This struct holds a complex number.
Operators ( \(a+b\), \(a-b\), \(a*b\), \(a/b\) and \(a^b\)) can be used. Passing \(a\) or \(b\) as double is supported. More...

Inheritance diagram for Complex:

Public Member Functions
double	Abs ()
	Returns absolute value of current Complex.

double	Arg ()
	Returns the argument (phase) of this complex number. The resulting angle is in the range of [-Pi, Pi).

	Complex (Complex c)
	Copy constructor.

	Complex (double Re)
	Constructs a complex number with given real part. The imaginary part is zero.

	Complex (double Re, double Im)
	Constructs a complex number with given real and imaginary parts.

double	EvaluateFielQuantity (FieldQuantity quantityToEvaluate)
	public support method to evaluate a specific field quantity of the complex number

double	FilteredPhase (double maximumAmplitude=0, double artifactsThreshold=Globals.MinimumRelativeAmplitude)
	Gets the phase of the complex value. In contrast to the Arg()-method, this method corrects numerical artifacts in the phase. (1) The phase is zero if the amplitude of the complex number is less than threshold times maximum amplitude. (2) The phase value is -π if its imaginary part value {Im} satisfies t⋅Re < -Abs(Im) < 0.

bool	InputIsNumericalLarger (Complex cfForComparison)
	Method to perform numerical comparison of two complex number. First the amplitudes are compared. If they are equal the phase values are compared.

Complex	ModifyComplexPart (ComplexPart complexPart)
	Returns passed ComplexPart.

double	Norm ()
	Returns the squared L2-norm of current Complex.

override string	ToString ()
	Returns a System.String that represents this instance.

string	ToString (ComplexToStringConversionFormat format)
	Returns formatted string, by default: {Real} + {Imaginary} \(\cdot\)i.

string	ToString (int numberOfDigits, ComplexToStringConversionFormat? format=null)
	Returns formatted string, by default: {Real} + {Imaginary} \(\cdot\)i.

string	ToString (PhysicalUnit physicalUnit, ComplexToStringConversionFormat ComplexToStringFormat, int ComplexToStringConversionDigits)
	Returns formatted string, either.

Static Public Member Functions
static double	ArgDifference (Complex c1, Complex c2)
	Determine the reduced phase difference of two complex numbers.

static Complex	Conjugate (Complex z)
	Returns conjugate complex number of current Complex.

static Complex	Cos (Complex z)
	Returns cosine of complex number.

static Complex	Exp (Complex c)
	Returns exponential function of complex number.

static Complex	FromFieldQuantity (double value, FieldQuantity fieldQuantity)
	Creates a complex number from the given double value which is written into the given field quantity.

static ? ComplexToStringConversionFormat	GetComplexFormat (string numberString)
	Determines the way how a complex number is represented by a string (for example "a + ib" is the RealImaginary format, "a exp ib" is the AmplitudePhase format).

static bool	IsNaN (Complex number)
	Checks whether either the real or the imaginary is NaN (not a number).

static Complex	Log (Complex z)
	Returns natural logarithm of complex number.

static Complex	operator* (Complex z, double d)
	Multiplies complex number with real number.

static Complex	operator* (Complex z1, Complex z2)
	Multiplies two complex numbers.

static Complex	operator* (double d, Complex z)
	Multiplies real number with real number.

static Complex	operator+ (Complex z1, Complex z2)
	Adds two complex numbers.

static Complex	operator+ (Complex z1, double d)
	Adds a complex number and a real number.

static Complex	operator+ (double d, Complex z1)
	Adds a real number and a complex number.

static Complex	operator- (Complex z)
	Multiplies a complex number with -1.

static Complex	operator- (Complex z1, Complex z2)
	Subtracts two complex numbers.

static Complex	operator- (Complex z1, double d)
	Subtracts real number from complex number.

static Complex	operator- (double d, Complex z1)
	Subtracts complex number from real number.

static Complex	operator/ (Complex z, double d)
	Divides complex number by real number.

static Complex	operator/ (Complex z1, Complex z2)
	Divides complex number by complex number.

static Complex	operator/ (double d, Complex z1)
	Divides a real number by complex number.

static Complex	Parse (string pureNumberStr, ComplexToStringConversionFormat complexFormat)
	Parses an string which represents a complex number.

static Complex	Parse (string pureNumberStr, ComplexToStringConversionFormat complexFormat, NumberFormatInfo doubleFormat)
	Parses an string which represents a complex number.

static Complex	Polar (double abs, double arg)
	Returns complex number created by given absolute value and argument.

static Complex	Pow (Complex basis, Complex exponent)
	public power function of the complex class

static Complex	Sin (Complex z)
	Returns sine of complex number.

static Complex	Sqrt (Complex z)
	Return square root of complex number.

static bool	TryParse (string pureNumberStr, out Complex parsedValue, out ComplexToStringConversionFormat? usedConversionFormat, NumberFormatInfo doubleFormat=null)
	Tries to parse a string which represents a complex number.

Public Attributes
double	Im
	Imaginary part of stored complex number.

double	Re
	Real part of stored complex number.

Static Public Attributes
static readonly Complex	i
	The imaginary unit.

static readonly Complex	Zero
	A constant containing the neutral element for addition (= (0, 0))

Detailed Description

This struct holds a complex number.
Operators ( \(a+b\), \(a-b\), \(a*b\), \(a/b\) and \(a^b\)) can be used. Passing \(a\) or \(b\) as double is supported.

Constructor & Destructor Documentation

◆ Complex() [1/3]

Complex	(	double	Re,
		double	Im
	)

Constructs a complex number with given real and imaginary parts.

Parameters

Re	Real part.
Im	Imaginary part.

◆ Complex() [2/3]

Complex ( double Re )

Constructs a complex number with given real part. The imaginary part is zero.

Parameters

Re	Real part.

◆ Complex() [3/3]

Complex ( Complex c )

Copy constructor.

Parameters

c	Complex number to copy.

Member Function Documentation

◆ Abs()

double Abs ( )

Returns absolute value of current Complex.

Returns: The absolute value

◆ Arg()

double Arg ( )

Returns the argument (phase) of this complex number. The resulting angle is in the range of [-Pi, Pi).

Returns: Result of operation.

◆ ArgDifference()

static double ArgDifference	(	Complex	c1,
		Complex	c2
	)

static

Determine the reduced phase difference of two complex numbers.

Parameters

c1	complex number with phase minuend
c2	complex number with phase subtrahend

Returns: reduced phase difference

◆ Conjugate()

static Complex Conjugate ( Complex z )

static

Returns conjugate complex number of current Complex.

Parameters

z	Complex number to conjugate.

Returns: Result of operation.

◆ Cos()

static Complex Cos ( Complex z )

static

Returns cosine of complex number.

Parameters

z	Complex number \(a\).

Returns: \(\cos(a)\).

◆ EvaluateFielQuantity()

double EvaluateFielQuantity ( FieldQuantity quantityToEvaluate )

public support method to evaluate a specific field quantity of the complex number

Parameters

quantityToEvaluate the field quantity which should be evaluated

Returns: the evaluated field quantity

◆ Exp()

static Complex Exp ( Complex c )

static

Returns exponential function of complex number.

Parameters

c	Complex number \(a\).

Returns: \(e^a\).

◆ FilteredPhase()

double FilteredPhase	(	double	maximumAmplitude = `0`,
		double	artifactsThreshold = `Globals::MinimumRelativeAmplitude`
	)

Gets the phase of the complex value. In contrast to the Arg()-method, this method corrects numerical artifacts in the phase. (1) The phase is zero if the amplitude of the complex number is less than threshold times maximum amplitude. (2) The phase value is -π if its imaginary part value {Im} satisfies t⋅Re < -Abs(Im) < 0.

Parameters

maximumAmplitude	The maximum amplitude. If this optional parameter is not specified, the filtering step (1) is not done.
artifactsThreshold	The artifacts threshold. 0.1 % is taken as default value.

Returns: The phase of the complex value.

◆ FromFieldQuantity()

static Complex FromFieldQuantity	(	double	value,
		FieldQuantity	fieldQuantity
	)

static

Creates a complex number from the given double value which is written into the given field quantity.

Parameters

value	The double value.
fieldQuantity	The field quantity into which the value is written.

Returns: A new complex number.

◆ GetComplexFormat()

static ? ComplexToStringConversionFormat GetComplexFormat ( string numberString )

static

Determines the way how a complex number is represented by a string (for example "a + ib" is the RealImaginary format, "a exp ib" is the AmplitudePhase format).

Parameters

numberString The number string.

Returns: The complex number format. null if the format cannot be determined, e.g. for a real number.

◆ InputIsNumericalLarger()

bool InputIsNumericalLarger ( Complex cfForComparison )

Method to perform numerical comparison of two complex number. First the amplitudes are compared. If they are equal the phase values are compared.

Parameters

cfForComparison The complex number which shall be used for comparison.

Returns: true of input is numerically larger than current instance of the complex number

◆ IsNaN()

static bool IsNaN ( Complex number )

static

Checks whether either the real or the imaginary is NaN (not a number).

Parameters

number The complex number to check.

Returns: TRUE if either the real or the imaginary is NaN.

◆ Log()

static Complex Log ( Complex z )

static

Returns natural logarithm of complex number.

Parameters

z	Complex number \(a\).

Returns: \(\ln(a)\).

◆ ModifyComplexPart()

Complex ModifyComplexPart ( ComplexPart complexPart )

Returns passed ComplexPart.

Parameters

complexPart ComplexPart to be applied on current Complex.

Returns: modified complex number

◆ Norm()

double Norm ( )

Returns the squared L2-norm of current Complex.

Returns: \(Re(this)^2 + Im(this)^2\).

◆ operator*() [1/3]

static Complex operator*	(	Complex	z,
		double	d
	)

static

Multiplies complex number with real number.

Parameters

z	complex number
d	real number

Returns: Product of the two numbers

◆ operator*() [2/3]

static Complex operator*	(	Complex	z1,
		Complex	z2
	)

static

Multiplies two complex numbers.

Parameters

z1	complex number
z2	complex number

Returns: Product of the two numbers

◆ operator*() [3/3]

static Complex operator*	(	double	d,
		Complex	z
	)

static

Multiplies real number with real number.

Parameters

z	complex number
d	real number

Returns: Product of the two numbers

◆ operator+() [1/3]

static Complex operator+	(	Complex	z1,
		Complex	z2
	)

static

Adds two complex numbers.

Parameters

z1	first complex number
z2	second complex number

Returns: sum of both complex numbers

◆ operator+() [2/3]

static Complex operator+	(	Complex	z1,
		double	d
	)

static

Adds a complex number and a real number.

Parameters

z1	complex number
d	real number

Returns: sum of both numbers

◆ operator+() [3/3]

static Complex operator+	(	double	d,
		Complex	z1
	)

static

Adds a real number and a complex number.

Parameters

d	real number
z1	complex number

Returns: sum of both numbers

◆ operator-() [1/4]

static Complex operator- ( Complex z )

static

Multiplies a complex number with -1.

Parameters

z	The complex number to negate.

Returns: the negated argument

◆ operator-() [2/4]

static Complex operator-	(	Complex	z1,
		Complex	z2
	)

static

Subtracts two complex numbers.

Parameters

z1	complex number
z2	complex number

Returns: difference of the two numbers

◆ operator-() [3/4]

static Complex operator-	(	Complex	z1,
		double	d
	)

static

Subtracts real number from complex number.

Parameters

z1	complex number
d	real number

Returns: difference of the two numbers

◆ operator-() [4/4]

static Complex operator-	(	double	d,
		Complex	z1
	)

static

Subtracts complex number from real number.

Parameters

d	real number
z1	complex number

Returns: difference of the two numbers

◆ operator/() [1/3]

static Complex operator/	(	Complex	z,
		double	d
	)

static

Divides complex number by real number.

Parameters

z	complex number
d	real number

Returns: Quotient of the two numbers

◆ operator/() [2/3]

static Complex operator/	(	Complex	z1,
		Complex	z2
	)

static

Divides complex number by complex number.

Parameters

z1	complex number
z2	complex number

Returns: Quotient of the two numbers

◆ operator/() [3/3]

static Complex operator/	(	double	d,
		Complex	z1
	)

static

Divides a real number by complex number.

Parameters

d	real number
z1	complex number

Returns: Quotient of the two numbers

◆ Parse() [1/2]

static Complex Parse	(	string	pureNumberStr,
		ComplexToStringConversionFormat	complexFormat
	)

static

Parses an string which represents a complex number.

Parameters

pureNumberStr	The string to be converted.
complexFormat	The format of the complex number. Valid formats are RealImaginary and AmplitudePhase.

Returns: Complex number.

◆ Parse() [2/2]

static Complex Parse	(	string	pureNumberStr,
		ComplexToStringConversionFormat	complexFormat,
		NumberFormatInfo	doubleFormat
	)

static

Parses an string which represents a complex number.

Parameters

pureNumberStr	The string to be converted.
complexFormat	The format of the complex number. The SinusCosinus format is not supported. RealImaginary, AmplitudePhase.
doubleFormat	The format of the double-numbers which form the real and imaginary part.

Returns: Complex number.

Exceptions

System.ArgumentException	Current complex format is not supported!
Exceptions.ComplexParseException	string is null-string or string is empty or Invalid complex number Format

◆ Polar()

static Complex Polar	(	double	abs,
		double	arg
	)

static

Returns complex number created by given absolute value and argument.

Parameters

abs	Absolute value.
arg	Argument.

Returns: New Complex object

◆ Pow()

static Complex Pow	(	Complex	basis,
		Complex	exponent
	)

static

public power function of the complex class

Parameters

basis	the basis for the power operation
exponent	the exponent for the power operation

Returns: the calculated power value

◆ Sin()

static Complex Sin ( Complex z )

static

Returns sine of complex number.

Parameters

z	Complex number \(a\).

Returns: \(\sin(a)\).

◆ Sqrt()

static Complex Sqrt ( Complex z )

static

Return square root of complex number.

Parameters

z	Complex number \(a\).

Returns: \(\sqrt{a}\).

◆ ToString() [1/4]

override string ToString ( )

Returns a System.String that represents this instance.

Returns: A System.String that represents this instance, formatted with the format of complex numbers as specified in the Global Options.

◆ ToString() [2/4]

string ToString ( ComplexToStringConversionFormat format )

Returns formatted string, by default: {Real} + {Imaginary} \(\cdot\)i.

Parameters

format

Optional enum parameter specifying which format to use. Format can be either

{Real} + {Imaginary} \(\cdot\)i
{Amplitude} \(\cdot\) exp(i \(\cdot\){Phase})
({Real}, {Imaginary})

If this parameter is not specified, the format of complex numbers as specified in the Global Options is used. /param>

Returns: Formatted string.

◆ ToString() [3/4]

string ToString	(	int	numberOfDigits,
		ComplexToStringConversionFormat?	format = `null`
	)

Returns formatted string, by default: {Real} + {Imaginary} \(\cdot\)i.

Parameters

numberOfDigits	The number of digits to use for the conversion of the double parts of the complex number.
format	Optional enum parameter specifying which format to use. Format can be either {Real} + {Imaginary} \(\cdot\)i {Amplitude} \(\cdot\) exp(i \(\cdot\){Phase}) ({Real}, {Imaginary}) If this parameter is not specified, the format of complex numbers as specified in the Global Options is used.

Returns: Formatted string.

◆ ToString() [4/4]

string ToString	(	PhysicalUnit	physicalUnit,
		ComplexToStringConversionFormat	ComplexToStringFormat,
		int	ComplexToStringConversionDigits
	)

Returns formatted string, either.

{Real} + {Imaginary} \(\cdot\)i
{Amplitude} \(\cdot\) exp({Phase} \(\cdot\) i)
({Real}, {Imaginary})

Parameters

physicalUnit	If the complex number contains/represents a physical unit the corresponding real and imaginary numbers (or amplitude) are returned in measures of the given physical unit. But the corresponding unit-description-string is not appended to the complex number.
ComplexToStringConversionDigits	Digits for the conversion of the double numbers of the real and imaginary part (amplitude or phase) of the complex number.
ComplexToStringFormat	Format of the complex number.

Returns: Formatted string.

◆ TryParse()

static bool TryParse	(	string	pureNumberStr,
		out Complex	parsedValue,
		out ComplexToStringConversionFormat?	usedConversionFormat,
		NumberFormatInfo	doubleFormat = `null`
	)

static

Tries to parse a string which represents a complex number.

Parameters

pureNumberStr	The string to be converted.
parsedValue	The parsed value if successful.
doubleFormat	The format of the double-numbers which form the real and imaginary part.
usedConversionFormat	Null if parsing failed. Otherwise the used ComplexToStringConversionFormat which was successful.

Returns: True if parsing was successful.

Exceptions

System.ArgumentException	Current complex format is not supported!
Exceptions.ComplexParseException	string is null-string or string is empty or Invalid complex number Format

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Complex() [1/3]

◆ Complex() [2/3]

◆ Complex() [3/3]

Member Function Documentation

◆ Abs()

◆ Arg()

◆ ArgDifference()

◆ Conjugate()

◆ Cos()

◆ EvaluateFielQuantity()

◆ Exp()

◆ FilteredPhase()

◆ FromFieldQuantity()

◆ GetComplexFormat()

◆ InputIsNumericalLarger()

◆ IsNaN()

◆ Log()

◆ ModifyComplexPart()

◆ Norm()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ Parse() [1/2]

◆ Parse() [2/2]

◆ Polar()

◆ Pow()

◆ Sin()

◆ Sqrt()

◆ ToString() [1/4]

◆ ToString() [2/4]

◆ ToString() [3/4]

◆ ToString() [4/4]

◆ TryParse()