mul_op.hpp

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# ifndef CPPAD_LOCAL_MUL_OP_HPP
# define CPPAD_LOCAL_MUL_OP_HPP

/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE
/*!
\file mul_op.hpp
Forward and reverse mode calculations for z = x * y.
*/

// --------------------------- Mulvv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails CppAD::local::forward_binary_op
*/

template <class Base>
inline void forward_mulvv_op(
     size_t        p           ,
     size_t        q           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( p <= q );

     // Taylor coefficients corresponding to arguments and result
     Base* x = taylor + arg[0] * cap_order;
     Base* y = taylor + arg[1] * cap_order;
     Base* z = taylor + i_z    * cap_order;

     size_t k;
     for(size_t d = p; d <= q; d++)
     {    z[d] = Base(0.0);
          for(k = 0; k <= d; k++)
               z[d] += x[d-k] * y[k];
     }
}
/*!
Multiple directions forward mode Taylor coefficients for op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails CppAD::local::forward_binary_op_dir
*/

template <class Base>
inline void forward_mulvv_op_dir(
     size_t        q           ,
     size_t        r           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( 0 < q );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );

     // Taylor coefficients corresponding to arguments and result
     size_t num_taylor_per_var = (cap_order-1) * r + 1;
     Base* x = taylor + arg[0] * num_taylor_per_var;
     Base* y = taylor + arg[1] * num_taylor_per_var;
     Base* z = taylor +    i_z * num_taylor_per_var;

     size_t k, ell, m;
     for(ell = 0; ell < r; ell++)
     {    m = (q-1)*r + ell + 1;
          z[m] = x[0] * y[m] + x[m] * y[0];
          for(k = 1; k < q; k++)
               z[m] += x[(q-k-1)*r + ell + 1] * y[(k-1)*r + ell + 1];
     }
}

/*!
Compute zero order forward mode Taylor coefficients for result of op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails CppAD::local::forward_binary_op_0
*/

template <class Base>
inline void forward_mulvv_op_0(
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );

     // Taylor coefficients corresponding to arguments and result
     Base* x = taylor + arg[0] * cap_order;
     Base* y = taylor + arg[1] * cap_order;
     Base* z = taylor + i_z    * cap_order;

     z[0] = x[0] * y[0];
}

/*!
Compute reverse mode partial derivatives for result of op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails CppAD::local::reverse_binary_op
*/

template <class Base>
inline void reverse_mulvv_op(
     size_t        d           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     const Base*   taylor      ,
     size_t        nc_partial  ,
     Base*         partial     )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // Arguments
     const Base* x  = taylor + arg[0] * cap_order;
     const Base* y  = taylor + arg[1] * cap_order;

     // Partial derivatives corresponding to arguments and result
     Base* px = partial + arg[0] * nc_partial;
     Base* py = partial + arg[1] * nc_partial;
     Base* pz = partial + i_z    * nc_partial;


     // number of indices to access
     size_t j = d + 1;
     size_t k;
     while(j)
     {    --j;
          for(k = 0; k <= j; k++)
          {
               px[j-k] += azmul(pz[j], y[k]);
               py[k]   += azmul(pz[j], x[j-k]);
          }
     }
}
// --------------------------- Mulpv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails CppAD::local::forward_binary_op
*/

template <class Base>
inline void forward_mulpv_op(
     size_t        p           ,
     size_t        q           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( p <= q );

     // Taylor coefficients corresponding to arguments and result
     Base* y = taylor + arg[1] * cap_order;
     Base* z = taylor + i_z    * cap_order;

     // Paraemter value
     Base x = parameter[ arg[0] ];

     for(size_t d = p; d <= q; d++)
          z[d] = x * y[d];
}
/*!
Multiple directions forward mode Taylor coefficients for op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails CppAD::local::forward_binary_op_dir
*/

template <class Base>
inline void forward_mulpv_op_dir(
     size_t        q           ,
     size_t        r           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( 0 < q );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );

     // Taylor coefficients corresponding to arguments and result
     size_t num_taylor_per_var = (cap_order-1) * r + 1;
     size_t m                  = (q-1) * r + 1;
     Base* y = taylor + arg[1] * num_taylor_per_var + m;
     Base* z = taylor + i_z    * num_taylor_per_var + m;

     // Paraemter value
     Base x = parameter[ arg[0] ];

     for(size_t ell = 0; ell < r; ell++)
          z[ell] = x * y[ell];
}
/*!
Compute zero order forward mode Taylor coefficient for result of op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails CppAD::local::forward_binary_op_0
*/

template <class Base>
inline void forward_mulpv_op_0(
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );

     // Paraemter value
     Base x = parameter[ arg[0] ];

     // Taylor coefficients corresponding to arguments and result
     Base* y = taylor + arg[1] * cap_order;
     Base* z = taylor + i_z    * cap_order;

     z[0] = x * y[0];
}

/*!
Compute reverse mode partial derivative for result of op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails CppAD::local::reverse_binary_op
*/

template <class Base>
inline void reverse_mulpv_op(
     size_t        d           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     const Base*   taylor      ,
     size_t        nc_partial  ,
     Base*         partial     )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // Arguments
     Base x  = parameter[ arg[0] ];

     // Partial derivatives corresponding to arguments and result
     Base* py = partial + arg[1] * nc_partial;
     Base* pz = partial + i_z    * nc_partial;

     // number of indices to access
     size_t j = d + 1;
     while(j)
     {    --j;
          py[j] += azmul(pz[j], x);
     }
}


} } // END_CPPAD_LOCAL_NAMESPACE
# endif