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base_complex.hpp.xml @upstream/2015.00.00.7 — raw · history · blame
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 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double Base enable use of ad<base> where base is std::complex<double> example include order condexpop condexprel equalopseq identical ordered erf integer isnan valid unary math invalid pow limits "/> <style type='text/css'> body { color : black } body { background-color : white } A:link { color : blue } A:visited { color : purple } A:active { color : purple } </style> <script type='text/javascript' language='JavaScript' src='_base_complex.hpp_xml.js'> </script> </head> <body> <table><tr> <td> <a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a> </td> <td><a href="base_double.hpp.xml" target="_top">Prev</a> </td><td><a href="complex_poly.cpp.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></option> <option>contents</option> <option>reference</option> <option>index</option> <option>search</option> <option>external</option> </select> </td> <td> <select onchange='choose_up0(this)'> <option>Up-></option> <option>CppAD</option> <option>AD</option> <option>base_require</option> <option>base_example</option> <option>base_complex.hpp</option> </select> </td> <td> <select onchange='choose_down3(this)'> <option>AD-></option> <option>ad_ctor</option> <option>ad_assign</option> <option>Convert</option> <option>ADValued</option> <option>BoolValued</option> <option>VecAD</option> <option>base_require</option> </select> </td> <td> <select onchange='choose_down2(this)'> <option>base_require-></option> <option>base_member</option> <option>base_cond_exp</option> <option>base_identical</option> <option>base_ordered</option> <option>base_std_math</option> <option>base_example</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>base_example-></option> <option>base_alloc.hpp</option> <option>base_require.cpp</option> <option>base_adolc.hpp</option> <option>base_float.hpp</option> <option>base_double.hpp</option> <option>base_complex.hpp</option> </select> </td> <td> <select onchange='choose_down0(this)'> <option>base_complex.hpp-></option> <option>complex_poly.cpp</option> </select> </td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Example</option> <option>Include Order</option> <option>CondExpOp</option> <option>CondExpRel</option> <option>EqualOpSeq</option> <option>Identical</option> <option>Ordered</option> <option>erf</option> <option>Integer</option> <option>isnan</option> <option>Valid Unary Math</option> <option>Invalid Unary Math</option> <option>pow</option> <option>limits</option> </select> </td> </tr></table><br/> <center><b><big><big>Enable use of AD<Base> where Base is std::complex<double></big></big></b></center> <br/> <b><big><a name="Example" id="Example">Example</a></big></b> <br/> The file <a href="complex_poly.cpp.xml" target="_top"><span style='white-space: nowrap'>complex_poly.cpp</span></a> contains an example use of <code><font color="blue">std::complex<double></font></code> type for a CppAD <code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code> type. It returns true if it succeeds and false otherwise. <br/> <br/> <b><big><a name="Include Order" id="Include Order">Include Order</a></big></b> <br/> This file is included before <code><font color="blue"><cppad/cppad.hpp></font></code> so it is necessary to define the error handler in addition to including <a href="base_require.xml#Include Order" target="_top"><span style='white-space: nowrap'>base_require.hpp</span></a> <code><font color='blue'><pre style='display:inline'> # include <limits> # include <complex> # include <cppad/base_require.hpp> # include <cppad/local/cppad_assert.hpp> </pre></font></code> <br/> <br/> <b><big><a name="CondExpOp" id="CondExpOp">CondExpOp</a></big></b> <br/> The type <code><font color="blue">std::complex<double></font></code> does not supports the <code><font color="blue"><</font></code>, <code><font color="blue"><=</font></code>, <code><font color="blue">==</font></code>, <code><font color="blue">>=</font></code>, and <code><font color="blue">></font></code> operators; see <a href="base_cond_exp.xml#CondExpTemplate.Not Ordered" target="_top"><span style='white-space: nowrap'>not ordered</span></a> . Hence its <code><font color="blue">CondExpOp</font></code> function is defined by <code><font color='blue'><pre style='display:inline'> namespace CppAD { inline std::complex<double> CondExpOp( enum CppAD::CompareOp cop , const std::complex<double> &left , const std::complex<double> &right , const std::complex<double> &trueCase , const std::complex<double> &falseCase ) { CppAD::ErrorHandler::Call( true , __LINE__ , __FILE__ , "std::complex<float> CondExpOp(...)", "Error: cannot use CondExp with a complex type" ); return std::complex<double>(0); } } </pre></font></code> <br/> <br/> <b><big><a name="CondExpRel" id="CondExpRel">CondExpRel</a></big></b> <br/> The <a href="base_cond_exp.xml#CondExpRel" target="_top"><span style='white-space: nowrap'>CPPAD_COND_EXP_REL</span></a> macro invocation <code><font color='blue'><pre style='display:inline'> namespace CppAD { CPPAD_COND_EXP_REL( std::complex<double> ) } </pre></font></code> used <code><font color="blue">CondExpOp</font></code> above to define <code><font color="blue"><span style='white-space: nowrap'>CondExp</span></font><i><font color="black"><span style='white-space: nowrap'>Rel</span></font></i></code> for <code><font color="blue">std::complex<double></font></code> arguments and <code><i><font color="black"><span style='white-space: nowrap'>Rel</span></font></i></code> equal to <code><font color="blue">Lt</font></code>, <code><font color="blue">Le</font></code>, <code><font color="blue">Eq</font></code>, <code><font color="blue">Ge</font></code>, and <code><font color="blue">Gt</font></code>. <br/> <br/> <b><big><a name="EqualOpSeq" id="EqualOpSeq">EqualOpSeq</a></big></b> <br/> Complex numbers do not carry operation sequence information. Thus they are equal in this sense if and only if there values are equal. <code><font color='blue'><pre style='display:inline'> namespace CppAD { inline bool EqualOpSeq( const std::complex<double> &x , const std::complex<double> &y ) { return x == y; } } </pre></font></code> <br/> <br/> <b><big><a name="Identical" id="Identical">Identical</a></big></b> <br/> Complex numbers do not carry operation sequence information. Thus they are all parameters so the identical functions just check values. <code><font color='blue'><pre style='display:inline'> namespace CppAD { inline bool IdenticalPar(const std::complex<double> &x) { return true; } inline bool IdenticalZero(const std::complex<double> &x) { return (x == std::complex<double>(0., 0.) ); } inline bool IdenticalOne(const std::complex<double> &x) { return (x == std::complex<double>(1., 0.) ); } inline bool IdenticalEqualPar( const std::complex<double> &x, const std::complex<double> &y) { return (x == y); } } </pre></font></code> <br/> <br/> <b><big><a name="Ordered" id="Ordered">Ordered</a></big></b> <br/> Complex types do not support comparison operators, <code><font color='blue'><pre style='display:inline'> # undef CPPAD_USER_MACRO # define CPPAD_USER_MACRO(Fun) \ inline bool Fun(const std::complex<double>& x) \ { CppAD::ErrorHandler::Call( \ true , __LINE__ , __FILE__ , \ #Fun"(x)", \ "Error: cannot use " #Fun " with x complex<double> " \ ); \ return false; \ } namespace CppAD { CPPAD_USER_MACRO(LessThanZero) CPPAD_USER_MACRO(LessThanOrZero) CPPAD_USER_MACRO(GreaterThanOrZero) CPPAD_USER_MACRO(GreaterThanZero) inline bool abs_geq( const std::complex<double>& x , const std::complex<double>& y ) { return std::abs(x) >= std::abs(y); } } </pre></font></code> <br/> <br/> <b><big><a name="erf" id="erf">erf</a></big></b> <br/> Complex types do not support the error function (use CPPAD_USER_MACRO define above). <code><font color='blue'><pre style='display:inline'> # if CPPAD_COMPILER_HAS_ERF namespace CppAD { CPPAD_USER_MACRO(erf) } # endif </pre></font></code> <br/> <br/> <b><big><a name="Integer" id="Integer">Integer</a></big></b> <br/> The implementation of this function must agree with the CppAD user specifications for complex arguments to the <a href="integer.xml#x.Complex Types" target="_top"><span style='white-space: nowrap'>Integer</span></a> function: <code><font color='blue'><pre style='display:inline'> namespace CppAD { inline int Integer(const std::complex<double> &x) { return static_cast<int>( x.real() ); } } </pre></font></code> <br/> <br/> <b><big><a name="isnan" id="isnan">isnan</a></big></b> <br/> The gcc 4.1.1 complier defines the function <code><font color="blue"><span style='white-space: nowrap'><br/>      int std::complex<double>::isnan( std::complex<double> </span></font><i><font color="black"><span style='white-space: nowrap'>z</span></font></i><font color="blue"><span style='white-space: nowrap'> )<br/> </span></font></code> (which is not specified in the C++ 1998 standard ISO/IEC 14882). This causes an ambiguity between the function above and the CppAD <a href="nan.xml" target="_top"><span style='white-space: nowrap'>isnan</span></a> template function. We avoid this ambiguity by defining a non-template version of this function in the CppAD namespace. <code><font color='blue'><pre style='display:inline'> namespace CppAD { inline bool isnan(const std::complex<double>& z) { return (z != z); } } </pre></font></code> <br/> <br/> <b><big><a name="Valid Unary Math" id="Valid Unary Math">Valid Unary Math</a></big></b> <br/> The following macro invocations define the standard unary math functions that are valid with complex arguments and are required to use <code><font color="blue">AD< std::complex<double> ></font></code>. <code><font color='blue'><pre style='display:inline'> namespace CppAD { CPPAD_STANDARD_MATH_UNARY(std::complex<double>, cos) CPPAD_STANDARD_MATH_UNARY(std::complex<double>, cosh) CPPAD_STANDARD_MATH_UNARY(std::complex<double>, exp) CPPAD_STANDARD_MATH_UNARY(std::complex<double>, log) CPPAD_STANDARD_MATH_UNARY(std::complex<double>, sin) CPPAD_STANDARD_MATH_UNARY(std::complex<double>, sinh) CPPAD_STANDARD_MATH_UNARY(std::complex<double>, sqrt) } </pre></font></code> <br/> <br/> <b><big><a name="Invalid Unary Math" id="Invalid Unary Math">Invalid Unary Math</a></big></b> <br/> The following macro definition and invocations define the standard unary math functions that are invalid with complex arguments and are required to use <code><font color="blue">AD< std::complex<double> ></font></code>. <code><font color='blue'><pre style='display:inline'> # undef CPPAD_USER_MACRO # define CPPAD_USER_MACRO(Fun) \ inline std::complex<double> Fun(const std::complex<double>& x) \ { CppAD::ErrorHandler::Call( \ true , __LINE__ , __FILE__ , \ #Fun"(x)", \ "Error: cannot use " #Fun " with x complex<double> " \ ); \ return std::complex<double>(0); \ } namespace CppAD { CPPAD_USER_MACRO(abs) CPPAD_USER_MACRO(acos) CPPAD_USER_MACRO(asin) CPPAD_USER_MACRO(atan) CPPAD_USER_MACRO(sign) } </pre></font></code> <br/> <br/> <b><big><a name="pow" id="pow">pow</a></big></b> <br/> The following defines a <code><font color="blue">CppAD::pow</font></code> function that is required to use <code><font color="blue">AD< std::complex<double> ></font></code>: <code><font color='blue'><pre style='display:inline'> namespace CppAD { inline std::complex<double> pow( const std::complex<double> &x , const std::complex<double> &y ) { return std::pow(x, y); } } </pre></font></code> <br/> <br/> <b><big><a name="limits" id="limits">limits</a></big></b> <br/> The following defines the numeric limits functions <code><font color="blue">epsilon</font></code>, <code><font color="blue">min</font></code>, and <code><font color="blue">max</font></code> for the type <code><font color="blue">std::complex<double></font></code>. It also defines the deprecated <code><font color="blue">epsilon</font></code> function: <code><font color='blue'><pre style='display:inline'> namespace CppAD { template <> class numeric_limits< std::complex<double> > { public: // machine epsilon static std::complex<double> epsilon(void) { double eps = std::numeric_limits<double>::epsilon(); return std::complex<double>(eps, 0.0); } // minimum positive normalized value static std::complex<double> min(void) { double min = std::numeric_limits<double>::min(); return std::complex<double>(min, 0.0); } // maximum finite value static std::complex<double> max(void) { double max = std::numeric_limits<double>::max(); return std::complex<double>(max, 0.0); } }; // deprecated machine epsilon template <> inline std::complex<double> epsilon< std::complex<double> > (void) { return numeric_limits< std::complex<double> >::epsilon(); } } </pre></font></code> <hr/>Input File: cppad/local/base_complex.hpp </body> </html> |