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#include <cmath>
#include <iostream>
#include <fstream>
#define PI 3.14159265
using namespace std;
int main()
{
srand((unsigned)time(0));
float sine10[10]={0.0}, sine100[100]={0.0}, sine1000[1000]={0.0}; ///sin
float a = 0.87;/// upper limit
float b = 0.13; /// lower limit
float N10[10]={0.0}; ///N=10 array
float N100[100]={0.0}; /// N=100 array
float N1000[1000]={0.0}; /// N=1000 array
float n10avg = 0, n100avg = 0, n1000avg = 0; /// averages
float err10[100]={0.0};
float err100[100]={0.0}; //// errors
float err1000[100]={0.0};
float sumerr10 =0.0, sumerr100 = 0.0, sumerr1000 = 0.0; ////sum of errors
float avgerr10 = 0.0, avgerr100 = 0.0, avgerr1000 = 0.0; /// average error
int Nten = 10, Nhun = 100, Nthou = 1000; /// N=10 N=100 N=1000
float sumI10 = 0.0, sumI100 = 0.0, sumI1000 = 0.0;
float Itru[100]; //// reference value for integral I
for(int i = 0; i < 100; i++)
{
Itru[i]=0.525833;
}
for(int i = 0; i < 100; i++) /// loop required to obtain 100 estimates I
{
float sumn10i[10]={0.0};
float avgfx10[100] = {0.0};
float I10[100]={0.0}; /// array for 100 estimates of I for N = 10
float sumn100i[100]={0.0};
float avgfx100[100] = {0.0};
float I100[100]={0.0}; /// N = 100
float sumn1000i[1000]={0.0};
float avgfx1000[100] = {0.0};
float I1000[100]={0.0}; /// N = 1000
for(int n = 0; n < 10; n++)
{
float array[n];
float x;
x = rand() % 740; /// obtain 10 random values
array[n]=(x+13)/1000; ///limit the 10 random values between 0.13 and 0.87
sine10[n] = sin (PI * array[n]); /// calculate the sin for every x
N10[n] = 0.9*sine10[n];
sumn10i[i]= sumn10i[i] + N10[n]; /// sum 10 N values
}
for(int n = 0; n < 100; n++)
{
float array[n];
float x;
x = rand() % 740;
array[n]=(x+13)/1000;
sine100[n] = sin (PI * array[n]);
N100[n] = 0.9*sine100[n];
sumn100i[i]= sumn100i[i] + N100[n];
}
for(int n = 0; n < 1000; n++)
{
float array[n];
float x;
x = rand() % 740;
array[n]=(x+13)/1000;
sine1000[n] = sin (PI * array[n]);
N1000[n] = 0.9*sine1000[n];
sumn1000i[i]= sumn1000i[i] + N1000[n];
}
avgfx10[i] = sumn10i[i]/Nten; //// average estimate of f(x) for every N (N=10)
I10[i] = (a - b) * avgfx10[i]; /// estimate I based on I = (a-b)[average f(x)]
sumI10 = sumI10 + I10[i];
err10[i]=Itru[i]-I10[i];
sumerr10 = sumerr10+err10[i];
avgfx100[i] = sumn100i[i]/Nhun; // N = 100
I100[i] = (a - b) * avgfx100[i];
sumI100 = sumI100 + I100[i];
err100[i]=Itru[i]-I100[i];
sumerr100 = sumerr100+err100[i];
avgfx1000[i] = sumn1000i[i]/Nthou; /// N = 1000
I1000[i] = (a - b) * avgfx1000[i];
sumI1000 = sumI10 + I1000[i];
err1000[i]=Itru[i]-I1000[i];
sumerr1000 = sumerr1000+err1000[i];
cout << I10[i]<<endl;
cout << I100[i]<< endl<<endl;
}
n10avg = sumI10/100; //// Average I value for N = 10
avgerr10=abs(sumerr10/100); // Average |I-Iest|
cout << "The average estimate of I for N = 10: " << n10avg << endl <<
"The average |I-Iest| = " << avgerr10 << endl;
n100avg = sumI100/100; /// N = 100
avgerr100=abs(sumerr100/100);
cout << "The average estimate of I for N = 100: " << n100avg << endl <<
"The average |I-Iest| = " << avgerr100 << endl;
n1000avg = sumI1000/100; /// N = 1000
avgerr1000=abs(sumerr1000/100);
cout << "The average estimate of I for N = 1000: " << n1000avg << endl <<
"The average |I-Iest| = " << avgerr1000 << endl;
return 0;
}
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