C-XSC - A C++ Class Library for Extended Scientific Computing: complex.hpp Source File

00001 /*
00002 **  CXSC is a C++ library for eXtended Scientific Computing (V 2.5.1)
00003 **
00004 **  Copyright (C) 1990-2000 Institut fuer Angewandte Mathematik,
00005 **                          Universitaet Karlsruhe, Germany
00006 **            (C) 2000-2011 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: complex.hpp,v 1.28 2011/06/07 15:17:38 cxsc Exp $ */
00025 
00026 #ifndef _CXSC_COMPLEX_HPP_INCLUDED
00027 #define _CXSC_COMPLEX_HPP_INCLUDED
00028 
00029 #include <iostream>
00030 #include <string>
00031 #include <list>  // Blomquist, 02.12.2008;
00032 #include "compiler.h"
00033 #include "except.hpp"
00034 #include "real.hpp"
00035 
00036 namespace cxsc {
00037 
00038 class cvector;
00039 class cmatrix;
00040 class cvector_slice;
00041 class cmatrix_slice;
00042 
00043 
00045 
00049 class complex
00050 {  
00051    private:
00052       // ---- Datenelemente ---------------------------------------
00053       real  re;
00054       real  im;
00055 
00056    public:
00057       // ---- Constructors  ---------------------------------------
00059       complex(void)  throw ()           {}
00061       complex(const real & a,const real & b) throw () : re(a), im(b) { }
00062       
00064       inline complex & operator= (const real & r) throw();
00065 
00066       // ---- Type-Casts    ---------------------------------------
00067 
00069       explicit inline complex(const real &r) throw() : re(r),im(0.0)     { }
00070 
00071 
00072 //     friend inline complex _complex(const real &a) throw ()             { return complex(a,0.0); }
00073 //     friend inline complex _complex(const real &a,const real &b) throw(){ return complex(a,b); }
00074 
00075 
00076       // The following are defined in the specific vector, matrix-files
00077 #if(CXSC_INDEX_CHECK) 
00078 
00079       explicit INLINE complex(const cvector &)       throw (ERROR_CVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_CVECTOR_USE_OF_UNINITIALIZED_OBJ);
00081       explicit INLINE complex(const cvector_slice &) throw (ERROR_CVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_CVECTOR_USE_OF_UNINITIALIZED_OBJ);
00083       explicit INLINE complex(const cmatrix &)       throw (ERROR_CMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_CMATRIX_USE_OF_UNINITIALIZED_OBJ);
00085       explicit INLINE complex(const cmatrix_slice &) throw (ERROR_CMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_CMATRIX_USE_OF_UNINITIALIZED_OBJ);
00087 
00092       friend INLINE complex _complex(const cvector &)       throw (ERROR_CVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_CVECTOR_USE_OF_UNINITIALIZED_OBJ);
00094 
00099       friend INLINE complex _complex(const cvector_slice &) throw (ERROR_CVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_CVECTOR_USE_OF_UNINITIALIZED_OBJ);
00101 
00106       friend INLINE complex _complex(const cmatrix &)       throw (ERROR_CMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_CMATRIX_USE_OF_UNINITIALIZED_OBJ);
00108 
00113       friend INLINE complex _complex(const cmatrix_slice &) throw (ERROR_CMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_CMATRIX_USE_OF_UNINITIALIZED_OBJ);
00114 #else
00115 
00116       explicit INLINE complex(const cvector &)       throw ();
00118       explicit INLINE complex(const cvector_slice &) throw ();
00120       explicit INLINE complex(const cmatrix &)       throw ();
00122       explicit INLINE complex(const cmatrix_slice &) throw ();
00124 
00129       friend INLINE complex _complex(const cvector &)       throw ();
00131 
00136       friend INLINE complex _complex(const cvector_slice &) throw ();
00138 
00143       friend INLINE complex _complex(const cmatrix &)       throw ();
00145 
00150       friend INLINE complex _complex(const cmatrix_slice &) throw ();
00151 #endif
00152 
00153       explicit        complex(const cdotprecision &) throw();
00155 
00160       friend inline complex _complex(const cdotprecision &a) throw() { return complex(a); }
00161       
00163       complex & operator =(const cdotprecision &) throw();
00164 
00165       // ---- Input/Output  ---------------------------------------
00167       friend std::ostream & operator <<(std::ostream &,const complex &) throw();
00169       friend std::istream & operator >>(std::istream &,complex &)       throw();
00171       friend std::string &  operator <<(std::string &,const complex &)  throw();
00173       friend std::string &  operator >>(std::string &,complex &)        throw();
00175       friend void           operator >>(const char *,complex &)         throw();
00177       friend void           operator >>(const std::string &,complex &)  throw();
00178 
00179       // ---- Std.Operators ---------------------------------------
00181       friend inline complex operator -(const complex &) throw ();
00183       friend inline complex operator +(const complex &) throw ();
00184 
00186       friend inline complex operator +(const complex &,const complex &) throw();
00188       friend inline complex operator -(const complex &,const complex &) throw();
00190       friend complex operator *(const complex &,const complex &) throw();
00192       friend complex operator /(const complex &,const complex &) throw();
00193 
00195       friend inline complex & operator +=(complex &, const complex &) throw();
00197       friend inline complex & operator -=(complex &, const complex &) throw();
00199       friend inline complex & operator *=(complex &, const complex &) throw();
00201       friend inline complex & operator /=(complex &, const complex &) throw();
00202 
00204       friend inline complex operator +(const complex &,const real &) throw();
00206       friend inline complex operator +(const real &,const complex &) throw();
00208       friend inline complex operator -(const complex &,const real &) throw();
00210       friend inline complex operator -(const real &,const complex &) throw();
00212       friend inline complex operator *(const complex &,const real &) throw();
00214       friend inline complex operator *(const real &,const complex &) throw();
00216       friend inline complex operator /(const complex &,const real &) throw();
00218       friend inline complex operator /(const real &,const complex &) throw();
00219 
00221       friend inline complex & operator +=(complex &, const real &) throw();
00223       friend inline complex & operator -=(complex &, const real &) throw();
00225       friend inline complex & operator *=(complex &, const real &) throw();
00227       friend inline complex & operator /=(complex &, const real &) throw();
00228 
00229       // ---- Comp.Operat.  ---------------------------------------
00230 //             inline       operator void *() const throw() { if(re) return (void *)1; if(im) return (void *)1; else return 0; }
00232       friend inline bool operator!  (const complex & a)                    throw();
00234       friend inline bool operator== (const complex & a, const complex & b) throw();
00236       friend inline bool operator!= (const complex & a, const complex & b) throw();
00238       friend inline bool operator== (const complex & a, const real & b)    throw();
00240       friend inline bool operator== (const real & a, const complex & b)    throw();
00242       friend inline bool operator!= (const complex & a, const real & b)    throw();
00244       friend inline bool operator!= (const real & a, const complex & b)    throw();
00245       
00247       friend        bool operator== (const complex & a, const dotprecision & b)    throw();
00249       friend        bool operator== (const dotprecision & a, const complex & b)    throw();
00251       friend        bool operator!= (const complex & a, const dotprecision & b)    throw();
00253       friend        bool operator!= (const dotprecision & a, const complex & b)    throw();
00254 
00255       // ---- Others   -------------------------------------------
00257       friend inline real & Re(complex & a); // { return a.re; }
00259       friend inline real   Re(const complex & a); // { return a.re; }
00261       friend inline real & Im(complex & a); // { return a.im; }
00263       friend inline real   Im(const complex & a); // { return a.im; }
00264       
00266       friend inline complex & SetRe(complex & a,const real & b); // { a.re=b; return a; }
00268       friend inline complex & SetIm(complex & a,const real & b); // { a.im=b; return a; } 
00269 
00271       friend        real abs(complex) throw();
00273       friend        real abs2(const complex &) throw();
00275       friend inline complex conj(const complex &) throw();
00276 
00277 // -------------- Directed rounding, Blomquist 07.11.02 --------------------
00278 
00280     friend complex divn (const complex &, const complex &);
00282     friend complex divd (const complex &, const complex &);
00284     friend complex divu (const complex &, const complex &);
00286     friend inline complex divd(const complex &, const real &) throw();
00288     friend inline complex divu(const complex &, const real &) throw();
00290     friend inline complex divd(const real &, const complex &) throw();
00292     friend inline complex divu(const real &, const complex &) throw();
00293 
00295     friend complex muld (const complex &, const complex &) throw();
00297     friend complex mulu (const complex &, const complex &) throw();
00299     friend inline complex muld(const complex &, const real &) throw();
00301     friend inline complex mulu(const complex &, const real &) throw();
00303     friend inline complex muld(const real &, const complex &) throw();
00305     friend inline complex mulu(const real &, const complex &) throw();
00306 
00307 
00309     friend inline complex addd(const complex &, const complex &) throw();
00311     friend inline complex addu(const complex &, const complex &) throw();
00313     friend inline complex addd(const complex &, const real &) throw();
00315     friend inline complex addu(const complex &, const real &) throw();
00317     friend inline complex addd(const real &, const complex &) throw();
00319     friend inline complex addu(const real &, const complex &) throw();
00320 
00321 
00323     friend inline complex subd(const complex &, const complex &) throw();
00325     friend inline complex subu(const complex &, const complex &) throw();
00327     friend inline complex subd(const complex &, const real &) throw();
00329     friend inline complex subu(const complex &, const real &) throw();
00331     friend inline complex subd(const real &, const complex &) throw();
00333     friend inline complex subu(const real &, const complex &) throw();
00334          
00336     complex & operator = (const lx_complex&) throw(); // Blomquist, 12.11.2008;
00338     complex & operator = (const l_complex&)  throw(); // Blomquist, 12.11.2008;
00339 }; // end class complex
00340 
00341 
00342 // ---------------------------------------------------------------------------
00343 // ----                                                                   ----
00344 // ---- friend functions of class real (not inline)                       ----
00345 // ----                                                                   ----
00346 // ---------------------------------------------------------------------------
00347 
00348 complex divn (const complex &, const complex &);
00349 complex divd (const complex &, const complex &);
00350 complex divu (const complex &, const complex &);
00351 complex muld (const complex &, const complex &) throw();
00352 complex mulu (const complex &, const complex &) throw();
00353 
00354 // ---------------------------------------------------------------------------
00355 // ----                                                                   ----
00356 // ---- global functions associated with class real                       ----
00357 // ----                                                                   ----
00358 // ---------------------------------------------------------------------------
00359 
00361 
00366 inline complex _complex(const real &a) throw ()             { return complex(a,0.0); }
00368 
00373 inline complex _complex(const real &a,const real &b) throw(){ return complex(a,b); }
00374 
00376 inline real & Re(complex & z) { return z.re; }
00378 inline real   Re(const complex & z) { return z.re; }
00380 inline real & Im(complex & z) { return z.im; }
00382 inline real   Im(const complex & z) { return z.im; }
00383 
00385 inline complex & SetRe(complex & z,const real & b) { z.re=b; return z; }
00387 inline complex & SetIm(complex & z,const real & b) { z.im=b; return z; } 
00388 
00390 inline complex sqr (const complex&) throw();
00392 complex sqrt(const complex&) throw();
00394 complex sqrtp1m1(const complex&) throw();
00396 complex sqrt1px2(const complex&) throw();
00398 complex sqrtx2m1(const complex&) throw();
00400 complex sqrt1mx2(const complex&) throw();
00401 
00403 complex exp(const complex&) throw();
00405 complex expm1(const complex&) throw();
00407 complex exp2(const complex&) throw();
00409 complex exp10(const complex&) throw();
00411 complex sin(const complex&) throw();
00413 complex cos(const complex&) throw();
00415 complex tan(const complex&) throw();
00417 complex cot(const complex&) throw();
00419 complex asin(const complex&) throw();
00421 complex acos(const complex&) throw();
00423 complex atan(const complex&) throw();
00425 complex acot(const complex&) throw();
00427 complex sinh(const complex&) throw();
00429 complex cosh(const complex&) throw();
00431 complex tanh(const complex&) throw();
00433 complex coth(const complex&) throw();
00435 complex asinh(const complex&) throw();
00437 complex acosh(const complex&) throw();
00439 complex atanh(const complex&) throw();
00441 complex acoth(const complex&) throw();
00443 std::list<complex>sqrt_all(const complex&);
00445 complex sqrt(const complex&, int) throw();
00447 real arg(const complex&) throw();
00449 real Arg(const complex&) throw();
00451 std::list<complex>sqrt_all(const complex&, int);
00453 complex ln(const complex&) throw();
00455 complex lnp1(const complex&) throw();
00457 complex log2(const complex&) throw();
00459 complex log10(const complex&) throw();
00461 complex power(const complex&,int) throw();
00463 complex power_fast(const complex&, int) throw();
00465 complex pow(const complex&, const real&) throw();
00467 complex pow(const complex&, const complex&) throw();
00468 
00469 } // namespace cxsc 
00470 
00471 
00472 #include "complex.inl"
00473 
00474 #endif
00475