MxDet
- calculate determinant of the matrix

Matrix functions
(AmiBroker 6.10)

• method = 0 - auto (use slow method for matrices of upto and including 5x5, fast for larger matrices)
• method = 1 - slow (Laplace expansion method, more accurate)
• method = 2 - fast (LU decomposition, less accurate)

LU decomposition is fast but subject to higher numerical errors. "Slow" method is slower yet produces much more reliable results.

For example Octave/MatLab that use LU decomposition would say that determinant of singular matrix like this

{ {16, 2, 3, 13}, { 5, 11, 10, 8}, {9, 7, 6, 12}, {4, 14, 15, 1 } }

is -1.4495e-012 due to roundoff errors of LU method.

If you want to calculate determinant using fast (LU decomposition) method, call MxDet with fast parameter set to 2.

CAVEAT: Laplace method has complexity of O(N!) and for this reason, even if you use method = 1, the maximum dimension for this method is limited to 10x10. Matrices larger than that are always calculated using LU method