/// <summary>
/// Optimized version of Determinant, that only uses double[,]
/// </summary>
/// <param name="array">Matrix array to compute</param>
/// <param name="scalar">The scalar.</param>
/// <returns>
/// Determinant of the matrix
/// </returns>
/// <acknowledgment>
/// https://github.com/PigDogBay/MpdbSharedLibrary/blob/master/MpdbSharedLibrary/Maths/Matrix.cs
/// </acknowledgment>
private static double Determinant2(double[][] array, double scalar = 1)
{
var length = array.GetLength(0);
if (length == 1)
{
return(array[0][0]);
}
else if (length == 2)
{
return((array[0][0] * array[1][1] - array[0][1] * array[1][0]) * scalar * scalar);
}
double det = 0;
// get minors and recurse down
for (var i = 0; i < length; i++)
{
// get the minor
var minor = JaggedGetMatrixMinorTests.GetMinor(array, i, 0);
// find correct sign
if (i % 2 == 0)
{
det += Determinant2(minor, scalar) * array[0][i] * scalar;
}
else
{
det -= Determinant2(minor, scalar) * array[0][i] * scalar;
}
}
return(det);
}
/// <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);
}