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  1. #include<iostream>
  2. #include<iomanip>
  3. using namespace std;
  4.  
  5. int main() {
  6.     int n;
  7.     cout << "Enter the order of square matrix: ";
  8.     cin >> n;
  9.  
  10.     double A[10][10], L[10][10], U[10][10], B[10], Y[10], X[10];
  11.  
  12.     // Input Matrix A
  13.     cout << "Enter matrix element:\n";
  14.     for(int i=0; i<n; i++) {
  15.         for(int j=0; j<n; j++) {
  16.             cin >> A[i][j];
  17.         }
  18.     }
  19.  
  20.     // Input Vector B
  21.     cout << "Enter the constant terms: ";
  22.     for(int i=0; i<n; i++) {
  23.         cin >> B[i];
  24.     }
  25.  
  26.     // Initialize L and U
  27.     for(int i=0; i<n; i++) {
  28.         for(int j=0; j<n; j++) {
  29.             if(i==j)
  30.                 L[i][j] = 1.0;
  31.             else
  32.                 L[i][j] = 0.0;
  33.             U[i][j] = 0.0;
  34.         }
  35.     }
  36.  
  37.     // LU Decomposition
  38.     for(int j=0; j<n; j++) {
  39.         for(int i=0; i<=j; i++) {
  40.             double sum = 0.0;
  41.             for(int k=0; k<i; k++)
  42.                 sum += L[i][k]*U[k][j];
  43.             U[i][j] = A[i][j] - sum;
  44.         }
  45.         for(int i=j+1; i<n; i++) {
  46.             double sum = 0.0;
  47.             for(int k=0; k<j; k++)
  48.                 sum += L[i][k]*U[k][j];
  49.             L[i][j] = (A[i][j] - sum) / U[j][j];
  50.         }
  51.     }
  52.  
  53.     // Display L
  54.     cout << fixed << setprecision(3);
  55.     cout << "\n[L]:\n";
  56.     for(int i=0; i<n; i++) {
  57.         for(int j=0; j<n; j++)
  58.             cout << L[i][j] << " ";
  59.         cout << endl;
  60.     }
  61.  
  62.     // Display U
  63.     cout << "\n[U]:\n";
  64.     for(int i=0; i<n; i++) {
  65.         for(int j=0; j<n; j++)
  66.             cout << U[i][j] << " ";
  67.         cout << endl;
  68.     }
  69.  
  70.     // Forward Substitution to solve L.Y = B
  71.     for(int i=0; i<n; i++) {
  72.         double sum = 0.0;
  73.         for(int j=0; j<i; j++)
  74.             sum += L[i][j] * Y[j];
  75.         Y[i] = (B[i] - sum) / L[i][i];
  76.     }
  77.  
  78.     // Display Y
  79.     cout << "\n[Y]: ";
  80.     for(int i=0; i<n; i++)
  81.         cout << Y[i] << " ";
  82.     cout << endl;
  83.  
  84.     // Backward Substitution to solve U.X = Y
  85.     for(int i=n-1; i>=0; i--) {
  86.         double sum = 0.0;
  87.         for(int j=i+1; j<n; j++)
  88.             sum += U[i][j] * X[j];
  89.         X[i] = (Y[i] - sum) / U[i][i];
  90.     }
  91.  
  92.     // Display X
  93.     cout << "\n[X]: ";
  94.     for(int i=0; i<n; i++)
  95.         cout << X[i] << " ";
  96.     cout << endl;
  97.  
  98.     return 0;
  99. }
  100.  
Success #stdin #stdout 0.01s 5316KB
comments (?)
stdin
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3
2 4 -2
4 9 -3
-2 -3 -7
stdout
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Enter the order of square matrix: Enter matrix element:
Enter the constant terms: 
[L]:
1.000 0.000 0.000 
2.000 1.000 0.000 
-1.000 1.000 1.000 

[U]:
2.000 4.000 -2.000 
0.000 1.000 1.000 
0.000 0.000 -10.000 

[Y]: 0.000 0.000 -0.000 

[X]: -0.000 0.000 0.000
https://ideone.com/42JtO3
language:
C++ (gcc 8.3)
created:
9 days ago
visibility:
public

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