pow_op.hpp

Go to the documentation of this file.

# ifndef CPPAD_LOCAL_POW_OP_HPP
# define CPPAD_LOCAL_POW_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 pow_op.hpp
Forward and reverse mode calculations for z = pow(x, y).
*/

// --------------------------- Powvv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = PowvvOp.

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_pow_op
*/

template <class Base>
inline void forward_powvv_op(
     size_t        p           ,
     size_t        q           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // convert from final result to first result
     i_z -= 2; // 2 = NumRes(PowvvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( p <= q );
     CPPAD_ASSERT_UNKNOWN( std::numeric_limits<addr_t>::max() >= i_z );

     // z_0 = log(x)
     forward_log_op(p, q, i_z, arg[0], cap_order, taylor);

     // z_1 = z_0 * y
     addr_t adr[2];
     adr[0] = addr_t( i_z );
     adr[1] = arg[1];
     forward_mulvv_op(p, q, i_z+1, adr, parameter, cap_order, taylor);

     // z_2 = exp(z_1)
     // final result for zero order case is exactly the same as for Base
     if( p == 0 )
     {    // Taylor coefficients corresponding to arguments and result
          Base* x   = taylor + arg[0]  * cap_order;
          Base* y   = taylor + arg[1]  * cap_order;
          Base* z_2 = taylor + (i_z+2) * cap_order;

          z_2[0] = pow(x[0], y[0]);
          p++;
     }
     if( p <= q )
          forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor);
}
/*!
Multiple directions forward mode Taylor coefficients for op = PowvvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op_dir
*/

template <class Base>
inline void forward_powvv_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      )
{
     // convert from final result to first result
     i_z -= 2; // 2 = NumRes(PowvvOp) - 1

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( 0 < q );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( std::numeric_limits<addr_t>::max() >= i_z );

     // z_0 = log(x)
     forward_log_op_dir(q, r, i_z, arg[0], cap_order, taylor);

     // z_1 = y * z_0
     addr_t adr[2];
     adr[0] = addr_t( i_z );
     adr[1] = arg[1];
     forward_mulvv_op_dir(q, r, i_z+1, adr, parameter, cap_order, taylor);

     // z_2 = exp(z_1)
     forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor);
}
/*!
Compute zero order forward mode Taylor coefficients for result of op = PowvvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op_0
*/

template <class Base>
inline void forward_powvv_op_0(
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // convert from final result to first result
     i_z -= 2; // NumRes(PowvvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 );

     // Taylor coefficients corresponding to arguments and result
     Base* x   = taylor + arg[0] * cap_order;
     Base* y   = taylor + arg[1] * cap_order;
     Base* z_0 = taylor + i_z    * cap_order;
     Base* z_1 = z_0    +          cap_order;
     Base* z_2 = z_1    +          cap_order;

     z_0[0] = log( x[0] );
     z_1[0] = z_0[0] * y[0];
     z_2[0] = pow(x[0], y[0]);

}

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

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op
*/

template <class Base>
inline void reverse_powvv_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     )
{
     // convert from final result to first result
     i_z -= 2; // NumRes(PowvvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );
     CPPAD_ASSERT_UNKNOWN( std::numeric_limits<addr_t>::max() >= i_z );

     // z_2 = exp(z_1)
     reverse_exp_op(
          d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial
     );

     // z_1 = z_0 * y
     addr_t adr[2];
     adr[0] = addr_t( i_z );
     adr[1] = arg[1];
     reverse_mulvv_op(
     d, i_z+1, adr, parameter, cap_order, taylor, nc_partial, partial
     );

     // z_0 = log(x)
     reverse_log_op(
          d, i_z, arg[0], cap_order, taylor, nc_partial, partial
     );
}

// --------------------------- Powpv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = PowpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op
*/

template <class Base>
inline void forward_powpv_op(
     size_t        p           ,
     size_t        q           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // convert from final result to first result
     i_z -= 2; // 2 = NumRes(PowpvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowpvOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( p <= q );

     // Taylor coefficients corresponding to arguments and result
     Base* z_0 = taylor + i_z    * cap_order;

     // z_0 = log(x)
     Base x    = parameter[ arg[0] ];
     size_t d;
     for(d = p; d <= q; d++)
     {    if( d == 0 )
               z_0[d] = log(x);
          else z_0[d] = Base(0.0);
     }

     // 2DO: remove requirement that i_z * cap_order <= max addr_t value
     CPPAD_ASSERT_KNOWN(
          std::numeric_limits<addr_t>::max() >= i_z * cap_order,
          "cppad_tape_addr_type maximum value has been exceeded\n"
          "This is due to a kludge in the pow operation and should be fixed."
     );

     // z_1 = z_0 * y
     addr_t adr[2];
     // offset of z_i in taylor (as if it were a parameter); i.e., log(x)
     adr[0] = addr_t( i_z * cap_order );
     // offset of y in taylor (as a variable)
     adr[1] = arg[1];

     // Trick: use taylor both for the parameter vector and variable values
     forward_mulpv_op(p, q, i_z+1, adr, taylor, cap_order, taylor);

     // z_2 = exp(z_1)
     // zero order case exactly same as Base type operation
     if( p == 0 )
     {    Base* y   = taylor + arg[1]  * cap_order;
          Base* z_2 = taylor + (i_z+2) * cap_order;
          z_2[0] = pow(x, y[0]);
          p++;
     }
     if( p <= q )
          forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor);
}
/*!
Multiple directions forward mode Taylor coefficients for op = PowpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op_dir
*/

template <class Base>
inline void forward_powpv_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      )
{
     // convert from final result to first result
     i_z -= 2; // 2 = NumRes(PowpvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowpvOp) == 3 );
     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* z_0 = taylor + i_z * num_taylor_per_var;

     // z_0 = log(x)
     size_t m  = (q-1) * r + 1;
     for(size_t ell = 0; ell < r; ell++)
          z_0[m+ell] = Base(0.0);

     // 2DO: remove requirement i_z * num_taylor_per_var <= max addr_t value
     CPPAD_ASSERT_KNOWN(
          std::numeric_limits<addr_t>::max() >= i_z * num_taylor_per_var,
          "cppad_tape_addr_type maximum value has been exceeded\n"
          "This is due to a kludge in the pow operation and should be fixed."
     );

     // z_1 = z_0 * y
     addr_t adr[2];
     // offset of z_0 in taylor (as if it were a parameter); i.e., log(x)
     adr[0] = addr_t( i_z * num_taylor_per_var );
     // ofset of y in taylor (as a variable)
     adr[1] = arg[1];

     // Trick: use taylor both for the parameter vector and variable values
     forward_mulpv_op_dir(q, r, i_z+1, adr, taylor, cap_order, taylor);

     // z_2 = exp(z_1)
     forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor);
}
/*!
Compute zero order forward mode Taylor coefficient for result of op = PowpvOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op_0
*/

template <class Base>
inline void forward_powpv_op_0(
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // convert from final result to first result
     i_z -= 2; // NumRes(PowpvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowpvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowpvOp) == 3 );

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

     // Taylor coefficients corresponding to arguments and result
     Base* y   = taylor + arg[1] * cap_order;
     Base* z_0 = taylor + i_z    * cap_order;
     Base* z_1 = z_0    +          cap_order;
     Base* z_2 = z_1    +          cap_order;

     // z_0 = log(x)
     z_0[0] = log(x);

     // z_1 = z_0 * y
     z_1[0] = z_0[0] * y[0];

     // z_2 = exp(z_1)
     // zero order case exactly same as Base type operation
     z_2[0] = pow(x, y[0]);
}

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

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op
*/

template <class Base>
inline void reverse_powpv_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     )
{
     // convert from final result to first result
     i_z -= 2; // NumRes(PowpvOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // z_2 = exp(z_1)
     reverse_exp_op(
          d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial
     );

     // 2DO: remove requirement that i_z * cap_order <= max addr_t value
     CPPAD_ASSERT_KNOWN(
          std::numeric_limits<addr_t>::max() >= i_z * cap_order,
          "cppad_tape_addr_type maximum value has been exceeded\n"
          "This is due to a kludge in the pow operation and should be fixed."
     );

     // z_1 = z_0 * y
     addr_t adr[2];
     adr[0] = addr_t( i_z * cap_order ); // offset of z_0[0] in taylor
     adr[1] = arg[1];                    // index of y in taylor and partial
     // use taylor both for parameter and variable values
     reverse_mulpv_op(
          d, i_z+1, adr, taylor, cap_order, taylor, nc_partial, partial
     );

     // z_0 = log(x)
     // x is a parameter
}

// --------------------------- Powvp -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = PowvpOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op
*/

template <class Base>
inline void forward_powvp_op(
     size_t        p           ,
     size_t        q           ,
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // convert from final result to first result
     i_z -= 2; // 2 = NumRes(PowvpOp) - 1

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( p <= q );
     CPPAD_ASSERT_UNKNOWN( std::numeric_limits<addr_t>::max() >= i_z );

     // z_0 = log(x)
     forward_log_op(p, q, i_z, arg[0], cap_order, taylor);

     // z_1 = y * z_0
     addr_t adr[2];
     adr[0] = arg[1];
     adr[1] = addr_t( i_z );
     forward_mulpv_op(p, q, i_z+1, adr, parameter, cap_order, taylor);

     // z_2 = exp(z_1)
     // zero order case exactly same as Base type operation
     if( p == 0 )
     {    Base* z_2 = taylor + (i_z+2) * cap_order;
          Base* x   = taylor + arg[0] * cap_order;
          Base  y   = parameter[ arg[1] ];
          z_2[0]  = pow(x[0], y);
          p++;
     }
     if( p <= q )
          forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor);
}
/*!
Multiple directions forward mode Taylor coefficients for op = PowvpOp.

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op_dir
*/

template <class Base>
inline void forward_powvp_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      )
{
     // convert from final result to first result
     i_z -= 2; // 2 = NumRes(PowvpOp) - 1

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( 0 < q );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( std::numeric_limits<addr_t>::max() >= i_z );

     // z_0 = log(x)
     forward_log_op_dir(q, r, i_z, arg[0], cap_order, taylor);

     // z_1 = y * z_0
     addr_t adr[2];
     adr[0] = arg[1];
     adr[1] = addr_t( i_z );
     forward_mulpv_op_dir(q, r, i_z+1, adr, parameter, cap_order, taylor);

     // z_2 = exp(z_1)
     forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor);
}

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

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op_0
*/

template <class Base>
inline void forward_powvp_op_0(
     size_t        i_z         ,
     const addr_t* arg         ,
     const Base*   parameter   ,
     size_t        cap_order   ,
     Base*         taylor      )
{
     // convert from final result to first result
     i_z -= 2; // NumRes(PowvpOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 );

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

     // Taylor coefficients corresponding to arguments and result
     Base* x   = taylor + arg[0] * cap_order;
     Base* z_0 = taylor + i_z    * cap_order;
     Base* z_1 = z_0    +          cap_order;
     Base* z_2 = z_1    +          cap_order;

     // z_0 = log(x)
     z_0[0] = log(x[0]);

     // z_1 = z_0 * y
     z_1[0] = z_0[0] * y;

     // z_2 = exp(z_1)
     // zero order case exactly same as Base type operation
     z_2[0] = pow(x[0], y);
}

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

The C++ source code corresponding to this operation is
\verbatim
     z = pow(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_pow_op
*/

template <class Base>
inline void reverse_powvp_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     )
{
     // convert from final result to first result
     i_z -= 2; // NumRes(PowvpOp) - 1;

     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 );
     CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );
     CPPAD_ASSERT_UNKNOWN( std::numeric_limits<addr_t>::max() >= i_z );

     // z_2 = exp(z_1)
     reverse_exp_op(
          d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial
     );

     // z_1 = y * z_0
     addr_t adr[2];
     adr[0] = arg[1];
     adr[1] = addr_t( i_z );
     reverse_mulpv_op(
     d, i_z+1, adr, parameter, cap_order, taylor, nc_partial, partial
     );

     // z_0 = log(x)
     reverse_log_op(
          d, i_z, arg[0], cap_order, taylor, nc_partial, partial
     );
}

} } // END_CPPAD_LOCAL_NAMESPACE
# endif