// Complex examples should supppress conversion warnings
# include <cppad/wno_conversion.hpp>

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_lu.hpp>

// The AD complex case is used by this example so must
// define a specializatgion of LeqZero,AbsGeq for the AD<Complex> case
namespace CppAD {
     CPPAD_BOOL_BINARY( std::complex<double> ,  AbsGeq   )
     CPPAD_BOOL_UNARY(  std::complex<double> ,  LeqZero )
}


bool HesLuDet(void)
{     bool ok = true;

     using namespace CppAD;
     typedef std::complex<double> Complex;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     size_t n = 2;

     // object for computing determinants
     det_by_lu< AD<Complex> > Det(n);

     // independent and dependent variable vectors
     CPPAD_TESTVECTOR(AD<Complex>)  X(n * n);
     CPPAD_TESTVECTOR(AD<Complex>)  D(1);

     // value of the independent variable
     size_t i;
     for(i = 0; i < n * n; i++)
          X[i] = Complex(int(i), -int(i) );

     // set the independent variables
     Independent(X);

     D[0]  = Det(X);

     // create the function object
     ADFun<Complex> f(X, D);

     // argument value
     CPPAD_TESTVECTOR(Complex)     x( n * n );
     for(i = 0; i < n * n; i++)
          x[i] = Complex(2 * i, i);

     // first derivative of the determinant
     CPPAD_TESTVECTOR(Complex) H( n * n * n * n );
     H = f.Hessian(x, 0);

     /*
     f(x)     = x[0] * x[3] - x[1] * x[2]
     f'(x)    = ( x[3], -x[2], -x[1], x[0] )
     */
     Complex zero(0., 0.);
     Complex one(1., 0.);
     Complex Htrue[]  = {
          zero, zero, zero,  one,
          zero, zero, -one, zero,
          zero, -one, zero, zero,
           one, zero, zero, zero
     };
     for( i = 0; i < n*n*n*n; i++)
          ok &= NearEqual( Htrue[i], H[i], eps99 , eps99 );

     return ok;
}