Thread: Determinant calculation

Does someone have any C++ code that calculates the determinant of an arbitary nxn matrix?

I assure you, that this is in no way a homework assignment.
I also assure you that I belive myself capable of writing my own algorithm, if some time is invested.

I just hate reinventing the wheel, that's all. A fast google search didn't return any relevant results, neither did a search on these boards.

Here's a quick scratchy one. I assumed you were using dynamic arrays instead of std::vectors:

Code:

#include <iostream>
#include <algorithm>

const int N = 3;

double matrix_det ( double **in_matrix, int n )
{
  int i, j, k;
  double **matrix;
  double det = 1;
  
  matrix = new double *[n];
  
  for ( i = 0; i < n; i++ )
    matrix[i] = new double[n];
  
  for ( i = 0; i < n; i++ ) {
    for ( j = 0; j < n; j++ )
      matrix[i][j] = in_matrix[i][j];
  }
  
  for ( k = 0; k < n; k++ ) {
    if ( matrix[k][k] == 0 ) {
      bool ok = false;
      
      for ( j = k; j < n; j++ ) {
        if ( matrix[j][k] != 0 )
          ok = true;
      }
      
      if ( !ok )
        return 0;
      
      for ( i = k; i < n; i++ )
        std::swap ( matrix[i][j], matrix[i][k] );
      
      det = -det;
    }
    
    det *= matrix[k][k];

    if ( k + 1 < n ) {
      for ( i = k + 1; i < n; i++ ) {
        for ( j = k + 1; j < n; j++ )
          matrix[i][j] = matrix[i][j] - matrix[i][k] * 
          matrix[k][j] / matrix[k][k];
      }
    }
  }

  for ( i = 0; i < n; i++ )
    delete [] matrix[i];

  delete [] matrix;
  
  return det;
}

int main()
{
  int i;
  double **array;
  
  array = new double *[N];
  
  for ( i = 0; i < N; i++ )
    array[i] = new double[N];
  
  array[0][0] = 4.0;
  array[0][1] = 6.0;
  array[0][2] = 3.0;

  array[1][0] = 9.0;
  array[1][1] = 1.0;
  array[1][2] = 6.0;

  array[2][0] = 5.0;
  array[2][1] = 9.0;
  array[2][2] = 2.0;

  std::cout<< matrix_det ( array, N ) <<std::endl;

  for ( i = 0; i < N; i++ )
    delete [] array[i];

  delete [] array;
}

-Prelude

Thanks alot!
That was exactly what I was looking for!

I think I'll add some optimizations for the simple cases n=2 and n=3.