This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class defines a 3x3 Matrix of double numbers.
Operators ( \(a+b\), \(a-b\)). Operator ( \(a*b\)) supports \(b\) as double or VectorD as well. More...

Public Member Functions
double	Determinant ()
	Calculates the determinant of current Matrix3x3. More...

override bool	Equals (object matrix)
	Compares two matrices for equality. More...

Vector3D	GetCol (int index)
	Returns specified column current Matrix3x3 as VectorD. More...

override int	GetHashCode ()
	Returns a hash code for this instance. More...

Matrix3x3D	GetInverse ()
	Calculates the inverse Matrix3x3 of current one. More...

Vector3D	GetRow (int index)
	Returns specified row current Matrix3x3 as VectorD. More...

Matrix3x3D	GetTransposed ()
	Returns transposed Matrix3x3 of current one. More...

bool	IsIdentity ()
	Checks whether the matrix is the identity matrix. More...

bool	IsIdentityNumericalChecks ()
	Checks whether the matrix is the identity matrix. More...

bool	IsOrthogonal ()
	Checks if matrix is orthogonal, i.e. if M * M^T is the identity matrix More...

	Matrix3x3D ()
	Standard constructor, creates an empty (all zero values) matrix. More...

	Matrix3x3D (double c)
	Constructor to get a diagonal matrix having constant value \(c\) on all diagonal elements. More...

	Matrix3x3D (double m11, double m21, double m31, double m12, double m22, double m32, double m13, double m23, double m33)
	Constructor taking nine doubles to initialize Matrix3x3. More...

	Matrix3x3D (Matrix3x3D matC)
	Copy constructor. More...

	Matrix3x3D (Vector3D firstCol, Vector3D secondCol, Vector3D thirdCol)
	Constructor taking three VectorD to initialize Matrix3x3. More...

override string	ToString ()
	Returns an output string representing current Matrix3x3. More...

string	ToString (int noOfDigits=-1)
	Returns an output string representing current Matrix3x3. More...

double	Trace ()
	Calculates the trace of this matrix. More...

Static Public Member Functions
static Matrix3x3D	InverseMatrix (Matrix3x3D mat)
	Calculates inverse current Matrix3x3 of the given one. More...

static bool	operator!= (Matrix3x3D a, Matrix3x3D b)
	Checks to matrices for inequality. More...

static Matrix3x3D	operator* (double b, Matrix3x3D a)
	Multiplies a Matrix3x3D with a scalar. More...

static Matrix3x3D	operator* (Matrix3x3D a, double b)
	Multiplies a Matrix3x3D with a scalar. More...

static Matrix3x3D	operator* (Matrix3x3D a, Matrix3x3D b)
	Multiplies the elements of two Matrix3x3D objects. More...

static Vector3C	operator* (Matrix3x3D a, Vector3C vec)
	Multiplies a Matrix with an 3-dim. complex Vector (A*Vec) More...

static Vector3D	operator* (Matrix3x3D a, Vector3D vec)
	Multiplies a Matrix with an 3-dim. Vector (A*Vec) More...

static Matrix3x3D	operator+ (Matrix3x3D a, Matrix3x3D b)
	Adds the elements of two Matrix3x3D objects. More...

static Matrix3x3D	operator- (Matrix3x3D a, Matrix3x3D b)
	Subtracts the elements of two Matrix3x3D objects. More...

static bool	operator== (Matrix3x3D a, Matrix3x3D b)
	Compares two matrices. Two matrices are equal when they are equal in all elements. More...

static bool	TryParse (string matrixText, out Matrix3x3D matrix3x3D)
	Tries to parse a Matrix3x3D object from a string. More...

Public Attributes
double[]	Elements
	The field in which the double elements are stored. Note that indices [1..9] are interpreted mathematical. [0] exists but contains no information. Mapping of rows [1..3] and columns [1..3] to one-dimensional index \(i\) is defined by: \(i := row + 3 * (column-1)\).

Properties
static Matrix3x3D	Identity `[get]`
	Static property which gives the identity matrix.

double	this[int row, int col] `[get, set]`
	Gets or sets a certain matrix element. More...

Detailed Description

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class defines a 3x3 Matrix of double numbers.
Operators ( \(a+b\), \(a-b\)). Operator ( \(a*b\)) supports \(b\) as double or VectorD as well.

Constructor & Destructor Documentation

◆ Matrix3x3D() [1/5]

Matrix3x3D ( )

Standard constructor, creates an empty (all zero values) matrix.

◆ Matrix3x3D() [2/5]

Matrix3x3D ( double c )

Constructor to get a diagonal matrix having constant value \(c\) on all diagonal elements.

Parameters

c	Value \(c\) used to initialize diagonal elements.

◆ Matrix3x3D() [3/5]

Matrix3x3D ( Matrix3x3D matC )

Copy constructor.

Parameters

matC	Matrix3x3D to be copied.

◆ Matrix3x3D() [4/5]

Matrix3x3D	(	Vector3D	firstCol,
		Vector3D	secondCol,
		Vector3D	thirdCol
	)

Constructor taking three VectorD to initialize Matrix3x3.

Parameters

firstCol	First column.
secondCol	Second column.
thirdCol	Third column.

◆ Matrix3x3D() [5/5]

Matrix3x3D	(	double	m11,
		double	m21,
		double	m31,
		double	m12,
		double	m22,
		double	m32,
		double	m13,
		double	m23,
		double	m33
	)

Constructor taking nine doubles to initialize Matrix3x3.

Parameters

m11	First element of first column.
m21	Second element of first column.
m31	Third element of first column.
m12	First element of second column.
m22	Second element of second column.
m32	Third element of second column.
m13	First element of third column.
m23	Second element of third column.
m33	Third element of third column.

Member Function Documentation

◆ Determinant()

double Determinant ( )

Calculates the determinant of current Matrix3x3.

Returns

◆ Equals()

override bool Equals ( object matrix )

Compares two matrices for equality.

Parameters

matrix matrix to compare with

Returns: True if the two matrices store the same values.

◆ GetCol()

Vector3D GetCol ( int index )

Returns specified column current Matrix3x3 as VectorD.

Parameters

index Column to return (index is one-based!).

Returns: Result of operation.

◆ GetHashCode()

override int GetHashCode ( )

Returns a hash code for this instance.

Returns: A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.

◆ GetInverse()

Matrix3x3D GetInverse ( )

Calculates the inverse Matrix3x3 of current one.

Returns

◆ GetRow()

Vector3D GetRow ( int index )

Returns specified row current Matrix3x3 as VectorD.

Parameters

index Row to return (index is one-based!).

Returns: Result of operation.

◆ GetTransposed()

Matrix3x3D GetTransposed ( )

Returns transposed Matrix3x3 of current one.

Returns: Result of operation..

◆ InverseMatrix()

static Matrix3x3D InverseMatrix ( Matrix3x3D mat )

static

Calculates inverse current Matrix3x3 of the given one.

Parameters

mat	Matrix3x3 to invert.

Returns: Result of operation.

◆ IsIdentity()

bool IsIdentity ( )

Checks whether the matrix is the identity matrix.

Returns: TRUE iff the matrix is the identity matrix

◆ IsIdentityNumericalChecks()

bool IsIdentityNumericalChecks ( )

Checks whether the matrix is the identity matrix.

Returns: TRUE iff the matrix is the identity matrix

◆ IsOrthogonal()

bool IsOrthogonal ( )

Checks if matrix is orthogonal, i.e. if M * M^T is the identity matrix

Returns: True iff matrix is orthogonal

◆ operator!=()

static bool operator!=	(	Matrix3x3D	a,
		Matrix3x3D	b
	)

static

Checks to matrices for inequality.

Parameters

a	first matrix
b	second matrix

Returns: FALSE if they are equal, otherwise TRUE.

◆ operator*() [1/5]

static Matrix3x3D operator*	(	double	b,
		Matrix3x3D	a
	)

static

Multiplies a Matrix3x3D with a scalar.

Parameters

b	scalar
a	Matrix

Returns: product

◆ operator*() [2/5]

static Matrix3x3D operator*	(	Matrix3x3D	a,
		double	b
	)

static

Multiplies a Matrix3x3D with a scalar.

Parameters

a	Matrix
b	scalar

Returns: product

◆ operator*() [3/5]

static Matrix3x3D operator*	(	Matrix3x3D	a,
		Matrix3x3D	b
	)

static

Multiplies the elements of two Matrix3x3D objects.

Parameters

a	the first matrix
b	the second matrix

Returns: The product of the two matrices.

◆ operator*() [4/5]

static Vector3C operator*	(	Matrix3x3D	a,
		Vector3C	vec
	)

static

Multiplies a Matrix with an 3-dim. complex Vector (A*Vec)

Parameters

a	3x3-Matrix
vec	Vector3C

Returns: Product: Vector3C

◆ operator*() [5/5]

static Vector3D operator*	(	Matrix3x3D	a,
		Vector3D	vec
	)

static

Multiplies a Matrix with an 3-dim. Vector (A*Vec)

Parameters

a	3x3-Matrix
vec	Vector

Returns: Product: Vector3D

◆ operator+()

static Matrix3x3D operator+	(	Matrix3x3D	a,
		Matrix3x3D	b
	)

static

Adds the elements of two Matrix3x3D objects.

Parameters

a	the first matrix
b	the second matrix

Returns: The sum of the two matrices.

◆ operator-()

static Matrix3x3D operator-	(	Matrix3x3D	a,
		Matrix3x3D	b
	)

static

Subtracts the elements of two Matrix3x3D objects.

Parameters

a	the first matrix
b	the second matrix

Returns: The Difference of the two matrices.

◆ operator==()

static bool operator==	(	Matrix3x3D	a,
		Matrix3x3D	b
	)

static

Compares two matrices. Two matrices are equal when they are equal in all elements.

Parameters

a	first matrix
b	second matrix

Returns: TRUE if they are equal, otherwise false.

◆ ToString() [1/2]

override string ToString ( )

Returns an output string representing current Matrix3x3.

Returns

◆ ToString() [2/2]

string ToString ( int noOfDigits = -1 )

Returns an output string representing current Matrix3x3.

Returns

◆ Trace()

double Trace ( )

Calculates the trace of this matrix.

Returns

◆ TryParse()

static bool TryParse	(	string	matrixText,
		out Matrix3x3D	matrix3x3D
	)

static

Tries to parse a Matrix3x3D object from a string.

Parameters

matrixText	String which have to be formatted like inside Marix3x3D.ToString()
matrix3x3D	The parsed matrix if parse has been possible. Null otherwise.

Returns: A flag indicating whether or not the parsing was successful.

Property Documentation

◆ this[int row, int col]

double this[int row, int col]

getset

Gets or sets a certain matrix element.

The selected matrix element.

Parameters

row	The zero-based row index.
col	The zero-based column index.

Returns: The element at the specified matrix position.

Exceptions

System.ArgumentOutOfRangeException At least one of the two given indices is out of range.

Public Member Functions

Static Public Member Functions

Public Attributes

Properties

Detailed Description

Constructor & Destructor Documentation

◆ Matrix3x3D() [1/5]

◆ Matrix3x3D() [2/5]

◆ Matrix3x3D() [3/5]

◆ Matrix3x3D() [4/5]

◆ Matrix3x3D() [5/5]

Member Function Documentation

◆ Determinant()

◆ Equals()

◆ GetCol()

◆ GetHashCode()

◆ GetInverse()

◆ GetRow()

◆ GetTransposed()

◆ InverseMatrix()

◆ IsIdentity()

◆ IsIdentityNumericalChecks()

◆ IsOrthogonal()

◆ operator!=()

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator+()

◆ operator-()

◆ operator==()

◆ ToString() [1/2]

◆ ToString() [2/2]

◆ Trace()

◆ TryParse()

Property Documentation

◆ this[int row, int col]