Inheritance diagram for OpenMD::SquareMatrix3< Real >:

Public Types
using	ElemType = Real
using	ElemPoinerType = Real*
Public Types inherited from OpenMD::SquareMatrix< Real, 3 >
using	ElemType
using	ElemPoinerType
Public Types inherited from OpenMD::RectMatrix< Real, Dim, Dim >
using	ElemType
using	ElemPoinerType

Public Member Functions
	SquareMatrix3 ()
	default constructor
	SquareMatrix3 (Real s)
	Constructs and initializes every element of this matrix to a scalar.
	SquareMatrix3 (Real *array)
	Constructs and initializes from an array.
	SquareMatrix3 (const SquareMatrix< Real, 3 > &m)
	copy constructor
	SquareMatrix3 (const RectMatrix< Real, 3, 3 > &m)
	Construct from a RectMatrix (e.g.
	SquareMatrix3 (const Vector3< Real > &eulerAngles)
	SquareMatrix3 (Real phi, Real theta, Real psi)
	SquareMatrix3 (const Quaternion< Real > &q)
	SquareMatrix3 (Real w, Real x, Real y, Real z)
SquareMatrix3< Real > &	operator= (const RectMatrix< Real, 3, 3 > &m)
	copy assignment operator
SquareMatrix3< Real > &	operator= (const Quaternion< Real > &q)
void	setupRotMat (const Vector3< Real > &eulerAngles)
	Sets this matrix to a rotation matrix by three euler angles @ param euler.
void	setupRotMat (Real phi, Real theta, Real psi)
	Sets this matrix to a rotation matrix by three euler angles.
void	setupRotMat (const Quaternion< Real > &quat)
	Sets this matrix to a rotation matrix by quaternion.
void	setupRotMat (Real w, Real x, Real y, Real z)
	Sets this matrix to a rotation matrix by quaternion.
void	setupSkewMat (Vector3< Real > v)
void	setupSkewMat (Real v1, Real v2, Real v3)
void	setupVoigtTensor (Vector< Real, 6 > vt)
	Sets this matrix to a symmetric tensor using Voigt Notation.
void	setupVoigtTensor (Real v1, Real v2, Real v3, Real v4, Real v5, Real v6)
void	setupUpperTriangularVoigtTensor (Vector< Real, 6 > vt)
	Sets this matrix to an upper-triangular (asymmetric) tensor using Voigt Notation.
void	setupUpperTriangularVoigtTensor (Real v1, Real v2, Real v3, Real v4, Real v5, Real v6)
void	axisAngle (Vector3d axis, RealType angle)
	Uses Rodrigues' rotation formula for a rotation matrix.
Quaternion< Real >	toQuaternion ()
	Returns the quaternion from this rotation matrix.
Vector3< Real >	toEulerAngles ()
	Returns the euler angles from this rotation matrix.
bool	closeEnough (const Real &a, const Real &b, const Real &epsilon=std::numeric_limits< Real >::epsilon())
Vector3< Real >	toRPY ()
Vector< Real, 6 >	toVoigtTensor ()
Real	determinant () const
	Returns the determinant of this matrix.
Real	trace () const
	Returns the trace of this matrix.
SquareMatrix3< Real >	inverse () const
	Sets the value of this matrix to the inverse of itself.
SquareMatrix3< Real >	transpose () const
Public Member Functions inherited from OpenMD::SquareMatrix< Real, 3 >
	SquareMatrix ()
	default constructor
SquareMatrix< Real, Dim > &	operator= (const RectMatrix< Real, Dim, Dim > &m)
	copy assignment operator
SquareMatrix< Real, Dim >	inverse ()
	Returns the inverse of this matrix.
Real	determinant () const
	Returns the determinant of this matrix.
SquareMatrix< Real, Dim - 1 >	cofactor (int p, int q)
Real	trace () const
	Returns the trace of this matrix.
bool	isSymmetric () const
	Tests if this matrix is symmetrix.
bool	isOrthogonal ()
	Tests if this matrix is orthogonal.
bool	isDiagonal () const
	Tests if this matrix is diagonal.
Vector< Real, Dim >	diagonals () const
	Returns a column vector that contains the elements from the diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so on.
bool	isUnitMatrix () const
	Tests if this matrix is the unit matrix.
SquareMatrix< Real, Dim >	transpose () const
	Return the transpose of this matrix.
void	diagonalize ()
Public Member Functions inherited from OpenMD::RectMatrix< Real, Dim, Dim >
	RectMatrix ()
	default constructor
	~RectMatrix ()
	destructor
RectMatrix< Real, Row, Col > &	operator= (const RectMatrix< Real, Row, Col > &m)
	copy assignment operator
Real &	operator() (unsigned int i, unsigned int j)
	Return the reference of a single element of this matrix.
void	getArray (Real *array)
	Copy the internal data to an array.
Real *	getArrayPointer ()
	Returns the pointer of internal array.
Vector< Real, Row >	getRow (unsigned int row)
	Returns a row of this matrix as a vector.
void	setRow (unsigned int row, const Vector< Real, Row > &v)
	Sets a row of this matrix.
Vector< Real, Col >	getColumn (unsigned int col)
	Returns a column of this matrix as a vector.
void	setColumn (unsigned int col, const Vector< Real, Col > &v)
	Sets a column of this matrix.
void	swapRow (unsigned int i, unsigned int j)
	swap two rows of this matrix
void	swapColumn (unsigned int i, unsigned int j)
	swap two Columns of this matrix
bool	operator== (const RectMatrix< Real, Row, Col > &m)
	Tests if this matrix is identical to matrix m.
bool	operator!= (const RectMatrix< Real, Row, Col > &m)
	Tests if this matrix is not equal to matrix m.
void	negate ()
	Negates the value of this matrix in place.
void	add (const RectMatrix< Real, Row, Col > &m)
	Sets the value of this matrix to the sum of itself and m (*this += m).
void	sub (const RectMatrix< Real, Row, Col > &m)
	Sets the value of this matrix to the difference of itself and m (*this -= m).
void	mul (Real s)
	Sets the value of this matrix to the scalar multiplication of itself (this = s).
void	div (Real s)
	Sets the value of this matrix to the scalar division of itself (*this /= s ).
RectMatrix< Real, Row, Col > &	operator*= (const Real s)
	Multiples a scalar into every element of this matrix.
RectMatrix< Real, Row, Col > &	operator/= (const Real s)
	Divides every element of this matrix by a scalar.
RectMatrix< Real, Row, Col > &	operator+= (const RectMatrix< Real, Row, Col > &m)
	Sets the value of this matrix to the sum of the other matrix and itself (*this += m).
RectMatrix< Real, Row, Col > &	operator-= (const RectMatrix< Real, Row, Col > &m)
	Sets the value of this matrix to the differerence of itself and the other matrix (*this -= m).
RectMatrix< Real, Col, Row >	transpose () const
	Return the transpose of this matrix.
void	setSubMatrix (unsigned int beginRow, unsigned int beginCol, const MatrixType &m)
void	getSubMatrix (unsigned int beginRow, unsigned int beginCol, MatrixType &m)
unsigned int	getNRow () const
unsigned int	getNCol () const
Real	frobeniusNorm ()

Static Public Member Functions
static void	diagonalize (SquareMatrix3< Real > &a, Vector3< Real > &w, SquareMatrix3< Real > &v)
	Extract the eigenvalues and eigenvectors from a 3x3 matrix.
Static Public Member Functions inherited from OpenMD::SquareMatrix< Real, 3 >
static SquareMatrix< Real, Dim >	identity ()
	Returns an identity matrix.
static int	jacobi (SquareMatrix< Real, Dim > &a, Vector< Real, Dim > &d, SquareMatrix< Real, Dim > &v)
	Jacobi iteration routines for computing eigenvalues/eigenvectors of real symmetric matrix.

Additional Inherited Members
Protected Attributes inherited from OpenMD::RectMatrix< Real, Dim, Dim >
Real	data_ [Row][Col]

Detailed Description

template<typename Real>
class OpenMD::SquareMatrix3< Real >

Definition at line 71 of file SquareMatrix3.hpp.

Member Typedef Documentation

◆ ElemPoinerType

template<typename Real>

using OpenMD::SquareMatrix3< Real >::ElemPoinerType = Real*

Definition at line 74 of file SquareMatrix3.hpp.

◆ ElemType

template<typename Real>

using OpenMD::SquareMatrix3< Real >::ElemType = Real

Definition at line 73 of file SquareMatrix3.hpp.

Constructor & Destructor Documentation

◆ SquareMatrix3() [1/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( )

inline

default constructor

Definition at line 77 of file SquareMatrix3.hpp.

Referenced by diagonalize().

◆ SquareMatrix3() [2/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( Real s )

inline

Constructs and initializes every element of this matrix to a scalar.

Definition at line 80 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [3/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( Real * array )

inline

Constructs and initializes from an array.

Definition at line 83 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [4/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( const SquareMatrix< Real, 3 > & m )

inline

copy constructor

Definition at line 86 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [5/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( const RectMatrix< Real, 3, 3 > & m )

inline

Construct from a RectMatrix (e.g.

the result of matrix arithmetic).

Definition at line 89 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [6/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( const Vector3< Real > & eulerAngles )

inline

Definition at line 91 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [7/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3	(	Real	phi,
		Real	theta,
		Real	psi )

inline

Definition at line 95 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [8/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3 ( const Quaternion< Real > & q )

inline

Definition at line 99 of file SquareMatrix3.hpp.

◆ SquareMatrix3() [9/9]

template<typename Real>

OpenMD::SquareMatrix3< Real >::SquareMatrix3	(	Real	w,
		Real	x,
		Real	y,
		Real	z )

inline

Definition at line 101 of file SquareMatrix3.hpp.

Member Function Documentation

◆ axisAngle()

template<typename Real>

void OpenMD::SquareMatrix3< Real >::axisAngle	(	Vector3d	axis,
		RealType	angle )

inline

Uses Rodrigues' rotation formula for a rotation matrix.

Parameters

axis	the axis to rotate around
angle	the angle to rotate (in radians)

Definition at line 232 of file SquareMatrix3.hpp.

◆ closeEnough()

template<typename Real>

bool OpenMD::SquareMatrix3< Real >::closeEnough	(	const Real &	a,
		const Real &	b,
		const Real &	epsilon = std::numeric_limits<Real>::epsilon() )

inline

Definition at line 348 of file SquareMatrix3.hpp.

◆ determinant()

template<typename Real>

Real OpenMD::SquareMatrix3< Real >::determinant ( ) const

inline

Returns the determinant of this matrix.

Definition at line 405 of file SquareMatrix3.hpp.

Referenced by OpenMD::MolecularRestraint::calcForce(), diagonalize(), OpenMD::Thermo::getGyrationalVolume(), OpenMD::Thermo::getGyrationalVolume(), and OpenMD::SquareMatrix3< RealType >::inverse().

◆ diagonalize()

template<typename Real>

void OpenMD::SquareMatrix3< Real >::diagonalize	(	SquareMatrix3< Real > &	a,
		Vector3< Real > &	w,
		SquareMatrix3< Real > &	v )

static

Extract the eigenvalues and eigenvectors from a 3x3 matrix.

The eigenvectors (the columns of V) will be normalized. The eigenvectors are aligned optimally with the x, y, and z axes respectively.

Parameters

a	symmetric matrix whose eigenvectors are to be computed. On return, the matrix is overwritten
w	will contain the eigenvalues of the matrix On return of this function
v	the columns of this matrix will contain the eigenvectors. The eigenvectors are normalized and mutually orthogonal.

Warning: a will be overwritten

Todo

Definition at line 493 of file SquareMatrix3.hpp.

References OpenMD::cross(), determinant(), OpenMD::RectMatrix< Real, Row, Col >::getRow(), OpenMD::SquareMatrix< Real, 3 >::identity(), OpenMD::SquareMatrix< Real, 3 >::jacobi(), OpenMD::Vector< Real, Dim >::normalize(), OpenMD::RectMatrix< Real, Row, Col >::setRow(), SquareMatrix3(), and OpenMD::RectMatrix< Real, Row, Col >::swapRow().

◆ inverse()

template<typename Real>

SquareMatrix3< Real > OpenMD::SquareMatrix3< Real >::inverse ( ) const

inline

Sets the value of this matrix to the inverse of itself.

Note: since this simple algorithm can be applied to invert a 3 by 3 matrix, we hide the implementation of inverse in SquareMatrix class

Definition at line 428 of file SquareMatrix3.hpp.

Referenced by OpenMD::Velocitizer::removeAngularDrift(), OpenMD::Snapshot::setBoundingBox(), and OpenMD::Snapshot::setHmat().

◆ operator=() [1/2]

template<typename Real>

SquareMatrix3< Real > & OpenMD::SquareMatrix3< Real >::operator= ( const Quaternion< Real > & q )

inline

Definition at line 110 of file SquareMatrix3.hpp.

◆ operator=() [2/2]

template<typename Real>

SquareMatrix3< Real > & OpenMD::SquareMatrix3< Real >::operator= ( const RectMatrix< Real, 3, 3 > & m )

inline

copy assignment operator

Definition at line 104 of file SquareMatrix3.hpp.

◆ setupRotMat() [1/4]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupRotMat ( const Quaternion< Real > & quat )

inline

Sets this matrix to a rotation matrix by quaternion.

Parameters

quat

Definition at line 157 of file SquareMatrix3.hpp.

◆ setupRotMat() [2/4]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupRotMat ( const Vector3< Real > & eulerAngles )

inline

Sets this matrix to a rotation matrix by three euler angles @ param euler.

Definition at line 119 of file SquareMatrix3.hpp.

Referenced by OpenMD::SquareMatrix3< RealType >::setupRotMat(), and OpenMD::SquareMatrix3< RealType >::setupRotMat().

◆ setupRotMat() [3/4]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupRotMat	(	Real	phi,
		Real	theta,
		Real	psi )

inline

Sets this matrix to a rotation matrix by three euler angles.

Parameters

phi
theta
psi

Definition at line 129 of file SquareMatrix3.hpp.

◆ setupRotMat() [4/4]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupRotMat	(	Real	w,
		Real	x,
		Real	y,
		Real	z )

inline

Sets this matrix to a rotation matrix by quaternion.

Parameters

w	the first element
x	the second element
y	the third element
z	the fourth element

Definition at line 168 of file SquareMatrix3.hpp.

◆ setupSkewMat() [1/2]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupSkewMat	(	Real	v1,
		Real	v2,
		Real	v3 )

inline

Definition at line 175 of file SquareMatrix3.hpp.

◆ setupSkewMat() [2/2]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupSkewMat ( Vector3< Real > v )

inline

Definition at line 173 of file SquareMatrix3.hpp.

◆ setupUpperTriangularVoigtTensor() [1/2]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupUpperTriangularVoigtTensor	(	Real	v1,
		Real	v2,
		Real	v3,
		Real	v4,
		Real	v5,
		Real	v6 )

inline

Definition at line 217 of file SquareMatrix3.hpp.

◆ setupUpperTriangularVoigtTensor() [2/2]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupUpperTriangularVoigtTensor ( Vector< Real, 6 > vt )

inline

Sets this matrix to an upper-triangular (asymmetric) tensor using Voigt Notation.

Parameters

vt

Definition at line 213 of file SquareMatrix3.hpp.

Referenced by OpenMD::SquareMatrix3< RealType >::setupUpperTriangularVoigtTensor().

◆ setupVoigtTensor() [1/2]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupVoigtTensor	(	Real	v1,
		Real	v2,
		Real	v3,
		Real	v4,
		Real	v5,
		Real	v6 )

inline

Definition at line 195 of file SquareMatrix3.hpp.

◆ setupVoigtTensor() [2/2]

template<typename Real>

void OpenMD::SquareMatrix3< Real >::setupVoigtTensor ( Vector< Real, 6 > vt )

inline

Sets this matrix to a symmetric tensor using Voigt Notation.

Parameters

vt

Definition at line 191 of file SquareMatrix3.hpp.

Referenced by OpenMD::SquareMatrix3< RealType >::setupVoigtTensor().

◆ toEulerAngles()

template<typename Real>

Vector3< Real > OpenMD::SquareMatrix3< Real >::toEulerAngles ( )

inline

Returns the euler angles from this rotation matrix.

Returns: the euler angles in a vector

Exceptions

invalid rotation matrix We use so-called "x-convention", which is the most common definition. In this convention, the rotation given by Euler angles (phi, theta, psi), where the first rotation is by an angle phi about the z-axis, the second is by an angle theta (0 <= theta <= 180) about the x-axis, and the third is by an angle psi about the z-axis (again).

Definition at line 301 of file SquareMatrix3.hpp.

◆ toQuaternion()

template<typename Real>

Quaternion< Real > OpenMD::SquareMatrix3< Real >::toQuaternion ( )

inline

Returns the quaternion from this rotation matrix.

Returns: the quaternion from this rotation matrix

Exceptions

invalid rotation matrix

Definition at line 247 of file SquareMatrix3.hpp.

Referenced by OpenMD::MolecularRestraint::calcForce(), and OpenMD::ObjectRestraint::calcForce().

◆ toRPY()

template<typename Real>

Vector3< Real > OpenMD::SquareMatrix3< Real >::toRPY ( )

inline

Definition at line 354 of file SquareMatrix3.hpp.

◆ toVoigtTensor()

template<typename Real>

Vector< Real, 6 > OpenMD::SquareMatrix3< Real >::toVoigtTensor ( )

inline

Definition at line 393 of file SquareMatrix3.hpp.

◆ trace()

template<typename Real>

Real OpenMD::SquareMatrix3< Real >::trace ( ) const

inline

Returns the trace of this matrix.

Definition at line 418 of file SquareMatrix3.hpp.

◆ transpose()

template<typename Real>

SquareMatrix3< Real > OpenMD::SquareMatrix3< Real >::transpose ( ) const

inline

Definition at line 453 of file SquareMatrix3.hpp.

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

math/SquareMatrix3.hpp

Public Types

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ElemPoinerType

◆ ElemType

Constructor & Destructor Documentation

◆ SquareMatrix3() [1/9]

◆ SquareMatrix3() [2/9]

◆ SquareMatrix3() [3/9]

◆ SquareMatrix3() [4/9]

◆ SquareMatrix3() [5/9]

◆ SquareMatrix3() [6/9]

◆ SquareMatrix3() [7/9]

◆ SquareMatrix3() [8/9]

◆ SquareMatrix3() [9/9]

Member Function Documentation

◆ axisAngle()

◆ closeEnough()

◆ determinant()

◆ diagonalize()

◆ inverse()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ setupRotMat() [1/4]

◆ setupRotMat() [2/4]

◆ setupRotMat() [3/4]

◆ setupRotMat() [4/4]

◆ setupSkewMat() [1/2]

◆ setupSkewMat() [2/2]

◆ setupUpperTriangularVoigtTensor() [1/2]

◆ setupUpperTriangularVoigtTensor() [2/2]

◆ setupVoigtTensor() [1/2]

◆ setupVoigtTensor() [2/2]

◆ toEulerAngles()

◆ toQuaternion()

◆ toRPY()

◆ toVoigtTensor()

◆ trace()

◆ transpose()