# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function cases<Vector> in empty namespace
template <typename Vector>
bool cases(void)
{ bool ok = true;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) X(n);
X[0] = 0.;
X[1] = 1.;
// declare independent variables and start recording
CppAD::Independent(X);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = X[0] * X[1];
// create f : X -> Y and stop recording
CppAD::ADFun<double> f(X, Y);
// define x^0 and compute y^0 using user zero order forward
Vector x0(n), y0(m);
x0[0] = 2.;
x0[1] = 3.;
y0 = f.Forward(0, x0);
// y^0 = F(x^0)
double check;
check = x0[0] * x0[1];
ok &= NearEqual(y0[0] , check, eps, eps);
// define x^1 and compute y^1 using first order forward mode
Vector x1(n), y1(m);
x1[0] = 4.;
x1[1] = 5.;
y1 = f.Forward(1, x1);
// Y^1 (x) = partial_t F( x^0 + x^1 * t )
// y^1 = Y^1 (0)
check = x1[0] * x0[1] + x0[0] * x1[1];
ok &= NearEqual(y1[0], check, eps, eps);
// define x^2 and compute y^2 using second order forward mode
Vector x2(n), y2(m);
x2[0] = 6.;
x2[1] = 7.;
y2 = f.Forward(2, x2);
// Y^2 (x) = partial_tt F( x^0 + x^1 * t + x^2 * t^2 )
// y^2 = (1/2) * Y^2 (0)
check = x2[0] * x0[1] + x1[0] * x1[1] + x0[0] * x2[1];
ok &= NearEqual(y2[0], check, eps, eps);
// W(x) = Y^0 (x) + 2 * Y^1 (x) + 3 * (1/2) * Y^2 (x)
size_t p = 3;
Vector dw(n*p), w(m*p);
w[0] = 1.;
w[1] = 2.;
w[2] = 3.;
dw = f.Reverse(p, w);
// check partial w.r.t x^0_0 of W(x)
check = x0[1] + 2. * x1[1] + 3. * x2[1];
ok &= NearEqual(dw[0*p+0], check, eps, eps);
// check partial w.r.t x^0_1 of W(x)
check = x0[0] + 2. * x1[0] + 3. * x2[0];
ok &= NearEqual(dw[1*p+0], check, eps, eps);
// check partial w.r.t x^1_0 of W(x)
check = 2. * x0[1] + 3. * x1[1];
ok &= NearEqual(dw[0*p+1], check, eps, eps);
// check partial w.r.t x^1_1 of W(x)
check = 2. * x0[0] + 3. * x1[0];
ok &= NearEqual(dw[1*p+1], check, eps, eps);
// check partial w.r.t x^2_0 of W(x)
check = 3. * x0[1];
ok &= NearEqual(dw[0*p+2], check, eps, eps);
// check partial w.r.t x^2_1 of W(x)
check = 3. * x0[0];
ok &= NearEqual(dw[1*p+2], check, eps, eps);
return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_three(void)
{ bool ok = true;
ok &= cases< CppAD::vector <double> >();
ok &= cases< std::vector <double> >();
ok &= cases< std::valarray <double> >();
return ok;
}