Detailed Description

template<typename Type>
class walberla::math::Matrix2< Type >

Efficient, generic implementation of a 2x2 matrix.

The Matrix2 class is the representation of a 2x2 matrix with a total of 9 statically allocated elements of arbitrary type. The naming convention of the elements is as follows:

                      \f[\left(\begin{array}{*{2}{c}}
                      xx & xy  \\
                      yx & yy  \\
                      \end{array}\right)\f]\n

These elements can be accessed directly with the 1D subscript operator or with the 2D function operator. The numbering of the matrix elements is

                      \f[\left(\begin{array}{*{3}{c}}
                      0 & 1  \\
                      2 & 3  \\
                      \end{array}\right)\f]

#include <Types.h>

Public Member Functions
constexpr	Matrix2 ()
	The default constructor for Matrix2. More...

constexpr	Matrix2 (Type init)
	Constructor for a homogeneous initialization of all elements. More...

constexpr	Matrix2 (Type xx, Type xy, Type yx, Type yy)
	Constructor for a direct initialization of all matrix elements. More...

constexpr	Matrix2 (const Type *init)
	Constructor for an array initializer. More...

constexpr	Matrix2 (const Matrix2 &m)
	The copy constructor for Matrix2. More...

template<typename Other >
constexpr	Matrix2 (const Matrix2< Other > &m)
	Conversion constructor from different Matrix2 instances. More...

template<typename Other >
Matrix2< Type > &	operator= (const Matrix2< Other > &set)

template<typename Other >
Matrix2< Type > &	operator+= (const Matrix2< Other > &rhs)

template<typename Other >
Matrix2< Type > &	operator-= (const Matrix2< Other > &rhs)

template<typename Other >
Matrix2< Type > &	operator*= (Other rhs)

template<typename Other >
Matrix2< Type > &	operator*= (const Matrix2< Other > &rhs)

Operators
Matrix2 &	operator= (Type set)
	Homogenous assignment to all matrix elements. More...

Matrix2 &	operator= (const Matrix2 &set)
	Copy assignment operator for Matrix2. More...

template<typename Other >
Matrix2 &	operator= (const Matrix2< Other > &set)
	Assignment operator for different Matrix2 instances. More...

template<typename Other >
bool	operator== (const Matrix2< Other > &rhs) const
	Equality operator for the comparison of two matrices. More...

template<typename Other >
bool	operator!= (const Matrix2< Other > &rhs) const
	Inequality operator for the comparison of two matrices. More...

Type &	operator[] (uint_t index)
	1D-access to the matrix elements. More...

const Type &	operator[] (uint_t index) const
	1D-access to the matrix elements. More...

Type &	operator() (uint_t i, uint_t j)
	2D-access to the matrix elements. More...

const Type &	operator() (uint_t i, uint_t j) const
	2D-access to the matrix elements. More...

Arithmetic operators
The return type of the arithmetic operators depends on the involved data types of the matrices. HIGH denotes the more significant data type of the arithmetic operation (for further detail see the MathTrait class description).
template<typename Other >
Matrix2 &	operator+= (const Matrix2< Other > &rhs)
	Addition assignment operator for the addition of two matrices ( \( A+=B \)). More...

template<typename Other >
Matrix2 &	operator-= (const Matrix2< Other > &rhs)
	Subtraction assignment operator for the subtraction of two matrices ( \( A-=B \)). More...

template<typename Other >
Matrix2 &	operator*= (Other rhs)
	Multiplication assignment operator for the multiplication between a matrix and. More...

template<typename Other >
Matrix2 &	operator*= (const Matrix2< Other > &rhs)
	Multiplication assignment operator for the multiplication between two matrices. More...

template<typename Other >
const Matrix2< typename MathTrait< Type, Other >::High >	operator+ (const Matrix2< Other > &rhs) const
	Addition operator for the addition of two matrices ( \( A=B+C \)). More...

template<typename Other >
const Matrix2< typename MathTrait< Type, Other >::High >	operator- (const Matrix2< Other > &rhs) const
	Subtraction operator for the subtraction of two matrices ( \( A=B-C \)). More...

template<typename Other >
const Matrix2< typename MathTrait< Type, Other >::High >	operator* (Other rhs) const
	Multiplication operator for the multiplication of a matrix and a scalar value. More...

template<typename Other >
const Vector2< typename MathTrait< Type, Other >::High >	operator* (const Vector2< Other > &rhs) const

template<typename Other >
const Matrix2< typename MathTrait< Type, Other >::High >	operator* (const Matrix2< Other > &rhs) const
	Multiplication operator for the multiplication of two matrices ( \( A=B*C \)). More...

Utility functions
The return type of the utility functions depends on the involved data types of the matrices. HIGH denotes the more significant data type of the utility operations (for further detail see the MathTrait class description).
Type	getDeterminant () const
	Calculation of the determinant of the matrix. More...

Matrix2 &	transpose ()
	Transposing the matrix. More...

const Matrix2	getTranspose () const
	Calculation of the transpose of the matrix. More...

Matrix2 &	invert ()
	Inverting the matrix. More...

const Matrix2	getInverse () const
	Calculation of the inverse of the matrix. More...

bool	isSingular () const
	Singularity check for the matrix (det=0). More...

bool	isSymmetric () const
	Checks if the matrix is symmetric. More...

Type *	data ()

Private Attributes
Member variables
Type	v_ [4]
	The nine statically allocated matrix elements. More...

Constructor & Destructor Documentation

◆ Matrix2() [1/6]

template<typename Type >

constexpr walberla::math::Matrix2< Type >::Matrix2

inlineexplicitconstexpr

The default constructor for Matrix2.

The diagonal matrix elements are initialized with 1, all other elements are initialized with 0.

◆ Matrix2() [2/6]

template<typename Type >

constexpr walberla::math::Matrix2< Type >::Matrix2 ( Type init )

inlineexplicitconstexpr

Constructor for a homogeneous initialization of all elements.

Parameters

init	Initial value for all matrix elements.

◆ Matrix2() [3/6]

template<typename Type >

constexpr walberla::math::Matrix2< Type >::Matrix2	(	Type	xx,
		Type	xy,
		Type	yx,
		Type	yy
	)

inlineexplicitconstexpr

Constructor for a direct initialization of all matrix elements.

Parameters

xx	The initial value for the xx-component.
xy	The initial value for the xy-component.
yx	The initial value for the yx-component.
yy	The initial value for the yy-component.

◆ Matrix2() [4/6]

template<typename Type >

constexpr walberla::math::Matrix2< Type >::Matrix2 ( const Type * init )

inlineexplicitconstexpr

Constructor for an array initializer.

Parameters

init	Pointer to the initialization array.

The array is assumed to have at least nine valid elements.

◆ Matrix2() [5/6]

template<typename Type >

constexpr walberla::math::Matrix2< Type >::Matrix2 ( const Matrix2< Type > & m )

inlineconstexpr

The copy constructor for Matrix2.

Parameters

m	Matrix to be copied.

The copy constructor is explicitly defined in order to enable/facilitate NRV optimization.

◆ Matrix2() [6/6]

template<typename Type >

template<typename Other >

constexpr walberla::math::Matrix2< Type >::Matrix2 ( const Matrix2< Other > & m )

inlineconstexpr

Conversion constructor from different Matrix2 instances.

Parameters

m	Matrix to be copied.

Member Function Documentation

◆ data()

template<typename Type >

Type* walberla::math::Matrix2< Type >::data ( )

inline

◆ getDeterminant()

template<typename Type >

Type walberla::math::Matrix2< Type >::getDeterminant

inline

Calculation of the determinant of the matrix.

Returns: The determinant of the matrix.

◆ getInverse()

template<typename Type >

const Matrix2< Type > walberla::math::Matrix2< Type >::getInverse

inline

Calculation of the inverse of the matrix.

Returns: The inverse of the matrix.

The calculation is performed with the matrix inversion by Cramer. This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data types will result in a compile time error.

◆ getTranspose()

template<typename Type >

const Matrix2< Type > walberla::math::Matrix2< Type >::getTranspose

inline

Calculation of the transpose of the matrix.

Returns: The transpose of the matrix.

◆ invert()

template<typename Type >

Matrix2< Type > & walberla::math::Matrix2< Type >::invert

inline

Inverting the matrix.

Returns: Reference to the inverted matrix.

The calculation is performed with the matrix inversion by Cramer. This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data types will result in a compile time error.

◆ isSingular()

template<typename Type >

bool walberla::math::Matrix2< Type >::isSingular

inline

Singularity check for the matrix (det=0).

Returns: true if the matrix is singular, false if not.

◆ isSymmetric()

template<typename Type >

bool walberla::math::Matrix2< Type >::isSymmetric

inline

Checks if the matrix is symmetric.

Returns: true if the matrix is symmetric, false if not.

◆ operator!=()

template<typename Type >

template<typename Other >

bool walberla::math::Matrix2< Type >::operator!= ( const Matrix2< Other > & rhs ) const

inline

Inequality operator for the comparison of two matrices.

Parameters

rhs	The right-hand-side matrix for the comparison.

Returns: bool

◆ operator()() [1/2]

template<typename Type >

Type & walberla::math::Matrix2< Type >::operator()	(	uint_t	i,
		uint_t	j
	)

inline

2D-access to the matrix elements.

Parameters

i	Access index for the row. The index has to be in the range [0..2].
j	Access index for the column. The index has to be in the range [0..2].

Returns: Reference to the accessed value.

◆ operator()() [2/2]

template<typename Type >

const Type & walberla::math::Matrix2< Type >::operator()	(	uint_t	i,
		uint_t	j
	)		const

inline

2D-access to the matrix elements.

Parameters

i	Access index for the row. The index has to be in the range [0..2].
j	Access index for the column. The index has to be in the range [0..2].

Returns: Reference-to-const to the accessed value.

◆ operator*() [1/3]

template<typename Type >

template<typename Other >

const Matrix2< typename MathTrait< Type, Other >::High > walberla::math::Matrix2< Type >::operator* ( const Matrix2< Other > & rhs ) const

inline

Multiplication operator for the multiplication of two matrices ( \( A=B*C \)).

Parameters

rhs	The right-hand-side matrix for the multiplication.

Returns: The resulting matrix.

◆ operator*() [2/3]

template<typename Type >

template<typename Other >

const Vector2< typename MathTrait< Type, Other >::High > walberla::math::Matrix2< Type >::operator* ( const Vector2< Other > & rhs ) const

inline

◆ operator*() [3/3]

template<typename Type >

template<typename Other >

const Matrix2< typename MathTrait< Type, Other >::High > walberla::math::Matrix2< Type >::operator* ( Other rhs ) const

inline

Multiplication operator for the multiplication of a matrix and a scalar value.

( \( A=B*s \)).

Parameters

rhs	The right-hand-side scalar value for the multiplication.

Returns: The scaled result matrix.

◆ operator*=() [1/4]

template<typename Type >

template<typename Other >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator*= ( const Matrix2< Other > & rhs )

inline

Multiplication assignment operator for the multiplication between two matrices.

( \( A*=B \)).

Parameters

rhs	The right-hand-side matrix for the multiplication.

Returns: Reference to the matrix.

◆ operator*=() [2/4]

template<typename Type >

template<typename Other >

Matrix2<Type>& walberla::math::Matrix2< Type >::operator*= ( const Matrix2< Other > & rhs )

inline

◆ operator*=() [3/4]

template<typename Type >

template<typename Other >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator*= ( Other rhs )

inline

Multiplication assignment operator for the multiplication between a matrix and.

a scalar value ( \( A*=s \)).

Parameters

rhs	The right-hand-side scalar value for the multiplication.

Returns: Reference to the matrix.

◆ operator*=() [4/4]

template<typename Type >

template<typename Other >

Matrix2<Type>& walberla::math::Matrix2< Type >::operator*= ( Other rhs )

inline

◆ operator+()

template<typename Type >

template<typename Other >

const Matrix2< typename MathTrait< Type, Other >::High > walberla::math::Matrix2< Type >::operator+ ( const Matrix2< Other > & rhs ) const

inline

Addition operator for the addition of two matrices ( \( A=B+C \)).

Parameters

rhs	The right-hand-side matrix to be added to the matrix.

Returns: The sum of the two matrices.

◆ operator+=() [1/2]

template<typename Type >

template<typename Other >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator+= ( const Matrix2< Other > & rhs )

inline

Addition assignment operator for the addition of two matrices ( \( A+=B \)).

Parameters

rhs	The right-hand-side matrix to be added to the matrix.

Returns: Reference to the matrix.

◆ operator+=() [2/2]

template<typename Type >

template<typename Other >

Matrix2<Type>& walberla::math::Matrix2< Type >::operator+= ( const Matrix2< Other > & rhs )

inline

◆ operator-()

template<typename Type >

template<typename Other >

const Matrix2< typename MathTrait< Type, Other >::High > walberla::math::Matrix2< Type >::operator- ( const Matrix2< Other > & rhs ) const

inline

Subtraction operator for the subtraction of two matrices ( \( A=B-C \)).

Parameters

rhs	The right-hand-side matrix to be subtracted from the matrix.

Returns: The difference of the two matrices.

◆ operator-=() [1/2]

template<typename Type >

template<typename Other >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator-= ( const Matrix2< Other > & rhs )

inline

Subtraction assignment operator for the subtraction of two matrices ( \( A-=B \)).

Parameters

rhs	The right-hand-side matrix to be subtracted from the matrix.

Returns: Reference to the matrix.

◆ operator-=() [2/2]

template<typename Type >

template<typename Other >

Matrix2<Type>& walberla::math::Matrix2< Type >::operator-= ( const Matrix2< Other > & rhs )

inline

◆ operator=() [1/4]

template<typename Type >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator= ( const Matrix2< Type > & set )

inline

Copy assignment operator for Matrix2.

Parameters

set	Matrix to be copied.

Returns: Reference to the assigned matrix.

Explicit definition of a copy assignment operator for performance reasons.

◆ operator=() [2/4]

template<typename Type >

template<typename Other >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator= ( const Matrix2< Other > & set )

inline

Assignment operator for different Matrix2 instances.

Parameters

set	Matrix to be copied.

Returns: Reference to the assigned matrix.

◆ operator=() [3/4]

template<typename Type >

template<typename Other >

Matrix2<Type>& walberla::math::Matrix2< Type >::operator= ( const Matrix2< Other > & set )

inline

◆ operator=() [4/4]

template<typename Type >

Matrix2< Type > & walberla::math::Matrix2< Type >::operator= ( Type set )

inline

Homogenous assignment to all matrix elements.

Parameters

set	Scalar value to be assigned to all matrix elements.

Returns: Reference to the assigned matrix.

◆ operator==()

template<typename Type >

template<typename Other >

bool walberla::math::Matrix2< Type >::operator== ( const Matrix2< Other > & rhs ) const

inline

Equality operator for the comparison of two matrices.

Parameters

rhs	The right-hand-side matrix for the comparison.

Returns: bool

◆ operator[]() [1/2]

template<typename Type >

Type & walberla::math::Matrix2< Type >::operator[] ( uint_t index )

inline

1D-access to the matrix elements.

Parameters

index Access index. The index has to be in the range \([0..8]\).

Returns: Reference to the accessed value.

◆ operator[]() [2/2]

template<typename Type >

const Type & walberla::math::Matrix2< Type >::operator[] ( uint_t index ) const

inline

1D-access to the matrix elements.

Parameters

index Access index. The index has to be in the range \([0..8]\).

Returns: Reference-to-const to the accessed value.

◆ transpose()

template<typename Type >

Matrix2< Type > & walberla::math::Matrix2< Type >::transpose

inline

Transposing the matrix.

Returns: Reference to the transposed matrix.

Member Data Documentation

◆ v_

template<typename Type >

Type walberla::math::Matrix2< Type >::v_[4]

private

The nine statically allocated matrix elements.

Access to the matrix elements is gained via the subscript or function call operator. The order of the elements is

\[\left(\begin{array}{*{2}{c}} 0 & 1 \\ 2 & 3 \\ \end{array}\right)\]

The documentation for this class was generated from the following file:

/builds/administration/walberla-website/walberla/src/core/math/Matrix2.h

Detailed Description

template<typename Type> class walberla::math::Matrix2< Type >

Public Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ Matrix2() [1/6]

◆ Matrix2() [2/6]

◆ Matrix2() [3/6]

◆ Matrix2() [4/6]

◆ Matrix2() [5/6]

◆ Matrix2() [6/6]

Member Function Documentation

◆ data()

◆ getDeterminant()

◆ getInverse()

◆ getTranspose()

◆ invert()

◆ isSingular()

◆ isSymmetric()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/4]

◆ operator*=() [2/4]

◆ operator*=() [3/4]

◆ operator*=() [4/4]

◆ operator+()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ transpose()

Member Data Documentation

◆ v_

template<typename Type>
class walberla::math::Matrix2< Type >