Atomic Vector Add Operator: Example Implementation

atomic_four_vector_add_op.hpp

@(@\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 . Atomic Vector Add Operator: Example Implementation
Forward Mode
see theory for forward mode addition .

Reverse Mode
see theory for reverse mode addition .

Example
The file atomic_four_vector_add.cpp contains an example and test for this operator.

Source


# include <cppad/example/atomic_four/vector/vector.hpp>

namespace CppAD { // BEGIN_CPPAD_NAMESPACE
// ---------------------------------------------------------------------------
// comment below is used by atomic_vector.omh
// BEGIN forward_add
template <class Base>
void atomic_vector<Base>::forward_add(
    size_t                                           m,
    size_t                                           p,
    size_t                                           q,
    const CppAD::vector<Base>&                       tx,
    CppAD::vector<Base>&                             ty)
{
    for(size_t k = p; k < q; ++k)
    {   for(size_t i = 0; i < m; ++i)
        {   size_t u_index  =       i * q + k;
            size_t v_index  = (m + i) * q + k;
            size_t y_index  =       i * q + k;
            // y_i^k = u_i^k + v_i^k
            ty[y_index]     = tx[u_index] + tx[v_index];
        }
    }
}
template <class Base>
void atomic_vector<Base>::forward_add(
    size_t                                           m,
    size_t                                           p,
    size_t                                           q,
    const CppAD::vector< CppAD::AD<Base> >&          atx,
    CppAD::vector< CppAD::AD<Base> >&                aty)
{   size_t n = 2 * m;
    assert( atx.size() == n * q );
    assert( aty.size() == m * q );
    //
    // atu, atv
    ad_const_iterator atu = atx.begin();
    ad_const_iterator atv = atu + ad_difference_type(m * q);
    //
    // ax
    ad_vector ax(n);
    ad_iterator au = ax.begin();
    ad_iterator av = au + ad_difference_type(m);
    //
    // ay
    ad_vector ay(m);
    //
    for(size_t k = p; k < q; ++k)
    {   // au = u^k
        copy_mat_to_vec(m, q, k, atu, au);
        // av = v^k
        copy_mat_to_vec(m, q, k, atv, av);
        // ay = au + av
        (*this)(add_enum, ax, ay); // atomic vector add
        // y^k = ay
        copy_vec_to_mat(m, q, k, ay.begin(), aty.begin() );
    }
}
// END forward_add
// comment above is used by atomic_vector.omh
// ---------------------------------------------------------------------------
// reverse_add
template <class Base>
void atomic_vector<Base>::reverse_add(
    size_t                                           m,
    size_t                                           q,
    const CppAD::vector<Base>&                       tx,
    const CppAD::vector<Base>&                       ty,
    CppAD::vector<Base>&                             px,
    const CppAD::vector<Base>&                       py)
{
    for(size_t k = 0; k < q; ++k)
    {   for(size_t i = 0; i < m; ++i)
        {   size_t u_index  =       i * q + k;
            size_t v_index  = (m + i) * q + k;
            size_t y_index  =       i * q + k;
            // y_i^k = u_i^k + v_i^k
            px[u_index] = py[y_index];
            px[v_index] = py[y_index];
        }
    }
}
template <class Base>
void atomic_vector<Base>::reverse_add(
    size_t                                           m,
    size_t                                           q,
    const CppAD::vector< CppAD::AD<Base> >&          atx,
    const CppAD::vector< CppAD::AD<Base> >&          aty,
    CppAD::vector< CppAD::AD<Base> >&                apx,
    const CppAD::vector< CppAD::AD<Base> >&          apy)
{
    //
    // just copying values does not add any operators to the tape.
    for(size_t k = 0; k < q; ++k)
    {   for(size_t i = 0; i < m; ++i)
        {   size_t u_index  =       i * q + k;
            size_t v_index  = (m + i) * q + k;
            size_t y_index  =       i * q + k;
            // y_i^k = u_i^k + v_i^k
            apx[u_index] = apy[y_index];
            apx[v_index] = apy[y_index];
        }
    }
}
} // END_CPPAD_NAMESPACE

Input File: include/cppad/example/atomic_four/vector/add_op.hpp