div_op.hpp

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# ifndef CPPAD_LOCAL_DIV_OP_HPP
# define CPPAD_LOCAL_DIV_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 div_op.hpp
Forward and reverse mode calculations for z = x / y.
*/

// --------------------------- Divvv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = DivvvOp.

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_divvv_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(DivvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 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;


     // Using CondExp, it can make sense to divide by zero,
     // so do not make it an error.
     size_t k;
     for(size_t d = p; d <= q; d++)
     {    z[d] = x[d];
          for(k = 1; k <= d; k++)
               z[d] -= z[d-k] * y[k];
          z[d] /= y[0];
     }
}
/*!
Multiple directions forward mode Taylor coefficients for op = DivvvOp.

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_divvv_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(DivvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 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;


     // Using CondExp, it can make sense to divide by zero,
     // so do not make it an error.
     size_t m = (q-1) * r + 1;
     for(size_t ell = 0; ell < r; ell++)
     {    z[m+ell] = x[m+ell] - z[0] * y[m+ell];
          for(size_t k = 1; k < q; k++)
               z[m+ell] -= z[(q-k-1)*r+1+ell] * y[(k-1)*r+1+ell];
          z[m+ell] /= y[0];
     }
}


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

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_divvv_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(DivvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 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 = DivvvOp.

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_divvv_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(DivvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // Arguments
     const Base* y  = taylor + arg[1] * cap_order;
     const Base* z  = taylor + i_z    * 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;

     // Using CondExp, it can make sense to divide by zero
     // so do not make it an error.
     Base inv_y0 = Base(1.0) / y[0];

     size_t k;
     // number of indices to access
     size_t j = d + 1;
     while(j)
     {    --j;
          // scale partial w.r.t. z[j]
          pz[j] = azmul(pz[j], inv_y0);

          px[j] += pz[j];
          for(k = 1; k <= j; k++)
          {    pz[j-k] -= azmul(pz[j], y[k]  );
               py[k]   -= azmul(pz[j], z[j-k]);
          }
          py[0] -= azmul(pz[j], z[j]);
     }
}

// --------------------------- Divpv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = DivpvOp.

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_divpv_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(DivpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivpvOp) == 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] ];

     // Using CondExp, it can make sense to divide by zero,
     // so do not make it an error.
     size_t k;
     if( p == 0 )
     {    z[0] = x / y[0];
          p++;
     }
     for(size_t d = p; d <= q; d++)
     {    z[d] = Base(0.0);
          for(k = 1; k <= d; k++)
               z[d] -= z[d-k] * y[k];
          z[d] /= y[0];
     }
}
/*!
Multiple directions forward mode Taylor coefficients for op = DivpvOp.

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_divpv_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(DivpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivpvOp) == 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* y = taylor + arg[1] * num_taylor_per_var;
     Base* z = taylor + i_z    * num_taylor_per_var;

     // Using CondExp, it can make sense to divide by zero,
     // so do not make it an error.
     size_t m = (q-1) * r + 1;
     for(size_t ell = 0; ell < r; ell++)
     {    z[m+ell] = - z[0] * y[m+ell];
          for(size_t k = 1; k < q; k++)
               z[m+ell] -= z[(q-k-1)*r+1+ell] * y[(k-1)*r+1+ell];
          z[m+ell] /= y[0];
     }
}

/*!
Compute zero order forward mode Taylor coefficient for result of op = DivpvOp.

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_divpv_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(DivpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivpvOp) == 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 = DivpvOp.

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_divpv_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(DivvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // Arguments
     const Base* y = taylor + arg[1] * cap_order;
     const Base* z = taylor + i_z    * cap_order;

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

     // Using CondExp, it can make sense to divide by zero so do not
     // make it an error.
     Base inv_y0 = Base(1.0) / y[0];

     size_t k;
     // number of indices to access
     size_t j = d + 1;
     while(j)
     {    --j;
          // scale partial w.r.t z[j]
          pz[j] = azmul(pz[j], inv_y0);

          for(k = 1; k <= j; k++)
          {    pz[j-k] -= azmul(pz[j], y[k]  );
               py[k]   -= azmul(pz[j], z[j-k] );
          }
          py[0] -= azmul(pz[j], z[j]);
     }
}


// --------------------------- Divvp -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = DivvvOp.

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 variable and y is a parameter.

\copydetails CppAD::local::forward_binary_op
*/

template <class Base>
inline void forward_divvp_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(DivvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 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* z = taylor + i_z    * cap_order;

     // Parameter value
     Base y = parameter[ arg[1] ];

     // Using CondExp and multiple levels of AD, it can make sense
     // to divide by zero so do not make it an error.
     for(size_t d = p; d <= q; d++)
          z[d] = x[d] / y;
}
/*!
Multiple direction forward mode Taylor coefficients for op = DivvvOp.

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 variable and y is a parameter.

\copydetails CppAD::local::forward_binary_op_dir
*/

template <class Base>
inline void forward_divvp_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(DivvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( 0 < q  );

     // 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* z = taylor +    i_z * num_taylor_per_var;

     // Parameter value
     Base y = parameter[ arg[1] ];

     // Using CondExp and multiple levels of AD, it can make sense
     // to divide by zero so do not make it an error.
     size_t m = (q-1)*r + 1;
     for(size_t ell = 0; ell < r; ell++)
          z[m + ell] = x[m + ell] / y;
}


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

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 variable and y is a parameter.

\copydetails CppAD::local::forward_binary_op_0
*/

template <class Base>
inline void forward_divvp_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(DivvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 );

     // Parameter value
     Base y = parameter[ arg[1] ];

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

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

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

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 variable and y is a parameter.

\copydetails CppAD::local::reverse_binary_op
*/

template <class Base>
inline void reverse_divvp_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(DivvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // Argument values
     Base  y = parameter[ arg[1] ];

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

     // Using CondExp, it can make sense to divide by zero
     // so do not make it an error.
     Base inv_y = Base(1.0) / y;

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

} } // END_CPPAD_LOCAL_NAMESPACE
# endif