public static double[,] Inverse1(double[,] matrix)
{
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
// Find determinant of [,]A
var det = GeneralMatrixDeterminantTests.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.GetLength(0);
var cols = matrix.GetLength(1);
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 = GeneralGetMatrixMinorTests.GetMinor(matrix, col, row);
var cofactor = GeneralMatrixDeterminantTests.Determinant(array);
// need to work out sign:
var i = col - row;
if ((i % 2) != 0)
{
cofactor = -cofactor;
}
return(cofactor);
}
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);
}
