public static DualMatrix Inverse(DualMatrix matrix)
{
int m = matrix.Rows;
if (matrix.Columns != m)
{
throw new ArgumentException("The matrix isn't a square matrix.");
}
if (m <= 3)
{
DualNumber determinant = DeterminantDirect(m, matrix);
return InverseDirect(m, matrix, determinant);
}
int n = GradientLength(m, matrix);
return Inverse(matrix, m, n, LUDecomposition.Inverse(matrix.GetValues()));
}
/// <summary>
/// This method saves some time if both the inverse and the determinant is needed by only having to compute
/// the inverse once.
/// </summary>
public static void InverseDeterminant(DualMatrix matrix, out DualMatrix inverse, out DualNumber determinant)
{
int m = matrix.Rows;
if (matrix.Columns != m)
{
throw new ArgumentException("The matrix isn't a square matrix.");
}
if (m <= 3)
{
// The naive implementation seems to be faster (for all values of n). Maybe it's
// faster to perform the LU decomposition directly on the DualNumbers?
determinant = DeterminantDirect(m, matrix);
inverse = InverseDirect(m, matrix, determinant);
return;
}
int n = GradientLength(m, matrix);
LUDecomposition lu = LUDecomposition.Decompose(matrix.GetValues());
Matrix inverse0 = lu.Inverse();
double determinant0 = lu.Determinant();
inverse = Inverse(matrix, m, n, inverse0);
determinant = Determinant(matrix, m, n, inverse0, determinant0);
}