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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <vector>
  4. #include <cmath>
  5. #include <algorithm>
  6. #include <string>
  7.  
  8. using namespace std;
  9.  
  10. void gauss_elimination(int n, vector<vector<double>>& A) {
  11.  
  12.     cout << setprecision(6) << fixed;
  13.  
  14.     cout << "--- Gauss Elimination Method ---" << endl;
  15.     cout << "Order of Square Matrix: " << n << endl;
  16.  
  17.  
  18.     for (int k = 0; k < n; ++k) {
  19.         int pivot = k;
  20.         for (int i = k + 1; i < n; ++i) {
  21.             if (abs(A[i][k]) > abs(A[pivot][k])) {
  22.                 pivot = i;
  23.             }
  24.         }
  25.         if (pivot != k) {
  26.             swap(A[k], A[pivot]);
  27.         }
  28.  
  29.         if (abs(A[k][k]) < 1e-9) {
  30.             cout << "Error: Near-zero pivot detected. Cannot solve." << endl;
  31.             return;
  32.         }
  33.  
  34.         for (int i = k + 1; i < n; ++i) {
  35.             double factor = A[i][k] / A[k][k];
  36.             for (int j = k; j < n + 1; ++j) {
  37.                 A[i][j] -= factor * A[k][j];
  38.             }
  39.         }
  40.     }
  41.  
  42.  
  43.     cout << "\n--- Upper Triangular Matrix ---" << endl;
  44.     for (int i = 0; i < n; ++i) {
  45.         for (int j = 0; j < n + 1; ++j) {
  46.             cout << setw(10) << A[i][j] << " ";
  47.         }
  48.         cout << endl;
  49.     }
  50.     cout << string(65, '-') << endl;
  51.  
  52.  
  53.     vector<double> x(n);
  54.     for (int i = n - 1; i >= 0; --i) {
  55.         double sum = 0.0;
  56.         for (int j = i + 1; j < n; ++j) {
  57.             sum += A[i][j] * x[j];
  58.         }
  59.         x[i] = (A[i][n] - sum) / A[i][i];
  60.     }
  61.  
  62.  
  63.     cout << "\nOutput:" << endl;
  64.     cout << "The solution is:" << endl;
  65.     for (int i = 0; i < n; ++i) {
  66.         cout << "x" << i + 1 << " = " << x[i] << endl;
  67.     }
  68. }
  69.  
  70. int main() {
  71.     int n = 3; 
  72.     vector<vector<double>> A = {
  73.         {3.0, 6.0, -9.0, 15.0},
  74.         {2.0, 4.0, -6.0, 10.0},
  75.         {-2.0, -3.0, 4.0, -6.0}
  76.     };
  77.  
  78.     gauss_elimination(n, A);
  79.  
  80.     return 0;
  81. }
Success #stdin #stdout 0.01s 5288KB
comments (?)
stdin 
Standard input is empty
stdout 
--- Gauss Elimination Method ---
Order of Square Matrix: 3
Error: Near-zero pivot detected. Cannot solve.
https://ideone.com/dCmvtq
language:
C++ (gcc 8.3)
created:
4 hours ago
visibility:
public

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