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  1. #include <iostream>
  2. #include <vector>
  3. #include <iomanip>
  4. using namespace std;
  5.  
  6. int main() {
  7.     int n;
  8.     cout << "Enter the order of square matrix: ";
  9.     cin >> n;
  10.  
  11.     vector<vector<double>> A(n, vector<double>(n));
  12.     vector<vector<double>> L(n, vector<double>(n, 0));
  13.     vector<vector<double>> U(n, vector<double>(n, 0));
  14.     vector<double> B(n), Y(n), X(n);
  15.  
  16.     cout << "Enter matrix elements:\n";
  17.     for (int i = 0; i < n; i++)
  18.         for (int j = 0; j < n; j++)
  19.             cin >> A[i][j];
  20.  
  21.     cout << "Enter the constant terms:\n";
  22.     for (int i = 0; i < n; i++)
  23.         cin >> B[i];
  24.  
  25.     // LU Decomposition
  26.     for (int j = 0; j < n; j++) {
  27.         for (int i = 0; i < n; i++) {
  28.             if (i <= j) {
  29.                 U[i][j] = A[i][j];
  30.                 for (int k = 0; k < i; k++)
  31.                     U[i][j] -= L[i][k] * U[k][j];
  32.                 if (i == j)
  33.                     L[i][j] = 1;
  34.             } else {
  35.                 L[i][j] = A[i][j];
  36.                 for (int k = 0; k < j; k++)
  37.                     L[i][j] -= L[i][k] * U[k][j];
  38.                 L[i][j] /= U[j][j];
  39.             }
  40.         }
  41.     }
  42.  
  43.     // Forward substitution to solve L*Y = B
  44.     for (int i = 0; i < n; i++) {
  45.         Y[i] = B[i];
  46.         for (int j = 0; j < i; j++)
  47.             Y[i] -= L[i][j] * Y[j];
  48.     }
  49.  
  50.     // Backward substitution to solve U*X = Y
  51.     for (int i = n - 1; i >= 0; i--) {
  52.         X[i] = Y[i];
  53.         for (int j = i + 1; j < n; j++)
  54.             X[i] -= U[i][j] * X[j];
  55.         X[i] /= U[i][i];
  56.     }
  57.  
  58.     // Output L
  59.     cout << "\n[L]:\n";
  60.     for (int i = 0; i < n; i++) {
  61.         for (int j = 0; j < n; j++)
  62.             cout << fixed << setprecision(3) << setw(8) << L[i][j];
  63.         cout << endl;
  64.     }
  65.  
  66.     // Output U
  67.     cout << "\n[U]:\n";
  68.     for (int i = 0; i < n; i++) {
  69.         for (int j = 0; j < n; j++)
  70.             cout << fixed << setprecision(3) << setw(8) << U[i][j];
  71.         cout << endl;
  72.     }
  73.  
  74.     // Output Y
  75.     cout << "\n[Y]: ";
  76.     for (int i = 0; i < n; i++)
  77.         cout << fixed << setprecision(3) << Y[i] << " ";
  78.     cout << endl;
  79.  
  80.     // Output X
  81.     cout << "\n[X]: ";
  82.     for (int i = 0; i < n; i++)
  83.         cout << fixed << setprecision(3) << X[i] << " ";
  84.     cout << endl;
  85.  
  86.     return 0;
  87. }
  88.  
Success #stdin #stdout 0s 5256KB
comments (?)
stdin
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2 4 -2
4 9 -3
-2 -3 -7
stdout
copy 
Enter the order of square matrix: Enter matrix elements:
Enter the constant terms:

[L]:
   1.000   0.000
   1.000   1.000

[U]:
   4.000  -2.000
   0.000  11.000

[Y]: -3.000 1.000 

[X]: -0.705 0.091
https://ideone.com/CeSEcn
language:
C++14 (gcc 8.3)
created:
8 days ago
visibility:
public

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