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atomic_four_mat_mul_reverse.hpp |
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@(@\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 Matrix Multiply Reverse Mode: Example Implementation
Purpose
The reverse routine overrides the virtual functions
used by the atomic_four base; see
reverse
.
Theory
See mat_mul reverse
theory.
Source
# include <cppad/example/atomic_four/mat_mul/mat_mul.hpp>
namespace CppAD { // BEGIN_CPPAD_NAMESPACE
//
// reverse override for Base matrix multiply
template <class Base>
bool atomic_mat_mul<Base>::reverse(
size_t call_id ,
const CppAD::vector<bool>& select_y ,
size_t order_up ,
const CppAD::vector<Base>& taylor_x ,
const CppAD::vector<Base>& taylor_y ,
CppAD::vector<Base>& partial_x ,
const CppAD::vector<Base>& partial_y )
{
// q
size_t q = order_up + 1;
//
// n_left, n_middle, n_right
size_t n_left, n_middle, n_right;
get(call_id, n_left, n_middle, n_right);
# ifndef NDEBUG
// n, m
size_t n = taylor_x.size();
size_t m = taylor_y.size();
//
// check sizes
assert( n == n_middle * ( n_left + n_right ) * q );
assert( m == n_left * n_right * q );
assert( n == partial_x.size() );
assert( m == partial_y.size() );
# endif
//
// offset
size_t x_offset = n_left * n_middle;
//
// u, v, u_offset
// note that resize only re-alocates when capacity is not large enough
CppAD::vector<Base> u;
CppAD::vector<Base> v;
size_t u_offset;
//
// partial_x
for(size_t i = 0; i < partial_x.size(); ++i)
partial_x[i] = Base(0);
//
// k
size_t k = q;
while(k > 0)
{ --k;
//
// for ell = 0, ..., k :
// bar{A}^ell += bar{C}^k [ B^{k-ell} ]^T
// bar{B}^{k-ell} += [ A^ell ]^T \bar{C}^k
for(size_t ell = 0; ell < q; ++ell)
{ //
// u = [ \bar{C}^k, B^{k-ell}^T ]
u.resize(0);
u.resize( n_left * n_right + n_right * n_middle );
u_offset = n_left * n_right;
for(size_t i = 0; i < n_left * n_right; ++i)
u[i] = partial_y[ i * q + k ];
for(size_t i = 0; i < n_middle; ++i)
{ for(size_t j = 0; j < n_right; ++j)
{ size_t ij = i * n_right + j;
size_t ji = j * n_middle + i;
u[u_offset + ji] =
taylor_x[(x_offset + ij) * q + (k - ell) ];
}
}
//
// v = \bar{C} * [ B^{k-ell} ]^T
v.resize(0);
v.resize( n_left * n_middle );
base_mat_mul(n_left, n_right, n_middle, u, v);
//
// \bar{A}^ell += v
for(size_t i = 0; i < n_left * n_middle; ++i)
partial_x[i * q + ell] += v[i];
//
// u = [ A^ell^T , \bar{C}^k ]
u.resize(0);
u.resize( n_middle * n_left + n_left * n_right );
u_offset = n_middle * n_left;
for(size_t i = 0; i < n_left; ++i)
{ for(size_t j = 0; j < n_middle; ++j)
{ size_t ij = i * n_middle + j;
size_t ji = j * n_left + i;
u[ji] = taylor_x[ij * q + ell];
}
}
for(size_t i = 0; i < n_left * n_right; ++i)
u[u_offset + i] = partial_y[ i * q + k ];
//
// v = [ A^ell ]^T * \bar{C}^k
v.resize(0);
v.resize( n_middle * n_right );
base_mat_mul(n_middle, n_left, n_right, u, v);
//
// \bar{B}^{k-\ell} += v
for(size_t i = 0; i < n_middle * n_right; ++i)
partial_x[ (x_offset + i) * q + (k - ell) ] += v[i];
}
}
return true;
}
//
// reverse override for AD<Base> matrix multiply
template <class Base>
bool atomic_mat_mul<Base>::reverse(
size_t call_id ,
const CppAD::vector<bool>& select_y ,
size_t order_up ,
const CppAD::vector< AD<Base> >& ataylor_x ,
const CppAD::vector< AD<Base> >& ataylor_y ,
CppAD::vector< AD<Base> >& apartial_x ,
const CppAD::vector< AD<Base> >& apartial_y )
{
// q
size_t q = order_up + 1;
//
// n_left, n_middle, n_right
size_t n_left, n_middle, n_right;
get(call_id, n_left, n_middle, n_right);
# ifndef NDEBUG
// n, m
size_t n = ataylor_x.size();
size_t m = ataylor_y.size();
//
// check sizes
assert( n == n_middle * ( n_left + n_right ) * q );
assert( m == n_left * n_right * q );
assert( n == apartial_x.size() );
assert( m == apartial_y.size() );
# endif
//
// offset
size_t x_offset = n_left * n_middle;
//
// u, v, u_offset
// note that resize only re-alocates when capacity is not large enough
CppAD::vector< AD<Base> > u;
CppAD::vector< AD<Base> > v;
size_t u_offset;
size_t i_call;
//
// apartial_x
for(size_t i = 0; i < apartial_x.size(); ++i)
apartial_x[i] = AD<Base> (0);
//
// k
size_t k = q;
while(k > 0)
{ --k;
//
// for ell = 0, ..., k :
// bar{A}^ell += bar{C}^k [ B^{k-ell} ]^T
// bar{B}^{k-ell} += [ A^ell ]^T \bar{C}^k
for(size_t ell = 0; ell < q; ++ell)
{ //
// u = [ \bar{C}^k, B^{k-ell}^T ]
u.resize(0);
u.resize( n_left * n_right + n_right * n_middle );
u_offset = n_left * n_right;
for(size_t i = 0; i < n_left * n_right; ++i)
u[i] = apartial_y[ i * q + k ];
for(size_t i = 0; i < n_middle; ++i)
{ for(size_t j = 0; j < n_right; ++j)
{ size_t ij = i * n_right + j;
size_t ji = j * n_middle + i;
u[u_offset + ji] =
ataylor_x[(x_offset + ij) * q + (k - ell) ];
}
}
//
// v = \bar{C} * [ B^{k-ell} ]^T
v.resize(0);
v.resize( n_left * n_middle );
i_call = set(n_left, n_right, n_middle);
(*this)(i_call, u, v);
//
// \bar{A}^ell += v
for(size_t i = 0; i < n_left * n_middle; ++i)
apartial_x[i * q + ell] += v[i];
//
// u = [ A^ell^T , \bar{C}^k ]
u.resize(0);
u.resize( n_middle * n_left + n_left * n_right );
u_offset = n_middle * n_left;
for(size_t i = 0; i < n_left; ++i)
{ for(size_t j = 0; j < n_middle; ++j)
{ size_t ij = i * n_middle + j;
size_t ji = j * n_left + i;
u[ji] = ataylor_x[ij * q + ell];
}
}
for(size_t i = 0; i < n_left * n_right; ++i)
u[u_offset + i] = apartial_y[ i * q + k ];
//
// v = [ A^ell ]^T * \bar{C}^k
v.resize(0);
v.resize( n_middle * n_right );
i_call = set(n_middle, n_left, n_right);
(*this)(i_call, u, v);
//
// \bar{B}^{k-\ell} += v
for(size_t i = 0; i < n_middle * n_right; ++i)
apartial_x[ (x_offset + i) * q + (k - ell) ] += v[i];
}
}
return true;
}
} // END_CPPAD_NAMESPACE
Input File: include/cppad/example/atomic_four/mat_mul/reverse.hpp