ROL_Types.hpp

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#ifndef ROL_TYPES_HPP
#define ROL_TYPES_HPP

#ifdef  HAVE_ROL_DEBUG
#define ROL_VALIDATE( A )  A
#else
#define ROL_VALIDATE( A ) /* empty */
#endif

#include <algorithm>
#include <string>
#include <limits>
#include <Teuchos_getConst.hpp>
#include <Teuchos_RCP.hpp>
#include <Teuchos_ScalarTraits.hpp>
#include <Teuchos_TestForException.hpp>
#include <ROL_Vector.hpp>

#define ROL_NUM_CHECKDERIV_STEPS 13

namespace ROL {

  template<class Real>
  struct AlgorithmState {
    int  iter;
    int  minIter;
    int  nfval;
    int  ncval;
    int  ngrad;
    Real value;              
    Real minValue;
    Real gnorm;
    Real cnorm;
    Real snorm;
    Real aggregateGradientNorm;
    Real aggregateModelError;
    bool flag;
    Teuchos::RCP<Vector<Real> > iterateVec;
    Teuchos::RCP<Vector<Real> > lagmultVec;
    Teuchos::RCP<Vector<Real> > minIterVec;
    AlgorithmState(void) : iter(0), minIter(0), nfval(0), ngrad(0), value(0), minValue(0), 
      gnorm(std::numeric_limits<Real>::max()),
      cnorm(std::numeric_limits<Real>::max()),
      snorm(std::numeric_limits<Real>::max()), 
      aggregateGradientNorm(std::numeric_limits<Real>::max()),
      aggregateModelError(std::numeric_limits<Real>::max()),
      flag(false),
      iterateVec(Teuchos::null), lagmultVec(Teuchos::null), minIterVec(Teuchos::null) {}
  };  
  
  template<class Real>
  struct StepState {
    Teuchos::RCP<Vector<Real> > gradientVec;
    Teuchos::RCP<Vector<Real> > descentVec;
    Teuchos::RCP<Vector<Real> > constraintVec;
    Real searchSize; // line search parameter (alpha) or trust-region radius (delta)
    StepState(void) : gradientVec(Teuchos::null), descentVec(Teuchos::null), constraintVec(Teuchos::null),
                      searchSize(0) {}
  };  
      
  static const double ROL_EPSILON   = std::abs(Teuchos::ScalarTraits<double>::eps());
    
  static const double ROL_THRESHOLD = 10.0 * ROL_EPSILON;

  static const double ROL_OVERFLOW  = std::abs(Teuchos::ScalarTraits<double>::rmax());

  static const double ROL_UNDERFLOW  = std::abs(Teuchos::ScalarTraits<double>::rmin());

  struct removeSpecialCharacters {
    bool operator()(char c) {
      return (c ==' ' || c =='-' || c == '(' || c == ')' || c=='\'' || c=='\r' || c=='\n' || c=='\t');
    }
  };

  inline std::string removeStringFormat( std::string s ) {
    std::string output = s;
    output.erase( std::remove_if( output.begin(), output.end(), removeSpecialCharacters()), output.end() );
    std::transform( output.begin(), output.end(), output.begin(), ::tolower );
    return output;
  }

  enum EStep{
    STEP_AUGMENTEDLAGRANGIAN = 0,
    STEP_BUNDLE,
    STEP_COMPOSITESTEP,
    STEP_LINESEARCH,
    STEP_MOREAUYOSIDAPENALTY,
    STEP_PRIMALDUALACTIVESET,
    STEP_TRUSTREGION,
    STEP_LAST
  };

  inline std::string EStepToString(EStep tr) {
    std::string retString;
    switch(tr) {
      case STEP_AUGMENTEDLAGRANGIAN: retString = "Augmented Lagrangian";   break;
      case STEP_BUNDLE:              retString = "Bundle";                 break;
      case STEP_COMPOSITESTEP:       retString = "Composite Step";         break;
      case STEP_LINESEARCH:          retString = "Line Search";            break;
      case STEP_MOREAUYOSIDAPENALTY: retString = "Moreau-Yosida Penalty";  break;
      case STEP_PRIMALDUALACTIVESET: retString = "Primal Dual Active Set"; break;
      case STEP_TRUSTREGION:         retString = "Trust Region";           break;
      case STEP_LAST:                retString = "Last Type (Dummy)";      break;
      default:                       retString = "INVALID EStep";
    }
    return retString;
  }
  
  inline int isValidStep(EStep ls) {
    return( (ls == STEP_AUGMENTEDLAGRANGIAN) ||
            (ls == STEP_BUNDLE) ||
            (ls == STEP_COMPOSITESTEP) ||
            (ls == STEP_LINESEARCH) ||
            (ls == STEP_MOREAUYOSIDAPENALTY) ||
            (ls == STEP_PRIMALDUALACTIVESET) ||
            (ls == STEP_TRUSTREGION) );
  }

  inline EStep & operator++(EStep &type) {
    return type = static_cast<EStep>(type+1);
  }

  inline EStep operator++(EStep &type, int) {
    EStep oldval = type;
    ++type;
    return oldval;
  }

  inline EStep & operator--(EStep &type) {
    return type = static_cast<EStep>(type-1);
  }

  inline EStep operator--(EStep &type, int) {
    EStep oldval = type;
    --type;
    return oldval;
  }

  inline EStep StringToEStep(std::string s) {
    s = removeStringFormat(s);
    for ( EStep tr = STEP_AUGMENTEDLAGRANGIAN; tr < STEP_LAST; tr++ ) {
      if ( !s.compare(removeStringFormat(EStepToString(tr))) ) {
        return tr;
      }
    }
    return STEP_TRUSTREGION;
  }

  enum EBoundAlgorithm{
    BOUNDALGORITHM_PROJECTED = 0,
    BOUNDALGORITHM_PRIMALDUALACTIVESET,
    BOUNDALGORITHM_INTERIORPOINTS,
    BOUNDALGORITHM_LAST
  };

  inline std::string EBoundAlgorithmToString(EBoundAlgorithm tr) {
    std::string retString;
    switch(tr) {
      case BOUNDALGORITHM_PROJECTED:           retString = "Projected";              break;
      case BOUNDALGORITHM_PRIMALDUALACTIVESET: retString = "Primal Dual Active Set"; break;
      case BOUNDALGORITHM_INTERIORPOINTS:      retString = "Interior Points";        break;
      case BOUNDALGORITHM_LAST:                retString = "Last Type (Dummy)";      break;
      default:                                 retString = "INVALID EBoundAlgorithm";
    }
    return retString;
  }

  inline int isValidBoundAlgorithm(EBoundAlgorithm d){
    return( (d == BOUNDALGORITHM_PROJECTED)           ||
            (d == BOUNDALGORITHM_PRIMALDUALACTIVESET) || 
            (d == BOUNDALGORITHM_INTERIORPOINTS)  
          );
  }

  inline EBoundAlgorithm & operator++(EBoundAlgorithm &type) {
    return type = static_cast<EBoundAlgorithm>(type+1);
  }

  inline EBoundAlgorithm operator++(EBoundAlgorithm &type, int) {
    EBoundAlgorithm oldval = type;
    ++type;
    return oldval;
  }

  inline EBoundAlgorithm & operator--(EBoundAlgorithm &type) {
    return type = static_cast<EBoundAlgorithm>(type-1);
  }

  inline EBoundAlgorithm operator--(EBoundAlgorithm &type, int) {
    EBoundAlgorithm oldval = type;
    --type;
    return oldval;
  }

  inline EBoundAlgorithm StringToEBoundAlgorithm(std::string s) {
    s = removeStringFormat(s);
    for ( EBoundAlgorithm des = BOUNDALGORITHM_PROJECTED; des < BOUNDALGORITHM_LAST; des++ ) {
      if ( !s.compare(removeStringFormat(EBoundAlgorithmToString(des))) ) {
        return des;
      }
    }
    return BOUNDALGORITHM_PROJECTED;
  }

  enum EDescent{
    DESCENT_STEEPEST = 0,
    DESCENT_NONLINEARCG,
    DESCENT_SECANT,
    DESCENT_NEWTON,
    DESCENT_NEWTONKRYLOV,
    DESCENT_LAST
  };

  inline std::string EDescentToString(EDescent tr) {
    std::string retString;
    switch(tr) {
      case DESCENT_STEEPEST:             retString = "Steepest Descent";                          break;
      case DESCENT_NONLINEARCG:          retString = "Nonlinear CG";                              break;
      case DESCENT_SECANT:               retString = "Quasi-Newton Method";                       break;
      case DESCENT_NEWTON:               retString = "Newton's Method";                           break;
      case DESCENT_NEWTONKRYLOV:         retString = "Newton-Krylov";                             break;
      case DESCENT_LAST:                 retString = "Last Type (Dummy)";                         break;
      default:                           retString = "INVALID ESecant";
    }
    return retString;
  }

  inline int isValidDescent(EDescent d){
    return( (d == DESCENT_STEEPEST)      ||
            (d == DESCENT_NONLINEARCG)   ||
            (d == DESCENT_SECANT)        ||
            (d == DESCENT_NEWTON)        ||
            (d == DESCENT_NEWTONKRYLOV)
          );
  }

  inline EDescent & operator++(EDescent &type) {
    return type = static_cast<EDescent>(type+1);
  }

  inline EDescent operator++(EDescent &type, int) {
    EDescent oldval = type;
    ++type;
    return oldval;
  }

  inline EDescent & operator--(EDescent &type) {
    return type = static_cast<EDescent>(type-1);
  }

  inline EDescent operator--(EDescent &type, int) {
    EDescent oldval = type;
    --type;
    return oldval;
  }

  inline EDescent StringToEDescent(std::string s) {
    s = removeStringFormat(s);
    for ( EDescent des = DESCENT_STEEPEST; des < DESCENT_LAST; des++ ) {
      if ( !s.compare(removeStringFormat(EDescentToString(des))) ) {
        return des;
      }
    }
    return DESCENT_SECANT;
  }
  
  enum ESecant{
    SECANT_LBFGS = 0,
    SECANT_LDFP,
    SECANT_LSR1,
    SECANT_BARZILAIBORWEIN,
    SECANT_USERDEFINED,
    SECANT_LAST
  };

  inline std::string ESecantToString(ESecant tr) {
    std::string retString;
    switch(tr) {
      case SECANT_LBFGS:           retString = "Limited-Memory BFGS"; break;
      case SECANT_LDFP:            retString = "Limited-Memory DFP";  break;
      case SECANT_LSR1:            retString = "Limited-Memory SR1";  break;
      case SECANT_BARZILAIBORWEIN: retString = "Barzilai-Borwein";    break;
      case SECANT_USERDEFINED:     retString = "User-Defined";        break;
      case SECANT_LAST:            retString = "Last Type (Dummy)";   break;
      default:                     retString = "INVALID ESecant";
    }
    return retString;
  }
  
  inline int isValidSecant(ESecant s) {
    return( (s == SECANT_LBFGS)           ||
            (s == SECANT_LDFP)            ||
            (s == SECANT_LSR1)            ||
            (s == SECANT_BARZILAIBORWEIN) ||
            (s == SECANT_USERDEFINED)
          );
  }

  inline ESecant & operator++(ESecant &type) {
    return type = static_cast<ESecant>(type+1);
  }

  inline ESecant operator++(ESecant &type, int) {
    ESecant oldval = type;
    ++type;
    return oldval;
  }

  inline ESecant & operator--(ESecant &type) {
    return type = static_cast<ESecant>(type-1);
  }

  inline ESecant operator--(ESecant &type, int) {
    ESecant oldval = type;
    --type;
    return oldval;
  }

  inline ESecant StringToESecant(std::string s) {
    s = removeStringFormat(s);
    for ( ESecant sec = SECANT_LBFGS; sec < SECANT_LAST; sec++ ) {
      if ( !s.compare(removeStringFormat(ESecantToString(sec))) ) {
        return sec;
      }
    }
    return SECANT_LBFGS;
  }
  
  enum EKrylov{
    KRYLOV_CG = 0,
    KRYLOV_CR,
    KRYLOV_USERDEFINED,
    KRYLOV_LAST
  };

  inline std::string EKrylovToString(EKrylov tr) {
    std::string retString;
    switch(tr) {
      case KRYLOV_CG:          retString = "Conjugate Gradients"; break;
      case KRYLOV_CR:          retString = "Conjugate Residuals"; break;
      case KRYLOV_USERDEFINED: retString = "User Defined";        break;
      case KRYLOV_LAST:        retString = "Last Type (Dummy)";   break;
      default:                 retString = "INVALID EKrylov";
    }
    return retString;
  }

  inline int isValidKrylov(EKrylov d){
    return( (d == KRYLOV_CG)      ||
            (d == KRYLOV_CR)      ||
            (d == KRYLOV_USERDEFINED) );
  }

  inline EKrylov & operator++(EKrylov &type) {
    return type = static_cast<EKrylov>(type+1);
  }

  inline EKrylov operator++(EKrylov &type, int) {
    EKrylov oldval = type;
    ++type;
    return oldval;
  }

  inline EKrylov & operator--(EKrylov &type) {
    return type = static_cast<EKrylov>(type-1);
  }

  inline EKrylov operator--(EKrylov &type, int) {
    EKrylov oldval = type;
    --type;
    return oldval;
  }

  inline EKrylov StringToEKrylov(std::string s) {
    s = removeStringFormat(s);
    for ( EKrylov des = KRYLOV_CG; des < KRYLOV_LAST; des++ ) {
      if ( !s.compare(removeStringFormat(EKrylovToString(des))) ) {
        return des;
      }
    }
    return KRYLOV_CG;
  }

  enum ENonlinearCG{
    NONLINEARCG_HESTENES_STIEFEL = 0,
    NONLINEARCG_FLETCHER_REEVES,
    NONLINEARCG_DANIEL,
    NONLINEARCG_POLAK_RIBIERE,
    NONLINEARCG_FLETCHER_CONJDESC,
    NONLINEARCG_LIU_STOREY,
    NONLINEARCG_DAI_YUAN,
    NONLINEARCG_HAGER_ZHANG,
    NONLINEARCG_OREN_LUENBERGER,
    NONLINEARCG_LAST
  };

  inline std::string ENonlinearCGToString(ENonlinearCG tr) {
    std::string retString;
    switch(tr) {
      case NONLINEARCG_HESTENES_STIEFEL:      retString = "Hestenes-Stiefel";            break;
      case NONLINEARCG_FLETCHER_REEVES:       retString = "Fletcher-Reeves";             break;
      case NONLINEARCG_DANIEL:                retString = "Daniel (uses Hessian)";       break;
      case NONLINEARCG_POLAK_RIBIERE:         retString = "Polak-Ribiere";               break;
      case NONLINEARCG_FLETCHER_CONJDESC:     retString = "Fletcher Conjugate Descent";  break;
      case NONLINEARCG_LIU_STOREY:            retString = "Liu-Storey";                  break;
      case NONLINEARCG_DAI_YUAN:              retString = "Dai-Yuan";                    break;
      case NONLINEARCG_HAGER_ZHANG:           retString = "Hager-Zhang";                 break;
      case NONLINEARCG_OREN_LUENBERGER:       retString = "Oren-Luenberger";             break;
      case NONLINEARCG_LAST:                  retString = "Last Type (Dummy)";           break;
      default:                                retString = "INVALID ENonlinearCG";
    }
    return retString;
  }
  
  inline int isValidNonlinearCG(ENonlinearCG s) {
    return( (s == NONLINEARCG_HESTENES_STIEFEL)  ||
            (s == NONLINEARCG_FLETCHER_REEVES)   ||
            (s == NONLINEARCG_DANIEL)            ||
            (s == NONLINEARCG_POLAK_RIBIERE)     ||
            (s == NONLINEARCG_FLETCHER_CONJDESC) ||
            (s == NONLINEARCG_LIU_STOREY)        ||
            (s == NONLINEARCG_DAI_YUAN)          ||
            (s == NONLINEARCG_HAGER_ZHANG)       ||
            (s == NONLINEARCG_OREN_LUENBERGER)      
          );
  }

  inline ENonlinearCG & operator++(ENonlinearCG &type) {
    return type = static_cast<ENonlinearCG>(type+1);
  }

  inline ENonlinearCG operator++(ENonlinearCG &type, int) {
    ENonlinearCG oldval = type;
    ++type;
    return oldval;
  }

  inline ENonlinearCG & operator--(ENonlinearCG &type) {
    return type = static_cast<ENonlinearCG>(type-1);
  }

  inline ENonlinearCG operator--(ENonlinearCG &type, int) {
    ENonlinearCG oldval = type;
    --type;
    return oldval;
  }

  inline ENonlinearCG StringToENonlinearCG(std::string s) {
    s = removeStringFormat(s);
    for ( ENonlinearCG nlcg = NONLINEARCG_HESTENES_STIEFEL; nlcg < NONLINEARCG_LAST; nlcg++ ) {
      if ( !s.compare(removeStringFormat(ENonlinearCGToString(nlcg))) ) {
        return nlcg;
      }
    }
    return NONLINEARCG_HESTENES_STIEFEL;
  }
  
  enum ELineSearch{
    LINESEARCH_ITERATIONSCALING = 0,
    LINESEARCH_PATHBASEDTARGETLEVEL,
    LINESEARCH_BACKTRACKING,
    LINESEARCH_BISECTION,
    LINESEARCH_GOLDENSECTION,
    LINESEARCH_CUBICINTERP,
    LINESEARCH_BRENTS,
    LINESEARCH_USERDEFINED,
    LINESEARCH_LAST
  };

  inline std::string ELineSearchToString(ELineSearch ls) {
    std::string retString;
    switch(ls) {
      case LINESEARCH_ITERATIONSCALING:     retString = "Iteration Scaling";       break;
      case LINESEARCH_PATHBASEDTARGETLEVEL: retString = "Path-Based Target Level"; break;
      case LINESEARCH_BACKTRACKING:         retString = "Backtracking";            break;
      case LINESEARCH_BISECTION:            retString = "Bisection";               break;
      case LINESEARCH_GOLDENSECTION:        retString = "Golden Section";          break;
      case LINESEARCH_CUBICINTERP:          retString = "Cubic Interpolation";     break;
      case LINESEARCH_BRENTS:               retString = "Brents";                  break;
      case LINESEARCH_USERDEFINED:          retString = "User Defined";            break;
      case LINESEARCH_LAST:                 retString = "Last Type (Dummy)";       break;
      default:                              retString = "INVALID ELineSearch";
    }
    return retString;
  }
  
  inline int isValidLineSearch(ELineSearch ls){
    return( (ls == LINESEARCH_BACKTRACKING)         ||
            (ls == LINESEARCH_ITERATIONSCALING)     ||
            (ls == LINESEARCH_PATHBASEDTARGETLEVEL) ||
            (ls == LINESEARCH_BISECTION)            ||
            (ls == LINESEARCH_GOLDENSECTION)        ||
            (ls == LINESEARCH_CUBICINTERP)          ||
            (ls == LINESEARCH_BRENTS)               ||
            (ls == LINESEARCH_USERDEFINED)
          );
  }

  inline ELineSearch & operator++(ELineSearch &type) {
    return type = static_cast<ELineSearch>(type+1);
  }

  inline ELineSearch operator++(ELineSearch &type, int) {
    ELineSearch oldval = type;
    ++type;
    return oldval;
  }

  inline ELineSearch & operator--(ELineSearch &type) {
    return type = static_cast<ELineSearch>(type-1);
  }

  inline ELineSearch operator--(ELineSearch &type, int) {
    ELineSearch oldval = type;
    --type;
    return oldval;
  }

  inline ELineSearch StringToELineSearch(std::string s) {
    s = removeStringFormat(s);
    for ( ELineSearch ls = LINESEARCH_ITERATIONSCALING; ls < LINESEARCH_LAST; ls++ ) {
      if ( !s.compare(removeStringFormat(ELineSearchToString(ls))) ) {
        return ls;
      }
    }
    return LINESEARCH_ITERATIONSCALING;
  }

  enum ECurvatureCondition{
    CURVATURECONDITION_WOLFE = 0,
    CURVATURECONDITION_STRONGWOLFE,
    CURVATURECONDITION_GENERALIZEDWOLFE,
    CURVATURECONDITION_APPROXIMATEWOLFE,
    CURVATURECONDITION_GOLDSTEIN,
    CURVATURECONDITION_NULL,
    CURVATURECONDITION_LAST
  };

  inline std::string ECurvatureConditionToString(ECurvatureCondition ls) {
    std::string retString;
    switch(ls) {
      case CURVATURECONDITION_WOLFE:            retString = "Wolfe Conditions";             break;
      case CURVATURECONDITION_STRONGWOLFE:      retString = "Strong Wolfe Conditions";      break;
      case CURVATURECONDITION_GENERALIZEDWOLFE: retString = "Generalized Wolfe Conditions"; break;
      case CURVATURECONDITION_APPROXIMATEWOLFE: retString = "Approximate Wolfe Conditions"; break;
      case CURVATURECONDITION_GOLDSTEIN:        retString = "Goldstein Conditions";         break;
      case CURVATURECONDITION_NULL:             retString = "Null Curvature Condition";     break;
      case CURVATURECONDITION_LAST:             retString = "Last Type (Dummy)";            break;
      default:                                  retString = "INVALID ECurvatureCondition";
    }
    return retString;
  }
  
  inline int isValidCurvatureCondition(ECurvatureCondition ls){
    return( (ls == CURVATURECONDITION_WOLFE)            ||
            (ls == CURVATURECONDITION_STRONGWOLFE)      ||
            (ls == CURVATURECONDITION_GENERALIZEDWOLFE) ||
            (ls == CURVATURECONDITION_APPROXIMATEWOLFE) ||
            (ls == CURVATURECONDITION_GOLDSTEIN)        ||
            (ls == CURVATURECONDITION_NULL)
          );
  }

  inline ECurvatureCondition & operator++(ECurvatureCondition &type) {
    return type = static_cast<ECurvatureCondition>(type+1);
  }

  inline ECurvatureCondition operator++(ECurvatureCondition &type, int) {
    ECurvatureCondition oldval = type;
    ++type;
    return oldval;
  }

  inline ECurvatureCondition & operator--(ECurvatureCondition &type) {
    return type = static_cast<ECurvatureCondition>(type-1);
  }

  inline ECurvatureCondition operator--(ECurvatureCondition &type, int) {
    ECurvatureCondition oldval = type;
    --type;
    return oldval;
  }

  inline ECurvatureCondition StringToECurvatureCondition(std::string s) {
    s = removeStringFormat(s);
    for ( ECurvatureCondition cc = CURVATURECONDITION_WOLFE; cc < CURVATURECONDITION_LAST; cc++ ) {
      if ( !s.compare(removeStringFormat(ECurvatureConditionToString(cc))) ) {
        return cc;
      }
    }
    return CURVATURECONDITION_WOLFE;
  }

  enum ETrustRegion{
    TRUSTREGION_CAUCHYPOINT = 0,
    TRUSTREGION_TRUNCATEDCG,
    TRUSTREGION_DOGLEG,
    TRUSTREGION_DOUBLEDOGLEG,
    TRUSTREGION_LAST
  };

  inline std::string ETrustRegionToString(ETrustRegion tr) {
    std::string retString;
    switch(tr) {
      case TRUSTREGION_CAUCHYPOINT:   retString = "Cauchy Point";        break;
      case TRUSTREGION_TRUNCATEDCG:   retString = "Truncated CG";        break;
      case TRUSTREGION_DOGLEG:        retString = "Dogleg";              break;
      case TRUSTREGION_DOUBLEDOGLEG:  retString = "Double Dogleg";       break;
      case TRUSTREGION_LAST:          retString = "Last Type (Dummy)";   break;
      default:                        retString = "INVALID ETrustRegion";
    }
    return retString;
  }
  
  inline int isValidTrustRegion(ETrustRegion ls){
    return( (ls == TRUSTREGION_CAUCHYPOINT)  ||
            (ls == TRUSTREGION_TRUNCATEDCG)  ||
            (ls == TRUSTREGION_DOGLEG)       ||
            (ls == TRUSTREGION_DOUBLEDOGLEG)
          );
  }

  inline ETrustRegion & operator++(ETrustRegion &type) {
    return type = static_cast<ETrustRegion>(type+1);
  }

  inline ETrustRegion operator++(ETrustRegion &type, int) {
    ETrustRegion oldval = type;
    ++type;
    return oldval;
  }

  inline ETrustRegion & operator--(ETrustRegion &type) {
    return type = static_cast<ETrustRegion>(type-1);
  }

  inline ETrustRegion operator--(ETrustRegion &type, int) {
    ETrustRegion oldval = type;
    --type;
    return oldval;
  }

  inline ETrustRegion StringToETrustRegion(std::string s) {
    s = removeStringFormat(s);
    for ( ETrustRegion tr = TRUSTREGION_CAUCHYPOINT; tr < TRUSTREGION_LAST; tr++ ) {
      if ( !s.compare(removeStringFormat(ETrustRegionToString(tr))) ) {
        return tr;
      }
    }
    return TRUSTREGION_CAUCHYPOINT;
  }

  enum ETestObjectives {
    TESTOBJECTIVES_ROSENBROCK = 0,
    TESTOBJECTIVES_FREUDENSTEINANDROTH,
    TESTOBJECTIVES_BEALE,
    TESTOBJECTIVES_POWELL,
    TESTOBJECTIVES_SUMOFSQUARES,
    TESTOBJECTIVES_LEASTSQUARES,
    TESTOBJECTIVES_POISSONCONTROL,
    TESTOBJECTIVES_POISSONINVERSION,
    TESTOBJECTIVES_ZAKHAROV,
    TESTOBJECTIVES_LAST
  };

  inline std::string ETestObjectivesToString(ETestObjectives to) {
    std::string retString;
    switch(to) {
      case TESTOBJECTIVES_ROSENBROCK:          retString = "Rosenbrock's Function";            break;
      case TESTOBJECTIVES_FREUDENSTEINANDROTH: retString = "Freudenstein and Roth's Function"; break;
      case TESTOBJECTIVES_BEALE:               retString = "Beale's Function";                 break;
      case TESTOBJECTIVES_POWELL:              retString = "Powell's Badly Scaled Function";   break;
      case TESTOBJECTIVES_SUMOFSQUARES:        retString = "Sum of Squares Function";          break;
      case TESTOBJECTIVES_LEASTSQUARES:        retString = "Least Squares Function";           break;
      case TESTOBJECTIVES_POISSONCONTROL:      retString = "Poisson Optimal Control";          break;
      case TESTOBJECTIVES_POISSONINVERSION:    retString = "Poisson Inversion Problem";        break;
      case TESTOBJECTIVES_ZAKHAROV:            retString = "Zakharov's Function";              break;
      case TESTOBJECTIVES_LAST:                retString = "Last Type (Dummy)";                break;
      default:                                 retString = "INVALID ETestObjectives";
    }
    return retString;
  }
  
  inline int isValidTestObjectives(ETestObjectives to){
    return( (to == TESTOBJECTIVES_ROSENBROCK)          ||
            (to == TESTOBJECTIVES_FREUDENSTEINANDROTH) ||
            (to == TESTOBJECTIVES_BEALE)               ||
            (to == TESTOBJECTIVES_POWELL)              ||
            (to == TESTOBJECTIVES_SUMOFSQUARES)        ||
            (to == TESTOBJECTIVES_LEASTSQUARES)        ||
            (to == TESTOBJECTIVES_POISSONCONTROL)      ||
            (to == TESTOBJECTIVES_POISSONINVERSION)    ||
            (to == TESTOBJECTIVES_ZAKHAROV)
          );
  }

  inline ETestObjectives & operator++(ETestObjectives &type) {
    return type = static_cast<ETestObjectives>(type+1);
  }

  inline ETestObjectives operator++(ETestObjectives &type, int) {
    ETestObjectives oldval = type;
    ++type;
    return oldval;
  }

  inline ETestObjectives & operator--(ETestObjectives &type) {
    return type = static_cast<ETestObjectives>(type-1);
  }

  inline ETestObjectives operator--(ETestObjectives &type, int) {
    ETestObjectives oldval = type;
    --type;
    return oldval;
  }

  inline ETestObjectives StringToETestObjectives(std::string s) {
    s = removeStringFormat(s);
    for ( ETestObjectives to = TESTOBJECTIVES_ROSENBROCK; to < TESTOBJECTIVES_LAST; to++ ) {
      if ( !s.compare(removeStringFormat(ETestObjectivesToString(to))) ) {
        return to;
      }
    }
    return TESTOBJECTIVES_ROSENBROCK;
  }

  enum ETestOptProblem {
    TESTOPTPROBLEM_HS1 = 0,
    TESTOPTPROBLEM_HS2,
    TESTOPTPROBLEM_HS3,
    TESTOPTPROBLEM_HS4,
    TESTOPTPROBLEM_HS5,
    TESTOPTPROBLEM_HS25,
    TESTOPTPROBLEM_HS38,
    TESTOPTPROBLEM_HS45,
    TESTOPTPROBLEM_BVP,
    TESTOPTPROBLEM_LAST
  };

  inline std::string ETestOptProblemToString(ETestOptProblem to) {
    std::string retString;
    switch(to) {
      case TESTOPTPROBLEM_HS1:  retString = "Hock and Schittkowski Test Problem #1";  break;
      case TESTOPTPROBLEM_HS2:  retString = "Hock and Schittkowski Test Problem #2";  break;
      case TESTOPTPROBLEM_HS3:  retString = "Hock and Schittkowski Test Problem #3";  break;
      case TESTOPTPROBLEM_HS4:  retString = "Hock and Schittkowski Test Problem #4";  break;
      case TESTOPTPROBLEM_HS5:  retString = "Hock and Schittkowski Test Problem #5";  break;
      case TESTOPTPROBLEM_HS25: retString = "Hock and Schittkowski Test Problem #25"; break;
      case TESTOPTPROBLEM_HS38: retString = "Hock and Schittkowski Test Problem #38"; break;
      case TESTOPTPROBLEM_HS45: retString = "Hock and Schittkowski Test Problem #45"; break;
      case TESTOPTPROBLEM_BVP:  retString = "Boundary Value Problem";                 break;
      case TESTOPTPROBLEM_LAST: retString = "Last Type (Dummy)";                      break;
      default:                  retString = "INVALID ETestOptProblem";
    }
    return retString;
  }
  
  inline int isValidTestOptProblem(ETestOptProblem to){
    return( (to == TESTOPTPROBLEM_HS1)  ||
            (to == TESTOPTPROBLEM_HS2)  ||
            (to == TESTOPTPROBLEM_HS3)  ||
            (to == TESTOPTPROBLEM_HS4)  ||
            (to == TESTOPTPROBLEM_HS5)  ||
            (to == TESTOPTPROBLEM_HS25) ||
            (to == TESTOPTPROBLEM_HS38) ||
            (to == TESTOPTPROBLEM_HS45) ||
            (to == TESTOPTPROBLEM_BVP) );
  }

  inline ETestOptProblem & operator++(ETestOptProblem &type) {
    return type = static_cast<ETestOptProblem>(type+1);
  }

  inline ETestOptProblem operator++(ETestOptProblem &type, int) {
    ETestOptProblem oldval = type;
    ++type;
    return oldval;
  }

  inline ETestOptProblem & operator--(ETestOptProblem &type) {
    return type = static_cast<ETestOptProblem>(type-1);
  }

  inline ETestOptProblem operator--(ETestOptProblem &type, int) {
    ETestOptProblem oldval = type;
    --type;
    return oldval;
  }

  inline ETestOptProblem StringToETestOptProblem(std::string s) {
    s = removeStringFormat(s);
    for ( ETestOptProblem to = TESTOPTPROBLEM_HS1; to < TESTOPTPROBLEM_LAST; to++ ) {
      if ( !s.compare(removeStringFormat(ETestOptProblemToString(to))) ) {
        return to;
      }
    }
    return TESTOPTPROBLEM_HS1;
  }


  enum EConstraint{
    CONSTRAINT_EQUALITY = 0,
    CONSTRAINT_INEQUALITY,
    CONSTRAINT_LAST
  };

  inline std::string EConstraintToString(EConstraint c) {
    std::string retString;
    switch(c) {
      case CONSTRAINT_EQUALITY:     retString = "Equality";                           break;
      case CONSTRAINT_INEQUALITY:   retString = "Inequality";                         break;
      case CONSTRAINT_LAST:         retString = "Last Type (Dummy)";                  break;
      default:                      retString = "INVALID EConstraint";
    }
    return retString;
  }

  inline int isValidConstraint(EConstraint c){
    return( (c == CONSTRAINT_EQUALITY)      ||
            (c == CONSTRAINT_INEQUALITY) );
  }

  inline EConstraint & operator++(EConstraint &type) {
    return type = static_cast<EConstraint>(type+1);
  }

  inline EConstraint operator++(EConstraint &type, int) {
    EConstraint oldval = type;
    ++type;
    return oldval;
  }

  inline EConstraint & operator--(EConstraint &type) {
    return type = static_cast<EConstraint>(type-1);
  }

  inline EConstraint operator--(EConstraint &type, int) {
    EConstraint oldval = type;
    --type;
    return oldval;
  }

  inline EConstraint StringToEConstraint(std::string s) {
    s = removeStringFormat(s);
    for ( EConstraint ctype = CONSTRAINT_EQUALITY; ctype < CONSTRAINT_LAST; ctype++ ) {
      if ( !s.compare(removeStringFormat(EConstraintToString(ctype))) ) {
        return ctype;
      }
    }
    return CONSTRAINT_EQUALITY;
  }

  // For use in gradient and Hessian checks
  namespace Finite_Difference_Arrays {

    // Finite difference steps in axpy form    
    const int shifts[4][4] = { {  1,  0,  0, 0 },  // First order
                               { -1,  2,  0, 0 },  // Second order
                               { -1,  2,  1, 0 },  // Third order
                               { -1, -1,  3, 1 }   // Fourth order
                             };

      // Finite difference weights     
     const double weights[4][5] = { { -1.0,          1.0, 0.0,      0.0,      0.0      },  // First order
                                    {  0.0,     -1.0/2.0, 1.0/2.0,  0.0,      0.0      },  // Second order
                                    { -1.0/2.0, -1.0/3.0, 1.0,     -1.0/6.0,  0.0      },  // Third order
                                    {  0.0,     -2.0/3.0, 1.0/12.0, 2.0/3.0, -1.0/12.0 }   // Fourth order
                                  };

  }



} // namespace ROL


#endif