- Generated by
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 /* CVS $Id: l_complex.hpp,v 1.19 2014/01/30 17:23:46 cxsc Exp $ */ 00024 00025 #ifndef _CXSC_L_COMPLEX_HPP_INCLUDED 00026 #define _CXSC_L_COMPLEX_HPP_INCLUDED 00027 00028 #include <iostream> 00029 #include <string> 00030 00031 #include "except.hpp" 00032 #include "complex.hpp" 00033 #include "l_real.hpp" 00034 #include "l_rmath.hpp" 00035 #include "cdot.hpp" 00036 00037 namespace cxsc { 00038 00040 00045 class l_complex 00046 { 00047 private: 00048 // ------------- Datenelemente ------------------------------------------- 00049 l_real re, im; 00050 00051 public: 00053 l_complex _l_complex(const cdotprecision &); 00054 // ------------- Constructors -------------------------------------------- 00056 l_complex(void) throw() {} 00058 l_complex(const l_real& a, const l_real& b) throw() : re(a), im(b) { } 00060 l_complex(const real& a, const real& b) throw() : re(a), im(b) { } 00061 00063 l_complex & operator = (const l_real & lr) throw() 00064 { re = lr; im = 0; return *this; } 00066 l_complex & operator = (const real & r) throw() 00067 { re = r; im = 0; return *this; } 00069 l_complex & operator = (const complex & c) throw() 00070 { re = Re(c); im = Im(c); return *this; } 00072 l_complex & operator = (const dotprecision & d) throw() 00073 { re = d; im = 0.0; return *this; } 00075 l_complex & operator = (const cdotprecision & cd) throw() 00076 { re = Re(_l_complex(cd)); im = Im(_l_complex(cd)); return *this; } 00077 00079 l_complex & operator = (const lx_complex &) throw(); 00080 00081 // ------------- Type-Casts ---------------------------------------------- 00083 explicit inline l_complex(const l_real &r) throw() : re(r), im(0.0) { } 00085 explicit inline l_complex(const real &r) throw() : re(r), im(0.0) { } 00087 explicit inline l_complex(const complex &r) throw() : re(Re(r)), im(Im(r)) 00088 { } 00090 explicit inline l_complex(const dotprecision &d) throw() 00091 : re(d), im(0.0) { } 00093 explicit inline l_complex(const cdotprecision &cd) throw() 00094 : re(Re(_l_complex(cd))), im(Im(_l_complex(cd))) { } 00095 00096 // friend inline l_complex _l_complex(const l_real &a) throw() 00097 // { return l_complex(a); } 00098 // friend inline l_complex _l_complex(const l_real &a, const l_real &b) 00099 // throw() { return l_complex(a,b); } 00100 // friend inline l_complex _l_complex(const real &a) throw() 00101 // { return l_complex(a); } 00102 // friend inline l_complex _l_complex(const real &a, const real &b) 00103 // throw() { return l_complex(a,b); } 00104 // friend inline l_complex _l_complex(const complex &c) 00105 // throw() { return l_complex(c); } 00106 // friend inline l_complex _l_complex(const dotprecision &d) 00107 // throw() { return l_complex(d); } 00113 friend inline l_complex _l_complex(const cdotprecision &cd) 00114 throw() { return l_complex(cd); } 00115 00116 // ---------------------------------------------------------------------- 00118 friend int StagPrec(const l_complex&) throw(); 00119 00120 // ------------- Arithmetic Operators --------------------------------------- 00121 // ---------------------------------------------------------------------- 00122 // ------------- Unary Operators ---------------------------------------- 00123 00125 friend l_complex operator-(const l_complex&); 00127 friend l_complex operator+(const l_complex&); 00128 00129 // ------------- Binary Operators --------------------------------------- 00130 // ----------------- l_complex +/- l_complex ---------------------------- 00132 friend inline l_complex operator + 00133 (const l_complex &, const l_complex &) throw(); 00134 00136 friend inline l_complex operator - 00137 (const l_complex &, const l_complex &) throw(); 00138 00139 // ----------------- l_complex + complex -------------------------------- 00141 inline l_complex operator + (const complex &) const throw(); 00142 00144 friend inline l_complex operator + 00145 (const complex &, const l_complex &) throw(); 00146 00147 // ---------------- l_complex + real ------------------------------------ 00149 inline l_complex operator + (const real &) const throw(); 00150 00152 friend inline l_complex operator + 00153 (const real &, const l_complex &) throw(); 00154 00155 // ---------------- l_complex + l_real ---------------------------------- 00157 inline l_complex operator + (const l_real &) const throw(); 00158 00160 friend inline l_complex operator + 00161 (const l_real &, const l_complex &) throw(); 00162 00163 // ---------------- l_complex - l_real ---------------------------------- 00165 inline l_complex operator - (const l_real &) const throw(); 00166 00168 friend inline l_complex operator - 00169 (const l_real &, const l_complex &) throw(); 00170 00171 // ----------------- l_complex - complex ------------------------------- 00173 inline l_complex operator - (const complex &) const throw(); 00174 00176 friend inline l_complex operator - 00177 (const complex &, const l_complex &) throw(); 00178 00179 // ---------------- l_complex - real ------------------------------------ 00181 inline l_complex operator - (const real &) const throw(); 00182 00184 friend inline l_complex operator - 00185 (const real &, const l_complex &) throw(); 00186 00187 // ---------------- l_complex + cdotprecision --------------------------- 00189 friend cdotprecision operator+ 00190 (const l_complex &, const cdotprecision &) throw(); 00191 00193 friend cdotprecision operator+ 00194 (const cdotprecision &, const l_complex &) throw(); 00195 00196 // ---------------- l_complex - cdotprecision --------------------------- 00198 friend cdotprecision operator- 00199 (const l_complex &, const cdotprecision &) throw(); 00200 00202 friend cdotprecision operator- 00203 (const cdotprecision &, const l_complex &) throw(); 00204 00205 // ---------------- l_complex + dotprecision ---------------------------- 00207 friend cdotprecision operator+ 00208 (const l_complex &, const dotprecision &) throw(); 00209 00211 friend cdotprecision operator+ 00212 (const dotprecision &, const l_complex &) throw(); 00213 00214 // ---------------- l_complex - dotprecision ---------------------------- 00216 friend cdotprecision operator- 00217 (const l_complex &, const dotprecision &) throw(); 00218 00220 friend cdotprecision operator- 00221 (const dotprecision &, const l_complex &) throw(); 00222 00223 00224 // ------------- Multiplication --------------------------------------------- 00225 // ------------------ l_complex * l_complex --------------------------------- 00226 00228 friend l_complex operator * (const l_complex& a, const l_complex& b) 00229 throw(); 00230 00231 // ------------------ l_complex * complex ----------------------------------- 00233 friend l_complex operator * (const l_complex& a, const complex& b) 00234 throw(); 00235 00237 friend l_complex operator * ( const complex& b, const l_complex& a ) 00238 throw(); 00239 00240 // ------------------ l_complex * real --------------------------------------- 00242 inline l_complex operator * (const real &) const throw(); 00243 00245 friend inline l_complex operator * 00246 (const real &, const l_complex &) throw(); 00247 00248 // ------------------ l_complex * l_real ------------------------------------- 00250 inline l_complex operator * (const l_real &) const throw(); 00251 00253 friend inline l_complex operator * 00254 (const l_real &, const l_complex &) throw(); 00255 00256 00257 // ----------------- Others -------------------------------------------------- 00259 friend l_real & Re(l_complex& a); // { return a.re; } 00261 friend l_real Re(const l_complex& a); // { return a.re; } 00263 friend l_real & Im(l_complex& a); // { return a.im; } 00265 friend l_real Im(const l_complex& a); // { return a.im; } 00266 00268 friend inline l_complex conj(const l_complex&) throw(); // conjugated value 00270 friend l_complex & SetRe(l_complex & a,const l_real & b); 00271 // { a.re=b; return a; } // The real part of a is substituted by b. 00272 // SetRe(lc,lr); --> Re(lc)=lr; 00273 // lc1 = SetRe(lc,lr); --> Re(lc)=lr; and lc1 = lc; 00275 friend l_complex & SetIm(l_complex & a,const l_real & b); 00276 // { a.im=b; return a; } // See SetRe(...); 00277 00278 00279 // ----- accumulate(cdotprecision,l_complex,l_complex|complex|real|l_real ---- 00281 friend void accumulate(cdotprecision&, const l_complex&, 00282 const l_complex&) throw(); 00283 00285 friend void accumulate(cdotprecision&, const l_complex&, 00286 const complex&) throw(); 00287 00289 friend void accumulate(cdotprecision&, const l_complex&, 00290 const real&) throw(); 00291 00293 friend void accumulate(cdotprecision&, const l_complex&, 00294 const l_real&) throw(); 00295 00296 // ---------------- cdotprecision +(-)= l_complex ---------------------------- 00298 friend inline cdotprecision & operator += (cdotprecision &cd, 00299 const l_complex &lc) throw(); 00301 friend inline cdotprecision & operator -= (cdotprecision &cd, 00302 const l_complex &lc) throw(); 00303 00304 // ---------------- l_complex +(-)= l_complex|complex|real|l_real ------------ 00306 friend inline l_complex & operator += (l_complex &,const l_complex &) throw(); 00308 friend inline l_complex & operator -= (l_complex &,const l_complex &) throw(); 00310 friend inline l_complex & operator += (l_complex &,const complex &) throw(); 00312 friend inline l_complex & operator -= (l_complex &,const complex &) throw(); 00314 friend inline l_complex & operator += (l_complex &,const real &) throw(); 00316 friend inline l_complex & operator -= (l_complex &,const real &) throw(); 00318 friend inline l_complex & operator += (l_complex &,const l_real &) throw(); 00320 friend inline l_complex & operator -= (l_complex &,const l_real &) throw(); 00321 00322 // ---------------- l_complex *= l_complex|complex|real|l_real --------------- 00324 friend inline l_complex & operator *= (l_complex &,const l_complex &) throw(); 00326 friend inline l_complex & operator *= (l_complex &,const complex &) throw(); 00328 friend inline l_complex & operator *= (l_complex &,const real &) throw(); 00330 friend inline l_complex & operator *= (l_complex &,const l_real &) throw(); 00331 00332 // ---------------- Compare Operators ---------------------------------------- 00333 friend inline bool operator! (const l_complex &) throw(); 00335 friend inline bool operator== (const l_complex &, const l_complex &) throw(); 00337 friend inline bool operator!= (const l_complex &, const l_complex &) throw(); 00339 friend inline bool operator== (const l_complex &, const complex &) throw(); 00341 friend inline bool operator== (const complex &, const l_complex &) throw(); 00343 friend inline bool operator!= (const l_complex &, const complex &) throw(); 00345 friend inline bool operator!= (const complex &, const l_complex &) throw(); 00347 friend inline bool operator== (const l_complex &, const real &) throw(); 00349 friend inline bool operator== (const real &, const l_complex &) throw(); 00351 friend inline bool operator!= (const l_complex &, const real &) throw(); 00353 friend inline bool operator!= (const real &, const l_complex &) throw(); 00355 friend inline bool operator== (const l_complex &, const l_real &) throw(); 00357 friend inline bool operator== (const l_real &, const l_complex &) throw(); 00359 friend inline bool operator!= (const l_complex &, const l_real &) throw(); 00361 friend inline bool operator!= (const l_real &, const l_complex &) throw(); 00363 friend inline bool operator== (const l_complex &, const dotprecision &) 00364 throw(); 00366 friend inline bool operator== (const dotprecision &, const l_complex &) 00367 throw(); 00369 friend inline bool operator!= (const l_complex &, const dotprecision &) 00370 throw(); 00372 friend inline bool operator!= (const dotprecision &, const l_complex &) 00373 throw(); 00374 00376 friend inline bool operator ==(const cdotprecision &, const l_complex &) 00377 throw(); // {l_complex.inl} 00379 friend inline bool operator ==(const l_complex &, const cdotprecision &) 00380 throw(); // {l_complex.inl} 00382 friend inline bool operator !=(const cdotprecision &, const l_complex &) 00383 throw(); // {l_complex.inl} 00385 friend inline bool operator !=(const l_complex &, const cdotprecision &) 00386 throw(); // {l_complex.inl} 00387 00388 // -------------- Division: Directed rounding, Blomquist 28.11.02 ------------ 00389 00391 friend l_complex divn (const l_complex &, const l_complex &); 00393 friend l_complex divd (const l_complex &, const l_complex &); 00395 friend l_complex divu (const l_complex &, const l_complex &); 00396 00397 // -------------- Division: Blomquist 28.11.02 ------------------------------ 00399 friend l_complex operator / (const l_complex &,const l_complex &) throw(); 00400 00402 friend inline l_complex operator / (const l_complex & a, 00403 const complex & b) throw(); 00405 friend inline l_complex operator / (const l_complex & a, 00406 const l_real & b) throw(); 00408 friend inline l_complex operator / (const l_complex & a, 00409 const real & b) throw(); 00410 00412 friend inline l_complex operator / (const complex& a, 00413 const l_complex& b) throw(); 00415 friend inline l_complex operator / (const real& a, 00416 const l_complex& b) throw(); 00418 friend inline l_complex operator / (const l_real& a, 00419 const l_complex& b) throw(); 00420 00422 friend inline l_complex& operator /=(l_complex&,const l_complex&) throw(); 00424 friend inline l_complex& operator /=(l_complex&,const complex&) throw(); 00426 friend inline l_complex& operator /=(l_complex&,const real&) throw(); 00428 friend inline l_complex& operator /=(l_complex&,const l_real&) throw(); 00429 00431 friend l_real abs2(const l_complex &a) throw(); // a.re*a.re + a.im*a.im; 00433 friend l_real abs (const l_complex &z) throw(); 00434 00435 // ----------------------- Output -------------------------------------------- 00436 00438 friend std::ostream& operator << (std::ostream& s,const l_complex& z ) throw() 00439 // A complex number z of type l_complex is written to the output channel. 00440 { 00441 s << '(' 00442 << z.re << ", " 00443 << z.im 00444 << ')'; 00445 return s; 00446 } 00447 00449 friend std::string & operator << (std::string &s, const l_complex& a) throw() 00450 // The value of a variable a of type l_complex is copied to a string s. 00451 // s has the form: (Re(a),Im(a)) 00452 { 00453 s+='('; 00454 s << a.re; 00455 s+=", "; 00456 s << a.im; 00457 s+=')'; 00458 return s; 00459 } 00460 00461 // ----------------------- Input --------------------------------------------- 00462 00464 friend std::istream & operator >> (std::istream &s, l_complex &a) throw() 00465 // An input of a complex number z of the form (Re(z),Im(z)) is copied to 00466 // the variable a of type l_complex. 00467 { 00468 char c; 00469 00470 skipeolnflag = inpdotflag = true; 00471 c = skipwhitespacessinglechar (s, '('); 00472 if (inpdotflag) 00473 s.putback(c); 00474 00475 s >> a.re; 00476 00477 skipeolnflag = inpdotflag = true; 00478 c = skipwhitespacessinglechar (s, ','); 00479 if (inpdotflag) s.putback(c); 00480 00481 s >> a.im >> RestoreOpt; 00482 00483 if (!waseolnflag) 00484 { 00485 skipeolnflag = false, inpdotflag = true; 00486 c = skipwhitespaces (s); 00487 if (inpdotflag && c != ')') 00488 s.putback(c); 00489 } 00490 return s; 00491 } 00492 00494 friend std::string & operator >> (std::string &s, l_complex &a) throw() 00495 // A complex number z of the form (Re(z),Im(z)), represented in a string s 00496 // is copied to a of type l_complex. 00497 { 00498 s = skipwhitespacessinglechar (s, '('); 00499 s >> SaveOpt >> a.re; 00500 s = skipwhitespacessinglechar (s, ','); 00501 s >> a.im >> RestoreOpt; 00502 s = skipwhitespaces (s); 00503 00504 if (s[0] == ')') 00505 s.erase(0,1); 00506 return s; 00507 } 00508 00509 }; // end of class l_complex 00510 00511 inline l_complex _l_complex(const l_real &a) throw() 00512 { return l_complex(a); } 00513 inline l_complex _l_complex(const l_real &a, const l_real &b) 00514 throw() { return l_complex(a,b); } 00515 inline l_complex _l_complex(const real &a) throw() 00516 { return l_complex(a); } 00517 inline l_complex _l_complex(const real &a, const real &b) 00518 throw() { return l_complex(a,b); } 00519 inline l_complex _l_complex(const complex &c) 00520 throw() { return l_complex(c); } 00521 inline l_complex _l_complex(const dotprecision &d) 00522 throw() { return l_complex(d); } 00523 inline l_complex conj(const l_complex&) throw(); 00524 //inline l_complex _l_complex(const cdotprecision &cd) 00525 // throw() { return l_complex(cd); } 00526 00527 l_real & Re(l_complex& a); 00528 l_real Re(const l_complex& a); 00529 l_real & Im(l_complex& a); 00530 l_real Im(const l_complex& a); 00531 00532 l_complex & SetRe(l_complex & a,const l_real & b); 00533 //{ a.re=b; return a; } // The real part of a is substituted by b. 00534 // SetRe(lc,lr); --> Re(lc)=lr; 00535 // lc1 = SetRe(lc,lr); --> Re(lc)=lr; and lc1 = lc; 00536 l_complex & SetIm(l_complex & a,const l_real & b); 00537 // { a.im=b; return a; } // See SetRe(...); 00538 00539 l_complex _l_complex(const cdotprecision &) throw(); 00540 00541 } // end namespace cxsc 00542 00543 #include "l_complex.inl" 00544 00545 #endif // _CXSC_L_COMPLEX_HPP_INCLUDED
1.7.5.1