CppAD: A C++ Algorithmic Differentiation Package  20130102
tanh_op.hpp
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00001 /* $Id$ */
00002 # ifndef CPPAD_TANH_OP_INCLUDED
00003 # define CPPAD_TANH_OP_INCLUDED
00004 
00005 /* --------------------------------------------------------------------------
00006 CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell
00007 
00008 CppAD is distributed under multiple licenses. This distribution is under
00009 the terms of the 
00010                     Eclipse Public License Version 1.0.
00011 
00012 A copy of this license is included in the COPYING file of this distribution.
00013 Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
00014 -------------------------------------------------------------------------- */
00015 
00016 
00017 CPPAD_BEGIN_NAMESPACE
00018 /*!
00019 \defgroup tanh_op_hpp tanh_op.hpp
00020 \{
00021 \file tanh_op.hpp
00022 Forward and reverse mode calculations for z = tanh(x).
00023 */
00024 
00025 
00026 /*!
00027 Compute forward mode Taylor coefficient for result of op = TanOp.
00028 
00029 The C++ source code corresponding to this operation is
00030 \verbatim
00031      z = tanh(x)
00032 \endverbatim
00033 The auxillary result is
00034 \verbatim
00035      y = tanh(x)^2
00036 \endverbatim
00037 The value of y, and its derivatives, are computed along with the value
00038 and derivatives of z.
00039 
00040 \copydetails forward_unary2_op
00041 */
00042 template <class Base>
00043 inline void forward_tanh_op(
00044      size_t j           ,
00045      size_t i_z         ,
00046      size_t i_x         ,
00047      size_t nc_taylor   , 
00048      Base*  taylor      )
00049 {    
00050      // check assumptions
00051      CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 );
00052      CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 );
00053      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00054      CPPAD_ASSERT_UNKNOWN( j < nc_taylor );
00055 
00056      // Taylor coefficients corresponding to argument and result
00057      Base* x = taylor + i_x * nc_taylor;
00058      Base* z = taylor + i_z * nc_taylor;
00059      Base* y = z      -       nc_taylor;
00060 
00061      size_t k;
00062      if( j == 0 )
00063      {    z[j] = tanh( x[0] );
00064           y[j] = z[j] * z[j];
00065      }
00066      else
00067      {    Base base_j = static_cast<Base>(j);
00068 
00069           z[j] = x[j];
00070           for(k = 1; k <= j; k++)
00071                z[j] -= Base(k) * x[k] * y[j-k] / base_j;
00072 
00073           y[j] = z[0] * z[j];
00074           for(k = 1; k <= j; k++)
00075                y[j] += z[k] * z[j-k];
00076      }
00077 }
00078 
00079 
00080 /*!
00081 Compute zero order forward mode Taylor coefficient for result of op = TanOp.
00082 
00083 The C++ source code corresponding to this operation is
00084 \verbatim
00085      z = tanh(x)
00086 \endverbatim
00087 The auxillary result is
00088 \verbatim
00089      y = cos(x)
00090 \endverbatim
00091 The value of y is computed along with the value of z.
00092 
00093 \copydetails forward_unary2_op_0
00094 */
00095 template <class Base>
00096 inline void forward_tanh_op_0(
00097      size_t i_z         ,
00098      size_t i_x         ,
00099      size_t nc_taylor   , 
00100      Base*  taylor      )
00101 {
00102      // check assumptions
00103      CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 );
00104      CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 );
00105      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00106      CPPAD_ASSERT_UNKNOWN( 0 < nc_taylor );
00107 
00108      // Taylor coefficients corresponding to argument and result
00109      Base* x = taylor + i_x * nc_taylor;
00110      Base* z = taylor + i_z * nc_taylor;  // called z in documentation
00111      Base* y = z      -       nc_taylor;  // called y in documentation
00112 
00113      z[0] = tanh( x[0] );
00114      y[0] = z[0] * z[0];
00115 }
00116 
00117 /*!
00118 Compute reverse mode partial derivatives for result of op = TanOp.
00119 
00120 The C++ source code corresponding to this operation is
00121 \verbatim
00122      z = tanh(x)
00123 \endverbatim
00124 The auxillary result is
00125 \verbatim
00126      y = cos(x)
00127 \endverbatim
00128 The value of y is computed along with the value of z.
00129 
00130 \copydetails reverse_unary2_op
00131 */
00132 
00133 template <class Base>
00134 inline void reverse_tanh_op(
00135      size_t      d            ,
00136      size_t      i_z          ,
00137      size_t      i_x          ,
00138      size_t      nc_taylor    , 
00139      const Base* taylor       ,
00140      size_t      nc_partial   ,
00141      Base*       partial      )
00142 {
00143      // check assumptions
00144      CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 );
00145      CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 );
00146      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00147      CPPAD_ASSERT_UNKNOWN( d < nc_taylor );
00148      CPPAD_ASSERT_UNKNOWN( d < nc_partial );
00149 
00150      // Taylor coefficients and partials corresponding to argument
00151      const Base* x  = taylor  + i_x * nc_taylor;
00152      Base* px       = partial + i_x * nc_partial;
00153 
00154      // Taylor coefficients and partials corresponding to first result
00155      const Base* z  = taylor  + i_z * nc_taylor; // called z in doc
00156      Base* pz       = partial + i_z * nc_partial;
00157 
00158      // Taylor coefficients and partials corresponding to auxillary result
00159      const Base* y  = z  - nc_taylor; // called y in documentation
00160      Base* py       = pz - nc_partial;
00161 
00162      size_t j = d;
00163      size_t k;
00164      Base base_two(2);
00165      while(j)
00166      {
00167           px[j]   += pz[j];
00168           pz[j]   /= Base(j);
00169           for(k = 1; k <= j; k++)
00170           {    px[k]   -= pz[j] * y[j-k] * Base(k);
00171                py[j-k] -= pz[j] * x[k] * Base(k);
00172           }
00173           for(k = 0; k < j; k++)
00174                pz[k] += py[j-1] * z[j-k-1] * base_two;
00175      
00176           --j;
00177      }
00178      px[0] += pz[0] * (Base(1) - y[0]);
00179 }
00180 
00181 /*! \} */
00182 CPPAD_END_NAMESPACE
00183 # endif
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