CppAD: A C++ Algorithmic Differentiation Package  20130918
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) 2003-14 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 namespace CppAD { // BEGIN_CPPAD_NAMESPACE
00018 /*!
00019 \file sin_op.hpp
00020 Forward and reverse mode calculations for z = sin(x).
00021 */
00022 
00023 
00024 /*!
00025 Compute forward mode Taylor coefficient for result of op = SinOp.
00026 
00027 The C++ source code corresponding to this operation is
00028 \verbatim
00029      z = sin(x)
00030 \endverbatim
00031 The auxillary result is
00032 \verbatim
00033      y = cos(x)
00034 \endverbatim
00035 The value of y, and its derivatives, are computed along with the value
00036 and derivatives of z.
00037 
00038 \copydetails forward_unary2_op
00039 */
00040 template <class Base>
00041 inline void forward_sin_op(
00042      size_t p           ,
00043      size_t q           ,
00044      size_t i_z         ,
00045      size_t i_x         ,
00046      size_t nc_taylor   , 
00047      Base*  taylor      )
00048 {    
00049      // check assumptions
00050      CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
00051      CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
00052      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00053      CPPAD_ASSERT_UNKNOWN( q < nc_taylor );
00054      CPPAD_ASSERT_UNKNOWN( p <= q );
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( p == 0 )
00065      {    s[0] = sin( x[0] );
00066           c[0] = cos( x[0] );
00067           p++;
00068      }
00069      for(size_t j = p; j <= q; j++)
00070      {
00071           s[j] = Base(0);
00072           c[j] = Base(0);
00073           for(k = 1; k <= j; k++)
00074           {    s[j] += Base(k) * x[k] * c[j-k];
00075                c[j] -= Base(k) * x[k] * s[j-k];
00076           }
00077           s[j] /= Base(j);
00078           c[j] /= Base(j);
00079      }
00080 }
00081 
00082 
00083 /*!
00084 Compute zero order forward mode Taylor coefficient for result of op = SinOp.
00085 
00086 The C++ source code corresponding to this operation is
00087 \verbatim
00088      z = sin(x)
00089 \endverbatim
00090 The auxillary result is
00091 \verbatim
00092      y = cos(x)
00093 \endverbatim
00094 The value of y is computed along with the value of z.
00095 
00096 \copydetails forward_unary2_op_0
00097 */
00098 template <class Base>
00099 inline void forward_sin_op_0(
00100      size_t i_z         ,
00101      size_t i_x         ,
00102      size_t nc_taylor   , 
00103      Base*  taylor      )
00104 {
00105      // check assumptions
00106      CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
00107      CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
00108      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00109      CPPAD_ASSERT_UNKNOWN( 0 < nc_taylor );
00110 
00111      // Taylor coefficients corresponding to argument and result
00112      Base* x = taylor + i_x * nc_taylor;
00113      Base* s = taylor + i_z * nc_taylor;  // called z in documentation
00114      Base* c = s      -       nc_taylor;  // called y in documentation
00115 
00116      s[0] = sin( x[0] );
00117      c[0] = cos( x[0] );
00118 }
00119 
00120 /*!
00121 Compute reverse mode partial derivatives for result of op = SinOp.
00122 
00123 The C++ source code corresponding to this operation is
00124 \verbatim
00125      z = sin(x)
00126 \endverbatim
00127 The auxillary result is
00128 \verbatim
00129      y = cos(x)
00130 \endverbatim
00131 The value of y is computed along with the value of z.
00132 
00133 \copydetails reverse_unary2_op
00134 */
00135 
00136 template <class Base>
00137 inline void reverse_sin_op(
00138      size_t      d            ,
00139      size_t      i_z          ,
00140      size_t      i_x          ,
00141      size_t      nc_taylor    , 
00142      const Base* taylor       ,
00143      size_t      nc_partial   ,
00144      Base*       partial      )
00145 {
00146      // check assumptions
00147      CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
00148      CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
00149      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00150      CPPAD_ASSERT_UNKNOWN( d < nc_taylor );
00151      CPPAD_ASSERT_UNKNOWN( d < nc_partial );
00152 
00153      // Taylor coefficients and partials corresponding to argument
00154      const Base* x  = taylor  + i_x * nc_taylor;
00155      Base* px       = partial + i_x * nc_partial;
00156 
00157      // Taylor coefficients and partials corresponding to first result
00158      const Base* s  = taylor  + i_z * nc_taylor; // called z in doc
00159      Base* ps       = partial + i_z * nc_partial;
00160 
00161      // Taylor coefficients and partials corresponding to auxillary result
00162      const Base* c  = s  - nc_taylor; // called y in documentation
00163      Base* pc       = ps - nc_partial;
00164 
00165      // rest of this routine is identical for the following cases:
00166      // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op.
00167      size_t j = d;
00168      size_t k;
00169      while(j)
00170      {
00171           ps[j]   /= Base(j);
00172           pc[j]   /= Base(j);
00173           for(k = 1; k <= j; k++)
00174           {
00175                px[k]   += ps[j] * Base(k) * c[j-k];
00176                px[k]   -= pc[j] * Base(k) * s[j-k];
00177      
00178                ps[j-k] -= pc[j] * Base(k) * x[k];
00179                pc[j-k] += ps[j] * Base(k) * x[k];
00180 
00181           }
00182           --j;
00183      }
00184      px[0] += ps[0] * c[0];
00185      px[0] -= pc[0] * s[0];
00186 }
00187 
00188 } // END_CPPAD_NAMESPACE
00189 # endif
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