nbcoll1k2.c

/*   
    Constrained N-Body simulation to test collateral gravity hypothesis
      (first order test) 
      Nathan E. Frick
*/



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*/



#include <stdio.h>
#include <math.h>
#include <malloc.h>


#define sqr(x) ((x)*(x))
#define PI 3.14159265358979323846 

/* prototype function definitions */

void initRand(int *idummy );
float randPM (float maxOut,int *idummy); /* plus maxOut to minus maxout */
float randP (float maxOut,int *idummy);
float gaussianDeviate (float mean,float variance, int *idummy);

/* data structures */

typedef struct bdType {
   int id;   /* body number */
   double c1,c2,c3;  /* center point (position of body) */
   double phi,theta,cm;  /* direction (from origin) associated with this position */
   double r,rplus;   /* radius of spherical body */ 
   double m,gx,gy,gz;  /* mass and gravitational accel */
   double cgx,cgy,cgz;  /* collateral gravity */
   double vx,vy,vz;  /* velocity of body */
   double ampF,ampDist;   /* amplification factor */
   double r2,c2_r2,discrim,t,c_dot_d,discrimP;  /* precalc variables */
   double c2_rplus2;
} bdType;

/* computational pages: designed to allow for millions of elements, if needed */

#define PARY_MAX 65520

typedef struct cmpPageNodeType {  /* break the large data into a list of pages (arrays) */
  int status;
  int n;
  bdType ary[PARY_MAX];   /* instead of a monolithic array, take this approach */
  struct cmpPageNodeType *nextnode;
}  cmpNode;

/* define a type cmpNode for convenience */
 
cmpNode cpNode0,*curNode;   /* cpNode0 is the the first page (base node) */
int largestID,obsID;
double collFraction,initVelocity;

char confine2Plane[128];

int allocMem4Arrays(int nbTotal)
/* initialization of memory - returns zero for normal alloc */
/* this modular approach does not require a giant block of memory from the system,
      and lends itself to multithreaded implementation, if required */
{  cmpNode *curNode; int i;
  
   curNode = &cpNode0; /* start at the base node */
   curNode->n = 0;
   for (i=0;i < nbTotal;i++)
   { if (curNode->n == PARY_MAX)
     { /* get next node */
       curNode->nextnode = (cmpNode *)malloc(sizeof(cmpNode));
       if (curNode->nextnode == NULL) return 1;
       curNode = curNode->nextnode;
       curNode->n = 0;
     }
     curNode->ary[curNode->n].id= i;   /* assign an enumeration id */
     curNode->status = 0;
     curNode->n++;
    
   }
   return 0;
}



void CheckForCollionsMerge(void)

/* here is a simple elastic merge of bodies into one */

{ cmpNode *curNode,*jcurNode; int i,j; int curId;
  double Fpi3;  double dx,dy,dz,dist2,r1,r2,totM,totV,averageDensity;
  double totalMomentumX,totalMomentumY,totalMomentumZ;
  double newV1,newM1,newR1,newP1x,newP1y,newP1z;
  Fpi3 = 4 * PI / 3.0;
   curNode = &cpNode0; /*  base node */
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)  if (curNode->ary[i].id != largestID) /* don't allow largest body to merge */
      {  curId = curNode->ary[i].id;
       jcurNode = &cpNode0;
     while (jcurNode != NULL) {
     for (j=0;j<jcurNode->n;j++) if (jcurNode->ary[j].id != curId)
         { dx = jcurNode->ary[j].c1 - curNode->ary[i].c1;
       dy = jcurNode->ary[j].c2 - curNode->ary[i].c2;
       dz = jcurNode->ary[j].c3 - curNode->ary[i].c3;
       dist2 = dx * dx + dy * dy + dz * dz;
       if (dist2 < sqr(jcurNode->ary[j].r +  curNode->ary[i].r) )
       { /* collision */
         r1 =  curNode->ary[i].r;
       r2 =  jcurNode->ary[j].r;
         totM = jcurNode->ary[j].m + curNode->ary[i].m;  /* get various totals */
       totV = Fpi3 * (r1*r1*r1 + r2*r2*r2);
       averageDensity =   totM / totV;
       totalMomentumX =  jcurNode->ary[j].m * jcurNode->ary[j].vx +   curNode->ary[i].m *  curNode->ary[i].vx;
       totalMomentumY =  jcurNode->ary[j].m * jcurNode->ary[j].vy +   curNode->ary[i].m *  curNode->ary[i].vy;
             totalMomentumZ =  jcurNode->ary[j].m * jcurNode->ary[j].vz +   curNode->ary[i].m *  curNode->ary[i].vz;
       newV1 = totV;     /* make some assumptions here regarding volume */
       newM1 = totM;
       newR1 = pow((newV1 / Fpi3),(1/3.0));
       newP1x = totalMomentumX; 
       newP1y = totalMomentumY;
       newP1z = totalMomentumZ;
       if (r1 > r2)  /* let the previously larger body remain so */
       {  curNode->ary[i].r = newR1;
          curNode->ary[i].m = newM1;
        curNode->ary[i].vx = newP1x / newM1;
        curNode->ary[i].vy = newP1y / newM1;
        curNode->ary[i].vz = newP1z / newM1;
        jcurNode->ary[j].r = 0.0;
          jcurNode->ary[j].m = 0.0;
        
       }
       else
       {  curNode->ary[i].r = 0.0;
          curNode->ary[i].m = 0.0;
        jcurNode->ary[j].r = newR1;
          jcurNode->ary[j].m = newM1;
        jcurNode->ary[j].vx = newP1x / newM1;
        jcurNode->ary[j].vy = newP1y / newM1;
        jcurNode->ary[j].vz = newP1z / newM1;
       }
       
         }
     }
             jcurNode = jcurNode->nextnode;
    }
        }
      curNode = curNode->nextnode;
   }   
  
}

void DumpZeroBodies( cmpNode *node0)
{ /* one step in ray-sphere intersection calc */
  cmpNode *curNode; int i,j;
   curNode = node0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
      { if (curNode->ary[i].m == 0.0)
        {  for (j=i+1;j<curNode->n;j++)  curNode->ary[j-1] = curNode->ary[j];  /* shift remaining elements over */
           curNode->n = curNode->n - 1;
        }
      }     
      curNode = curNode->nextnode;
   }
}

void DumpFarBodies( cmpNode *node0,double ex)
{ /* one step in ray-sphere intersection calc */
  cmpNode *curNode; int i,j;
   curNode = node0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
      { if (  (fabs(curNode->ary[i].c1) > ex) ||
              (fabs(curNode->ary[i].c2) > ex) ||
              (fabs(curNode->ary[i].c3) > ex) )
        {  for (j=i+1;j<curNode->n;j++)  curNode->ary[j-1] = curNode->ary[j];  /* shift remaining elements over */
           curNode->n = curNode->n - 1;
        }
      }     
      curNode = curNode->nextnode;
   }
}


void buildBodiesN(double initExtent, double avgDensity, double sigDensity, 
         double smallestRadius, double incRadius,double rFacBump,
         int iRandSkip)

/* seed a normal distribution to the mass density, and a lognormal distribution to the radius */

{  double m,r,rnd,rndRadius,largest,rFac;
   int j,iTotal,iTt,idk;
   cmpNode *curNode; int i; int idmy;
   initRand(&idmy);  /* seed random number gen */
   /* first, seed radii based on a sort of lognormal */
   iTotal = 0;
   curNode = &cpNode0; /*  base node */
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
      { iTotal++;
        curNode->ary[i].r = smallestRadius; 
      }
      curNode = curNode->nextnode;
   }
   rFac = rFacBump;
   iTt = iTotal /  2.0;
   while (iTt > 0)
   { j = 0;
     while (j < iTt)
     { idk = randP(iTotal,&idmy);
       curNode = &cpNode0; /*  base node */
       while (curNode != NULL)
       { for (i=0;i<curNode->n;i++)
         if (idk == curNode->ary[i].id)
        { curNode->ary[i].r += rFac * smallestRadius; 
        }
         curNode = curNode->nextnode;
       } 
       j++;
     }
     iTt /= 2.0;
     rFac *= rFacBump;    /* bump factor for next round of increments */
   }
   curNode = &cpNode0;  /* attach a gaussian noise */
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) curNode->ary[i].r *= (1 + gaussianDeviate(0.0,0.16,&idmy));     
      curNode = curNode->nextnode;
   }

   /* now, seed the masses */
   curNode = &cpNode0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)curNode->ary[i].m = gaussianDeviate(avgDensity,sigDensity,&idmy);    
      curNode = curNode->nextnode;
   }
   curNode = &cpNode0; /* check to make sure there are no negative values */
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) if (curNode->ary[i].m < 0.0) curNode->ary[i].m = avgDensity;      
      curNode = curNode->nextnode;
   }
   
   /* now, multiply the volume and density to get total mass per body */
   curNode = &cpNode0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
      { r = curNode->ary[i].r;
        curNode->ary[i].m = curNode->ary[i].m * (4 * PI / 3) * r * r * r;    
      }
      curNode = curNode->nextnode;
   }
   /* determine which elements is very largest */
   curNode = &cpNode0;
   largest= 0.0;  largestID = 0;
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
      if (curNode->ary[i].m > largest)  {
         largestID = curNode->ary[i].id;
         largest = curNode->ary[i].m;
      }
      curNode = curNode->nextnode;
   }
   /* assign random position within a given space */
   curNode = &cpNode0;  initRand(&idmy);
   for (i=0;i<=iRandSkip;i++) randPM(initExtent,&idmy);  /* seed random num */
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) curNode->ary[i].c1 = randPM(initExtent,&idmy);
      curNode = curNode->nextnode;
   }
   curNode = &cpNode0;  
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) curNode->ary[i].c2 = randPM(initExtent,&idmy);  /* y coordinate */
      curNode = curNode->nextnode;
   }
   
   curNode = &cpNode0;  
   while (curNode != NULL)
   {  if (confine2Plane[0] != 'Y') 
     for (i=0;i<curNode->n;i++) curNode->ary[i].c3 = randPM(initExtent,&idmy);  /* z coordinate */
      else
         for (i=0;i<curNode->n;i++) curNode->ary[i].c3 = 0.0;     
      curNode = curNode->nextnode;
   }
   /* now,  initialize velocities */
   curNode = &cpNode0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) curNode->ary[i].vx = randPM(initVelocity,&idmy);
      curNode = curNode->nextnode;
   }
   curNode = &cpNode0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) curNode->ary[i].vy = randPM(initVelocity,&idmy);
      curNode = curNode->nextnode;
   }
   curNode = &cpNode0; 
   while (curNode != NULL)
   {  if (confine2Plane[0] != 'Y')
     for (i=0;i<curNode->n;i++) curNode->ary[i].vz = randPM(initVelocity,&idmy);
      else 
         for (i=0;i<curNode->n;i++) curNode->ary[i].vz = 0.0;
      curNode = curNode->nextnode;
   }
}

void FixUpLargest000(  cmpNode *node0,double lFactor)
/* this gives the largest mass an unfair advantage */
{  cmpNode *curNode; int i;
  curNode = node0; while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) 
      if (curNode->ary[i].id == largestID)
      {  curNode->ary[i].m *= lFactor;
         curNode->ary[i].r *= sqrt(lFactor);  /* somewhat arbitrary */
         curNode->ary[i].c1 = 0.0;   /* init largest mass to be at the origin */
         curNode->ary[i].c2 = 0.0;
         curNode->ary[i].c3 = 0.0;
         
      }       
      curNode = curNode->nextnode;
   }
}



void displaceOrigin( double xDelta, double yDelta, double zDelta)
/* global: shifts centers of all bodies by xDelta,yDelta */
{ cmpNode *curNode; int i;
  curNode = &cpNode0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
     { curNode->ary[i].c1 += xDelta;
       curNode->ary[i].c2 += yDelta;
       curNode->ary[i].c3 += zDelta;
     }
      curNode = curNode->nextnode;
   }
} 


void OutputAllPoints(char *fStr)
/* global: outputs position,mass,radius,etc. of all points */
{
  cmpNode *curNode; int i;
  FILE *fH;
  fH = fopen(fStr,"w");
  curNode = &cpNode0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
     { fprintf(fH,"%lf,%lf,%lf,%d,%lf,%lf,%lf,%lf,%lf\n",
       curNode->ary[i].c1,
       curNode->ary[i].c2,
       curNode->ary[i].c3,
       curNode->ary[i].id,
       curNode->ary[i].m,
       curNode->ary[i].r,
       curNode->ary[i].vx,
       curNode->ary[i].vy,
       curNode->ary[i].vz);
     }
      curNode = curNode->nextnode;
   }
   fclose(fH);
} 


/* used by below, possibly unneeded 
void clearGs(  cmpNode *node0)
{ cmpNode *curNode; int i;
  curNode = node0;  while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++) curNode->ary[i].gx = curNode->ary[i].gy = curNode->ary[i].gz 0.0;     
      curNode = curNode->nextnode;
   }
}
*/

void calcNewtonianGM(cmpNode *node0, double smallestRFac)
{ /* basic Newtonian gravity attraction, calc, where we retain for each body,
   the individual attractions (i.e. postpone summation for total attraction) */
   cmpNode *curNode; int i;
   double dx,dy,dz,dw,fmag,rsqrd,smallestRS;
   /* clearGs(node0); */
   curNode = node0; 
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)
       { /* dx = x0 - curNode->ary[i].c1;
         dy = y0 - curNode->ary[i].c2;
         dz = z0 - curNode->ary[i].c3; */
         dx = curNode->ary[i].c1; 
         dy = curNode->ary[i].c2;
         dz = curNode->ary[i].c3;
         rsqrd =  sqr(dx) + sqr(dy) + sqr(dz);
         
         if (rsqrd != 0.0)
         {  /* limit how close r exists */
           smallestRS = sqr(curNode->ary[i].r * smallestRFac);
           if (rsqrd < smallestRS) rsqrd = smallestRS;
           /* ubiquitous  1 / r^3/2 formula */
           fmag = curNode->ary[i].m / (rsqrd * sqrt(rsqrd));
               curNode->ary[i].gx = fmag * dx;
               curNode->ary[i].gy = fmag * dy;
               curNode->ary[i].gz = fmag * dz;
             }
             else
             { curNode->ary[i].gx = 0.0;   /* no self attraction ... rigid bodies */
               curNode->ary[i].gy = 0.0;
               curNode->ary[i].gz = 0.0;
             }
       }
                     
      curNode = curNode->nextnode;
   }
}

#define NEWTONS_G 6.67384e-11

  
#define MAX_DOUBLE 1.79e308 



void applyGravity( cmpNode *n0, int i0, double dt)
/* apply the effect of the gravitation of all bodies on body i0 (in buffer n0) ... 
   so we are going to bump each object at a time during the simulation, rather 
   than trying to effect infinitesimal change to all bodies at once */
{  cmpNode *curNode; int i;
  double gTx,gTy,gTz,ampF; 
  double xN1,xN2,xN3;
  double lBarrier2;
  gTx = gTy = gTz = 0.0;
   curNode = &cpNode0; /* start of buffer */
   while (curNode != NULL)
   {  for (i=0;i<curNode->n;i++)  /* if (curNode->ary[i].id != largestID) */
     {{ gTx += curNode->ary[i].gx ; 
        gTy += curNode->ary[i].gy ; 
        gTz += curNode->ary[i].gz ;
       } 
     }
      curNode = curNode->nextnode;
   }
   /* multiply by Newtons G */
   gTx *= NEWTONS_G;
   gTy *= NEWTONS_G;
   gTz *= NEWTONS_G;
   /*  printf("%d:Newton=%f %f ... \n ",i0,gTx,gTy); */
   xN1 = n0->ary[i0].c1;
   xN2 = n0->ary[i0].c2;
   xN3 = n0->ary[i0].c3;
   xN1 += dt * n0->ary[i0].vx;  /* v nought dt */
   xN2 += dt * n0->ary[i0].vy;
   xN3 += dt * n0->ary[i0].vz;
   xN1 += 0.5 * gTx * sqr(dt);
   xN2 += 0.5 * gTy * sqr(dt);
   xN3 += 0.5 * gTz * sqr(dt);
   /* bump the position of this body */
   n0->ary[i0].c1 = xN1;
   n0->ary[i0].c2 = xN2;
   n0->ary[i0].c3 = xN3;
   /* now, bump velocities */
   n0->ary[i0].vx += gTx * dt;
   n0->ary[i0].vy += gTy * dt;
   n0->ary[i0].vz += gTz * dt;
   
} 

void initCollG(  void )
{ cmpNode *curNode; int i; 
  curNode = &cpNode0; /* start of buffer */
  while (curNode != NULL)
  {  for (i=0;i<curNode->n;i++)  
       {  curNode->ary[i].cgx =0; /* clear collateral gravity attribute */
          curNode->ary[i].cgy =0; 
          curNode->ary[i].cgz =0;
       } 
     curNode = curNode->nextnode;
   }
} 


void Calc_CollF( cmpNode *epiNode, int epi )

/* epiNode and epi give the observation point (center body) */

{ cmpNode *curNode,*curNodeJ; int i,j;
  double dx,dy,dz,dw,fmag,rsqrd,smallestRS;
  double rAv1,rAv2,rAv3;
  double FC1,FC2,FC3;
  FC1 = 0.0; FC2 = 0.0; FC3 = 0.0;
  curNode = &cpNode0; while (curNode != NULL)
   { for (i=0;i<curNode->n;i++) if (curNode->ary[i].id != obsID)
     { curNodeJ = &cpNode0;
       while (curNodeJ != NULL)
       { /* for (j=0;j<curNodeJ->n;j++) */
    /* for now, since we only have one comp node working, just use j=i+1 */
        for (j=i+1;j<curNodeJ->n;j++)   /* temporary */  
         if ( (curNode->ary[i].id != curNodeJ->ary[j].id) && 
        (curNodeJ->ary[j].id != obsID))
         {  /* ok, end bodies are i and j, and the center body is at origin */
            rAv1 =  (curNode->ary[i].c1 +  curNodeJ->ary[j].c1) / 2.0;
              rAv2 =  (curNode->ary[i].c2 +  curNodeJ->ary[j].c2) / 2.0;
            rAv3 =  (curNode->ary[i].c3 +  curNodeJ->ary[j].c3) / 2.0;
        
         rsqrd =  ( sqr(rAv1) + sqr(rAv2) + sqr(rAv3) ) ;
         if (rsqrd != 0.0)
         {  /* limit how close r exists */
           smallestRS = sqr(epiNode->ary[epi].r);  /* collateral gravity does not happen if the center body intercepts path */
           if (rsqrd < smallestRS) rsqrd = smallestRS;
           /* coll gravity: outside body masses! ,   1 / r^3/2 formula */
           fmag = ( curNode->ary[i].m * curNodeJ->ary[j].m) / (rsqrd * sqrt(rsqrd));
           /* apply sigma later */
               FC1 += fmag * rAv1;
               FC2 += fmag * rAv2;
               FC3 += fmag * rAv3;            
         }
       }  /* end for loop ... j */
       curNodeJ = curNodeJ->nextnode;
     }
     
     } /* end for loop ... i */
     curNode = curNode->nextnode;
   }
   epiNode->ary[epi].cgx = FC1;
   epiNode->ary[epi].cgy = FC2;
   epiNode->ary[epi].cgz = FC3;
   
     
}


void applyCollGravity(cmpNode * curNode, int i, double collFract, double dt )
/* apply the effect of the collateral grav to all bodies at once */
{   double gTx,gTy,gTz,xN1,xN2,xN3;
  double sigma,m;
  
       {  sigma = (collFract * NEWTONS_G);
          m = curNode->ary[i].m;  /* mass of self */
          gTx = curNode->ary[i].cgx; /* collateral was assign directly to body attribute */
          gTy = curNode->ary[i].cgy ; 
          gTz = curNode->ary[i].cgz ;
     gTx *= (sigma / m); gTy *= (sigma / m); gTz *= (sigma / m);
     /* printf("%d:coll=%f %f ... ",i,gTx,gTy); */
     xN1 = curNode->ary[i].c1;
     xN2 = curNode->ary[i].c2;
     xN3 = curNode->ary[i].c3;
     xN1 += dt * curNode->ary[i].vx;  /* v nought dt */
     xN2 += dt * curNode->ary[i].vy;
     xN3 += dt * curNode->ary[i].vz;
     xN1 += 0.5 * gTx * sqr(dt);
     xN2 += 0.5 * gTy * sqr(dt);
     xN3 += 0.5 * gTz * sqr(dt);
     curNode->ary[i].c1 = xN1;/* bump the position of this body */
     curNode->ary[i].c2 = xN2;
     curNode->ary[i].c3 = xN3;
     curNode->ary[i].vx += gTx * dt; /* now, bump velocities */
     curNode->ary[i].vy += gTy * dt;
     curNode->ary[i].vz += gTz * dt;
       } 

} 



/* ************** Execution   *********** */

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

{
  int iEpoch,epi;
  cmpNode *epNode;
  int nbTotal,totalEpochs,i;
  double dt,initExtent,avgDensity,sigDensity,smRadius,incRadius,rFacBump;
  double degSwath;
  double globalOffset1,globalOffset2,globalOffset3;
  double lFactor,rBarrierFraction;
  char outFileStr[256];
  int initRandI;
  FILE *fPtrEP;
  /* get number of bodies, dt, fAmp, min sizes, etc. */
  printf("  Collateral gravity simulation\n");
  printf("    by Nathan E. Frick, summer 2011 \n");  
   
  printf("Enter the total number of bodies (e.g. 3000):\n");
  scanf("%d",&nbTotal);
  printf("Enter time increment in seconds (e.g. 10):\n");
  scanf("%lf",&dt);
  printf("Enter extent of simulation:\n");
  scanf("%lf",&initExtent);
  printf(" Confine to x-y plane (Y/N)?\n");
  scanf("%s",confine2Plane);
  printf("Enter extent of velocity seed (e.g. 1 m/s):\n");
  scanf("%lf",&initVelocity);
  printf("Enter average density in g/cc:\n");
  scanf("%lf",&avgDensity);
  printf("Enter density variance in g/cc:\n");
  scanf("%lf",&sigDensity);
  printf("Enter smallest radius to create (in meters):\n");
  scanf("%lf",&smRadius);
  printf("Enter radius increment (in meters):\n");
  scanf("%lf",&incRadius);
  printf("Enter radius bump for lognormal seed (e.g. 1.02) :\n");
  scanf("%lf",&rFacBump);
  

  printf("Enter factor to multiply times by G for collateral grav (e.g. 0.0043):\n");
  printf("This will be divided by a million before using ...\n");
  scanf("%lf",&collFraction);
  collFraction /= 1000000.0;
  printf("Enter number of epochs for simulation:\n");
  scanf("%d",&totalEpochs);
  
  printf("Enter direction swath (e.g. 4.0):\n");
  scanf("%lf",&degSwath);

  printf("Enter output filename:\n");
  scanf("%s",outFileStr);
  printf("Pre-multiply largest body by factor (e.g. 100):\n");
  scanf("%lf",&lFactor);
  printf("Enter an integer to seed random number generator for positions:\n");
  scanf("%d",&initRandI);
  /* convert units of density from g/cc to kg/m^3 */
  avgDensity *= 1000.0;
  sigDensity *= 1000.0;
  /* ok, now, begin */
  if (allocMem4Arrays(nbTotal) == 1) { printf("failed to allocate all mem\n"); return 1; }
  printf("initializing body radius, mass, position, etc ...\n");
  buildBodiesN((initExtent * 1.5),avgDensity,sigDensity,smRadius,incRadius,rFacBump,initRandI);
  FixUpLargest000(&cpNode0,lFactor);  /* initial mass increase */
  CheckForCollionsMerge();
  DumpZeroBodies(&cpNode0);
  OutputAllPoints(outFileStr);
  rBarrierFraction = 1.5;   /* (fraction of radius) distance where largest body -> no gravity */
  for (iEpoch=0;iEpoch < totalEpochs;iEpoch++)
  { printf("---------------------- EPOCH %d ----------------------\n",iEpoch);
    /*   if (iEpoch == 10) { FixUpLargest(&cpNode0,(1.0/lFactor)); } */  
     /* these can collapse on largest ?? */  
    initCollG();  /* must recalc each epoch */        
    epNode = &cpNode0; while (epNode != NULL)
     {  for (epi=0;epi<epNode->n;epi++) 
      {  /* epi is the current point of observation */
     obsID = epNode->ary[epi].id;
         globalOffset1 = epNode->ary[epi].c1;      
         globalOffset2 = epNode->ary[epi].c2;
         globalOffset3 = epNode->ary[epi].c3;
         displaceOrigin(-globalOffset1,-globalOffset2,-globalOffset3);
         /* calcBDirections(&cpNode0); */ 
         /* printf("global offset is %lf,%lf,%lf for observation point %d\n",
            globalOffset1,globalOffset2,globalOffset3,epNode->ary[epi].id); */
         /* printf("Calc of Newtonian gravity \n"); */
         calcNewtonianGM(&cpNode0,rBarrierFraction);  /* basic Newtonian gravity for this point */
         /* printf("Calc of collG\n"); */
         Calc_CollF(epNode,epi); 
         applyCollGravity(epNode,epi,collFraction,dt);
           /* printf("\n");
            for (i=0;i<cpNode0.n;i++) printf("for body %d: ampF=%lf \n",i,cpNode0.ary[i].ampF);  */       
         /* printf("Applying grav acceleration to point %d\r",epNode->ary[epi].id); */
         applyGravity(epNode,epi,dt);
         /* restore coordinates to original position */
         displaceOrigin(globalOffset1,globalOffset2,globalOffset3);
         /* PrintCollStats(); */
      }            
        epNode = epNode->nextnode;
        
     }
     OutputAllPoints(outFileStr);
     printf("epoch number %d is finished\n",iEpoch);
     fPtrEP = fopen("EPOCHNOW.TXT","w");
     fprintf(fPtrEP,"epoch number %d is finished\n",iEpoch);
     fclose(fPtrEP);
  /*  CheckForCollionsMerge();
     DumpZeroBodies(&cpNode0); */
     DumpFarBodies(&cpNode0,(initExtent * 1000.0));
  
  }


  return 0;
}







#define IA 16807
#define IM 2147483647
#define AM (1.0/IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1)/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0-EPS)

float ran1(int *idum)
{
  int j;
  long k;
  static long iy=0;
  static long iv[NTAB];
  float temp;

  if (*idum <= 0 || !iy) {
    if (-(*idum) < 1) *idum=1;
    else *idum = -(*idum);
    for (j=NTAB+7;j>=0;j--) {
      k=(*idum)/IQ;
      *idum=IA*(*idum-k*IQ)-IR*k;
      if (*idum < 0) *idum += IM;
      if (j < NTAB) iv[j] = *idum;
    }
    iy=iv[0];
  }
  k=(*idum)/IQ;
  *idum=IA*(*idum-k*IQ)-IR*k;
  if (*idum < 0) *idum += IM;
  j=iy/NDIV;
  iy=iv[j];
  iv[j] = *idum;
  if ((temp=AM*iy) > RNMX) return RNMX;
  else return temp;
}
#undef IA
#undef IM
#undef AM
#undef IQ
#undef IR
#undef NTAB
#undef NDIV
#undef EPS
#undef RNMX

float gasdev(int *idum)
/* returns a normally distrbuted deviate with zero mean
     and unit variance */
{
  static int iset=0;
  static float gset;
  float fac,r,v1,v2;
  float ran1();

  if  (iset == 0) {
    do {
      v1=2.0*ran1(idum)-1.0; /* pick two numbers from -1 to 1 */
      v2=2.0*ran1(idum)-1.0;
      r=v1*v1 + v2*v2;
    } while (r >= 1.0);  /* if they are not in the unity circle, try again */
    fac=sqrt(-2.0*log(r)/r);
    gset=v1*fac;  /* save for later */
    iset=1;
    return v2*fac;
  } else {
    iset=0;
    return gset;
  }
}



void initRand(int *idummy )

{ int idm;
  idm=-1;
  ran1(&idm);
  *idummy = idm;
}
  
float randPM (float maxOut,int *idummy)
/* plus maxOut to minus maxout */
{ return ((2*maxOut)*ran1(idummy)-maxOut);
}

float randP (float maxOut,int *idummy)
{ return (maxOut*ran1(idummy));
}

float gaussianDeviate (float mean,float variance, int *idummy)
{  return(mean + variance*gasdev(idummy));
}