# include <math.h>
# include <stdio.h>
# include <stdlib.h>
# include <time.h>

int main ( int argc, char *argv[] );
void compute ( int np, int nd, double pos[], double vel[], 
  double mass, double f[], double *pot, double *kin );
double cpu_time ( );
double dist ( int nd, double r1[], double r2[], double dr[] );
void initialize ( int np, int nd, double pos[], double vel[], double acc[] );
void r8mat_uniform_ab ( int m, int n, double a, double b, int *seed, double r[] );
void timestamp ( );
void update ( int np, int nd, double pos[], double vel[], double f[], 
  double acc[], double mass, double dt );

/******************************************************************************/

int main ( int argc, char *argv[] )

/******************************************************************************/
/*
  Purpose:

    MAIN is the main program for MD.

  Discussion:

    MD implements a simple molecular dynamics simulation.

    The velocity Verlet time integration scheme is used. 

    The particles interact with a central pair potential.

    This program is based on a FORTRAN90 program by Bill Magro.

  Usage:

    md nd np step_num dt

    where:

    * nd is the spatial dimension (2 or 3);
    * np is the number of particles (500, for instance);
    * step_num is the number of time steps (500, for instance).
    * dt is the time step (0.1 for instance)

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    27 December 2014

  Author:

    John Burkardt.
*/
{
  double *acc;
  double ctime;
  double dt;
  double e0;
  double *force;
  double kinetic;
  double mass = 1.0;
  int nd;
  int np;
  double *pos;
  double potential;
  int step;
  int step_num;
  int step_print;
  int step_print_index;
  int step_print_num;
  double *vel;

  timestamp ( );
  printf ( "\n" );
  printf ( "MD\n" );
  printf ( "  C version\n" );
  printf ( "  A molecular dynamics program.\n" );
/*
  Get the spatial dimension.
*/
  if ( 1 < argc )
  {
    nd = atoi ( argv[1] );
  }
  else
  {
    printf ( "\n" );
    printf ( "  Enter ND, the spatial dimension (2 or 3).\n" );
    scanf ( "%d", &nd );
  }
//
//  Get the number of particles.
//
  if ( 2 < argc )
  {
    np = atoi ( argv[2] );
  }
  else
  {
    printf ( "\n" );
    printf ( "  Enter NP, the number of particles (500, for instance).\n" );
    scanf ( "%d", &np );
  }
//
//  Get the number of time steps.
//
  if ( 3 < argc )
  {
    step_num = atoi ( argv[3] );
  }
  else
  {
    printf ( "\n" );
    printf ( "  Enter ND, the number of time steps (500 or 1000, for instance).\n" );
    scanf ( "%d", &step_num );
  }
//
//  Get the time steps.
//
  if ( 4 < argc )
  {
    dt = atof ( argv[4] );
  }
  else
  {
    printf ( "\n" );
    printf ( "  Enter DT, the size of the time step (0.1, for instance).\n" );
    scanf ( "%lf", &dt );
  }
/*
  Report.
*/
  printf ( "\n" );
  printf ( "  ND, the spatial dimension, is %d\n", nd );
  printf ( "  NP, the number of particles in the simulation, is %d\n", np );
  printf ( "  STEP_NUM, the number of time steps, is %d\n", step_num );
  printf ( "  DT, the size of each time step, is %f\n", dt );
/*
  Allocate memory.
*/
  acc = ( double * ) malloc ( nd * np * sizeof ( double ) );
  force = ( double * ) malloc ( nd * np * sizeof ( double ) );
  pos = ( double * ) malloc ( nd * np * sizeof ( double ) );
  vel = ( double * ) malloc ( nd * np * sizeof ( double ) );
/*
  This is the main time stepping loop:
    Compute forces and energies,
    Update positions, velocities, accelerations.
*/
  printf ( "\n" );
  printf ( "  At each step, we report the potential and kinetic energies.\n" );
  printf ( "  The sum of these energies should be a constant.\n" );
  printf ( "  As an accuracy check, we also print the relative error\n" );
  printf ( "  in the total energy.\n" );
  printf ( "\n" );
  printf ( "      Step      Potential       Kinetic        (P+K-E0)/E0\n" );
  printf ( "                Energy P        Energy K       Relative Energy Error\n" );
  printf ( "\n" );

  step_print = 0;
  step_print_index = 0;
  step_print_num = 10;
  
  ctime = cpu_time ( );

  for ( step = 0; step <= step_num; step++ )
  {
    if ( step == 0 )
    {
      initialize ( np, nd, pos, vel, acc );
    }
    else
    {
      update ( np, nd, pos, vel, force, acc, mass, dt );
    }

    compute ( np, nd, pos, vel, mass, force, &potential, &kinetic );

    if ( step == 0 )
    {
      e0 = potential + kinetic;
    }

    if ( step == step_print )
    {
      printf ( "  %8d  %14f  %14f  %14e\n", step, potential, kinetic,
       ( potential + kinetic - e0 ) / e0 );
      step_print_index = step_print_index + 1;
      step_print = ( step_print_index * step_num ) / step_print_num;
    }

  }
/*
  Report timing.
*/
  ctime = cpu_time ( ) - ctime;
  printf ( "\n" );
  printf ( "  Elapsed cpu time: %f seconds.\n", ctime );
/*
  Free memory.
*/
  free ( acc );
  free ( force );
  free ( pos );
  free ( vel );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "MD\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

  return 0;
}
/******************************************************************************/

void compute ( int np, int nd, double pos[], double vel[], double mass, 
  double f[], double *pot, double *kin )

/******************************************************************************/
/*
  Purpose:

    COMPUTE computes the forces and energies.

  Discussion:

    The computation of forces and energies is fully parallel.

    The potential function V(X) is a harmonic well which smoothly
    saturates to a maximum value at PI/2:

      v(x) = ( sin ( min ( x, PI/2 ) ) )^2

    The derivative of the potential is:

      dv(x) = 2.0 * sin ( min ( x, PI/2 ) ) * cos ( min ( x, PI/2 ) )
            = sin ( 2.0 * min ( x, PI/2 ) )

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    21 November 2007

  Author:

    John Burkardt.

  Parameters:

    Input, int NP, the number of particles.

    Input, int ND, the number of spatial dimensions.

    Input, double POS[ND*NP], the positions.

    Input, double VEL[ND*NP], the velocities.

    Input, double MASS, the mass of each particle.

    Output, double F[ND*NP], the forces.

    Output, double *POT, the total potential energy.

    Output, double *KIN, the total kinetic energy.
*/
{
  double d;
  double d2;
  int i;
  int j;
  int k;
  double ke;
  double pe;
  double PI2 = 3.141592653589793 / 2.0;
  double rij[3];

  pe = 0.0;
  ke = 0.0;

  for ( k = 0; k < np; k++ )
  {
/*
  Compute the potential energy and forces.
*/
    for ( i = 0; i < nd; i++ )
    {
      f[i+k*nd] = 0.0;
    }

    for ( j = 0; j < np; j++ )
    {
      if ( k != j )
      {
        d = dist ( nd, pos+k*nd, pos+j*nd, rij );
/*
  Attribute half of the potential energy to particle J.
*/
        if ( d < PI2 )
        {
          d2 = d;
        }
        else
        {
          d2 = PI2;
        }

        pe = pe + 0.5 * pow ( sin ( d2 ), 2 );

        for ( i = 0; i < nd; i++ )
        {
          f[i+k*nd] = f[i+k*nd] - rij[i] * sin ( 2.0 * d2 ) / d;
        }
      }
    }
/*
  Compute the kinetic energy.
*/
    for ( i = 0; i < nd; i++ )
    {
      ke = ke + vel[i+k*nd] * vel[i+k*nd];
    }
  }

  ke = ke * 0.5 * mass;
  
  *pot = pe;
  *kin = ke;

  return;
}
/*******************************************************************************/

double cpu_time ( )

/*******************************************************************************/
/*
  Purpose:
 
    CPU_TIME reports the total CPU time for a program.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    27 September 2005

  Author:

    John Burkardt

  Parameters:

    Output, double CPU_TIME, the current total elapsed CPU time in second.
*/
{
  double value;

  value = ( double ) clock ( ) / ( double ) CLOCKS_PER_SEC;

  return value;
}
/******************************************************************************/

double dist ( int nd, double r1[], double r2[], double dr[] )

/******************************************************************************/
/*
  Purpose:

    DIST computes the displacement (and its norm) between two particles.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    21 November 2007

  Author:

    John Burkardt.

  Parameters:

    Input, int ND, the number of spatial dimensions.

    Input, double R1[ND], R2[ND], the positions of the particles.

    Output, double DR[ND], the displacement vector.

    Output, double D, the Euclidean norm of the displacement.
*/
{
  double d;
  int i;

  d = 0.0;
  for ( i = 0; i < nd; i++ )
  {
    dr[i] = r1[i] - r2[i];
    d = d + dr[i] * dr[i];
  }
  d = sqrt ( d );

  return d;
}
/******************************************************************************/

void initialize ( int np, int nd, double pos[], double vel[], double acc[] )

/******************************************************************************/
/*
  Purpose:

    INITIALIZE initializes the positions, velocities, and accelerations.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    26 December 2014

  Author:

    John Burkardt.

  Parameters:

    Input, int NP, the number of particles.

    Input, int ND, the number of spatial dimensions.

    Output, double POS[ND*NP], the positions.

    Output, double VEL[ND*NP], the velocities.

    Output, double ACC[ND*NP], the accelerations.
*/
{
  int i;
  int j;
  int seed;
/*
  Set positions.
*/
  seed = 123456789;
  r8mat_uniform_ab ( nd, np, 0.0, 10.0, &seed, pos );
/*
  Set velocities.
*/
  for ( j = 0; j < np; j++ )
  {
    for ( i = 0; i < nd; i++ )
    {
      vel[i+j*nd] = 0.0;
    }
  }
/*
  Set accelerations.
*/
  for ( j = 0; j < np; j++ )
  {
    for ( i = 0; i < nd; i++ )
    {
      acc[i+j*nd] = 0.0;
    }
  }

  return;
}
/******************************************************************************/

void r8mat_uniform_ab ( int m, int n, double a, double b, int *seed, double r[] )

/******************************************************************************/
/*
  Purpose:

    R8MAT_UNIFORM_AB returns a scaled pseudorandom R8MAT.

  Discussion:

    This routine implements the recursion

      seed = 16807 * seed mod ( 2^31 - 1 )
      unif = seed / ( 2^31 - 1 )

    The integer arithmetic never requires more than 32 bits,
    including a sign bit.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    03 October 2005

  Author:

    John Burkardt

  Reference:

    Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673,
    LC: QA76.9.C65.B73.

    Bennett Fox,
    Algorithm 647:
    Implementation and Relative Efficiency of Quasirandom
    Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, December 1986, pages 362-376.

    Pierre L'Ecuyer,
    Random Number Generation,
    in Handbook of Simulation,
    edited by Jerry Banks,
    Wiley, 1998,
    ISBN: 0471134031,
    LC: T57.62.H37.

    Peter Lewis, Allen Goodman, James Miller,
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, Number 2, 1969, pages 136-143.

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A, B, the limits of the pseudorandom values.

    Input/output, int *SEED, the "seed" value.  Normally, this
    value should not be 0.  On output, SEED has 
    been updated.

    Output, double R[M*N], a matrix of pseudorandom values.
*/
{
  int i;
  const int i4_huge = 2147483647;
  int j;
  int k;

  if ( *seed == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8MAT_UNIFORM_AB - Fatal error!\n" );
    fprintf ( stderr, "  Input value of SEED = 0.\n" );
    exit ( 1 );
  }

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      k = *seed / 127773;

      *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

      if ( *seed < 0 )
      {
        *seed = *seed + i4_huge;
      }
      r[i+j*m] = a + ( b - a ) * ( double ) ( *seed ) * 4.656612875E-10;
    }
  }

  return;
}
/******************************************************************************/

void timestamp ( )

/******************************************************************************/
/*
  Purpose:

    TIMESTAMP prints the current YMDHMS date as a time stamp.

  Example:

    31 May 2001 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    24 September 2003

  Author:

    John Burkardt

  Parameters:

    None
*/
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}
/******************************************************************************/

void update ( int np, int nd, double pos[], double vel[], double f[], 
  double acc[], double mass, double dt )

/******************************************************************************/
/*
  Purpose:

    UPDATE updates positions, velocities and accelerations.

  Discussion:

    The time integration is fully parallel.

    A velocity Verlet algorithm is used for the updating.

    x(t+dt) = x(t) + v(t) * dt + 0.5 * a(t) * dt * dt
    v(t+dt) = v(t) + 0.5 * ( a(t) + a(t+dt) ) * dt
    a(t+dt) = f(t) / m

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    21 November 2007

  Author:

    John Burkardt.

  Parameters:

    Input, int NP, the number of particles.

    Input, int ND, the number of spatial dimensions.

    Input/output, double POS[ND*NP], the positions.

    Input/output, double VEL[ND*NP], the velocities.

    Input, double F[ND*NP], the forces.

    Input/output, double ACC[ND*NP], the accelerations.

    Input, double MASS, the mass.

    Input, double DT, the time step.
*/
{
  int i;
  int j;
  double rmass;

  rmass = 1.0 / mass;

  for ( j = 0; j < np; j++ )
  {
    for ( i = 0; i < nd; i++ )
    {
      pos[i+j*nd] = pos[i+j*nd] + vel[i+j*nd] * dt + 0.5 * acc[i+j*nd] * dt * dt;
      vel[i+j*nd] = vel[i+j*nd] + 0.5 * dt * ( f[i+j*nd] * rmass + acc[i+j*nd] );
      acc[i+j*nd] = f[i+j*nd] * rmass;
    }
  }

  return;
}