CppAD: A C++ Algorithmic Differentiation Package  20130918
cosh_op.hpp
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00001 /* $Id$ */
00002 # ifndef CPPAD_COSH_OP_INCLUDED
00003 # define CPPAD_COSH_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 cosh_op.hpp
00020 Forward and reverse mode calculations for z = cosh(x).
00021 */
00022 
00023 
00024 /*!
00025 Compute forward mode Taylor coefficient for result of op = CoshOp.
00026 
00027 The C++ source code corresponding to this operation is
00028 \verbatim
00029      z = cosh(x)
00030 \endverbatim
00031 The auxillary result is
00032 \verbatim
00033      y = sinh(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_cosh_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(CoshOp) == 1 );
00051      CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 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* c = taylor + i_z * nc_taylor;
00059      Base* s = c      -       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] = sinh( x[0] );
00066           c[0] = cosh( 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 Compute zero order forward mode Taylor coefficient for result of op = CoshOp.
00084 
00085 The C++ source code corresponding to this operation is
00086 \verbatim
00087      z = cosh(x)
00088 \endverbatim
00089 The auxillary result is
00090 \verbatim
00091      y = sinh(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_cosh_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(CoshOp) == 1 );
00106      CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 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* c = taylor + i_z * nc_taylor;  // called z in documentation
00113      Base* s = c      -       nc_taylor;  // called y in documentation
00114 
00115      c[0] = cosh( x[0] );
00116      s[0] = sinh( x[0] );
00117 }
00118 /*!
00119 Compute reverse mode partial derivatives for result of op = CoshOp.
00120 
00121 The C++ source code corresponding to this operation is
00122 \verbatim
00123      z = cosh(x)
00124 \endverbatim
00125 The auxillary result is
00126 \verbatim
00127      y = sinh(x)
00128 \endverbatim
00129 The value of y is computed along with the value of z.
00130 
00131 \copydetails reverse_unary2_op
00132 */
00133 
00134 template <class Base>
00135 inline void reverse_cosh_op(
00136      size_t      d            ,
00137      size_t      i_z          ,
00138      size_t      i_x          ,
00139      size_t      nc_taylor    , 
00140      const Base* taylor       ,
00141      size_t      nc_partial   ,
00142      Base*       partial      )
00143 {
00144      // check assumptions
00145      CPPAD_ASSERT_UNKNOWN( NumArg(CoshOp) == 1 );
00146      CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 2 );
00147      CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
00148      CPPAD_ASSERT_UNKNOWN( d < nc_taylor );
00149      CPPAD_ASSERT_UNKNOWN( d < nc_partial );
00150 
00151      // Taylor coefficients and partials corresponding to argument
00152      const Base* x  = taylor  + i_x * nc_taylor;
00153      Base* px       = partial + i_x * nc_partial;
00154 
00155      // Taylor coefficients and partials corresponding to first result
00156      const Base* c  = taylor  + i_z * nc_taylor; // called z in doc
00157      Base* pc       = partial + i_z * nc_partial;
00158 
00159      // Taylor coefficients and partials corresponding to auxillary result
00160      const Base* s  = c  - nc_taylor; // called y in documentation
00161      Base* ps       = pc - nc_partial;
00162 
00163      // rest of this routine is identical for the following cases:
00164      // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op.
00165      size_t j = d;
00166      size_t k;
00167      while(j)
00168      {
00169           ps[j]   /= Base(j);
00170           pc[j]   /= Base(j);
00171           for(k = 1; k <= j; k++)
00172           {
00173                px[k]   += ps[j] * Base(k) * c[j-k];
00174                px[k]   += pc[j] * Base(k) * s[j-k];
00175      
00176                ps[j-k] += pc[j] * Base(k) * x[k];
00177                pc[j-k] += ps[j] * Base(k) * x[k];
00178 
00179           }
00180           --j;
00181      }
00182      px[0] += ps[0] * c[0];
00183      px[0] += pc[0] * s[0];
00184 }
00185 
00186 } // END_CPPAD_NAMESPACE
00187 # endif
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