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208 lines
7 KiB
C++
208 lines
7 KiB
C++
/*
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* This file is part of libcxxsupport.
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*
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* libcxxsupport is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* libcxxsupport is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with libcxxsupport; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/*
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* libcxxsupport is being developed at the Max-Planck-Institut fuer Astrophysik
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* and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
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* (DLR).
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*/
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/*! \file xcomplex.h
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* Class for representing complex numbers, strongly inspired by C++'s
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* std::complex
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*
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* Copyright (C) 2003-2010 Max-Planck-Society
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* \author Martin Reinecke
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*/
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#ifndef PLANCK_XCOMPLEX_H
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#define PLANCK_XCOMPLEX_H
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#include <iostream>
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#include <complex>
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/*! \defgroup complexgroup Complex number support */
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/*! \{ */
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/*! A class for representing complex numbers.
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This template is intended as an (under-encapsulated) replacement for
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the (over-encapsulated) std::complex<>. The goal is to include the
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whole functionality of std::complex<>, with some additional methods
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that allow higher performance.
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The (known and intentional) differences between xcomplex<> and
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std::complex<> are:
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- the default constructor of xcomplex<> does nothing, in contrast to
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std::complex<>, which initialises its members to zero.
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- xcomplex<> implements the methods real() and imag() according
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to defect report DR387
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*/
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template<typename T> class xcomplex
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{
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public:
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T re, /*!< real part */
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im; /*!< imaginary part */
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/*! Default constructor. \a re and \a im are not initialised. */
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xcomplex () {}
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/*! Creates the complex number (\a re_, \a im_). */
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xcomplex (const T &re_, const T &im_)
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: re(re_), im(im_) {}
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/*! Creates the complex number (\a re_, 0). */
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xcomplex (const T &re_)
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: re(re_), im(0) {}
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/*! Creates an xcomplex from a std::complex of identical precision. */
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xcomplex (const std::complex<T> &orig)
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: re(orig.real()), im(orig.imag()) {}
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/*! Creates a complex number as a copy of \a orig. */
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template<typename U> explicit xcomplex (const xcomplex<U> &orig)
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: re(T(orig.re)), im(T(orig.im)) {}
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/*! Conversion operator to std::complex<T> */
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operator std::complex<T> () const
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{ return std::complex<T>(re,im); }
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/*! Returns the real part as lvalue. */
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T &real() { return re; }
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/*! Returns the real part. */
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const T &real() const { return re; }
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/*! Returns the imaginary part as lvalue. */
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T &imag() { return im; }
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/*! Returns the imaginary part. */
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const T &imag() const { return im; }
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/*! Sets the number to (\a re_, \a im_). */
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void Set (const T &re_, const T &im_)
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{ re = re_; im = im_; }
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/*! Sets the number to \a orig. */
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xcomplex &operator= (const xcomplex &orig)
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{ re=orig.re; im=orig.im; return *this; }
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/*! Sets the number to \a orig. */
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xcomplex &operator= (const std::complex<T> &orig)
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{ re=orig.real(); im=orig.imag(); return *this; }
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/*! Sets the number to (\a orig, 0). */
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xcomplex &operator= (const T &orig)
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{ re=orig; im=0; return *this; }
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/*! Adds \a b to \a *this. */
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xcomplex &operator+= (const xcomplex &b)
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{ re+=b.re; im+=b.im; return *this; }
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/*! Subtracts \a b from \a *this. */
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xcomplex &operator-= (const xcomplex &b)
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{ re-=b.re; im-=b.im; return *this; }
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/*! Multiplies \a *this by \a b. */
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xcomplex &operator*= (const xcomplex &b)
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{
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T tmp=re;
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re=tmp*b.re-im*b.im; im=tmp*b.im+im*b.re;
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return *this;
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}
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/*! Divides \a *this by \a b. */
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xcomplex &operator/= (const xcomplex &b)
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{
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std::complex<T> tmp=*this;
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std::complex<T> tmp2=b;
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tmp /= tmp2;
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*this=tmp;
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return *this;
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}
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/*! Multiplies \a *this by \a fact. */
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xcomplex &operator*= (const T &fact)
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{ re*=fact; im*=fact; return *this; }
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/*! Divides \a *this by \a div. */
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xcomplex &operator/= (const T &div)
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{ re/=div; im/=div; return *this; }
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/*! Returns \a *this * \a fact. */
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xcomplex operator* (const T &fact) const
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{ return xcomplex (re*fact,im*fact); }
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/*! Returns \a *this * \a b. */
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xcomplex operator* (const xcomplex &b) const
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{ return xcomplex (re*b.re-im*b.im, re*b.im+im*b.re); }
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/*! Returns \a *this / \a b. */
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xcomplex operator/ (const xcomplex &b) const
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{ return xcomplex(std::complex<T>(*this)/std::complex<T>(b)); }
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/*! Returns \a *this / \a div. */
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xcomplex operator/ (const T &div) const
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{ return xcomplex (re/div,im/div); }
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/*! Returns \a *this + \a b. */
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xcomplex operator+ (const xcomplex &b) const
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{ return xcomplex (re+b.re, im+b.im); }
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/*! Returns \a *this - \a b. */
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xcomplex operator- (const xcomplex &b) const
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{ return xcomplex (re-b.re, im-b.im); }
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/*! Returns \a -(*this) */
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xcomplex operator- () const
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{ return xcomplex (-re,-im); }
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/*! Flips the signs of both components. */
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void Negate()
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{ re=-re; im=-im; }
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/*! Flips the signs of the imaginary component. */
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void Conjugate()
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{ im=-im; }
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/*! Multiplies the number by exp(i*\a angle) */
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void Rotate(T angle)
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{
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T ca=cos(angle), sa=sin(angle);
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T tmp=re;
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re=tmp*ca-im*sa; im=tmp*sa+im*ca;
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}
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/*! Returns the complex conjugate of \a *this. */
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xcomplex conj() const
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{ return xcomplex (re,-im); }
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/*! Returns the norm of \a *this. */
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T norm() const
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{ return re*re + im*im; }
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};
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/*! Returns the complex conjugate of \a num.
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\relates xcomplex */
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template <typename T> inline xcomplex<T> conj (const xcomplex<T> &num)
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{ return xcomplex<T> (num.re, -num.im); }
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/*! Returns the norm of \a num.
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\relates xcomplex */
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template <typename T> inline T norm (const xcomplex<T> &num)
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{ return num.re*num.re + num.im*num.im; }
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/*! Returns the absolute value of \a num.
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\relates xcomplex */
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template <typename T> inline T abs (const xcomplex<T> &num)
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{
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using namespace std;
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return abs(complex<T>(num));
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}
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/*! Returns \a f1*f2.
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\relates xcomplex */
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template <typename T> inline xcomplex<T> operator*
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(const T &f1, const xcomplex<T> &f2)
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{ return xcomplex<T> (f1*f2.re, f1*f2.im); }
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/*! Returns \a f1/f2.
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\relates xcomplex */
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template <typename T> inline xcomplex<T> operator/
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(const T &f1, const xcomplex<T> &f2)
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{ return xcomplex<T>(f1)/f2; }
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/*! Writes \a val to \a os.
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\relates xcomplex */
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template<typename T>
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inline std::ostream &operator<< (std::ostream &os, const xcomplex<T> &val)
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{ os << "(" << val.re << "," << val.im << ")"; return os; }
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/*! \} */
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#endif
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