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1.7.5.1
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C-XSC - A C++ Class Library for Extended Scientific Computing
2.5.4
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00001 /* 00002 ** CXSC is a C++ library for eXtended Scientific Computing (V 2.5.4) 00003 ** 00004 ** Copyright (C) 1990-2000 Institut fuer Angewandte Mathematik, 00005 ** Universitaet Karlsruhe, Germany 00006 ** (C) 2000-2014 Wiss. Rechnen/Softwaretechnologie 00007 ** Universitaet Wuppertal, Germany 00008 ** 00009 ** This library is free software; you can redistribute it and/or 00010 ** modify it under the terms of the GNU Library General Public 00011 ** License as published by the Free Software Foundation; either 00012 ** version 2 of the License, or (at your option) any later version. 00013 ** 00014 ** This library is distributed in the hope that it will be useful, 00015 ** but WITHOUT ANY WARRANTY; without even the implied warranty of 00016 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00017 ** Library General Public License for more details. 00018 ** 00019 ** You should have received a copy of the GNU Library General Public 00020 ** License along with this library; if not, write to the Free 00021 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 00022 */ 00023 00024 /* CVS $Id: lx_complex.hpp,v 1.9 2014/01/30 17:23:47 cxsc Exp $ */ 00025 00026 00027 /* 00028 ** F. Blomquist, University of Wuppertal, 19.09.2007; 00029 */ 00030 00031 /* 00032 ** Implementation of the classes 00033 ** 00034 ** lx_complex with all tools and elementary functions for complex 00035 ** point and interval aruments 00036 ** 00037 */ 00038 00039 #ifndef _CXSC_LX_COMPLEX_HPP_INCLUDED 00040 #define _CXSC_LX_COMPLEX_HPP_INCLUDED 00041 00042 #include <iostream> 00043 #include <except.hpp> 00044 #include <l_cinterval.hpp> 00045 #include <l_complex.hpp> 00046 #include "lx_interval.hpp" 00047 00048 namespace cxsc { 00049 // -------------------------------------------------------------------------- 00050 // Class lx_complex 00051 // -------------------------------------------------------------------------- 00052 00053 class lx_complex 00054 { 00055 private: 00056 // ------------- Data Elements ------------------------------------------- 00057 lx_real re; 00058 lx_real im; 00059 00060 public: 00061 // ------------- Constructors -------------------------------------------- 00062 00064 lx_complex(void) throw() {} 00066 lx_complex(const real& nr, const l_real &ar, const real& ni, const l_real &ai) 00067 throw() : re(lx_real(nr,ar)), im(lx_real(ni,ai)) { } 00069 lx_complex(const real& n, const real &a) 00070 throw() : re(lx_real(n,a)), im(lx_real(0.0)) { } 00072 lx_complex(const lx_real &a, const lx_real &b) 00073 throw() : re(a), im(b) { } 00075 lx_complex(const lx_real &a) throw() : re(a), im(lx_real(0.0)) { } 00077 explicit lx_complex(const l_real &a, const l_real &b) 00078 throw() : re(a), im(b) { } 00080 explicit lx_complex(const l_real &a) 00081 throw() : re(a), im(lx_real(0.0)) { } 00083 explicit lx_complex(const real &a) 00084 throw() : re(a), im(lx_real(0.0)) { } 00086 explicit lx_complex(const complex &a) 00087 throw() : re(Re(a)), im(Im(a)) { } 00089 explicit lx_complex(const l_complex &a) 00090 throw() : re(lx_real(0,Re(a))), im(lx_real(0,Im(a))) { } 00092 lx_complex(const real& pr, const string& sr, 00093 const real& pi, const string& si) 00094 throw() : re(lx_real(pr,sr)), im(lx_real(pi,si)) { } 00095 00096 // ------------- Assignments --------------------------------------------- 00098 lx_complex & operator = (const lx_real & lr) throw() 00099 { re = lr; im = 0; return *this; } 00101 lx_complex & operator = (const l_real & lr) throw() 00102 { re = lr; im = 0; return *this; } 00104 lx_complex & operator = (const real & lr) throw() 00105 { re = lr; im = 0; return *this; } 00107 lx_complex & operator = (const l_complex & c) throw() 00108 { re = Re(c); im = Im(c); return *this; } 00110 lx_complex & operator = (const complex & c) throw() 00111 { re = Re(c); im = Im(c); return *this; } 00112 00113 // ------------- Functions ----------------------------------------------- 00114 00116 friend inline lx_real Re(const lx_complex&); 00118 friend inline lx_real Im(const lx_complex&); 00120 friend inline int StagPrec(const lx_complex&) throw(); 00122 friend inline real expoRe(const lx_complex&) throw(); 00124 friend inline real expoIm(const lx_complex&) throw(); 00126 friend inline l_real lr_partRe(const lx_complex&) throw(); 00128 friend inline l_real lr_partIm(const lx_complex&) throw(); 00129 00131 friend inline lx_complex & SetRe(lx_complex&, const lx_real&); 00133 friend inline lx_complex & SetRe(lx_complex&, const l_real&); 00135 friend inline lx_complex & SetRe(lx_complex&, const real&); 00136 00138 friend inline lx_complex & SetIm(lx_complex&, const lx_real&); 00140 friend inline lx_complex & SetIm(lx_complex&, const l_real&); 00142 friend inline lx_complex & SetIm(lx_complex&, const real&); 00143 00145 friend inline lx_complex conj(const lx_complex& a) throw(); 00147 friend lx_real abs (const lx_complex&) throw(); 00149 friend lx_real abs2 (const lx_complex&) throw(); 00150 00152 friend inline bool operator ! (const lx_complex& ) throw(); 00153 00155 friend inline bool operator == (const lx_complex&, const lx_complex&) 00156 throw(); 00158 friend inline bool operator == (const lx_complex&, const l_complex&) 00159 throw(); 00161 friend inline bool operator == (const lx_complex&, const complex&) 00162 throw(); 00164 friend inline bool operator == (const l_complex&, const lx_complex&) 00165 throw(); 00167 friend inline bool operator == (const complex&, const lx_complex&) 00168 throw(); 00170 friend inline bool operator == (const lx_complex&, const lx_real&) throw(); 00172 friend inline bool operator == (const lx_complex&, const l_real&) throw(); 00174 friend inline bool operator == (const lx_complex&, const real&) throw(); 00176 friend inline bool operator == (const lx_real&, const lx_complex&) throw(); 00178 friend inline bool operator == (const l_real&, const lx_complex&) throw(); 00180 friend inline bool operator == (const real&, const lx_complex&) throw(); 00181 00183 friend inline lx_complex operator - (const lx_complex &) throw(); 00184 00185 00186 // ----------------------- Output -------------------------------------------- 00187 00189 friend inline std::ostream& operator << (std::ostream& s, const lx_complex& a) 00190 throw(); // A value a of type lx_complex is written to the output channel. 00192 friend inline std::string & operator << (std::string &s, const lx_complex& a) 00193 throw(); 00194 // The value of a variable a of type lx_complex is copied to a string s. 00195 // s has the form: ({2**()*...} , {2**()*...}) 00196 00197 // ----------------------- Input -------------------------------------------- 00198 00200 friend std::string & operator >> (std::string& s, lx_complex& a) throw(); 00201 00203 friend std::istream & operator >> (std::istream &s, lx_complex &a) throw() 00204 // An input of a complex number z of the form ({...,...},{...,...}) is 00205 // copied to the variable a of type lx_complex. 00206 { 00207 char c; 00208 std::cout << "Real part: {Exponent to base 10, real number} = ?" 00209 << std::endl; 00210 s >> a.re; 00211 std::cout << "Img. part: {Exponent to base 10, real number} = ?" 00212 << std::endl; 00213 s >> a.im >> RestoreOpt; 00214 00215 if (!waseolnflag) 00216 { 00217 skipeolnflag = false, inpdotflag = true; 00218 c = skipwhitespaces (s); 00219 if (inpdotflag && c != ')') 00220 s.putback(c); 00221 } 00222 return s; 00223 } 00224 00226 friend inline lx_complex operator + (const lx_complex&, const lx_complex&) 00227 throw(); 00229 friend inline lx_complex operator + (const lx_complex&, const lx_real&) throw(); 00231 friend inline lx_complex operator + (const lx_real&, const lx_complex&) throw(); 00233 friend inline lx_complex operator + (const lx_complex&, const l_real&) throw(); 00235 friend inline lx_complex operator + (const l_real&, const lx_complex&) throw(); 00237 friend inline lx_complex operator + (const lx_complex&, const real&) throw(); 00239 friend inline lx_complex operator + (const real&, const lx_complex&) throw(); 00240 00242 friend inline lx_complex operator * (const lx_complex&, const lx_complex&) 00243 throw(); 00244 00246 friend inline lx_complex operator / (const lx_complex&, const lx_complex&) 00247 throw(); 00248 00249 }; // end of class lx_complex 00250 00251 // *********************************************************************** 00252 // ---------Functions related to type lx_complex ------------------------- 00253 // *********************************************************************** 00254 00255 inline std::ostream& operator << (std::ostream& s, const lx_complex&) 00256 throw(); 00257 inline std::string & operator << (std::string& s, const lx_complex&) 00258 throw(); 00259 00260 // ------- friend functions declared in class lx_complex: ----------- 00261 00262 inline lx_real Re(const lx_complex&); 00263 inline lx_real Im(const lx_complex&); 00264 inline int StagPrec(const lx_complex&) throw(); 00265 inline real expoRe(const lx_complex&) throw(); 00266 inline real expoIm(const lx_complex&) throw(); 00267 inline l_real lr_partRe(const lx_complex&) throw(); 00268 inline l_real lr_partIm(const lx_complex&) throw(); 00269 00270 inline lx_complex & SetRe(lx_complex&, const lx_real&); 00271 inline lx_complex & SetRe(lx_complex&, const l_real&); 00272 inline lx_complex & SetRe(lx_complex&, const real&); 00273 00274 inline lx_complex & SetIm(lx_complex&, const lx_real&); 00275 inline lx_complex & SetIm(lx_complex&, const l_real&); 00276 inline lx_complex & SetIm(lx_complex&, const real&); 00277 00278 inline lx_complex conj(const lx_complex&) throw(); 00279 00280 lx_real abs (const lx_complex&) throw(); 00281 lx_real abs2 (const lx_complex&) throw(); 00282 00283 inline bool operator == (const lx_complex&, const lx_complex&) throw(); 00284 00285 inline bool operator == (const lx_complex&, const l_complex&) throw(); 00286 inline bool operator == (const lx_complex&, const complex&) throw(); 00287 inline bool operator == (const l_complex&, const lx_complex&) throw(); 00288 inline bool operator == (const complex&, const lx_complex&) throw(); 00289 00290 inline bool operator == (const lx_complex&, const lx_real&) throw(); 00291 inline bool operator == (const lx_complex&, const l_real&) throw(); 00292 inline bool operator == (const lx_complex&, const real&) throw(); 00293 inline bool operator == (const lx_real&, const lx_complex&) throw(); 00294 inline bool operator == (const l_real&, const lx_complex&) throw(); 00295 inline bool operator == (const real&, const lx_complex&) throw(); 00296 00297 // ---------------------------------------------------------------------- 00298 00300 inline bool operator != (const lx_complex&, const lx_complex&) throw(); 00302 inline bool operator != (const lx_complex&, const l_complex&) throw(); 00304 inline bool operator != (const lx_complex&, const complex&) throw(); 00306 inline bool operator != (const l_complex&, const lx_complex&) throw(); 00308 inline bool operator != (const complex&, const lx_complex&) throw(); 00309 00311 inline bool operator != (const lx_complex&, const lx_real&) throw(); 00313 inline bool operator != (const lx_complex&, const l_real&) throw(); 00315 inline bool operator != (const lx_complex&, const real&) throw(); 00317 inline bool operator != (const lx_real&, const lx_complex&) throw(); 00319 inline bool operator != (const l_real&, const lx_complex&) throw(); 00321 inline bool operator != (const real&, const lx_complex&) throw(); 00322 00323 inline lx_complex operator - (const lx_complex &) throw(); 00324 00325 // -------------------------- Output ------------------------------------ 00326 00327 inline std::ostream& operator << (std::ostream& s, const lx_complex& a) 00328 throw(); // A value a of type lx_complex is written to the output channel. 00329 inline std::string & operator << (std::string& s, const lx_complex& a) 00330 throw(); 00331 // The value of a variable a of type lx_complex is copied to a string s. 00332 // s has the form: { ? , ? } 00333 00334 // -------------------------- Input ------------------------------------ 00335 00337 std::string & operator >> (std::string& s, lx_complex& a) throw(); 00338 // Writes string s to variable a of type lx_complex; 00339 // and returns an empty string s; 00340 // Example: s = "{-4000,2}" delivers a value a 00341 // with: 10^(-4000)*2 ~ a; 00342 00344 void operator >> (const std::string &s, lx_complex &a) throw(); 00346 void operator >> (const char *s, lx_complex& a) throw(); 00347 00348 // ---- function and operator declarations outside the class lx_complex ---- 00349 00351 inline lx_complex operator + (const lx_complex&) throw(); 00352 00354 inline lx_complex operator + (const lx_complex&, const l_complex&) throw(); 00356 inline lx_complex operator + (const lx_complex&, const complex&) throw(); 00358 inline lx_complex operator + (const l_complex&, const lx_complex&) throw(); 00360 inline lx_complex operator + (const complex&, const lx_complex&) throw(); 00362 inline lx_complex operator + (const lx_complex&, const lx_real&) throw(); 00364 inline lx_complex operator + (const lx_real&, const lx_complex&) throw(); 00366 inline lx_complex operator + (const lx_complex&, const l_real&) throw(); 00368 inline lx_complex operator + (const l_real&, const lx_complex&) throw(); 00370 inline lx_complex operator + (const lx_complex&, const real&) throw(); 00372 inline lx_complex operator + (const real&, const lx_complex&) throw(); 00373 00375 inline lx_complex & operator +=(lx_complex &, const lx_complex &) throw(); 00377 inline lx_complex & operator +=(lx_complex &, const l_complex &) throw(); 00379 inline lx_complex & operator +=(lx_complex &, const complex &) throw(); 00381 inline lx_complex & operator +=(lx_complex &, const lx_real &) throw(); 00383 inline lx_complex & operator +=(lx_complex &, const l_real &) throw(); 00385 inline lx_complex & operator +=(lx_complex &, const real &) throw(); 00386 00388 inline lx_complex operator - (const lx_complex&, const lx_complex&) throw(); 00390 inline lx_complex operator - (const lx_complex&, const l_complex&) throw(); 00392 inline lx_complex operator - (const lx_complex&, const complex&) throw(); 00394 inline lx_complex operator - (const l_complex&, const lx_complex&) throw(); 00396 inline lx_complex operator - (const complex&, const lx_complex&) throw(); 00398 inline lx_complex operator - (const lx_complex&, const lx_real&) throw(); 00400 inline lx_complex operator - (const lx_complex&, const l_real&) throw(); 00402 inline lx_complex operator - (const lx_complex&, const real&) throw(); 00404 inline lx_complex operator - (const lx_real&, const lx_complex&) throw(); 00406 inline lx_complex operator - (const l_real&, const lx_complex&) throw(); 00408 inline lx_complex operator - (const real&, const lx_complex&) throw(); 00409 00411 inline lx_complex & operator -=(lx_complex &, const lx_complex &) throw(); 00413 inline lx_complex & operator -=(lx_complex &, const l_complex &) throw(); 00415 inline lx_complex & operator -=(lx_complex &, const complex &) throw(); 00417 inline lx_complex & operator -=(lx_complex &, const lx_real &) throw(); 00419 inline lx_complex & operator -=(lx_complex &, const l_real &) throw(); 00421 inline lx_complex & operator -=(lx_complex &, const real &) throw(); 00422 00424 inline lx_complex operator * (const lx_complex&, const lx_complex&) throw(); 00426 inline lx_complex operator * (const lx_complex&, const l_complex&) throw(); 00428 inline lx_complex operator * (const lx_complex&, const complex&) throw(); 00430 inline lx_complex operator * (const l_complex&, const lx_complex&) throw(); 00432 inline lx_complex operator * (const complex&, const lx_complex&) throw(); 00434 inline lx_complex operator * (const lx_complex&, const lx_real&) throw(); 00436 inline lx_complex operator * (const lx_complex&, const l_real&) throw(); 00438 inline lx_complex operator * (const lx_complex&, const real&) throw(); 00440 inline lx_complex operator * (const lx_real&, const lx_complex&) throw(); 00442 inline lx_complex operator * (const l_real&, const lx_complex&) throw(); 00444 inline lx_complex operator * (const real&, const lx_complex&) throw(); 00445 00447 inline lx_complex & operator *=(lx_complex &, const lx_complex &) throw(); 00449 inline lx_complex & operator *=(lx_complex &, const l_complex &) throw(); 00451 inline lx_complex & operator *=(lx_complex &, const complex &) throw(); 00453 inline lx_complex & operator *=(lx_complex &, const lx_real &) throw(); 00455 inline lx_complex & operator *=(lx_complex &, const l_real &) throw(); 00457 inline lx_complex & operator *=(lx_complex &, const real &) throw(); 00458 00460 inline lx_complex operator / (const lx_complex&, const lx_complex&) throw(); 00462 inline lx_complex operator / (const lx_complex&, const l_complex&) throw(); 00464 inline lx_complex operator / (const lx_complex&, const complex&) throw(); 00466 inline lx_complex operator / (const l_complex&, const lx_complex&) throw(); 00468 inline lx_complex operator / (const complex&, const lx_complex&) throw(); 00470 inline lx_complex operator / (const lx_complex&, const lx_real&) throw(); 00472 inline lx_complex operator / (const lx_complex&, const l_real&) throw(); 00474 inline lx_complex operator / (const lx_complex&, const real&) throw(); 00476 inline lx_complex operator / (const lx_real&, const lx_complex&) throw(); 00478 inline lx_complex operator / (const l_real&, const lx_complex&) throw(); 00480 inline lx_complex operator / (const real&, const lx_complex&) throw(); 00481 00483 inline lx_complex & operator /=(lx_complex &, const lx_complex &) throw(); 00485 inline lx_complex & operator /=(lx_complex &, const l_complex &) throw(); 00487 inline lx_complex & operator /=(lx_complex &, const complex &) throw(); 00489 inline lx_complex & operator /=(lx_complex &, const lx_real &) throw(); 00491 inline lx_complex & operator /=(lx_complex &, const l_real &) throw(); 00493 inline lx_complex & operator /=(lx_complex &, const real &) throw(); 00494 00495 00496 00497 // --------------------------------------------------------------------------- 00498 // ----- Elementary functions related to lx_complex 00499 // --------------------------------------------------------------------------- 00500 00502 lx_complex sqr(const lx_complex&) throw(); 00504 lx_complex sqrt(const lx_complex&) throw(); 00506 lx_complex sqrt(const lx_complex& ,int) throw(); 00508 lx_complex exp(const lx_complex&) throw(); 00510 lx_complex exp2(const lx_complex&) throw(); 00512 lx_complex exp10(const lx_complex&) throw(); 00514 lx_complex sin(const lx_complex&) throw(); 00516 lx_complex cos(const lx_complex&) throw(); 00518 lx_complex tan(const lx_complex&) throw(); 00520 lx_complex cot(const lx_complex&) throw(); 00522 lx_complex asin(const lx_complex&) throw(); 00524 lx_complex acos(const lx_complex&) throw(); 00526 lx_complex atan(const lx_complex&) throw(); 00528 lx_complex acot(const lx_complex&) throw(); 00530 lx_complex sinh(const lx_complex&) throw(); 00532 lx_complex cosh(const lx_complex&) throw(); 00534 lx_complex tanh(const lx_complex&) throw(); 00536 lx_complex coth(const lx_complex&) throw(); 00538 lx_complex asinh(const lx_complex&) throw(); 00540 lx_complex acosh(const lx_complex&) throw(); 00542 lx_complex atanh(const lx_complex&) throw(); 00544 lx_complex acoth(const lx_complex&) throw(); 00546 std::list<lx_complex>sqrt_all(const lx_complex&); 00548 lx_real arg(const lx_complex&) throw(); 00550 lx_real Arg(const lx_complex&) throw(); 00552 std::list<lx_complex>sqrt_all(const lx_complex&, int); 00554 lx_complex ln(const lx_complex&) throw(); 00556 lx_complex log2(const lx_complex&) throw(); 00558 lx_complex log10(const lx_complex&) throw(); 00560 lx_complex power_fast(const lx_complex&, const real&) throw(); 00562 lx_complex power(const lx_complex&, const real&) throw(); 00564 lx_complex pow(const lx_complex&, const lx_real&) throw(); 00566 lx_complex pow(const lx_complex&, const lx_complex&) throw(); 00567 00569 lx_complex sqrt1px2(const lx_complex&) throw(); 00571 lx_complex sqrt1mx2(const lx_complex&) throw(); 00573 lx_complex sqrtx2m1(const lx_complex&) throw(); 00575 lx_complex sqrtp1m1(const lx_complex&) throw(); 00577 lx_complex expm1(const lx_complex&) throw(); 00579 lx_complex lnp1(const lx_complex&) throw(); 00580 00581 } // end namespace cxsc 00582 00583 #include "lx_complex.inl" 00584 00585 #endif // _CXSC_LX_COMPLEX_HPP_INCLUDED
1.7.5.1