CppAD: A C++ Algorithmic Differentiation Package
20130102
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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