/// <summary>
/// Recursive function for finding determinant of matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns></returns>
/// <acknowledgment>
/// https://www.geeksforgeeks.org/determinant-of-a-matrix/
/// https://www.geeksforgeeks.org/adjoint-inverse-matrix/
/// </acknowledgment>
//[DisplayName("Determinant of Matrix.")]
//[Description("Finds the Determinant of a Matrix.")]
//[Acknowledgment("https://www.geeksforgeeks.org/determinant-of-a-matrix/", "https://www.geeksforgeeks.org/adjoint-inverse-matrix/")]
//[SourceCodeLocationProvider]
//[DebuggerStepThrough]
//[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static double Determinant1(double[,] matrix)
{
// This method is broken. It does not provide the correct values for anything over 2 rows.
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
var rows = matrix.GetLength(0);
//var cols = matrix.GetLength(1);
var result = 0d; // Initialize result
// Base case : if matrix contains single element
if (rows == 1)
{
return(matrix[0, 0]);
}
else if (rows == 2)
{
result = matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
return(result);
}
var sign = 1d; // To store sign multiplier
// Iterate for each element of first row
for (var f = 0; f < rows; f++)
{
// Getting Cofactor of A[0,f]
var temp = GeneralMatrixSparseCofactorTests.Cofactor(matrix, 0, f);
result += sign * matrix[0, f] * Determinant(temp);
// Terms are to be added with alternate sign
sign = -sign;
}
return(result);
}
public static double[,] Adjoint1(double[,] matrix)
{
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
var rows = matrix.GetLength(0);
var cols = matrix.GetLength(1);
if (rows == 1)
{
return(new double[1, 1] {
{ 1d }
});
}
var adj = new double[rows, cols];
for (var i = 0; i < rows; i++)
{
for (var j = 0; j < cols; j++)
{
// Get cofactor of A[i,j]
var temp = GeneralMatrixSparseCofactorTests.Cofactor(matrix, i, j);
// Sign of adj[j,i] positive if sum of row and column indexes is even.
var sign = ((i + j) % 2d == 0d) ? 1d : -1d;
// Interchanging rows and columns to get the transpose of the cofactor matrix
adj[j, i] = sign * GeneralMatrixDeterminantTests.Determinant(temp);
}
}
return(adj);
}