public static double Determinant2(double[,] matrix)
//{
// var result = 0d;
// var rows = matrix.GetLength(0);
// var cols = matrix.GetLength(1);
// if (rows == 1)
// {
// return matrix[0, 0];
// }
// else if (rows == 2)
// {
// return matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
// }
// for (var i = 0; i < cols; i++)
// {
// var temp = new double[rows - 1, cols - 1];
// for (var j = 1; j < rows; j++)
// {
// Array.Copy(matrix, 0, temp[j - 1], 0, i);
// Array.Copy(matrix, i + 1, temp[j - 1], i, cols - i - 1);
// }
// result += matrix[0, i] * Math.Pow(-1, i) * Determinant(temp);
// }
// return result;
//}
=> JaggedMatrixDeterminantTests.Determinant(matrix.ToJaggedArray()); // Convert to jagged array until the above copy code can be understood and fixed.
public static double[][] Inverse1(double[][] matrix)
{
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
// Find determinant of [][]A
var det = JaggedMatrixDeterminantTests.Determinant(matrix);
if (det == 0)
{
return(default);
/// <summary>
/// The co-factor is the determinant of the matrix that remains when the row and column containing the
/// specified element is removed. The co-factor may also be multiplied by -1, depending on the element's position:
/// + - + -
/// - + - +
/// + - + -
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <param name="col">column number (starting at 0)</param>
/// <param name="row">row number (starting at 0)</param>
/// <returns>
/// The cofactor of the specified element
/// </returns>
/// <exception cref="InvalidOperationException">Matrix must have the same number of rows and columns for the co-factor to be calculated</exception>
public static double CoFactor1(double[][] matrix, int col, int row)
{
var rows = matrix.Length;
var cols = matrix[0].Length;
if (cols != rows)
{
throw new InvalidOperationException("Matrix must have the same number of rows and columns for the co-factor to be calculated");
}
var array = JaggedGetMatrixMinorTests.GetMinor(matrix, col, row);
var cofactor = JaggedMatrixDeterminantTests.Determinant(array);
// need to work out sign:
var i = col - row;
if ((i % 2) != 0)
{
cofactor = -cofactor;
}
return(cofactor);
}
/// <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);
}
