@(@\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}} }@)@
This is cppad-20221105 documentation. Here is a link to its
current documentation
.
AD Absolute Zero Multiplication: Example and Test
# include <cppad/cppad.hpp>
# include <cmath>
bool azmul(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double inf = std::numeric_limits<double>::infinity();
double eps = 10. * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 2;
double x = 0.5;
double y = 2.0;
CPPAD_TESTVECTOR(AD<double>) axy(n);
axy[0] = x;
axy[1] = y;
// declare independent variables and start tape recording
CppAD::Independent(axy);
// range space vector
size_t m = 5;
CPPAD_TESTVECTOR(AD<double>) az(m);
az[0] = CppAD::azmul(axy[0], axy[1]); // azmul(variable, variable)
az[1] = CppAD::azmul(axy[0], inf); // azmul(variable, parameter=inf)
az[2] = CppAD::azmul(axy[0], 3.0); // azmul(variable, parameter=3.0)
az[3] = CppAD::azmul(0.0, axy[1]); // azmul(parameter=0.0, variable)
az[4] = CppAD::azmul(4.0, axy[1]); // azmul(parameter=4.0, variable)// create f: axy -> az and stop tape recording
CppAD::ADFun<double> f(axy, az);
// check value when x is not zero
ok &= NearEqual(az[0] , x * y, eps, eps);
ok &= az[1] == inf;
ok &= NearEqual(az[2] , x * 3.0, eps, eps);
ok &= az[3] == 0.0;
ok &= NearEqual(az[4] , 4.0 * y, eps, eps);
// check value x is zero and y is infinityCPPAD_TESTVECTOR(double) xy(n), z(m);
xy[0] = 0.0;
xy[1] = inf;
z = f.Forward(0, xy);
ok &= z[0] == 0.0;
ok &= z[1] == 0.0;
ok &= z[2] == 0.0;
ok &= z[3] == 0.0;
ok &= z[4] == inf;
return ok;
}
