This class defines 3-dimensional vectors of complex numbers. The class saves the x,y and z coordinates. More...

Inheritance diagram for Vector3C:

Public Member Functions
double	Abs ()
	Calculates the absolute value of this Vector3C object. The absolute value is defined as the square root of Norm().

Complex	ComplexAbs ()
	Calculates the complex Norm of the Vector3C object.

bool	IsRealVector ()
	Determines whether this vector is a pure real one, i.e. all imaginary parts are zero.

double	Norm ()
	Calculates the norm of the present Vector3C object. The norm is defined as (X * Complex.Conjugate(X) + Y * Complex.Conjugate(Y) + Z * Complex.Conjugate(Z)).Re which is equal to the sum of the norms of the vector components.

void	Normalize ()
	Normalizes the present Vector3C object.

override string	ToString ()
	Converts a Vector3C into a string of format (X.Re + iX.Im;Y.Re + iY.Im;Z.Re + iZ.Im).

	Vector3C (Complex x, Complex y, Complex z)
	Creates a Vector3C from three double values.

	Vector3C (Vector3C vec)
	Creates a new Vector3C object from an existing object.

Static Public Member Functions
static Vector3C	CrossProduct (Vector3C a, Vector3C b)
	Calculates the cross product of two Vector3C objects.

static implicit	operator Vector3C (Vector3D vector3D)
	Converts a Vector3D object into a Vector3C object.

static bool	operator!= (Vector3C vector1, Vector3C vector2)
	Compares two Vector3C for inequality. The comparison will be done by comparing the values of the two x-, y- and z- components respectively.

static Vector3C	operator* (Complex factor, Vector3C vector)
	Multiplies a Vector3C objects with a Complex value.

static Vector3C	operator* (Vector3C a, Vector3C b)
	Multiplies two Vector3C objects.

static Vector3C	operator* (Vector3C vector, Complex factor)
	Multiplies a Vector3C object with a Complex value.

static Vector3C	operator+ (Vector3C a, Vector3C b)
	Adds two Vector3C objects.

static Vector3C	operator- (Vector3C a, Vector3C b)
	Subtracts two Vector3C objects.

static Vector3C	operator/ (Complex number, Vector3C vector)
	Performs a component wise division of a double value and a Vector3C object. The result is defined as new Vector3C(number / vector.X, number / vector.Y).

static Vector3C	operator/ (Vector3C a, Vector3C b)
	Performs a component wise division of two Vector3C objects.

static Vector3C	operator/ (Vector3C vector, Complex divisor)
	Performs a component wise division of a Vector3C object and a Complex value.

static bool	operator== (Vector3C vector1, Vector3C vector2)
	Compares two Vector3C for equality. The comparison will be done by comparing the values of the two x-, y- and z- components respectively.

static Complex	operator\| (Vector3C a, Vector3C b)
	Calculates the scalar product of two Vector3C objects. The scalar product is defined as a.X * b.X + a.Y * b.Y + a.Z * b.Z.

Public Attributes
Complex	X
	X value of the Vector3C object.

Complex	Y
	Y value of the Vector3C object.

Complex	Z
	Z value of the Vector3C object.

Static Public Attributes
static readonly Vector3C	UnitVectorX
	A constant containing the unit vector in x-direction.

static readonly Vector3C	UnitVectorY
	A constant containing the unit vector in y-direction.

static readonly Vector3C	UnitVectorZ
	A constant containing the unit vector in z-direction.

static readonly Vector3C	ZeroVector
	A constant containing the zero vector (0, 0).

Properties
Vector3D	Im `[get, set]`
	Sets or gets a Vector3D object containing the the imaginary part of the x-, y- and z- components of the present Vector3C object. If an Vector3D object is set then the real parts of all components is not influences.

bool	IsUndefined `[get]`
	Gets whether a least one component of the vector is undefined.

Vector3D	Re `[get, set]`
	Sets or gets a Vector3D object containing the the real part of the x-, y- and z- components of the present Vector3C object. If an Vector3D object is set then the imaginary parts of all components is not influences.

Detailed Description

This class defines 3-dimensional vectors of complex numbers. The class saves the x,y and z coordinates.

Constructor & Destructor Documentation

◆ Vector3C() [1/2]

Vector3C	(	Complex	x,
		Complex	y,
		Complex	z
	)

Creates a Vector3C from three double values.

Parameters

x	X value of new Vector3C object.
y	Y value of new Vector3C object.
z	Z value of new Vector3C object.

◆ Vector3C() [2/2]

Vector3C ( Vector3C vec )

Creates a new Vector3C object from an existing object.

Parameters

vec	Vector3C object to copy.

Member Function Documentation

◆ Abs()

double Abs ( )

Calculates the absolute value of this Vector3C object. The absolute value is defined as the square root of Norm().

Returns: The absolute value of the Vector3C.

◆ ComplexAbs()

Complex ComplexAbs ( )

Calculates the complex Norm of the Vector3C object.

Returns: the norm of the vector

◆ CrossProduct()

static Vector3C CrossProduct	(	Vector3C	a,
		Vector3C	b
	)

static

Calculates the cross product of two Vector3C objects.

Parameters

a	First operant used for cross product calculation.
b	Second operant used for cross product calculation.

Returns: A Vector3C object containing the cross product

◆ IsRealVector()

bool IsRealVector ( )

Determines whether this vector is a pure real one, i.e. all imaginary parts are zero.

Returns: True iff the imaginary parts of all vector components are zero.

◆ Norm()

double Norm ( )

Calculates the norm of the present Vector3C object. The norm is defined as (X * Complex.Conjugate(X) + Y * Complex.Conjugate(Y) + Z * Complex.Conjugate(Z)).Re which is equal to the sum of the norms of the vector components.

Returns: The norm of the Vector3C object.

◆ operator Vector3C()

static implicit operator Vector3C ( Vector3D vector3D )

static

Converts a Vector3D object into a Vector3C object.

Parameters

vector3D Vector3D object to convert into Vector3C object.

Returns: The converted Vector3C object.

◆ operator!=()

static bool operator!=	(	Vector3C	vector1,
		Vector3C	vector2
	)

static

Compares two Vector3C for inequality. The comparison will be done by comparing the values of the two x-, y- and z- components respectively.

Parameters

vector1	First Vector3C object to compare.
vector2	Second Vector3C object to compare.

Returns: Returns true if the two objects are unequal.

◆ operator*() [1/3]

static Vector3C operator*	(	Complex	factor,
		Vector3C	vector
	)

static

Multiplies a Vector3C objects with a Complex value.

Parameters

factor	The Complex value to multiply.
vector	The Vector3C object to multiply.

Returns: Returns the product of the Vector3C object and the Complex value.

◆ operator*() [2/3]

static Vector3C operator*	(	Vector3C	a,
		Vector3C	b
	)

static

Multiplies two Vector3C objects.

Parameters

a	The first Vector3C object to multiply.
b	The second Vector3C object to multiply.

Returns: Returns the product of the two Vector3C objects.

◆ operator*() [3/3]

static Vector3C operator*	(	Vector3C	vector,
		Complex	factor
	)

static

Multiplies a Vector3C object with a Complex value.

Parameters

vector	The Vector3C object to multiply.
factor	The Complex value to multiply.

Returns: Returns the product of the Vector3C object and the Complex value.

◆ operator+()

static Vector3C operator+	(	Vector3C	a,
		Vector3C	b
	)

static

Adds two Vector3C objects.

Parameters

a	The first Vector3C object to add.
b	The second Vector3C object to add.

Returns: Returns the sum of the two Vector3C objects.

◆ operator-()

static Vector3C operator-	(	Vector3C	a,
		Vector3C	b
	)

static

Subtracts two Vector3C objects.

Parameters

a	The first Vector3C object to subtract from.
b	The second Vector3C object to subtract.

Returns: Returns the difference of the two Vector3C objects.

◆ operator/() [1/3]

static Vector3C operator/	(	Complex	number,
		Vector3C	vector
	)

static

Performs a component wise division of a double value and a Vector3C object. The result is defined as new Vector3C(number / vector.X, number / vector.Y).

Parameters

number	The double value to divide by the components of the Vector3C object.
vector	The Vector3C object used as divisor.

Returns: Returns the quotient of the double value and the Vector3C object.

◆ operator/() [2/3]

static Vector3C operator/	(	Vector3C	a,
		Vector3C	b
	)

static

Performs a component wise division of two Vector3C objects.

Parameters

a	The first Vector3C object to divide by parameter b.
b	The second Vector3C object used as divisor.

Returns: Returns the quotient of the two Vector3C objects.

◆ operator/() [3/3]

static Vector3C operator/	(	Vector3C	vector,
		Complex	divisor
	)

static

Performs a component wise division of a Vector3C object and a Complex value.

Parameters

vector	The Vector3C object to divide by the Complex value.
divisor	The Complex value used as divisor.

Returns: Returns the quotient of the Vector3C object and the Complex value.

◆ operator==()

static bool operator==	(	Vector3C	vector1,
		Vector3C	vector2
	)

static

Compares two Vector3C for equality. The comparison will be done by comparing the values of the two x-, y- and z- components respectively.

Parameters

vector1	First Vector3C object to compare.
vector2	Second Vector3C object to compare.

Returns: Returns true if the two objects are equal.

◆ operator|()

static Complex operator\|	(	Vector3C	a,
		Vector3C	b
	)

static

Calculates the scalar product of two Vector3C objects. The scalar product is defined as a.X * b.X + a.Y * b.Y + a.Z * b.Z.

Parameters

a	First Vector3C object.
b	Second Vector3C object.

Returns: Scalar product of the two Vector3C objects.

◆ ToString()

override string ToString ( )

Converts a Vector3C into a string of format (X.Re + iX.Im;Y.Re + iY.Im;Z.Re + iZ.Im).

Returns: String containing the Vector3C information.

Property Documentation

◆ IsUndefined

bool IsUndefined

get

Gets whether a least one component of the vector is undefined.

Returns: true iff at least one component of the vector is NaN.

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Properties

Detailed Description

Constructor & Destructor Documentation

◆ Vector3C() [1/2]

◆ Vector3C() [2/2]

Member Function Documentation

◆ Abs()

◆ ComplexAbs()

◆ CrossProduct()

◆ IsRealVector()

◆ Norm()

◆ operator Vector3C()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator==()

◆ operator|()

◆ ToString()

Property Documentation

◆ IsUndefined