I\'m having trouble computing the magnitude of residual of solution (error vecto

Question

I'm having trouble computing the magnitude of residual of solution (error vector) after gaussian elimination for matrices. My program is supposed to solve for matrices of the form A*x=b, where A and b are given. My code does this just fine, but I'm having trouble computing the error vector. I know the formula should be b-A*x, but I'm having trouble getting it right with the vectors I have. Any suggestions?

Here's my code:

#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>
#include "assignment1.h"
using namespace std;

vector<double> gaussianElimination ( vector< vector<double> > A ) {
int n = A.size();

for ( int i = 0; i < n; i++ ) {
double maxElement = abs ( A[i][i] );
int maxRow = i;
for ( int k = i + 1; k < n; k++ ) {
if ( abs ( A[k][i] ) > maxElement ) {
maxElement = abs ( A[k][i] );
maxRow = k;
}
}

for ( int k = i; k < n + 1; k++ ) {
double tmp = A[maxRow][k];
A[maxRow][k] = A[i][k];
A[i][k] = tmp;
}

for ( int k = i + 1; k < n; k++ ) {
double c = -A[k][i] / A[i][i];
for ( int j = i; j < n + 1; j++ ) {
if ( i == j ) {
A[k][j] = 0;
} else {
A[k][j] += c * A[i][j];
}
}
}
}

vector<double> x ( n );
for ( int i = n - 1; i >= 0; i-- ) {
x[i] = A[i][n] / A[i][i];
for ( int k = i - 1; k >= 0; k-- ) {
A[k][n] -= A[k][i] * x[i];
}
}

return x;
}

void print ( vector< vector<double> > A ) {
int n = A.size();

for ( int i = 0; i < n; i++ ) {
for ( int j = 0; j < n + 1; j++ ) {
cout << A[i][j] << " ";
outputFile << A[i][j] << " ";
if ( j == n - 1 ) {
cout << "| ";
outputFile << "| ";
}
}
cout << " ";
outputFile << " ";
}
cout << endl;
outputFile << endl;
}

int main() {
int n;
cin >> n;
vector<double> line ( n + 1, 0 );
vector< vector<double> > A ( n,line );

// Read data from the input file
for ( int i = 0; i < n; i++ ) {
for ( int j = 0; j < n; j++ ) {
cin >> A[i][j];
}
}

for ( int i = 0; i < n; i++ ) {
cin >> A[i][n];
}

//Print the data from the input file
print(A);

//Compute the solution
vector<double> x ( n );
x = gaussianElimination ( A );

// Print the result to the screen and the output file
cout << "The unknown matrix: ";
outputFile << "The unknown matrix: ";
for ( int i = 0; i < n; i++ ) {
cout << "| " << x[i] << " | ";
outputFile << "| " << x[i] << " | ";
}
cout << endl;
outputFile << endl;

return 0;
}

Explanation / Answer

#include<iostream>

#define MAX 10

using namespace std;

int lcm(int x,int y);

int main()

{

int i,j,k,r,c,a[MAX][MAX],b[MAX][MAX],det=1,l,d1,d2;

cout<<" Enter the number of Rows of the Matrix: ";

cin>>r;

cout<<" Enter the number of Columns of the Matrix: ";

cin>>c;

if(r==c)

{

cout<<" Enter the Elements of the Matrix: ";

for(i=0;i<r;i++)

{

for(j=0;j<c;j++)

{

cin>>a[i][j];

}

}

for(i=0;i<r-1;i++)

{

for(j=i+1;j<r;j++)

{

l=lcm(a[i][i],a[j][i]);

if(l!=0&&(a[i][i]!=0&&a[j][i]!=0))

{

l=(a[i][i]*a[j][i])/l;

d1=l/a[i][i];

d2=l/a[j][i];

a[j][i]=0;

for(k=i+1;k<r;k++)

{

a[j][k]=(d2*a[j][k])-(d1*a[i][k]);

}

}

}

}

cout<<" The given Matrix after Gauss Elimination is: ";

for(i=0;i<r;i++)

{

for(j=0;j<c;j++)

{

cout<<a[i][j]<<" ";

}

cout<<" ";

}

}

else

{

cout<<" This is not a Square Matrix!!! ";

}

return 0;

}

int lcm(int x,int y)

{

int t;

while (y != 0)

{

t=y;

y=x%y;

x=t;

}

return x;

}

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