/// <summary>
/// generates the inverse of a matrix
/// </summary>
/// <param name="matrix"></param>
/// <returns></returns>
public static Matrix GetInverse(Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException();
}
// todo: is returning null the best option?
if (!matrix.isInvertible())
{
return(null);
}
int n = matrix.rows;
Matrix toRref = new Matrix(n, 2 * n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
toRref[i, j] = matrix[i, j];
}
for (int j = n; j < 2 * n; j++)
{
toRref[i, j] = 0;
}
toRref[i, i + n] = 1;
}
Matrix rref = RREF(toRref);
Matrix result = new Matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = n; j < 2 * n; j++)
{
result[i, j - n] = rref[i, j];
}
}
return(result);
}
