Antisymmetric matrix with 3 rows and 3 columns. More...

#include <antisymmetric_matrix_3x3.h>

Public Member Functions
	operator at2_e3_row_dofs_type< T > & () const
	Operator to convert current to at2_e3_row_dofs_type. More...

T *	operator[] (int xrow)
	Pointer to the first element in row xrow of this matrix. Facilitates accessing elements via matrix[i][j]. More...

const T *	operator[] (int xrow) const
	Pointer to the first element in row xrow of this matrix. Facilitates accessing elements via matrix[i][j]. More...

	operator T* ()
	Conversion (cast) operator to convert to the associated matrix type (non const version). More...

	operator const T * () const
	Conversion (cast) operator to convert to the associated matrix type (const version). More...

int	row_index (int xrow) const
	Index for row xrow in the linear storage array. More...

	operator general_matrix_3x3< T > () const
	Conversion operator to convert to the associated general matrix type. More...

general_matrix_1x3< T >	row (int xrow) const
	A 1x3 matrix containing the elements or row xrow. More...

general_matrix_3x1< T >	column (int xcolumn) const
	A 3x1 matrix containing the elements or column xcolumn. More...

void	adjoint (general_matrix_3x3< T > &xresult) const
	The adjoint of the matrix (pre-allocated). More...

general_matrix_3x3< T >	adjoint () const
	The adjoint of the matrix (auto-allocated). More...

void	assign (const T &xscalar)
	Assign all elements of this matrix to the value xvalue. More...

void	determinant (T &xresult) const
	The determinant of the matrix (pre-allocated). More...

T	determinant () const
	The determinant of the matrix (auto-allocated). More...

void	inverse (antisymmetric_matrix_3x3< T > &xresult) const
	The inverse of the matrix (pre-allocated). More...

antisymmetric_matrix_3x3< T >	inverse () const
	The inverse of the matrix (auto-allocated). More...

bool	is_positive_definite () const
	True if this matrix is positive definite. Always returns false for antisymmetric_matrices. More...

void	multiply (const T &xscalar, antisymmetric_matrix_3x3< T > &xresult) const
	This matrix multiplied by a scalar (pre-allocated). More...

antisymmetric_matrix_3x3< T >	multiply (const T &xscalar) const
	This matrix multiplied by a scalar (auto-allocated). More...

void	multiply (const general_matrix_3x1< T > &xother, general_matrix_3x1< T > &xresult) const
	Premultiply matrix xother by this matrix (pre-allocated). More...

general_matrix_3x1< T >	multiply (const general_matrix_3x1< T > &xother) const
	Premultiply matrix xother by this matrix (auto-allocated). More...

void	multiply (const general_matrix_3x2< T > &xother, general_matrix_3x2< T > &xresult) const
	Premultiply matrix xother by this matrix (pre-allocated). More...

general_matrix_3x2< T >	multiply (const general_matrix_3x2< T > &xother) const
	Premultiply matrix xother by this matrix (auto-allocated). More...

void	multiply (const general_matrix_3x3< T > &xother, general_matrix_3x3< T > &xresult) const
	Premultiply matrix xother by this matrix (pre-allocated). More...

general_matrix_3x3< T >	multiply (const general_matrix_3x3< T > &xother) const
	Premultiply matrix xother by this matrix (auto-allocated). More...

void	multiply (const antisymmetric_matrix_3x3< T > &xother, general_matrix_3x3< T > &xresult) const
	Premultiply matrix xother by this matrix (pre-allocated). Note that multiplying 2 antisymmetric matrices results (in general) in a general square matrix. More...

general_matrix_3x3< T >	multiply (const antisymmetric_matrix_3x3< T > &xother) const
	Premultiply matrix xother by this matrix (auto-allocated). Note that multiplying 2 antisymmetric matrices results (in general) in a general square matrix. More...

void	trace (T &xresult) const
	The trace of the matrix (pre-allocated). More...

T	trace () const
	The trace of the matrix (auto-allocated). More...

void	transpose (antisymmetric_matrix_3x3< T > &xresult) const
	The transpose of the matrix (pre-allocated). More...

antisymmetric_matrix_3x3< T >	transpose () const
	The transpose of the matrix (auto-allocated). More...

Static Public Member Functions
static int	number_of_rows ()
	The number of rows. More...

static int	number_of_columns ()
	The number of columns. More...

static int	d ()
	Dimension of the underlying elements. More...

Public Attributes
T	components [3]
	Linear storage array. More...

Detailed Description

template<typename T>
class fiber_bundle::antisymmetric_matrix_3x3< T >

Antisymmetric matrix with 3 rows and 3 columns.

Class antisymmetric_matrix_3x3 is a special kind of matrix class intended to be used in conjunction with various row_dofs_type classes (pod types). The pod types will be converted (cast) to appropriate matrix types. So, this class is also required to be a pod type also (ie: really just a struct with no inheritance, no constructors, no virtual functions, etc.).

Definition at line 55 of file antisymmetric_matrix_3x3.h.

Member Function Documentation

◆ adjoint() [1/2]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::adjoint ( general_matrix_3x3< T > & xresult ) const

The adjoint of the matrix (pre-allocated).

Definition at line 384 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::adjoint().

◆ adjoint() [2/2]

template<typename T >

general_matrix_3x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::adjoint ( ) const

The adjoint of the matrix (auto-allocated).

Definition at line 451 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::assign().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::adjoint(), and fiber_bundle::antisymmetric_matrix_3x3< T >::column().

◆ assign()

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::assign ( const T & xscalar )

Assign all elements of this matrix to the value xvalue.

Definition at line 471 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::determinant().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::adjoint().

◆ column()

template<typename T >

general_matrix_3x1< T > fiber_bundle::antisymmetric_matrix_3x3< T >::column ( int xcolumn ) const

A 3x1 matrix containing the elements or column xcolumn.

Precondition

xcolumn >= 0 && xcolumn < number_of_columns()

Definition at line 342 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::adjoint(), and fiber_bundle::general_matrix_3x1< T >::components.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::row().

◆ d()

template<typename T >

int fiber_bundle::antisymmetric_matrix_3x3< T >::d ( )

static

Dimension of the underlying elements.

Definition at line 132 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::operator[]().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_columns().

◆ determinant() [1/2]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::determinant ( T & xresult ) const

The determinant of the matrix (pre-allocated).

Definition at line 492 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::determinant().

◆ determinant() [2/2]

template<typename T >

T fiber_bundle::antisymmetric_matrix_3x3< T >::determinant ( ) const

The determinant of the matrix (auto-allocated).

Definition at line 513 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::determinant(), and fiber_bundle::antisymmetric_matrix_3x3< T >::inverse().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::assign(), and fiber_bundle::antisymmetric_matrix_3x3< T >::determinant().

◆ inverse() [1/2]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::inverse ( antisymmetric_matrix_3x3< T > & xresult ) const

The inverse of the matrix (pre-allocated).

Definition at line 535 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::inverse().

◆ inverse() [2/2]

template<typename T >

antisymmetric_matrix_3x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::inverse ( ) const

The inverse of the matrix (auto-allocated).

Definition at line 552 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::inverse(), and fiber_bundle::antisymmetric_matrix_3x3< T >::is_positive_definite().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::determinant(), and fiber_bundle::antisymmetric_matrix_3x3< T >::inverse().

◆ is_positive_definite()

template<typename T >

bool fiber_bundle::antisymmetric_matrix_3x3< T >::is_positive_definite ( ) const

True if this matrix is positive definite. Always returns false for antisymmetric_matrices.

Postcondition

result == false

Definition at line 572 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::inverse().

◆ multiply() [1/10]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::multiply	(	const T &	xscalar,
		antisymmetric_matrix_3x3< T > &	xresult
	)		const

This matrix multiplied by a scalar (pre-allocated).

Definition at line 593 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::components.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::is_positive_definite(), and fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

◆ multiply() [2/10]

template<typename T >

antisymmetric_matrix_3x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::multiply ( const T & xscalar ) const

This matrix multiplied by a scalar (auto-allocated).

Definition at line 619 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply(), and fiber_bundle::vd_algebra::multiply().

◆ multiply() [3/10]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::multiply	(	const general_matrix_3x1< T > &	xother,
		general_matrix_3x1< T > &	xresult
	)		const

Premultiply matrix xother by this matrix (pre-allocated).

Definition at line 639 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

◆ multiply() [4/10]

template<typename T >

general_matrix_3x1< T > fiber_bundle::antisymmetric_matrix_3x3< T >::multiply ( const general_matrix_3x1< T > & xother ) const

Premultiply matrix xother by this matrix (auto-allocated).

Definition at line 682 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply(), and fiber_bundle::vd_algebra::multiply().

◆ multiply() [5/10]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::multiply	(	const general_matrix_3x2< T > &	xother,
		general_matrix_3x2< T > &	xresult
	)		const

Premultiply matrix xother by this matrix (pre-allocated).

Definition at line 702 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

◆ multiply() [6/10]

template<typename T >

general_matrix_3x2< T > fiber_bundle::antisymmetric_matrix_3x3< T >::multiply ( const general_matrix_3x2< T > & xother ) const

Premultiply matrix xother by this matrix (auto-allocated).

Definition at line 760 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply(), and fiber_bundle::vd_algebra::multiply().

◆ multiply() [7/10]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::multiply	(	const general_matrix_3x3< T > &	xother,
		general_matrix_3x3< T > &	xresult
	)		const

Premultiply matrix xother by this matrix (pre-allocated).

Definition at line 780 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

◆ multiply() [8/10]

template<typename T >

general_matrix_3x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::multiply ( const general_matrix_3x3< T > & xother ) const

Premultiply matrix xother by this matrix (auto-allocated).

Definition at line 848 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply(), and fiber_bundle::vd_algebra::multiply().

◆ multiply() [9/10]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::multiply	(	const antisymmetric_matrix_3x3< T > &	xother,
		general_matrix_3x3< T > &	xresult
	)		const

Premultiply matrix xother by this matrix (pre-allocated). Note that multiplying 2 antisymmetric matrices results (in general) in a general square matrix.

Definition at line 868 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

◆ multiply() [10/10]

template<typename T >

general_matrix_3x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::multiply ( const antisymmetric_matrix_3x3< T > & xother ) const

Premultiply matrix xother by this matrix (auto-allocated). Note that multiplying 2 antisymmetric matrices results (in general) in a general square matrix.

Definition at line 933 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::vd_algebra::multiply(), and fiber_bundle::antisymmetric_matrix_3x3< T >::trace().

◆ number_of_columns()

template<typename T >

int fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_columns ( )

static

The number of columns.

Definition at line 115 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::d().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_rows().

◆ number_of_rows()

template<typename T >

int fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_rows ( )

static

The number of rows.

Definition at line 98 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_columns().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::operator at2_e3_row_dofs_type< T > &(), and fiber_bundle::operator<<().

◆ operator at2_e3_row_dofs_type< T > &()

template<typename T >

fiber_bundle::antisymmetric_matrix_3x3< T >::operator at2_e3_row_dofs_type< T > & ( ) const

Operator to convert current to at2_e3_row_dofs_type.

Definition at line 76 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::number_of_rows().

◆ operator const T *()

template<typename T >

fiber_bundle::antisymmetric_matrix_3x3< T >::operator const T * ( ) const

Conversion (cast) operator to convert to the associated matrix type (const version).

Postcondition

result != 0

Definition at line 215 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::row_index().

◆ operator general_matrix_3x3< T >()

template<typename T >

fiber_bundle::antisymmetric_matrix_3x3< T >::operator general_matrix_3x3< T > ( ) const

Conversion operator to convert to the associated general matrix type.

Postcondition

-unexecutable( "result == *this" )

Definition at line 264 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::row().

◆ operator T*()

template<typename T >

fiber_bundle::antisymmetric_matrix_3x3< T >::operator T* ( )

Conversion (cast) operator to convert to the associated matrix type (non const version).

Postcondition

result != 0

Definition at line 193 of file antisymmetric_matrix_3x3.impl.h.

◆ operator[]() [1/2]

template<typename T >

T * fiber_bundle::antisymmetric_matrix_3x3< T >::operator[] ( int xrow )

Pointer to the first element in row xrow of this matrix. Facilitates accessing elements via matrix[i][j].

Precondition

nrow >= 0 && nrow < number_of_rows()

Postcondition

result != 0

Definition at line 149 of file antisymmetric_matrix_3x3.impl.h.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::d().

◆ operator[]() [2/2]

template<typename T >

const T * fiber_bundle::antisymmetric_matrix_3x3< T >::operator[] ( int xrow ) const

Pointer to the first element in row xrow of this matrix. Facilitates accessing elements via matrix[i][j].

Precondition

nrow >= 0 && nrow < number_of_rows()

Postcondition

result != 0

Definition at line 171 of file antisymmetric_matrix_3x3.impl.h.

◆ row()

template<typename T >

general_matrix_1x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::row ( int xrow ) const

A 1x3 matrix containing the elements or row xrow.

Precondition

xrow >= 0 && xrow < number_of_rows()

Definition at line 299 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::column(), and fiber_bundle::general_matrix_1x3< T >::components.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::operator general_matrix_3x3< T >().

◆ row_index()

template<typename T >

int fiber_bundle::antisymmetric_matrix_3x3< T >::row_index ( int xrow ) const

Index for row xrow in the linear storage array.

Precondition

xrow >= 0 && xrow < number_of_rows()-1

Postcondition

result == (xrow*(2*number_of_rows()-1-xrow))/2 - 1 - xrow

Definition at line 238 of file antisymmetric_matrix_3x3.impl.h.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::operator const T *().

◆ trace() [1/2]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::trace ( T & xresult ) const

The trace of the matrix (pre-allocated).

Postcondition

xresult == 0

Definition at line 953 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::trace().

◆ trace() [2/2]

template<typename T >

T fiber_bundle::antisymmetric_matrix_3x3< T >::trace ( ) const

The trace of the matrix (auto-allocated).

Definition at line 972 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::trace(), and fiber_bundle::antisymmetric_matrix_3x3< T >::transpose().

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::multiply(), and fiber_bundle::antisymmetric_matrix_3x3< T >::trace().

◆ transpose() [1/2]

template<typename T >

void fiber_bundle::antisymmetric_matrix_3x3< T >::transpose ( antisymmetric_matrix_3x3< T > & xresult ) const

The transpose of the matrix (pre-allocated).

Definition at line 993 of file antisymmetric_matrix_3x3.impl.h.

References fiber_bundle::antisymmetric_matrix_3x3< T >::transpose().

◆ transpose() [2/2]

template<typename T >

antisymmetric_matrix_3x3< T > fiber_bundle::antisymmetric_matrix_3x3< T >::transpose ( ) const

The transpose of the matrix (auto-allocated).

Definition at line 1017 of file antisymmetric_matrix_3x3.impl.h.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::trace(), and fiber_bundle::antisymmetric_matrix_3x3< T >::transpose().

Member Data Documentation

◆ components

template<typename T>

T fiber_bundle::antisymmetric_matrix_3x3< T >::components[3]

Linear storage array.

Definition at line 126 of file antisymmetric_matrix_3x3.h.

Referenced by fiber_bundle::antisymmetric_matrix_3x3< T >::multiply().

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

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<typename T> class fiber_bundle::antisymmetric_matrix_3x3< T >

Member Function Documentation

◆ adjoint() [1/2]

◆ adjoint() [2/2]

◆ assign()

◆ column()

◆ d()

◆ determinant() [1/2]

◆ determinant() [2/2]

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ is_positive_definite()

◆ multiply() [1/10]

◆ multiply() [2/10]

◆ multiply() [3/10]

◆ multiply() [4/10]

◆ multiply() [5/10]

◆ multiply() [6/10]

◆ multiply() [7/10]

◆ multiply() [8/10]

◆ multiply() [9/10]

◆ multiply() [10/10]

◆ number_of_columns()

◆ number_of_rows()

◆ operator at2_e3_row_dofs_type< T > &()

◆ operator const T *()

◆ operator general_matrix_3x3< T >()

◆ operator T*()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ row()

◆ row_index()

◆ trace() [1/2]

◆ trace() [2/2]

◆ transpose() [1/2]

◆ transpose() [2/2]

Member Data Documentation

◆ components

template<typename T>
class fiber_bundle::antisymmetric_matrix_3x3< T >