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:

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#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;
}

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-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.

Although definitely not as efficient as Prelude's code, I still like my determinant function. It calculates it via expansion by minors/cofactors with recursion.

Code:

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Matrix findMinor(Matrix *A, int row, int col)
{
    int x;
    int y;
    int a;
    a = A->numR();
    int b;
    b = A->numC();
    Matrix M(a-1,b-1);

    for(x=0; x<a; x++)
    {
              for(y=0; y<b; y++)
                    {
                    if(x == (row-1));
                                if(y == (col-1));
                             
                                if(x > (row-1) && y > (col-1)) M.Array[x-1][y-1] = A->Array[x][y];
              if(x > (row-1)) M.Array[x-1][y] = A->Array[x][y];
              if(y > (col-1)) M.Array[x][y-1] = A->Array[x][y];
              else M.Array[x][y] = A->Array[x][y];
              }
    }
 
    return M;
}

float Matrix::Determinant()
{
    float det;
    Matrix temp;
    float temp2;
    float multiple;
    int y;
    det = 0;
    if(a==b && b==2)
    {
              det = (Array[0][0]*Array[1][1])-(Array[0][1]*Array[1][0]);
              return det;
    }
    if(a != b)
    {
        return 0;
    }
    else
    {
        for(y=0; y<b; y++)
        {
                if(y == b) break;
                else
                {
                    multiple = power(-1, y);
                    temp = findMinor(this,1,y+1);
                    temp2 = temp.Determinant();
                    det = (multiple * (Array[0][y] * temp2)) + det;
                }
        }
        return det;
    }
}

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