expm1_op.hpp

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# ifndef CPPAD_LOCAL_EXPM1_OP_HPP
# define CPPAD_LOCAL_EXPM1_OP_HPP
# if CPPAD_USE_CPLUSPLUS_2011

/* --------------------------------------------------------------------------
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 expm1_op.hpp
Forward and reverse mode calculations for z = expm1(x).
*/


/*!
Forward mode Taylor coefficient for result of op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
     z = expm1(x)
\endverbatim

\copydetails CppAD::local::forward_unary1_op
*/
template <class Base>
inline void forward_expm1_op(
     size_t p           ,
     size_t q           ,
     size_t i_z         ,
     size_t i_x         ,
     size_t cap_order   ,
     Base*  taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( p <= q );

     // Taylor coefficients corresponding to argument and result
     Base* x = taylor + i_x * cap_order;
     Base* z = taylor + i_z * cap_order;

     size_t k;
     if( p == 0 )
     {    z[0] = expm1( x[0] );
          p++;
     }
     for(size_t j = p; j <= q; j++)
     {
          z[j] = x[1] * z[j-1];
          for(k = 2; k <= j; k++)
               z[j] += Base(double(k)) * x[k] * z[j-k];
          z[j] /= Base(double(j));
          z[j] += x[j];
     }
}


/*!
Multiple direction forward mode Taylor coefficient for op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
     z = expm1(x)
\endverbatim

\copydetails CppAD::local::forward_unary1_op_dir
*/
template <class Base>
inline void forward_expm1_op_dir(
     size_t q           ,
     size_t r           ,
     size_t i_z         ,
     size_t i_x         ,
     size_t cap_order   ,
     Base*  taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( q < cap_order );
     CPPAD_ASSERT_UNKNOWN( 0 < q );

     // Taylor coefficients corresponding to argument and result
     size_t num_taylor_per_var = (cap_order-1) * r + 1;
     Base* x = taylor + i_x * num_taylor_per_var;
     Base* z = taylor + i_z * num_taylor_per_var;

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

/*!
Zero order forward mode Taylor coefficient for result of op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
     z = expm1(x)
\endverbatim

\copydetails CppAD::local::forward_unary1_op_0
*/
template <class Base>
inline void forward_expm1_op_0(
     size_t i_z         ,
     size_t i_x         ,
     size_t cap_order   ,
     Base*  taylor      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( 0 < cap_order );

     // Taylor coefficients corresponding to argument and result
     Base* x = taylor + i_x * cap_order;
     Base* z = taylor + i_z * cap_order;

     z[0] = expm1( x[0] );
}
/*!
Reverse mode partial derivatives for result of op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
     z = expm1(x)
\endverbatim

\copydetails CppAD::local::reverse_unary1_op
*/

template <class Base>
inline void reverse_expm1_op(
     size_t      d            ,
     size_t      i_z          ,
     size_t      i_x          ,
     size_t      cap_order    ,
     const Base* taylor       ,
     size_t      nc_partial   ,
     Base*       partial      )
{
     // check assumptions
     CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
     CPPAD_ASSERT_UNKNOWN( d < cap_order );
     CPPAD_ASSERT_UNKNOWN( d < nc_partial );

     // Taylor coefficients and partials corresponding to argument
     const Base* x  = taylor  + i_x * cap_order;
     Base* px       = partial + i_x * nc_partial;

     // Taylor coefficients and partials corresponding to result
     const Base* z  = taylor  + i_z * cap_order;
     Base* pz       = partial + i_z * nc_partial;

     // If pz is zero, make sure this operation has no effect
     // (zero times infinity or nan would be non-zero).
     bool skip(true);
     for(size_t i_d = 0; i_d <= d; i_d++)
          skip &= IdenticalZero(pz[i_d]);
     if( skip )
          return;

     // loop through orders in reverse
     size_t j, k;
     j = d;
     while(j)
     {    px[j] += pz[j];

          // scale partial w.r.t z[j]
          pz[j] /= Base(double(j));

          for(k = 1; k <= j; k++)
          {    px[k]   += Base(double(k)) * azmul(pz[j], z[j-k]);
               pz[j-k] += Base(double(k)) * azmul(pz[j], x[k]);
          }
          --j;
     }
     px[0] += pz[0] + azmul(pz[0], z[0]);
}

} } // END_CPPAD_LOCAL_NAMESPACE
# endif
# endif