Detailed Description

template<typename Type>
class walberla::math::Matrix3< Type >

Efficient, generic implementation of a 3x3 matrix.

The Matrix3 class is the representation of a 3x3 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}{*{3}{c}}
                      xx & xy & xz \\
                      yx & yy & yz \\
                      zx & zy & zz \\
                      \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 & 4 & 5 \\
                      6 & 7 & 8 \\
                      \end{array}\right)\f]

#include <Types.h>

Public Member Functions
constexpr	Matrix3 ()=default

constexpr	Matrix3 (Type init)
	Constructor for a homogeneous initialization of all elements. More...

constexpr	Matrix3 (const Vector3< Type > &a, const Vector3< Type > &b, const Vector3< Type > &c)

constexpr	Matrix3 (Type xx, Type xy, Type xz, Type yx, Type yy, Type yz, Type zx, Type zy, Type zz)
	Constructor for a direct initialization of all matrix elements. More...

constexpr	Matrix3 (const Type *init)
	Constructor for an array initializer. More...

template<typename Axis , typename Angle >
	Matrix3 (Vector3< Axis > axis, Angle angle)
	Rotation matrix constructor. More...

	Matrix3 (const Matrix3 &m)=default

template<typename Other >
	Matrix3 (const Matrix3< Other > &m)
	Conversion constructor from different Matrix3 instances. More...

template<typename Other >
Matrix3< Type > &	operator= (const Matrix3< Other > &set)

template<typename Other >
Matrix3< Type > &	operator+= (const Matrix3< Other > &rhs)

template<typename Other >
Matrix3< Type > &	operator-= (const Matrix3< Other > &rhs)

template<typename Other >
Matrix3< Type > &	operator*= (const Matrix3< Other > &rhs)

Operators
Matrix3 &	operator= (Type set)
	Homogenous assignment to all matrix elements. More...

Matrix3 &	operator= (const Matrix3 &set)=default

template<typename Other >
Matrix3 &	operator= (const Matrix3< Other > &set)
	Assignment operator for different Matrix3 instances. More...

template<typename Other >
bool	operator== (const Matrix3< Other > &rhs) const
	Equality operator for the comparison of two matrices. More...

template<typename Other >
bool	operator!= (const Matrix3< 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 >
Matrix3 &	operator+= (const Matrix3< Other > &rhs)
	Addition assignment operator for the addition of two matrices ( \( A+=B \)). More...

template<typename Other >
Matrix3 &	operator-= (const Matrix3< Other > &rhs)
	Subtraction assignment operator for the subtraction of two matrices ( \( A-=B \)). More...

template<typename Other >
Matrix3 &	operator*= (const Matrix3< Other > &rhs)
	Multiplication assignment operator for the multiplication between two matrices. More...

template<typename Other >
const Matrix3< typename MathTrait< Type, Other >::High >	operator+ (const Matrix3< Other > &rhs) const
	Addition operator for the addition of two matrices ( \( A=B+C \)). More...

template<typename Other >
const Matrix3< typename MathTrait< Type, Other >::High >	operator- (const Matrix3< Other > &rhs) const
	Subtraction operator for the subtraction of two matrices ( \( A=B-C \)). More...

template<typename Other >
const Vector3< typename MathTrait< Type, Other >::High >	operator* (const Vector3< Other > &rhs) const
	Multiplication operator for the multiplication of a matrix and a vector. More...

template<typename Other >
const Matrix3< typename MathTrait< Type, Other >::High >	operator* (const Matrix3< Other > &rhs) const
	Multiplication operator for the multiplication of two matrices ( \( A=B*C \)). More...

template<typename Other >
std::enable_if< std::is_arithmetic< Other >::value, Matrix3 & >::type	operator*= (Other rhs)
	Multiplication assignment operator for the multiplication between a matrix and. More...

template<typename Other >
std::enable_if< std::is_arithmetic< Other >::value, const Matrix3< typename MathTrait< Type, Other >::High > >::type	operator* (Other rhs) const
	Multiplication operator for the multiplication of a matrix and a scalar value. More...

Euler rotations
For the classification of the Euler rotation, the following characteristics are defined: Inner axis: the inner axis is the axis of the first rotation matrix multiplied to a vector. Parity: the parity is even, if the inner axis X is followed by the middle axis Y, or Y is followed by Z, or Z is followed by X; otherwise parity is odd. Repetition: repetition tells, if the first and last axes are the same or different. Frame: the frame refers to the frame from which the Euler angles are calculated. Altogether, there are 24 possible Euler rotations. The possibilities are consisting of the choice of the inner axis (X,Y or Z), the parity (even or odd), repetition (yes or no) and the frame (static or rotating). E.g., an Euler order of XYZs stands for the rotation order of x-, y- and z-axis in a static frame (inner axis: X, parity: even, repetition: no, frame: static), whereas YXYr stands for the rotation order y-, x- and y-axis in a rotating frame ( inner axis: Y, parity: odd, repetition: yes, frame: rotating).
const Vector3< Type >	getEulerAngles (EulerRotation order) const
	Calculation of the Euler angles for a specific rotation order. More...

const Vector3< Type >	getEulerAnglesXYZ () const
	Calculation of the Euler angles (in radian measure). More...

Static Public Member Functions
static Matrix3	makeDiagonalMatrix (const Type xx, const Type yy, const Type zz)
	Named constructor to create a diagonal matrix. All non-diagonal elements are initialized with zero. More...

static Matrix3	makeDiagonalMatrix (const Type d)
	Named constructor to create a diagonal matrix. All non-diagonal elements are initialized with zero. More...

static Matrix3	makeIdentityMatrix ()
	Named constructor to create the identity matrix. More...

Private Attributes
Member variables
std::array< Type, 9 >	v_
	The nine statically allocated matrix elements. 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).
enum	EulerRotation { XYZs = 0, ZYXr = 1, XYXs = 2, XYXr = 3, XZYs = 4, YZXr = 5, XZXs = 6, XZXr = 7, YZXs = 8, XZYr = 9, YZYs = 10, YZYr = 11, YXZs = 12, ZXYr = 13, YXYs = 14, YXYr = 15, ZXYs = 16, YXZr = 17, ZXZs = 18, ZXZr = 19, ZYXs = 20, XYZr = 21, ZYZs = 22, ZYZr = 23 }
	Order of the Euler rotation. More...

Type	getDeterminant () const
	Calculation of the determinant of the matrix. More...

Matrix3 &	transpose ()
	Transposing the matrix. More...

const Matrix3	getTranspose () const
	Calculation of the transpose of the matrix. More...

Matrix3 &	invert ()
	Inverting the matrix. More...

const Matrix3	getInverse () const
	Calculation of the inverse of the matrix. More...

template<typename Other >
const Vector3< typename MathTrait< Type, Other >::High >	multTranspose (const Vector3< Other > &rhs) const
	Multiplication of the transpose of the matrix and a vector ( \( \vec{a}=B^T*\vec{c} \)). More...

template<typename Other >
const Matrix3< typename MathTrait< Type, Other >::High >	rotate (const Matrix3< Other > &m) const
	Rotation of a matrix M ( \( ROT=RMR^{-1} \)). More...

template<typename Other >
const Matrix3< typename MathTrait< Type, Other >::High >	diagRotate (const Matrix3< Other > &m) const
	Rotation of a diagonal matrix M ( \( ROT=RMR^{-1} \)). More...

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

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

bool	isZero () const
	Checks if all matrix entries are zero. More...

const Matrix3	getCholesky () const
	Cholesky decomposition of the matrix ( \( A = LR \)). More...

template<typename Other >
const Vector3< typename MathTrait< Type, Other >::High >	solve (const Vector3< Other > &rhs) const
	Solving the linear system of equations \(A*x=b\) with the decomposed matrix. More...

Type	trace () const
	Computes the trace of the matrix (sum of diagonal elements). More...

Type *	data ()

const Type *	data () const

Member Enumeration Documentation

◆ EulerRotation

template<typename Type >

enum walberla::math::Matrix3::EulerRotation

Order of the Euler rotation.

This codes are needed for the EulerAngles function in order to calculate the Euler angles for a specific combination of rotations.

Enumerator
XYZs	Rotation order x, y, z in a static frame.
ZYXr	Rotation order z, y, x in a rotating frame.
XYXs	Rotation order x, y, x in a static frame.
XYXr	Rotation order x, y, z in a rotating frame.
XZYs	Rotation order x, z, y in a static frame.
YZXr	Rotation order y, z, x in a rotating frame.
XZXs	Rotation order x, z, x in a static frame.
XZXr	Rotation order x, z, x in a rotating frame.
YZXs	Rotation order y, z, x in a static frame.
XZYr	Rotation order x, z, y in a rotating frame.
YZYs	Rotation order y, z, y in a static frame.
YZYr	Rotation order y, z, y in a rotating frame.
YXZs	Rotation order y, x, z in a static frame.
ZXYr	Rotation order z, x, y in a rotating frame.
YXYs	Rotation order y, x, y in a static frame.
YXYr	Rotation order y, x, y in a rotating frame.
ZXYs	Rotation order z, x, y in a static frame.
YXZr	Rotation order y, x, z in a rotating frame.
ZXZs	Rotation order z, x, z in a static frame.
ZXZr	Rotation order z, x, z in a rotating frame.
ZYXs	Rotation order z, y, x in a static frame.
XYZr	Rotation order x, y, z in a rotating frame.
ZYZs	Rotation order z, y, z in a static frame.
ZYZr	Rotation order z, y, z in a rotating frame.

Constructor & Destructor Documentation

◆ Matrix3() [1/8]

template<typename Type >

constexpr walberla::math::Matrix3< Type >::Matrix3 ( )

inlineexplicitconstexprdefault

◆ Matrix3() [2/8]

template<typename Type >

constexpr walberla::math::Matrix3< Type >::Matrix3 ( Type init )

inlineexplicitconstexpr

Constructor for a homogeneous initialization of all elements.

Parameters

init	Initial value for all matrix elements.

◆ Matrix3() [3/8]

template<typename Type >

constexpr walberla::math::Matrix3< Type >::Matrix3	(	const Vector3< Type > &	a,
		const Vector3< Type > &	b,
		const Vector3< Type > &	c
	)

inlineexplicitconstexpr

◆ Matrix3() [4/8]

template<typename Type >

constexpr walberla::math::Matrix3< Type >::Matrix3	(	Type	xx,
		Type	xy,
		Type	xz,
		Type	yx,
		Type	yy,
		Type	yz,
		Type	zx,
		Type	zy,
		Type	zz
	)

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.
xz	The initial value for the xz-component.
yx	The initial value for the yx-component.
yy	The initial value for the yy-component.
yz	The initial value for the yz-component.
zx	The initial value for the zx-component.
zy	The initial value for the zy-component.
zz	The initial value for the zz-component.

◆ Matrix3() [5/8]

template<typename Type >

constexpr walberla::math::Matrix3< Type >::Matrix3 ( 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.

◆ Matrix3() [6/8]

template<typename Type >

template<typename Axis , typename Angle >

walberla::math::Matrix3< Type >::Matrix3	(	Vector3< Axis >	axis,
		Angle	angle
	)

explicit

Rotation matrix constructor.

Parameters

axis	The rotation axis.
angle	The rotation angle.

This constructor is only defined for floating point vectors. The attempt to use this constructor for vectors of integral data type results in a compile time error.

◆ Matrix3() [7/8]

template<typename Type >

walberla::math::Matrix3< Type >::Matrix3 ( const Matrix3< Type > & m )

inlinedefault

◆ Matrix3() [8/8]

template<typename Type >

template<typename Other >

walberla::math::Matrix3< Type >::Matrix3 ( const Matrix3< Other > & m )

inline

Conversion constructor from different Matrix3 instances.

Parameters

m	Matrix to be copied.

Member Function Documentation

◆ data() [1/2]

template<typename Type >

Type* walberla::math::Matrix3< Type >::data ( )

inline

◆ data() [2/2]

template<typename Type >

const Type* walberla::math::Matrix3< Type >::data ( ) const

inline

◆ diagRotate()

template<typename Type >

template<typename Other >

const Matrix3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::diagRotate ( const Matrix3< Other > & m ) const

inline

Rotation of a diagonal matrix M ( \( ROT=R*M*R^{-1} \)).

Parameters

m	The diagonal matrix to be rotated.

Returns: The rotated matrix.

The DiagRotate function is a special case of the Rotate function. The matrix is assumed to be a diagonal matrix, which reduces the number of floating point operations of the rotation. This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data type will result in a compile time error.

◆ getCholesky()

template<typename Type >

const Matrix3< Type > walberla::math::Matrix3< Type >::getCholesky

inline

Cholesky decomposition of the matrix ( \( A = LR \)).

Returns: The decomposed matrix \( L \).

This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data type will result in a compile time error.

◆ getDeterminant()

template<typename Type >

Type walberla::math::Matrix3< Type >::getDeterminant

inline

Calculation of the determinant of the matrix.

Returns: The determinant of the matrix.

◆ getEulerAngles()

template<typename Type >

const Vector3< Type > walberla::math::Matrix3< Type >::getEulerAngles ( EulerRotation order ) const

Calculation of the Euler angles for a specific rotation order.

Parameters

order The specific rotation order.

Returns: The specific Euler angles.

This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data type will result in a compile time error.

◆ getEulerAnglesXYZ()

template<typename Type >

const Vector3< Type > walberla::math::Matrix3< Type >::getEulerAnglesXYZ

inline

Calculation of the Euler angles (in radian measure).

Returns: The Euler angles for a rotation order of x, y, z.

The Euler angles are calculated for a rotation order of x-, y- and z-axis. This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data type will result in a compile time error.

◆ getInverse()

template<typename Type >

const Matrix3< Type > walberla::math::Matrix3< 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 Matrix3< Type > walberla::math::Matrix3< Type >::getTranspose

inline

Calculation of the transpose of the matrix.

Returns: The transpose of the matrix.

◆ invert()

template<typename Type >

Matrix3< Type > & walberla::math::Matrix3< 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::Matrix3< 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::Matrix3< Type >::isSymmetric

inline

Checks if the matrix is symmetric.

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

◆ isZero()

template<typename Type >

bool walberla::math::Matrix3< Type >::isZero

inline

Checks if all matrix entries are zero.

Returns: true if all entries are zero otherwise false.

◆ makeDiagonalMatrix() [1/2]

template<typename Type >

Matrix3< Type > walberla::math::Matrix3< Type >::makeDiagonalMatrix ( const Type d )

inlinestatic

Named constructor to create a diagonal matrix. All non-diagonal elements are initialized with zero.

Parameters

d	value for diagonal elements.

◆ makeDiagonalMatrix() [2/2]

template<typename Type >

Matrix3< Type > walberla::math::Matrix3< Type >::makeDiagonalMatrix	(	const Type	xx,
		const Type	yy,
		const Type	zz
	)

inlinestatic

Named constructor to create a diagonal matrix. All non-diagonal elements are initialized with zero.

Parameters

xx	value for element (0,0).
yy	value for element (1,1).
zz	value for element (2,2).

◆ makeIdentityMatrix()

template<typename Type >

Matrix3< Type > walberla::math::Matrix3< Type >::makeIdentityMatrix

inlinestatic

Named constructor to create the identity matrix.

All diagonal elements are initialized to one, alls others to zero.

◆ multTranspose()

template<typename Type >

template<typename Other >

const Vector3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::multTranspose ( const Vector3< Other > & rhs ) const

inline

Multiplication of the transpose of the matrix and a vector ( \( \vec{a}=B^T*\vec{c} \)).

Parameters

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

Returns: The resulting vector.

◆ operator!=()

template<typename Type >

template<typename Other >

bool walberla::math::Matrix3< Type >::operator!= ( const Matrix3< 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::Matrix3< 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::Matrix3< 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 Matrix3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::operator* ( const Matrix3< 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 Vector3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::operator* ( const Vector3< Other > & rhs ) const

inline

Multiplication operator for the multiplication of a matrix and a vector.

( \( \vec{a}=B*\vec{c} \)).

Parameters

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

Returns: The resulting vector.

◆ operator*() [3/3]

template<typename Type >

template<typename Other >

std::enable_if< std::is_arithmetic< Other >::value,const Matrix3< typename MathTrait< Type, Other >::High > >::type walberla::math::Matrix3< 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*=() [1/3]

template<typename Type >

template<typename Other >

Matrix3< Type > & walberla::math::Matrix3< Type >::operator*= ( const Matrix3< 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*=() [2/3]

template<typename Type >

template<typename Other >

Matrix3<Type>& walberla::math::Matrix3< Type >::operator*= ( const Matrix3< Other > & rhs )

inline

◆ operator*=() [3/3]

template<typename Type >

template<typename Other >

std::enable_if< std::is_arithmetic< Other >::value, Matrix3< Type > & >::type walberla::math::Matrix3< 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+()

template<typename Type >

template<typename Other >

const Matrix3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::operator+ ( const Matrix3< 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 >

Matrix3< Type > & walberla::math::Matrix3< Type >::operator+= ( const Matrix3< 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 >

Matrix3<Type>& walberla::math::Matrix3< Type >::operator+= ( const Matrix3< Other > & rhs )

inline

◆ operator-()

template<typename Type >

template<typename Other >

const Matrix3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::operator- ( const Matrix3< 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 >

Matrix3< Type > & walberla::math::Matrix3< Type >::operator-= ( const Matrix3< 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 >

Matrix3<Type>& walberla::math::Matrix3< Type >::operator-= ( const Matrix3< Other > & rhs )

inline

◆ operator=() [1/4]

template<typename Type >

Matrix3& walberla::math::Matrix3< Type >::operator= ( const Matrix3< Type > & set )

inlinedefault

◆ operator=() [2/4]

template<typename Type >

template<typename Other >

Matrix3< Type > & walberla::math::Matrix3< Type >::operator= ( const Matrix3< Other > & set )

inline

Assignment operator for different Matrix3 instances.

Parameters

set	Matrix to be copied.

Returns: Reference to the assigned matrix.

◆ operator=() [3/4]

template<typename Type >

template<typename Other >

Matrix3<Type>& walberla::math::Matrix3< Type >::operator= ( const Matrix3< Other > & set )

inline

◆ operator=() [4/4]

template<typename Type >

Matrix3< Type > & walberla::math::Matrix3< 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::Matrix3< Type >::operator== ( const Matrix3< 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::Matrix3< 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::Matrix3< 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.

◆ rotate()

template<typename Type >

template<typename Other >

const Matrix3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::rotate ( const Matrix3< Other > & m ) const

inline

Rotation of a matrix M ( \( ROT=R*M*R^{-1} \)).

Parameters

m	The matrix to be rotated.

Returns: The rotated matrix.

This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data type will result in a compile time error.

◆ solve()

template<typename Type >

template<typename Other >

const Vector3< typename MathTrait< Type, Other >::High > walberla::math::Matrix3< Type >::solve ( const Vector3< Other > & rhs ) const

inline

Solving the linear system of equations \(A*x=b\) with the decomposed matrix.

\(LR = A\).

Parameters

rhs	The right-hand-side of the linear system of equations.

Returns: The solution of the linear system of equations.

This function is only defined for matrices of floating point type. The attempt to use this function with matrices of integral data type will result in a compile time error.

◆ trace()

template<typename Type >

Type walberla::math::Matrix3< Type >::trace

inline

Computes the trace of the matrix (sum of diagonal elements).

Returns: The trace of the matrix.

◆ transpose()

template<typename Type >

Matrix3< Type > & walberla::math::Matrix3< Type >::transpose

inline

Transposing the matrix.

Returns: Reference to the transposed matrix.

Member Data Documentation

◆ v_

template<typename Type >

std::array<Type, 9> walberla::math::Matrix3< Type >::v_

private

Initial value:

= {{Type(1), Type(0), Type(0),
                              Type(0), Type(1), Type(0),
                              Type(0), Type(0), Type(1)}}

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

\[\left(\begin{array}{*{3}{c}} 0 & 1 & 2 \\ 3 & 4 & 5 \\ 6 & 7 & 8 \\ \end{array}\right)\]

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

/builds/administration/walberla-website/walberla/src/core/math/Matrix3.h

Detailed Description

template<typename Type> class walberla::math::Matrix3< Type >

Public Member Functions

Static Public Member Functions

Private Attributes

Utility functions

Member Enumeration Documentation

◆ EulerRotation

Constructor & Destructor Documentation

◆ Matrix3() [1/8]

◆ Matrix3() [2/8]

◆ Matrix3() [3/8]

◆ Matrix3() [4/8]

◆ Matrix3() [5/8]

◆ Matrix3() [6/8]

◆ Matrix3() [7/8]

◆ Matrix3() [8/8]

Member Function Documentation

◆ data() [1/2]

◆ data() [2/2]

◆ diagRotate()

◆ getCholesky()

◆ getDeterminant()

◆ getEulerAngles()

◆ getEulerAnglesXYZ()

◆ getInverse()

◆ getTranspose()

◆ invert()

◆ isSingular()

◆ isSymmetric()

◆ isZero()

◆ makeDiagonalMatrix() [1/2]

◆ makeDiagonalMatrix() [2/2]

◆ makeIdentityMatrix()

◆ multTranspose()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ 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]

◆ rotate()

◆ solve()

◆ trace()

◆ transpose()

Member Data Documentation

◆ v_

template<typename Type>
class walberla::math::Matrix3< Type >