Function brown_hessian

dlib/test/optimization_test_functions.cpp:347–398

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

        matrix<double,4,4> brown_hessian ( const matrix<double,4,1>& x)
        {
            double c;
            double df1dx1;
            double df1dx2;
            double df2dx3;
            double df2dx4;
            double f1;
            double f2;
            matrix<double,4,4> h;
            int i;

            h = 0;

            for (i = 1; i <= 20; ++i)
            {

                c = double ( i ) / 5.0E+00;

                f1 = x(0) + c * x(1) - std::exp ( c );
                f2 = x(2) + std::sin ( c ) * x(3) - std::cos ( c );

                df1dx1 = 1.0E+00;
                df1dx2 = c;
                df2dx3 = 1.0E+00;
                df2dx4 = std::sin ( c );

                using std::pow;
                h(0,0) = h(0,0) + 12.0E+00 * pow(f1,2) * df1dx1 * df1dx1 + 4.0E+00 * pow(f2,2) * df1dx1 * df1dx1;
                h(0,1) = h(0,1) + 12.0E+00 * pow(f1,2) * df1dx1 * df1dx2 + 4.0E+00 * pow(f2,2) * df1dx1 * df1dx2;
                h(0,2) = h(0,2) + 8.0E+00 * f1 * f2 * df1dx1 * df2dx3;
                h(0,3) = h(0,3) + 8.0E+00 * f1 * f2 * df1dx1 * df2dx4;

                h(1,0) = h(1,0) + 12.0E+00 * pow(f1,2) * df1dx2 * df1dx1 + 4.0E+00 * pow(f2,2) * df1dx2 * df1dx1;
                h(1,1) = h(1,1) + 12.0E+00 * pow(f1,2) * df1dx2 * df1dx2 + 4.0E+00 * pow(f2,2) * df1dx2 * df1dx2;
                h(1,2) = h(1,2) + 8.0E+00 * f1 * f2 * df1dx2 * df2dx3;
                h(1,3) = h(1,3) + 8.0E+00 * f1 * f2 * df1dx2 * df2dx4;

                h(2,0) = h(2,0) + 8.0E+00 * f1 * f2 * df2dx3 * df1dx1;
                h(2,1) = h(2,1) + 8.0E+00 * f1 * f2 * df2dx3 * df1dx2;
                h(2,2) = h(2,2) + 4.0E+00 * pow(f1,2) * df2dx3 * df2dx3 + 12.0E+00 * pow(f2,2) * df2dx3 * df2dx3;
                h(2,3) = h(2,3) + 4.0E+00 * pow(f1,2) * df2dx4 * df2dx3 + 12.0E+00 * pow(f2,2) * df2dx3 * df2dx4;

                h(3,0) = h(3,0) + 8.0E+00 * f1 * f2 * df2dx4 * df1dx1;
                h(3,1) = h(3,1) + 8.0E+00 * f1 * f2 * df2dx4 * df1dx2;
                h(3,2) = h(3,2) + 4.0E+00 * pow(f1,2) * df2dx3 * df2dx4 + 12.0E+00 * pow(f2,2) * df2dx4 * df2dx3;
                h(3,3) = h(3,3) + 4.0E+00 * pow(f1,2) * df2dx4 * df2dx4 + 12.0E+00 * pow(f2,2) * df2dx4 * df2dx4;

            }

            return make_symmetric(h);
        }

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