CppAD: A C++ Algorithmic Differentiation Package  20130102
sin_op.hpp
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00001 /* $Id$ */
00002 # ifndef CPPAD_SIN_OP_INCLUDED
00003 # define CPPAD_SIN_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 sin_op_hpp sin_op.hpp
00020 \{
00021 \file sin_op.hpp
00022 Forward and reverse mode calculations for z = sin(x).
00023 */
00024 
00025 
00026 /*!
00027 Compute forward mode Taylor coefficient for result of op = SinOp.
00028 
00029 The C++ source code corresponding to this operation is
00030 \verbatim
00031      z = sin(x)
00032 \endverbatim
00033 The auxillary result is
00034 \verbatim
00035      y = cos(x)
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_sin_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(SinOp) == 1 );
00052      CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 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* s = taylor + i_z * nc_taylor;
00059      Base* c = s      -       nc_taylor;
00060 
00061      // rest of this routine is identical for the following cases:
00062      // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op.
00063      size_t k;
00064      if( j == 0 )
00065      {    s[j] = sin( x[0] );
00066           c[j] = cos( x[0] );
00067      }
00068      else
00069      {
00070           s[j] = Base(0);
00071           c[j] = Base(0);
00072           for(k = 1; k <= j; k++)
00073           {    s[j] += Base(k) * x[k] * c[j-k];
00074                c[j] -= Base(k) * x[k] * s[j-k];
00075           }
00076           s[j] /= Base(j);
00077           c[j] /= Base(j);
00078      }
00079 }
00080 
00081 
00082 /*!
00083 Compute zero order forward mode Taylor coefficient for result of op = SinOp.
00084 
00085 The C++ source code corresponding to this operation is
00086 \verbatim
00087      z = sin(x)
00088 \endverbatim
00089 The auxillary result is
00090 \verbatim
00091      y = cos(x)
00092 \endverbatim
00093 The value of y is computed along with the value of z.
00094 
00095 \copydetails forward_unary2_op_0
00096 */
00097 template <class Base>
00098 inline void forward_sin_op_0(
00099      size_t i_z         ,
00100      size_t i_x         ,
00101      size_t nc_taylor   , 
00102      Base*  taylor      )
00103 {
00104      // check assumptions
00105      CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
00106      CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
00107      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00108      CPPAD_ASSERT_UNKNOWN( 0 < nc_taylor );
00109 
00110      // Taylor coefficients corresponding to argument and result
00111      Base* x = taylor + i_x * nc_taylor;
00112      Base* s = taylor + i_z * nc_taylor;  // called z in documentation
00113      Base* c = s      -       nc_taylor;  // called y in documentation
00114 
00115      s[0] = sin( x[0] );
00116      c[0] = cos( x[0] );
00117 }
00118 
00119 /*!
00120 Compute reverse mode partial derivatives for result of op = SinOp.
00121 
00122 The C++ source code corresponding to this operation is
00123 \verbatim
00124      z = sin(x)
00125 \endverbatim
00126 The auxillary result is
00127 \verbatim
00128      y = cos(x)
00129 \endverbatim
00130 The value of y is computed along with the value of z.
00131 
00132 \copydetails reverse_unary2_op
00133 */
00134 
00135 template <class Base>
00136 inline void reverse_sin_op(
00137      size_t      d            ,
00138      size_t      i_z          ,
00139      size_t      i_x          ,
00140      size_t      nc_taylor    , 
00141      const Base* taylor       ,
00142      size_t      nc_partial   ,
00143      Base*       partial      )
00144 {
00145      // check assumptions
00146      CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
00147      CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
00148      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00149      CPPAD_ASSERT_UNKNOWN( d < nc_taylor );
00150      CPPAD_ASSERT_UNKNOWN( d < nc_partial );
00151 
00152      // Taylor coefficients and partials corresponding to argument
00153      const Base* x  = taylor  + i_x * nc_taylor;
00154      Base* px       = partial + i_x * nc_partial;
00155 
00156      // Taylor coefficients and partials corresponding to first result
00157      const Base* s  = taylor  + i_z * nc_taylor; // called z in doc
00158      Base* ps       = partial + i_z * nc_partial;
00159 
00160      // Taylor coefficients and partials corresponding to auxillary result
00161      const Base* c  = s  - nc_taylor; // called y in documentation
00162      Base* pc       = ps - nc_partial;
00163 
00164      // rest of this routine is identical for the following cases:
00165      // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op.
00166      size_t j = d;
00167      size_t k;
00168      while(j)
00169      {
00170           ps[j]   /= Base(j);
00171           pc[j]   /= Base(j);
00172           for(k = 1; k <= j; k++)
00173           {
00174                px[k]   += ps[j] * Base(k) * c[j-k];
00175                px[k]   -= pc[j] * Base(k) * s[j-k];
00176      
00177                ps[j-k] -= pc[j] * Base(k) * x[k];
00178                pc[j-k] += ps[j] * Base(k) * x[k];
00179 
00180           }
00181           --j;
00182      }
00183      px[0] += ps[0] * c[0];
00184      px[0] -= pc[0] * s[0];
00185 }
00186 
00187 /*! \} */
00188 CPPAD_END_NAMESPACE
00189 # endif
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