$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
// 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; }