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Gradient of Determinant Using Expansion by Minors: Example and Test
`

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

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

    typedef std::complex<double>     Complex;
    typedef CppAD::AD<Complex>       ADComplex;
    typedef CPPAD_TESTVECTOR(ADComplex)   ADVector;

    // ----------------------------------------------------------------------------

    bool HesMinorDet(void)
    {     bool ok = true;

         using namespace CppAD;

         size_t n = 2;

         // object for computing determinants
         det_by_minor<ADComplex> Det(n);

         // independent and dependent variable vectors
         CPPAD_TESTVECTOR(ADComplex)  X(n * n);
         CPPAD_TESTVECTOR(ADComplex)  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);

         // comupute the determinant
         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 &= Htrue[i] == H[i];

         return ok;

    }

`

Input File: example/general/hes_minor_det.cpp