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| #include<iostream>
#include<cmath>
using namespace std ;
const int row=4, column=4;
void DiagonalMatrix(double Array[row][column],double arr[row][column]);
void PrintArray (double arr[row][column]);
void SubstractArray(double Array[row][column],double arr[row][column],double R[row][column]);
void PrintR (double R[row][column]);
void MatrixToVector(double matrix[row][column],double I[row],double B[row]);
void PrintVector (double B[row]);
void SubstractVector(double B[row],double b[row],double C[row]);
void DiagonalMatrixInverse(double diagonal[row][column],double Inverse[row][column] );
void Jacobi(double Xnew[row]);
int main()
{
double R[row][column];
double arr[row][column];
double matrix[row][column]={{-1,1,0,0},
{7,2,4,-6},
{0,-2,-4,8},
{0,1,-1,6}};
double I[row]={1,1,1,1};
double B[row];
double b[row]={5,20,-10,0};
double C[row];
double Inverse[row][column];
double Xnew[row];
DiagonalMatrix(matrix,arr);
PrintArray(arr);
SubstractArray(matrix,arr,R);
PrintR(R);
MatrixToVector(R,I,B);
PrintVector(B);
SubstractVector(B, b,C);
DiagonalMatrixInverse(arr,Inverse );
Jacobi(Xnew);
return 0;
}
void PrintArray (double arr[row][column])
{
for(int i=0; i<row;i++)
{cout<<endl;
{
for(int j=0;j<column;j++)
cout<<" "<<arr[i][j];
}
}
cout<<endl;
}
void DiagonalMatrix(double Array[row][column],double arr[row][column])
{
for(int i=0;i<row;i++)
{cout<<endl;
{
for(int j=0;j<column;j++)
{
if(i==j)
arr[i][j]=Array[i][j];
else
arr[i][j]=0;
}
}
}
}
void SubstractArray(double Array[row][column],double arr[row][column],double R[row][column])
{
for(int i=0;i<row;i++)
{
{
for(int j=0;j<column;j++)
R[i][j]=(Array[i][j]-arr[i][j]);
}
}
}
void PrintR (double R[row][column])
{
for(int i=0;i<row;i++)
{
cout<<endl;
{for(int j=0;j<column; j++)
cout<<" "<<R[i][j];
}
}
cout<<endl;
}
void MatrixToVector(double matrix[row][column],double I[row],double B[row])
{
double sum=0;
for(int i =0;i<row;i++)
{for(int j=0;j<column;j++)
{
sum+=matrix[i][j]*I[j];
B[i]=sum;
if(j==column-1)
sum=0;
}
}
}
void PrintVector (double B[row])
{
for(int i=0; i<row;i++)
{ cout<<endl;
cout<<B[i];}
cout<<endl;
}
void SubstractVector(double B[row],double b[row],double C[row])
{
for(int i =0;i<row;i++)
C[i] =b[i]-B[i];
for(int j=0;j<row;j++)
cout<<C[j]<<endl;
}
void DiagonalMatrixInverse(double diagonal[row][column],double Inverse[row][column] )
{
for(int i=0;i<row;i++)
{cout<<endl;
for(int j=0;j<column;j++)
{if(i==j)
Inverse[i][j]=1.0/diagonal[i][j];
else
Inverse[i][j]=0;
cout<<" "<<Inverse[i][j];
}
}
}
void Jacobi(double Xnew[row])
{
double Array[row][column]={{-1,1,0,0},
{7,2,4,-6},
{0,-2,-4,8},
{0,1,-1,6}};
int counter=0;
double Diagonal[row][column];
double R[row][column];
double Xold[row]={0,0,0,0};
double B[row];
double b[row]={5,20,-10,0};
double C[row];
double Inverse[row][column];
DiagonalMatrix(Array,Diagonal);
SubstractArray(Array,Diagonal,R);
DiagonalMatrixInverse(Diagonal,Inverse);
while (counter<2)
{ MatrixToVector(R,Xold,B);
SubstractVector(B,b,C);
MatrixToVector(Inverse,C,Xnew);
PrintVector (Xnew);
for(int i=0;i<row;i++)
Xold[i]=Xnew[i];
counter++;}
}
bool Error(double Xold[row],double Xnew[row])
{bool check=false;
double sum=0;
for(int i=0;i<row;i++)
{sum+=( abs(Xold[i]-Xnew[i]));
if( sum<=pow(10,-6))
check=true;
}
return check;
} |
