#include <complex.h>

详细描述

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

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation x2 = -1, that is, i2 = -1.[1] In this expression, a is the real part and b is the imaginary part of the complex number.

Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b) in the complex plane. A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with real numbers alone.

Examples for using complex numbers are the famous Mandelbrot set or the Fourier Transform of a signal. In the latter case the imaginary part stores the phase information.

公共成员函数
	Complex ()
MAXON_IMPLICIT	Complex (const T real )
MAXON_IMPLICIT	Complex (const T real , const T imag )
const Complex &	operator+= (const Complex &c)
const Complex &	operator-= (const Complex &c)
const Complex &	operator*= (const Complex &c)
Complex	operator+ (const Complex &c) const
Complex	operator- (const Complex &c) const
Complex	operator* (const Complex &c) const
Complex	operator* (const T s) const
void	SetLength (const T len)
void	SetPhase (const T phase)
void	SetPolar (const T len, const T phase)
void	SetExp (const T x)
T	GetSquaredLength () const
T	GetLength () const
T	GetPhase () const
Complex	GetNormalized () const
Complex	GetConjugate () const
Complex	GetSqrt () const
Result < Complex >	GetLog () const
Result < Complex >	GetDivision (const Complex &divisor) const
String	ToString (const FormatStatement *formatStatement=nullptr) const
	MAXON_OPERATOR_EQUALITY_HASHCODE ( Complex , real , imag )

静态公共成员函数
static Result < void >	DescribeIO (const DataSerializeInterface &stream)

Public Attributes
T	real
T	imag

Friends
Complex	operator* (const T s, const Complex &c)

构造函数 & 析构函数文档编制

◆  Complex() [1/3]

Complex

Creates a Complex initialized with default values (all components 0.0).

◆  Complex() [2/3]

Complex

(

const T

real

)

Creates a Complex initialized with given real and default ( = 0.0) imaginary values.

◆  Complex() [3/3]

Complex	(	const T	real ,
		const T	imag
	)

Creates a Complex initialized with given real and imaginary values.

成员函数文档编制

◆  operator+=()

const Complex < T > & operator+=

(

const Complex < T > &

c

)

Adds two Complex numbers.

◆  operator-=()

const Complex < T > & operator-=

(

const Complex < T > &

c

)

Subtracts two Complex numbers.

◆  operator*=()

const Complex < T > & operator*=

(

const Complex < T > &

c

)

Multiplies two Complex operations.

◆  operator+()

Complex < T > operator+

(

const Complex < T > &

c

)

const

Adds two Complex numbers.

◆  operator-()

Complex < T > operator-

(

const Complex < T > &

c

)

const

Subtracts two Complex numbers.

◆  operator*() [1/2]

Complex < T > operator*

(

const Complex < T > &

c

)

const

Multiplies two Complex numbers.

◆  operator*() [2/2]

Complex < T > operator*

(

const T

s

)

const

Scales the Complex .

◆  SetLength()

void SetLength

(

const T

len

)

Set polar length (magnitude) in the Argand plane.

◆  SetPhase()

void SetPhase

(

const T

phase

)

Set polar phase (angle) in the Argand plane.

◆  SetPolar()

void SetPolar	(	const T	len ,
		const T	phase
	)

初始化 Complex number by given polar coordinates.

◆  SetExp()

void SetExp

(

const T

x

)

set Complex number according to e^(i*x)

◆  GetSquaredLength()

T GetSquaredLength

Computes the squared magnitude/length/norm in the Argand plane.

返回

length