@(@\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
.
Optimize Forward Activity Analysis: Example and Test
# include <cppad/cppad.hpp>
namespace {
struct tape_size { size_t n_var; size_t n_op; };
template <class Vector> void fun(
const Vector& x, Vector& y, tape_size& before, tape_size& after
)
{ typedeftypename Vector::value_type scalar;
// phantom variable with index 0 and independent variables// begin operator, independent variable operators and end operator
before.n_var = 1 + x.size(); before.n_op = 2 + x.size();
after.n_var = 1 + x.size(); after.n_op = 2 + x.size();
// adding the constant zero does not take any operations
scalar zero = 0.0 + x[0];
before.n_var += 0; before.n_op += 0;
after.n_var += 0; after.n_op += 0;
// multiplication by the constant one does not take any operations
scalar one = 1.0 * x[1];
before.n_var += 0; before.n_op += 0;
after.n_var += 0; after.n_op += 0;
// multiplication by the constant zero does not take any operations// and results in the constant zero.
scalar two = 0.0 * x[0];
// operations that only involve constants do not take any operations
scalar three = (1.0 + two) * 3.0;
before.n_var += 0; before.n_op += 0;
after.n_var += 0; after.n_op += 0;
// The optimizer will reconize that zero + one = one + zero// for all values of x.
scalar four = zero + one;
scalar five = one + zero;
before.n_var += 2; before.n_op += 2;
after.n_var += 1; after.n_op += 1;
// The optimizer will reconize that sin(x[3]) = sin(x[3])// for all values of x. Note that, for computation of derivatives,// sin(x[3]) and cos(x[3]) are stored on the tape as a pair.
scalar six = sin(x[2]);
scalar seven = sin(x[2]);
before.n_var += 4; before.n_op += 2;
after.n_var += 2; after.n_op += 1;
// If we used addition here, five + seven = zero + one + seven// which would get converted to a cumulative summation operator.
scalar eight = five * seven;
before.n_var += 1; before.n_op += 1;
after.n_var += 1; after.n_op += 1;
// Use two, three, four and six in order to avoid a compiler warning// Note that addition of two and three does not take any operations.// Also note that optimizer reconizes four * six == five * seven.
scalar nine = eight + four * six * (two + three);
before.n_var += 3; before.n_op += 3;
after.n_var += 2; after.n_op += 2;
// results for this operation sequence
y[0] = nine;
before.n_var += 0; before.n_op += 0;
after.n_var += 0; after.n_op += 0;
}
}
bool forward_active(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps10 = 10.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 3;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.5;
ax[1] = 1.5;
ax[2] = 2.0;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
tape_size before, after;
fun(ax, ay, before, after);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
ok &= f.size_order() == 1; // this constructor does 0 order forward
ok &= f.size_var() == before.n_var;
ok &= f.size_op() == before.n_op;
// Optimize the operation sequence// Note that, for this case, all the optimization was done during// the recording and there is no benifit to the optimization.
f.optimize();
ok &= f.size_order() == 0; // 0 order forward not present
ok &= f.size_var() == after.n_var;
ok &= f.size_op() == after.n_op;
// check zero order forward with different argument valueCPPAD_TESTVECTOR(double) x(n), y(m), check(m);
for(size_t i = 0; i < n; i++)
x[i] = double(i + 2);
y = f.Forward(0, x);
fun(x, check, before, after);
ok &= NearEqual(y[0], check[0], eps10, eps10);
return ok;
}
