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Comparing trunk/OOPSE/libmdtools/Integrator.hpp (file contents):
Revision 780 by mmeineke, Mon Sep 22 21:23:25 2003 UTC vs.
Revision 1330 by gezelter, Fri Jul 16 16:29:44 2004 UTC

# Line 4 | Line 4
4   #include <string>
5   #include <vector>
6   #include "Atom.hpp"
7 + #include "StuntDouble.hpp"
8   #include "Molecule.hpp"
9   #include "SRI.hpp"
10   #include "AbstractClasses.hpp"
# Line 12 | Line 13
13   #include "Thermo.hpp"
14   #include "ReadWrite.hpp"
15   #include "ZConsWriter.hpp"
16 + #include "Restraints.hpp"
17  
18   using namespace std;
19   const double kB = 8.31451e-7;// boltzmann constant amu*Ang^2*fs^-2/K
# Line 20 | Line 22 | const double tol = 1.0e-6;
22   const int maxIteration = 300;
23   const double tol = 1.0e-6;
24  
25 <
25 > class VelVerletConsFramework;
26   template<typename T = BaseIntegrator> class Integrator : public T {
27  
28   public:
# Line 28 | Line 30 | template<typename T = BaseIntegrator> class Integrator
30    virtual ~Integrator();
31    void integrate( void );
32    virtual double  getConservedQuantity(void);
33 +  virtual string getAdditionalParameters(void);
34  
35   protected:
36  
37    virtual void integrateStep( int calcPot, int calcStress );
38 <  virtual void preMove( void );
38 >  //virtual void preMove( void );
39    virtual void moveA( void );
40    virtual void moveB( void );
41 <  virtual void constrainA( void );
42 <  virtual void constrainB( void );
41 >  //virtual void constrainA( void );
42 >  //virtual void constrainB( void );
43    virtual int  readyCheck( void ) { return 1; }
44  
45    virtual void resetIntegrator( void ) { }
46 <
47 <  virtual void calcForce( int calcPot, int calcStress );  
46 >
47 >  virtual void calcForce( int calcPot, int calcStress );
48    virtual void thermalize();
46 –  
47 –  virtual void rotationPropagation( DirectionalAtom* dAtom, double ji[3] );
49  
50 <  void checkConstraints( void );
51 <  void rotate( int axes1, int axes2, double angle, double j[3],
50 >  virtual bool stopIntegrator() {return false;}
51 >
52 >  virtual void rotationPropagation( StuntDouble* sd, double ji[3] );
53 >
54 >  //void checkConstraints( void );
55 >  void rotate( int axes1, int axes2, double angle, double j[3],
56           double A[3][3] );
57 <        
57 >
58    ForceFields* myFF;
59  
60    SimInfo *info; // all the info we'll ever need
61 +  vector<StuntDouble*> integrableObjects;
62    int nAtoms;  /* the number of atoms */
63    int oldAtoms;
64    Atom **atoms; /* array of atom pointers */
65    Molecule* molecules;
66    int nMols;
67  
68 <  int isConstrained; // boolean to know whether the systems contains
63 <         // constraints.
64 <  int nConstrained;  // counter for number of constraints
65 <  int *constrainedA; // the i of a constraint pair
66 <  int *constrainedB; // the j of a constraint pair
67 <  double *constrainedDsqr; // the square of the constraint distance
68 <  
69 <  int* moving; // tells whether we are moving atom i
70 <  int* moved;  // tells whether we have moved atom i
71 <  double* oldPos; // pre constrained positions
68 >  VelVerletConsFramework* consFramework;
69  
70 +  //int isConstrained; // boolean to know whether the systems contains constraints.
71 +  //int nConstrained;  // counter for number of constraints
72 +  //int *constrainedA; // the i of a constraint pair
73 +  //int *constrainedB; // the j of a constraint pair
74 +  //double *constrainedDsqr; // the square of the constraint distance
75 +
76 +  //int* moving; // tells whether we are moving atom i
77 +  //int* moved;  // tells whether we have moved atom i
78 +  //double* oldPos; // pre constrained positions
79 +
80    short isFirst; /*boolean for the first time integrate is called */
81 <  
81 >
82    double dt;
83    double dt2;
84  
85    Thermo *tStats;
86    StatWriter*  statOut;
87    DumpWriter*  dumpOut;
88 <  
88 >
89   };
90  
91   typedef Integrator<BaseIntegrator> RealIntegrator;
92  
93 + // ansi instantiation
94 + // template class Integrator<BaseIntegrator>;
95 +
96 +
97   template<typename T> class NVE : public T {
98  
99   public:
100    NVE ( SimInfo *theInfo, ForceFields* the_ff ):
101      T( theInfo, the_ff ){}
102 <  virtual ~NVE(){}  
102 >  virtual ~NVE(){}
103   };
104  
105  
# Line 103 | Line 114 | template<typename T> class NVT : public T { (public)
114    void setTargetTemp(double tt) {targetTemp = tt; have_target_temp = 1;}
115    void setChiTolerance(double tol) {chiTolerance = tol;}
116    virtual double  getConservedQuantity(void);
117 +  virtual string getAdditionalParameters(void);
118  
119   protected:
120  
# Line 124 | Line 136 | template<typename T> class NVT : public T { (public)
136  
137    double targetTemp;
138    double tauThermostat;
139 <  
139 >
140    short int have_tau_thermostat, have_target_temp;
141  
142    double *oldVel;
# Line 143 | Line 155 | template<typename T> class NPT : public T{ (public)
155  
156    NPT ( SimInfo *theInfo, ForceFields* the_ff);
157    virtual ~NPT();
158 <  
158 >
159    virtual void integrateStep( int calcPot, int calcStress ){
160      calcStress = 1;
161      T::integrateStep( calcPot, calcStress );
162    }
163  
164    virtual double getConservedQuantity(void) = 0;
165 +  virtual string getAdditionalParameters(void) = 0;
166 +  
167 +  double myTauThermo( void ) { return tauThermostat; }
168 +  double myTauBaro( void ) { return tauBarostat; }
169  
170    void setTauThermostat(double tt) {tauThermostat = tt; have_tau_thermostat=1;}
171    void setTauBarostat(double tb) {tauBarostat = tb; have_tau_barostat=1;}
# Line 170 | Line 186 | template<typename T> class NPT : public T{ (public)
186  
187    virtual void getVelScaleA( double sc[3], double vel[3] ) = 0;
188    virtual void getVelScaleB( double sc[3], int index ) = 0;
189 <  virtual void getPosScale(double pos[3], double COM[3],
189 >  virtual void getPosScale(double pos[3], double COM[3],
190                             int index, double sc[3]) = 0;
191  
192 +  virtual void calcVelScale( void ) = 0;
193 +
194    virtual bool chiConverged( void );
195    virtual bool etaConverged( void ) = 0;
196 <  
196 >
197    virtual void evolveChiA( void );
198    virtual void evolveEtaA( void ) = 0;
199    virtual void evolveChiB( void );
# Line 201 | Line 219 | template<typename T> class NPT : public T{ (public)
219  
220    double integralOfChidt;
221  
222 <  // targetTemp, targetPressure, and tauBarostat must be set.  
222 >  // targetTemp, targetPressure, and tauBarostat must be set.
223    // One of qmass or tauThermostat must be set;
224  
225    double targetTemp;
# Line 226 | Line 244 | template<typename T> class NPTi : public T{
244   };
245  
246   template<typename T> class NPTi : public T{
247 <  
247 >
248   public:
249    NPTi( SimInfo *theInfo, ForceFields* the_ff);
250    ~NPTi();
251  
252    virtual double getConservedQuantity(void);
253    virtual void resetIntegrator(void);
254 <
254 >  virtual string getAdditionalParameters(void);
255   protected:
256  
239 –
257  
258 +
259    virtual void evolveEtaA(void);
260    virtual void evolveEtaB(void);
261  
# Line 247 | Line 265 | template<typename T> class NPTi : public T{
265  
266    virtual void getVelScaleA( double sc[3], double vel[3] );
267    virtual void getVelScaleB( double sc[3], int index );
268 <  virtual void getPosScale(double pos[3], double COM[3],
268 >  virtual void getPosScale(double pos[3], double COM[3],
269                             int index, double sc[3]);
270  
271 <  double eta, oldEta, prevEta;
254 < };
271 >  virtual void calcVelScale( void );
272  
273 < template<typename T> class NPTzm : public T{
274 <
258 < public:
259 <
260 <  NPTzm ( SimInfo *theInfo, ForceFields* the_ff);
261 <  virtual ~NPTzm() {};
262 <
263 <  virtual void integrateStep( int calcPot, int calcStress ){
264 <    calcStress = 1;
265 <    T::integrateStep( calcPot, calcStress );
266 <  }
267 <
268 <  void setTauThermostat(double tt) {tauThermostat = tt; have_tau_thermostat=1;}
269 <  void setTauBarostat(double tb) {tauBarostat = tb; have_tau_barostat=1;}
270 <  void setTargetTemp(double tt) {targetTemp = tt; have_target_temp = 1;}
271 <  void setTargetPressure(double tp) {targetPressure = tp; have_target_pressure = 1;}
272 <
273 < protected:
274 <
275 <  virtual void moveA( void );
276 <  virtual void moveB( void );
277 <
278 <  virtual int readyCheck();
279 <
280 <  virtual void resetIntegrator( void );
281 <
282 <  Molecule* myMolecules;
283 <  Atom** myAtoms;
284 <
285 <  // chi and eta are the propagated degrees of freedom
286 <
287 <  double chi;
288 <  double eta;
289 <  double etaZ;
290 <  double NkBT;
291 <
292 <  // targetTemp, targetPressure, and tauBarostat must be set.  
293 <  // One of qmass or tauThermostat must be set;
294 <
295 <  double targetTemp;
296 <  double targetPressure;
297 <  double tauThermostat;
298 <  double tauBarostat;
299 <
300 <  short int have_tau_thermostat, have_tau_barostat, have_target_temp;
301 <  short int have_target_pressure;
302 <
273 >  double eta, oldEta, prevEta;
274 >  double vScale;
275   };
276  
277   template<typename T> class NPTf : public T{
# Line 310 | Line 282 | template<typename T> class NPTf : public T{ (public)
282    virtual ~NPTf();
283  
284    virtual double getConservedQuantity(void);
285 +  virtual string getAdditionalParameters(void);
286    virtual void resetIntegrator(void);
287  
288   protected:
# Line 323 | Line 296 | template<typename T> class NPTf : public T{ (public)
296  
297    virtual void getVelScaleA( double sc[3], double vel[3] );
298    virtual void getVelScaleB( double sc[3], int index );
299 <  virtual void getPosScale(double pos[3], double COM[3],
299 >  virtual void getPosScale(double pos[3], double COM[3],
300                             int index, double sc[3]);
301  
302 +  virtual void calcVelScale( void );
303 +
304    double eta[3][3];
305    double oldEta[3][3];
306    double prevEta[3][3];
307 +  double vScale[3][3];
308   };
309  
310 < template<typename T> class NPTxym : public T{
310 > template<typename T> class NPTxyz : public T{
311  
312   public:
313  
314 <  NPTxym ( SimInfo *theInfo, ForceFields* the_ff);
315 <  virtual ~NPTxym() {};
314 >  NPTxyz ( SimInfo *theInfo, ForceFields* the_ff);
315 >  virtual ~NPTxyz();
316  
317 <  virtual void integrateStep( int calcPot, int calcStress ){
318 <    calcStress = 1;
319 <    T::integrateStep( calcPot, calcStress );
344 <  }
317 >  virtual double getConservedQuantity(void);
318 >  virtual string getAdditionalParameters(void);
319 >  virtual void resetIntegrator(void);
320  
346 –  void setTauThermostat(double tt) {tauThermostat = tt; have_tau_thermostat=1;}
347 –  void setTauBarostat(double tb) {tauBarostat = tb; have_tau_barostat=1;}
348 –  void setTargetTemp(double tt) {targetTemp = tt; have_target_temp = 1;}
349 –  void setTargetPressure(double tp) {targetPressure = tp; have_target_pressure = 1;}
350 –
321   protected:
322  
323 <  virtual void moveA( void );
324 <  virtual void moveB( void );
323 >  virtual void evolveEtaA(void);
324 >  virtual void evolveEtaB(void);
325  
326 <  virtual int readyCheck();
326 >  virtual bool etaConverged( void );
327  
328 <  virtual void resetIntegrator( void );
328 >  virtual void scaleSimBox( void );
329  
330 <  Molecule* myMolecules;
331 <  Atom** myAtoms;
330 >  virtual void getVelScaleA( double sc[3], double vel[3] );
331 >  virtual void getVelScaleB( double sc[3], int index );
332 >  virtual void getPosScale(double pos[3], double COM[3],
333 >                           int index, double sc[3]);
334  
335 <  // chi and eta are the propagated degrees of freedom
364 <
365 <  double chi;
366 <  double eta;
367 <  double etaX;
368 <  double etaY;
369 <  double NkBT;
370 <
371 <  // targetTemp, targetPressure, and tauBarostat must be set.  
372 <  // One of qmass or tauThermostat must be set;
373 <
374 <  double targetTemp;
375 <  double targetPressure;
376 <  double tauThermostat;
377 <  double tauBarostat;
378 <
379 <  short int have_tau_thermostat, have_tau_barostat, have_target_temp;
380 <  short int have_target_pressure;
381 <
382 < };
383 <
384 <
385 < template<typename T> class NPTfm : public T{
386 <
387 < public:
388 <
389 <  NPTfm ( SimInfo *theInfo, ForceFields* the_ff);
390 <  virtual ~NPTfm() {};
391 <
392 <  virtual void integrateStep( int calcPot, int calcStress ){
393 <    calcStress = 1;
394 <    T::integrateStep( calcPot, calcStress );
395 <    accIntegralOfChidt();
396 <  }
397 <
398 <  virtual double getConservedQuantity(void);
399 <  
400 <  void setTauThermostat(double tt) {tauThermostat = tt; have_tau_thermostat=1;}
401 <  void setTauBarostat(double tb) {tauBarostat = tb; have_tau_barostat=1;}
402 <  void setTargetTemp(double tt) {targetTemp = tt; have_target_temp = 1;}
403 <  void setTargetPressure(double tp) {targetPressure = tp; have_target_pressure = 1;}
404 <  void setChiTolerance(double tol) {chiTolerance = tol;}
405 <  void setPosIterTolerance(double tol) {posIterTolerance = tol;}
335 >  virtual void calcVelScale( void );
336  
407 – protected:
408 –
409 –  virtual void  moveA( void );
410 –  virtual void moveB( void );
411 –
412 –  virtual void resetIntegrator( void );
413 –
414 –  virtual int readyCheck();
415 –
416 –  void accIntegralOfChidt(void) { integralOfChidt += dt * chi;}
417 –
418 –  Molecule* myMolecules;
419 –  Atom** myAtoms;
420 –
421 –  // chi and eta are the propagated degrees of freedom
422 –
423 –  double chi;
337    double eta[3][3];
338 <  double NkBT;
339 <  double integralOfChidt;
340 <
428 <  // targetTemp, targetPressure, and tauBarostat must be set.  
429 <  // One of qmass or tauThermostat must be set;
430 <
431 <  double targetTemp;
432 <  double targetPressure;
433 <  double tauThermostat;
434 <  double tauBarostat;
435 <
436 <  short int have_tau_thermostat, have_tau_barostat, have_target_temp;
437 <  short int have_target_pressure;
438 <  double chiTolerance;
439 <  short int have_chi_tolerance;
440 <  double posIterTolerance;
441 <  short int have_pos_iter_tolerance;
442 <
338 >  double oldEta[3][3];
339 >  double prevEta[3][3];
340 >  double vScale[3][3];
341   };
342  
343  
446 – template<typename T> class NPTpr : public T{
447 –
448 – public:
449 –
450 –  NPTpr ( SimInfo *theInfo, ForceFields* the_ff);
451 –  virtual ~NPTpr() {};
452 –
453 –  virtual void integrateStep( int calcPot, int calcStress ){
454 –    calcStress = 1;
455 –    T::integrateStep( calcPot, calcStress );
456 –  }
457 –
458 –  void setTauThermostat(double tt) {tauThermostat = tt; have_tau_thermostat=1;}
459 –  void setTauBarostat(double tb) {tauBarostat = tb; have_tau_barostat=1;}
460 –  void setTargetTemp(double tt) {targetTemp = tt; have_target_temp = 1;}
461 –  void setTargetPressure(double tp) {targetPressure = tp; have_target_pressure = 1;}
462 –  void setChiTolerance(double tol) {chiTolerance = tol;}
463 –  void setPosIterTolerance(double tol) {posIterTolerance = tol;}
464 –
465 – protected:
466 –
467 –  virtual void  moveA( void );
468 –  virtual void moveB( void );
469 –
470 –  virtual int readyCheck();
471 –
472 –  virtual void resetIntegrator( void );
473 –
474 –  // chi and eta are the propagated degrees of freedom
475 –
476 –  double chi;
477 –  double eta[3][3];
478 –  double NkBT;
479 –
480 –  // targetTemp, targetPressure, and tauBarostat must be set.  
481 –  // One of qmass or tauThermostat must be set;
482 –
483 –  double targetTemp;
484 –  double targetPressure;
485 –  double tauThermostat;
486 –  double tauBarostat;
487 –
488 –  short int have_tau_thermostat, have_tau_barostat, have_target_temp;
489 –  short int have_target_pressure;
490 –  double chiTolerance;
491 –  short int have_chi_tolerance;
492 –  double posIterTolerance;
493 –  short int have_pos_iter_tolerance;
494 –
495 – };
496 –
497 –
344   template<typename T> class ZConstraint : public T {
345 <  
346 <  public:
345 >
346 >  public:
347    class ForceSubtractionPolicy{
348      public:
349        ForceSubtractionPolicy(ZConstraint<T>* integrator) {zconsIntegrator = integrator;}
350  
351 <      virtual void update() = 0;    
351 >      virtual void update() = 0;
352        virtual double getZFOfFixedZMols(Molecule* mol, Atom* atom, double totalForce) = 0;
353        virtual double getZFOfMovingMols(Atom* atom, double totalForce) = 0;
354        virtual double getHFOfFixedZMols(Molecule* mol, Atom* atom, double totalForce) = 0;
355        virtual double getHFOfUnconsMols(Atom* atom, double totalForce) = 0;
356 <    
356 >
357     protected:
358 <     ZConstraint<T>* zconsIntegrator;;
358 >     ZConstraint<T>* zconsIntegrator;
359    };
360  
361    class PolicyByNumber : public ForceSubtractionPolicy{
362  
363      public:
364 <      PolicyByNumber(ZConstraint<T>* integrator) :ForceSubtractionPolicy(integrator) {}    
365 <      virtual void update();    
364 >      PolicyByNumber(ZConstraint<T>* integrator) :ForceSubtractionPolicy(integrator) {}
365 >      virtual void update();
366        virtual double getZFOfFixedZMols(Molecule* mol, Atom* atom, double totalForce) ;
367        virtual double getZFOfMovingMols(Atom* atom, double totalForce) ;
368        virtual double getHFOfFixedZMols(Molecule* mol, Atom* atom, double totalForce);
369        virtual double getHFOfUnconsMols(Atom* atom, double totalForce);
370 <    
370 >
371      private:
372        int totNumOfMovingAtoms;
373    };
# Line 529 | Line 375 | template<typename T> class ZConstraint : public T {
375    class PolicyByMass : public ForceSubtractionPolicy{
376  
377      public:
378 <      PolicyByMass(ZConstraint<T>* integrator) :ForceSubtractionPolicy(integrator) {}  
379 <      
380 <      virtual void update();    
378 >      PolicyByMass(ZConstraint<T>* integrator) :ForceSubtractionPolicy(integrator) {}
379 >
380 >      virtual void update();
381        virtual double getZFOfFixedZMols(Molecule* mol, Atom* atom, double totalForce) ;
382        virtual double getZFOfMovingMols(Atom* atom, double totalForce) ;
383        virtual double getHFOfFixedZMols(Molecule* mol, Atom* atom, double totalForce);
# Line 545 | Line 391 | template<typename T> class ZConstraint : public T {
391  
392    ZConstraint( SimInfo *theInfo, ForceFields* the_ff);
393    ~ZConstraint();
394 <    
394 >
395    void setZConsTime(double time)                  {this->zconsTime = time;}
396    void getZConsTime()                             {return zconsTime;}
397 <  
397 >
398    void setIndexOfAllZConsMols(vector<int> index) {indexOfAllZConsMols = index;}
399    void getIndexOfAllZConsMols()                  {return indexOfAllZConsMols;}
400 <  
400 >
401    void setZConsOutput(const char * fileName)          {zconsOutput = fileName;}
402    string getZConsOutput()                         {return zconsOutput;}
403 <  
403 >
404    virtual void integrate();
559 –  
405  
406 +
407   #ifdef IS_MPI
408    virtual void update();                      //which is called to indicate the molecules' migration
409   #endif
410  
411 +  enum ZConsState {zcsMoving, zcsFixed};
412 +
413 +  vector<Molecule*> zconsMols;              //z-constraint molecules array
414 +  vector<ZConsState> states;                 //state of z-constraint molecules
415 +
416 +
417 +
418 +  int totNumOfUnconsAtoms;              //total number of uncontraint atoms
419 +  double totalMassOfUncons;                //total mas of unconstraint molecules
420 +
421 +
422   protected:
423  
424 <  enum ZConsState {zcsMoving, zcsFixed};  
425 <
426 <  virtual void calcForce( int calcPot, int calcStress );
424 >
425 >
426 >  virtual void calcForce( int calcPot, int calcStress );
427    virtual void thermalize(void);
428 <  
428 >
429    void zeroOutVel();
430    void doZconstraintForce();
431 <  void doHarmonic();
431 >  void doHarmonic(vector<double>& resPos);
432    bool checkZConsState();
433  
434    bool haveFixedZMols();
# Line 586 | Line 443 | template<typename T> class ZConstraint : public T {
443    double zconsTol;                                 //tolerance of z-contratint
444    double zForceConst;                           //base force constant term
445                                                            //which is estimate by OOPSE
446 <  
447 <  vector<Molecule*> zconsMols;              //z-constraint molecules array
448 <  vector<double> massOfZConsMols;       //mass of z-constraint molecule
446 >
447 >
448 >  vector<double> massOfZConsMols;       //mass of z-constraint molecule
449    vector<double> kz;                              //force constant array
450 <  vector<ZConsState> states;                 //state of z-constraint molecules
450 >
451    vector<double> zPos;                          //
452 <  
453 <  
452 >
453 >
454    vector<Molecule*> unconsMols;           //unconstraint molecules array
455    vector<double> massOfUnconsMols;    //mass array of unconstraint molecules
599 –  double totalMassOfUncons;                //total mas of unconstraint molecules
456  
457 +
458    vector<ZConsParaItem>* parameters; //
459 <  
459 >
460    vector<int> indexOfAllZConsMols;     //index of All Z-Constraint Molecuels
461  
462 <  int* indexOfZConsMols;                   //index of local Z-Constraint Molecules  
463 <  double* fz;
464 <  double* curZPos;
608 <  
609 <  int totNumOfUnconsAtoms;              //total number of uncontraint atoms
462 >  vector<int> indexOfZConsMols;                   //index of local Z-Constraint Molecules
463 >  vector<double> fz;
464 >  vector<double> curZPos;
465  
466 <  int whichDirection;                           //constraint direction
466 >  bool usingSMD;
467 >  vector<double> prevCantPos;
468 >  vector<double> cantPos;
469 >  vector<double> cantVel;
470 >
471 >  double zconsFixTime;  
472 >  double zconsGap;
473 >  bool hasZConsGap;
474 >  vector<double> endFixTime;
475    
476 +  int whichDirection;                           //constraint direction
477 +
478   private:
479 <  
479 >
480    string zconsOutput;                         //filename of zconstraint output
481    ZConsWriter* fzOut;                         //z-constraint writer
482  
483 <  double curZconsTime;                      
483 >  double curZconsTime;
484  
485    double calcMovingMolsCOMVel();
486    double calcSysCOMVel();
487    double calcTotalForce();
488 +  void updateZPos();
489 +  void updateCantPos();
490    
491    ForceSubtractionPolicy* forcePolicy; //force subtraction policy
492    friend class ForceSubtractionPolicy;
493  
494   };
495  
496 +
497 + //Sympletic quaternion Scheme Integrator
498 + //Reference:
499 + // T.F. Miller, M. Eleftheriou, P. Pattnaik, A. Ndirango, D. Newns and G.J. Martyna
500 + //Symplectic quaternion Scheme for biophysical molecular dynamics
501 + //116(20), 8649, J. Chem. Phys. (2002)
502 + template<typename T> class SQSIntegrator : public T{
503 +  public:
504 +    virtual void moveA();
505 +    virtual void moveB();
506 +  protected:
507 +    void freeRotor();
508 +    void rotate(int k, double dt);
509 +    
510 + };
511   #endif

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