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00001 /******************************************************************************** 00002 * * 00003 * D o u b l e - P r e c i s i o n C o m p l e x N u m b e r * 00004 * * 00005 ********************************************************************************* 00006 * Copyright (C) 2006,2009 by Jeroen van der Zijp. All Rights Reserved. * 00007 ********************************************************************************* 00008 * This library is free software; you can redistribute it and/or modify * 00009 * it under the terms of the GNU Lesser General Public License as published by * 00010 * the Free Software Foundation; either version 3 of the License, or * 00011 * (at your option) any later version. * 00012 * * 00013 * This library is distributed in the hope that it will be useful, * 00014 * but WITHOUT ANY WARRANTY; without even the implied warranty of * 00015 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * 00016 * GNU Lesser General Public License for more details. * 00017 * * 00018 * You should have received a copy of the GNU Lesser General Public License * 00019 * along with this program. If not, see <http://www.gnu.org/licenses/> * 00020 ********************************************************************************* 00021 * $Id: FXComplexd.h,v 1.13 2009/01/26 09:40:52 fox Exp $ * 00022 ********************************************************************************/ 00023 #ifndef FXCOMPLEXD_H 00024 #define FXCOMPLEXD_H 00025 00026 00027 namespace FX { 00028 00029 00030 /// Double-precision complex 00031 class FXAPI FXComplexd { 00032 public: 00033 FXdouble re; 00034 FXdouble im; 00035 public: 00036 00037 /// Default constructor; value is not initialized 00038 FXComplexd(){ } 00039 00040 /// Construct from real 00041 FXComplexd(FXdouble r):re(r),im(0.0){ } 00042 00043 /// Construct from components 00044 FXComplexd(FXdouble r,FXdouble i):re(r),im(i){ } 00045 00046 /// Initialize from another complex 00047 FXComplexd(const FXComplexd& c):re(c.re),im(c.im){ } 00048 00049 /// Set value from real 00050 FXComplexd& set(FXdouble r){ re=r; im=0.0; return *this; } 00051 00052 /// Set value from components 00053 FXComplexd& set(FXdouble r,FXdouble i){ re=r; im=i; return *this;} 00054 00055 /// Set value from another complex 00056 FXComplexd& set(const FXComplexd& c){ re=c.re; im=c.im; return *this;} 00057 00058 /// Test for non-zero 00059 operator FXbool() const { return (re!=0.0) || (im!=0.0); } 00060 00061 /// Test if zero 00062 FXbool operator!() const { return (re==0.0) && (im==0.0); } 00063 00064 /// Squared modulus 00065 FXdouble modulus2() const { return re*re+im*im; } 00066 00067 /// Modulus or absolute value of complex 00068 FXdouble modulus() const { return sqrt(modulus2()); } 00069 00070 /// Argument of complex 00071 FXdouble argument() const { return atan2(im,re); } 00072 00073 /// Return a non-const reference to the ith element 00074 FXdouble& operator[](FXint i){ return (&re)[i]; } 00075 00076 /// Return a const reference to the ith element 00077 const FXdouble& operator[](FXint i) const { return (&re)[i]; } 00078 00079 /// Unary 00080 FXComplexd operator+() const { return *this; } 00081 FXComplexd operator-() const { return FXComplexd(-re,-im); } 00082 00083 /// Assignment from real 00084 FXComplexd& operator=(const FXdouble r){ return set(r); } 00085 00086 /// Assignment from another complex 00087 FXComplexd& operator=(const FXComplexd& c){ return set(c); } 00088 00089 /// Assigning operators with real 00090 FXComplexd& operator+=(FXdouble r){ re+=r; return *this; } 00091 FXComplexd& operator-=(FXdouble r){ re-=r; return *this; } 00092 FXComplexd& operator*=(FXdouble r){ re*=r; im*=r; return *this; } 00093 FXComplexd& operator/=(FXdouble r){ re/=r; im/=r; return *this; } 00094 00095 /// Assigning operators with another complex 00096 FXComplexd& operator+=(const FXComplexd& c){ return set(re+c.re,im+c.im); } 00097 FXComplexd& operator-=(const FXComplexd& c){ return set(re-c.re,im-c.im); } 00098 FXComplexd& operator*=(const FXComplexd& c){ return set(re*c.re-im*c.im,re*c.im+im*c.re); } 00099 FXComplexd& operator/=(const FXComplexd& c){ FXdouble m=c.modulus2(); return set((re*c.re+im*c.im)/m,(im*c.re-re*c.im)/m); } 00100 00101 /// Equality between one complex and another 00102 FXbool operator==(const FXComplexd& c) const { return re==c.re && im==c.im; } 00103 FXbool operator!=(const FXComplexd& c) const { return re!=c.re || im!=c.im; } 00104 00105 /// Return complex complex conjugate 00106 friend inline FXComplexd conjugate(const FXComplexd& c); 00107 00108 /// Return complex number from modulus and argument 00109 friend inline FXComplexd polar(FXdouble mod,FXdouble arg); 00110 00111 /// Returns the complex base e exponential of c 00112 friend inline FXComplexd exponent(const FXComplexd& c); 00113 00114 /// Returns the complex base e logarithm of c 00115 friend inline FXComplexd logarithm(const FXComplexd& c); 00116 00117 /// Equality between one complex and real 00118 friend inline FXbool operator==(const FXComplexd& c,FXdouble r); 00119 friend inline FXbool operator!=(const FXComplexd& c,FXdouble r); 00120 00121 /// Equality between one real and complex 00122 friend inline FXbool operator==(FXdouble r,const FXComplexd& c); 00123 friend inline FXbool operator!=(FXdouble r,const FXComplexd& c); 00124 00125 /// Operators between one complex and another 00126 friend inline FXComplexd operator+(const FXComplexd& a,const FXComplexd& b); 00127 friend inline FXComplexd operator-(const FXComplexd& a,const FXComplexd& b); 00128 friend inline FXComplexd operator*(const FXComplexd& a,const FXComplexd& b); 00129 friend inline FXComplexd operator/(const FXComplexd& a,const FXComplexd& b); 00130 00131 /// Operators between complex and real 00132 friend inline FXComplexd operator+(const FXComplexd& a,FXdouble b); 00133 friend inline FXComplexd operator-(const FXComplexd& a,FXdouble b); 00134 friend inline FXComplexd operator*(const FXComplexd& a,FXdouble b); 00135 friend inline FXComplexd operator/(const FXComplexd& a,FXdouble b); 00136 00137 /// Operators between real and complex 00138 friend inline FXComplexd operator+(FXdouble a,const FXComplexd& b); 00139 friend inline FXComplexd operator-(FXdouble a,const FXComplexd& b); 00140 friend inline FXComplexd operator*(FXdouble a,const FXComplexd& b); 00141 friend inline FXComplexd operator/(FXdouble a,const FXComplexd& b); 00142 00143 /// Save to a stream 00144 friend FXAPI FXStream& operator<<(FXStream& store,const FXComplexd& c); 00145 00146 /// Load from a stream 00147 friend FXAPI FXStream& operator>>(FXStream& store,FXComplexd& c); 00148 }; 00149 00150 00151 00152 inline FXComplexd conjugate(const FXComplexd& c){ return FXComplexd(c.re,-c.im); } 00153 inline FXComplexd polar(FXdouble mod,FXdouble arg){ return FXComplexd(cos(arg)*mod,sin(arg)*mod); } 00154 inline FXComplexd exponent(const FXComplexd& c){ return polar(exp(c.re),c.im); } 00155 inline FXComplexd logarithm(const FXComplexd& c){ return FXComplexd(log(c.modulus()),c.argument()); } 00156 00157 inline FXbool operator==(const FXComplexd& c,FXdouble r){ return c.re==r && c.im==0.0; } 00158 inline FXbool operator!=(const FXComplexd& c,FXdouble r){ return c.re!=r || c.im!=0.0; } 00159 00160 inline FXbool operator==(FXdouble r,const FXComplexd& c){ return r==c.re && c.im==0.0; } 00161 inline FXbool operator!=(FXdouble r,const FXComplexd& c){ return r!=c.re || c.im!=0.0; } 00162 00163 00164 inline FXComplexd operator+(const FXComplexd& a,const FXComplexd& b){ return FXComplexd(a.re+b.re,a.im+b.im); } 00165 inline FXComplexd operator-(const FXComplexd& a,const FXComplexd& b){ return FXComplexd(a.re-b.re,a.im-b.im); } 00166 inline FXComplexd operator*(const FXComplexd& a,const FXComplexd& b){ return FXComplexd(a.re*b.re-a.im*b.im,a.re*b.im+a.im*b.re); } 00167 inline FXComplexd operator/(const FXComplexd& a,const FXComplexd& b){ FXdouble m=b.modulus2(); return FXComplexd((a.re*b.re+a.im*b.im)/m,(a.im*b.re-a.re*b.im)/m); } 00168 00169 00170 inline FXComplexd operator+(const FXComplexd& a,FXdouble b){ return FXComplexd(a.re+b,a.im); } 00171 inline FXComplexd operator-(const FXComplexd& a,FXdouble b){ return FXComplexd(a.re-b,a.im); } 00172 inline FXComplexd operator*(const FXComplexd& a,FXdouble b){ return FXComplexd(a.re*b,a.im*b); } 00173 inline FXComplexd operator/(const FXComplexd& a,FXdouble b){ return FXComplexd(a.re/b,a.im/b); } 00174 00175 00176 inline FXComplexd operator+(FXdouble a,const FXComplexd& b){ return FXComplexd(a+b.re,b.im); } 00177 inline FXComplexd operator-(FXdouble a,const FXComplexd& b){ return FXComplexd(a-b.re,b.im); } 00178 inline FXComplexd operator*(FXdouble a,const FXComplexd& b){ return FXComplexd(a*b.re,a*b.im); } 00179 inline FXComplexd operator/(FXdouble a,const FXComplexd& b){ FXdouble m=b.modulus2(); return FXComplexd((a*b.re)/m,(-a*b.im)/m); } 00180 00181 extern FXAPI FXStream& operator<<(FXStream& store,const FXComplexd& c); 00182 extern FXAPI FXStream& operator>>(FXStream& store,FXComplexd& c); 00183 00184 } 00185 00186 #endif
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