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 #include #include #include #include "assignment1.h" using namespace std;

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

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

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