/// <summary>
/// Function to get adjoint of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns></returns>
/// <acknowledgment>
/// https://www.geeksforgeeks.org/adjoint-inverse-matrix/
/// </acknowledgment>
//[DisplayName("Matrix Adjoint")]
//[Description("Adjoint a matrix.")]
//[Acknowledgment("https://www.geeksforgeeks.org/adjoint-inverse-matrix/")]
//[SourceCodeLocationProvider]
//[DebuggerStepThrough]
//[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static double[][] Adjoint1(double[][] matrix)
{
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
var rows = matrix.Length;
var cols = matrix[0].Length;
if (rows == 1)
{
return(new double[][] { new double[] { 1d } });
}
var adj = new double[rows][];
for (var i = 0; i < rows; i++)
{
adj[i] = new double[cols];
}
for (var i = 0; i < rows; i++)
{
for (var j = 0; j < cols; j++)
{
// Get cofactor of A[i,j]
var temp = JaggedMatrixSparseCofactorTests.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 * JaggedMatrixDeterminantTests.Determinant(temp);
}
}
return(adj);
}
public static double Determinant0(double[][] matrix)
{
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
var rows = matrix.Length;
//var cols = matrix[0].Length;
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 = JaggedMatrixSparseCofactorTests.Cofactor(matrix, 0, f);
result += sign * matrix[0][f] * Determinant(temp);
// terms are to be added with alternate sign
sign = -sign;
}
return(result);
}