Complex< T > Class Template Reference

#include <complex.h>

Detailed Description

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.

Public Member Functions
	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)

Static Public Member Functions
static Result< void >	DescribeIO (const DataSerializeInterface &stream)

Public Attributes
T	real
T	imag

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

Constructor & Destructor Documentation

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.

Member Function Documentation

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
	)

Initialize 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.

Returns

length

GetLength()

T GetLength

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

Returns

length

GetPhase()

T GetPhase

Computes the angle of the complex vector in the Argand plane.

Returns

phase

GetNormalized()

Complex< T > GetNormalized

Get a complex vector with normalized length in the Argand plane.

Returns

normalized complex vector

GetConjugate()

Complex< T > GetConjugate

Get the complex conjugate of a complex vector

Returns

complex conjugate

GetSqrt()

Complex< T > GetSqrt

Compute the square root.

Returns

square root of vector

GetLog()

Result< Complex< T > > GetLog

Compute the natural logarithm.

Returns

Log of complex vector. Returns an error if length of vector is zero

GetDivision()

Result< Complex< T > > GetDivision

(

const Complex< T > &

divisor

)

const

Divides the complex value by another complex value.

Parameters

[in]

divisor

divisor

Returns

The divided result. Returns an error if divisor is zero.

ToString()

String ToString

(

const FormatStatement *

formatStatement = nullptr

)

const

Returns a readable string of the content.

Parameters

[in]

formatStatement

Nullptr or additional formatting instruction. See also Formatting Floating point values.

Returns

The converted result.

DescribeIO()

Result< void > DescribeIO ( const DataSerializeInterface &  stream )

static

Describe all elements of this class for I/O operations.

Parameters

[in]

stream

The stream that is used to register the class members.

Returns

OK on success.

MAXON_OPERATOR_EQUALITY_HASHCODE()

MAXON_OPERATOR_EQUALITY_HASHCODE	(	Complex< T >	,
		real	,
		imag
	)

Friends And Related Function Documentation

operator*

Complex operator* ( const T  s, const Complex< T > &  c  )

friend

Scales the components of a Complex.

Member Data Documentation

real

T real

real part

imag

T imag

imaginary part