Additional example using a very light md implementation using openmp. Data is saved during simulation.

1 files changed, 880 insertions, 0 deletions

diff --git a/src/tests/md_openmp.c b/src/tests/md_openmp.c
new file mode 100644
index 0000000..0b5241a
--- /dev/null
+++ b/src/tests/md_openmp.c
@@ -0,0 +1,880 @@
+# include <stdlib.h>
+# include <stdio.h>
+# include <time.h>
+# include <math.h>
+# include <omp.h>
+# include <tng_io.h>
+#include "tng_io_testing.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 dist ( int nd, double r1[], double r2[], double dr[] );
+void initialize ( int np, int nd, double box[], int *seed, double pos[], 
+    double vel[], double acc[] );
+double r8_uniform_01 ( int *seed );
+void timestamp ( void );
+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_OPENMP.
+
+    Discussion:
+
+        MD implements a simple molecular dynamics simulation.
+
+        The program uses Open MP directives to allow parallel computation.
+
+        The velocity Verlet time integration scheme is used.
+
+        The particles interact with a central pair potential.
+
+    Licensing:
+
+        This code is distributed under the GNU LGPL license.
+
+    Modified:
+
+        30 July 2009
+
+    Author:
+
+        Original FORTRAN77 version by Bill Magro.
+        C version by John Burkardt.
+        TNG trajectory output by Magnus Lundborg.
+
+    Parameters:
+
+        None
+*/
+{
+    double *acc;
+    double *box;
+    double *box_shape;
+    double dt = 0.0001;
+    double e0;
+    double *force;
+    int i;
+    double kinetic;
+    double mass = 1.0;
+    int nd = 3;
+    int np = 100;
+    double *pos;
+    double potential;
+    int proc_num;
+    int seed = 123456789;
+    int step;
+    int step_num = 1000;
+    int step_print;
+    int step_print_index;
+    int step_print_num;
+    int step_save;
+    double *vel;
+    double wtime;
+    tng_trajectory_t traj;
+    tng_molecule_t molecule;
+    tng_chain_t chain;
+    tng_residue_t residue;
+    tng_atom_t atom;
+    int64_t n_frames_per_frame_set;
+    int frames_saved_cnt = 0;
+    int frame_set_cnt = 0;
+    double **data;
+
+    timestamp ( );
+
+    proc_num = omp_get_num_procs ( );
+
+    acc = ( double * ) malloc ( nd * np * sizeof ( double ) );
+    box = ( double * ) malloc ( nd * sizeof ( double ) );
+    box_shape = (double *) malloc (9 * sizeof (double));
+    force = ( double * ) malloc ( nd * np * sizeof ( double ) );
+    pos = ( double * ) malloc ( nd * np * sizeof ( double ) );
+    vel = ( double * ) malloc ( nd * np * sizeof ( double ) );
+
+    printf ( "\n" );
+    printf ( "MD_OPENMP\n" );
+    printf ( "  C/OpenMP version\n" );
+    printf ( "\n" );
+    printf ( "  A molecular dynamics program.\n" );
+
+    printf ( "\n" );
+    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 );
+
+    printf ( "\n" );
+    printf ( "  Number of processors available = %d\n", omp_get_num_procs ( ) );
+    printf ( "  Number of threads =              %d\n", omp_get_max_threads ( ) );
+
+    
+    printf("\n");
+    printf("  Initializing trajectory storage.\n");
+    if(tng_trajectory_init(&traj) != TNG_SUCCESS)
+    {
+        tng_trajectory_destroy(&traj);
+        printf("  Cannot init trajectory.\n");
+        exit(1);
+    }
+#ifdef EXAMPLE_FILES_DIR
+    tng_output_file_set(traj, EXAMPLE_FILES_DIR "tng_md_out.tng");
+#else
+    tng_output_file_set(traj, "/tmp/tng_md_out.tng");
+#endif
+
+
+
+    /* Set molecules data */
+    printf("  Creating molecules in trajectory.\n");
+    tng_molecule_add(traj, "water", &molecule);
+    tng_molecule_chain_add(traj, molecule, "W", &chain);
+    tng_chain_residue_add(traj, chain, "WAT", &residue);
+    if(tng_residue_atom_add(traj, residue, "O", "O", &atom) == TNG_CRITICAL)
+    {
+        tng_trajectory_destroy(&traj);
+        printf("  Cannot create molecules.\n");
+        exit(1);
+    }
+    tng_molecule_cnt_set(traj, molecule, np);
+
+    
+/*
+    Set the dimensions of the box.
+*/
+    for(i = 0; i < 9; i++)
+    {
+        box_shape[i] = 0.0;
+    }
+    for ( i = 0; i < nd; i++ )
+    {
+        box[i] = 10.0;
+        box_shape[i*nd + i] = box[i];
+    }
+
+
+    if(tng_data_block_add(traj, TNG_TRAJ_BOX_SHAPE, "BOX SHAPE", TNG_DOUBLE_DATA,
+                       TNG_NON_TRAJECTORY_BLOCK, 1, 9, 1, TNG_UNCOMPRESSED,
+                       box_shape) == TNG_CRITICAL ||
+                       tng_file_headers_write(traj, TNG_USE_HASH) == TNG_CRITICAL)
+    {
+        tng_trajectory_destroy(&traj);
+        printf("  Cannot write trajectory headers and box shape.\n");
+        exit(1);
+    }
+
+    printf ( "\n" );
+    printf ( "  Initializing positions, velocities, and accelerations.\n" );
+/*
+    Set initial positions, velocities, and accelerations.
+*/
+    initialize ( np, nd, box, &seed, pos, vel, acc );
+/*
+    Compute the forces and energies.
+*/
+    printf ( "\n" );
+    printf ( "  Computing initial forces and energies.\n" );
+
+    compute ( np, nd, pos, vel, mass, force, &potential, &kinetic );
+
+    e0 = potential + kinetic;
+/*
+    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;
+    
+    step = 0;
+    printf ( "  %8d  %14f  %14f  %14e\n",
+        step, potential, kinetic, ( potential + kinetic - e0 ) / e0 );
+    step_print_index++;
+    step_print = ( step_print_index * step_num ) / step_print_num;
+
+    /* Saving frequency */
+    step_save = 5;
+
+    wtime = omp_get_wtime ( );
+
+    /* Create a frame set for writing data */
+    tng_num_frames_per_frame_set_get(traj, &n_frames_per_frame_set);
+    if(tng_frame_set_new(traj, 0,
+        n_frames_per_frame_set) != TNG_SUCCESS)
+    {
+        printf("Error creating frame set %d. %s: %d\n",
+                i, __FILE__, __LINE__);
+        exit(1);
+    }
+    frame_set_cnt++;
+
+    /* Setup an empty data array - this will be written to the frame set
+     * (since the block size needs to be correct in the file. After that it
+     * is filled with data. */
+    data = malloc(n_frames_per_frame_set * 3 * np * sizeof(double));
+
+    for(i = 0; i < n_frames_per_frame_set * 3 * np; i++)
+    {
+        data[i] = 0;
+    }
+
+    
+    /* Add data blocks */
+    if(tng_particle_data_block_add(traj, TNG_TRAJ_POSITIONS,
+                                "POSITIONS",
+                                TNG_DOUBLE_DATA,
+                                TNG_TRAJECTORY_BLOCK,
+                                n_frames_per_frame_set, 3,
+                                1, 0, np,
+                                TNG_UNCOMPRESSED,
+                                data) != TNG_SUCCESS)
+    {
+        printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+    if(tng_particle_data_block_add(traj, TNG_TRAJ_VELOCITIES,
+                                "VELOCITIES",
+                                TNG_DOUBLE_DATA,
+                                TNG_TRAJECTORY_BLOCK,
+                                n_frames_per_frame_set, 3,
+                                1, 0, np,
+                                TNG_UNCOMPRESSED,
+                                data) != TNG_SUCCESS)
+    {
+        printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+    if(tng_particle_data_block_add(traj, TNG_TRAJ_FORCES,
+                                "FORCES",
+                                TNG_DOUBLE_DATA,
+                                TNG_TRAJECTORY_BLOCK,
+                                n_frames_per_frame_set, 3,
+                                1, 0, np,
+                                TNG_UNCOMPRESSED,
+                                data) != TNG_SUCCESS)
+    {
+        printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+    
+    /* Write the frame set to disk */
+    if(tng_frame_set_write(traj, TNG_SKIP_HASH) != TNG_SUCCESS)
+    {
+        printf("Error writing frame set. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+
+    if(tng_frame_particle_data_write(traj, 0,
+                                    TNG_TRAJ_POSITIONS, 0, np,
+                                    pos, TNG_USE_HASH) != TNG_SUCCESS)
+    {
+        printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+    if(tng_frame_particle_data_write(traj, 0,
+                                    TNG_TRAJ_VELOCITIES, 0, np,
+                                    vel, TNG_USE_HASH) != TNG_SUCCESS)
+    {
+        printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+    if(tng_frame_particle_data_write(traj, 0,
+                                    TNG_TRAJ_FORCES, 0, np,
+                                    force, TNG_USE_HASH) != TNG_SUCCESS)
+    {
+        printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+        free(data);
+        exit(1);
+    }
+    frames_saved_cnt++;
+
+    
+//     printf("pos: %f, vel: %f, force: %f\n", pos[0], vel[0], force[0]);
+        
+    for ( step = 1; step <= step_num; step++ )
+    {
+        compute ( np, nd, pos, vel, mass, force, &potential, &kinetic );
+
+        if ( step == step_print )
+        {
+            printf ( "  %8d  %14f  %14f  %14e\n", step, potential, kinetic,
+             ( potential + kinetic - e0 ) / e0 );
+            step_print_index++;
+            step_print = ( step_print_index * step_num ) / step_print_num;
+        }
+        if(step % step_save == 0)
+        {
+            if(frames_saved_cnt % n_frames_per_frame_set == 0)
+            {
+                if(tng_frame_set_new(traj, frames_saved_cnt,
+                    n_frames_per_frame_set) != TNG_SUCCESS)
+                {
+                    printf("Error creating frame set %d. %s: %d\n",
+                            i, __FILE__, __LINE__);
+                    free(data);
+                    exit(1);
+                }
+                /* Add data blocks */
+                if(tng_particle_data_block_add(traj, TNG_TRAJ_POSITIONS,
+                                            "POSITIONS",
+                                            TNG_DOUBLE_DATA,
+                                            TNG_TRAJECTORY_BLOCK,
+                                            n_frames_per_frame_set, 3,
+                                            1, 0, np,
+                                            TNG_UNCOMPRESSED,
+                                            data) != TNG_SUCCESS)
+                {
+                    printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+                    free(data);
+                    exit(1);
+                }
+                if(tng_particle_data_block_add(traj, TNG_TRAJ_VELOCITIES,
+                                            "VELOCITIES",
+                                            TNG_DOUBLE_DATA,
+                                            TNG_TRAJECTORY_BLOCK,
+                                            n_frames_per_frame_set, 3,
+                                            1, 0, np,
+                                            TNG_UNCOMPRESSED,
+                                            data) != TNG_SUCCESS)
+                {
+                    printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+                    free(data);
+                    exit(1);
+                }
+                if(tng_particle_data_block_add(traj, TNG_TRAJ_FORCES,
+                                            "FORCES",
+                                            TNG_DOUBLE_DATA,
+                                            TNG_TRAJECTORY_BLOCK,
+                                            n_frames_per_frame_set, 3,
+                                            1, 0, np,
+                                            TNG_UNCOMPRESSED,
+                                            data) != TNG_SUCCESS)
+                {
+                    printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+                    free(data);
+                    exit(1);
+                }
+
+                /* Write the frame set to disk */
+                if(tng_frame_set_write(traj, TNG_SKIP_HASH) != TNG_SUCCESS)
+                {
+                    printf("Error writing frame set. %s: %d\n", __FILE__, __LINE__);
+                    free(data);
+                    exit(1);
+                }
+
+            }
+            if(tng_frame_particle_data_write(traj, frames_saved_cnt,
+                                            TNG_TRAJ_POSITIONS, 0, np,
+                                            pos, TNG_USE_HASH) != TNG_SUCCESS)
+            {
+                printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+                free(data);
+                exit(1);
+            }
+            if(tng_frame_particle_data_write(traj, frames_saved_cnt,
+                                            TNG_TRAJ_VELOCITIES, 0, np,
+                                            vel, TNG_USE_HASH) != TNG_SUCCESS)
+            {
+                printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+                free(data);
+                exit(1);
+            }
+            if(tng_frame_particle_data_write(traj, frames_saved_cnt,
+                                            TNG_TRAJ_FORCES, 0, np,
+                                            force, TNG_USE_HASH) != TNG_SUCCESS)
+            {
+                printf("Error adding data. %s: %d\n", __FILE__, __LINE__);
+                free(data);
+                exit(1);
+            }
+            frames_saved_cnt++;
+
+        }
+        update ( np, nd, pos, vel, force, acc, mass, dt );
+    }
+    wtime = omp_get_wtime ( ) - wtime;
+
+    printf ( "\n" );
+    printf ( "  Elapsed time for main computation:\n" );
+    printf ( "  %f seconds.\n", wtime );
+
+    free ( acc );
+    free ( box );
+    free ( force );
+    free ( pos );
+    free ( vel );
+/*
+    Terminate.
+*/
+    printf ( "\n" );
+    printf ( "MD_OPENMP\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, PI2 ) ) )**2
+
+        The derivative of the potential is:
+
+            dv(x) = 2.0 * sin ( min ( x, PI2 ) ) * cos ( min ( x, PI2 ) )
+                        = sin ( 2.0 * min ( x, PI2 ) )
+
+    Licensing:
+
+        This code is distributed under the GNU LGPL license.
+
+    Modified:
+
+        21 November 2007
+
+    Author:
+
+        Original FORTRAN77 version by Bill Magro.
+        C version by John Burkardt.
+
+    Parameters:
+
+        Input, int NP, the number of particles.
+
+        Input, int ND, the number of spatial dimensions.
+
+        Input, double POS[ND*NP], the position of each particle.
+
+        Input, double VEL[ND*NP], the velocity of each particle.
+
+        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;
+
+# pragma omp parallel \
+    shared ( f, nd, np, pos, vel ) \
+    private ( i, j, k, rij, d, d2 )
+    
+
+# pragma omp for reduction ( + : pe, ke )
+    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 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 GNU LGPL license.
+
+    Modified:
+
+        21 November 2007
+
+    Author:
+
+        Original FORTRAN77 version by Bill Magro.
+        C version by 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 box[], int *seed, double pos[], 
+    double vel[], double acc[] )
+
+/******************************************************************************/
+/*
+    Purpose:
+
+        INITIALIZE initializes the positions, velocities, and accelerations.
+
+    Licensing:
+
+        This code is distributed under the GNU LGPL license.
+
+    Modified:
+
+        21 November 2007
+
+    Author:
+
+        Original FORTRAN77 version by Bill Magro.
+        C version by John Burkardt.
+
+    Parameters:
+
+        Input, int NP, the number of particles.
+
+        Input, int ND, the number of spatial dimensions.
+
+        Input, double BOX[ND], specifies the maximum position
+        of particles in each dimension.
+
+        Input, int *SEED, a seed for the random number generator.
+
+        Output, double POS[ND*NP], the position of each particle.
+
+        Output, double VEL[ND*NP], the velocity of each particle.
+
+        Output, double ACC[ND*NP], the acceleration of each particle.
+*/
+{
+    int i;
+    int j;
+/*
+    Give the particles random positions within the box.
+*/
+    for ( i = 0; i < nd; i++ )
+    {
+        for ( j = 0; j < np; j++ )
+        {
+            pos[i+j*nd] = box[i] * r8_uniform_01 ( seed );
+        }
+    }
+
+    for ( j = 0; j < np; j++ )
+    {
+        for ( i = 0; i < nd; i++ )
+        {
+            vel[i+j*nd] = 0.0;
+        }
+    }
+    for ( j = 0; j < np; j++ )
+    {
+        for ( i = 0; i < nd; i++ )
+        {
+            acc[i+j*nd] = 0.0;
+        }
+    }
+    return;
+}
+/******************************************************************************/
+
+double r8_uniform_01 ( int *seed )
+
+/******************************************************************************/
+/*
+    Purpose:
+
+        R8_UNIFORM_01 is a unit pseudorandom R8.
+
+    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 GNU LGPL license.
+
+    Modified:
+
+        11 August 2004
+
+    Author:
+
+        John Burkardt
+
+    Reference:
+
+        Paul Bratley, Bennett Fox, Linus Schrage,
+        A Guide to Simulation,
+        Springer Verlag, pages 201-202, 1983.
+
+        Bennett Fox,
+        Algorithm 647:
+        Implementation and Relative Efficiency of Quasirandom
+        Sequence Generators,
+        ACM Transactions on Mathematical Software,
+        Volume 12, Number 4, pages 362-376, 1986.
+
+    Parameters:
+
+        Input/output, int *SEED, a seed for the random number generator.
+
+        Output, double R8_UNIFORM_01, a new pseudorandom variate, strictly between
+        0 and 1.
+*/
+{
+    int k;
+    double r;
+
+    k = *seed / 127773;
+
+    *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;
+
+    if ( *seed < 0 )
+    {
+        *seed = *seed + 2147483647;
+    }
+
+    r = ( double ) ( *seed ) * 4.656612875E-10;
+
+    return r;
+}
+/******************************************************************************/
+
+void timestamp ( void )
+
+/******************************************************************************/
+/*
+    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 GNU LGPL license.
+
+    Modified:
+
+        24 September 2003
+
+    Author:
+
+        John Burkardt
+
+    Parameters:
+
+        None
+*/
+{
+# define TIME_SIZE 40
+
+    static char time_buffer[TIME_SIZE];
+    const struct tm *tm;
+    size_t len;
+    time_t now;
+
+    now = time ( NULL );
+    tm = localtime ( &now );
+
+    len = 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 GNU LGPL license.
+
+    Modified:
+
+        17 April 2009
+
+    Author:
+
+        Original FORTRAN77 version by Bill Magro.
+        C version by 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 position of each particle.
+
+        Input/output, double VEL[ND*NP], the velocity of each particle.
+
+        Input, double F[ND*NP], the force on each particle.
+
+        Input/output, double ACC[ND*NP], the acceleration of each particle.
+
+        Input, double MASS, the mass of each particle.
+
+        Input, double DT, the time step.
+*/
+{
+    int i;
+    int j;
+    double rmass;
+
+    rmass = 1.0 / mass;
+
+# pragma omp parallel \
+    shared ( acc, dt, f, nd, np, pos, rmass, vel ) \
+    private ( i, j )
+
+# pragma omp for
+    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;
+}