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#include <stdio.h>
#include <string.h>
#include <math.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <time.h>
#include <stdlib.h>
#include <sstream>
using namespace std;
int main()
{
int a,b,c,f,i,j,k,m,n,s;
double p,Time,Averagetime,Energy,energy,Distance,Length,DotProdForce,Forcemagnitude,
ForceMagnitude[101],Force[101][4],E[10001],En[501],x[101][4],y[101][4];
clock_t t1,t2;
t1=clock();
b=1;
c=1;
Time=0.0;
while(b<26){
clock_t t3,t4;
t3=clock();
/* set the number of points */
n=45;
/* check that there are no more than 100 points */
if(n>100){
cout << n << " is too many points for me :( \n";
exit(0);
}
/* reset the random number generator */
srand((unsigned)time(0));
for (i=1;i<=n;i++){
x[i][1]=((rand()*1.0)/(1.0*RAND_MAX)0.5)*2.0;
x[i][2]=((rand()*1.0)/(1.0*RAND_MAX)0.5)*2.0;
x[i][3]=((rand()*1.0)/(1.0*RAND_MAX)0.5)*2.0;
Length=sqrt(pow(x[i][1],2)+pow(x[i][2],2)+pow(x[i][3],2));
for (k=1;k<=3;k++){
x[i][k]=x[i][k]/Length;
}
}
/* calculate the energy */
Energy=0.0;
for(i=1;i<=n;i++){
for(j=i+1;j<=n;j++){
Distance=sqrt(pow(x[i][1]x[j][1],2)+pow(x[i][2]x[j][2],2)
+pow(x[i][3]x[j][3],2));
Energy=Energy+1.0/Distance;
}
}
/* Save Original Points */
for(i=1;i<=n;i++){
y[i][1]=x[i][1];
y[i][2]=x[i][2];
y[i][3]=x[i][3];
}
/* Loop for random points m times*/
m=10;
if (m>100){
cout << "The m="<< m << " loop is inefficient...lessen m \n";
exit(0);
}
a=1;
while(a<m){
/* assign random points */
for (i=1;i<=n;i++){
x[i][1]=((rand()*1.0)/(1.0*RAND_MAX)0.5)*2.0;
x[i][2]=((rand()*1.0)/(1.0*RAND_MAX)0.5)*2.0;
x[i][3]=((rand()*1.0)/(1.0*RAND_MAX)0.5)*2.0;
Length=sqrt(pow(x[i][1],2)+pow(x[i][2],2)+pow(x[i][3],2));
for (k=1;k<=3;k++){
x[i][k]=x[i][k]/Length;
}
}
/* calculate the energy */
energy=0.0;
for(i=1;i<=n;i++){
for(j=i+1;j<=n;j++){
Distance=sqrt(pow(x[i][1]x[j][1],2)+pow(x[i][2]x[j][2],2)
+pow(x[i][3]x[j][3],2));
energy=energy+1.0/Distance;
}
}
if(energy<Energy)
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
Energy=energy;
y[i][j]=x[i][j];
}
}
else
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
energy=Energy;
x[i][j]=y[i][j];
}
}
a=a+1;
}
/* Create string stream 1 */
ostringstream String1;
String1 << "Bestrandonpoints_" << n; //add number
/* Output these points */
ofstream File1 (String1.str().c_str());
File1 << "Energy=" << Energy << "\n";
for(i=1;i<=n;i++){
File1 << x[i][1] << " " << x[i][2] << " " << x[i][3] << "\n";
}
File1.close();
/* For energy file later */
E[0]=Energy;
/* Start doing gradient flow approach */
a=1;
s=0;
f=0;
Forcemagnitude=1.0;
if(n>80)
p=0.005;
else if(n>60)
p=0.01;
else if(n>40)
p=0.02;
else
p=0.05;
while(Forcemagnitude>0.00005){
/* Reset initial force and energy change */
for(i=1;i<=n;i++){
Force[i][1]=0.0;
Force[i][2]=0.0;
Force[i][3]=0.0;
}
/* Calculate force on each particle */
for(i=1;i<=n;i++){
for(j=1;j<i;j++){
Distance=sqrt(pow(x[i][1]x[j][1],2)+pow(x[i][2]x[j][2],2)
+pow(x[i][3]x[j][3],2));
Force[i][1]=Force[i][1]+((x[i][1]x[j][1])/(pow((Distance),3)));
Force[i][2]=Force[i][2]+((x[i][2]x[j][2])/(pow((Distance),3)));
Force[i][3]=Force[i][3]+((x[i][3]x[j][3])/(pow((Distance),3)));
}
for (j=i+1;j<=n;j++){
Distance=sqrt(pow(x[i][1]x[j][1],2)+pow(x[i][2]x[j][2],2)
+pow(x[i][3]x[j][3],2));
Force[i][1]=Force[i][1]+((x[i][1]x[j][1])/(pow((Distance),3)));
Force[i][2]=Force[i][2]+((x[i][2]x[j][2])/(pow((Distance),3)));
Force[i][3]=Force[i][3]+((x[i][3]x[j][3])/(pow((Distance),3)));
}
}
/* Add the force to my points */
for(i=1;i<=n;i++){
DotProdForce=Force[i][1]*x[i][1]+Force[i][2]*x[i][2]+Force[i][3]*x[i][3];
y[i][1]=x[i][1];
y[i][2]=x[i][2];
y[i][3]=x[i][3];
Force[i][1]=Force[i][1]DotProdForce*y[i][1];
Force[i][2]=Force[i][2]DotProdForce*y[i][2];
Force[i][3]=Force[i][3]DotProdForce*y[i][3];
x[i][1] = y[i][1]+p*(Force[i][1]);
x[i][2] = y[i][2]+p*(Force[i][2]);
x[i][3] = y[i][3]+p*(Force[i][3]);
/* Bring it back onto sphere */
Length=sqrt(pow(x[i][1],2)+pow(x[i][2],2)+pow(x[i][3],2));
for (j=1;j<=3;j++){
x[i][j]=x[i][j]/Length;
}
}
/* Calculate the new energy */
energy=0.0;
for(i=1;i<=n;i++){
for(j=i+1;j<=n;j++){
Distance=sqrt(pow(x[i][1]x[j][1],2)+pow(x[i][2]x[j][2],2)
+pow(x[i][3]x[j][3],2));
energy=energy+1.0/Distance;
}
}
E[a]=energy;
/* Choose best energy and therefore best points */
if (energy<Energy)
Energy=energy,s=s+1;
else
energy=Energy,f=f+1,p=(9.5*p)/10;
for(i=1;i<=n;i++){
ForceMagnitude[i]=pow((pow(Force[i][1],2)+pow(Force[i][2],2)
+pow(Force[i][3],2)),0.5);
}
for(i=1;i<=n1;i++){
if(ForceMagnitude[i]<ForceMagnitude[i+1])
ForceMagnitude[i]=ForceMagnitude[i+1];
else
ForceMagnitude[i+1]=ForceMagnitude[i];
}
Forcemagnitude=ForceMagnitude[n];
a=a+1;
}
En[b]=Energy;
b=b+1;
t4=clock();
float diff ((float)t4(float)t3);
float seconds = diff / CLOCKS_PER_SEC;
Time = Time + seconds;
}
Averagetime = Time/(b1);
cout << fixed << setprecision (4) << "Average Time: " << Averagetime << "(s) \n";
cout << fixed << setprecision(10) << "Energy=" << Energy << "\n";
t2=clock();
float diff ((float)t2(float)t1);
float seconds = diff / CLOCKS_PER_SEC;
/* Create string stream 2 */
ostringstream String2;
String2 << "GFPoints_" << n; //add number
/* Output these points */
ofstream File2 (String2.str().c_str());
for(i=1;i<=n;i++){
File2 << x[i][1] << " " << x[i][2] << " " << x[i][3] << "\n";
}
File2.close();
/* Create string stream 3 */
ostringstream String3;
String3 << "GFEnergies_" << n; //add number
/* Output these points */
ofstream File3 (String3.str().c_str());
for(i=1;i<a;i++){
File3 << fixed << setprecision (10) << E[i] << "\n";
}
File3.close();
/* Output to help with gnuin.txt */
ofstream File4 ("mypoints");
for(i=1;i<=n;i++){
File4 << x[i][1] << " " << x[i][2] << " " << x[i][3] << "\n";
}
File4.close();
/* Create string stream 4 */
ostringstream String4;
String4 << "GFInfo_" << n; //add number
/* Output these points */
ofstream File5 (String4.str().c_str());
File5 << "Iterations=" << a1 << "\n";
File5 << "Successes=" << s << " Failures=" << f << "\n";
File5 << fixed << setprecision(20) << "Energy=" << Energy << "\n";
File5 << fixed << setprecision(5) << "Total run time: " << seconds << "(s) \n";
File5 << fixed << setprecision(5) << "Average run time: " << Averagetime << "(s) \n";
File5.close();
/* Create string stream 5 */
ostringstream String5;
String5 << "GF%Energies_" << n << "_" << c; //add number
/* Output these points */
ofstream File6 (String5.str().c_str());
for(i=1;i<b;i++){
File6 << fixed << setprecision(20) << En[i] << "\n";
}
File6.close();
cout << fixed << setprecision(5) << "Run time: " << seconds << "(s)" << "\n";
return 0;
}
 