?? thesecond.cpp
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/* 04計B 林傳敏 2004131301 */
#include <iostream.h>
#include <iomanip.h>
#include <math.h>
const int N=45;
double x[10];
int checkRoot(double); // 檢查某個根是否為重根
int binary(double, double); // 二分法
int Newton(double, double); // Newton法
int xianjie(double, double); // 弦截法
int NewtonDownMou(double, double); // Newton下山法
int main()
{
cout << "請輸入運行次數 t:";
int t;
cin >> t;
for(int kk=0; kk < t; kk++)
{
cout << "Input the range of the root" << endl;
int a, b,count;
cin >> a >> b;
cout << "the range is : [" << a << "," << b << "]" << endl;
cout << "m != 0,說明這個數是方程的m重根, or, 這個數不是方程的根." << endl;
binary(a, b);
cout.setf(ios::left, ios::adjustfield);
cout << "二分法" << endl;
cout.width(10);
cout << "roots" << "\t" << "m" << endl << "-----------------" << endl;
for(int i=0; i < 5; i++)
{
cout.width(10);
cout << (x[2*i] + x[2*i+1]) / 2 << "\t";
count = checkRoot((x[2*i] + x[2*i+1]) / 2);
cout << count << endl;
} // for
cout << "\n";
Newton(a, b);
cout << "Newton法" << endl;
cout.width(10);
cout << "roots" << "\t" << "m" << endl << "-----------------" << endl;
for(i=0; i < 5; i++)
{
count = checkRoot(x[i]);
cout.width(10);
cout << x[i] << "\t" << count << endl;
} // for
cout << "\n";
xianjie(a, b);
cout << "XianJie法" << endl;
cout.width(10);
cout << "roots" << "\t" << "m" << endl << "-----------------" << endl;
for(i=0; i < 5; i++)
{
count = checkRoot(x[i]);
cout.width(10);
cout << x[i] << "\t" << count << endl;
} // for
cout << "\n";
NewtonDownMou(a, b);
cout << "Newton下山法" << endl;
cout.width(10);
cout << "roots" << "\t" << "m" << endl << "-----------------" << endl;
for(i=0; i < 5; i++)
{
count = checkRoot(x[i]);
cout.width(10);
cout << x[i] << "\t" << count << endl;
} // for
} // for
cout << "Bye-Bye!!!" << endl;
return 0;
} // main
int checkRoot(double x0) //檢查某個根是否為重根
{
double x, y, y0;
x = x0 + 0.001;
y = pow(x, 5) - 3*pow(x, 3) + x - 1;
y0 = pow(x0, 5) - 3*pow(x0, 3) + x0 - 1;
int i=0;
double k;
if(fabs(y0) <= 0.0001)
{
i++;
k = (y0-y) / (x0-x); // 一階導數
if(fabs(k) <= 0.00001)
{
i++;
y = 5*pow(x, 4) - 9*pow(x, 2) + 1;
y0 = 5*pow(x0, 4) - 9*pow(x0, 2) + 1;
k = (y0-y) / (x0-x); // 二階導數
if(fabs(k) <= 0.00001)
{
i++;
y = 20*pow(x, 3) - 18*x;
y0 = 20*pow(x0, 3) - 18*x0;
k = (y0-y) / (x0-x); // 三階導數
if(fabs(k) <= 0.00001)
{
i++;
y = 60*pow(x, 2) - 18;
y0 = 60*pow(x0, 2) - 18;
k=(y0-y) / (x0-x); // 四階導數
if(fabs(k) <= 0.00001)
i++;
}
}
}
}
return i;
}
int binary(double a, double b) // 二分法
{
int i,j;
double n,x1,x2,y1,y2;
for(i=0; i < 10; i++)
{
x[i]=0;
}
n = fabs(a-b) / N;
for(i=0,j=0; (i<N) && (j<10); i++)
{
x1 = a + i*n;
x2 = a + (i+1)*n;
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
if((y1<0) && (y2>0))
{
x[j++] = x1;
x[j++] = x2;
}
else if((y1>0) && (y2<0))
{
x[j++] = x2;
x[j++] = x1;
}
} // for
for(i=0; i < 5; i++)
{
while(fabs(x[2*i]-x[2*i+1]) > 0.00001)
{
x1 = (x[2*i] + x[2*i+1]) / 2;
y1 = pow(x1, 5)-3*pow(x1, 3) + x1 - 1;
if(y1 < 0)
{
x[2*i] = x1;
}
else if(y1 > 0)
{
x[2*i+1] = x1;
}
}
}
return 0;
}
int Newton(double a, double b) // Newton法
{
int i,j;
double n,x1,x2,y1,y2,k;
for(i=0; i < 10; i++)
{
x[i] = 0;
}
n = fabs(a-b) / N;
for(i=0,j=0; (i < N) && (j < 5); i++)
{
x1 = a + i*n;
x2 = a + (i+1)*n;
y1=pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
y2=pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
if((y1<0) && (y2>0))
{
x[2*j] = x1;
x[2*j+1] = x2;
j++;
} // if
else if((y1>0) && (y2<0))
{
x[2*j] = x2;
x[2*j+1] = x1;
j++;
} // else
} // for
for(i=0; i < j; i++)
{
x1 = x[2*i];
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
x2 = x[2*i] + 0.00001;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
k = (y2-y1) / (x2-x1); //一次導數
x2 = x1 - y2/k;
while(fabs(x1-x2) > 0.00001)
{
y1 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
x1 = x2;
x2 = x2 + 0.00001;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
k = (y2-y1) / (x2-x1);
x2 = x1 - y1/k;
} // while
x[i] = x2;
x[i+1] = 0;
} // for
x[i+1] = 0;
return 0;
}
int xianjie(double a, double b) // 弦截法
{
double n,x1,x2,y1,y2,temp;
for(int i=0; i < 10; i++)
{
x[i]=0;
} // for
n = fabs(a-b)/N;
int j;
for(i=0,j=0; (i < N) && (j < 5); i++)
{
x1 = a + i*n;
x2 = a + (i+1)*n;
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
y2=pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
if((y1 < 0) && (y2 > 0))
{
x[2*j] = x1;
x[2*j+1] = x2;
j++;
} // if
else if((y1 > 0) && (y2 < 0))
{
x[2*j] = x2;
x[2*j+1] = x1;
j++;
} // else
} // for
for(i=0; i < j; i++)
{
x1 = x[2*i];
x2 = x[2*i] + 0.1;
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
temp = x2;
x2 = x2 - y2*(x2-x1)/(y2-y1);
x1 = temp;
while(fabs(x2-x1) > 0.00001)
{
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
temp = x2;
x2 = x2 - y2*(x2-x1)/(y2-y1);
x1 = temp;
} // while
x[i] = x2;
x[i+1] = 0;
} // for
x[i+1] = 0;
return 0;
} // xianjie
int NewtonDownMou(double a, double b) // Newton下山法
{
int i, j, flag=0;
double n, x1, x2, y1, y2, temp, k, r;
for(i=0; i < 10; i++)
{
x[i]=0;
} // for
n = fabs(a-b) / N;
i = 0;
label:
for(r=1,j=0; i < N; i++)
{
x1 = a + i*n;
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
x2 = x1 + 0.000001;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
k = (y2-y1) / (x2-x1);
x2 = temp = x1 - r*y1/k;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
while(1)
{
if(fabs(y2) < fabs(y1))
{
x2 = temp;
break;
}
else
{
if(r < 0.00001)
{
cout << "Fail to down moutain "
<< "choose the oher first_value"
<< endl;
goto label;
}
r = r*0.5;
temp = x1 - r*y1/k;
y2 = pow(temp, 5) - 3*pow(temp, 3) + temp - 1;
}
} // while
for(r=1; fabs(x2-x1) > 0.00001; r=1 )
{
x1 = x2;
y1 = pow(x1, 5) - 3*pow(x1, 3) + x1 - 1;
x2 = x2 + 0.000001;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
k = (y2-y1) / (x2-x1);
x2 = temp = x1 - r*y1/k;
y2 = pow(x2, 5) - 3*pow(x2, 3) + x2 - 1;
while(1)
{
if(fabs(y2) < fabs(y1))
{
x2 = temp;
break;
} // if
else
{
if(r < 0.00001)
{
cout << "Fail to down moutain"
<< "choose the oher first_value"
<< endl;
goto label;
} // if
r = r*0.5;
temp = x1 - r*y1/k;
y2 = pow(temp, 5) - 3*temp*temp*temp+temp-1;
} // else
} // while
} // for
j = 0;
while(j < 10)
{
if(fabs(x2-x[j]) > 0.1)
{
j++;
} // if
else
break;
} // while
if(j == 10)
{
x[flag++] = x2;
} // if
}
return 0;
} // NewtonDownMoutain
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