(spxout, spxout << "Converting number greater than UINT_MAX to uint.\n");
         }
         else
            value = (unsigned int) parseval;

         setRandomSeed(value);
         return true;
      }

      MSG_INFO1(spxout, spxout << "Error parsing settings file for uint parameter <random_seed>.\n");
      return false;
   }

   MSG_INFO1(spxout, spxout << "Error parsing settings file: invalid parameter type <" <<
             paramTypeString << "> for parameter <" << paramName << "> in line " << lineNumber << ".\n");

   return false;
}
} // namespace soplex