dburgess | b3a0ca4 | 2011-10-12 07:44:40 +0000 | [diff] [blame] | 1 | /**@file templates for Complex classes |
| 2 | unlike the built-in complex<> templates, these inline most operations for speed |
| 3 | */ |
| 4 | |
| 5 | /* |
| 6 | * Copyright 2008 Free Software Foundation, Inc. |
| 7 | * |
| 8 | * This software is distributed under multiple licenses; see the COPYING file in the main directory for licensing information for this specific distribuion. |
| 9 | * |
| 10 | * This use of this software may be subject to additional restrictions. |
| 11 | * See the LEGAL file in the main directory for details. |
| 12 | |
| 13 | This program is distributed in the hope that it will be useful, |
| 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. |
| 16 | |
| 17 | */ |
| 18 | |
| 19 | |
| 20 | |
| 21 | |
| 22 | #ifndef COMPLEXCPP_H |
| 23 | #define COMPLEXCPP_H |
| 24 | |
| 25 | #include <math.h> |
| 26 | #include <ostream> |
| 27 | |
| 28 | |
| 29 | template<class Real> class Complex { |
| 30 | |
| 31 | public: |
| 32 | |
| 33 | Real r, i; |
| 34 | |
| 35 | /**@name constructors */ |
| 36 | //@{ |
| 37 | /**@name from real */ |
| 38 | //@{ |
| 39 | Complex(Real real, Real imag) {r=real; i=imag;} // x=complex(a,b) |
| 40 | Complex(Real real) {r=real; i=0;} // x=complex(a) |
| 41 | //@} |
| 42 | /**@name from nothing */ |
| 43 | //@{ |
| 44 | Complex() {r=(Real)0; i=(Real)0;} // x=complex() |
| 45 | //@} |
| 46 | /**@name from other complex */ |
| 47 | //@{ |
| 48 | Complex(const Complex<float>& z) {r=z.r; i=z.i;} // x=complex(z) |
| 49 | Complex(const Complex<double>& z) {r=z.r; i=z.i;} // x=complex(z) |
| 50 | Complex(const Complex<long double>& z) {r=z.r; i=z.i;} // x=complex(z) |
| 51 | //@} |
| 52 | //@} |
| 53 | |
| 54 | /**@name casting up from basic numeric types */ |
| 55 | //@{ |
| 56 | Complex& operator=(char a) { r=(Real)a; i=(Real)0; return *this; } |
| 57 | Complex& operator=(int a) { r=(Real)a; i=(Real)0; return *this; } |
| 58 | Complex& operator=(long int a) { r=(Real)a; i=(Real)0; return *this; } |
| 59 | Complex& operator=(short a) { r=(Real)a; i=(Real)0; return *this; } |
| 60 | Complex& operator=(float a) { r=(Real)a; i=(Real)0; return *this; } |
| 61 | Complex& operator=(double a) { r=(Real)a; i=(Real)0; return *this; } |
| 62 | Complex& operator=(long double a) { r=(Real)a; i=(Real)0; return *this; } |
| 63 | //@} |
| 64 | |
| 65 | /**@name arithmetic */ |
| 66 | //@{ |
| 67 | /**@ binary operators */ |
| 68 | //@{ |
| 69 | Complex operator+(const Complex<Real>& a) const { return Complex<Real>(r+a.r, i+a.i); } |
| 70 | Complex operator+(Real a) const { return Complex<Real>(r+a,i); } |
| 71 | Complex operator-(const Complex<Real>& a) const { return Complex<Real>(r-a.r, i-a.i); } |
| 72 | Complex operator-(Real a) const { return Complex<Real>(r-a,i); } |
| 73 | Complex operator*(const Complex<Real>& a) const { return Complex<Real>(r*a.r-i*a.i, r*a.i+i*a.r); } |
| 74 | Complex operator*(Real a) const { return Complex<Real>(r*a, i*a); } |
| 75 | Complex operator/(const Complex<Real>& a) const { return operator*(a.inv()); } |
| 76 | Complex operator/(Real a) const { return Complex<Real>(r/a, i/a); } |
| 77 | //@} |
| 78 | /*@name component-wise product */ |
| 79 | //@{ |
| 80 | Complex operator&(const Complex<Real>& a) const { return Complex<Real>(r*a.r, i*a.i); } |
| 81 | //@} |
| 82 | /*@name inplace operations */ |
| 83 | //@{ |
| 84 | Complex& operator+=(const Complex<Real>&); |
| 85 | Complex& operator-=(const Complex<Real>&); |
| 86 | Complex& operator*=(const Complex<Real>&); |
| 87 | Complex& operator/=(const Complex<Real>&); |
| 88 | Complex& operator+=(Real); |
| 89 | Complex& operator-=(Real); |
| 90 | Complex& operator*=(Real); |
| 91 | Complex& operator/=(Real); |
| 92 | //@} |
| 93 | //@} |
| 94 | |
| 95 | /**@name comparisons */ |
| 96 | //@{ |
| 97 | bool operator==(const Complex<Real>& a) const { return ((i==a.i)&&(r==a.r)); } |
| 98 | bool operator!=(const Complex<Real>& a) const { return ((i!=a.i)||(r!=a.r)); } |
| 99 | bool operator<(const Complex<Real>& a) const { return norm2()<a.norm2(); } |
| 100 | bool operator>(const Complex<Real>& a) const { return norm2()>a.norm2(); } |
| 101 | //@} |
| 102 | |
| 103 | /// reciprocation |
| 104 | Complex inv() const; |
| 105 | |
| 106 | // unary functions -- inlined |
| 107 | /**@name unary functions */ |
| 108 | //@{ |
| 109 | /**@name inlined */ |
| 110 | //@{ |
| 111 | Complex conj() const { return Complex<Real>(r,-i); } |
| 112 | Real norm2() const { return i*i+r*r; } |
| 113 | Complex flip() const { return Complex<Real>(i,r); } |
| 114 | Real real() const { return r;} |
| 115 | Real imag() const { return i;} |
| 116 | Complex neg() const { return Complex<Real>(-r, -i); } |
| 117 | bool isZero() const { return ((r==(Real)0) && (i==(Real)0)); } |
| 118 | //@} |
| 119 | /**@name not inlined due to outside calls */ |
| 120 | //@{ |
| 121 | Real abs() const { return ::sqrt(norm2()); } |
| 122 | Real arg() const { return ::atan2(i,r); } |
| 123 | float dB() const { return 10.0*log10(norm2()); } |
| 124 | Complex exp() const { return expj(i)*(::exp(r)); } |
| 125 | Complex unit() const; ///< unit phasor with same angle |
| 126 | Complex log() const { return Complex(::log(abs()),arg()); } |
| 127 | Complex pow(double n) const { return expj(arg()*n)*(::pow(abs(),n)); } |
| 128 | Complex sqrt() const { return pow(0.5); } |
| 129 | //@} |
| 130 | //@} |
| 131 | |
| 132 | }; |
| 133 | |
| 134 | |
| 135 | /**@name standard Complex manifestations */ |
| 136 | //@{ |
| 137 | typedef Complex<float> complex; |
| 138 | typedef Complex<double> dcomplex; |
| 139 | typedef Complex<short> complex16; |
| 140 | typedef Complex<long> complex32; |
| 141 | //@} |
| 142 | |
| 143 | |
| 144 | template<class Real> inline Complex<Real> Complex<Real>::inv() const |
| 145 | { |
| 146 | Real nVal; |
| 147 | |
| 148 | nVal = norm2(); |
| 149 | return Complex<Real>(r/nVal, -i/nVal); |
| 150 | } |
| 151 | |
| 152 | template<class Real> Complex<Real>& Complex<Real>::operator+=(const Complex<Real>& a) |
| 153 | { |
| 154 | r += a.r; |
| 155 | i += a.i; |
| 156 | return *this; |
| 157 | } |
| 158 | |
| 159 | template<class Real> Complex<Real>& Complex<Real>::operator*=(const Complex<Real>& a) |
| 160 | { |
| 161 | operator*(a); |
| 162 | return *this; |
| 163 | } |
| 164 | |
| 165 | template<class Real> Complex<Real>& Complex<Real>::operator-=(const Complex<Real>& a) |
| 166 | { |
| 167 | r -= a.r; |
| 168 | i -= a.i; |
| 169 | return *this; |
| 170 | } |
| 171 | |
| 172 | template<class Real> Complex<Real>& Complex<Real>::operator/=(const Complex<Real>& a) |
| 173 | { |
| 174 | operator/(a); |
| 175 | return *this; |
| 176 | } |
| 177 | |
| 178 | |
| 179 | /* op= style operations with reals */ |
| 180 | |
| 181 | template<class Real> Complex<Real>& Complex<Real>::operator+=(Real a) |
| 182 | { |
| 183 | r += a; |
| 184 | return *this; |
| 185 | } |
| 186 | |
| 187 | template<class Real> Complex<Real>& Complex<Real>::operator*=(Real a) |
| 188 | { |
| 189 | r *=a; |
| 190 | i *=a; |
| 191 | return *this; |
| 192 | } |
| 193 | |
| 194 | template<class Real> Complex<Real>& Complex<Real>::operator-=(Real a) |
| 195 | { |
| 196 | r -= a; |
| 197 | return *this; |
| 198 | } |
| 199 | |
| 200 | template<class Real> Complex<Real>& Complex<Real>::operator/=(Real a) |
| 201 | { |
| 202 | r /= a; |
| 203 | i /= a; |
| 204 | return *this; |
| 205 | } |
| 206 | |
| 207 | |
| 208 | template<class Real> Complex<Real> Complex<Real>::unit() const |
| 209 | { |
| 210 | Real absVal = abs(); |
| 211 | return (Complex<Real>(r/absVal, i/absVal)); |
| 212 | } |
| 213 | |
| 214 | |
| 215 | |
| 216 | /**@name complex functions outside of the Complex<> class. */ |
| 217 | //@{ |
| 218 | |
| 219 | /** this allows type-commutative multiplication */ |
| 220 | template<class Real> Complex<Real> operator*(Real a, const Complex<Real>& z) |
| 221 | { |
| 222 | return Complex<Real>(z.r*a, z.i*a); |
| 223 | } |
| 224 | |
| 225 | |
| 226 | /** this allows type-commutative addition */ |
| 227 | template<class Real> Complex<Real> operator+(Real a, const Complex<Real>& z) |
| 228 | { |
| 229 | return Complex<Real>(z.r+a, z.i); |
| 230 | } |
| 231 | |
| 232 | |
| 233 | /** this allows type-commutative subtraction */ |
| 234 | template<class Real> Complex<Real> operator-(Real a, const Complex<Real>& z) |
| 235 | { |
| 236 | return Complex<Real>(z.r-a, z.i); |
| 237 | } |
| 238 | |
| 239 | |
| 240 | |
| 241 | /// e^jphi |
| 242 | template<class Real> Complex<Real> expj(Real phi) |
| 243 | { |
| 244 | return Complex<Real>(cos(phi),sin(phi)); |
| 245 | } |
| 246 | |
| 247 | /// phasor expression of a complex number |
| 248 | template<class Real> Complex<Real> phasor(Real C, Real phi) |
| 249 | { |
| 250 | return (expj(phi)*C); |
| 251 | } |
| 252 | |
| 253 | /// formatted stream output |
| 254 | template<class Real> std::ostream& operator<<(std::ostream& os, const Complex<Real>& z) |
| 255 | { |
| 256 | os << z.r << ' '; |
| 257 | //os << z.r << ", "; |
| 258 | //if (z.i>=0) { os << "+"; } |
| 259 | os << z.i << "j"; |
dburgess | b3a0ca4 | 2011-10-12 07:44:40 +0000 | [diff] [blame] | 260 | return os; |
| 261 | } |
| 262 | |
| 263 | //@} |
| 264 | |
| 265 | |
| 266 | #endif |