/// <summary>
/// Calculates and returns the adjunct for the specified matrix
/// </summary>
/// <param name="matrix">The matrix</param>
/// <returns>The adjunct matrix</returns>
public static int[,] Adjunct(int[,] matrix)
{
if (!MatrixHelper.IsMatrixValid(matrix))
{
return(new int[0, 0]);
}
int rows = matrix.GetLength(0),
cols = matrix.GetLength(1);
if (rows != cols)
{
Console.WriteLine("The matrix is not square");
return(new int[0, 0]);
}
int[,] transpose = MatrixHelper.Transpose(matrix);
if (!MatrixHelper.IsMatrixValid(transpose))
{
return(new int[0, 0]);
}
int rowsTranspose = transpose.GetLength(0),
colsTranspose = transpose.GetLength(1);
int[,] adjunct = new int[rowsTranspose, colsTranspose];
for (int i = 0; i < rowsTranspose; i++)
{
for (int j = 0; j < colsTranspose; j++)
{
int sign = ((i + j) % 2 == 0) ? 1 : -1;
int minor = MatrixHelper.Determinant(MatrixHelper.RemoveRowAndColumn(transpose, i, j));
adjunct[i, j] = sign * minor;
}
}
return(adjunct);
}
/// <summary>
/// Calculates the determinant of a square (n X n) matrix
/// using a recursive implementation of the Laplace expansion calculation method
/// </summary>
/// <param name="squareMatrix">The square (n X n) matrix</param>
/// <returns>The determinant value</returns>
public static int Determinant(int[,] squareMatrix)
{
// Uses Laplace expansion
// Inspiration came from: http://www.mathsisfun.com/algebra/matrix-determinant.html
// See also: https://en.wikipedia.org/wiki/Laplace_expansion
if (!MatrixHelper.IsMatrixValid(squareMatrix))
{
return(0);
}
int rows = squareMatrix.GetLength(0),
cols = squareMatrix.GetLength(1);
if (rows != cols)
{
Console.WriteLine("The matrix is not square");
return(0);
}
if (rows == 1)
{
return(MatrixHelper.DeterminantMatrix1_1(squareMatrix));
}
else if (rows == 2)
{
return(MatrixHelper.DeterminantMatrix2_2(squareMatrix));
}
else
{
int det = 0;
for (int i = 0; i < cols; i++)
{
int sign = (i % 2 == 0) ? 1 : (-1);
det += sign * squareMatrix[0, i] * MatrixHelper.Determinant(MatrixHelper.RemoveRowAndColumn(squareMatrix, 0, i));
}
return(det);
}
}
