Class for complex numbers. More...

#include <Complex.h>

Public Member Functions
	Complex (T re=0, T im=0)
	Constructor. More...

template<typename U >
	Complex (const Complex< U > &other)
	Constructor. More...

template<typename U , typename std::enable_if< std::is_convertible< T, U >::value >::type * = nullptr>
	operator Complex< U > ()

Complex &	operator= (const Complex &other)
	Assigns the complex number to another complex number. More...

Complex &	operator= (const T &other)
	Assigns the complex number to the real number other. More...

Complex &	operator+= (const Complex &other)

Complex &	operator+= (const T &other)

Complex &	operator-= (const Complex &other)

Complex &	operator-= (const T &other)

Complex &	operator*= (const Complex &other)

Complex &	operator*= (const T &other)

Complex &	operator/= (const Complex &other)

Complex &	operator/= (const T &other)

Complex< T >	operator- () const

Static Public Member Functions
static Complex< T >	i ()
	Static function. More...

Public Attributes
T	Re

T	Im

Friends
Complex< T >	operator+ (Complex< T > z, const Complex< T > &w)
	Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(z+w=(a+c)+(b+d)i\). More...

Complex< T >	operator+ (Complex< T > z, const T &x)
	Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(z+x=(a+x)+bi\). More...

Complex< T >	operator+ (const T &x, const Complex< T > &z)
	Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(x+z=(x+a)+bi\). More...

Complex< T >	operator- (Complex< T > z, const Complex< T > &w)
	Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(z-w=(a-c)+(b-d)i\). More...

Complex< T >	operator- (Complex< T > z, const T &x)
	Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(z-x=(a-x)+bi\). More...

Complex< T >	operator- (const T &x, const Complex< T > &z)
	Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(x-z=(x-a)-bi\). More...

Complex< T >	operator* (Complex< T > z, const Complex< T > &w)
	Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(zw=(ac-bd)+(ad+bc)i\). More...

Complex< T >	operator* (Complex< T > z, const T &x)
	Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(zx=ax+bxi\). More...

Complex< T >	operator* (const T &x, Complex< T > z)
	Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(xz=xa+xbi\). More...

Complex< T >	operator/ (Complex< T > z, const Complex< T > &w)
	Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(\frac{z}{w}=\frac{1}{c^2+d^2}((ac+bd)+(bc-ad)i)\). More...

Complex< T >	operator/ (Complex< T > z, const T &x)
	Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(\frac{z}{x}=\frac{a}{x}+\frac{b}{x}i\). More...

Complex< T >	operator/ (const T &x, const Complex< T > &z)
	Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(\frac{x}{z}=\frac{1}{a^2+b^2}(xa-xbi)\). More...

std::ostream &	operator<< (std::ostream &out, const Complex< T > &z)
	Takes a complex number \(z=a+bi\) and writes to out. More...

bool	operator== (const Complex< T > &z, const Complex< T > &w)
	Compares two complex numbers \(z=a+bi\) and \(w=c+di\). More...

bool	operator== (const Complex< T > &z, const T &x)
	Compares a complex number \(z=a+bi\) and a real number \(x\). More...

bool	operator== (const T &x, const Complex< T > &z)
	Compares a real number \(x\) and a complex numbers \(z=a+bi\). More...

bool	operator!= (const Complex< T > &z, const Complex< T > &w)
	Compares two complex numbers \(z=a+bi\) and \(w=c+di\). More...

bool	operator!= (const Complex< T > &z, const T &x)
	Compares a complex number \(z=a+bi\) and a real number \(x\). More...

bool	operator!= (const T &x, const Complex< T > &z)
	Compares a real number \(x\) and a complex numbers \(z=a+bi\). More...

Detailed Description

template<typename T>
class Linear::Complex< T >

Class for complex numbers.

Parameters

T	Type to store the real and imaginary part as.

Constructor & Destructor Documentation

◆ Complex() [1/2]

template<typename T >

Linear::Complex< T >::Complex	(	T	re = `0`,
		T	im = `0`
	)

inline

Constructor.

Creates the complex number re+im*i.

Parameters

re	The real part of the complex number. (default = 0)
im	The imaginary part of the complex number. (default = 0)

◆ Complex() [2/2]

template<typename T >

template<typename U >

Linear::Complex< T >::Complex ( const Complex< U > & other )

inline

Constructor.

Copies a complex number.

Parameters

other Complex number to copy.

Member Function Documentation

◆ i()

template<typename T >

static Complex<T> Linear::Complex< T >::i ( )

inlinestatic

Static function.

Creates and returns the complex number i.

Returns: Complex

◆ operator Complex< U >()

template<typename T >

template<typename U , typename std::enable_if< std::is_convertible< T, U >::value >::type * = nullptr>

Linear::Complex< T >::operator Complex< U > ( )

inline

◆ operator*=() [1/2]

template<typename T >

Complex& Linear::Complex< T >::operator*= ( const Complex< T > & other )

inline

◆ operator*=() [2/2]

template<typename T >

Complex& Linear::Complex< T >::operator*= ( const T & other )

inline

◆ operator+=() [1/2]

template<typename T >

Complex& Linear::Complex< T >::operator+= ( const Complex< T > & other )

inline

◆ operator+=() [2/2]

template<typename T >

Complex& Linear::Complex< T >::operator+= ( const T & other )

inline

◆ operator-()

template<typename T >

Complex<T> Linear::Complex< T >::operator- ( ) const

inline

◆ operator-=() [1/2]

template<typename T >

Complex& Linear::Complex< T >::operator-= ( const Complex< T > & other )

inline

◆ operator-=() [2/2]

template<typename T >

Complex& Linear::Complex< T >::operator-= ( const T & other )

inline

◆ operator/=() [1/2]

template<typename T >

Complex& Linear::Complex< T >::operator/= ( const Complex< T > & other )

inline

◆ operator/=() [2/2]

template<typename T >

Complex& Linear::Complex< T >::operator/= ( const T & other )

inline

◆ operator=() [1/2]

template<typename T >

Complex& Linear::Complex< T >::operator= ( const Complex< T > & other )

inline

Assigns the complex number to another complex number.

Parameters

other Complex number.

Returns: Reference to complex number.

◆ operator=() [2/2]

template<typename T >

Complex& Linear::Complex< T >::operator= ( const T & other )

inline

Assigns the complex number to the real number other.

Parameters

other Real number

Returns: Reference to complex number.

Friends And Related Function Documentation

◆ operator!= [1/3]

template<typename T >

bool operator!=	(	const Complex< T > &	z,
		const Complex< T > &	w
	)

friend

Compares two complex numbers \(z=a+bi\) and \(w=c+di\).

Parameters

z	Complex number.
w	Complex number.

Returns: If \(a\ne c\) or \(b\ne d\) it returns true. Otherwise it returns false.

◆ operator!= [2/3]

template<typename T >

bool operator!=	(	const Complex< T > &	z,
		const T &	x
	)

friend

Compares a complex number \(z=a+bi\) and a real number \(x\).

Parameters

z	Complex number.
x	Real number.

Returns: If \(a\ne x\) or \(b\ne 0\) it returns true. Otherwise it returns false.

◆ operator!= [3/3]

template<typename T >

bool operator!=	(	const T &	x,
		const Complex< T > &	z
	)

friend

Compares a real number \(x\) and a complex numbers \(z=a+bi\).

Parameters

x	Real number.
z	Complex number.

Returns: If \(a\ne x\) or \(b\ne 0\) it returns true. Otherwise it returns false.

◆ operator* [1/3]

template<typename T >

Complex<T> operator*	(	Complex< T >	z,
		const Complex< T > &	w
	)

friend

Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(zw=(ac-bd)+(ad+bc)i\).

Parameters

z	Complex number.
w	Complex number.

Returns: Complex number.

◆ operator* [2/3]

template<typename T >

Complex<T> operator*	(	Complex< T >	z,
		const T &	x
	)

friend

Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(zx=ax+bxi\).

Parameters

z	Complex number.
x	Real number.

Returns: Complex number.

◆ operator* [3/3]

template<typename T >

Complex<T> operator*	(	const T &	x,
		Complex< T >	z
	)

friend

Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(xz=xa+xbi\).

Parameters

x	Real number.
z	Complex number.

Returns: Complex number.

◆ operator+ [1/3]

template<typename T >

Complex<T> operator+	(	Complex< T >	z,
		const Complex< T > &	w
	)

friend

Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(z+w=(a+c)+(b+d)i\).

Parameters

z	Complex number.
w	Complex number.

Returns: Complex number.

◆ operator+ [2/3]

template<typename T >

Complex<T> operator+	(	Complex< T >	z,
		const T &	x
	)

friend

Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(z+x=(a+x)+bi\).

Parameters

z	Complex number.
x	Real number.

Returns: Complex number.

◆ operator+ [3/3]

template<typename T >

Complex<T> operator+	(	const T &	x,
		const Complex< T > &	z
	)

friend

Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(x+z=(x+a)+bi\).

Parameters

x	Real number.
z	Complex number.

Returns: Complex number.

◆ operator- [1/3]

template<typename T >

Complex<T> operator-	(	Complex< T >	z,
		const Complex< T > &	w
	)

friend

Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(z-w=(a-c)+(b-d)i\).

Parameters

z	Complex number.
w	Complex number.

Returns: Complex number.

◆ operator- [2/3]

template<typename T >

Complex<T> operator-	(	Complex< T >	z,
		const T &	x
	)

friend

Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(z-x=(a-x)+bi\).

Parameters

z	Complex number.
x	Real number.

Returns: Complex number.

◆ operator- [3/3]

template<typename T >

Complex<T> operator-	(	const T &	x,
		const Complex< T > &	z
	)

friend

Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(x-z=(x-a)-bi\).

Parameters

x	Real number.
z	Complex number.

Returns: Complex number.

◆ operator/ [1/3]

template<typename T >

Complex<T> operator/	(	Complex< T >	z,
		const Complex< T > &	w
	)

friend

Takes two complex numbers \(z=a+bi\) and \(w=c+di\) and returns the complex number \(\frac{z}{w}=\frac{1}{c^2+d^2}((ac+bd)+(bc-ad)i)\).

Parameters

z	Complex number.
w	Complex number.

Returns: Complex number.

◆ operator/ [2/3]

template<typename T >

Complex<T> operator/	(	Complex< T >	z,
		const T &	x
	)

friend

Takes a complex number \(z=a+bi\) and real number \(x\) and returns the complex number \(\frac{z}{x}=\frac{a}{x}+\frac{b}{x}i\).

Parameters

z	Complex number.
x	Real number.

Returns: Complex number.

◆ operator/ [3/3]

template<typename T >

Complex<T> operator/	(	const T &	x,
		const Complex< T > &	z
	)

friend

Takes a real number \(x\) and complex number \(z=a+bi\) returns the complex number \(\frac{x}{z}=\frac{1}{a^2+b^2}(xa-xbi)\).

Parameters

x	Real number.
z	Complex number.

Returns: Complex number.

◆ operator<<

template<typename T >

std::ostream& operator<<	(	std::ostream &	out,
		const Complex< T > &	z
	)

friend

Takes a complex number \(z=a+bi\) and writes to out.

If \(z=0\), then simply \(0\) will be written. If \(z=bi\), then it will write just \(bi\). If \(z=a\), then it will write just \(a\). Otherwise the full \(a+bi\) will be written, with "+" replaced by "-" if \(b<0\).

Parameters

out	Reference to std::ostream.
z	Complex number.

◆ operator== [1/3]

template<typename T >

bool operator==	(	const Complex< T > &	z,
		const Complex< T > &	w
	)

friend

Compares two complex numbers \(z=a+bi\) and \(w=c+di\).

Parameters

z	Complex number.
w	Complex number.

Returns: If \(a=c\) and \(b=d\) it returns true. Otherwise it returns false.

◆ operator== [2/3]

template<typename T >

bool operator==	(	const Complex< T > &	z,
		const T &	x
	)

friend

Compares a complex number \(z=a+bi\) and a real number \(x\).

Parameters

z	Complex number.
x	Real number.

Returns: If \(a=x\) and \(b=0\) it returns true. Otherwise it returns false.

◆ operator== [3/3]

template<typename T >

bool operator==	(	const T &	x,
		const Complex< T > &	z
	)

friend

Compares a real number \(x\) and a complex numbers \(z=a+bi\).

Parameters

x	Real number.
z	Complex number.

Returns: If \(a=x\) and \(b=0\) it returns true. Otherwise it returns false.

Member Data Documentation

◆ Im

template<typename T >

T Linear::Complex< T >::Im

Imaginary part of the complex number

◆ Re

template<typename T >

T Linear::Complex< T >::Re

Real part of the complex number

The documentation for this class was generated from the following file:

src/Complex.h

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

template<typename T> class Linear::Complex< T >

Constructor & Destructor Documentation

◆ Complex() [1/2]

◆ Complex() [2/2]

Member Function Documentation

◆ i()

◆ operator Complex< U >()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

Friends And Related Function Documentation

◆ operator!= [1/3]

◆ operator!= [2/3]

◆ operator!= [3/3]

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/3]

◆ operator- [2/3]

◆ operator- [3/3]

◆ operator/ [1/3]

◆ operator/ [2/3]

◆ operator/ [3/3]

◆ operator<<

◆ operator== [1/3]

◆ operator== [2/3]

◆ operator== [3/3]

Member Data Documentation

◆ Im

◆ Re

template<typename T>
class Linear::Complex< T >