Example Optimizing Atomic Vector Usage

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atomic_four_vector_rev_depend.cpp

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$ This is cppad-20221105 documentation. Here is a link to its current documentation . Example Optimizing Atomic Vector Usage
f(u, v)
For this example,

$f : \B{R}^{3m} \rightarrow \B{R}$ is defined by

$f(u, v, w) = - ( u_0 + v_0 ) * w_0$ . where u , v , and w are in

$\B{R}^m$ .

Source


# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/vector/vector.hpp>
bool rev_depend(void)
{   bool ok = true;
    using CppAD::NearEqual;
    using CppAD::AD;
    //
    // vec_op
    // atomic vector_op object
    CppAD::atomic_vector<double> vec_op("atomic_vector");
    //
    // m
    // size of u, v, and w
    size_t m = 6;
    //
    // n
    size_t n = 3 * m;
    //
    // add_op, mul_op, neg_op
    typedef CppAD::atomic_vector<double>::op_enum_t op_enum_t;
    op_enum_t add_op = CppAD::atomic_vector<double>::add_enum;
    op_enum_t mul_op = CppAD::atomic_vector<double>::mul_enum;
    op_enum_t neg_op = CppAD::atomic_vector<double>::neg_enum;
    // -----------------------------------------------------------------------
    // Record f(u, v, w) = - (u + v) * w
    // -----------------------------------------------------------------------
    // Independent variable vector
    CPPAD_TESTVECTOR( CppAD::AD<double> ) a_ind(n);
    for(size_t j = 0; j < n; ++j)
        a_ind[j] = AD<double>(1 + j);
    CppAD::Independent(a_ind);
    //
    // au, av, aw
    CPPAD_TESTVECTOR( CppAD::AD<double> ) au(m), av(m), aw(m);
    for(size_t i = 0; i < m; ++i)
    {   au[i] = a_ind[0 * m + i];
        av[i] = a_ind[1 * m + i];
        aw[i] = a_ind[2 * m + i];
    }
    //
    // ax = (au, av)
    CPPAD_TESTVECTOR( CppAD::AD<double> ) ax(2 * m);
    for(size_t i = 0; i < m; ++i)
    {   ax[i]     = au[i];
        ax[m + i] = av[i];
    }
    //
    // ay = u + v
    CPPAD_TESTVECTOR( CppAD::AD<double> ) ay(m);
    vec_op(add_op, ax, ay);
    //
    // ax = (ay, aw)
    for(size_t i = 0; i < m; ++i)
    {   ax[i]     = ay[i];
        ax[m + i] = aw[i];
    }
    //
    // az = ay * w
    CPPAD_TESTVECTOR( CppAD::AD<double> ) az(m);
    vec_op(mul_op, ax, az);
    //
    // ay = - az
    vec_op(neg_op, az, ay);
    //
    // f
    CPPAD_TESTVECTOR( CppAD::AD<double> ) a_dep(1);
    a_dep[0] = ay[0];
    CppAD::ADFun<double> f(a_ind, a_dep);
    //
    // size_var
    // phantom variable, independent variables, operator results
    ok   &= f.size_var() == 1 + n + 3 * m;
    //
    // optimize
    // The atomic funciton rev_depend routine is called by optimizer
    f.optimize();
    //
    // size_var
    // phantom variablem, independent variables, operator variables
    ok &= f.size_var() == 1 + n + 3;
    //
    //
    return ok;
}

Input File: example/atomic_four/vector/rev_depend.cpp