# include <cppad/cppad.hpp>
# include <complex>

// BEGIN CppAD namespace
namespace CppAD {

// The AD complex case is used by examples by not used by speed tests 
// Must define a specializatgion of LeqZero,AbsGeq for the ADComplex case
typedef std::complex<double>     Complex;
typedef CppAD::AD<Complex>     ADComplex;
CPPAD_BOOL_UNARY(Complex,  LeqZero )
CPPAD_BOOL_BINARY(Complex, AbsGeq )

template <class Scalar>
class det_by_lu {
private:
	const size_t m;
	const size_t n;
	CppADvector<Scalar> A;
	CppADvector<Scalar> B;
	CppADvector<Scalar> X;
public:
	det_by_lu(size_t n_) : m(0), n(n_), A(n_ * n_)
	{	}

	template <class Vector>
	inline Scalar operator()(const Vector &x)
	{
		using CppAD::exp;

		Scalar         logdet;
		Scalar         det;
		int          signdet;
		size_t       i;

		// copy matrix so it is not overwritten
		for(i = 0; i < n * n; i++)
			A[i] = x[i];
 
		// comput log determinant
		signdet = CppAD::LuSolve(
			n, m, A, B, X, logdet);

/*
		// Do not do this for speed test because it makes floating 
		// point operation sequence very simple.
		if( signdet == 0 )
			det = 0;
		else	det =  Scalar( signdet ) * exp( logdet );
*/

		// convert to determinant
		det     = Scalar( signdet ) * exp( logdet ); 

# ifdef FADBAD
		// Fadbad requires tempories to be set to constants
		for(i = 0; i < n * n; i++)
			A[i] = 0;
# endif

		return det;
	}
};
} // END CppAD namespace