Homework SourseThis must be done in c You are to implement the Gaussian Eli
This must be done in c++.
You are to implement the Gaussian Elimination Algorithm to solve matrix problems provided in a data.txt file The format of the file should be as follows n A[n][n] b[n] that is for file 2 12 34 10 20 would represent A*x = b |1 2 3 4|* [x0 x1] = [10 20] Your solver should be designed to solve diagonally dominant matrices, so rotations are not required. You must use a dynamic matrix object. Your algorithm should take the provided matrix, reduce it to upper row echelon form, then compute the solution with a back-solver Then compute the magnitude of the residual of your solution. ||b - a*x||Solution
#include <iostream>
#include <cmath>
#include <vector>
using namespace std;
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] << \"\\t\";
if (j == n-1) {
cout << \"| \";
}
}
cout << \"\ \";
}
cout << endl;
}
vector<double> gauss(vector< vector<double> > A) {
int n = A.size();
for (int i=0; i<n; i++) {
// Search for maximum in this column
double maxEl = abs(A[i][i]);
int maxRow = i;
for (int k=i+1; k<n; k++) {
if (abs(A[k][i]) > maxEl) {
maxEl = abs(A[k][i]);
maxRow = k;
}
}
// Swap maximum row with current row (column by column)
for (int k=i; k<n+1;k++) {
double tmp = A[maxRow][k];
A[maxRow][k] = A[i][k];
A[i][k] = tmp;
}
// Make all rows below this one 0 in current column
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];
}
}
}
}
// Solve equation Ax=b for an upper triangular matrix A
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;
}
int main() {
int n;
cin >> n;
vector<double> line(n+1,0);
vector< vector<double> > A(n,line);
// Read input data
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 input
print(A);
// Calculate solution
vector<double> x(n);
x = gauss(A);
// Print result
cout << \"Result:\\t\";
for (int i=0; i<n; i++) {
cout << x[i] << \" \";
}
cout << endl;
}
