\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
atomic_four_vector_div_op.hpp¶
View page sourceAtomic Vector Divide Operator: Example Implementation¶
Forward Mode¶
see theory for forward mode Division .
Reverse Mode¶
see theory for reverse mode Division .
Example¶
The file atomic_four_vector_div.cpp contains an example and test for this operator.
Source¶
# include <cppad/example/atomic_four/vector/vector.hpp>
namespace CppAD { // BEGIN_CPPAD_NAMESPACE
// ---------------------------------------------------------------------------
// forward_div
template <class Base>
void atomic_vector<Base>::forward_div(
size_t m,
size_t p,
size_t q,
const CppAD::vector<Base>& tx,
CppAD::vector<Base>& ty)
{
for(size_t i = 0; i < m; ++i)
{ for(size_t k = p; k < q; ++k)
{ size_t y_index = i * q + k;
size_t u_index = i * q + k;
// y^k = u^k
ty[y_index] = tx[u_index];
for(size_t d = 1; d <= k; d++)
{ size_t y_other = i * q + (k-d);
size_t v_index = (i + m) * q + d;
// y^k -= y^{k-d} * v^d
ty[y_index] -= ty[y_other] * tx[v_index];
}
size_t v0_index = (i + m) * q + 0;
// y^k /= v^0
ty[y_index] /= tx[v0_index];
}
}
}
template <class Base>
void atomic_vector<Base>::forward_div(
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_div
ad_vector ax_div(n);
ad_iterator au_div = ax_div.begin();
ad_iterator av_div = ax_div.begin() + ad_difference_type(m);
//
// ax_mul
ad_vector ax_mul(n);
ad_iterator au_mul = ax_mul.begin();
ad_iterator av_mul = ax_mul.begin() + ad_difference_type(m);
//
// ax_sub
ad_vector ax_sub(n);
ad_iterator au_sub = ax_sub.begin();
ad_iterator av_sub = ax_sub.begin() + ad_difference_type(m);
//
// ay
ad_vector ay(m);
//
for(size_t k = p; k < q; ++k)
{ // u_sub = u^k
copy_mat_to_vec(m, q, k, atu, au_sub);
for(size_t d = 1; d <= k; d++)
{ // u_mul = y^{k-d}
copy_mat_to_vec(m, q, k-d, aty.begin(), au_mul);
// v_mul = v^d
copy_mat_to_vec(m, q, d, atv, av_mul);
// ay = u_mul * v_mul
(*this)(mul_enum, ax_mul, ay); // atomic vector multiply
// v_sub = ay
for(size_t i = 0; i < m; ++i)
av_sub[i] = ay[i];
// ay = u_sub - v_sub
(*this)(sub_enum, ax_sub, ay); // atomic vector subtract
// u_sub = ay
for(size_t i = 0; i < m; ++i)
au_sub[i] = ay[i];
}
// u_div = u_sub
for(size_t i = 0; i < m; ++i)
au_div[i] = *(au_sub + ad_difference_type(i));
// v_div = v^0
copy_mat_to_vec(m, q, 0, atv, av_div);
// ay = u_div / v_div
(*this)(div_enum, ax_div, ay); // atomic vector divide
// y^k = ay
copy_vec_to_mat(m, q, k, ay.begin(), aty.begin());
}
}
// ---------------------------------------------------------------------------
// reverse_div
template <class Base>
void atomic_vector<Base>::reverse_div(
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)
{
# ifndef NDEBUG
size_t n = 2 * m;
assert( tx.size() == n * q );
assert( ty.size() == m * q );
assert( px.size() == n * q );
assert( py.size() == m * q );
# endif
//
// py_copy
CppAD::vector<Base> py_copy( py );
//
// pv
for(size_t i = 0; i < m; ++i)
{ for(size_t k = 0; k < q; ++k)
{ size_t v_index = (i + m) * q + k;
px[v_index] = 0.0;
}
}
// px
for(size_t i = 0; i < m; ++i)
{ size_t v0_index = (i + m) * q + 0;
//
// k
size_t k = q;
while(k)
{ --k;
//
// y_index
size_t y_index = i * q + k;
//
// py_scaled
double py_scaled = py_copy[y_index] / tx[v0_index];
//
for(size_t d = 1; d <= k; d++)
{ size_t y_other = i * q + (k-d);
size_t v_index = (i + m) * q + d;
//
py_copy[y_other] -= py_scaled * tx[v_index];
px[v_index] -= py_scaled * ty[y_other];
}
size_t u_index = i * q + k;
px[u_index] = py_scaled;
px[v0_index] -= py_scaled * ty[y_index];
}
}
}
template <class Base>
void atomic_vector<Base>::reverse_div(
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)
{ 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 );
//
// atu, atv, apu, apv
ad_const_iterator atu = atx.begin();
ad_const_iterator atv = atu + ad_difference_type(m * q);
ad_iterator apu = apx.begin();
ad_iterator apv = apu + ad_difference_type(m * q);
//
// ax_sub
ad_vector ax_sub(n);
ad_iterator au_sub = ax_sub.begin();
ad_iterator av_sub = ax_sub.begin() + ad_difference_type(m);
//
// ax_mul
ad_vector ax_mul(n);
ad_iterator au_mul = ax_mul.begin();
ad_iterator av_mul = ax_mul.begin() + ad_difference_type(m);
//
// ax_div
ad_vector ax_div(n);
ad_iterator au_div = ax_div.begin();
ad_iterator av_div = ax_div.begin() + ad_difference_type(m);
//
// ay, apy_scaled
ad_vector ay(m), apy_scaled(m);
//
// apy_copy
ad_vector apy_copy( apy );
//
// apv
for(size_t i = 0; i < m; ++i)
{ for(size_t k = 0; k < q; ++k)
{ size_t v_index = (i + m) * q + k;
apx[v_index] = 0.0;
}
}
//
// av_div = atv^0
copy_mat_to_vec(m, q, 0, atv, av_div);
//
// k
size_t k = q;
while(k)
{ --k;
//
// au_div = apy^k
copy_mat_to_vec(m, q, k, apy_copy.begin(), au_div);
//
// apy_scaled = au_div / av_dir
(*this)(div_enum, ax_div, apy_scaled);
//
// au_mul = apy_scaled
for(size_t i = 0; i < m; ++i)
au_mul[i] = apy_scaled[i];
//
for(size_t d = 1; d <= k; ++d)
{ //
// av_mul = atv^d
copy_mat_to_vec(m, q, d, atv, av_mul);
//
// ay = au_mul * av_mul
(*this)(mul_enum, ax_mul, ay);
//
// au_sub = apy^{k-d}
copy_mat_to_vec(m, q, k-d, apy_copy.begin(), au_sub);
//
// av_sub = ay
for(size_t i = 0; i < m; ++i)
av_sub[i] = ay[i];
//
// ay = au_sub - av_sub
(*this)(sub_enum, ax_sub, ay);
//
// apy^{k-d} = ay
copy_vec_to_mat(m, q, k-d, ay.begin(), apy_copy.begin());
//
// av_mul = aty^{k-d}
copy_mat_to_vec(m, q, k-d, aty.begin(), av_mul);
//
// ay = au_mul * av_mul
(*this)(mul_enum, ax_mul, ay);
//
// au_sub = apv^d
copy_mat_to_vec(m, q, d, apv, au_sub);
//
// av_sub = ay
for(size_t i = 0; i < m; ++i)
av_sub[i] = ay[i];
//
// ay = au_sub - av_sub
(*this)(sub_enum, ax_sub, ay);
//
// apv^d = ay
copy_vec_to_mat(m, q, d, ay.begin(), apv);
}
//
// apu^k = apy_scaled
copy_vec_to_mat(m, q, k, apy_scaled.begin(), apu);
//
// av_mul = aty^k
copy_mat_to_vec(m, q, k, aty.begin(), av_mul);
//
// ay = au_mul * av_mul
(*this)(mul_enum, ax_mul, ay);
//
// au_sub = apv^0
copy_mat_to_vec(m, q, 0, apv, au_sub);
//
// av_sub = ay
for(size_t i = 0; i < m; ++i)
av_sub[i] = ay[i];
//
// ay = au_sub - av_sub
(*this)(sub_enum, ax_sub, ay);
//
// apv^0 = ay
copy_vec_to_mat(m, q, 0, ay.begin(), apv);
}
}
} // END_CPPAD_NAMESPACE