Opt.cpp

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 *   Copyright (C) 2015 by Laboratoire d'Economie Forestière               *
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#include <stdlib.h>

#include <cassert>

#include <map>
#include <adolc/drivers/drivers.h>
#include <adolc/adolc_sparse.h>

#include "Opt.h"

#include "ModelData.h"
#include "Pixel.h"
#include "ThreadManager.h"
#include "Scheduler.h"
#include "ModelRegion.h"
#include "Opt.h"

#define CONSTRAIN_START_LOOP(pVector,cn) \
  for (uint r1=0;r1<l2r.size();r1++){ \
    for (uint r2=0;r2<l2r[r1].size();r2++){ \
      for (uint p=0;p<(pVector).size();p++){ \
        int psec = p+nPriPr; \
        cix = gix((cn), r1, r2, p);
#define CONSTRAIN_END_LOOP \
  }}}


using namespace Ipopt;

typedef std::map<string, endvar>        VarMap;
typedef std::pair<std::string, endvar > VarPair;

// ****** MODEL IMPLEMENTATION START HERE ********************************


void
Opt::declareVariables(){
    // filling the list of variables and their domain and optionally their bonds
    // if you add variables in the model that enter optimisation you'll have to add them here
    // the underlying map goes automatically in alphabetical order
    // original order: pc,pl,dc,dl,da,sc,sl,sa,exp
    // 20140328: if these vars have a lower bound > 0 the model doesn't solve when volumes in a region go to zero !!!

    // syntax: declareVariable("name", domainType, lbound[default=0], ubound[default= +inf], variable defining lower bounds[default=""], variable defining upper bound[default=""])

    // all variables have upper or equal than zero bound:
    declareVariable("da", DOM_SEC_PR,    "Demand from abroad (imports)");
    declareVariable("dc", DOM_SEC_PR,    "Demand, composite");
    declareVariable("dl", DOM_ALL_PR,    "Demand from local");
    declareVariable("pc", DOM_ALL_PR,    "Price, composite");
    declareVariable("pl", DOM_ALL_PR,    "Price, local") ;
    declareVariable("rt", DOM_R2_ALL_PR, "Regional trade"); //it was exp in gams
    declareVariable("sa", DOM_PRI_PR,    "Supply to abroad (exports)");
    declareVariable("sc", DOM_PRI_PR,    "Supply, composite");
    declareVariable("sl", DOM_ALL_PR,    "Supply to locals");
    //declareVariable("st", DOM_PRI_PR,    "Supply, total", 0.0,UBOUND_MAX,"","in");
}
/**
Declare the constrains and their properties. For the domain type @see BaseClass
*/
void
Opt::declareConstrains (){
  // domain of constrains variables
  // for domain
  constrain mkeq2;
  mkeq2.name="mkeq2";
  mkeq2.comment="[h1] Conservation of matters of transformed products";
  mkeq2.domain=DOM_SEC_PR;
  mkeq2.direction = CONSTR_EQ;
  //mkeq2.evaluate = Opt::mkteq2f;

  constrain mkeq3;
  mkeq3.name="mkeq3";
  mkeq3.comment="[h2] Conservation of matters of raw products";
  mkeq3.domain=DOM_PRI_PR;
  mkeq3.direction = CONSTR_EQ;
  //mkeq3.evaluate = Opt::mkteq3f;

  constrain mkeq4;
  mkeq4.name="mkeq4";
  mkeq4.comment="[eq 13] Leontief transformation function";
  mkeq4.domain=DOM_PRI_PR;
  mkeq4.direction = CONSTR_EQ;

  constrain mkeq5;
  mkeq5.name="mkeq5";
  mkeq5.comment="[eq 21] Raw product supply function";
  mkeq5.domain=DOM_PRI_PR;
  mkeq5.direction = CONSTR_EQ;

  constrain mkeq6;
  mkeq6.name="mkeq6";
  mkeq6.comment="[eq 20] Trasformed products demand function";
  mkeq6.domain=DOM_SEC_PR;
  mkeq6.direction = CONSTR_EQ;

  constrain mkeq7;
  mkeq7.name="mkeq7";
  mkeq7.comment="[h7 and h3] Transformed products import function";
  mkeq7.domain=DOM_SEC_PR;
  mkeq7.direction = CONSTR_EQ;

  constrain mkeq8;
  mkeq8.name="mkeq8";
  mkeq8.comment="[h8 and h4] Raw products export function";
  mkeq8.domain=DOM_PRI_PR;
  mkeq8.direction = CONSTR_EQ;

  constrain mkeq13;
  mkeq13.name="mkeq13";
  mkeq13.comment="[h9] Calculation of the composite price of transformed products (PPC_Dp)";
  mkeq13.domain=DOM_SEC_PR;
  mkeq13.direction = CONSTR_EQ;

  constrain mkeq14;
  mkeq14.name="mkeq14";
  mkeq14.comment="[h10] Calculation of the composite price of raw products (PPC_Sw)";
  mkeq14.domain=DOM_PRI_PR;
  mkeq14.direction = CONSTR_EQ;

  constrain mkeq17;
  mkeq17.name="mkeq17";
  mkeq17.comment="[h16] Constrain of the transformaton supply (lower than the regional maximal production capacity)";
  mkeq17.domain=DOM_SEC_PR;
  mkeq17.direction = CONSTR_LE0;


  constrain mkeq23;
  mkeq23.name="mkeq23";
  mkeq23.comment="[h3] Composit demand eq. (Dp)";
  mkeq23.domain=DOM_SEC_PR;
  mkeq23.direction = CONSTR_EQ;

  constrain mkeq24;
  mkeq24.name="mkeq24";
  mkeq24.comment="[h4] Composite supply eq. (Sw)";
  mkeq24.domain=DOM_PRI_PR;
  mkeq24.direction = CONSTR_EQ;

  constrain mkeq26;
  mkeq26.name="mkeq26";
  mkeq26.comment="[eq ] Verification of the null transport agents supply";
  mkeq26.domain=DOM_R2_ALL_PR;
  mkeq26.direction = CONSTR_LE0;

  constrain mkeq25;
  mkeq25.name="mkeq25";
  mkeq25.comment="Verification of the null trasformers supply (price of raw product + trasf product > trasf product)";
  mkeq25.domain=DOM_SEC_PR;
  mkeq25.direction = CONSTR_GE0;

  constrain mkeq18;
  mkeq18.name="mkeq18";
  mkeq18.comment="Constrain on raw material supply (lower than inventory)";
  mkeq18.domain=DOM_PRI_PR;
  mkeq18.direction = CONSTR_LE0;

  constrain resbounds;
  resbounds.name="resbounds";
  resbounds.comment="Constrain on raw material supply (lower than inventory, for each possible combination of primary products)";
  resbounds.domain=DOM_PRI_PR_ALLCOMBS;
  resbounds.direction = CONSTR_LE0;



  //constrain steq;
  //steq.name="steq";
  //steq.comment="computation of total supply";
  //steq.domain=DOM_PRI_PR;
  //steq.direction = CONSTR_EQ;

  cons.push_back(mkeq2);
  cons.push_back(mkeq6);
  cons.push_back(mkeq7);
  cons.push_back(mkeq13);
  cons.push_back(mkeq23);
  cons.push_back(mkeq3);
  cons.push_back(mkeq4);
  cons.push_back(mkeq5);
  cons.push_back(mkeq8);
  cons.push_back(mkeq14);
  cons.push_back(mkeq24);
  cons.push_back(mkeq17);
  cons.push_back(mkeq26);
  cons.push_back(mkeq25);
  //cons.push_back(mkeq18);
  cons.push_back(resbounds);
  //cons.push_back(steq);
;



}
/**
Define the objective function
*/
template<class T> bool
Opt::eval_obj(Index n, const T *x, T& obj_value){

  double aa, bb, dc0, sigma, a_pr, ct, m, zeromax,supCorr2;
  obj_value = 0.;
  zeromax = 0.;

  for (uint r1=0;r1<l2r.size();r1++){
    for (uint r2=0;r2<l2r[r1].size();r2++){
    //  // consumer's surplus..
    //  sum ((i,p_tr),
    //    AA(i,p_tr)*(RVAR('dc',i,p_tr)**((sigma(p_tr)+1)/sigma(p_tr)))
    //    - AA(i,p_tr)*((0.5*dc0(i,p_tr))**((sigma(p_tr)+1)/sigma(p_tr)))
    //    - RVAR('pc',i,p_tr)*RVAR('dc',i,p_tr)
    //  )
    // 20161003: TODO: check if subsidies should enter also the obj function other than the bounds equations. For the moment, as agreed with Sylvain, they are left outside the obj function, but I am not sure of it.
    // 20170306: Subsides (but not substitute products) added to the aa and bb parameters. They do not change anything.
    // 20170307: obj_value does not account for the minus 0-5dc0 part anymore. It doesn't chang anything if not that the "reported" surplus is negative.
    //           The integral of a power function p=q^a with a < -1 (derived from an q=p^b function with b between 0 and -1) is negative ranging from -inf at q=0
    //           to 0- with q = +inf
      for (uint p=0;p<secPr.size();p++){
        aa = gpd("aa",l2r[r1][r2],secPr[p]);
        sigma = gpd("sigma",l2r[r1][r2],secPr[p]);
        dc0 = gpd("dc",l2r[r1][r2],secPr[p],secondYear);
        //obj_value += aa*pow(mymax(zeromax,x[gix("dc",r1,r2,p)]),(sigma+1)/sigma)-aa*pow(mymax(zeromax,0.5*dc0),(sigma+1)/sigma)-x[gix("pc",r1,r2,p+nPriPr)]*x[gix("dc",r1,r2,p)];
        obj_value += aa*pow(mymax(zeromax,x[gix("dc",r1,r2,p)]),(sigma+1)/sigma)-x[gix("pc",r1,r2,p+nPriPr)]*x[gix("dc",r1,r2,p)];

      }
      //  // producers surplus..
      //  + sum((i,p_pr),
      //    RVAR('pc',i,p_pr)*RVAR('sc',i,p_pr)
      //    - BB(i,p_pr)*(RVAR('sc',i,p_pr)**((sigma(p_pr)+1)/sigma(p_pr)))
      //  )
      for (uint p=0;p<priPr.size();p++){
        bb = gpd("bb",l2r[r1][r2],priPr[p]);
        sigma = gpd("sigma",l2r[r1][r2],priPr[p]);
        //supCorr2 = gpd("supCorr2",l2r[r1][r2],priPr[p]);
        obj_value += x[gix("pc",r1,r2,p)]*x[gix("sc",r1,r2,p)] - bb*pow(mymax(zeromax,x[gix("sc",r1,r2,p)]),((sigma+1)/sigma));
      }
      //  // trasformations between primary products
      //  + sum ((i,p_pr,p_pr2),
      //  +RVAR('pc',i,p_pr2)*pres(p_pr,p_pr2)*RVAR('sc',i,p_pr)
      //  -BB(i,p_pr2)*(pres(p_pr,p_pr2)*RVAR('sc',i,p_pr))**((sigma(p_pr2)+1)/sigma(p_pr2))
      //   )

      for (uint p1=0;p1<priPr.size();p1++){
        for (uint p2=0;p2<priPr.size();p2++){
          a_pr = gpd("a_pr",l2r[r1][r2],priPr[p1],DATA_NOW,priPr[p2]);
          bb = gpd("bb",l2r[r1][r2],priPr[p2]);
          sigma = gpd("sigma",l2r[r1][r2],priPr[p2]);
          obj_value += x[gix("pc",r1,r2,p2)]*a_pr*x[gix("sc",r1,r2,p1)]-bb*pow(mymax(zeromax,a_pr*x[gix("sc",r1,r2,p1)]),(sigma+1)/sigma);
        }
      }
      //  // surplus of transport agents..
      //  + sum((i,j,prd), (RVAR('pl',j,prd)-RVAR('pl',i,prd)-CT(i,j,prd))*EXP(i,j,prd))
      for (uint p=0;p<allPr.size();p++){
        for (uint r2To=0;r2To<l2r[r1].size();r2To++){
          ct = (gpd("ct",l2r[r1][r2],allPr[p],DATA_NOW,i2s(l2r[r1][r2To])) * gpd("pol_tcSub",l2r[r1][r2],allPr[p]));
          obj_value += (x[gix("pl",r1,r2To,p)]-x[gix("pl",r1,r2,p)]-ct)*x[gix("rt",r1,r2,p,r2To)];
        }
      }

      //  // transformers surplus..
      //  + sum((i,p_tr), (RVAR('pl',i,p_tr)-m(i,p_tr))*(RVAR('sl',i,p_tr))) // attenction it's local. if we include w imports or p expports this have to change
      for (uint p=0;p<secPr.size();p++){
        m = (gpd("m",l2r[r1][r2],secPr[p]) * gpd("pol_trSub",l2r[r1][r2],secPr[p]));
        obj_value += (x[gix("pl",r1,r2,p+nPriPr)]-m)*x[gix("sl",r1,r2,p+nPriPr)];
      }
      //  - sum((i,p_pr), RVAR('pl',i,p_pr)*RVAR('dl',i,p_pr))               // to total and an other equation total=local+abroad should be added
      for (uint p=0;p<priPr.size();p++){
        obj_value -= x[gix("pl",r1,r2,p)]*x[gix("dl",r1,r2,p)];
      }
    } // end of each lev2 regions

  } //end of each r1 regions

  //obj_value = -obj_value; // we want maximisation, ipopt minimize! (donei n the options - scaling obj function)

 //exit(0);
  return true;
  // checked 20120802 this function is ok with gams, both in input and in output of the preoptimisation stage

}



/** Template function to implement (define) the previously declared constains.
To the initial macro loop it must be passed the product vector over where to loop (priPr, secPr or allPr) and the order of the constrain has it has been added to the const vector.
It could be possible to change this in a map and uses name, but then we would loose control on the constrains order, and we saw that it matters for finding the equilibrium.

*/
template<class T> bool
Opt::eval_constraints(Index n, const T *x, Index m, T* g){

  double a_pr, a, sigma, ff, pol_mktDirInt_s, pol_mktDirInt_d, pol_mktDirInt_d_pSubstituted, pol_mktDirInt_d_1, pol_mktDirInt_d_1_pSubstituted, gg, q1, p1v, t1, r1v, psi, eta, pworld, ct, k, dispor, mv, in, in_1, supCorr, es_d, pc_1, pc_pSubstituted, pc_1_pSubstituted, additionalDemand;
  Index cix = 0;
  Index debug = 0;

  // mkteq2(i,p_tr)..  RVAR('dl',i,p_tr)+sum(j,EXP(i,j,p_tr))  =e=  RVAR('sl',i,p_tr)+ sum(b,EXP(b,i,p_tr)); // h1
  CONSTRAIN_START_LOOP(secPr, 0) // attenction! you have to give the same order number as you inserted in the cons vector
    //g[cix] = x[gix("dl",r1,r2,psec)]-x[gix("sl",r1,r2,psec)]+x[gix("da",r1,r2,p)];
    g[cix] = x[gix("dl",r1,r2,psec)]-x[gix("sl",r1,r2,psec)];
    for (uint r2To=0;r2To<l2r[r1].size();r2To++){
      g[cix] += x[gix("rt",r1,r2,psec,r2To)]-x[gix("rt",r1,r2To,psec,r2)];
    }
  CONSTRAIN_END_LOOP


  // mkteq6(i,p_tr)..  RVAR('dc',i,p_tr)  =e=  GG(i,p_tr)*(RVAR('pc',i,p_tr)**sigma(p_tr)); // eq. 20 20160216: added sustitution elasticity in the demand
  // DEMAND EQUATION of transformed products
  CONSTRAIN_START_LOOP(secPr,1)
    gg         = gpd("gg",l2r[r1][r2],secPr[p]);
    sigma      = gpd("sigma",l2r[r1][r2],secPr[p]);
    pc_1       = gpd("pc",l2r[r1][r2],secPr[p],previousYear);
    pol_mktDirInt_d   = gpd("pol_mktDirInt_d",l2r[r1][r2],secPr[p]);              // market policies (subs or taxes) this year
    pol_mktDirInt_d_1 = gpd("pol_mktDirInt_d",l2r[r1][r2],secPr[p],previousYear); // market policies previous year
    additionalDemand = gpd("additionalDemand",l2r[r1][r2],secPr[p]);
    g[cix]     = - gg*pow(x[gix("pc",r1,r2,psec)]*pol_mktDirInt_d,sigma);  // note that putting 0.0 and 0.000 IS NOT the same thing. With 0.000 I have a seg fault in ADOL-C !!
    vector<string> debug = secPr;
    // Substitution part within forest producs (whose price is endogenous to the model)..
    for (uint p2=0;p2<secPr.size();p2++){
      es_d     = gpd("es_d",l2r[r1][r2],secPr[p],DATA_NOW,secPr[p2]);
      if(es_d){
        pc_1_pSubstituted    = gpd("pc",l2r[r1][r2],secPr[p2],previousYear);
        pol_mktDirInt_d_pSubstituted   = gpd("pol_mktDirInt_d",l2r[r1][r2],secPr[p2]);               // market policies this year for the substitute product
        pol_mktDirInt_d_1_pSubstituted = gpd("pol_mktDirInt_d",l2r[r1][r2],secPr[p2],previousYear);  // market policies last year for the substitute product

        g[cix] *= pow(
                 (
                   ((x[gix("pc",r1,r2,psec)]*pol_mktDirInt_d) / (x[gix("pc",r1,r2,priPr.size()+p2)]*pol_mktDirInt_d_pSubstituted))
                      /
                   ((pc_1*pol_mktDirInt_d_1) / (pc_1_pSubstituted*pol_mktDirInt_d_1_pSubstituted))
                 ), es_d
               );
      }
    }
    // Substitution part with other products with exogenous prices (e.g. fossilFuels)..
    for (uint p3=0;p3<othPr.size();p3++){
      es_d     = gpd("es_d",l2r[r1][r2],secPr[p],DATA_NOW,othPr[p3]);
      if(es_d){
        pc_pSubstituted    = gpd("pl",l2r[r1][r2],othPr[p3],DATA_NOW);
        pc_1_pSubstituted  = gpd("pl",l2r[r1][r2],othPr[p3],previousYear);

        g[cix] *= pow(
                 (
                   (x[gix("pc",r1,r2,psec)] / pc_pSubstituted)
                      /
                   (pc_1 / pc_1_pSubstituted)
                 ), es_d
               );
      }
    }
    //g[cix] = x[gix("dc",r1,r2,p)]-gg*pow(x[gix("pc",r1,r2,psec)],sigma); // original without substitution elasticity
    g[cix] += x[gix("dc",r1,r2,p)]-additionalDemand;
  CONSTRAIN_END_LOOP


  // mkteq7(i,p_tr)..  RVAR('da',i,p_tr)/RVAR('dl',i,p_tr)  =e=  ((q1(i,p_tr)*RVAR('pl',i,p_tr))/(p1(i,p_tr)*PT_t(p_tr)))**psi(i,p_tr); // h7 and h3 ?
  CONSTRAIN_START_LOOP(secPr,2)
    q1 = gpd("q1_polCorr",l2r[r1][r2],secPr[p]);
    p1v = 1-q1;
    psi = gpd("psi",l2r[r1][r2],secPr[p]);
    pworld = gpd("pl", worldCodeLev2,secPr[p]);
    g[cix] = x[gix("da",r1,r2,p)]/x[gix("dl",r1,r2,psec)] - pow((q1*x[gix("pl",r1,r2,psec)])/(p1v*pworld),psi);
  CONSTRAIN_END_LOOP

  // mkteq13(i,p_tr).. RVAR('pc',i,p_tr)*RVAR('dc',i,p_tr)  =e=  RVAR('dl',i,p_tr)*RVAR('pl',i,p_tr)+RVAR('da',i,p_tr)*PT_t(p_tr);  // h9
  CONSTRAIN_START_LOOP(secPr,3)
    pworld = gpd("pl", worldCodeLev2,secPr[p]);
    g[cix] = x[gix("pc",r1,r2,psec)]*x[gix("dc",r1,r2,p)]-x[gix("dl",r1,r2,psec)]*x[gix("pl",r1,r2,psec)]-x[gix("da",r1,r2,p)]*pworld;
  CONSTRAIN_END_LOOP

  // mkteq23(i,p_tr).. RVAR('dc',i,p_tr)  =e=  (q1(i,p_tr)*(RVAR('da',i,p_tr)**((psi(i,p_tr)-1)/psi(i,p_tr)))+ p1(i,p_tr)*(RVAR('dl',i,p_tr)**((psi(i,p_tr)-1)/psi(i,p_tr))))**(psi(i,p_tr)/(psi(i,p_tr)-1)); // h3
  CONSTRAIN_START_LOOP(secPr,4)
    q1 = gpd("q1_polCorr",l2r[r1][r2],secPr[p]);
    psi = gpd("psi",l2r[r1][r2],secPr[p]);
    p1v = 1-q1;
    g[cix] = x[gix("dc",r1,r2,p)] -
      pow(
            q1 * pow(x[gix("da",r1,r2,p)],(psi-1)/psi)
          + p1v * pow(x[gix("dl",r1,r2,psec)],(psi-1)/psi),
          psi/(psi-1)
      );
  CONSTRAIN_END_LOOP

  // mkteq3(i,p_pr)..  RVAR('dl',i,p_pr)+sum(j,EXP(i,j,p_pr))   =e=  RVAR('sl',i,p_pr)+ sum(b,EXP(b,i,p_pr))+sum(p_pr2, pres(p_pr2,p_pr)* RVAR('sl',i,p_pr2)); // h2
  CONSTRAIN_START_LOOP(priPr,5)
    //g[cix] = x[gix("dl",r1,r2,p)]-x[gix("sl",r1,r2,p)]-x[gix("sa",r1,r2,p)];
    g[cix] = x[gix("dl",r1,r2,p)]-x[gix("sl",r1,r2,p)];
    for (uint r2To=0;r2To<l2r[r1].size();r2To++){
      g[cix] += x[gix("rt",r1,r2,p,r2To)]-x[gix("rt",r1,r2To,p,r2)];
    }
    for (uint p2=0;p2<priPr.size();p2++){
      a_pr = gpd("a_pr",l2r[r1][r2],priPr[p2],DATA_NOW,priPr[p]);
      g[cix] -= a_pr*x[gix("sl",r1,r2,p2)];
    }
  CONSTRAIN_END_LOOP

  //mkteq4(i,p_pr)..  RVAR('dl',i,p_pr)  =e=  sum(p_tr, a(p_pr,p_tr)*(RVAR('sl',i,p_tr))); // eq. 13
  CONSTRAIN_START_LOOP(priPr,6)
    g[cix] = x[gix("dl",r1,r2,p)];
    for (uint p2=0;p2<secPr.size();p2++){
      a = gpd("a",l2r[r1][r2],priPr[p],DATA_NOW,secPr[p2]);
      g[cix] -= a*x[gix("sl",r1,r2,p2+nPriPr)];
    }
  CONSTRAIN_END_LOOP


  // mkteq5(i,p_pr)..  RVAR('sc',i,p_pr)  =e=  FF(i,p_pr)*(RVAR('pc',i,p_pr)**sigma(p_pr)); // eq. 21
  // SUPPLY EQUATION OF PRIMARY PRODUCTS


  CONSTRAIN_START_LOOP(priPr,7)
    ff = gpd("ff",l2r[r1][r2],priPr[p]);
    pol_mktDirInt_s = gpd("pol_mktDirInt_s",l2r[r1][r2],priPr[p]);
    sigma = gpd("sigma",l2r[r1][r2],priPr[p]);

    // Added for carbon project ----------------------
    double carbonPrice = gpd("carbonPrice",l2r[r1][r2],"",DATA_NOW); //using dummy region until Anto solves issue // Solved and generalised ;-)
    double intRate     = MTHREAD->MD->getDoubleSetting("ir");
    double Pct         = carbonPrice*intRate;
    double omega       = gpd("co2content_products", l2r[r1][r2], priPr[p])/1000;  // Generalised
    // ------------------------------------------------

    g[cix] = x[gix("sc",r1,r2,p)]-ff*pow((x[gix("pc",r1,r2,p)]-omega*Pct)*pol_mktDirInt_s,sigma);
    // -----------------------------------------------

    //g[cix] = x[gix("sc",r1,r2,p)]-ff*pow(x[gix("pc",r1,r2,p)]*pol_mktDirInt_s,sigma);
  CONSTRAIN_END_LOOP


 // mkteq8(i,p_pr)..  RVAR('sa',i,p_pr)/RVAR('sl',i,p_pr)  =e=  ((t1(i,p_pr)*RVAR('pl',i,p_pr))/(r1(i,p_pr)*PT_t(p_pr)))**eta(i,p_pr); // h8 and h4 ?
  CONSTRAIN_START_LOOP(priPr,8)
    t1 = gpd("t1_polCorr",l2r[r1][r2],priPr[p]);
    r1v = 1-t1;
    eta = gpd("eta",l2r[r1][r2],priPr[p]);
    pworld = gpd("pl", worldCodeLev2,priPr[p]);
    g[cix] = x[gix("sa",r1,r2,p)]/x[gix("sl",r1,r2,p)] - pow((t1*x[gix("pl",r1,r2,p)])/(r1v*pworld),eta);
  CONSTRAIN_END_LOOP

  // mkteq14(i,p_pr).. RVAR('pc',i,p_pr)*RVAR('sc',i,p_pr)  =e=  RVAR('sl',i,p_pr)*RVAR('pl',i,p_pr)+RVAR('sa',i,p_pr)*PT_t(p_pr);  // h10
  CONSTRAIN_START_LOOP(priPr,9)
    pworld = gpd("pl", worldCodeLev2,priPr[p]);
    g[cix] = x[gix("pc",r1,r2,p)]*x[gix("sc",r1,r2,p)]-x[gix("sl",r1,r2,p)]*x[gix("pl",r1,r2,p)]-x[gix("sa",r1,r2,p)]*pworld;
  CONSTRAIN_END_LOOP

  //mkteq24(i,p_pr).. RVAR('sc',i,p_pr)  =e=  (t1(i,p_pr)*(RVAR('sa',i,p_pr)**((eta(i,p_pr)-1)/eta(i,p_pr)))+ r1(i,p_pr)*(RVAR('sl',i,p_pr)**((eta(i,p_pr)-1)/eta(i,p_pr))))**(eta(i,p_pr)/(eta(i,p_pr)-1)); // h4
  CONSTRAIN_START_LOOP(priPr,10)
    t1 = gpd("t1_polCorr",l2r[r1][r2],priPr[p]);
    r1v = 1-t1;
    eta = gpd("eta",l2r[r1][r2],priPr[p]);
    g[cix] = x[gix("sc",r1,r2,p)] -
          pow(
             t1 * pow(x[gix("sa",r1,r2,p)],(eta-1)/eta)
          + r1v * pow(x[gix("sl",r1,r2,p)],(eta-1)/eta),
          eta/(eta-1)
        );
  CONSTRAIN_END_LOOP

  // mkteq17(i,p_tr).. RVAR('sl',i,p_tr)  =l=  Kt(i,p_tr);     // h16 in the presentation paper
  CONSTRAIN_START_LOOP(secPr,11)
    k = gpd("k",l2r[r1][r2],secPr[p]);
    g[cix] = x[gix("sl",r1,r2,p+nPriPr)]-k;
  CONSTRAIN_END_LOOP

  // mkeq26(i,prd,j).. RVAR('pl',j,prd)-RVAR('pl',i,prd)-CT(i,j,prd) =l= 0;
  CONSTRAIN_START_LOOP(allPr,12)
    for (uint r2To=0;r2To<l2r[r1].size();r2To++){
      cix = gix(12, r1, r2, p,r2To); // attenction we must redefine it, as we are now in a r2to loop
      ct = (gpd("ct",l2r[r1][r2],allPr[p],DATA_NOW,i2s(l2r[r1][r2To])) *  gpd("pol_tcSub",l2r[r1][r2],allPr[p])) ;
      g[cix] = (x[gix("pl",r1,r2To,p)]-x[gix("pl",r1,r2,p)]-ct);
    }
  CONSTRAIN_END_LOOP

  // mkteq25(i,p_tr).. sum(p_pr, a(p_pr,p_tr)*RVAR('pl',i,p_pr))+m(i,p_tr)  =g=  (RVAR('pl',i,p_tr));        // price of raw products + transf cost > trasf product
  CONSTRAIN_START_LOOP(secPr,13)
    mv = (gpd("m",l2r[r1][r2],secPr[p]) * gpd("pol_trSub",l2r[r1][r2],secPr[p]));
    g[cix] = mv - x[gix("pl",r1,r2,p+nPriPr)];
    for (uint p2=0;p2<priPr.size();p2++){
      a = gpd("a",l2r[r1][r2],priPr[p2],DATA_NOW,secPr[p]);
      g[cix] += a * x[gix("pl",r1,r2,p2)];
    }
  CONSTRAIN_END_LOOP

//  // mkteq18(i,p_pr).. RVAR('sa',i,p_pr)+RVAR('sl',i,p_pr)  =l=  dispor(i,p_pr); // total supply lower than the available stock
//  CONSTRAIN_START_LOOP(priPr,14)
//    in = gpd("in",l2r[r1][r2],priPr[p]);
//    double d1 = gix("sa",r1,r2,p);
//    double d2 = gix("sl",r1,r2,p);
//    g[cix] = x[gix("sa",r1,r2,p)]+x[gix("sl",r1,r2,p)]-in;
//  CONSTRAIN_END_LOOP

  // resbounds(i, p_pr_comb).. RVAR('sa',i,p_pr)+RVAR('sl',i,p_pr)  =l=  dispor(i,p_pr); // total supply lower than the available stock - FOR all combination subsets of ins
  CONSTRAIN_START_LOOP(priPrCombs,14)
    //ModelRegion* REG = MTHREAD->MD->getRegion(l2r[r1][r2]); // possibly slower
    //in = REG->inResByAnyCombination[p];
    in = ins[r1][r2][p];
    //if(p==0){
    //  in = 1.0; // workaround to lead -1<0 rather than 0<0 for the first (empty) subset - notneeded
    //}
    g[cix] = -in;
    for(uint i=0;i<priPrCombs[p].size();i++){
      g[cix] += x[gix("sa",r1,r2,priPrCombs[p][i])]+x[gix("sl",r1,r2,priPrCombs[p][i])];
    }
    g[cix] -= overharvestingAllowance; //0.02 don't work always, expecially intermediate scnearios, 0.1 seems to work but produce a large artefact 20160219: made it a parameter

  CONSTRAIN_END_LOOP

  //CONSTRAIN_START_LOOP(priPr,15)
  //    g[cix] = x[gix("st",r1,r2,p)]-(x[gix("sl",r1,r2,p)]+x[gix("sa",r1,r2,p)]);
  //CONSTRAIN_END_LOOP

  return true;
}


//  ******** NOTHING TO DO BELOW THIS LINE ********************************

Opt::Opt(ThreadManager* MTHREAD_h){
  MTHREAD = MTHREAD_h;
  nVar    = 0;
  nCons   = 0;
  debugRunOnce = false;
  initOpt = true;
}

Opt::~Opt(){

}


bool
Opt::get_nlp_info(Index& n, Index& m, Index& nnz_jac_g,
                  Index& nnz_h_lag, IndexStyleEnum& index_style){


  if(initOpt){
    // does this initialisation code only once
    priPr = MTHREAD->MD->getStringVectorSetting("priProducts");
    secPr = MTHREAD->MD->getStringVectorSetting("secProducts");
    othPr = MTHREAD->MD->getStringVectorSetting("othExogenousProducts");
    allPr = priPr;
    allPr.insert( allPr.end(), secPr.begin(), secPr.end() );
    nPriPr = priPr.size();
    nSecPr = secPr.size();
    nAllPr = allPr.size();
    nOthPr = othPr.size();
    std::vector<int> l1regIds =  MTHREAD->MD->getRegionIds(1, true);
    nL2r =  MTHREAD->MD->getRegionIds(2, true).size();
    firstYear = MTHREAD->MD->getIntSetting("initialYear");
    secondYear = firstYear+1;
    worldCodeLev2 = MTHREAD->MD->getIntSetting("worldCodeLev2");

    for(uint i=0;i<l1regIds.size();i++){
      std::vector<int> l2ChildrenIds;
      ModelRegion* l1Region = MTHREAD->MD->getRegion(l1regIds[i]);
      std::vector<ModelRegion*> l2Childrens = l1Region->getChildren(true);
      for(uint j=0;j<l2Childrens.size();j++){
        l2ChildrenIds.push_back(l2Childrens[j]->getRegId());
      }
      if(l2ChildrenIds.size()){
        l2r.push_back(l2ChildrenIds);
      }
    }

    // Create a vector with all possible combinations of primary products
    priPrCombs = MTHREAD->MD->createCombinationsVector(nPriPr);
    nPriPrCombs = priPrCombs.size();

    // put the variables and their domain in the vars map
    declareVariables();

    // declaring the contrains...
    declareConstrains();

    // calculate number of variables and constrains..
    calculateNumberVariablesConstrains();

    // cache initial positions (variables and constrains)..
    cacheInitialPosition();

    // cache initial positions (variables and constrains)..
    cachePositions();

    //tempDebug();

    //debugPrintParameters();

  } // finish initialisation things to be done only the first year

  previousYear = MTHREAD->SCD->getYear()-1; // this has to be done EVERY years !!

  n = nVar; // 300; // nVar;
  m = nCons; // 70; // nCons;

  overharvestingAllowance = MTHREAD->MD->getDoubleSetting("overharvestingAllowance",DATA_NOW);

  copyInventoryResourses();

  generate_tapes(n, m, nnz_jac_g, nnz_h_lag);

  //if(initOpt){
  //  calculateSparsityPatternJ();
  //  calculateSparsityPatternH();
    //tempDebug();
  //}

  // use the C style indexing (0-based)
  index_style = C_STYLE;

  initOpt=false;
  return true;
}

bool
Opt::get_bounds_info(Index n, Number* x_l, Number* x_u, Index m, Number* g_l, Number* g_u){

  // Set the bounds for the endogenous variables..
  for (Index i=0; i<n; i++) {
    x_l[i] =  getBoundByIndex(LBOUND,i);
    x_u[i] =  getBoundByIndex(UBOUND,i);
  }

  // Set the bounds for the constraints..
  for (Index i=0; i<m; i++) {
    int direction = getConstrainDirectionByIndex(i);
    switch (direction){
      case CONSTR_EQ:
        g_l[i] = 0.;
        g_u[i] = 0.;
        break;
      case CONSTR_LE0:
        g_l[i] = -2e19;
        g_u[i] = 0.;
        break;
      case CONSTR_GE0:
        g_l[i] = 0.;
        g_u[i] = 2e19;
        break;
    }
  }
  return true;
}

bool
Opt::get_starting_point(Index n, bool init_x, Number* x, bool init_z, Number* z_L, Number* z_U,
                        Index m, bool init_lambda, Number* lambda){

  // function checked on 20120724 on a subset of 3 regions and 4 products. All variables initial values are correctly those outputed by gams in 2006.
  //int thisYear = MTHREAD->SCD->getYear();
  //int initialOptYear = MTHREAD->MD->getIntSetting("initialOptYear");
  //if(thisYear != initialOptYear) return true;

  //msgOut(MSG_DEBUG,"Giving optimising variables previous years value as starting point");
  // Here, we assume we only have starting values for x, if you code
  // your own NLP, you can provide starting values for the others if
  // you wish.
  assert(init_x == true);
  assert(init_z == false);
  assert(init_lambda == false);

  VarMap::iterator viter;

  // fixing the starting points for each variable at the level of the previous years
  for (viter = vars.begin(); viter != vars.end(); ++viter) {
    //string debugs = viter->first;
    int vdomtype = viter->second.domain;
    if(vdomtype==DOM_PRI_PR){
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<priPr.size();p++){
            x[gix(viter->first,r1,r2,p)]= gpd(viter->first,l2r[r1][r2],priPr[p],previousYear);
          }
        }
      }
    } else if (vdomtype==DOM_SEC_PR) {
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<secPr.size();p++){
            x[gix(viter->first,r1,r2,p)]= gpd(viter->first,l2r[r1][r2],secPr[p],previousYear);
          }
        }
      }
    } else if (vdomtype==DOM_ALL_PR) {
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<allPr.size();p++){
            x[gix(viter->first,r1,r2,p)]= gpd(viter->first,l2r[r1][r2],allPr[p],previousYear);
          }
        }
      }
    } else if (vdomtype==DOM_R2_ALL_PR) {
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<allPr.size();p++){
            for(uint r2To=0;r2To<l2r[r1].size();r2To++){
              x[gix(viter->first,r1,r2,p,r2To)]= gpd(viter->first,l2r[r1][r2],allPr[p],previousYear,i2s(l2r[r1][r2To]));
            }
          }
        }
      }
    } else {
      msgOut(MSG_CRITICAL_ERROR,"Try to setting the initial value of a variable of unknow type ("+viter->first+")");
    }
  }

  //msgOut(MSG_DEBUG,"Finisced initial value assignments");

  return true;
}


void
Opt::finalize_solution(SolverReturn status,
                       Index n, const Number* x, const Number* z_L, const Number* z_U,
                       Index m, const Number* g, const Number* lambda,
                       Number obj_value, const IpoptData* ip_data, IpoptCalculatedQuantities* ip_cq){

  printf("\n\nObjective value\n");
  printf("f(x*) = %e\n", obj_value);

  // --> here is where to code the assignment of optimal values to to spd()

  VarMap::iterator viter;

  // fixing the starting points for each variable at the level of the previous years
  for (viter = vars.begin(); viter != vars.end(); ++viter) {
    //string debugs = viter->first;
    int vdomtype = viter->second.domain;
    if(vdomtype==DOM_PRI_PR){
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<priPr.size();p++){
            spd(x[gix(viter->first,r1,r2,p)],viter->first,l2r[r1][r2],priPr[p]);
          }
        }
      }
    } else if (vdomtype==DOM_SEC_PR) {
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<secPr.size();p++){
            spd(x[gix(viter->first,r1,r2,p)],viter->first,l2r[r1][r2],secPr[p]);

          }
        }
      }
    } else if (vdomtype==DOM_ALL_PR) {
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<allPr.size();p++){
            spd(x[gix(viter->first,r1,r2,p)],viter->first,l2r[r1][r2],allPr[p]);
          }
        }
      }
    } else if (vdomtype==DOM_R2_ALL_PR) {
      for(uint r1=0;r1<l2r.size();r1++){
        for(uint r2=0;r2<l2r[r1].size();r2++){
          for(uint p=0;p<allPr.size();p++){
            for(uint r2To=0;r2To<l2r[r1].size();r2To++){
              //if(x[gix(viter->first,r1,r2,p,r2To)] > 0){
              //  cout << l2r[r1][r2] << "\t" << allPr[p] << "\t" << l2r[r1][r2To] << "\t" << x[gix(viter->first,r1,r2,p,r2To)] << endl;
              //}
              spd(x[gix(viter->first,r1,r2,p,r2To)],viter->first,l2r[r1][r2],allPr[p],DATA_NOW,false,i2s(l2r[r1][r2To]));
            }
          }
        }
      }
    } else {
      msgOut(MSG_CRITICAL_ERROR,"Try to setting the solved value of a variable of unknow type ("+viter->first+")");
    }
  }

    // memory deallocation of ADOL-C variables
    delete[] x_lam;

    free(rind_g);
    free(cind_g);

    delete[] rind_L;
    delete[] cind_L;

    free(rind_L_total);
    free(cind_L_total);
    free(jacval);
    free(hessval);

    for (int i=0;i<n+m+1;i++) {
        free(HP_t[i]);
    }
    free(HP_t);

}

//*************************************************************************
//
//
//         Nothing has to be changed below this point !!
//
//
//*************************************************************************


bool
Opt::eval_f(Index n, const Number* x, bool new_x, Number& obj_value){
  eval_obj(n,x,obj_value);

  return true;
}

bool
Opt::eval_grad_f(Index n, const Number* x, bool new_x, Number* grad_f){

  gradient(tag_f,n,x,grad_f);

  return true;
}

bool
Opt::eval_g(Index n, const Number* x, bool new_x, Index m, Number* g){

  eval_constraints(n,x,m,g);

  return true;
}

bool
Opt::eval_jac_g(Index n, const Number *x, bool new_x,Index m, Index nele_jac,
                Index* iRow, Index *jCol, Number* values){
  if (values == NULL) {
    // return the structure of the jacobian

    for(Index idx=0; idx<nnz_jac; idx++)
      {
  iRow[idx] = rind_g[idx];
  jCol[idx] = cind_g[idx];
      }
  }
  else {
    // return the values of the jacobian of the constraints

    sparse_jac(tag_g, m, n, 1, x, &nnz_jac, &rind_g, &cind_g, &jacval, options_g);

    for(Index idx=0; idx<nnz_jac; idx++)
      {
  values[idx] = jacval[idx];

      }
  }
  return true;
}

bool
Opt::eval_h(Index n, const Number* x, bool new_x, Number obj_factor, Index m, const Number* lambda,
            bool new_lambda, Index nele_hess, Index* iRow, Index* jCol, Number* values){

  //return false;

  if (values == NULL) {
    // return the structure. This is a symmetric matrix, fill the lower left
    // triangle only.

    for(Index idx=0; idx<nnz_L; idx++)
      {
  iRow[idx] = rind_L[idx];
  jCol[idx] = cind_L[idx];
      }
  }
  else {
    // return the values. This is a symmetric matrix, fill the lower left
    // triangle only

    for(Index idx = 0; idx<n ; idx++)
      x_lam[idx] = x[idx];
    for(Index idx = 0; idx<m ; idx++)
      x_lam[n+idx] = lambda[idx];
    x_lam[n+m] = obj_factor;

    sparse_hess(tag_L, n+m+1, 1, x_lam, &nnz_L_total, &rind_L_total, &cind_L_total, &hessval, options_L);

    Index idx = 0;
    for(Index idx_total = 0; idx_total <nnz_L_total ; idx_total++)
      {
  if((rind_L_total[idx_total] < (unsigned int) n) && (cind_L_total[idx_total] < (unsigned int) n))
    {
      values[idx] = hessval[idx_total];
      idx++;
    }
      }
  }

  return true;

  //return false;
}


//***************    ADOL-C part ***********************************

void
Opt::generate_tapes(Index n, Index m, Index& nnz_jac_g, Index& nnz_h_lag){
    /// Copied from http://bocop.org/
    Number *xp    = new double[n];
    Number *lamp  = new double[m];
    Number *zl    = new double[m];
    Number *zu    = new double[m];

    adouble *xa   = new adouble[n];
    adouble *g    = new adouble[m];
    adouble *lam  = new adouble[m];
    adouble sig;
    adouble obj_value;

    double dummy;
//  double *jacval;

    int i,j,k,l,ii;

    x_lam   = new double[n+m+1];

//  cout << " Avant get_start" << endl;
    get_starting_point(n, 1, xp, 0, zl, zu, m, 0, lamp);
//   cout << " Apres get_start" << endl;

    //if(initOpt){ // that's funny, if I use this I get it slighly longer times, whatever I then use trace_off() or trace_off(1) (save to disk, seems unnecessary). If I use regenerated tapes I have also slighly inaccurate results.
    trace_on(tag_f);

    for(Index idx=0;idx<n;idx++)
        xa[idx] <<= xp[idx];

    eval_obj(n,xa,obj_value);

    obj_value >>= dummy;

    trace_off();

    trace_on(tag_g);

    for(Index idx=0;idx<n;idx++)
        xa[idx] <<= xp[idx];

    eval_constraints(n,xa,m,g);


    for(Index idx=0;idx<m;idx++)
        g[idx] >>= dummy;

    trace_off();

    trace_on(tag_L);

    for(Index idx=0;idx<n;idx++)
        xa[idx] <<= xp[idx];
    for(Index idx=0;idx<m;idx++)
        lam[idx] <<= 1.0;
    sig <<= 1.0;

    eval_obj(n,xa,obj_value);

    obj_value *= sig;
    eval_constraints(n,xa,m,g);

    for(Index idx=0;idx<m;idx++)
        obj_value += g[idx]*lam[idx];

    obj_value >>= dummy;

    trace_off();
    //} // end of if initOpt()



    rind_g = NULL;
    cind_g = NULL;

    options_g[0] = 0;          /* sparsity pattern by index domains (default) */
    options_g[1] = 0;          /*                         safe mode (default) */
    options_g[2] = -1;         /*                     &jacval is not computed */
    options_g[3] = 0;          /*                column compression (default) */

    jacval=NULL;

    sparse_jac(tag_g, m, n, 0, xp, &nnz_jac, &rind_g, &cind_g, &jacval, options_g);

    options_g[2] = 0;
    nnz_jac_g = nnz_jac;

    unsigned int  **JP_f=NULL;                /* compressed block row storage */
    unsigned int  **JP_g=NULL;                /* compressed block row storage */
    unsigned int  **HP_f=NULL;                /* compressed block row storage */
    unsigned int  **HP_g=NULL;                /* compressed block row storage */
    unsigned int  *HP_length=NULL;            /* length of arrays */
    unsigned int  *temp=NULL;                 /* help array */

    int ctrl_H;

    JP_f = (unsigned int **) malloc(sizeof(unsigned int*));
    JP_g = (unsigned int **) malloc(m*sizeof(unsigned int*));
    HP_f = (unsigned int **) malloc(n*sizeof(unsigned int*));
    HP_g = (unsigned int **) malloc(n*sizeof(unsigned int*));
    HP_t = (unsigned int **) malloc((n+m+1)*sizeof(unsigned int*));
    HP_length = (unsigned int *) malloc((n)*sizeof(unsigned int));
    ctrl_H = 0;

    hess_pat(tag_f, n, xp, HP_f, ctrl_H);

    indopro_forward_safe(tag_f, 1, n, xp, JP_f);
    indopro_forward_safe(tag_g, m, n, xp, JP_g);
    nonl_ind_forward_safe(tag_g, m, n, xp, HP_g);

    for (i=0;i<n;i++)
    {
        if (HP_f[i][0]+HP_g[i][0]!=0)
        {
            if (HP_f[i][0]==0) // number of non zeros in the i-th row
            {
                HP_t[i] = (unsigned int *) malloc((HP_g[i][0]+HPOFF)*sizeof(unsigned int));
                for(j=0;j<=(int) HP_g[i][0];j++)
                {
                    HP_t[i][j] = HP_g[i][j];
                }
                HP_length[i] = HP_g[i][0]+HPOFF;
            }
            else
            {
                if (HP_g[i][0]==0) // number of non zeros in the i-th row
                {
                    HP_t[i] = (unsigned int *) malloc((HP_f[i][0]+HPOFF)*sizeof(unsigned int));
                    for(j=0;j<=(int) HP_f[i][0];j++)
                    {
                        HP_t[i][j] = HP_f[i][j];
                    }
                    HP_length[i] = HP_f[i][0]+HPOFF;
                }
                else
                {
                    HP_t[i] = (unsigned int *) malloc((HP_f[i][0]+HP_g[i][0]+HPOFF)*sizeof(unsigned int));
                    k = l = j = 1;
                    while ((k<=(int) HP_f[i][0]) && (l <= (int) HP_g[i][0]))
                    {
                        if (HP_f[i][k] < HP_g[i][l])
                        {
                            HP_t[i][j]=HP_f[i][k];
                            j++; k++;
                        }
                        else
                        {
                            if (HP_f[i][k] == HP_g[i][l])
                            {
                                HP_t[i][j]=HP_f[i][k];
                                l++;j++;k++;
                            }
                            else
                            {
                                HP_t[i][j]=HP_g[i][l];
                                j++;l++;
                            }
                        }
                    } // end while

                    // Fill the end of the vector if HP_g[i][0] < HP_f[i][0]
                    for(ii=k;ii<=(int) HP_f[i][0];ii++)
                    {
                        HP_t[i][j] = HP_f[i][ii];
                        j++;
                    }

                    // Fill the end of the vector if HP_f[i][0] < HP_g[i][0]
                    for(ii=l;ii<=(int) HP_g[i][0];ii++)
                    {
                        HP_t[i][j] = HP_g[i][ii];
                        j++;
                    }

                }
            }
            HP_t[i][0]=j-1; // set the first element with the number of non zeros in the i-th line
            HP_length[i] = HP_f[i][0]+HP_g[i][0]+HPOFF; // length of the i-th line
        }
        else
        {
            HP_t[i] = (unsigned int *) malloc((HPOFF+1)*sizeof(unsigned int));
            HP_t[i][0]=0;
            HP_length[i]=HPOFF;
        }

//     if (i==(int)n-1)
//     {
//       cout << " DISPLAY FINAL TIME HP : " << endl;
//       for (ii=0;ii<=(int)HP_length[i];ii++)
//         cout << " -------> HP[last][" << ii << "] = " << HP_t[i][ii] << endl;
//     }
    }

//   cout << " Avant les boucles" << endl;
//   cout << " m = " << m << endl;

    for (i=0;i<m;i++)
    {
//     cout << i << " --> nnz JP_g = " << JP_g[i][0]+1 << " -- ";
        HP_t[n+i] = (unsigned int *) malloc((JP_g[i][0]+1)*sizeof(unsigned int));
        HP_t[n+i][0]=JP_g[i][0];

//     cout << HP_t[n+i][0] << endl;

        for(j=1;j<= (int) JP_g[i][0];j++)
        {
            HP_t[n+i][j]=JP_g[i][j];
//       cout << " ---------> " << HP_t[n+i][j] << endl;
//       cout << " --> HP_length[" << JP_g[i][j] << "] = " << HP_length[JP_g[i][j]] << "  --  HP_t[" << JP_g[i][j] << "][0] = " << HP_t[JP_g[i][j]][0]+1 << endl;
            // We write the rows allocated in the previous "for" loop
            // If the memory allocated for the row is not big enough :
            if (HP_length[JP_g[i][j]] <= HP_t[JP_g[i][j]][0]+1) //! test avec "<=" (avant on avait "<" : bug, acces memoire non allouee)
            {
//         cout << " ---------> WARNING " << endl;
//         cout << " At index " << JP_g[i][j] << endl;


                // save a copy of existing vector elements :
                temp = (unsigned int *) malloc((HP_t[JP_g[i][j]][0]+1)*sizeof(unsigned int));
                for(l=0;l<=(int)HP_t[JP_g[i][j]][0];l++)
                {
                    temp[l] = HP_t[JP_g[i][j]][l]; //! valgrind : invalid read
//           cout << " -------> l = " << l << " -- " << temp[l] << endl;
                }

//         cout << " ----------->  DISPLAY " << endl;
//         for(l=0;l<=(int)HP_t[JP_g[i][j]][0];l++)
//         {
//           temp[l] = HP_t[JP_g[i][j]][l]; //! valgrind : invalid read & write
//           cout << " -------> HP[machin][" << l << "] = " << HP_t[JP_g[i][j]][l] << endl; //! valgrind : invalid read
//         }


                // Free existing row, and allocate more memory for it :
//         cout << " Avant free  --> pointeur = " <<HP_t[JP_g[i][j]]<< endl;
                unsigned int machin = JP_g[i][j];
                free(HP_t[machin]); // !Problem double free or corruption
//         cout << " Apres free --> pointeur = " <<HP_t[JP_g[i][j]]<< endl;

                HP_t[JP_g[i][j]] = (unsigned int *) malloc(2*HP_length[JP_g[i][j]]*sizeof(unsigned int));
                HP_length[JP_g[i][j]] = 2*HP_length[JP_g[i][j]];

                // Put back the values in this bigger vector :
                for(l=0;l<=(int)temp[0];l++)
                    HP_t[JP_g[i][j]][l] =temp[l];
                free(temp);

//         HP_t[JP_g[i][j]] = (unsigned int*) realloc (HP_t[JP_g[i][j]], 2*HP_length[JP_g[i][j]] * sizeof(unsigned int));
//         HP_length[JP_g[i][j]] = 2*HP_length[JP_g[i][j]];
            }
            HP_t[JP_g[i][j]][0] = HP_t[JP_g[i][j]][0]+1; // The size of the row is one greater than before
            HP_t[JP_g[i][j]][HP_t[JP_g[i][j]][0]] = i+n; // Now adding the element at the end //! valgrind : invalid write
        }
    }
//   cout << " Apres les boucles" << endl;

    for(j=1;j<= (int) JP_f[0][0];j++)
    {
        if (HP_length[JP_f[0][j]] <= HP_t[JP_f[0][j]][0]+1) //! test avec "<=" (pour etre coherent avec la remarque ci dessus, mais pas de cas test, a verifier)
        {
            temp = (unsigned int *) malloc((HP_t[JP_f[0][j]][0])*sizeof(unsigned int));
            for(l=0;l<=(int)HP_t[JP_f[0][j]][0];l++)
                temp[l] = HP_t[JP_f[0][j]][l];
            free(HP_t[JP_f[0][j]]);
            HP_t[JP_f[0][j]] = (unsigned int *) malloc(2*HP_length[JP_f[0][j]]*sizeof(unsigned int));
            HP_length[JP_f[0][j]] = 2*HP_length[JP_f[0][j]];
            for(l=0;l<=(int)temp[0];l++)
                HP_t[JP_f[0][j]][l] =temp[l];
            free(temp);
        }
        HP_t[JP_f[0][j]][0] = HP_t[JP_f[0][j]][0]+1;
        HP_t[JP_f[0][j]][HP_t[JP_f[0][j]][0]] = n+m;
    }

    HP_t[n+m] = (unsigned int *) malloc((JP_f[0][0]+2)*sizeof(unsigned int));
    HP_t[n+m][0]=JP_f[0][0]+1;
    for(j=1;j<= (int) JP_f[0][0];j++)
        HP_t[n+m][j]=JP_f[0][j];
    HP_t[n+m][JP_f[0][0]+1]=n+m;

    set_HP(tag_L,n+m+1,HP_t); // set sparsity pattern for the Hessian

    nnz_h_lag = 0;
    for (i=0;i<n;i++)
    {
        for (j=1;j<=(int) HP_t[i][0];j++)
            if ((int) HP_t[i][j] <= i)
                nnz_h_lag++;
        free(HP_f[i]);
        free(HP_g[i]);
    }
    nnz_L = nnz_h_lag;

    options_L[0] = 0;
    options_L[1] = 1;

    rind_L_total = NULL;
    cind_L_total = NULL;
    hessval = NULL;

    sparse_hess(tag_L, n+m+1, -1, xp, &nnz_L_total, &rind_L_total, &cind_L_total, &hessval, options_L);

    rind_L = new unsigned int[nnz_L];
    cind_L = new unsigned int[nnz_L];
    rind_L_total = (unsigned int*) malloc(nnz_L_total*sizeof(unsigned int)); //! test
    cind_L_total = (unsigned int*) malloc(nnz_L_total*sizeof(unsigned int)); //! test

    unsigned int ind = 0;

    for (int i=0;i<n;i++)
        for (unsigned int j=1;j<=HP_t[i][0];j++)
    {
        if (((int) HP_t[i][j]>=i) &&((int) HP_t[i][j]<n))
        {
            rind_L[ind] = i;
            cind_L[ind++] = HP_t[i][j];
        }
    }

    ind = 0;
    for (int i=0;i<n+m+1;i++)
        for (unsigned int j=1;j<=HP_t[i][0];j++)
    {
        if ((int) HP_t[i][j]>=i)
        {
            rind_L_total[ind] = i;
            cind_L_total[ind++] = HP_t[i][j];
        }
    }

    for (i=0;i<m;i++) {
        free(JP_g[i]);
    }

    free(JP_f[0]);
    free(JP_f);
    free(JP_g);
    free(HP_f);
    free(HP_g);
    free(HP_length);

    delete[] lam;
    delete[] g;
    delete[] xa;
    delete[] zu;
    delete[] zl;
    delete[] lamp;
    delete[] xp;

}


// ***************    FFSM OPT specific part ***********************************

const int
Opt::gip(const string &varName) const{ // get initial position
  map<string, int>::const_iterator p;
  p=initPos.find(varName);
  if(p != initPos.end()) {
    return p->second;
  }
  else {
    msgOut(MSG_CRITICAL_ERROR, "Asking the initial position in the concatenated array of a variable ("+varName+") that doesn't exist!");
    return 0;
  }
}

const int
Opt::gip(const int &cn) const { // get initial position
  return cInitPos.at(cn);
}

const int
Opt::gdt(const string &varName){ // get domain type
  VarMap::const_iterator p;
  p=vars.find(varName);
  if(p != vars.end()) {
    return p->second.domain;
  }
  else {
    msgOut(MSG_CRITICAL_ERROR, "Asking the domain type of a variable ("+varName+") that doesn't exist!");
    return 0;
  }
}

const int
Opt::gdt(const int &cn){ // get domain type
  return cons.at(cn).domain;
}

template<class T> const int
Opt::gix_uncached(const T &v_or_c, int r1Ix, int r2Ix, int prIx, int r2IxTo){

  // attenction, for computational reason we are not checking the call is within vectors limits!!!

  int dType = gdt(v_or_c);
  int othCountriesRegions = 0;
  int othCountriesRegions_r2case = 0;
  for (uint i=0;i<r1Ix;i++){
    othCountriesRegions += l2r[i].size();
  }
  for (uint i=0;i<r1Ix;i++){
    othCountriesRegions_r2case +=l2r[i].size()*l2r[i].size();
  }

  switch (dType){
    case DOM_PRI_PR:
      return gip(v_or_c)+(othCountriesRegions+r2Ix)*nPriPr+prIx;
    case DOM_SEC_PR:
      return gip(v_or_c)+(othCountriesRegions+r2Ix)*nSecPr+prIx;;
    case DOM_ALL_PR:
      return gip(v_or_c)+(othCountriesRegions+r2Ix)*nAllPr+prIx;
    case DOM_R2_PRI_PR:
      return gip(v_or_c)+(othCountriesRegions_r2case)*nAllPr+(r2Ix*nPriPr+prIx)*l2r[r1Ix].size()+r2IxTo;
    case DOM_R2_SEC_PR:
      return gip(v_or_c)+(othCountriesRegions_r2case)*nAllPr+(r2Ix*nSecPr+prIx)*l2r[r1Ix].size()+r2IxTo;
    case DOM_R2_ALL_PR:
      return gip(v_or_c)+(othCountriesRegions_r2case)*nAllPr+(r2Ix*nAllPr+prIx)*l2r[r1Ix].size()+r2IxTo; // new 20120814, looping r1,r2,p,r2to
      // initial position + (other countries region pairs + same country other regions from pair + regions to)* number of all products+product
      //return gip(v_or_c)+(othCountriesRegions_r2case+r2Ix*l2r[r1Ix].size()+r2IxTo)*nAllPr+prIx; // looping r1,r2,r2to,p
    case DOM_SCALAR:
      return gip(v_or_c);
    case DOM_PRI_PR_ALLCOMBS:
      return gip(v_or_c)+(othCountriesRegions+r2Ix)*nPriPrCombs+prIx;
  default:
    msgOut(MSG_CRITICAL_ERROR,"Try to calculate the position of a variable (or constrain) of unknow type.");
    return 0;
  }
}


const int
Opt::gix(const string &varName, const int& r1Ix, const int& r2Ix, const int& prIx, const int& r2IxTo) const{
  // attenction, for computational reasons we are not checking the call is within vectors limits!!!
  map <string, vector < vector < vector < vector <int> > > > >::const_iterator p;
  p=vpositions.find(varName);
  if(p != vpositions.end()) {
    return p->second[r1Ix][r2Ix][prIx][r2IxTo];
  }
  else {
    msgOut(MSG_CRITICAL_ERROR, "Asking the position of a variable ("+varName+") that doesn't exist!");
    return 0;
  }
}

const int
Opt::gix(const int &cn, const int& r1Ix, const int& r2Ix, const int& prIx, const int& r2IxTo) const{
  return cpositions[cn][r1Ix][r2Ix][prIx][r2IxTo];
}

void
Opt::cacheInitialPosition(){
  int vInitialPosition = 0;
  int cInitialPosition = 0;
  VarMap::iterator viter;
  for (viter = vars.begin(); viter != vars.end(); ++viter) {
    initPos.insert(pair<string, int>(viter->first, vInitialPosition));
    initPos_rev.insert(pair<int, string>(vInitialPosition,viter->first));
    vInitialPosition += getDomainElements(viter->second.domain);
  }
  for (uint i=0;i<cons.size();i++){
    cInitPos.push_back(cInitialPosition);
    cInitialPosition += getDomainElements(cons[i].domain);
  }
}

void
Opt::cachePositions(){

  // variables..
  VarMap::iterator viter;
  for (viter = vars.begin(); viter != vars.end(); ++viter) {
    vpositions.insert(pair<string, vector < vector < vector < vector <int> > > > >(viter->first,  buildPositionVector(viter->first, viter->second.domain)));
  }
  // constrains..
  for (uint i=0; i<cons.size();i++){
    cpositions.push_back(buildPositionVector(i, cons[i].domain));
  }

}

template<class T> vector < vector < vector < vector <int> > > >
Opt::buildPositionVector(const T &v_or_c, int dType){
  int pVectorSize;

  switch (dType){
    case DOM_PRI_PR:
      pVectorSize= priPr.size();
      break;
    case DOM_SEC_PR:
      pVectorSize= secPr.size();
      break;
    case DOM_ALL_PR:
      pVectorSize= allPr.size();
      break;
    case DOM_R2_PRI_PR:
      pVectorSize= priPr.size();
      break;
    case DOM_R2_SEC_PR:
      pVectorSize= secPr.size();
      break;
    case DOM_R2_ALL_PR:
      pVectorSize= allPr.size();
      break;
    case DOM_SCALAR:
      pVectorSize= allPr.size(); // it will simply fill the matrix all with the same value (the ip)
      break;
    case DOM_PRI_PR_ALLCOMBS:
      pVectorSize= priPrCombs.size();
      break;
    default:
      msgOut(MSG_CRITICAL_ERROR,"Try to build the position of a variable (or contrain) of unknow type.");
  }


  vector < vector < vector < vector <int> > > > positionsToAdd;
  for(uint r1=0;r1<l2r.size();r1++){
    vector < vector < vector <int> > > dim1;
    for(uint r2=0;r2<l2r[r1].size();r2++){
      vector < vector <int> > dim2;
      for(uint p=0;p<pVectorSize;p++){
        vector <int> dim3;
          for(uint r2To=0;r2To<l2r[r1].size();r2To++){
            dim3.push_back(gix_uncached(v_or_c,r1,r2,p,r2To));
          }
        dim2.push_back(dim3);
      }
      dim1.push_back(dim2);
    }
    positionsToAdd.push_back(dim1);
  }
  return positionsToAdd;
}


void
Opt::calculateNumberVariablesConstrains(){
    // calculating the number of variables and the initial positions in the concatenated array..
    nVar = 0;
    VarMap::iterator viter;
    for (viter = vars.begin(); viter != vars.end(); ++viter) {
        nVar += getDomainElements(viter->second.domain);
    }

    // calculating the number of constrains..
    nCons = 0;
    nEqualityConstrains = 0;
    nLowerEqualZeroConstrains = 0;
    nGreaterEqualZeroConstrains = 0;
    for(uint i=0;i<cons.size();i++){
      nCons += getDomainElements(cons[i].domain);
      if(cons[i].direction == CONSTR_EQ){
        nEqualityConstrains += getDomainElements(cons[i].domain);
        continue;
      } else if (cons[i].direction == CONSTR_LE0) {
        nLowerEqualZeroConstrains += getDomainElements(cons[i].domain);
        continue;
      } else if (cons[i].direction == CONSTR_GE0) {
        nGreaterEqualZeroConstrains += getDomainElements(cons[i].domain);
        continue;
      } else {
        msgOut(MSG_CRITICAL_ERROR, "Asking for a constrain with unknown direction ("+i2s(cons[i].direction)+")");
      }
    }

    msgOut(MSG_INFO,"The model will work with "+i2s(nVar)+" variables and "+i2s(nCons)+" constrains ("+i2s(nEqualityConstrains)+" equalities, "+i2s(nLowerEqualZeroConstrains)+" lower than 0 and "+i2s(nGreaterEqualZeroConstrains)+" greater than 0)");
}

int
Opt::getDomainElements(int domain){
  int elements = 0;
  switch (domain){
    case DOM_PRI_PR:
      return nL2r*nPriPr;
    case DOM_SEC_PR:
      return nL2r*nSecPr;
    case DOM_ALL_PR:
      return nL2r*nAllPr;
    case DOM_R2_PRI_PR:
      for(uint r1=0;r1<l2r.size();r1++){
          elements += l2r[r1].size()*l2r[r1].size()*nPriPr; // EXP(i,j,p_pr)
      }
      return elements;
    case DOM_R2_SEC_PR:
      for(uint r1=0;r1<l2r.size();r1++){
          elements += l2r[r1].size()*l2r[r1].size()*nSecPr; // EXP(i,j,p_tr)
      }
      return elements;
    case DOM_R2_ALL_PR:
      for(uint r1=0;r1<l2r.size();r1++){
          elements += l2r[r1].size()*l2r[r1].size()*nAllPr; // EXP(i,j,prd)
      }
      return elements;
    case DOM_SCALAR:
      return 1;
    case DOM_PRI_PR_ALLCOMBS:
      return nL2r*nPriPrCombs;
  default:
    msgOut(MSG_CRITICAL_ERROR, "Asking for an unknown domain type ("+i2s(domain)+")");
  }
}

int
Opt::getConstrainDirectionByIndex(int idx){
  for(uint i=0;i<cons.size();i++){
    if(i!=cons.size()-1){
      if (idx >= gip(i) && idx < gip(i+1)){
        return cons[i].direction;
      }
    } else {
      if (idx >= gip(i) && idx < nCons){
      return cons[i].direction;
      }
    }
  }
  msgOut(MSG_CRITICAL_ERROR, "Asking contrain direction for an out of range contrain index!");
}

double
Opt::getBoundByIndex(const int & bound_type, const int & idx){

  map <int, string>::const_iterator p;
  p=initPos_rev.upper_bound(idx);
  p--;
  VarMap::const_iterator p2;
  p2=vars.find(p->second);
  if(p2 != vars.end()) {
    if (bound_type==LBOUND){
      if (p2->second.l_bound_var == ""){ // this var don't specific a variable as bound
        return p2->second.l_bound;
      } else {
        return getDetailedBoundByVarAndIndex(p2->second,idx,LBOUND);
      }
    } else if (bound_type==UBOUND){
      if (p2->second.u_bound_var == ""){ // this var don't specific a variable as bound
        return p2->second.u_bound;
      } else {
        return getDetailedBoundByVarAndIndex(p2->second,idx,UBOUND);
      }
    } else {
      msgOut(MSG_CRITICAL_ERROR, "Asking the bound with a type ("+i2s(bound_type)+") that I don't know how to handle !");
    }
  }
  else {
    msgOut(MSG_CRITICAL_ERROR, "Asking the bound from a variable ("+p->second+") that doesn't exist!");
  }
  return 0.;
}

double
Opt::getDetailedBoundByVarAndIndex(const endvar & var, const int & idx, const int & bType){
  // Tested 2015.01.08 with DOM_ALL_PR, DOM_PRI_PR, DOM_ALL_PR, DOM_R2_ALL_PR.
  int r1,r2,p,r2to;
  unpack(idx,var.domain,gip(var.name),r1,r2,p,r2to,true);
  //cout << "getBoundByVarAndIndex():\t" << var.name << '\t' << idx << '\t' << gip(var.name) << '\t' << r1 << '\t' << r2 << '\t' << p << '\t' << r2to << endl;
  //cout << "  --variables:\t" << var.l_bound_var << '\t' << var.u_bound_var << '\t' << "" << '\t' << l2r[r1][r2] << '\t' << "" << '\t' << allPr[p] << '\t' << l2r[r1][r2to] << endl;
  if(bType==LBOUND){
    if(r2to){
       return gpd(var.l_bound_var,l2r[r1][r2],allPr[p],DATA_NOW,i2s(l2r[r1][r2to]));
    } else {
      return gpd(var.l_bound_var,l2r[r1][r2],allPr[p],DATA_NOW,i2s(l2r[r1][r2to]));
    }
  } else {
    if(r2to){
       return gpd(var.u_bound_var,l2r[r1][r2],allPr[p]);
    } else {
      //cout << gpd(var.u_bound_var,l2r[r1][r2],allPr[p]) << endl;
      return gpd(var.u_bound_var,l2r[r1][r2],allPr[p]);
    }
  }
}

constrain*
Opt::getConstrainByIndex(int idx){
  for(uint i=0;i<cons.size();i++){
    if(i!=cons.size()-1){
      if (idx >= gip(i) && idx < gip(i+1)){
        return &cons[i];
      }
    } else {
      if (idx >= gip(i) && idx < nCons){
      return &cons[i];
      }
    }
  }
  msgOut(MSG_CRITICAL_ERROR, "Asking contrain direction for an out of range contrain index!");
}


void
Opt::unpack(int ix_h, int domain, int initial, int &r1_h, int &r2_h, int&p_h, int&r2to_h, bool fullp){
  ix_h = ix_h-initial;
  double ix=0;
  bool r2flag = false;
  int pIndexToAdd = 0;
  int np=0;
  if(domain==DOM_PRI_PR || domain==DOM_R2_PRI_PR) {
    np = nPriPr;
  } else if (domain==DOM_SEC_PR || domain==DOM_R2_SEC_PR) {
    np = nSecPr;
  } else if (domain==DOM_ALL_PR || domain==DOM_R2_ALL_PR) {
    np = nAllPr;
  } else if (domain=DOM_SCALAR){
    r1_h=0;r2_h=0;p_h=0;r2to_h=0;
    return;
  } else {
    msgOut(MSG_CRITICAL_ERROR,"unknow domain ("+i2s(domain)+") in unpack() function.");
  }
  if(domain==DOM_R2_PRI_PR || domain==DOM_R2_SEC_PR ||domain==DOM_R2_ALL_PR){
    r2flag = true;
  }
  if(fullp && (domain==DOM_SEC_PR || domain==DOM_R2_SEC_PR)){ // changed 20140107 (any how, previously the unpack() function was not used!!)
    pIndexToAdd = nPriPr;
    //cout << "pindexToAdd: " << pIndexToAdd << endl;
  }

  for (uint r1=0;r1<l2r.size();r1++){
    for (uint r2=0;r2<l2r[r1].size();r2++){
      for (uint p=0;p<np;p++){
        if(!r2flag){
          if(ix==ix_h){
            r1_h=r1;
            r2_h=r2;
            p_h=p+pIndexToAdd;
            r2to_h=0;
            return;
          }
          ix++;
        } else {
          for (uint r2To=0;r2To<l2r[r1].size();r2To++){
            if(ix==ix_h){
              r1_h=r1;
              r2_h=r2;
              p_h=p+pIndexToAdd;
              r2to_h=r2To;
              return;
            }
            ix++;
          }
        }
      }
    }
  }
  msgOut(MSG_CRITICAL_ERROR, "Error in unpack() function. Ix ("+i2s(ix_h)+") can not be unpacked");
}

int
Opt::getConNumber(constrain *con){
  for(uint i=0;i<cons.size();i++){
    if(   cons[i].name       == con->name
       && cons[i].comment    == con->comment
       && cons[i].domain     == con->domain
       && cons[i].direction  == con->direction){
      return i;
       }
  }
  msgOut(MSG_CRITICAL_ERROR,"Constrain didn't found in list.");
}


void
Opt::calculateSparsityPatternJ(){

  unsigned int  **jacpat=NULL; // compressed row storage
  int           options_j[3]; // options for the jacobian patterns
  double        *x;
  int retv_j = -1; // return value

  options_j[0] = 0; // index domain propagation
  options_j[1] = 0; // automatic mode choice (ignored here)
  options_j[2] = 0; // safe
  jacpat = new unsigned int* [nCons];
  x = new double[nVar];

  nzjelements.clear();

  retv_j = jac_pat(tag_g, nCons, nVar,  x, jacpat, options_j);

  for (int i=0;i<nCons;i++) {
    for (int j=1;j<=jacpat[i][0];j++){
      vector <int> nzjelement;
      nzjelement.push_back(i);
      nzjelement.push_back(jacpat[i][j]);
      nzjelements.push_back(nzjelement);
    }
  }
}

void
Opt::calculateSparsityPatternH(){

  unsigned int  **hesspat=NULL; // compressed row storage
  int           options_h=0; // options for the hessian patterns
  double        *x;
  int retv_h = -1; // return value

  hesspat = new unsigned int* [(nVar+nCons+1)];
  x = new double[(nVar+nCons+1)];

  retv_h = hess_pat(tag_L,nVar+nCons+1,  x, hesspat, options_h);

  for (int i=0;i<(nVar);i++) {
    for (int j=1;j<=hesspat[i][0];j++){
      if(hesspat[i][j]<=i){
        vector <int> nzhelement;
        nzhelement.push_back(i);
        nzhelement.push_back(hesspat[i][j]);
        nzhelements.push_back(nzhelement);
      }
    }
  }
}

void
Opt::tempDebug(){

  cout << "Num of variables: " <<  nVar << " - Num of constrains:" << nCons << endl;
  cout << "IDX;ROW;COL" << endl;
  for(uint i=0;i<nzhelements.size();i++){
    cout << i << ";" << nzhelements[i][0] << ";" << nzhelements[i][1] << endl;
  }

  cout << "Dense jacobian: " << nCons * nVar << " elements" << endl;
  cout << "Dense hessian:  " << nVar*(nVar-1)/2+nVar << " elements" << endl;
  //exit(0);

}


const  Number&
Opt::mymax(const Number& a, const Number& b){
  return (a<b)?b:a;
}
const adouble&
Opt::mymax(const adouble& a, const adouble& b){
  return (a<b)?b:a;
}


bool
Opt::intermediate_callback(AlgorithmMode mode, Index iter, Number obj_value, Number inf_pr, Number inf_du, Number mu, Number d_norm, Number regularization_size, Number alpha_du, Number alpha_pr, Index ls_trials, const IpoptData *ip_data, IpoptCalculatedQuantities *ip_cq){
    int itnumber = iter;
    if(itnumber%10==0){
        msgOut(MSG_DEBUG,"Running ("+i2s(itnumber)+" iter) ..");
    }
    return true;
}

int
Opt::getVarInstances(const string& varName){
  return getDomainElements(gdt(varName));
}

/*
template <class T> const T&
Opt::mymax ( const T& a, const T& b ){
  return (a<b)?b:a;
}
*/
/**
 * @brief Opt::declareVariable
 * Define a single variable together with its domain and optionally its lower and upper bound (default 0.0, +inf)
 *
 * @param name    var name
 * @param domain  domain of the variable
 * @param l_bound lower bound (fixed)
 * @param u_bound upper bound (fixed)
 * @param l_bound_var variable name defining lower bound
 * @param u_bound_var variable name defining upper bound
 */

void
Opt::declareVariable(const string &name, const int & domain, const string &desc, const double & l_bound, const double & u_bound, const string & l_bound_var, const string & u_bound_var){
   endvar end_var;
   end_var.name = name;
   end_var.domain = domain;
   end_var.l_bound = l_bound;
   end_var.u_bound = u_bound;
   end_var.l_bound_var = l_bound_var;
   end_var.u_bound_var = u_bound_var;
   end_var.desc= desc;
   vars.insert(std::pair<std::string, endvar >(name, end_var));
}
/**
 * @brief Opt::createCombinationsVector
 * Return a vector containing any possible combination of nItems items (including all subsets).
 *
 * For example with nItems = 3:
 * 0: []; 1: [0]; 2: [1]; 3: [0,1]; 4: [2]; 5: [0,2]; 6: [1,2]; 7: [0,1,2]

 * @param nItems number of items to create p
 * @return A vector with in each slot the items present in that specific combination subset.
 */
/*
vector < vector <int> >
Opt::createCombinationsVector(const int& nItems) {
  // Not confuse combination with permutation where order matter. Here it doesn't matter, as much as the algorithm is the same and returns
  // to as each position always the same subset
  vector < vector <int> > toReturn;
  int nCombs = pow(2,nItems);
  //int nCombs = nItems;
  for (uint i=0; i<nCombs; i++){
    vector<int> thisCombItems; //concernedPriProducts;
    for(uint j=0;j<nItems;j++){
      uint j2 = pow(2,j);
      if(i & j2){ // bit a bit operator, p217 C++ book
        thisCombItems.push_back(j);
      }
    }
    toReturn.push_back(thisCombItems);
  }

//    cout << "N items:\t" << nItems << endl;
//    for (uint i=0;i<nCombs; i++){
//      cout << "  "<< i << ":\t";
//      for (uint j=0;j<toReturn[i].size();j++){
//        cout << toReturn[i][j] << "  ";
//      }
//      cout << endl;
//    }
//    exit(0);
  return toReturn;
}
*/

void
Opt::copyInventoryResourses(){
  // This function is not really needed, as actually the solver works also picking the region and the in dynamically
  // Caching the inventories in a vector should however be faster.
  // We now need it, as the vector inResByAnyCombination() account for the union between the inv set of the various pp. Also it now include the total mortality (alive plus death, if modelled)
  vector < vector < vector <double> > >  in_temp;
  for (uint r1=0;r1<l2r.size();r1++){
     vector < vector <double> > dim1;
    for (uint r2=0;r2<l2r[r1].size();r2++){
      vector <double> dim2;
      ModelRegion* REG = MTHREAD->MD->getRegion(l2r[r1][r2]);
      for (uint p=0;p<priPrCombs.size();p++){
        double this_in = REG->inResByAnyCombination[p];
        dim2.push_back(this_in);
      }
      dim1.push_back(dim2);
    }
    in_temp.push_back(dim1);
  }
  ins = in_temp;
}