scip_var.c

Go to the documentation of this file.

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
/*                                                                           */
/*  Copyright 2002-2022 Zuse Institute Berlin                                */
/*                                                                           */
/*  Licensed under the Apache License, Version 2.0 (the "License");          */
/*  you may not use this file except in compliance with the License.         */
/*  You may obtain a copy of the License at                                  */
/*                                                                           */
/*      http://www.apache.org/licenses/LICENSE-2.0                           */
/*                                                                           */
/*  Unless required by applicable law or agreed to in writing, software      */
/*  distributed under the License is distributed on an "AS IS" BASIS,        */
/*  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */
/*  See the License for the specific language governing permissions and      */
/*  limitations under the License.                                           */
/*                                                                           */
/*  You should have received a copy of the Apache-2.0 license                */
/*  along with SCIP; see the file LICENSE. If not visit scipopt.org.         */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   scip_var.c
 * @ingroup OTHER_CFILES
 * @brief  public methods for SCIP variables
 * @author Tobias Achterberg
 * @author Timo Berthold
 * @author Gerald Gamrath
 * @author Leona Gottwald
 * @author Stefan Heinz
 * @author Gregor Hendel
 * @author Thorsten Koch
 * @author Alexander Martin
 * @author Marc Pfetsch
 * @author Michael Winkler
 * @author Kati Wolter
 *
 * @todo check all SCIP_STAGE_* switches, and include the new stages TRANSFORMED and INITSOLVE
 */

/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/

#include "blockmemshell/memory.h"
#include "lpi/lpi.h"
#include "scip/branch.h"
#include "scip/clock.h"
#include "scip/conflict.h"
#include "scip/debug.h"
#include "scip/history.h"
#include "scip/implics.h"
#include "scip/lp.h"
#include "scip/prob.h"
#include "scip/pub_cons.h"
#include "scip/pub_implics.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_tree.h"
#include "scip/pub_var.h"
#include "scip/relax.h"
#include "scip/scip_general.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_numerics.h"
#include "scip/scip_prob.h"
#include "scip/scip_probing.h"
#include "scip/scip_sol.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_tree.h"
#include "scip/scip_var.h"
#include "scip/set.h"
#include "scip/sol.h"
#include "scip/solve.h"
#include "scip/stat.h"
#include "scip/struct_lp.h"
#include "scip/struct_mem.h"
#include "scip/struct_primal.h"
#include "scip/struct_prob.h"
#include "scip/struct_scip.h"
#include "scip/struct_set.h"
#include "scip/struct_stat.h"
#include "scip/struct_tree.h"
#include "scip/struct_var.h"
#include "scip/tree.h"
#include "scip/var.h"
#include <ctype.h>


/** creates and captures problem variable; if variable is of integral type, fractional bounds are automatically rounded;
 *  an integer variable with bounds zero and one is automatically converted into a binary variable;
 *
 *  @warning When doing column generation and the original problem is a maximization problem, notice that SCIP will
 *           transform the problem into a minimization problem by multiplying the objective function by -1.  Thus, the
 *           original objective function value of variables created during the solving process has to be multiplied by
 *           -1, too.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note the variable gets captured, hence at one point you have to release it using the method SCIPreleaseVar()
 */
SCIP_RETCODE SCIPcreateVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            var,                /**< pointer to variable object */
   const char*           name,               /**< name of variable, or NULL for automatic name creation */
   SCIP_Real             lb,                 /**< lower bound of variable */
   SCIP_Real             ub,                 /**< upper bound of variable */
   SCIP_Real             obj,                /**< objective function value */
   SCIP_VARTYPE          vartype,            /**< type of variable */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable, or NULL */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data, or NULL */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable, or NULL */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_VARDATA*         vardata             /**< user data for this specific variable */
   )
{
   assert(var != NULL);
   assert(lb <= ub);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPcreateVar", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   /* forbid infinite objective function values */
   if( SCIPisInfinity(scip, REALABS(obj)) )
   {
      SCIPerrorMessage("invalid objective function value: value is infinite\n");
      return SCIP_INVALIDDATA;
   }

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      SCIP_CALL( SCIPvarCreateOriginal(var, scip->mem->probmem, scip->set, scip->stat,
            name, lb, ub, obj, vartype, initial, removable, vardelorig, vartrans, vardeltrans, varcopy, vardata) );
      break;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_INITPRESOLVE:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_PRESOLVED:
   case SCIP_STAGE_SOLVING:
      SCIP_CALL( SCIPvarCreateTransformed(var, scip->mem->probmem, scip->set, scip->stat,
            name, lb, ub, obj, vartype, initial, removable, vardelorig, vartrans, vardeltrans, varcopy, vardata) );
      break;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/

   return SCIP_OKAY;
}

/** creates and captures problem variable with optional callbacks and variable data set to NULL, which can be set
 *  afterwards using SCIPvarSetDelorigData(), SCIPvarSetTransData(),
 *  SCIPvarSetDeltransData(), SCIPvarSetCopy(), and SCIPvarSetData(); sets variable flags initial=TRUE
 *  and removable = FALSE, which can be adjusted by using SCIPvarSetInitial() and SCIPvarSetRemovable(), resp.;
 *  if variable is of integral type, fractional bounds are automatically rounded;
 *  an integer variable with bounds zero and one is automatically converted into a binary variable;
 *
 *  @warning When doing column generation and the original problem is a maximization problem, notice that SCIP will
 *           transform the problem into a minimization problem by multiplying the objective function by -1.  Thus, the
 *           original objective function value of variables created during the solving process has to be multiplied by
 *           -1, too.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note the variable gets captured, hence at one point you have to release it using the method SCIPreleaseVar()
 */
SCIP_RETCODE SCIPcreateVarBasic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            var,                /**< pointer to variable object */
   const char*           name,               /**< name of variable, or NULL for automatic name creation */
   SCIP_Real             lb,                 /**< lower bound of variable */
   SCIP_Real             ub,                 /**< upper bound of variable */
   SCIP_Real             obj,                /**< objective function value */
   SCIP_VARTYPE          vartype             /**< type of variable */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPcreateVarBasic", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIP_CALL( SCIPcreateVar(scip, var, name, lb, ub, obj, vartype, TRUE, FALSE, NULL, NULL, NULL, NULL, NULL) );

   return SCIP_OKAY;
}

/** outputs the variable name to the file stream
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPwriteVarName(
   SCIP*                 scip,               /**< SCIP data structure */
   FILE*                 file,               /**< output file, or NULL for stdout */
   SCIP_VAR*             var,                /**< variable to output */
   SCIP_Bool             type                /**< should the variable type be also posted */
   )
{
   assert(scip != NULL);
   assert(var != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPwriteVarName", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   /* print variable name */
   if( SCIPvarIsNegated(var) )
   {
      SCIP_VAR* negatedvar;

      SCIP_CALL( SCIPgetNegatedVar(scip, var, &negatedvar) );
      SCIPinfoMessage(scip, file, "<~%s>", SCIPvarGetName(negatedvar));
   }
   else
   {
      SCIPinfoMessage(scip, file, "<%s>", SCIPvarGetName(var));
   }

   if( type )
   {
      /* print variable type */
      SCIPinfoMessage(scip, file, "[%c]",
         SCIPvarGetType(var) == SCIP_VARTYPE_BINARY ? SCIP_VARTYPE_BINARY_CHAR :
         SCIPvarGetType(var) == SCIP_VARTYPE_INTEGER ? SCIP_VARTYPE_INTEGER_CHAR :
         SCIPvarGetType(var) == SCIP_VARTYPE_IMPLINT ? SCIP_VARTYPE_IMPLINT_CHAR : SCIP_VARTYPE_CONTINUOUS_CHAR);
   }

   return SCIP_OKAY;
}

/** print the given list of variables to output stream separated by the given delimiter character;
 *
 *  i. e. the variables x1, x2, ..., xn with given delimiter ',' are written as: <x1>, <x2>, ..., <xn>;
 *
 *  the method SCIPparseVarsList() can parse such a string
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 *
 *  @note The printing process is done via the message handler system.
 */
SCIP_RETCODE SCIPwriteVarsList(
   SCIP*                 scip,               /**< SCIP data structure */
   FILE*                 file,               /**< output file, or NULL for stdout */
   SCIP_VAR**            vars,               /**< variable array to output */
   int                   nvars,              /**< number of variables */
   SCIP_Bool             type,               /**< should the variable type be also posted */
   char                  delimiter           /**< character which is used for delimitation */
   )
{
   int v;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPwriteVarsList", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   for( v = 0; v < nvars; ++v )
   {
      if( v > 0 )
      {
         SCIPinfoMessage(scip, file, "%c", delimiter);
      }

      /* print variable name */
      SCIP_CALL( SCIPwriteVarName(scip, file, vars[v], type) );
   }

   return SCIP_OKAY;
}

/** print the given variables and coefficients as linear sum in the following form
 *  c1 <x1> + c2 <x2>   ... + cn <xn>
 *
 *  This string can be parsed by the method SCIPparseVarsLinearsum().
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 *
 *  @note The printing process is done via the message handler system.
 */
SCIP_RETCODE SCIPwriteVarsLinearsum(
   SCIP*                 scip,               /**< SCIP data structure */
   FILE*                 file,               /**< output file, or NULL for stdout */
   SCIP_VAR**            vars,               /**< variable array to output */
   SCIP_Real*            vals,               /**< array of coefficients or NULL if all coefficients are 1.0 */
   int                   nvars,              /**< number of variables */
   SCIP_Bool             type                /**< should the variable type be also posted */
   )
{
   int v;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPwriteVarsLinearsum", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   for( v = 0; v < nvars; ++v )
   {
      if( vals != NULL )
      {
         if( vals[v] == 1.0 )
         {
            if( v > 0 )
               SCIPinfoMessage(scip, file, " +");
         }
         else if( vals[v] == -1.0 )
            SCIPinfoMessage(scip, file, " -");
         else
            SCIPinfoMessage(scip, file, " %+.15g", vals[v]);
      }
      else if( nvars > 0 )
         SCIPinfoMessage(scip, file, " +");

      /* print variable name */
      SCIP_CALL( SCIPwriteVarName(scip, file, vars[v], type) );
   }

   return SCIP_OKAY;
}

/** print the given terms as signomial in the following form
 *  c1 <x11>^e11 <x12>^e12 ... <x1n>^e1n + c2 <x21>^e21 <x22>^e22 ... + ... + cn <xn1>^en1 ...
 *
 *  This string can be parsed by the method SCIPparseVarsPolynomial().
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 *
 *  @note The printing process is done via the message handler system.
 */
SCIP_RETCODE SCIPwriteVarsPolynomial(
   SCIP*                 scip,               /**< SCIP data structure */
   FILE*                 file,               /**< output file, or NULL for stdout */
   SCIP_VAR***           monomialvars,       /**< arrays with variables for each monomial */
   SCIP_Real**           monomialexps,       /**< arrays with variable exponents, or NULL if always 1.0 */
   SCIP_Real*            monomialcoefs,      /**< array with monomial coefficients */
   int*                  monomialnvars,      /**< array with number of variables for each monomial */
   int                   nmonomials,         /**< number of monomials */
   SCIP_Bool             type                /**< should the variable type be also posted */
   )
{
   int i;
   int v;

   assert(scip != NULL);
   assert(monomialvars  != NULL || nmonomials == 0);
   assert(monomialcoefs != NULL || nmonomials == 0);
   assert(monomialnvars != NULL || nmonomials == 0);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPwriteVarsPolynomial", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   if( nmonomials == 0 )
   {
      SCIPinfoMessage(scip, file, " 0 ");
      return SCIP_OKAY;
   }

   for( i = 0; i < nmonomials; ++i )
   {
      if( monomialcoefs[i] == 1.0 ) /*lint !e613*/
      {
         if( i > 0 )
            SCIPinfoMessage(scip, file, " +");
      }
      else if( monomialcoefs[i] == -1.0 ) /*lint !e613*/
         SCIPinfoMessage(scip, file, " -");
      else
         SCIPinfoMessage(scip, file, " %+.15g", monomialcoefs[i]); /*lint !e613*/

      assert(monomialvars[i] != NULL || monomialnvars[i] == 0); /*lint !e613*/

      for( v = 0; v < monomialnvars[i]; ++v ) /*lint !e613*/
      {
         SCIP_CALL( SCIPwriteVarName(scip, file, monomialvars[i][v], type) ); /*lint !e613*/
         if( monomialexps != NULL && monomialexps[i] != NULL && monomialexps[i][v] != 1.0 )
         {
            SCIPinfoMessage(scip, file, "^%.15g", monomialexps[i][v]);
         }
      }
   }

   return SCIP_OKAY;
}

/** parses variable information (in cip format) out of a string; if the parsing process was successful a variable is
 *  created and captured; if variable is of integral type, fractional bounds are automatically rounded; an integer
 *  variable with bounds zero and one is automatically converted into a binary variable
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPparseVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            var,                /**< pointer to store the problem variable */
   const char*           str,                /**< string to parse */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable */
   SCIP_VARDATA*         vardata,            /**< user data for this specific variable */
   char**                endptr,             /**< pointer to store the final string position if successful */
   SCIP_Bool*            success             /**< pointer store if the paring process was successful */
   )
{
   assert(var != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPparseVar", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      SCIP_CALL( SCIPvarParseOriginal(var, scip->mem->probmem, scip->set, scip->messagehdlr, scip->stat,
            str, initial, removable, varcopy, vardelorig, vartrans, vardeltrans, vardata, endptr, success) );
      break;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_INITPRESOLVE:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_PRESOLVED:
   case SCIP_STAGE_SOLVING:
      SCIP_CALL( SCIPvarParseTransformed(var, scip->mem->probmem, scip->set, scip->messagehdlr, scip->stat,
            str, initial, removable, varcopy, vardelorig, vartrans, vardeltrans, vardata, endptr, success) );
      break;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/

   return SCIP_OKAY;
}

/** parses the given string for a variable name and stores the variable in the corresponding pointer if such a variable
 *  exits and returns the position where the parsing stopped
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPparseVarName(
   SCIP*                 scip,               /**< SCIP data structure */
   const char*           str,                /**< string to parse */
   SCIP_VAR**            var,                /**< pointer to store the problem variable, or NULL if it does not exit */
   char**                endptr              /**< pointer to store the final string position if successful */
   )
{
   char varname[SCIP_MAXSTRLEN];

   assert(str != NULL);
   assert(var != NULL);
   assert(endptr != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPparseVarName", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIPstrCopySection(str, '<', '>', varname, SCIP_MAXSTRLEN, endptr);
   assert(*endptr != NULL);

   if( *varname == '\0' )
   {
      SCIPerrorMessage("invalid variable name string given: could not find '<'\n");
      return SCIP_INVALIDDATA;
   }

   /* check if we have a negated variable */
   if( *varname == '~' )
   {
      SCIPdebugMsg(scip, "parsed negated variable name <%s>\n", &varname[1]);

      /* search for the variable and ignore '~' */
      (*var) = SCIPfindVar(scip, &varname[1]);

      if( *var  != NULL )
      {
         SCIP_CALL( SCIPgetNegatedVar(scip, *var, var) );
      }
   }
   else
   {
      SCIPdebugMsg(scip, "parsed variable name <%s>\n", varname);

      /* search for the variable */
      (*var) = SCIPfindVar(scip, varname);
   }

   str = *endptr;

   /* skip additional variable type marker */
   if( *str == '[' && (str[1] == SCIP_VARTYPE_BINARY_CHAR || str[1] == SCIP_VARTYPE_INTEGER_CHAR ||
       str[1] == SCIP_VARTYPE_IMPLINT_CHAR || str[1] == SCIP_VARTYPE_CONTINUOUS_CHAR )  && str[2] == ']' )
      (*endptr) += 3;

   return SCIP_OKAY;
}

/** parse the given string as variable list (here ',' is the delimiter)) (<x1>, <x2>, ..., <xn>) (see
 *  SCIPwriteVarsList() ); if it was successful, the pointer success is set to TRUE
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note The pointer success in only set to FALSE in the case that a variable with a parsed variable name does not exist.
 *
 *  @note If the number of (parsed) variables is greater than the available slots in the variable array, nothing happens
 *        except that the required size is stored in the corresponding integer; the reason for this approach is that we
 *        cannot reallocate memory, since we do not know how the memory has been allocated (e.g., by a C++ 'new' or SCIP
 *        memory functions).
 */
SCIP_RETCODE SCIPparseVarsList(
   SCIP*                 scip,               /**< SCIP data structure */
   const char*           str,                /**< string to parse */
   SCIP_VAR**            vars,               /**< array to store the parsed variable */
   int*                  nvars,              /**< pointer to store number of parsed variables */
   int                   varssize,           /**< size of the variable array */
   int*                  requiredsize,       /**< pointer to store the required array size for the active variables */
   char**                endptr,             /**< pointer to store the final string position if successful */
   char                  delimiter,          /**< character which is used for delimitation */
   SCIP_Bool*            success             /**< pointer to store the whether the parsing was successful or not */
   )
{
   SCIP_VAR** tmpvars;
   SCIP_VAR* var;
   int ntmpvars = 0;
   int v;

   assert( nvars != NULL );
   assert( requiredsize != NULL );
   assert( endptr != NULL );
   assert( success != NULL );

   SCIP_CALL( SCIPcheckStage(scip, "SCIPparseVarsList", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   /* allocate buffer memory for temporary storing the parsed variables */
   SCIP_CALL( SCIPallocBufferArray(scip, &tmpvars, varssize) );

   (*success) = TRUE;

   do
   {
      *endptr = (char*)str;

      /* parse variable name */
      SCIP_CALL( SCIPparseVarName(scip, str, &var, endptr) );

      if( var == NULL )
      {
         SCIPdebugMsg(scip, "variable with name <%s> does not exist\n", SCIPvarGetName(var));
         (*success) = FALSE;
         break;
      }

      /* store the variable in the tmp array */
      if( ntmpvars < varssize )
         tmpvars[ntmpvars] = var;

      ntmpvars++;

      str = *endptr;

      while( isspace((unsigned char)*str) )
         str++;
   }
   while( *str == delimiter );

   *endptr = (char*)str;

   /* if all variable name searches were successful and the variable array has enough slots, copy the collected variables */
   if( (*success) && ntmpvars <= varssize )
   {
      for( v = 0; v < ntmpvars; ++v )
         vars[v] = tmpvars[v];

      (*nvars) = ntmpvars;
   }
   else
      (*nvars) = 0;

   (*requiredsize) = ntmpvars;

   /* free buffer arrays */
   SCIPfreeBufferArray(scip, &tmpvars);

   return SCIP_OKAY;
}

/** parse the given string as linear sum of variables and coefficients (c1 <x1> + c2 <x2> + ... + cn <xn>)
 *  (see SCIPwriteVarsLinearsum() ); if it was successful, the pointer success is set to TRUE
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note The pointer success in only set to FALSE in the case that a variable with a parsed variable name does not exist.
 *
 *  @note If the number of (parsed) variables is greater than the available slots in the variable array, nothing happens
 *        except that the required size is stored in the corresponding integer; the reason for this approach is that we
 *        cannot reallocate memory, since we do not know how the memory has been allocated (e.g., by a C++ 'new' or SCIP
 *        memory functions).
 */
SCIP_RETCODE SCIPparseVarsLinearsum(
   SCIP*                 scip,               /**< SCIP data structure */
   const char*           str,                /**< string to parse */
   SCIP_VAR**            vars,               /**< array to store the parsed variables */
   SCIP_Real*            vals,               /**< array to store the parsed coefficients */
   int*                  nvars,              /**< pointer to store number of parsed variables */
   int                   varssize,           /**< size of the variable array */
   int*                  requiredsize,       /**< pointer to store the required array size for the active variables */
   char**                endptr,             /**< pointer to store the final string position if successful */
   SCIP_Bool*            success             /**< pointer to store the whether the parsing was successful or not */
   )
{
   SCIP_VAR*** monomialvars;
   SCIP_Real** monomialexps;
   SCIP_Real*  monomialcoefs;
   int*        monomialnvars;
   int         nmonomials;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPparseVarsLinearsum", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   assert(scip != NULL);
   assert(str != NULL);
   assert(vars != NULL || varssize == 0);
   assert(vals != NULL || varssize == 0);
   assert(nvars != NULL);
   assert(requiredsize != NULL);
   assert(endptr != NULL);
   assert(success != NULL);

   *requiredsize = 0;

   SCIP_CALL( SCIPparseVarsPolynomial(scip, str, &monomialvars, &monomialexps, &monomialcoefs, &monomialnvars, &nmonomials, endptr, success) );

   if( !*success )
   {
      assert(nmonomials == 0); /* SCIPparseVarsPolynomial should have freed all buffers, so no need to call free here */
      return SCIP_OKAY;
   }

   /* check if linear sum is just "0" */
   if( nmonomials == 1 && monomialnvars[0] == 0 && monomialcoefs[0] == 0.0 )
   {
      *nvars = 0;
      *requiredsize = 0;

      SCIPfreeParseVarsPolynomialData(scip, &monomialvars, &monomialexps, &monomialcoefs, &monomialnvars, nmonomials);

      return SCIP_OKAY;
   }

   *nvars = nmonomials;
   *requiredsize = nmonomials;

   /* if we have enough slots in the variables array, copy variables over */
   if( varssize >= nmonomials )
   {
      int v;

      for( v = 0; v < nmonomials; ++v )
      {
         if( monomialnvars[v] == 0 )
         {
            SCIPerrorMessage("constant in linear sum\n");
            *success = FALSE;
            break;
         }
         if( monomialnvars[v] > 1 || monomialexps[v][0] != 1.0 )
         {
            SCIPerrorMessage("nonlinear monomial in linear sum\n");
            *success = FALSE;
            break;
         }
         assert(monomialnvars[v]   == 1);
         assert(monomialvars[v][0] != NULL);
         assert(monomialexps[v][0] == 1.0);

         vars[v] = monomialvars[v][0]; /*lint !e613*/
         vals[v] = monomialcoefs[v]; /*lint !e613*/
      }
   }

   SCIPfreeParseVarsPolynomialData(scip, &monomialvars, &monomialexps, &monomialcoefs, &monomialnvars, nmonomials);

   return SCIP_OKAY;
}

/** parse the given string as signomial of variables and coefficients
 *  (c1 <x11>^e11 <x12>^e12 ... <x1n>^e1n + c2 <x21>^e21 <x22>^e22 ... + ... + cn <xn1>^en1 ...)
 *  (see SCIPwriteVarsPolynomial()); if it was successful, the pointer success is set to TRUE
 *
 *  The user has to call SCIPfreeParseVarsPolynomialData(scip, monomialvars, monomialexps,
 *  monomialcoefs, monomialnvars, *nmonomials) short after SCIPparseVarsPolynomial to free all the
 *  allocated memory again.
 *
 *  Parsing is stopped at the end of string (indicated by the \\0-character) or when no more monomials
 *  are recognized.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPparseVarsPolynomial(
   SCIP*                 scip,               /**< SCIP data structure */
   const char*           str,                /**< string to parse */
   SCIP_VAR****          monomialvars,       /**< pointer to store arrays with variables for each monomial */
   SCIP_Real***          monomialexps,       /**< pointer to store arrays with variable exponents */
   SCIP_Real**           monomialcoefs,      /**< pointer to store array with monomial coefficients */
   int**                 monomialnvars,      /**< pointer to store array with number of variables for each monomial */
   int*                  nmonomials,         /**< pointer to store number of parsed monomials */
   char**                endptr,             /**< pointer to store the final string position if successful */
   SCIP_Bool*            success             /**< pointer to store the whether the parsing was successful or not */
   )
{
   typedef enum
   {
      SCIPPARSEPOLYNOMIAL_STATE_BEGIN,       /* we are at the beginning of a monomial */
      SCIPPARSEPOLYNOMIAL_STATE_INTERMED,    /* we are in between the factors of a monomial */
      SCIPPARSEPOLYNOMIAL_STATE_COEF,        /* we parse the coefficient of a monomial */
      SCIPPARSEPOLYNOMIAL_STATE_VARS,        /* we parse monomial variables */
      SCIPPARSEPOLYNOMIAL_STATE_EXPONENT,    /* we parse the exponent of a variable */
      SCIPPARSEPOLYNOMIAL_STATE_END,         /* we are at the end the polynomial */
      SCIPPARSEPOLYNOMIAL_STATE_ERROR        /* a parsing error occured */
   } SCIPPARSEPOLYNOMIAL_STATES;

   SCIPPARSEPOLYNOMIAL_STATES state;
   int monomialssize;

   /* data of currently parsed monomial */
   int varssize;
   int nvars;
   SCIP_VAR** vars;
   SCIP_Real* exponents;
   SCIP_Real coef;

   assert(scip != NULL);
   assert(str != NULL);
   assert(monomialvars != NULL);
   assert(monomialexps != NULL);
   assert(monomialnvars != NULL);
   assert(monomialcoefs != NULL);
   assert(nmonomials != NULL);
   assert(endptr != NULL);
   assert(success != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPparseVarsPolynomial", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   *success = FALSE;
   *nmonomials = 0;
   monomialssize = 0;
   *monomialvars = NULL;
   *monomialexps = NULL;
   *monomialcoefs = NULL;
   *monomialnvars = NULL;

   /* initialize state machine */
   state = SCIPPARSEPOLYNOMIAL_STATE_BEGIN;
   varssize = 0;
   nvars = 0;
   vars = NULL;
   exponents = NULL;
   coef = SCIP_INVALID;

   SCIPdebugMsg(scip, "parsing polynomial from '%s'\n", str);

   while( *str && state != SCIPPARSEPOLYNOMIAL_STATE_END && state != SCIPPARSEPOLYNOMIAL_STATE_ERROR )
   {
      /* skip white space */
      while( isspace((unsigned char)*str) )
         str++;

      assert(state != SCIPPARSEPOLYNOMIAL_STATE_END);

      switch( state )
      {
      case SCIPPARSEPOLYNOMIAL_STATE_BEGIN:
      {
         if( coef != SCIP_INVALID  ) /*lint !e777*/
         {
            SCIPdebugMsg(scip, "push monomial with coefficient <%g> and <%d> vars\n", coef, nvars);

            /* push previous monomial */
            if( monomialssize <= *nmonomials )
            {
               monomialssize = SCIPcalcMemGrowSize(scip, *nmonomials+1);

               SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialvars,  *nmonomials, monomialssize) );
               SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialexps,  *nmonomials, monomialssize) );
               SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialnvars, *nmonomials, monomialssize) );
               SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialcoefs, *nmonomials, monomialssize) );
            }

            if( nvars > 0 )
            {
               SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*monomialvars)[*nmonomials], vars, nvars) ); /*lint !e866*/
               SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*monomialexps)[*nmonomials], exponents, nvars) ); /*lint !e866*/
            }
            else
            {
               (*monomialvars)[*nmonomials] = NULL;
               (*monomialexps)[*nmonomials] = NULL;
            }
            (*monomialcoefs)[*nmonomials] = coef;
            (*monomialnvars)[*nmonomials] = nvars;
            ++*nmonomials;

            nvars = 0;
            coef = SCIP_INVALID;
         }

         if( *str == '<' )
         {
            /* there seem to come a variable at the beginning of a monomial
             * so assume the coefficient is 1.0
             */
            state = SCIPPARSEPOLYNOMIAL_STATE_VARS;
            coef = 1.0;
         }
         else if( *str == '-' || *str == '+' || isdigit(*str) )
            state = SCIPPARSEPOLYNOMIAL_STATE_COEF;
         else
            state = SCIPPARSEPOLYNOMIAL_STATE_END;

         break;
      }

      case SCIPPARSEPOLYNOMIAL_STATE_INTERMED:
      {
         if( *str == '<' )
         {
            /* there seem to come another variable */
            state = SCIPPARSEPOLYNOMIAL_STATE_VARS;
         }
         else if( *str == '-' || *str == '+' || isdigit(*str) )
         {
            /* there seem to come a coefficient, which means the next monomial */
            state = SCIPPARSEPOLYNOMIAL_STATE_BEGIN;
         }
         else /* since we cannot detect the symbols we stop parsing the polynomial */
            state = SCIPPARSEPOLYNOMIAL_STATE_END;

         break;
      }

      case SCIPPARSEPOLYNOMIAL_STATE_COEF:
      {
         if( *str == '+' && !isdigit(str[1]) )
         {
            /* only a plus sign, without number */
            coef =  1.0;
            ++str;
         }
         else if( *str == '-' && !isdigit(str[1]) )
         {
            /* only a minus sign, without number */
            coef = -1.0;
            ++str;
         }
         else if( SCIPstrToRealValue(str, &coef, endptr) )
         {
            str = *endptr;
         }
         else
         {
            SCIPerrorMessage("could not parse number in the beginning of '%s'\n", str);
            state = SCIPPARSEPOLYNOMIAL_STATE_ERROR;
            break;
         }

         /* after the coefficient we go into the intermediate state, i.e., expecting next variables */
         state = SCIPPARSEPOLYNOMIAL_STATE_INTERMED;  /*lint !e838*/

         break;
      }

      case SCIPPARSEPOLYNOMIAL_STATE_VARS:
      {
         SCIP_VAR* var;

         assert(*str == '<');

         /* parse variable name */
         SCIP_CALL( SCIPparseVarName(scip, str, &var, endptr) );

         /* check if variable name was parsed */
         if( *endptr == str )
         {
            state = SCIPPARSEPOLYNOMIAL_STATE_END;
            break;
         }

         if( var == NULL )
         {
            SCIPerrorMessage("did not find variable in the beginning of %s\n", str);
            state = SCIPPARSEPOLYNOMIAL_STATE_ERROR;
            break;
         }

         /* add variable to vars array */
         if( nvars + 1 > varssize )
         {
            varssize = SCIPcalcMemGrowSize(scip, nvars+1);
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &vars,      nvars, varssize) );
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &exponents, nvars, varssize) );
         }
         assert(vars != NULL);
         assert(exponents != NULL);

         vars[nvars] = var;
         exponents[nvars] = 1.0;
         ++nvars;

         str = *endptr;

         if( *str == '^' )
            state = SCIPPARSEPOLYNOMIAL_STATE_EXPONENT;
         else
            state = SCIPPARSEPOLYNOMIAL_STATE_INTERMED;

         break;
      }

      case SCIPPARSEPOLYNOMIAL_STATE_EXPONENT:
      {
         assert(*str == '^');
         assert(nvars > 0); /* we should be in a monomial that has already a variable */
         assert(exponents != NULL);
         ++str;

         if( !SCIPstrToRealValue(str, &exponents[nvars-1], endptr) )
         {
            SCIPerrorMessage("could not parse number in the beginning of '%s'\n", str);
            state = SCIPPARSEPOLYNOMIAL_STATE_ERROR;
            break;
         }
         str = *endptr;

         /* after the exponent we go into the intermediate state, i.e., expecting next variables */
         state = SCIPPARSEPOLYNOMIAL_STATE_INTERMED;  /*lint !e838*/
         break;
      }

      case SCIPPARSEPOLYNOMIAL_STATE_END:
      case SCIPPARSEPOLYNOMIAL_STATE_ERROR:
      default:
         SCIPerrorMessage("unexpected state\n");
         return SCIP_READERROR;
      }
   }

   /* set end pointer */
   *endptr = (char*)str;

   /* check state at end of string */
   switch( state )
   {
   case SCIPPARSEPOLYNOMIAL_STATE_BEGIN:
   case SCIPPARSEPOLYNOMIAL_STATE_END:
   case SCIPPARSEPOLYNOMIAL_STATE_INTERMED:
   {
      if( coef != SCIP_INVALID ) /*lint !e777*/
      {
         /* push last monomial */
         SCIPdebugMsg(scip, "push monomial with coefficient <%g> and <%d> vars\n", coef, nvars);
         if( monomialssize <= *nmonomials )
         {
            monomialssize = *nmonomials+1;
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialvars,  *nmonomials, monomialssize) );
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialexps,  *nmonomials, monomialssize) );
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialnvars, *nmonomials, monomialssize) );
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialcoefs, *nmonomials, monomialssize) );
         }

         if( nvars > 0 )
         {
            /* shrink vars and exponents array to needed size and take over ownership */
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &vars, varssize, nvars) );
            SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &exponents, varssize, nvars) );
            (*monomialvars)[*nmonomials] = vars;
            (*monomialexps)[*nmonomials] = exponents;
            vars = NULL;
            exponents = NULL;
         }
         else
         {
            (*monomialvars)[*nmonomials] = NULL;
            (*monomialexps)[*nmonomials] = NULL;
         }
         (*monomialcoefs)[*nmonomials] = coef;
         (*monomialnvars)[*nmonomials] = nvars;
         ++*nmonomials;
      }

      *success = TRUE;
      break;
   }

   case SCIPPARSEPOLYNOMIAL_STATE_COEF:
   case SCIPPARSEPOLYNOMIAL_STATE_VARS:
   case SCIPPARSEPOLYNOMIAL_STATE_EXPONENT:
   {
      SCIPerrorMessage("unexpected parsing state at end of polynomial string\n");
   }
   /*lint -fallthrough*/
   case SCIPPARSEPOLYNOMIAL_STATE_ERROR:
      assert(!*success);
      break;
   }

   /* free memory to store current monomial, if still existing */
   SCIPfreeBlockMemoryArrayNull(scip, &vars, varssize);
   SCIPfreeBlockMemoryArrayNull(scip, &exponents, varssize);

   if( *success && *nmonomials > 0 )
   {
      /* shrink arrays to required size, so we do not need to keep monomialssize around */
      assert(*nmonomials <= monomialssize);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialvars,  monomialssize, *nmonomials) );
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialexps,  monomialssize, *nmonomials) );
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialnvars, monomialssize, *nmonomials) );
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, monomialcoefs, monomialssize, *nmonomials) );

      /* SCIPwriteVarsPolynomial(scip, NULL, *monomialvars, *monomialexps, *monomialcoefs, *monomialnvars, *nmonomials, FALSE); */
   }
   else
   {
      /* in case of error, cleanup all data here */
      SCIPfreeParseVarsPolynomialData(scip, monomialvars, monomialexps, monomialcoefs, monomialnvars, *nmonomials);
      *nmonomials = 0;
   }

   return SCIP_OKAY;
}

/** frees memory allocated when parsing a signomial from a string
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
void SCIPfreeParseVarsPolynomialData(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR****          monomialvars,       /**< pointer to store arrays with variables for each monomial */
   SCIP_Real***          monomialexps,       /**< pointer to store arrays with variable exponents */
   SCIP_Real**           monomialcoefs,      /**< pointer to store array with monomial coefficients */
   int**                 monomialnvars,      /**< pointer to store array with number of variables for each monomial */
   int                   nmonomials          /**< pointer to store number of parsed monomials */
   )
{
   int i;

   assert(scip != NULL);
   assert(monomialvars  != NULL);
   assert(monomialexps  != NULL);
   assert(monomialcoefs != NULL);
   assert(monomialnvars != NULL);
   assert((*monomialvars  != NULL) == (nmonomials > 0));
   assert((*monomialexps  != NULL) == (nmonomials > 0));
   assert((*monomialcoefs != NULL) == (nmonomials > 0));
   assert((*monomialnvars != NULL) == (nmonomials > 0));

   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPfreeParseVarsPolynomialData", FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( nmonomials == 0 )
      return;

   for( i = nmonomials - 1; i >= 0; --i )
   {
      SCIPfreeBlockMemoryArrayNull(scip, &(*monomialexps)[i], (*monomialnvars)[i]);
      SCIPfreeBlockMemoryArrayNull(scip, &(*monomialvars)[i], (*monomialnvars)[i]);
   }

   SCIPfreeBlockMemoryArray(scip, monomialcoefs, nmonomials);
   SCIPfreeBlockMemoryArray(scip, monomialnvars, nmonomials);
   SCIPfreeBlockMemoryArray(scip, monomialexps, nmonomials);
   SCIPfreeBlockMemoryArray(scip, monomialvars, nmonomials);
}

/** increases usage counter of variable
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 */
SCIP_RETCODE SCIPcaptureVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to capture */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPcaptureVar", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE) );
   assert(var->scip == scip);

   SCIPvarCapture(var);

   return SCIP_OKAY;
}

/** decreases usage counter of variable, if the usage pointer reaches zero the variable gets freed
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 *
 *  @note the pointer of the variable will be NULLed
 */
SCIP_RETCODE SCIPreleaseVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            var                 /**< pointer to variable */
   )
{
   assert(var != NULL);
   assert(*var != NULL);
   assert((*var)->scip == scip);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPreleaseVar", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      SCIP_CALL( SCIPvarRelease(var, scip->mem->probmem, scip->set, scip->eventqueue, scip->lp) );
      return SCIP_OKAY;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_TRANSFORMED:
   case SCIP_STAGE_INITPRESOLVE:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_PRESOLVED:
   case SCIP_STAGE_INITSOLVE:
   case SCIP_STAGE_SOLVING:
   case SCIP_STAGE_SOLVED:
   case SCIP_STAGE_EXITSOLVE:
   case SCIP_STAGE_FREETRANS:
      if( !SCIPvarIsTransformed(*var) && (*var)->nuses == 1 && (*var)->data.original.transvar != NULL )
      {
         SCIPerrorMessage("cannot release last use of original variable while associated transformed variable exists\n");
         return SCIP_INVALIDCALL;
      }
      SCIP_CALL( SCIPvarRelease(var, scip->mem->probmem, scip->set, scip->eventqueue, scip->lp) );
      return SCIP_OKAY;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/
}

/** changes the name of a variable
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can only be called if @p scip is in stage \ref SCIP_STAGE_PROBLEM
 *
 *  @note to get the current name of a variable, use SCIPvarGetName() from pub_var.h
 */
SCIP_RETCODE SCIPchgVarName(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable */
   const char*           name                /**< new name of constraint */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarName", FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE) );
   assert( var->scip == scip );

   if( SCIPgetStage(scip) != SCIP_STAGE_PROBLEM )
   {
      SCIPerrorMessage("variable names can only be changed in problem creation stage\n");
      SCIPABORT();
      return SCIP_INVALIDCALL; /*lint !e527*/
   }

   /* remove variable's name from the namespace if the variable was already added */
   if( SCIPvarGetProbindex(var) != -1 )
   {
      SCIP_CALL( SCIPprobRemoveVarName(scip->origprob, var) );
   }

   /* change variable name */
   SCIP_CALL( SCIPvarChgName(var, SCIPblkmem(scip), name) );

   /* add variable's name to the namespace if the variable was already added */
   if( SCIPvarGetProbindex(var) != -1 )
   {
      SCIP_CALL( SCIPprobAddVarName(scip->origprob, var) );
   }

   return SCIP_OKAY;
}

/** gets and captures transformed variable of a given variable; if the variable is not yet transformed,
 *  a new transformed variable for this variable is created
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPtransformVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get/create transformed variable for */
   SCIP_VAR**            transvar            /**< pointer to store the transformed variable */
   )
{
   assert(transvar != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPtransformVar", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( SCIPvarIsTransformed(var) )
   {
      *transvar = var;
      SCIPvarCapture(*transvar);
   }
   else
   {
      SCIP_CALL( SCIPvarTransform(var, scip->mem->probmem, scip->set, scip->stat, scip->origprob->objsense, transvar) );
   }

   return SCIP_OKAY;
}

/** gets and captures transformed variables for an array of variables;
 *  if a variable of the array is not yet transformed, a new transformed variable for this variable is created;
 *  it is possible to call this method with vars == transvars
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPtransformVars(
   SCIP*                 scip,               /**< SCIP data structure */
   int                   nvars,              /**< number of variables to get/create transformed variables for */
   SCIP_VAR**            vars,               /**< array with variables to get/create transformed variables for */
   SCIP_VAR**            transvars           /**< array to store the transformed variables */
   )
{
   int v;

   assert(nvars == 0 || vars != NULL);
   assert(nvars == 0 || transvars != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPtransformVars", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   for( v = 0; v < nvars; ++v )
   {
      if( SCIPvarIsTransformed(vars[v]) )
      {
         transvars[v] = vars[v];
         SCIPvarCapture(transvars[v]);
      }
      else
      {
         SCIP_CALL( SCIPvarTransform(vars[v], scip->mem->probmem, scip->set, scip->stat, scip->origprob->objsense,
               &transvars[v]) );
      }
   }

   return SCIP_OKAY;
}

/** gets corresponding transformed variable of a given variable;
 *  returns NULL as transvar, if transformed variable is not yet existing
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPgetTransformedVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get transformed variable for */
   SCIP_VAR**            transvar            /**< pointer to store the transformed variable */
   )
{
   assert(transvar != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetTransformedVar", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   if( SCIPvarIsTransformed(var) )
      *transvar = var;
   else
   {
      SCIP_CALL( SCIPvarGetTransformed(var, scip->mem->probmem, scip->set, scip->stat, transvar) );
   }

   return SCIP_OKAY;
}

/** gets corresponding transformed variables for an array of variables;
 *  stores NULL in a transvars slot, if the transformed variable is not yet existing;
 *  it is possible to call this method with vars == transvars, but remember that variables that are not
 *  yet transformed will be replaced with NULL
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPgetTransformedVars(
   SCIP*                 scip,               /**< SCIP data structure */
   int                   nvars,              /**< number of variables to get transformed variables for */
   SCIP_VAR**            vars,               /**< array with variables to get transformed variables for */
   SCIP_VAR**            transvars           /**< array to store the transformed variables */
   )
{
   int v;

   assert(nvars == 0 || vars != NULL);
   assert(nvars == 0 || transvars != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetTransformedVars", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   for( v = 0; v < nvars; ++v )
   {
      if( SCIPvarIsTransformed(vars[v]) )
         transvars[v] = vars[v];
      else
      {
         SCIP_CALL( SCIPvarGetTransformed(vars[v], scip->mem->probmem, scip->set, scip->stat, &transvars[v]) );
      }
   }

   return SCIP_OKAY;
}

/** gets negated variable x' = lb + ub - x of variable x; negated variable is created, if not yet existing;
 *  in difference to \ref SCIPcreateVar, the negated variable must not be released (unless captured explicitly)
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPgetNegatedVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get negated variable for */
   SCIP_VAR**            negvar              /**< pointer to store the negated variable */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetNegatedVar", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );
   assert( var->scip == scip );

   SCIP_CALL( SCIPvarNegate(var, scip->mem->probmem, scip->set, scip->stat, negvar) );

   return SCIP_OKAY;
}

/** gets negated variables x' = lb + ub - x of variables x; negated variables are created, if not yet existing
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPgetNegatedVars(
   SCIP*                 scip,               /**< SCIP data structure */
   int                   nvars,              /**< number of variables to get negated variables for */
   SCIP_VAR**            vars,               /**< array of variables to get negated variables for */
   SCIP_VAR**            negvars             /**< array to store the negated variables */
   )
{
   int v;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetNegatedVars", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   for( v = 0; v < nvars; ++v )
   {
      SCIP_CALL( SCIPvarNegate(vars[v], scip->mem->probmem, scip->set, scip->stat, &(negvars[v])) );
   }

   return SCIP_OKAY;
}

/** gets a binary variable that is equal to the given binary variable, and that is either active, fixed, or
 *  multi-aggregated, or the negated variable of an active, fixed, or multi-aggregated variable
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 */
SCIP_RETCODE SCIPgetBinvarRepresentative(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< binary variable to get binary representative for */
   SCIP_VAR**            repvar,             /**< pointer to store the binary representative */
   SCIP_Bool*            negated             /**< pointer to store whether the negation of an active variable was returned */
   )
{
   assert(scip != NULL);
   assert(var != NULL);
   assert(repvar != NULL);
   assert(negated != NULL);
   assert(var->scip == scip);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetBinvarRepresentative", FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE) );

   /* get the active representative of the given variable */
   *repvar = var;
   *negated = FALSE;
   SCIP_CALL( SCIPvarGetProbvarBinary(repvar, negated) );

   /* negate the representative, if it corresponds to the negation of the given variable */
   if( *negated )
   {
      SCIP_CALL( SCIPgetNegatedVar(scip, *repvar, repvar) );
   }

   return SCIP_OKAY;
}

/** gets binary variables that are equal to the given binary variables, and which are either active, fixed, or
 *  multi-aggregated, or the negated variables of active, fixed, or multi-aggregated variables
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 */
SCIP_RETCODE SCIPgetBinvarRepresentatives(
   SCIP*                 scip,               /**< SCIP data structure */
   int                   nvars,              /**< number of binary variables to get representatives for */
   SCIP_VAR**            vars,               /**< binary variables to get binary representatives for */
   SCIP_VAR**            repvars,            /**< array to store the binary representatives */
   SCIP_Bool*            negated             /**< array to store whether the negation of an active variable was returned */
   )
{
   int v;

   assert(scip != NULL);
   assert(vars != NULL || nvars == 0);
   assert(repvars != NULL || nvars == 0);
   assert(negated != NULL || nvars == 0);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetBinvarRepresentatives", FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE) );

   if( nvars == 0 )
      return SCIP_OKAY;

   /* get the active representative of the given variable */
   BMScopyMemoryArray(repvars, vars, nvars);
   BMSclearMemoryArray(negated, nvars);
   SCIP_CALL( SCIPvarsGetProbvarBinary(&repvars, &negated, nvars) );

   /* negate the representatives, if they correspond to the negation of the given variables */
   for( v = nvars - 1; v >= 0; --v )
      if( negated[v] )
      {
         SCIP_CALL( SCIPgetNegatedVar(scip, repvars[v], &(repvars[v])) );
      }

   return SCIP_OKAY;
}

/** flattens aggregation graph of multi-aggregated variable in order to avoid exponential recursion later on
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 */
SCIP_RETCODE SCIPflattenVarAggregationGraph(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< problem variable */
   )
{
   assert( scip != NULL );
   assert( var != NULL );
   SCIP_CALL( SCIPcheckStage(scip, "SCIPflattenVarAggregationGraph", FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE) );

   SCIP_CALL( SCIPvarFlattenAggregationGraph(var, scip->mem->probmem, scip->set, scip->eventqueue) );

   return SCIP_OKAY;
}

/** Transforms a given linear sum of variables, that is a_1*x_1 + ... + a_n*x_n + c into a corresponding linear sum of
 *  active variables, that is b_1*y_1 + ... + b_m*y_m + d.
 *
 *  If the number of needed active variables is greater than the available slots in the variable array, nothing happens
 *  except that the required size is stored in the corresponding variable (requiredsize). Otherwise, the active variable
 *  representation is stored in the variable array, scalar array and constant.
 *
 *  The reason for this approach is that we cannot reallocate memory, since we do not know how the memory has been
 *  allocated (e.g., by a C++ 'new' or SCIP functions).
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 *
 *  @note The resulting linear sum is stored into the given variable array, scalar array, and constant. That means the
 *        given entries are overwritten.
 *
 *  @note That method can be used to convert a single variables into variable space of active variables. Therefore call
 *        the method with the linear sum 1.0*x + 0.0.
 */
SCIP_RETCODE SCIPgetProbvarLinearSum(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            vars,               /**< variable array x_1, ..., x_n in the linear sum which will be
                                              *   overwritten by the variable array y_1, ..., y_m in the linear sum
                                              *   w.r.t. active variables */
   SCIP_Real*            scalars,            /**< scalars a_1, ..., a_n in linear sum which will be overwritten to the
                                              *   scalars b_1, ..., b_m in the linear sum of the active variables  */
   int*                  nvars,              /**< pointer to number of variables in the linear sum which will be
                                              *   overwritten by the number of variables in the linear sum corresponding
                                              *   to the active variables */
   int                   varssize,           /**< available slots in vars and scalars array which is needed to check if
                                              *   the array are large enough for the linear sum w.r.t. active
                                              *   variables */
   SCIP_Real*            constant,           /**< pointer to constant c in linear sum a_1*x_1 + ... + a_n*x_n + c which
                                              *   will chnage to constant d in the linear sum b_1*y_1 + ... + b_m*y_m +
                                              *   d w.r.t. the active variables */
   int*                  requiredsize,       /**< pointer to store the required array size for the linear sum w.r.t. the
                                              *   active variables */
   SCIP_Bool             mergemultiples      /**< should multiple occurrences of a var be replaced by a single coeff? */
   )
{
   assert( scip != NULL );
   assert( nvars != NULL );
   assert( vars != NULL || *nvars == 0 );
   assert( scalars != NULL || *nvars == 0 );
   assert( constant != NULL );
   assert( requiredsize != NULL );
   assert( *nvars <= varssize );

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetProbvarLinearSum", FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );
   SCIP_CALL( SCIPvarGetActiveRepresentatives(scip->set, vars, scalars, nvars, varssize, constant, requiredsize, mergemultiples) );

   return SCIP_OKAY;
}

/** transforms given variable, scalar and constant to the corresponding active, fixed, or
 *  multi-aggregated variable, scalar and constant; if the variable resolves to a fixed variable,
 *  "scalar" will be 0.0 and the value of the sum will be stored in "constant"; a multi-aggregation
 *  with only one active variable (this can happen due to fixings after the multi-aggregation),
 *  is treated like an aggregation; if the multi-aggregation constant is infinite, "scalar" will be 0.0
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPgetProbvarSum(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            var,                /**< pointer to problem variable x in sum a*x + c */
   SCIP_Real*            scalar,             /**< pointer to scalar a in sum a*x + c */
   SCIP_Real*            constant            /**< pointer to constant c in sum a*x + c */
   )
{
   assert(scip != NULL);
   assert(var != NULL);
   assert(scalar != NULL);
   assert(constant != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetProbvarSum", FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );
   SCIP_CALL( SCIPvarGetProbvarSum(var, scip->set, scalar, constant) );

   return SCIP_OKAY;
}

/** return for given variables all their active counterparts; all active variables will be pairwise different
 *  @note It does not hold that the first output variable is the active variable for the first input variable.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPgetActiveVars(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            vars,               /**< variable array with given variables and as output all active
                                              *   variables, if enough slots exist
                                              */
   int*                  nvars,              /**< number of given variables, and as output number of active variables,
                                              *   if enough slots exist
                                              */
   int                   varssize,           /**< available slots in vars array */
   int*                  requiredsize        /**< pointer to store the required array size for the active variables */
   )
{
   assert(scip != NULL);
   assert(nvars != NULL);
   assert(vars != NULL || *nvars == 0);
   assert(varssize >= *nvars);
   assert(requiredsize != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetActiveVars", FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );
   SCIP_CALL( SCIPvarsGetActiveVars(scip->set, vars, nvars, varssize, requiredsize) );

   return SCIP_OKAY;
}

/** returns the reduced costs of the variable in the current node's LP relaxation;
 *  the current node has to have a feasible LP.
 *
 *  returns SCIP_INVALID if the variable is active but not in the current LP;
 *  returns 0 if the variable has been aggregated out or fixed in presolving.
 *
 *  @pre This method can only be called if @p scip is in stage \ref SCIP_STAGE_SOLVING
 *
 *  @note The return value of this method should be used carefully if the dual feasibility check was explictely disabled.
 */
SCIP_Real SCIPgetVarRedcost(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get reduced costs, should be a column in current node LP */
   )
{
   assert( scip != NULL );
   assert( var != NULL );
   assert( var->scip == scip );

   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      if( var->data.original.transvar == NULL )
         return SCIP_INVALID;
      return SCIPgetVarRedcost(scip, var->data.original.transvar);

   case SCIP_VARSTATUS_COLUMN:
      return SCIPgetColRedcost(scip, SCIPvarGetCol(var));

   case SCIP_VARSTATUS_LOOSE:
      return SCIP_INVALID;

   case SCIP_VARSTATUS_FIXED:
   case SCIP_VARSTATUS_AGGREGATED:
   case SCIP_VARSTATUS_MULTAGGR:
   case SCIP_VARSTATUS_NEGATED:
      return 0.0;

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return 0.0; /*lint !e527*/
   }
}

/** returns the implied reduced costs of the variable in the current node's LP relaxation;
 *  the current node has to have a feasible LP.
 *
 *  returns SCIP_INVALID if the variable is active but not in the current LP;
 *  returns 0 if the variable has been aggregated out or fixed in presolving.
 *
 *  @pre This method can only be called if @p scip is in stage \ref SCIP_STAGE_SOLVING
 *
 *  @note The return value of this method should be used carefully if the dual feasibility check was explictely disabled.
 */
SCIP_Real SCIPgetVarImplRedcost(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get reduced costs, should be a column in current node LP */
   SCIP_Bool             varfixing           /**< FALSE if for x == 0, TRUE for x == 1 */
   )
{
   assert( scip != NULL );
   assert( var != NULL );
   assert( var->scip == scip );

   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      if( var->data.original.transvar == NULL )
         return SCIP_INVALID;
      return SCIPgetVarImplRedcost(scip, var->data.original.transvar, varfixing);

   case SCIP_VARSTATUS_COLUMN:
      return SCIPvarGetImplRedcost(var, scip->set, varfixing, scip->stat, scip->transprob, scip->lp);

   case SCIP_VARSTATUS_LOOSE:
      return SCIP_INVALID;

   case SCIP_VARSTATUS_FIXED:
   case SCIP_VARSTATUS_AGGREGATED:
   case SCIP_VARSTATUS_MULTAGGR:
   case SCIP_VARSTATUS_NEGATED:
      return 0.0;

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return 0.0; /*lint !e527*/
   }
}


/** returns the Farkas coefficient of the variable in the current node's LP relaxation;
 *  the current node has to have an infeasible LP.
 *
 *  returns SCIP_INVALID if the variable is active but not in the current LP;
 *  returns 0 if the variable has been aggregated out or fixed in presolving.
 *
 *  @pre This method can only be called if @p scip is in stage \ref SCIP_STAGE_SOLVING
 */
SCIP_Real SCIPgetVarFarkasCoef(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get reduced costs, should be a column in current node LP */
   )
{
   assert(scip != NULL);
   assert(var != NULL);
   assert(var->scip == scip);

   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      if( var->data.original.transvar == NULL )
         return SCIP_INVALID;
      return SCIPgetVarFarkasCoef(scip,var->data.original.transvar);

   case SCIP_VARSTATUS_COLUMN:
      return SCIPgetColFarkasCoef(scip,SCIPvarGetCol(var));

   case SCIP_VARSTATUS_LOOSE:
      return SCIP_INVALID;

   case SCIP_VARSTATUS_FIXED:
   case SCIP_VARSTATUS_AGGREGATED:
   case SCIP_VARSTATUS_MULTAGGR:
   case SCIP_VARSTATUS_NEGATED:
      return 0.0;

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return 0.0; /*lint !e527*/
   }
}

/** returns lower bound of variable directly before or after the bound change given by the bound change index
 *  was applied
 */
SCIP_Real SCIPgetVarLbAtIndex(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_BDCHGIDX*        bdchgidx,           /**< bound change index representing time on path to current node */
   SCIP_Bool             after               /**< should the bound change with given index be included? */
   )
{
   SCIP_VARSTATUS varstatus;
   SCIP_BDCHGINFO* bdchginfo;
   assert(var != NULL);

   varstatus = SCIPvarGetStatus(var);

   /* get bounds of attached variables */
   switch( varstatus )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      assert(var->data.original.transvar != NULL);
      return SCIPgetVarLbAtIndex(scip, var->data.original.transvar, bdchgidx, after);

   case SCIP_VARSTATUS_COLUMN:
   case SCIP_VARSTATUS_LOOSE:
      if( bdchgidx == NULL )
         return SCIPvarGetLbLocal(var);
      else
      {
         bdchginfo = SCIPvarGetLbchgInfo(var, bdchgidx, after);
         if( bdchginfo != NULL )
            return SCIPbdchginfoGetNewbound(bdchginfo);
         else
            return var->glbdom.lb;
      }

   case SCIP_VARSTATUS_FIXED:
      return var->glbdom.lb;

   case SCIP_VARSTATUS_AGGREGATED: /* x = a*y + c  ->  y = (x-c)/a */
      assert(var->data.aggregate.var != NULL);
      if( var->data.aggregate.scalar > 0.0 )
      {
         SCIP_Real lb;

         lb = SCIPgetVarLbAtIndex(scip, var->data.aggregate.var, bdchgidx, after);

         /* a > 0 -> get lower bound of y */
         if( SCIPisInfinity(scip, -lb) )
            return -SCIPinfinity(scip);
         else if( SCIPisInfinity(scip, lb) )
            return SCIPinfinity(scip);
         else
            return var->data.aggregate.scalar * lb + var->data.aggregate.constant;
      }
      else if( var->data.aggregate.scalar < 0.0 )
      {
         SCIP_Real ub;

         ub = SCIPgetVarUbAtIndex(scip, var->data.aggregate.var, bdchgidx, after);

         /* a < 0 -> get upper bound of y */
         if( SCIPisInfinity(scip, -ub) )
            return SCIPinfinity(scip);
         else if( SCIPisInfinity(scip, ub) )
            return -SCIPinfinity(scip);
         else
            return var->data.aggregate.scalar * ub + var->data.aggregate.constant;
      }
      else
      {
         SCIPerrorMessage("scalar is zero in aggregation\n");
         SCIPABORT();
         return SCIP_INVALID; /*lint !e527*/
      }

   case SCIP_VARSTATUS_MULTAGGR:
      /* handle multi-aggregated variables depending on one variable only (possibly caused by SCIPvarFlattenAggregationGraph()) */
      if ( var->data.multaggr.nvars == 1 )
      {
         assert(var->data.multaggr.vars != NULL);
         assert(var->data.multaggr.scalars != NULL);
         assert(var->data.multaggr.vars[0] != NULL);

         if( var->data.multaggr.scalars[0] > 0.0 )
         {
            SCIP_Real lb;

            lb = SCIPgetVarLbAtIndex(scip, var->data.multaggr.vars[0], bdchgidx, after);

            /* a > 0 -> get lower bound of y */
            if( SCIPisInfinity(scip, -lb) )
               return -SCIPinfinity(scip);
            else if( SCIPisInfinity(scip, lb) )
               return SCIPinfinity(scip);
            else
               return var->data.multaggr.scalars[0] * lb + var->data.multaggr.constant;
         }
         else if( var->data.multaggr.scalars[0] < 0.0 )
         {
            SCIP_Real ub;

            ub = SCIPgetVarUbAtIndex(scip, var->data.multaggr.vars[0], bdchgidx, after);

            /* a < 0 -> get upper bound of y */
            if( SCIPisInfinity(scip, -ub) )
               return SCIPinfinity(scip);
            else if( SCIPisInfinity(scip, ub) )
               return -SCIPinfinity(scip);
            else
               return var->data.multaggr.scalars[0] * ub + var->data.multaggr.constant;
         }
         else
         {
            SCIPerrorMessage("scalar is zero in multi-aggregation\n");
            SCIPABORT();
            return SCIP_INVALID; /*lint !e527*/
         }
      }
      SCIPerrorMessage("cannot get the bounds of a multi-aggregated variable.\n");
      SCIPABORT();
      return SCIP_INVALID; /*lint !e527*/

   case SCIP_VARSTATUS_NEGATED: /* x' = offset - x  ->  x = offset - x' */
      assert(var->negatedvar != NULL);
      assert(SCIPvarGetStatus(var->negatedvar) != SCIP_VARSTATUS_NEGATED);
      assert(var->negatedvar->negatedvar == var);
      return var->data.negate.constant - SCIPgetVarUbAtIndex(scip, var->negatedvar, bdchgidx, after);

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return SCIP_INVALID; /*lint !e527*/
   }
}

/** returns upper bound of variable directly before or after the bound change given by the bound change index
 *  was applied
 */
SCIP_Real SCIPgetVarUbAtIndex(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_BDCHGIDX*        bdchgidx,           /**< bound change index representing time on path to current node */
   SCIP_Bool             after               /**< should the bound change with given index be included? */
   )
{
   SCIP_VARSTATUS varstatus;
   SCIP_BDCHGINFO* bdchginfo;
   assert(var != NULL);

   varstatus = SCIPvarGetStatus(var);

   /* get bounds of attached variables */
   switch( varstatus )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      assert(var->data.original.transvar != NULL);
      return SCIPgetVarUbAtIndex(scip, var->data.original.transvar, bdchgidx, after);

   case SCIP_VARSTATUS_COLUMN:
   case SCIP_VARSTATUS_LOOSE:
      if( bdchgidx == NULL )
         return SCIPvarGetUbLocal(var);
      else
      {
         bdchginfo = SCIPvarGetUbchgInfo(var, bdchgidx, after);
         if( bdchginfo != NULL )
            return SCIPbdchginfoGetNewbound(bdchginfo);
         else
            return var->glbdom.ub;
      }

   case SCIP_VARSTATUS_FIXED:
      return var->glbdom.ub;

   case SCIP_VARSTATUS_AGGREGATED: /* x = a*y + c  ->  y = (x-c)/a */
      assert(var->data.aggregate.var != NULL);
      if( var->data.aggregate.scalar > 0.0 )
      {
         SCIP_Real ub;

         ub = SCIPgetVarUbAtIndex(scip, var->data.aggregate.var, bdchgidx, after);

         /* a > 0 -> get lower bound of y */
         if( SCIPisInfinity(scip, -ub) )
            return -SCIPinfinity(scip);
         else if( SCIPisInfinity(scip, ub) )
            return SCIPinfinity(scip);
         else
            return var->data.aggregate.scalar * ub + var->data.aggregate.constant;
      }
      else if( var->data.aggregate.scalar < 0.0 )
      {
         SCIP_Real lb;

         lb = SCIPgetVarLbAtIndex(scip, var->data.aggregate.var, bdchgidx, after);

         /* a < 0 -> get upper bound of y */
         if ( SCIPisInfinity(scip, -lb) )
            return SCIPinfinity(scip);
         else if ( SCIPisInfinity(scip, lb) )
            return -SCIPinfinity(scip);
         else
            return var->data.aggregate.scalar * lb + var->data.aggregate.constant;
      }
      else
      {
         SCIPerrorMessage("scalar is zero in aggregation\n");
         SCIPABORT();
         return SCIP_INVALID; /*lint !e527*/
      }

   case SCIP_VARSTATUS_MULTAGGR:
      /* handle multi-aggregated variables depending on one variable only (possibly caused by SCIPvarFlattenAggregationGraph()) */
      if ( var->data.multaggr.nvars == 1 )
      {
         assert(var->data.multaggr.vars != NULL);
         assert(var->data.multaggr.scalars != NULL);
         assert(var->data.multaggr.vars[0] != NULL);

         if( var->data.multaggr.scalars[0] > 0.0 )
         {
            SCIP_Real ub;

            ub = SCIPgetVarUbAtIndex(scip, var->data.multaggr.vars[0], bdchgidx, after);

            /* a > 0 -> get lower bound of y */
            if ( SCIPisInfinity(scip, -ub) )
               return -SCIPinfinity(scip);
            else if ( SCIPisInfinity(scip, ub) )
               return SCIPinfinity(scip);
            else
               return var->data.multaggr.scalars[0] * ub + var->data.multaggr.constant;
         }
         else if( var->data.multaggr.scalars[0] < 0.0 )
         {
            SCIP_Real lb;

            lb = SCIPgetVarLbAtIndex(scip, var->data.multaggr.vars[0], bdchgidx, after);

            /* a < 0 -> get upper bound of y */
            if ( SCIPisInfinity(scip, -lb) )
               return SCIPinfinity(scip);
            else if ( SCIPisInfinity(scip, lb) )
               return -SCIPinfinity(scip);
            else
               return var->data.multaggr.scalars[0] * lb + var->data.multaggr.constant;
         }
         else
         {
            SCIPerrorMessage("scalar is zero in multi-aggregation\n");
            SCIPABORT();
            return SCIP_INVALID; /*lint !e527*/
         }
      }
      SCIPerrorMessage("cannot get the bounds of a multiple aggregated variable.\n");
      SCIPABORT();
      return SCIP_INVALID; /*lint !e527*/

   case SCIP_VARSTATUS_NEGATED: /* x' = offset - x  ->  x = offset - x' */
      assert(var->negatedvar != NULL);
      assert(SCIPvarGetStatus(var->negatedvar) != SCIP_VARSTATUS_NEGATED);
      assert(var->negatedvar->negatedvar == var);
      return var->data.negate.constant - SCIPgetVarLbAtIndex(scip, var->negatedvar, bdchgidx, after);

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return SCIP_INVALID; /*lint !e527*/
   }
}

/** returns lower or upper bound of variable directly before or after the bound change given by the bound change index
 *  was applied
 */
SCIP_Real SCIPgetVarBdAtIndex(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_BOUNDTYPE        boundtype,          /**< type of bound: lower or upper bound */
   SCIP_BDCHGIDX*        bdchgidx,           /**< bound change index representing time on path to current node */
   SCIP_Bool             after               /**< should the bound change with given index be included? */
   )
{
   if( boundtype == SCIP_BOUNDTYPE_LOWER )
      return SCIPgetVarLbAtIndex(scip, var, bdchgidx, after);
   else
   {
      assert(boundtype == SCIP_BOUNDTYPE_UPPER);
      return SCIPgetVarUbAtIndex(scip, var, bdchgidx, after);
   }
}

/** returns whether the binary variable was fixed at the time given by the bound change index */
SCIP_Bool SCIPgetVarWasFixedAtIndex(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_BDCHGIDX*        bdchgidx,           /**< bound change index representing time on path to current node */
   SCIP_Bool             after               /**< should the bound change with given index be included? */
   )
{
   assert(var != NULL);
   assert(SCIPvarIsBinary(var));

   /* check the current bounds first in order to decide at which bound change information we have to look
    * (which is expensive because we have to follow the aggregation tree to the active variable)
    */
   return ((SCIPvarGetLbLocal(var) > 0.5 && SCIPgetVarLbAtIndex(scip, var, bdchgidx, after) > 0.5)
      || (SCIPvarGetUbLocal(var) < 0.5 && SCIPgetVarUbAtIndex(scip, var, bdchgidx, after) < 0.5));
}

/** gets solution value for variable in current node
 *
 *  @return solution value for variable in current node
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_Real SCIPgetVarSol(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get solution value for */
   )
{
   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPgetVarSol", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );
   assert( var->scip == scip );

   return SCIPvarGetSol(var, SCIPtreeHasCurrentNodeLP(scip->tree));
}

/** gets solution values of multiple variables in current node
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPgetVarSols(
   SCIP*                 scip,               /**< SCIP data structure */
   int                   nvars,              /**< number of variables to get solution value for */
   SCIP_VAR**            vars,               /**< array with variables to get value for */
   SCIP_Real*            vals                /**< array to store solution values of variables */
   )
{
   int v;

   assert(nvars == 0 || vars != NULL);
   assert(nvars == 0 || vals != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarSols", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( SCIPtreeHasCurrentNodeLP(scip->tree) )
   {
      for( v = 0; v < nvars; ++v )
         vals[v] = SCIPvarGetLPSol(vars[v]);
   }
   else
   {
      for( v = 0; v < nvars; ++v )
         vals[v] = SCIPvarGetPseudoSol(vars[v]);
   }

   return SCIP_OKAY;
}

/** sets the solution value of all variables in the global relaxation solution to zero
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPclearRelaxSolVals(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_RELAX*           relax               /**< relaxator data structure */
   )
{
   SCIP_VAR** vars;
   int nvars;
   int v;

   assert(scip != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPclearRelaxSolVals", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   /* update the responsible relax pointer */
   SCIPrelaxationSetSolRelax(scip->relaxation, relax);

   /* the relaxation solution is already cleared */
   if( SCIPrelaxationIsSolZero(scip->relaxation) )
      return SCIP_OKAY;

   SCIP_CALL( SCIPgetVarsData(scip, &vars, &nvars, NULL, NULL, NULL, NULL) );

   for( v = 0; v < nvars; v++ )
   {
      SCIP_CALL( SCIPvarSetRelaxSol(vars[v], scip->set, scip->relaxation, 0.0, FALSE) );
   }

   SCIPrelaxationSetSolObj(scip->relaxation, 0.0);
   SCIPrelaxationSetSolZero(scip->relaxation, TRUE);

   return SCIP_OKAY;
}

/** sets the value of the given variable in the global relaxation solution;
 *  this solution can be filled by the relaxation handlers  and can be used by heuristics and for separation;
 *  You can use SCIPclearRelaxSolVals() to set all values to zero, initially;
 *  after setting all solution values, you have to call SCIPmarkRelaxSolValid()
 *  to inform SCIP that the stored solution is valid
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note This method incrementally updates the objective value of the relaxation solution. If the whole solution
 *        should be updated, using SCIPsetRelaxSolVals() instead or calling SCIPclearRelaxSolVals() before setting
 *        the first value to reset the solution and the objective value to 0 may help the numerics.
 */
SCIP_RETCODE SCIPsetRelaxSolVal(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_RELAX*           relax,              /**< relaxator data structure */
   SCIP_VAR*             var,                /**< variable to set value for */
   SCIP_Real             val                 /**< solution value of variable */
   )
{
   assert(scip != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPsetRelaxSolVal", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIP_CALL( SCIPvarSetRelaxSol(var, scip->set, scip->relaxation, val, TRUE) );

   if( val != 0.0 )
      SCIPrelaxationSetSolZero(scip->relaxation, FALSE);
   SCIPrelaxationSetSolValid(scip->relaxation, FALSE, FALSE);
   SCIPrelaxationSetSolRelax(scip->relaxation, relax);

   return SCIP_OKAY;
}

/** sets the values of the given variables in the global relaxation solution and informs SCIP about the validity
 *  and whether the solution can be enforced via linear cuts;
 *  this solution can be filled by the relaxation handlers  and can be used by heuristics and for separation;
 *  the solution is automatically cleared, s.t. all other variables get value 0.0
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPsetRelaxSolVals(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_RELAX*           relax,              /**< relaxator data structure */
   int                   nvars,              /**< number of variables to set relaxation solution value for */
   SCIP_VAR**            vars,               /**< array with variables to set value for */
   SCIP_Real*            vals,               /**< array with solution values of variables */
   SCIP_Bool             includeslp          /**< does the relaxator contain all cuts in the LP? */
   )
{
   int v;

   assert(scip != NULL);
   assert(nvars == 0 || vars != NULL);
   assert(nvars == 0 || vals != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPsetRelaxSolVals", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIP_CALL( SCIPclearRelaxSolVals(scip, relax) );

   for( v = 0; v < nvars; v++ )
   {
      SCIP_CALL( SCIPvarSetRelaxSol(vars[v], scip->set, scip->relaxation, vals[v], TRUE) );
   }

   SCIPrelaxationSetSolZero(scip->relaxation, FALSE);
   SCIPrelaxationSetSolValid(scip->relaxation, TRUE, includeslp);
   SCIPrelaxationSetSolRelax(scip->relaxation, relax);

   return SCIP_OKAY;
}

/** sets the values of the variables in the global relaxation solution to the values in the given primal solution
 *  and informs SCIP about the validity and whether the solution can be enforced via linear cuts;
 *  the relaxation solution can be filled by the relaxation handlers and might be used by heuristics and for separation
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPsetRelaxSolValsSol(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_RELAX*           relax,              /**< relaxator data structure */
   SCIP_SOL*             sol,                /**< primal relaxation solution */
   SCIP_Bool             includeslp          /**< does the relaxator contain all cuts in the LP? */
   )
{
   SCIP_VAR** vars;
   SCIP_Real* vals;
   int nvars;
   int v;

   assert(scip != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPsetRelaxSolValsSol", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIP_CALL( SCIPgetVarsData(scip, &vars, &nvars, NULL, NULL, NULL, NULL) );

   /* alloc buffer array for solution values of the variables and get the values */
   SCIP_CALL( SCIPallocBufferArray(scip, &vals, nvars) );
   SCIP_CALL( SCIPgetSolVals(scip, sol, nvars, vars, vals) );

   SCIP_CALL( SCIPclearRelaxSolVals(scip, relax) );

   for( v = 0; v < nvars; v++ )
   {
      SCIP_CALL( SCIPvarSetRelaxSol(vars[v], scip->set, scip->relaxation, vals[v], FALSE) );
   }

   SCIPrelaxationSetSolObj(scip->relaxation, SCIPsolGetObj(sol, scip->set, scip->transprob, scip->origprob));

   SCIPrelaxationSetSolZero(scip->relaxation, FALSE);
   SCIPrelaxationSetSolValid(scip->relaxation, TRUE, includeslp);
   SCIPrelaxationSetSolRelax(scip->relaxation, relax);

   SCIPfreeBufferArray(scip, &vals);

   return SCIP_OKAY;
}

/** returns whether the relaxation solution is valid
 *
 *  @return TRUE, if the relaxation solution is valid; FALSE, otherwise
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_Bool SCIPisRelaxSolValid(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   assert(scip != NULL);

   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPisRelaxSolValid", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   return SCIPrelaxationIsSolValid(scip->relaxation);
}

/** informs SCIP that the relaxation solution is valid and whether the relaxation can be enforced through linear cuts
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPmarkRelaxSolValid(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_RELAX*           relax,              /**< relaxator data structure that set the current relaxation solution */
   SCIP_Bool             includeslp          /**< does the relaxator contain all cuts in the LP? */
   )
{
   assert(scip != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPmarkRelaxSolValid", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIPrelaxationSetSolValid(scip->relaxation, TRUE, includeslp);
   SCIPrelaxationSetSolRelax(scip->relaxation, relax);

   return SCIP_OKAY;
}

/** informs SCIP, that the relaxation solution is invalid
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPmarkRelaxSolInvalid(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   assert(scip != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPmarkRelaxSolInvalid", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIPrelaxationSetSolValid(scip->relaxation, FALSE, FALSE);

   return SCIP_OKAY;
}

/** gets the relaxation solution value of the given variable
 *
 *  @return the relaxation solution value of the given variable
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_Real SCIPgetRelaxSolVal(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get value for */
   )
{
   assert(scip != NULL);
   assert(var != NULL);
   assert(var->scip == scip);

   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPgetRelaxSolVal", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( !SCIPrelaxationIsSolValid(scip->relaxation) )
   {
      SCIPerrorMessage("Relaxation Solution is not valid!\n");
      SCIPABORT();
      return SCIP_INVALID; /*lint !e527*/
   }

   return SCIPvarGetRelaxSol(var, scip->set);
}

/** gets the relaxation solution objective value
 *
 *  @return the objective value of the relaxation solution
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_Real SCIPgetRelaxSolObj(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   assert(scip != NULL);

   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPgetRelaxSolObj", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( !SCIPrelaxationIsSolValid(scip->relaxation) )
   {
      SCIPerrorMessage("Relaxation Solution is not valid!\n");
      SCIPABORT();
      return SCIP_INVALID; /*lint !e527*/
   }

   return SCIPrelaxationGetSolObj(scip->relaxation);
}

/** determine which branching direction should be evaluated first by strong branching
 *
 *  @return TRUE iff strong branching should first evaluate the down child
 *
 */
SCIP_Bool SCIPisStrongbranchDownFirst(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to determine the branching direction on */
   )
{
   switch( scip->set->branch_firstsbchild )
   {
      case 'u':
         return FALSE;
      case 'd':
         return TRUE;
      case 'a':
         return (SCIPvarGetNLocksDown(var) > SCIPvarGetNLocksUp(var));
      default:
         assert(scip->set->branch_firstsbchild == 'h');
         return (SCIPgetVarAvgCutoffs(scip, var, SCIP_BRANCHDIR_DOWNWARDS) > SCIPgetVarAvgCutoffs(scip, var, SCIP_BRANCHDIR_UPWARDS));
   }
}

/** start strong branching - call before any strong branching
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note if propagation is enabled, strong branching is not done directly on the LP, but probing nodes are created
 *        which allow to perform propagation but also creates some overhead
 */
SCIP_RETCODE SCIPstartStrongbranch(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Bool             enablepropagation   /**< should propagation be done before solving the strong branching LP? */
   )
{
   assert( scip != NULL );
   SCIP_CALL( SCIPcheckStage(scip, "SCIPstartStrongbranch", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   assert(!SCIPinProbing(scip));

   SCIPdebugMsg(scip, "starting strong branching mode%s: lpcount=%" SCIP_LONGINT_FORMAT "\n", enablepropagation ? " with propagation" : "", scip->stat->lpcount - scip->stat->nsbdivinglps);

   /* start probing mode to allow propagation before solving the strong branching LPs; if no propagation should be done,
    * start the strong branching mode in the LP interface
    */
   if( enablepropagation )
   {
      if( SCIPtreeProbing(scip->tree) )
      {
         SCIPerrorMessage("cannot start strong branching with propagation while in probing mode\n");
         return SCIP_INVALIDCALL;
      }

      if( scip->lp != NULL && SCIPlpDiving(scip->lp) )
      {
         SCIPerrorMessage("cannot start strong branching with propagation while in diving mode\n");
         return SCIP_INVALIDCALL;
      }

      /* other then in SCIPstartProbing(), we do not disable collecting variable statistics during strong branching;
       * we cannot disable it, because the pseudo costs would not be updated, otherwise,
       * and reliability branching would end up doing strong branching all the time
       */
      SCIP_CALL( SCIPtreeStartProbing(scip->tree, scip->mem->probmem, scip->set, scip->lp, scip->relaxation, scip->transprob, TRUE) );

      /* inform the LP that the current probing mode is used for strong branching */
      SCIPlpStartStrongbranchProbing(scip->lp);
   }
   else
   {
      SCIP_CALL( SCIPlpStartStrongbranch(scip->lp) );
   }

   /* reset local strong branching info */
   scip->stat->lastsblpsolstats[0] = scip->stat->lastsblpsolstats[1] = SCIP_LPSOLSTAT_NOTSOLVED;

   return SCIP_OKAY;
}

/** end strong branching - call after any strong branching
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPendStrongbranch(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   assert( scip != NULL );

   SCIP_CALL( SCIPcheckStage(scip, "SCIPendStrongbranch", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   /* depending on whether the strong branching mode was started with propagation enabled or not, we end the strong
    * branching probing mode or the LP strong branching mode
    */
   if( SCIPtreeProbing(scip->tree) )
   {
      SCIP_NODE* node;
      SCIP_DOMCHG* domchg;
      SCIP_VAR** boundchgvars;
      SCIP_Real* bounds;
      SCIP_BOUNDTYPE* boundtypes;
      int nboundchgs;
      int nbnds;
      int i;

      /* collect all bound changes deducted during probing, which were applied at the probing root and apply them to the
       * focusnode
       */
      node = SCIPgetCurrentNode(scip);
      assert(SCIPnodeGetType(node) == SCIP_NODETYPE_PROBINGNODE);
      assert(SCIPgetProbingDepth(scip) == 0);

      domchg = SCIPnodeGetDomchg(node);
      nboundchgs = SCIPdomchgGetNBoundchgs(domchg);

      SCIP_CALL( SCIPallocBufferArray(scip, &boundchgvars, nboundchgs) );
      SCIP_CALL( SCIPallocBufferArray(scip, &bounds, nboundchgs) );
      SCIP_CALL( SCIPallocBufferArray(scip, &boundtypes, nboundchgs) );

      for( i = 0, nbnds = 0; i < nboundchgs; ++i )
      {
         SCIP_BOUNDCHG* boundchg;

         boundchg = SCIPdomchgGetBoundchg(domchg, i);

         /* ignore redundant bound changes */
         if( SCIPboundchgIsRedundant(boundchg) )
            continue;

         boundchgvars[nbnds] = SCIPboundchgGetVar(boundchg);
         bounds[nbnds] = SCIPboundchgGetNewbound(boundchg);
         boundtypes[nbnds] = SCIPboundchgGetBoundtype(boundchg);
         ++nbnds;
      }

      SCIPdebugMsg(scip, "ending strong branching with probing: %d bound changes collected\n", nbnds);

      /* inform the LP that the probing mode is not used for strong branching anymore */
      SCIPlpEndStrongbranchProbing(scip->lp);

      /* switch back from probing to normal operation mode and restore variables and constraints to focus node */
      SCIP_CALL( SCIPtreeEndProbing(scip->tree, scip->reopt, scip->mem->probmem, scip->set, scip->messagehdlr, scip->stat,
         scip->transprob, scip->origprob, scip->lp, scip->relaxation, scip->primal,
         scip->branchcand, scip->eventqueue, scip->eventfilter, scip->cliquetable) );

      /* apply the collected bound changes */
      for( i = 0; i < nbnds; ++i )
      {
         if( boundtypes[i] == SCIP_BOUNDTYPE_LOWER )
         {
            SCIPdebugMsg(scip, "apply probing lower bound change <%s> >= %.9g\n", SCIPvarGetName(boundchgvars[i]), bounds[i]);
            SCIP_CALL( SCIPchgVarLb(scip, boundchgvars[i], bounds[i]) );
         }
         else
         {
            SCIPdebugMsg(scip, "apply probing upper bound change <%s> <= %.9g\n", SCIPvarGetName(boundchgvars[i]), bounds[i]);
            SCIP_CALL( SCIPchgVarUb(scip, boundchgvars[i], bounds[i]) );
         }
      }

      SCIPfreeBufferArray(scip, &boundtypes);
      SCIPfreeBufferArray(scip, &bounds);
      SCIPfreeBufferArray(scip, &boundchgvars);
   }
   else
   {
      SCIPdebugMsg(scip, "ending strong branching\n");

      SCIP_CALL( SCIPlpEndStrongbranch(scip->lp) );
   }

   return SCIP_OKAY;
}

/** analyze the strong branching for the given variable; that includes conflict analysis for infeasible branches and
 *  storing of root reduced cost information
 */
static
SCIP_RETCODE analyzeStrongbranch(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to analyze */
   SCIP_Bool*            downinf,            /**< pointer to store whether the downwards branch is infeasible, or NULL */
   SCIP_Bool*            upinf,              /**< pointer to store whether the upwards branch is infeasible, or NULL */
   SCIP_Bool*            downconflict,       /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible downwards branch, or NULL */
   SCIP_Bool*            upconflict          /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible upwards branch, or NULL */
   )
{
   SCIP_COL* col;
   SCIP_Bool downcutoff;
   SCIP_Bool upcutoff;

   col = SCIPvarGetCol(var);
   assert(col != NULL);

   downcutoff = col->sbdownvalid && SCIPsetIsGE(scip->set, col->sbdown, scip->lp->cutoffbound);
   upcutoff = col->sbupvalid && SCIPsetIsGE(scip->set, col->sbup, scip->lp->cutoffbound);

   if( downinf != NULL )
      *downinf = downcutoff;
   if( upinf != NULL )
      *upinf = upcutoff;

   /* analyze infeasible strong branching sub problems:
    * because the strong branching's bound change is necessary for infeasibility, it cannot be undone;
    * therefore, infeasible strong branchings on non-binary variables will not produce a valid conflict constraint
    */
   if( scip->set->conf_enable && scip->set->conf_usesb && scip->set->nconflicthdlrs > 0
      && SCIPvarIsBinary(var) && SCIPtreeGetCurrentDepth(scip->tree) > 0 )
   {
      if( (downcutoff && SCIPsetFeasCeil(scip->set, col->primsol-1.0) >= col->lb - 0.5)
         || (upcutoff && SCIPsetFeasFloor(scip->set, col->primsol+1.0) <= col->ub + 0.5) )
      {
         assert(downconflict != NULL);
         assert(upconflict   != NULL);
         SCIP_CALL( SCIPconflictAnalyzeStrongbranch(scip->conflict, scip->conflictstore, scip->mem->probmem, scip->set, scip->stat,
               scip->transprob, scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue, scip->cliquetable, col, downconflict, upconflict) );
      }
   }

   /* the strong branching results can be used to strengthen the root reduced cost information which is used for example
    * to propagate against the cutoff bound
    *
    * @note Ignore the results if the LP solution of the down (up) branch LP is smaller which should not happened by
    *       theory but can arise due to numerical issues.
    */
   if( SCIPtreeGetCurrentDepth(scip->tree) == 0 && SCIPvarIsBinary(var) && SCIPlpIsDualReliable(scip->lp) )
   {
      SCIP_Real lpobjval;

      assert(SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_OPTIMAL);

      lpobjval =  SCIPlpGetObjval(scip->lp, scip->set, scip->transprob);

      if( col->sbdownvalid && SCIPsetFeasCeil(scip->set, col->primsol-1.0) >= col->lb - 0.5 && lpobjval < col->sbdown )
         SCIPvarUpdateBestRootSol(var, scip->set, SCIPvarGetUbGlobal(var), -(col->sbdown - lpobjval), lpobjval);
      if( col->sbupvalid && SCIPsetFeasFloor(scip->set, col->primsol+1.0) <= col->ub + 0.5 && lpobjval < col->sbup )
         SCIPvarUpdateBestRootSol(var, scip->set, SCIPvarGetLbGlobal(var), col->sbup - lpobjval,  lpobjval);
   }

   return SCIP_OKAY;
}

/** gets strong branching information on column variable with fractional value
 *
 *  Before calling this method, the strong branching mode must have been activated by calling SCIPstartStrongbranch();
 *  after strong branching was done for all candidate variables, the strong branching mode must be ended by
 *  SCIPendStrongbranch(). Since this method does not apply domain propagation before strongbranching,
 *  propagation should not be enabled in the SCIPstartStrongbranch() call.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPgetVarStrongbranchFrac(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get strong branching values for */
   int                   itlim,              /**< iteration limit for strong branchings */
   SCIP_Bool             idempotent,         /**< should scip's state remain the same after the call (statistics, column states...), or should it be updated ? */
   SCIP_Real*            down,               /**< stores dual bound after branching column down */
   SCIP_Real*            up,                 /**< stores dual bound after branching column up */
   SCIP_Bool*            downvalid,          /**< stores whether the returned down value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Bool*            upvalid,            /**< stores whether the returned up value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Bool*            downinf,            /**< pointer to store whether the downwards branch is infeasible, or NULL */
   SCIP_Bool*            upinf,              /**< pointer to store whether the upwards branch is infeasible, or NULL */
   SCIP_Bool*            downconflict,       /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible downwards branch, or NULL */
   SCIP_Bool*            upconflict,         /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible upwards branch, or NULL */
   SCIP_Bool*            lperror             /**< pointer to store whether an unresolved LP error occurred or the
                                              *   solving process should be stopped (e.g., due to a time limit) */
   )
{
   SCIP_COL* col;
   SCIP_Real localdown;
   SCIP_Real localup;
   SCIP_Bool localdownvalid;
   SCIP_Bool localupvalid;

   assert(scip != NULL);
   assert(var != NULL);
   assert(lperror != NULL);
   assert(!SCIPtreeProbing(scip->tree)); /* we should not be in strong branching with propagation mode */
   assert(var->scip == scip);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarStrongbranchFrac", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( downvalid != NULL )
      *downvalid = FALSE;
   if( upvalid != NULL )
      *upvalid = FALSE;
   if( downinf != NULL )
      *downinf = FALSE;
   if( upinf != NULL )
      *upinf = FALSE;
   if( downconflict != NULL )
      *downconflict = FALSE;
   if( upconflict != NULL )
      *upconflict = FALSE;

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
   {
      SCIPerrorMessage("cannot get strong branching information on non-COLUMN variable <%s>\n", SCIPvarGetName(var));
      return SCIP_INVALIDDATA;
   }

   col = SCIPvarGetCol(var);
   assert(col != NULL);

   if( !SCIPcolIsInLP(col) )
   {
      SCIPerrorMessage("cannot get strong branching information on variable <%s> not in current LP\n", SCIPvarGetName(var));
      return SCIP_INVALIDDATA;
   }

   /* check if the solving process should be aborted */
   if( SCIPsolveIsStopped(scip->set, scip->stat, FALSE) )
   {
      /* mark this as if the LP failed */
      *lperror = TRUE;
      return SCIP_OKAY;
   }

   /* call strong branching for column with fractional value */
   SCIP_CALL( SCIPcolGetStrongbranch(col, FALSE, scip->set, scip->stat, scip->transprob, scip->lp, itlim, !idempotent, !idempotent,
         &localdown, &localup, &localdownvalid, &localupvalid, lperror) );

   /* check, if the branchings are infeasible; in exact solving mode, we cannot trust the strong branching enough to
    * declare the sub nodes infeasible
    */
   if( !(*lperror) && SCIPprobAllColsInLP(scip->transprob, scip->set, scip->lp) && !scip->set->misc_exactsolve )
   {
      if( !idempotent ) /*lint !e774*/
      {
         SCIP_CALL( analyzeStrongbranch(scip, var, downinf, upinf, downconflict, upconflict) );
      }
      else
      {
         if( downinf != NULL )
            *downinf = localdownvalid && SCIPsetIsGE(scip->set, localdown, scip->lp->cutoffbound);
         if( upinf != NULL )
            *upinf = localupvalid && SCIPsetIsGE(scip->set, localup, scip->lp->cutoffbound);
      }
   }

   if( down != NULL )
      *down = localdown;
   if( up != NULL )
      *up = localup;
   if( downvalid != NULL )
      *downvalid = localdownvalid;
   if( upvalid != NULL )
      *upvalid = localupvalid;

   return SCIP_OKAY;
}

/** create, solve, and evaluate a single strong branching child (for strong branching with propagation) */
static
SCIP_RETCODE performStrongbranchWithPropagation(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get strong branching values for */
   SCIP_Bool             down,               /**< do we regard the down child? */
   SCIP_Bool             firstchild,         /**< is this the first of the two strong branching children? */
   SCIP_Bool             propagate,          /**< should domain propagation be performed? */
   SCIP_Real             newbound,           /**< new bound to apply at the strong branching child */
   int                   itlim,              /**< iteration limit for strong branchings */
   int                   maxproprounds,      /**< maximum number of propagation rounds (-1: no limit, -2: parameter
                                              *   settings) */
   SCIP_Real*            value,              /**< stores dual bound for strong branching child */
   SCIP_Bool*            valid,              /**< stores whether the returned value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Longint*         ndomreductions,     /**< pointer to store the number of domain reductions found, or NULL */
   SCIP_Bool*            conflict,           /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible strong branching child, or NULL */
   SCIP_Bool*            lperror,            /**< pointer to store whether an unresolved LP error occurred or the
                                              *   solving process should be stopped (e.g., due to a time limit) */
   SCIP_VAR**            vars,               /**< active problem variables */
   int                   nvars,              /**< number of active problem variables */
   SCIP_Real*            newlbs,             /**< array to store valid lower bounds for all active variables, or NULL */
   SCIP_Real*            newubs,             /**< array to store valid upper bounds for all active variables, or NULL */
   SCIP_Bool*            foundsol,           /**< pointer to store whether a primal solution was found during strong branching */
   SCIP_Bool*            cutoff              /**< pointer to store whether the strong branching child is infeasible */
   )
{
   SCIP_Longint ndomreds;

   assert(value != NULL);
   assert(foundsol != NULL);
   assert(cutoff != NULL);
   assert(lperror != NULL);
   assert(valid != NULL ? !(*valid) : TRUE);

   *foundsol = FALSE;
   *cutoff = FALSE;
   *lperror = FALSE;

   /* check whether the strong branching child is already infeasible due to the bound change */
   if( down )
   {
      /* the down branch is infeasible due to the branching bound change; since this means that solval is not within the
       * bounds, this should only happen if previous strong branching calls on other variables detected bound changes which
       * are valid for and were already applied at the probing root
       */
      if( newbound < SCIPvarGetLbLocal(var) - 0.5 )
      {
         *value = SCIPinfinity(scip);

         if( valid != NULL )
            *valid = TRUE;

         /* bound changes are applied in SCIPendStrongbranch(), which can be seen as a conflict constraint */
         if( conflict != NULL )
            *conflict = TRUE;

         *cutoff = TRUE;

         return SCIP_OKAY;
      }
   }
   else
   {
      /* the up branch is infeasible due to the branching bound change; since this means that solval is not within the
       * bounds, this should only happen if previous strong branching calls on other variables detected bound changes which
       * are valid for and were already applied at the probing root
       */
      if( newbound > SCIPvarGetUbLocal(var) + 0.5 )
      {
         *value = SCIPinfinity(scip);

         if( valid != NULL )
            *valid = TRUE;

         /* bound changes are applied in SCIPendStrongbranch(), which can be seen as a conflict constraint */
         if( conflict != NULL )
            *conflict = TRUE;

         *cutoff = TRUE;

         return SCIP_OKAY;
      }
   }

   /* we need to ensure that we can create at least one new probing node without exceeding the maximal tree depth */
   if( SCIP_MAXTREEDEPTH > SCIPtreeGetProbingDepth(scip->tree) )
   {
      /* create a new probing node for the strong branching child and apply the new bound for the variable */
      SCIP_CALL( SCIPnewProbingNode(scip) );

      if( down )
      {
         assert(SCIPisGE(scip, newbound, SCIPvarGetLbLocal(var)));
         if( SCIPisLT(scip, newbound, SCIPvarGetUbLocal(var)) )
         {
            SCIP_CALL( SCIPchgVarUbProbing(scip, var, newbound) );
         }
      }
      else
      {
         assert(SCIPisLE(scip, newbound, SCIPvarGetUbLocal(var)));
         if( SCIPisGT(scip, newbound, SCIPvarGetLbLocal(var)) )
         {
            SCIP_CALL( SCIPchgVarLbProbing(scip, var, newbound) );
         }
      }
   }
   else
   {
      if( valid != NULL )
         *valid = FALSE;

      *cutoff = FALSE;

      if( conflict != NULL )
         *conflict = FALSE;

      return SCIP_OKAY;
   }

   /* propagate domains at the probing node */
   if( propagate )
   {
      /* start time measuring */
      SCIPclockStart(scip->stat->strongpropclock, scip->set);

      ndomreds = 0;
      SCIP_CALL( SCIPpropagateProbing(scip, maxproprounds, cutoff, &ndomreds) );

      /* store number of domain reductions in strong branching */
      if( down )
         SCIPstatAdd(scip->stat, scip->set, nsbdowndomchgs, ndomreds);
      else
         SCIPstatAdd(scip->stat, scip->set, nsbupdomchgs, ndomreds);

      if( ndomreductions != NULL )
         *ndomreductions = ndomreds;

      /* stop time measuring */
      SCIPclockStop(scip->stat->strongpropclock, scip->set);

      if( *cutoff )
      {
         *value = SCIPinfinity(scip);

         if( valid != NULL )
            *valid = TRUE;

         SCIPdebugMsg(scip, "%s branch of var <%s> detected infeasible during propagation\n",
            down ? "down" : "up", SCIPvarGetName(var));
      }
   }

   /* if propagation did not already detect infeasibility, solve the probing LP */
   if( !(*cutoff) )
   {
      SCIP_CALL( SCIPsolveProbingLP(scip, itlim, lperror, cutoff) );
      assert(SCIPisLPRelax(scip));

      if( *cutoff )
      {
         assert(!(*lperror));

         *value = SCIPinfinity(scip);

         if( valid != NULL )
            *valid = TRUE;

         SCIPdebugMsg(scip, "%s branch of var <%s> detected infeasible in LP solving: status=%d\n",
            down ? "down" : "up", SCIPvarGetName(var), SCIPgetLPSolstat(scip));
      }
      else if( !(*lperror) )
      {
         /* save the lp solution status */
         scip->stat->lastsblpsolstats[down ? 0 : 1] = SCIPgetLPSolstat(scip);

         switch( SCIPgetLPSolstat(scip) )
         {
         case SCIP_LPSOLSTAT_OPTIMAL:
         {
            *value = SCIPgetLPObjval(scip);
            assert(SCIPisLT(scip, *value, SCIPgetCutoffbound(scip)));

            SCIPdebugMsg(scip, "probing LP solved to optimality, objective value: %16.9g\n", *value);

            if( valid != NULL )
               *valid = TRUE;

            /* check the strong branching LP solution for feasibility */
            SCIP_CALL( SCIPtryStrongbranchLPSol(scip, foundsol, cutoff) );
            break;
         }
         case SCIP_LPSOLSTAT_ITERLIMIT:
            ++scip->stat->nsbtimesiterlimhit;
            /*lint -fallthrough*/
         case SCIP_LPSOLSTAT_TIMELIMIT:
         {
            /* use LP value as estimate */
            SCIP_LPI* lpi;
            SCIP_Real objval;
            SCIP_Real looseobjval;

            SCIPdebugMsg(scip, "probing LP hit %s limit\n", SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_ITERLIMIT ? "iteration" : "time");

            /* we access the LPI directly, because when a time limit was hit, we cannot access objective value and dual
             * feasibility using the SCIPlp... methods; we should try to avoid direct calls to the LPI, but this is rather
             * uncritical here, because we are immediately after the SCIPsolveProbingLP() call, because we access the LPI
             * read-only, and we check SCIPlpiWasSolved() first
             */
            SCIP_CALL( SCIPgetLPI(scip, &lpi) );

            if( SCIPlpiWasSolved(lpi) )
            {
               SCIP_CALL( SCIPlpiGetObjval(lpi, &objval) );
               looseobjval = SCIPlpGetLooseObjval(scip->lp, scip->set, scip->transprob);

               /* the infinity value in the LPI should not be smaller than SCIP's infinity value */
               assert(!SCIPlpiIsInfinity(lpi, objval) || SCIPisInfinity(scip, objval));

               /* we use SCIP's infinity value here because a value larger than this is counted as infeasible by SCIP */
               if( SCIPisInfinity(scip, objval) )
                  *value = SCIPinfinity(scip);
               else if( SCIPisInfinity(scip, -looseobjval) )
                  *value = -SCIPinfinity(scip);
               else
                  *value = objval + looseobjval;

               if( SCIPlpiIsDualFeasible(lpi) )
               {
                  if( valid != NULL )
                     *valid = TRUE;

                  if( SCIPisGE(scip, *value, SCIPgetCutoffbound(scip)) )
                     *cutoff = TRUE;
               }
            }
            break;
         }
         case SCIP_LPSOLSTAT_ERROR:
         case SCIP_LPSOLSTAT_UNBOUNDEDRAY:
            *lperror = TRUE;
            break;
         case SCIP_LPSOLSTAT_NOTSOLVED: /* should only be the case for *cutoff = TRUE or *lperror = TRUE */
         case SCIP_LPSOLSTAT_OBJLIMIT: /* in this case, *cutoff should be TRUE and we should not get here */
         case SCIP_LPSOLSTAT_INFEASIBLE: /* in this case, *cutoff should be TRUE and we should not get here */
         default:
            SCIPerrorMessage("invalid LP solution status <%d>\n", SCIPgetLPSolstat(scip));
            return SCIP_INVALIDDATA;
         }  /*lint !e788*/
      }

      /* If columns are missing in the LP, the cutoff flag may be wrong. Therefore, we need to set it and the valid pointer
       * to false here.
       */
      if( (*cutoff) && !SCIPallColsInLP(scip) )
      {
         *cutoff = FALSE;
      }

#ifndef NDEBUG
      if( *lperror )
      {
         SCIPdebugMsg(scip, "error during strong branching probing LP solving: status=%d\n", SCIPgetLPSolstat(scip));
      }
#endif
   }

   /* if the subproblem was feasible, we store the local bounds of the variables after propagation and (possibly)
    * conflict analysis
    * @todo do this after propagation? should be able to get valid bounds more often, but they might be weaker
    */
   if( !(*cutoff) && newlbs != NULL)
   {
      int v;

      assert(newubs != NULL);

      /* initialize the newlbs and newubs to the current local bounds */
      if( firstchild )
      {
         for( v = 0; v < nvars; ++v )
         {
            newlbs[v] = SCIPvarGetLbLocal(vars[v]);
            newubs[v] = SCIPvarGetUbLocal(vars[v]);
         }
      }
      /* update newlbs and newubs: take the weaker of the already stored bounds and the current local bounds */
      else
      {
         for( v = 0; v < nvars; ++v )
         {
            SCIP_Real lb = SCIPvarGetLbLocal(vars[v]);
            SCIP_Real ub = SCIPvarGetUbLocal(vars[v]);

            newlbs[v] = MIN(newlbs[v], lb);
            newubs[v] = MAX(newubs[v], ub);
         }
      }
   }

   /* revert all changes at the probing node */
   SCIP_CALL( SCIPbacktrackProbing(scip, 0) );

   return SCIP_OKAY;
}

/** gets strong branching information with previous domain propagation on column variable
 *
 *  Before calling this method, the strong branching mode must have been activated by calling SCIPstartStrongbranch();
 *  after strong branching was done for all candidate variables, the strong branching mode must be ended by
 *  SCIPendStrongbranch(). Since this method applies domain propagation before strongbranching, propagation has to be be
 *  enabled in the SCIPstartStrongbranch() call.
 *
 *  Before solving the strong branching LP, domain propagation can be performed. The number of propagation rounds
 *  can be specified by the parameter @p maxproprounds.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @warning When using this method, LP banching candidates and solution values must be copied beforehand, because
 *           they are updated w.r.t. the strong branching LP solution.
 */
SCIP_RETCODE SCIPgetVarStrongbranchWithPropagation(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get strong branching values for */
   SCIP_Real             solval,             /**< value of the variable in the current LP solution */
   SCIP_Real             lpobjval,           /**< LP objective value of the current LP solution */
   int                   itlim,              /**< iteration limit for strong branchings */
   int                   maxproprounds,      /**< maximum number of propagation rounds (-1: no limit, -2: parameter
                                              *   settings) */
   SCIP_Real*            down,               /**< stores dual bound after branching column down */
   SCIP_Real*            up,                 /**< stores dual bound after branching column up */
   SCIP_Bool*            downvalid,          /**< stores whether the returned down value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Bool*            upvalid,            /**< stores whether the returned up value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Longint*         ndomredsdown,       /**< pointer to store the number of domain reductions down, or NULL */
   SCIP_Longint*         ndomredsup,         /**< pointer to store the number of domain reductions up, or NULL */
   SCIP_Bool*            downinf,            /**< pointer to store whether the downwards branch is infeasible, or NULL */
   SCIP_Bool*            upinf,              /**< pointer to store whether the upwards branch is infeasible, or NULL */
   SCIP_Bool*            downconflict,       /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible downwards branch, or NULL */
   SCIP_Bool*            upconflict,         /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible upwards branch, or NULL */
   SCIP_Bool*            lperror,            /**< pointer to store whether an unresolved LP error occurred or the
                                              *   solving process should be stopped (e.g., due to a time limit) */
   SCIP_Real*            newlbs,             /**< array to store valid lower bounds for all active variables, or NULL */
   SCIP_Real*            newubs              /**< array to store valid upper bounds for all active variables, or NULL */
   )
{
   SCIP_COL* col;
   SCIP_VAR** vars;
   SCIP_Longint oldniters;
   SCIP_Real newub;
   SCIP_Real newlb;
   SCIP_Bool propagate;
   SCIP_Bool cutoff;
   SCIP_Bool downchild;
   SCIP_Bool firstchild;
   SCIP_Bool foundsol;
   SCIP_Bool downvalidlocal;
   SCIP_Bool upvalidlocal;
   SCIP_Bool allcolsinlp;
   SCIP_Bool enabledconflict;
   int oldnconflicts;
   int nvars;

   assert(scip != NULL);
   assert(var != NULL);
   assert(SCIPvarIsIntegral(var));
   assert(down != NULL);
   assert(up != NULL);
   assert(lperror != NULL);
   assert((newlbs != NULL) == (newubs != NULL));
   assert(SCIPinProbing(scip));
   assert(var->scip == scip);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarStrongbranchWithPropagation", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   /* check whether propagation should be performed */
   propagate = (maxproprounds != 0 && maxproprounds != -3);

   /* Check, if all existing columns are in LP.
    * If this is not the case, we may still return that the up and down dual bounds are valid, because the branching
    * rule should not apply them otherwise.
    * However, we must not set the downinf or upinf pointers to TRUE based on the dual bound, because we cannot
    * guarantee that this node can be cut off.
    */
   allcolsinlp = SCIPallColsInLP(scip);

   /* if maxproprounds is -2, change it to 0, which for the following calls means using the parameter settings */
   if( maxproprounds == -2 )
      maxproprounds = 0;

   *down = lpobjval;
   *up = lpobjval;
   if( downvalid != NULL )
      *downvalid = FALSE;
   if( upvalid != NULL )
      *upvalid = FALSE;
   if( downinf != NULL )
      *downinf = FALSE;
   if( upinf != NULL )
      *upinf = FALSE;
   if( downconflict != NULL )
      *downconflict = FALSE;
   if( upconflict != NULL )
      *upconflict = FALSE;
   if( ndomredsdown != NULL )
      *ndomredsdown = 0;
   if( ndomredsup != NULL )
      *ndomredsup = 0;

   *lperror = FALSE;

   vars = SCIPgetVars(scip);
   nvars = SCIPgetNVars(scip);

   scip->stat->lastsblpsolstats[0] = scip->stat->lastsblpsolstats[1] = SCIP_LPSOLSTAT_NOTSOLVED;

   /* check if the solving process should be aborted */
   if( SCIPsolveIsStopped(scip->set, scip->stat, FALSE) )
   {
      /* mark this as if the LP failed */
      *lperror = TRUE;
      return SCIP_OKAY;
   }

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
   {
      SCIPerrorMessage("cannot get strong branching information on non-COLUMN variable <%s>\n", SCIPvarGetName(var));
      return SCIP_INVALIDDATA;
   }

   col = SCIPvarGetCol(var);
   assert(col != NULL);

   if( !SCIPcolIsInLP(col) )
   {
      SCIPerrorMessage("cannot get strong branching information on variable <%s> not in current LP\n", SCIPvarGetName(var));
      return SCIP_INVALIDDATA;
   }

   newlb = SCIPfeasFloor(scip, solval + 1.0);
   newub = SCIPfeasCeil(scip, solval - 1.0);

   SCIPdebugMsg(scip, "strong branching on var <%s>: solval=%g, lb=%g, ub=%g\n", SCIPvarGetName(var), solval,
      SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var));

   /* the up branch is infeasible due to the branching bound change; since this means that solval is not within the
    * bounds, this should only happen if previous strong branching calls on other variables detected bound changes which
    * are valid for and were already applied at the probing root
    */
   if( newlb > SCIPvarGetUbLocal(var) + 0.5 )
   {
      *up = SCIPinfinity(scip);

      if( upinf != NULL )
         *upinf = TRUE;

      if( upvalid != NULL )
         *upvalid = TRUE;

      /* bound changes are applied in SCIPendStrongbranch(), which can be seen as a conflict constraint */
      if( upconflict != NULL )
         *upconflict = TRUE;

      SCIPcolSetStrongbranchData(col, scip->set, scip->stat, scip->lp, lpobjval, solval,
         *down, *up, FALSE, TRUE, 0LL, INT_MAX);

      /* we do not regard the down branch; its valid pointer stays set to FALSE */
      return SCIP_OKAY;
   }

   /* the down branch is infeasible due to the branching bound change; since this means that solval is not within the
    * bounds, this should only happen if previous strong branching calls on other variables detected bound changes which
    * are valid for and were already applied at the probing root
    */
   if( newub < SCIPvarGetLbLocal(var) - 0.5 )
   {
      *down = SCIPinfinity(scip);

      if( downinf != NULL )
         *downinf = TRUE;

      if( downvalid != NULL )
         *downvalid = TRUE;

      /* bound changes are applied in SCIPendStrongbranch(), which can be seen as a conflict constraint */
      if( downconflict != NULL )
         *downconflict = TRUE;

      SCIPcolSetStrongbranchData(col, scip->set, scip->stat, scip->lp, lpobjval, solval,
         *down, *up, TRUE, FALSE, 0LL, INT_MAX);

      /* we do not regard the up branch; its valid pointer stays set to FALSE */
      return SCIP_OKAY;
   }

   /* We now do strong branching by creating the two potential child nodes as probing nodes and solving them one after
    * the other. We will stop when the first child is detected infeasible, saving the effort we would need for the
    * second child. Since empirically, the up child tends to be infeasible more often, we do strongbranching first on
    * the up branch.
    */
   oldniters = scip->stat->nsbdivinglpiterations;
   firstchild = TRUE;
   cutoff = FALSE;

   /* switch conflict analysis according to usesb parameter */
   enabledconflict = scip->set->conf_enable;
   scip->set->conf_enable = (scip->set->conf_enable && scip->set->conf_usesb);

   /* @todo: decide the branch to look at first based on the cutoffs in previous calls? */
   downchild = SCIPisStrongbranchDownFirst(scip, var);

   downvalidlocal = FALSE;
   upvalidlocal = FALSE;

   do
   {
      oldnconflicts = SCIPconflictGetNConflicts(scip->conflict);

      if( downchild )
      {
         SCIP_CALL( performStrongbranchWithPropagation(scip, var, downchild, firstchild, propagate, newub, itlim, maxproprounds,
               down, &downvalidlocal, ndomredsdown, downconflict, lperror, vars, nvars, newlbs, newubs, &foundsol, &cutoff) );

         /* check whether a new solutions rendered the previous child infeasible */
         if( foundsol && !firstchild && allcolsinlp )
         {
            if( SCIPisGE(scip, *up, SCIPgetCutoffbound(scip)) )
            {
               if( upinf != NULL )
                  *upinf = TRUE;
            }
         }

         /* check for infeasibility */
         if( cutoff )
         {
            if( downinf != NULL )
               *downinf = TRUE;

            if( downconflict != NULL &&
               (SCIPvarGetLbLocal(var) > newub + 0.5 || SCIPconflictGetNConflicts(scip->conflict) > oldnconflicts) )
            {
               *downconflict = TRUE;
            }

            if( !scip->set->branch_forceall )
            {
               /* if this is the first call, we do not regard the up branch, its valid pointer is initially set to FALSE */
               break;
            }
         }
      }
      else
      {
         SCIP_CALL( performStrongbranchWithPropagation(scip, var, downchild, firstchild, propagate, newlb, itlim, maxproprounds,
               up, &upvalidlocal, ndomredsup, upconflict, lperror, vars, nvars, newlbs, newubs, &foundsol, &cutoff) );

         /* check whether a new solutions rendered the previous child infeasible */
         if( foundsol && !firstchild && allcolsinlp )
         {
            if( SCIPisGE(scip, *down, SCIPgetCutoffbound(scip)) )
            {
               if( downinf != NULL )
                  *downinf = TRUE;
            }
         }

         /* check for infeasibility */
         if( cutoff )
         {
            if( upinf != NULL )
               *upinf = TRUE;

            assert(upinf == NULL || (*upinf) == TRUE);

            if( upconflict != NULL &&
               (SCIPvarGetUbLocal(var) < newlb - 0.5 || SCIPconflictGetNConflicts(scip->conflict) > oldnconflicts) )
            {
               *upconflict = TRUE;
            }

            if( !scip->set->branch_forceall )
            {
               /* if this is the first call, we do not regard the down branch, its valid pointer is initially set to FALSE */
               break;
            }
         }
      }

      downchild = !downchild;
      firstchild = !firstchild;
   }
   while( !firstchild );

   /* set strong branching information in column */
   if( *lperror )
   {
      SCIPcolInvalidateStrongbranchData(col, scip->set, scip->stat, scip->lp);
   }
   else
   {
      SCIPcolSetStrongbranchData(col, scip->set, scip->stat, scip->lp, lpobjval, solval,
         *down, *up, downvalidlocal, upvalidlocal, scip->stat->nsbdivinglpiterations - oldniters, itlim);
   }

   if( downvalid != NULL )
      *downvalid = downvalidlocal;
   if( upvalid != NULL )
      *upvalid = upvalidlocal;

   scip->set->conf_enable = enabledconflict;

   return SCIP_OKAY;   /*lint !e438*/
}

/** gets strong branching information on column variable x with integral LP solution value (val); that is, the down branch
 *  is (val -1.0) and the up brach ins (val +1.0)
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note If the integral LP solution value is the lower or upper bound of the variable, the corresponding branch will be
 *        marked as infeasible. That is, the valid pointer and the infeasible pointer are set to TRUE.
 */
SCIP_RETCODE SCIPgetVarStrongbranchInt(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get strong branching values for */
   int                   itlim,              /**< iteration limit for strong branchings */
   SCIP_Bool             idempotent,         /**< should scip's state remain the same after the call (statistics, column states...), or should it be updated ? */
   SCIP_Real*            down,               /**< stores dual bound after branching column down */
   SCIP_Real*            up,                 /**< stores dual bound after branching column up */
   SCIP_Bool*            downvalid,          /**< stores whether the returned down value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Bool*            upvalid,            /**< stores whether the returned up value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Bool*            downinf,            /**< pointer to store whether the downwards branch is infeasible, or NULL */
   SCIP_Bool*            upinf,              /**< pointer to store whether the upwards branch is infeasible, or NULL */
   SCIP_Bool*            downconflict,       /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible downwards branch, or NULL */
   SCIP_Bool*            upconflict,         /**< pointer to store whether a conflict constraint was created for an
                                              *   infeasible upwards branch, or NULL */
   SCIP_Bool*            lperror             /**< pointer to store whether an unresolved LP error occurred or the
                                              *   solving process should be stopped (e.g., due to a time limit) */
   )
{
   SCIP_COL* col;
   SCIP_Real localdown;
   SCIP_Real localup;
   SCIP_Bool localdownvalid;
   SCIP_Bool localupvalid;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarStrongbranchInt", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   assert(lperror != NULL);
   assert(var->scip == scip);

   if( downvalid != NULL )
      *downvalid = FALSE;
   if( upvalid != NULL )
      *upvalid = FALSE;
   if( downinf != NULL )
      *downinf = FALSE;
   if( upinf != NULL )
      *upinf = FALSE;
   if( downconflict != NULL )
      *downconflict = FALSE;
   if( upconflict != NULL )
      *upconflict = FALSE;

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
   {
      SCIPerrorMessage("cannot get strong branching information on non-COLUMN variable <%s>\n", SCIPvarGetName(var));
      return SCIP_INVALIDDATA;
   }

   col = SCIPvarGetCol(var);
   assert(col != NULL);

   if( !SCIPcolIsInLP(col) )
   {
      SCIPerrorMessage("cannot get strong branching information on variable <%s> not in current LP\n", SCIPvarGetName(var));
      return SCIP_INVALIDDATA;
   }

   /* check if the solving process should be aborted */
   if( SCIPsolveIsStopped(scip->set, scip->stat, FALSE) )
   {
      /* mark this as if the LP failed */
      *lperror = TRUE;
      return SCIP_OKAY;
   }

   /* call strong branching for column */
   SCIP_CALL( SCIPcolGetStrongbranch(col, TRUE, scip->set, scip->stat, scip->transprob, scip->lp, itlim, !idempotent, !idempotent,
         &localdown, &localup, &localdownvalid, &localupvalid, lperror) );

   /* check, if the branchings are infeasible; in exact solving mode, we cannot trust the strong branching enough to
    * declare the sub nodes infeasible
    */
   if( !(*lperror) && SCIPprobAllColsInLP(scip->transprob, scip->set, scip->lp) && !scip->set->misc_exactsolve )
   {
      if( !idempotent ) /*lint !e774*/
      {
         SCIP_CALL( analyzeStrongbranch(scip, var, downinf, upinf, downconflict, upconflict) );
      }
      else
      {
         if( downinf != NULL )
            *downinf = localdownvalid && SCIPsetIsGE(scip->set, localdown, scip->lp->cutoffbound);
         if( upinf != NULL )
            *upinf = localupvalid && SCIPsetIsGE(scip->set, localup, scip->lp->cutoffbound);
      }
   }

   if( down != NULL )
      *down = localdown;
   if( up != NULL )
      *up = localup;
   if( downvalid != NULL )
      *downvalid = localdownvalid;
   if( upvalid != NULL )
      *upvalid = localupvalid;

   return SCIP_OKAY;
}

/** gets strong branching information on column variables with fractional values
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPgetVarsStrongbranchesFrac(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            vars,               /**< variables to get strong branching values for */
   int                   nvars,              /**< number of variables */
   int                   itlim,              /**< iteration limit for strong branchings */
   SCIP_Real*            down,               /**< stores dual bounds after branching variables down */
   SCIP_Real*            up,                 /**< stores dual bounds after branching variables up */
   SCIP_Bool*            downvalid,          /**< stores whether the returned down values are valid dual bounds, or NULL;
                                              *   otherwise, they can only be used as an estimate value */
   SCIP_Bool*            upvalid,            /**< stores whether the returned up values are valid dual bounds, or NULL;
                                              *   otherwise, they can only be used as an estimate value */
   SCIP_Bool*            downinf,            /**< array to store whether the downward branches are infeasible, or NULL */
   SCIP_Bool*            upinf,              /**< array to store whether the upward branches are infeasible, or NULL */
   SCIP_Bool*            downconflict,       /**< array to store whether conflict constraints were created for
                                              *   infeasible downward branches, or NULL */
   SCIP_Bool*            upconflict,         /**< array to store whether conflict constraints were created for
                                              *   infeasible upward branches, or NULL */
   SCIP_Bool*            lperror             /**< pointer to store whether an unresolved LP error occurred or the
                                              *   solving process should be stopped (e.g., due to a time limit) */
   )
{
   SCIP_COL** cols;
   int j;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarsStrongbranchesFrac", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   assert( lperror != NULL );
   assert( vars != NULL );

   /* set up data */
   cols = NULL;
   SCIP_CALL( SCIPallocBufferArray(scip, &cols, nvars) );
   assert(cols != NULL);
   for( j = 0; j < nvars; ++j )
   {
      SCIP_VAR* var;
      SCIP_COL* col;

      if( downvalid != NULL )
         downvalid[j] = FALSE;
      if( upvalid != NULL )
         upvalid[j] = FALSE;
      if( downinf != NULL )
         downinf[j] = FALSE;
      if( upinf != NULL )
         upinf[j] = FALSE;
      if( downconflict != NULL )
         downconflict[j] = FALSE;
      if( upconflict != NULL )
         upconflict[j] = FALSE;

      var = vars[j];
      assert( var != NULL );
      if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
      {
         SCIPerrorMessage("cannot get strong branching information on non-COLUMN variable <%s>\n", SCIPvarGetName(var));
         SCIPfreeBufferArray(scip, &cols);
         return SCIP_INVALIDDATA;
      }

      col = SCIPvarGetCol(var);
      assert(col != NULL);
      cols[j] = col;

      if( !SCIPcolIsInLP(col) )
      {
         SCIPerrorMessage("cannot get strong branching information on variable <%s> not in current LP\n", SCIPvarGetName(var));
         SCIPfreeBufferArray(scip, &cols);
         return SCIP_INVALIDDATA;
      }
   }

   /* check if the solving process should be aborted */
   if( SCIPsolveIsStopped(scip->set, scip->stat, FALSE) )
   {
      /* mark this as if the LP failed */
      *lperror = TRUE;
   }
   else
   {
      /* call strong branching for columns with fractional value */
      SCIP_CALL( SCIPcolGetStrongbranches(cols, nvars, FALSE, scip->set, scip->stat, scip->transprob, scip->lp, itlim,
            down, up, downvalid, upvalid, lperror) );

      /* check, if the branchings are infeasible; in exact solving mode, we cannot trust the strong branching enough to
       * declare the sub nodes infeasible
       */
      if( !(*lperror) && SCIPprobAllColsInLP(scip->transprob, scip->set, scip->lp) && !scip->set->misc_exactsolve )
      {
         for( j = 0; j < nvars; ++j )
         {
            SCIP_CALL( analyzeStrongbranch(scip, vars[j], (downinf != NULL) ? (&(downinf[j])) : NULL,
                  (upinf != NULL) ? (&(upinf[j])) : NULL, (downconflict != NULL) ? (&(downconflict[j])) : NULL,
                  (upconflict != NULL) ? (&(upconflict[j])) : NULL) );
         }
      }
   }
   SCIPfreeBufferArray(scip, &cols);

   return SCIP_OKAY;
}

/** gets strong branching information on column variables with integral values
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPgetVarsStrongbranchesInt(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            vars,               /**< variables to get strong branching values for */
   int                   nvars,              /**< number of variables */
   int                   itlim,              /**< iteration limit for strong branchings */
   SCIP_Real*            down,               /**< stores dual bounds after branching variables down */
   SCIP_Real*            up,                 /**< stores dual bounds after branching variables up */
   SCIP_Bool*            downvalid,          /**< stores whether the returned down values are valid dual bounds, or NULL;
                                              *   otherwise, they can only be used as an estimate value */
   SCIP_Bool*            upvalid,            /**< stores whether the returned up values are valid dual bounds, or NULL;
                                              *   otherwise, they can only be used as an estimate value */
   SCIP_Bool*            downinf,            /**< array to store whether the downward branches are infeasible, or NULL */
   SCIP_Bool*            upinf,              /**< array to store whether the upward branches are infeasible, or NULL */
   SCIP_Bool*            downconflict,       /**< array to store whether conflict constraints were created for
                                              *   infeasible downward branches, or NULL */
   SCIP_Bool*            upconflict,         /**< array to store whether conflict constraints were created for
                                              *   infeasible upward branches, or NULL */
   SCIP_Bool*            lperror             /**< pointer to store whether an unresolved LP error occurred or the
                                              *   solving process should be stopped (e.g., due to a time limit) */
   )
{
   SCIP_COL** cols;
   int j;

   assert(lperror != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarsStrongbranchesInt", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   assert( vars != NULL );

   /* set up data */
   cols = NULL;
   SCIP_CALL( SCIPallocBufferArray(scip, &cols, nvars) );
   assert(cols != NULL);
   for( j = 0; j < nvars; ++j )
   {
      SCIP_VAR* var;
      SCIP_COL* col;

      if( downvalid != NULL )
         downvalid[j] = FALSE;
      if( upvalid != NULL )
         upvalid[j] = FALSE;
      if( downinf != NULL )
         downinf[j] = FALSE;
      if( upinf != NULL )
         upinf[j] = FALSE;
      if( downconflict != NULL )
         downconflict[j] = FALSE;
      if( upconflict != NULL )
         upconflict[j] = FALSE;

      var = vars[j];
      assert( var != NULL );
      if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
      {
         SCIPerrorMessage("cannot get strong branching information on non-COLUMN variable <%s>\n", SCIPvarGetName(var));
         SCIPfreeBufferArray(scip, &cols);
         return SCIP_INVALIDDATA;
      }

      col = SCIPvarGetCol(var);
      assert(col != NULL);
      cols[j] = col;

      if( !SCIPcolIsInLP(col) )
      {
         SCIPerrorMessage("cannot get strong branching information on variable <%s> not in current LP\n", SCIPvarGetName(var));
         SCIPfreeBufferArray(scip, &cols);
         return SCIP_INVALIDDATA;
      }
   }

   /* check if the solving process should be aborted */
   if( SCIPsolveIsStopped(scip->set, scip->stat, FALSE) )
   {
      /* mark this as if the LP failed */
      *lperror = TRUE;
   }
   else
   {
      /* call strong branching for columns */
      SCIP_CALL( SCIPcolGetStrongbranches(cols, nvars, TRUE, scip->set, scip->stat, scip->transprob, scip->lp, itlim,
            down, up, downvalid, upvalid, lperror) );

      /* check, if the branchings are infeasible; in exact solving mode, we cannot trust the strong branching enough to
       * declare the sub nodes infeasible
       */
      if( !(*lperror) && SCIPprobAllColsInLP(scip->transprob, scip->set, scip->lp) && !scip->set->misc_exactsolve )
      {
         for( j = 0; j < nvars; ++j )
         {
            SCIP_CALL( analyzeStrongbranch(scip, vars[j], (downinf != NULL) ? (&(downinf[j])) : NULL,
                  (upinf != NULL) ? (&(upinf[j])) : NULL, (downconflict != NULL) ? (&(downconflict[j])) : NULL,
                  (upconflict != NULL) ? (&(upconflict[j])) : NULL) );
         }
      }
   }
   SCIPfreeBufferArray(scip, &cols);

   return SCIP_OKAY;
}

/** get LP solution status of last strong branching call (currently only works for strong branching with propagation) */
SCIP_LPSOLSTAT SCIPgetLastStrongbranchLPSolStat(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_BRANCHDIR        branchdir           /**< branching direction for which LP solution status is requested */
   )
{
   assert(NULL != scip);
   assert(branchdir == SCIP_BRANCHDIR_DOWNWARDS || branchdir == SCIP_BRANCHDIR_UPWARDS);

   return scip->stat->lastsblpsolstats[branchdir == SCIP_BRANCHDIR_DOWNWARDS ? 0 : 1];
}

/** gets strong branching information on COLUMN variable of the last SCIPgetVarStrongbranch() call;
 *  returns values of SCIP_INVALID, if strong branching was not yet called on the given variable;
 *  keep in mind, that the returned old values may have nothing to do with the current LP solution
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 */
SCIP_RETCODE SCIPgetVarStrongbranchLast(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to get last strong branching values for */
   SCIP_Real*            down,               /**< stores dual bound after branching column down */
   SCIP_Real*            up,                 /**< stores dual bound after branching column up */
   SCIP_Bool*            downvalid,          /**< stores whether the returned down value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Bool*            upvalid,            /**< stores whether the returned up value is a valid dual bound, or NULL;
                                              *   otherwise, it can only be used as an estimate value */
   SCIP_Real*            solval,             /**< stores LP solution value of variable at the last strong branching call, or NULL */
   SCIP_Real*            lpobjval            /**< stores LP objective value at last strong branching call, or NULL */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPgetVarStrongbranchLast", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, FALSE, FALSE, FALSE) );

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
   {
      SCIPerrorMessage("cannot get strong branching information on non-COLUMN variable\n");
      return SCIP_INVALIDDATA;
   }

   SCIPcolGetStrongbranchLast(SCIPvarGetCol(var), down, up, downvalid, upvalid, solval, lpobjval);

   return SCIP_OKAY;
}

/** sets strong branching information for a column variable
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPsetVarStrongbranchData(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to set last strong branching values for */
   SCIP_Real             lpobjval,           /**< objective value of the current LP */
   SCIP_Real             primsol,            /**< primal solution value of the column in the current LP */
   SCIP_Real             down,               /**< dual bound after branching column down */
   SCIP_Real             up,                 /**< dual bound after branching column up */
   SCIP_Bool             downvalid,          /**< is the returned down value a valid dual bound? */
   SCIP_Bool             upvalid,            /**< is the returned up value a valid dual bound? */
   SCIP_Longint          iter,               /**< total number of strong branching iterations */
   int                   itlim               /**< iteration limit applied to the strong branching call */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPsetVarStrongbranchData", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
   {
      SCIPerrorMessage("cannot set strong branching information on non-COLUMN variable\n");
      return SCIP_INVALIDDATA;
   }

   SCIPcolSetStrongbranchData(SCIPvarGetCol(var), scip->set, scip->stat, scip->lp, lpobjval, primsol,
      down, up, downvalid, upvalid, iter, itlim);

   return SCIP_OKAY;
}

/** rounds the current solution and tries it afterwards; if feasible, adds it to storage
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPtryStrongbranchLPSol(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Bool*            foundsol,           /**< stores whether solution was feasible and good enough to keep */
   SCIP_Bool*            cutoff              /**< stores whether solution was cutoff due to exceeding the cutoffbound */
   )
{
   assert(scip != NULL);
   assert(foundsol != NULL);
   assert(cutoff != NULL);

   SCIP_CALL( SCIPcheckStage(scip, "SCIPtryStrongbranchLPSol", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( scip->set->branch_checksbsol )
   {
      SCIP_SOL* sol;
      SCIP_Bool rounded = TRUE;
      SCIP_Real value = SCIPgetLPObjval(scip);
      SCIP_Longint oldnbestsolsfound = scip->primal->nbestsolsfound;

      /* start clock for strong branching solutions */
      SCIPclockStart(scip->stat->sbsoltime, scip->set);

      SCIP_CALL( SCIPcreateLPSol(scip, &sol, NULL) );
      SCIPsolSetStrongbranching(sol);

      /* try to round the strong branching solution */
      if( scip->set->branch_roundsbsol )
      {
         SCIP_CALL( SCIProundSol(scip, sol, &rounded) );
      }

      /* check the solution for feasibility if rounding worked well (or was not tried) */
      if( rounded )
      {
         SCIP_CALL( SCIPtrySolFree(scip, &sol, FALSE, FALSE, FALSE, TRUE, FALSE, foundsol) );
      }
      else
      {
         SCIP_CALL( SCIPfreeSol(scip, &sol) );
      }

      if( *foundsol )
      {
         SCIPdebugMsg(scip, "found new solution in strong branching\n");

         scip->stat->nsbsolsfound++;

         if( scip->primal->nbestsolsfound != oldnbestsolsfound )
         {
            scip->stat->nsbbestsolsfound++;
         }

         if( SCIPisGE(scip, value, SCIPgetCutoffbound(scip)) )
            *cutoff = TRUE;
      }

      /* stop clock for strong branching solutions */
      SCIPclockStop(scip->stat->sbsoltime, scip->set);
   }
   return SCIP_OKAY;
}


/** gets node number of the last node in current branch and bound run, where strong branching was used on the
 *  given variable, or -1 if strong branching was never applied to the variable in current run
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 */
SCIP_Longint SCIPgetVarStrongbranchNode(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get last strong branching node for */
   )
{
   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPgetVarStrongbranchNode", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE) );

   assert( var->scip == scip );

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
      return -1;

   return SCIPcolGetStrongbranchNode(SCIPvarGetCol(var));
}

/** if strong branching was already applied on the variable at the current node, returns the number of LPs solved after
 *  the LP where the strong branching on this variable was applied;
 *  if strong branching was not yet applied on the variable at the current node, returns INT_MAX
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 */
SCIP_Longint SCIPgetVarStrongbranchLPAge(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get strong branching LP age for */
   )
{
   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPgetVarStrongbranchLPAge", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE) );

   assert( var->scip == scip );

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
      return SCIP_LONGINT_MAX;

   return SCIPcolGetStrongbranchLPAge(SCIPvarGetCol(var), scip->stat);
}

/** gets number of times, strong branching was applied in current run on the given variable
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 */
int SCIPgetVarNStrongbranchs(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var                 /**< variable to get last strong branching node for */
   )
{
   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPgetVarNStrongbranchs", FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE) );

   assert( var->scip == scip );

   if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_COLUMN )
      return 0;

   return SCIPcolGetNStrongbranchs(SCIPvarGetCol(var));
}

/** adds given values to lock numbers of type @p locktype of variable for rounding
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPaddVarLocksType(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_LOCKTYPE         locktype,           /**< type of the variable locks */
   int                   nlocksdown,         /**< modification in number of rounding down locks */
   int                   nlocksup            /**< modification in number of rounding up locks */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPaddVarLocksType", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE) );

   assert( var->scip == scip );

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      /*lint -fallthrough*/
   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_TRANSFORMED:
   case SCIP_STAGE_INITPRESOLVE:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_PRESOLVED:
   case SCIP_STAGE_INITSOLVE:
   case SCIP_STAGE_SOLVING:
   case SCIP_STAGE_EXITSOLVE:
   case SCIP_STAGE_FREETRANS:
      SCIP_CALL( SCIPvarAddLocks(var, scip->mem->probmem, scip->set, scip->eventqueue, locktype, nlocksdown, nlocksup) );
      return SCIP_OKAY;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/
}

/** adds given values to lock numbers of variable for rounding
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 *
 *  @note This method will always add variable locks of type model
 *
 *  @note It is recommented to use SCIPaddVarLocksType()
 */
SCIP_RETCODE SCIPaddVarLocks(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   int                   nlocksdown,         /**< modification in number of rounding down locks */
   int                   nlocksup            /**< modification in number of rounding up locks */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPaddVarLocks", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE) );

   SCIP_CALL( SCIPaddVarLocksType(scip, var, SCIP_LOCKTYPE_MODEL, nlocksdown, nlocksup) );

   return SCIP_OKAY;
}

/** add locks of variable with respect to the lock status of the constraint and its negation;
 *  this method should be called whenever the lock status of a variable in a constraint changes, for example if
 *  the coefficient of the variable changed its sign or if the left or right hand sides of the constraint were
 *  added or removed
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPlockVarCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_Bool             lockdown,           /**< should the rounding be locked in downwards direction? */
   SCIP_Bool             lockup              /**< should the rounding be locked in upwards direction? */
   )
{
   int nlocksdown[NLOCKTYPES];
   int nlocksup[NLOCKTYPES];
   int i;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPlockVarCons", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE) );

   assert( var->scip == scip );

   for( i = 0; i < NLOCKTYPES; i++ )
   {
      nlocksdown[i] = 0;
      nlocksup[i] = 0;

      if( SCIPconsIsLockedTypePos(cons, (SCIP_LOCKTYPE) i) )
      {
         if( lockdown )
            ++nlocksdown[i];
         if( lockup )
            ++nlocksup[i];
      }
      if( SCIPconsIsLockedTypeNeg(cons, (SCIP_LOCKTYPE) i) )
      {
         if( lockdown )
            ++nlocksup[i];
         if( lockup )
            ++nlocksdown[i];
      }
   }

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      /*lint -fallthrough*/
   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_TRANSFORMED:
   case SCIP_STAGE_INITPRESOLVE:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_INITSOLVE:
   case SCIP_STAGE_SOLVING:
   case SCIP_STAGE_EXITSOLVE:
   case SCIP_STAGE_FREETRANS:
      for( i = 0; i < NLOCKTYPES; i++ )
      {
         if( nlocksdown[i] == 0 && nlocksup[i] == 0 )
            continue;

         SCIP_CALL( SCIPvarAddLocks(var, scip->mem->probmem, scip->set, scip->eventqueue, (SCIP_LOCKTYPE) i, nlocksdown[i], nlocksup[i]) );
      }
      return SCIP_OKAY;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/
}

/** remove locks of type @p locktype of variable with respect to the lock status of the constraint and its negation;
 *  this method should be called whenever the lock status of a variable in a constraint changes, for example if
 *  the coefficient of the variable changed its sign or if the left or right hand sides of the constraint were
 *  added or removed
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_RETCODE SCIPunlockVarCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_Bool             lockdown,           /**< should the rounding be unlocked in downwards direction? */
   SCIP_Bool             lockup              /**< should the rounding be unlocked in upwards direction? */
   )
{
   int nlocksdown[NLOCKTYPES];
   int nlocksup[NLOCKTYPES];
   int i;

   SCIP_CALL( SCIPcheckStage(scip, "SCIPunlockVarCons", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE) );

   assert( var->scip == scip );

   for( i = 0; i < NLOCKTYPES; i++ )
   {
      nlocksdown[i] = 0;
      nlocksup[i] = 0;

      if( SCIPconsIsLockedTypePos(cons, (SCIP_LOCKTYPE) i) )
      {
         if( lockdown )
            ++nlocksdown[i];
         if( lockup )
            ++nlocksup[i];
      }
      if( SCIPconsIsLockedTypeNeg(cons, (SCIP_LOCKTYPE) i) )
      {
         if( lockdown )
            ++nlocksup[i];
         if( lockup )
            ++nlocksdown[i];
      }
   }
   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      /*lint -fallthrough*/
   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_TRANSFORMED:
   case SCIP_STAGE_INITPRESOLVE:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_INITSOLVE:
   case SCIP_STAGE_SOLVING:
   case SCIP_STAGE_EXITSOLVE:
   case SCIP_STAGE_FREETRANS:
      for( i = 0; i < NLOCKTYPES; i++ )
      {
         if( nlocksdown[i] == 0 && nlocksup[i] == 0 )
            continue;

         SCIP_CALL( SCIPvarAddLocks(var, scip->mem->probmem, scip->set, scip->eventqueue, (SCIP_LOCKTYPE)  i, -nlocksdown[i], -nlocksup[i]) );
      }
      return SCIP_OKAY;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/
}

/** changes variable's objective value
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_PRESOLVED
 */
SCIP_RETCODE SCIPchgVarObj(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to change the objective value for */
   SCIP_Real             newobj              /**< new objective value */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarObj", FALSE, TRUE, TRUE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE) );

   assert( var->scip == scip );

   /* forbid infinite objective values */
   if( SCIPisInfinity(scip, REALABS(newobj)) )
   {
      SCIPerrorMessage("invalid objective value: objective value is infinite\n");
      return SCIP_INVALIDDATA;
   }

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      SCIP_CALL( SCIPvarChgObj(var, scip->mem->probmem, scip->set, scip->origprob, scip->primal, scip->lp, scip->eventqueue, newobj) );
      return SCIP_OKAY;

   case SCIP_STAGE_TRANSFORMED:
   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_PRESOLVED:
      SCIP_CALL( SCIPvarChgObj(var, scip->mem->probmem, scip->set,  scip->transprob, scip->primal, scip->lp, scip->eventqueue, newobj) );
      return SCIP_OKAY;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/
}

/** adds value to variable's objective value
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 */
SCIP_RETCODE SCIPaddVarObj(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to change the objective value for */
   SCIP_Real             addobj              /**< additional objective value */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPaddVarObj", FALSE, TRUE, TRUE, FALSE, FALSE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE) );

   assert( var->scip == scip );

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      SCIP_CALL( SCIPvarAddObj(var, scip->mem->probmem, scip->set, scip->stat, scip->transprob, scip->origprob, scip->primal,
            scip->tree, scip->reopt, scip->lp, scip->eventfilter, scip->eventqueue, addobj) );
      return SCIP_OKAY;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_PRESOLVING:
   case SCIP_STAGE_EXITPRESOLVE:
   case SCIP_STAGE_PRESOLVED:
      SCIP_CALL( SCIPvarAddObj(var, scip->mem->probmem, scip->set, scip->stat, scip->transprob, scip->origprob, scip->primal,
            scip->tree, scip->reopt, scip->lp, scip->eventfilter, scip->eventqueue, addobj) );
      return SCIP_OKAY;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/
}

/** returns the adjusted (i.e. rounded, if the given variable is of integral type) lower bound value;
 *  does not change the bounds of the variable
 *
 *  @return adjusted lower bound for the given variable; the bound of the variable is not changed
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_Real SCIPadjustedVarLb(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to adjust the bound for */
   SCIP_Real             lb                  /**< lower bound value to adjust */
   )
{
   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPadjustedVarLb", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   SCIPvarAdjustLb(var, scip->set, &lb);

   return lb;
}

/** returns the adjusted (i.e. rounded, if the given variable is of integral type) upper bound value;
 *  does not change the bounds of the variable
 *
 *  @return adjusted upper bound for the given variable; the bound of the variable is not changed
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_INITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_EXITPRESOLVE
 *       - \ref SCIP_STAGE_PRESOLVED
 *       - \ref SCIP_STAGE_INITSOLVE
 *       - \ref SCIP_STAGE_SOLVING
 *       - \ref SCIP_STAGE_SOLVED
 *       - \ref SCIP_STAGE_EXITSOLVE
 *       - \ref SCIP_STAGE_FREETRANS
 */
SCIP_Real SCIPadjustedVarUb(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to adjust the bound for */
   SCIP_Real             ub                  /**< upper bound value to adjust */
   )
{
   SCIP_CALL_ABORT( SCIPcheckStage(scip, "SCIPadjustedVarUb", FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) );

   SCIPvarAdjustUb(var, scip->set, &ub);

   return ub;
}

/** depending on SCIP's stage, changes lower bound of variable in the problem, in preprocessing, or in current node;
 *  if possible, adjusts bound to integral value; doesn't store any inference information in the bound change, such
 *  that in conflict analysis, this change is treated like a branching decision
 *
 *  @warning If SCIP is in presolving stage, it can happen that the internal variable array (which can be accessed via
 *           SCIPgetVars()) gets resorted.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note During presolving, an integer variable whose bound changes to {0,1} is upgraded to a binary variable.
 */
SCIP_RETCODE SCIPchgVarLb(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to change the bound for */
   SCIP_Real             newbound            /**< new value for bound */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarLb", FALSE, TRUE, TRUE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIPvarAdjustLb(var, scip->set, &newbound);

   /* ignore tightenings of lower bounds to +infinity during solving process */
   if( SCIPisInfinity(scip, newbound) && SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
   {
#ifndef NDEBUG
      SCIPwarningMessage(scip, "ignore lower bound tightening for %s from %e to +infinity\n", SCIPvarGetName(var),
         SCIPvarGetLbLocal(var));
#endif
      return SCIP_OKAY;
   }

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      SCIP_CALL( SCIPvarChgLbGlobal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, scip->cliquetable, newbound) );
      SCIP_CALL( SCIPvarChgLbLocal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, newbound) );
      SCIP_CALL( SCIPvarChgLbOriginal(var, scip->set, newbound) );
      break;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_PRESOLVED:
      SCIP_CALL( SCIPvarChgLbGlobal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, scip->cliquetable, newbound) );
      break;

   case SCIP_STAGE_PRESOLVING:
      if( !SCIPinProbing(scip) )
      {
         assert(SCIPtreeGetCurrentDepth(scip->tree) == 0);
         assert(scip->tree->root == SCIPtreeGetCurrentNode(scip->tree));

         SCIP_CALL( SCIPnodeAddBoundchg(scip->tree->root, scip->mem->probmem, scip->set, scip->stat, scip->transprob,
               scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue, scip->cliquetable,
               var, newbound, SCIP_BOUNDTYPE_LOWER, FALSE) );

         if( (SCIP_VARTYPE)var->vartype == SCIP_VARTYPE_INTEGER && SCIPvarIsBinary(var) )
         {
            SCIP_Bool infeasible;

            SCIP_CALL( SCIPchgVarType(scip, var, SCIP_VARTYPE_BINARY, &infeasible) );
            assert(!infeasible);
         }
         break;
      }
      /*lint -fallthrough*/
   case SCIP_STAGE_SOLVING:
      SCIP_CALL( SCIPnodeAddBoundchg(SCIPtreeGetCurrentNode(scip->tree), scip->mem->probmem, scip->set, scip->stat,
            scip->transprob, scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue,
            scip->cliquetable, var, newbound,
            SCIP_BOUNDTYPE_LOWER, FALSE) );
      break;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/

   return SCIP_OKAY;
}

/** depending on SCIP's stage, changes upper bound of variable in the problem, in preprocessing, or in current node;
 *  if possible, adjusts bound to integral value; doesn't store any inference information in the bound change, such
 *  that in conflict analysis, this change is treated like a branching decision
 *
 *  @warning If SCIP is in presolving stage, it can happen that the internal variable array (which can be accessed via
 *           SCIPgetVars()) gets resorted.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note During presolving, an integer variable whose bound changes to {0,1} is upgraded to a binary variable.
 */
SCIP_RETCODE SCIPchgVarUb(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to change the bound for */
   SCIP_Real             newbound            /**< new value for bound */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarUb", FALSE, TRUE, TRUE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIPvarAdjustUb(var, scip->set, &newbound);

   /* ignore tightenings of upper bounds to -infinity during solving process */
   if( SCIPisInfinity(scip, -newbound) && SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
   {
#ifndef NDEBUG
      SCIPwarningMessage(scip, "ignore upper bound tightening for %s from %e to -infinity\n", SCIPvarGetName(var),
         SCIPvarGetUbLocal(var));
#endif
      return SCIP_OKAY;
   }

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      SCIP_CALL( SCIPvarChgUbGlobal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, scip->cliquetable, newbound) );
      SCIP_CALL( SCIPvarChgUbLocal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, newbound) );
      SCIP_CALL( SCIPvarChgUbOriginal(var, scip->set, newbound) );
      break;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_PRESOLVED:
      SCIP_CALL( SCIPvarChgUbGlobal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, scip->cliquetable, newbound) );
      break;

   case SCIP_STAGE_PRESOLVING:
      if( !SCIPinProbing(scip) )
      {
         assert(SCIPtreeGetCurrentDepth(scip->tree) == 0);
         assert(scip->tree->root == SCIPtreeGetCurrentNode(scip->tree));

         SCIP_CALL( SCIPnodeAddBoundchg(scip->tree->root, scip->mem->probmem, scip->set, scip->stat, scip->transprob,
               scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue,
               scip->cliquetable, var, newbound, SCIP_BOUNDTYPE_UPPER, FALSE) );

         if( (SCIP_VARTYPE)var->vartype == SCIP_VARTYPE_INTEGER && SCIPvarIsBinary(var) )
         {
            SCIP_Bool infeasible;

            SCIP_CALL( SCIPchgVarType(scip, var, SCIP_VARTYPE_BINARY, &infeasible) );
            assert(!infeasible);
         }
         break;
      }
      /*lint -fallthrough*/
   case SCIP_STAGE_SOLVING:
      SCIP_CALL( SCIPnodeAddBoundchg(SCIPtreeGetCurrentNode(scip->tree), scip->mem->probmem, scip->set, scip->stat,
            scip->transprob, scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue,
            scip->cliquetable, var, newbound, SCIP_BOUNDTYPE_UPPER, FALSE) );
      break;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/

   return SCIP_OKAY;
}

/** changes lower bound of variable in the given node; if possible, adjust bound to integral value; doesn't store any
 *  inference information in the bound change, such that in conflict analysis, this change is treated like a branching
 *  decision
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can only be called if @p scip is in stage \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPchgVarLbNode(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_NODE*            node,               /**< node to change bound at, or NULL for current node */
   SCIP_VAR*             var,                /**< variable to change the bound for */
   SCIP_Real             newbound            /**< new value for bound */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarLbNode", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( node == NULL )
   {
      SCIP_CALL( SCIPchgVarLb(scip, var, newbound) );
   }
   else
   {
      SCIPvarAdjustLb(var, scip->set, &newbound);

      /* ignore tightenings of lower bounds to +infinity during solving process */
      if( SCIPisInfinity(scip, newbound) && SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
      {
#ifndef NDEBUG
         SCIPwarningMessage(scip, "ignore lower bound tightening for %s from %e to +infinity\n", SCIPvarGetName(var),
            SCIPvarGetLbLocal(var));
#endif
         return SCIP_OKAY;
      }

      SCIP_CALL( SCIPnodeAddBoundchg(node, scip->mem->probmem, scip->set, scip->stat, scip->transprob, scip->origprob,
            scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue, scip->cliquetable, var, newbound,
            SCIP_BOUNDTYPE_LOWER, FALSE) );
   }

   return SCIP_OKAY;
}

/** changes upper bound of variable in the given node; if possible, adjust bound to integral value; doesn't store any
 *  inference information in the bound change, such that in conflict analysis, this change is treated like a branching
 *  decision
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can only be called if @p scip is in stage \ref SCIP_STAGE_SOLVING
 */
SCIP_RETCODE SCIPchgVarUbNode(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_NODE*            node,               /**< node to change bound at, or NULL for current node */
   SCIP_VAR*             var,                /**< variable to change the bound for */
   SCIP_Real             newbound            /**< new value for bound */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarUbNode", FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   if( node == NULL )
   {
      SCIP_CALL( SCIPchgVarUb(scip, var, newbound) );
   }
   else
   {
      SCIPvarAdjustUb(var, scip->set, &newbound);

      /* ignore tightenings of upper bounds to -infinity during solving process */
      if( SCIPisInfinity(scip, -newbound) && SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
      {
#ifndef NDEBUG
         SCIPwarningMessage(scip, "ignore upper bound tightening for %s from %e to -infinity\n", SCIPvarGetName(var),
            SCIPvarGetUbLocal(var));
#endif
         return SCIP_OKAY;
      }

      SCIP_CALL( SCIPnodeAddBoundchg(node, scip->mem->probmem, scip->set, scip->stat, scip->transprob, scip->origprob,
            scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue, scip->cliquetable, var, newbound,
            SCIP_BOUNDTYPE_UPPER, FALSE) );
   }

   return SCIP_OKAY;
}

/** changes global lower bound of variable; if possible, adjust bound to integral value; also tightens the local bound,
 *  if the global bound is better than the local bound
 *
 *  @warning If SCIP is in presolving stage, it can happen that the internal variable array (which can be accessed via
 *           SCIPgetVars()) gets resorted.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note During presolving, an integer variable whose bound changes to {0,1} is upgraded to a binary variable.
 */
SCIP_RETCODE SCIPchgVarLbGlobal(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR*             var,                /**< variable to change the bound for */
   SCIP_Real             newbound            /**< new value for bound */
   )
{
   SCIP_CALL( SCIPcheckStage(scip, "SCIPchgVarLbGlobal", FALSE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   SCIPvarAdjustLb(var, scip->set, &newbound);

   /* ignore tightenings of lower bounds to +infinity during solving process */
   if( SCIPisInfinity(scip, newbound) && SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
   {
#ifndef NDEBUG
      SCIPwarningMessage(scip, "ignore lower bound tightening for %s from %e to +infinity\n", SCIPvarGetName(var),
         SCIPvarGetLbLocal(var));
#endif
      return SCIP_OKAY;
   }

   switch( scip->set->stage )
   {
   case SCIP_STAGE_PROBLEM:
      assert(!SCIPvarIsTransformed(var));
      SCIP_CALL( SCIPvarChgLbGlobal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, scip->cliquetable, newbound) );
      SCIP_CALL( SCIPvarChgLbLocal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, newbound) );
      SCIP_CALL( SCIPvarChgLbOriginal(var, scip->set, newbound) );
      break;

   case SCIP_STAGE_TRANSFORMING:
   case SCIP_STAGE_TRANSFORMED:
      SCIP_CALL( SCIPvarChgLbGlobal(var, scip->mem->probmem, scip->set, scip->stat, scip->lp,
            scip->branchcand, scip->eventqueue, scip->cliquetable, newbound) );
      break;

   case SCIP_STAGE_PRESOLVING:
      if( !SCIPinProbing(scip) )
      {
         assert(SCIPtreeGetCurrentDepth(scip->tree) == 0);
         assert(scip->tree->root == SCIPtreeGetCurrentNode(scip->tree));

         SCIP_CALL( SCIPnodeAddBoundchg(scip->tree->root, scip->mem->probmem, scip->set, scip->stat, scip->transprob,
               scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue, scip->cliquetable, var, newbound,
               SCIP_BOUNDTYPE_LOWER, FALSE) );

         if( (SCIP_VARTYPE)var->vartype == SCIP_VARTYPE_INTEGER && SCIPvarIsBinary(var) )
         {
            SCIP_Bool infeasible;

            SCIP_CALL( SCIPchgVarType(scip, var, SCIP_VARTYPE_BINARY, &infeasible) );
            assert(!infeasible);
         }
         break;
      }
      /*lint -fallthrough*/
   case SCIP_STAGE_SOLVING:
      SCIP_CALL( SCIPnodeAddBoundchg(scip->tree->root, scip->mem->probmem, scip->set, scip->stat, scip->transprob,
            scip->origprob, scip->tree, scip->reopt, scip->lp, scip->branchcand, scip->eventqueue, scip->cliquetable, var, newbound,
            SCIP_BOUNDTYPE_LOWER, FALSE) );
      break;

   default:
      SCIPerrorMessage("invalid SCIP stage <%d>\n", scip->set->stage);
      return SCIP_INVALIDCALL;
   }  /*lint !e788*/

   return SCIP_OKAY;
}

/** changes global upper bound of variable; if possible, adjust bound to integral value; also tightens the local bound,
 *  if the global bound is better than the local bound
 *
 *  @warning If SCIP is in presolving stage, it can happen that the internal variable array (which can be accessed via
 *           SCIPgetVars()) gets resorted.
 *
 *  @return \ref SCIP_OKAY is returned if everything worked. Otherwise a suitable error code is passed. See \ref
 *          SCIP_Retcode "SCIP_RETCODE" for a complete list of error codes.
 *
 *  @pre This method can be called if @p scip is in one of the following stages:
 *       - \ref SCIP_STAGE_PROBLEM
 *       - \ref SCIP_STAGE_TRANSFORMING
 *       - \ref SCIP_STAGE_TRANSFORMED
 *       - \ref SCIP_STAGE_PRESOLVING
 *       - \ref SCIP_STAGE_SOLVING
 *
 *  @note During presolving, an integer variable whose bound changes to {0,1} is upgraded to a binary variable.
 */
SCIP_RETCODE