我的代码如下（为了便于阅读，我对其进行了简化，对于缺少功能而感到抱歉）：
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <time.h>
#include <stdlib.h>
#include <sstream>
#include <gmpxx.h>
using namespace std;
#define PI 3.14159265358979323846
int main()
{
int a,b,c,d,f,i,j,k,m,n,s,t,Success,Fails;
double p,theta,phi,Time,Averagetime,Energy,energy,Distance,Length,DotProdForce,
Forcemagnitude,ForceMagnitude[201],Force[201][4],E[1000001],En[501],Epsilon[4],Ep,
x[201][4],new_x[201][4],y[201][4],A[201],alpha[201][201],degree,bestalpha[501];
clock_t t1,t2;
t1=clock();
t=1;
/* Set parameter t, the power in the energy function */
while(t<1001){
n=2;
/*set parameter n, the number of points going onto the sphere */
while(n<51){
cout << "N=" << n << "\n";
b=0;
Time=0.0;
/* Set parameter b, just a loop to distribute points many times (100) */
while(b<100){
clock_t t3,t4;
t3=clock();
if(n>200){
cout << n << " is too many points for me :-( \n";
exit(0);
}
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;
}
}
/* Points have now been distributed randomly and normalised so they sit on
unit sphere */
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/pow(Distance,t);
}
}
/*Energy has now been calculated for the system of points as a summation
function this is where accuracy is lost */
for(i=1;i<=n;i++){
y[i][1]=x[i][1];
y[i][2]=x[i][2];
y[i][3]=x[i][3];
}
m=100;
if (m>100){
cout << "The m="<< m << " loop is inefficient...lessen m \n";
exit(0);
}
a=1;
/* Distributing points m-1 times and choosing the best random distribution */
while(a<m){
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;
}
}
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/pow(Distance,t);
}
}
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;
}
/* End of random distribution loop, the loop for a<m */
En[b]=Energy;
b=b+1;
t4=clock();
float diff ((float)t4-(float)t3);
float seconds = diff / CLOCKS_PER_SEC;
Time = Time + seconds;
}
/* End of looping the entire body of the program, used to get an average reading */
t2=clock();
float diff ((float)t2-(float)t1);
float seconds = diff / CLOCKS_PER_SEC;
n=n+1;
}
/* End of n loop, here n increases so I get outputs for n from 2 to 50 for each t */
if(t==1)
t=2;
else if(t==2)
t=5;
else if(t==5)
t=10;
else if(t==10)
t=25;
else if(t==25)
t=50;
else if(t==50)
t=100;
else if(t==100)
t=250;
else if(t==250)
t=500;
else if(t==500)
t=1000;
else
t=t+1;
}
/* End of t loop, t changes to previously decided values to estimate Tammes's problem
would like t to be as large as possible but t>200 makes energy calculations lose
accuracy */
return 0;
} /* End of main function and therefore program. In original as seen by following link
below the code will use gradient flow algorithm before end of b, n and t loops to
minimise the energy function and therefore get accurate solutions. */
每次运行t> 200的代码时，能量输出都会失去准确性（因为它被提升到高功率），我被告知需要使用任意精度整数并获得GMP库。我已经完成了这个并且设法在我的范围内使用GMP库运行代码，但是我并没有真正得到我应该改变的内容。
我是否改变能量（和能量）或距离或三者（/ 4）？我真的不明白我应该改变什么，但我现在正在阅读如何从手册中做到这一点。
注意：我原来的问题在这里，但我认为这确实得到了回答，这保证了一个新问题。当这实际有效时，我会接受答案：Losing accuracy for large integers (pow?)
我已经改变了我的代码（如下所示），但我只是在初始化En [b]时想出了Segmentation fault 11。如果评论对我要做的事情更深入一点，我将非常感激。感谢迄今为止的所有帮助，A。
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <time.h>
#include <stdlib.h>
#include <sstream>
#include <gmpxx.h>
using namespace std;
#define PI 3.14159265358979323846
int main()
{
int a,b,c,d,f,i,j,k,m,n,s,Success,Fails;
double p,theta,phi,Time,Averagetime,Distance,Length,DotProdForce,
Forcemagnitude,ForceMagnitude[201],Force[201][4],E[1000001],Epsilon[4],Ep,
x[201][4],new_x[201][4],y[201][4],A[201],alpha[201][201],degree,bestalpha[501];
unsigned long int t;
mpf_t Energy,energy,Power,D,En[501];
mpf_set_default_prec(1024);
mpf_init(Power);
mpf_init(D);
clock_t t1,t2;
t1=clock();
t=1000;
/* Set parameter t, the power in the energy function */
while(t<1001){
n=2;
/*set parameter n, the number of points going onto the sphere */
while(n<51){
cout << "N=" << n << "\n";
b=0;
Time=0.0;
/* Set parameter b, just a loop to distribute points many times (100) */
while(b<101){
clock_t t3,t4;
t3=clock();
if(n>200){
cout << n << " is too many points for me :-( \n";
exit(0);
}
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;
}
}
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
cout << "x[" << i << "][" << j << "]=" << x[i][j] << "\n";
}
}
/* Points distributed randomly and normalised so they sit on unit sphere */
mpf_init (Energy);
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));
mpf_set_d(D,Distance);
mpf_pow_ui(Power,D,t);
mpf_ui_div(Power,1.0,Power);
mpf_add(Energy,Energy,Power);
}
}
cout << "Energy=" << Energy << "\n";
/*Energy calculated as a summation function this is where accuracy is lost */
for(i=1;i<=n;i++){
y[i][1]=x[i][1];
y[i][2]=x[i][2];
y[i][3]=x[i][3];
}
m=100;
if (m>100){
cout << "The m="<< m << " loop is inefficient...lessen m \n";
exit(0);
}
a=1;
/* Distributing points m-1 times and choosing the best random distribution */
while(a<m){
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;
}
}
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
cout << "x[" << i << "][" << j << "]=" << x[i][j] << "\n";
}
}
mpf_init(energy);
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));
mpf_set_d(D,Distance);
mpf_pow_ui(Power,D,t);
mpf_ui_div(Power,1.0,Power);
mpf_add(energy,energy,Power);
}
}
cout << "energy=" << energy << "\n";
if(energy<Energy)
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
mpf_set(Energy,energy);
y[i][j]=x[i][j];
}
}
else
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
mpf_set(energy,Energy);
x[i][j]=y[i][j];
}
}
a=a+1;
}
/* End of random distribution loop, the loop for a<m */
cout << "Energy=" << Energy << "\n";
mpf_init(En[b]);
mpf_set(En[b],Energy);
for(i=0;i<=b;i++){
cout << "En[" << i << "]=" << En[i] << "\n";
}
b=b+1;
t4=clock();
float diff ((float)t4-(float)t3);
float seconds = diff / CLOCKS_PER_SEC;
Time = Time + seconds;
}
/* End of looping the entire body of the program, used to get an average reading */
t2=clock();
float diff ((float)t2-(float)t1);
float seconds = diff / CLOCKS_PER_SEC;
n=n+1;
}
/* End of n loop, here n increases so I get outputs for n from 2 to 50 for each t */
if(t==1)
t=2;
else if(t==2)
t=5;
else if(t==5)
t=10;
else if(t==10)
t=25;
else if(t==25)
t=50;
else if(t==50)
t=100;
else if(t==100)
t=250;
else if(t==250)
t=500;
else if(t==500)
t=1000;
else
t=1001;
}
/* End of t loop, t changes to previously decided values to estimate Tammes's problem
would like t to be as large as possible but t>200 makes energy calculations lose
accuracy */
return 0;
} /* End of main function and therefore program. In original as seen by following link
below the code will use gradient flow algorithm before end of b, n and t loops to
minimise the energy function and therefore get accurate solutions. */
答案 0 :(得分：0)
代码现在看起来像是这样，对于未来的人来说显然你必须真正学会如何使用可以在http://gmplib.org找到的GMP库，我所遇到的大部分问题都是由所有有帮助的人解决的。评论，如果您遇到问题，请查看它们。感谢。
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <time.h>
#include <stdlib.h>
#include <sstream>
#include <gmpxx.h>
using namespace std;
#define PI 3.14159265358979323846
int main()
{
int a,b,c,d,f,i,j,k,m,n,s,Success,Fails;
double p,theta,phi,Time,Averagetime,Distance,Length,DotProdForce,
Forcemagnitude,ForceMagnitude[201],Force[201][4],E[1000001],Epsilon[4],Ep,
x[201][4],new_x[201][4],y[201][4],A[201],alpha[201][201],degree,bestalpha[501];
unsigned long int t;
mpf_t Energy,energy,Power,D,En[501];
mpf_set_default_prec(1024);
mpf_init(Power);
mpf_init(D);
clock_t t1,t2;
t1=clock();
t=1000;
/* Set parameter t, the power in the energy function */
while(t<1001){
n=2;
/*set parameter n, the number of points going onto the sphere */
while(n<3){
cout << "N=" << n << "\n";
b=0;
Time=0.0;
/* Set parameter b, just a loop to distribute points many times (100) */
while(b<2){
clock_t t3,t4;
t3=clock();
if(n>200){
cout << n << " is too many points for me :-( \n";
exit(0);
}
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;
}
}
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
cout << "x[" << i << "][" << j << "]=" << x[i][j] << "\n";
}
}
/* Points distributed randomly and normalised so they sit on unit sphere */
mpf_init (Energy);
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));
mpf_set_d(D,Distance);
mpf_pow_ui(Power,D,t);
mpf_ui_div(Power,1.0,Power);
mpf_add(Energy,Energy,Power);
}
}
cout << "Energy=" << Energy << "\n";
/*Energy calculated as a summation function this is where accuracy is lost */
for(i=1;i<=n;i++){
y[i][1]=x[i][1];
y[i][2]=x[i][2];
y[i][3]=x[i][3];
}
m=100;
if (m>100){
cout << "The m="<< m << " loop is inefficient...lessen m \n";
exit(0);
}
a=1;
/* Distributing points m-1 times and choosing the best random distribution */
while(a<m){
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;
}
}
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
cout << "x[" << i << "][" << j << "]=" << x[i][j] << "\n";
}
}
mpf_init(energy);
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));
mpf_set_d(D,Distance);
mpf_pow_ui(Power,D,t);
mpf_ui_div(Power,1.0,Power);
mpf_add(energy,energy,Power);
}
}
cout << "energy=" << energy << "\n";
if(energy<Energy)
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
mpf_set(Energy,energy);
y[i][j]=x[i][j];
}
}
else
for(i=1;i<=n;i++){
for(j=1;j<=3;j++){
mpf_set(energy,Energy);
x[i][j]=y[i][j];
}
}
a=a+1;
}
/* End of random distribution loop, the loop for a<m */
cout << "Energy=" << Energy << "\n";
mpf_init(En[b]);
mpf_set(En[b],Energy);
for(i=0;i<=b;i++){
cout << "En[" << i << "]=" << En[i] << "\n";
}
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));
degree=(180/PI);
alpha[i][j]=degree*acos((2.0-pow(Distance,2))/2.0);
}
}
for(i=1;i<=n;i++){
for(j=i+1;j<=n;j++){
cout << "alpha[" << i << "][" << j << "]=" << alpha[i][j] << "\n";
}
}
for(i=1;i<=n-1;i++){
for(j=i+1;j<=n-1;j++){
if(alpha[i][j]>alpha[i][j+1])
alpha[i][j]=alpha[i][j+1];
else
alpha[i][j+1]=alpha[i][j];
}
}
for(i=1;i<=n;i++){
for(j=i+1;j<=n;j++){
cout << "alpha[" << i << "][" << j << "]=" << alpha[i][j] << "\n";
}
}
for(i=1;i<=n-2;i++){
if(alpha[i][n]>alpha[i+1][n])
alpha[i][n]=alpha[i+1][n];
else
alpha[i+1][n]=alpha[i][n];
}
for(i=1;i<=n;i++){
for(j=i+1;j<=n;j++){
cout << "alpha[" << i << "][" << j << "]=" << alpha[i][j] << "\n";
}
}
bestalpha[b]=alpha[n-1][n];
for(i=1;i<=b;i++){
cout << "Best Angle[" << i << "]: " << bestalpha[b] << "\n";
}
b=b+1;
t4=clock();
float diff ((float)t4-(float)t3);
float seconds = diff / CLOCKS_PER_SEC;
Time = Time + seconds;
}
/* End of looping the entire body of the program, used to get an average reading */
t2=clock();
float diff ((float)t2-(float)t1);
float seconds = diff / CLOCKS_PER_SEC;
n=n+1;
}
/* End of n loop, here n increases so I get outputs for n from 2 to 50 for each t */
if(t==1)
t=2;
else if(t==2)
t=5;
else if(t==5)
t=10;
else if(t==10)
t=25;
else if(t==25)
t=50;
else if(t==50)
t=100;
else if(t==100)
t=250;
else if(t==250)
t=500;
else if(t==500)
t=1000;
else
t=1001;
}
/* End of t loop, t changes to previously decided values to estimate Tammes's problem
would like t to be as large as possible but t>200 makes energy calculations lose
accuracy */
return 0;
} /* End of main function and therefore program. In original as seen by following link
below the code will use gradient flow algorithm before end of b, n and t loops to
minimise the energy function and therefore get accurate solutions. */