\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

atomic_four_vector_sub_op.hpp

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Atomic Vector Subtract Operator: Example Implementation

Forward Mode

see theory for forward mode Subtraction .

Reverse Mode

see theory for reverse mode Subtraction .

Example

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

Source

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

namespace CppAD { // BEGIN_CPPAD_NAMESPACE
// --------------------------------------------------------------------------
// forward_sub
template <class Base>
void atomic_vector<Base>::forward_sub(
    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_sub(
    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)(sub_enum, ax, ay); // atomic vector sub
        // y^k = ay
        copy_vec_to_mat(m, q, k, ay.begin(), aty.begin());
    }
}
// --------------------------------------------------------------------------
// reverse_sub
template <class Base>
void atomic_vector<Base>::reverse_sub(
    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_sub(
    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)
{
# ifndef NDEBUG
    size_t n = 2 * m;
    assert( atx.size() == n * q );
    assert( aty.size() == m * q );
    assert( apx.size() == n * q );
    assert( apy.size() == m * q );
# endif
    //
    // apu, apv
    ad_iterator apu = apx.begin();
    ad_iterator apv = apu + ad_difference_type(m * q);
    //
    // ax
    ad_vector ax(m);
    ad_iterator au = ax.begin();
    //
    // ay
    ad_vector ay(m);
    //
    for(size_t k = 0; k < q; ++k)
    {   // au = apy^k
        copy_mat_to_vec(m, q, k, apy.begin(), au);
        // apu^k = au
        copy_vec_to_mat(m, q, k, au, apu);
        // ay = - au
        (*this)(neg_enum, ax, ay); // atomic vector neg
        // apv^k = ay
        copy_vec_to_mat(m, q, k, ay.begin(), apv);
    }
}
} // END_CPPAD_NAMESPACE