API tools faq
paste
Advertisement
bero_0401

adjoint and inverse of matrix

bero_0401
Jul 11th, 2024
56
0
Never
Add comment
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
C++ 3.83 KB | Source Code | 0 0
raw download clone embed print report
  1. #include <iostream>
  2. #include <iomanip>
  3. using namespace std;
  4.  
  5. const int N = 4;
  6.  
  7. // Function to get cofactor of A[p][q] in temp[][]. n is current dimension of A[][]
  8. void getCofactor(int A[N][N], int temp[N][N], int p, int q, int n)
  9. {
  10.     int i = 0, j = 0;
  11.  
  12.     // Looping for each element of the matrix
  13.     for (int row = 0; row < n; row++)
  14.     {
  15.         for (int col = 0; col < n; col++)
  16.         {
  17.             // Copying into temporary matrix only those element which are not in given row and column
  18.             if (row != p && col != q)
  19.             {
  20.                 temp[i][j++] = A[row][col];
  21.  
  22.                 // Row is filled, so increase row index and reset col index
  23.                 if (j == n - 1)
  24.                 {
  25.                     j = 0;
  26.                     i++;
  27.                 }
  28.             }
  29.         }
  30.     }
  31. }
  32.  
  33. /* Recursive function for finding determinant of matrix. n is current dimension of A[][]. */
  34. int determinant(int A[N][N], int n)
  35. {
  36.     int D = 0; // Initialize result
  37.  
  38.     // Base case : if matrix contains single element
  39.     if (n == 1)
  40.         return A[0][0];
  41.  
  42.     int temp[N][N]; // To store cofactors
  43.     int sign = 1; // To store sign multiplier
  44.  
  45.     // Iterate for each element of first row
  46.     for (int f = 0; f < n; f++)
  47.     {
  48.         // Getting Cofactor of A[0][f]
  49.         getCofactor(A, temp, 0, f, n);
  50.         D += sign * A[0][f] * determinant(temp, n - 1);
  51.  
  52.         // terms are to be added with alternate sign
  53.         sign = -sign;
  54.     }
  55.  
  56.     return D;
  57. }
  58.  
  59. // Function to get adjoint of A[N][N] in adj[N][N].
  60. void adjoint(int A[N][N], int adj[N][N])
  61. {
  62.     if (N == 1)
  63.     {
  64.         adj[0][0] = 1;
  65.         return;
  66.     }
  67.  
  68.     // temp is used to store cofactors of A[][]
  69.     int sign = 1;
  70.     int temp[N][N];
  71.  
  72.     for (int i = 0; i < N; i++)
  73.     {
  74.         for (int j = 0; j < N; j++)
  75.         {
  76.             // Get cofactor of A[i][j]
  77.             getCofactor(A, temp, i, j, N);
  78.  
  79.             // sign of adj[j][i] positive if sum of row and column indexes is even.
  80.             sign = ((i + j) % 2 == 0) ? 1 : -1;
  81.  
  82.             // Interchanging rows and columns to get the transpose of the cofactor matrix
  83.             adj[j][i] = (sign) * (determinant(temp, N - 1));
  84.         }
  85.     }
  86. }
  87.  
  88. // Function to calculate and store inverse, returns false if matrix is singular
  89. bool inverse(int A[N][N], float inv[N][N])
  90. {
  91.     // Find determinant of A[][]
  92.     int det = determinant(A, N);
  93.     if (det == 0)
  94.     {
  95.         cout << "Singular matrix, can't find its inverse";
  96.         return false;
  97.     }
  98.  
  99.     // Find adjoint
  100.     int adj[N][N];
  101.     adjoint(A, adj);
  102.  
  103.     // Find Inverse using formula "inverse(A) = adj(A)/det(A)"
  104.     for (int i = 0; i < N; i++)
  105.         for (int j = 0; j < N; j++)
  106.             inv[i][j] = adj[i][j] / float(det);
  107.  
  108.     return true;
  109. }
  110. // Generic function to display the matrix. We use it to display both adjoint and inverse. Adjoint is integer matrix and inverse is a float.
  111. void display(int A[N][N])
  112. {
  113.     for (int i = 0; i < N; i++)
  114.     {
  115.         for (int j = 0; j < N; j++)
  116.             cout << A[i][j] << " ";
  117.         cout << endl;
  118.     }
  119. }
  120.  
  121. void display(float A[N][N])
  122. {
  123.     for (int i = 0; i < N; i++)
  124.     {
  125.         for (int j = 0; j < N; j++)
  126.             cout << fixed << setprecision(6) << A[i][j] << " ";
  127.         cout << endl;
  128.     }
  129. }
  130.  
  131.  
  132. int main()
  133. {
  134.     int A[N][N] = { {5, -2, 2, 7},
  135.                     {1, 0, 0, 3},
  136.                     {-3, 1, 5, 0},
  137.                     {3, -1, -9, 4}};
  138.  
  139.     int adj[N][N]; // To store adjoint of A[][]
  140.     float inv[N][N]; // To store inverse of A[][]
  141.  
  142.     cout << "Input matrix is :\n";
  143.     display(A);
  144.  
  145.     cout << "\nThe Adjoint is :\n";
  146.     adjoint(A, adj);
  147.     display(adj);
  148.  
  149.     cout << "\nThe Inverse is :\n";
  150.     if (inverse(A, inv))
  151.         display(inv);
  152.  
  153.     return 0;
  154. }
  155.  
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement
Public Pastes
Advertisement
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.  OK, I Understand
Not a member of Pastebin yet?
Sign Up, it unlocks many cool features!