numeric::xyzMatrix< typename > Class Template Reference

xyzMatrix: Fast 3x3 xyz matrix template More...

#include <xyzMatrix.hh>

Public Types
typedef T	Value
typedef T &	Reference
typedef T const &	ConstReference
typedef T *	Pointer
typedef T const *	ConstPointer
typedef xyzVector< T >	Vector
typedef T	value_type
typedef T &	reference
typedef T const &	const_reference
typedef T *	pointer
typedef T const *	const_pointer

Public Member Functions
	xyzMatrix ()
	Default constructor. More...
	xyzMatrix (xyzMatrix const &m)
	Copy constructor. More...
template<typename U >
	xyzMatrix (xyzMatrix< U > const &m)
	Copy constructor. More...
	xyzMatrix (Value const &t)
	Uniform value constructor. More...
	~xyzMatrix ()
	Destructor. More...
template<typename U >
	xyzMatrix (ColsPointer< U > const &c)
	Pointer to contiguous column-ordered values constructor. More...
template<typename U >
	xyzMatrix (ColPointers< U > const &c)
	Pointers to contiguous columns constructor. More...
template<typename U >
	xyzMatrix (ColVectors< U > const &c)
	Columns constructor. More...
template<typename U >
	xyzMatrix (RowsPointer< U > const &r)
	Pointer to contiguous row-ordered values constructor. More...
template<typename U >
	xyzMatrix (RowPointers< U > const &r)
	Pointers to contiguous rows constructor. More...
template<typename U >
	xyzMatrix (RowVectors< U > const &r)
	Rows constructor. More...
xyzMatrix &	operator= (xyzMatrix const &m)
	Copy assignment. More...
template<typename U >
xyzMatrix &	operator= (xyzMatrix< U > const &m)
	Copy assignment. More...
template<typename U >
xyzMatrix &	operator+= (xyzMatrix< U > const &m)
	+= xyzMatrix More...
template<typename U >
xyzMatrix &	operator-= (xyzMatrix< U > const &m)
	-= xyzMatrix More...
template<typename U >
xyzMatrix &	operator*= (xyzMatrix< U > const &m)
	*= xyzMatrix More...
template<typename U >
xyzMatrix &	operator= (ColsPointer< U > const &c)
	Assignment from pointer to contiguous column-ordered values. More...
template<typename U >
xyzMatrix &	operator= (RowsPointer< U > const &r)
	Assignment from pointer to contiguous row-ordered values. More...
template<typename U >
xyzMatrix &	operator= (ColPointers< U > const &c)
	Assignment from pointers to contiguous columns. More...
template<typename U >
xyzMatrix &	operator= (RowPointers< U > const &r)
	Assignment from pointers to contiguous rows. More...
template<typename U >
xyzMatrix &	operator= (ColVectors< U > const &c)
	xyzVector columns assignment More...
template<typename U >
xyzMatrix &	operator= (RowVectors< U > const &r)
	xyzVector rows assignment More...
xyzMatrix &	operator= (Value const &t)
	= Value More...
xyzMatrix &	operator+= (Value const &t)
	+= Value More...
xyzMatrix &	operator-= (Value const &t)
	-= Value More...
xyzMatrix &	operator*= (Value const &t)
	*= Value More...
xyzMatrix &	operator/= (Value const &t)
	/= Value More...
xyzMatrix &	clear ()
	Clear. More...
xyzMatrix &	zero ()
	Set to the zero xyzMatrix. More...
xyzMatrix &	to_identity ()
	Set to the identity xyzMatrix. More...
xyzMatrix &	to_diag (Value const &xx_a, Value const &yy_a, Value const &zz_a)
	Set to diagonal xyzMatrix from value. More...
template<typename U >
xyzMatrix &	to_diag (xyzVector< U > const &diag_a)
	Set to diagonal xyzMatrix from xyzVector. More...
xyzMatrix &	set_diagonal (Value const &xx_a, Value const &yy_a, Value const &zz_a)
	set diagonal of xyzMatrix from value More...
template<typename U >
xyzMatrix &	set_diagonal (xyzVector< U > const &diag_a)
	Set diagonal of xyzMatrix from xyzVector. More...
xyzMatrix &	add_diagonal (Value const &xx_a, Value const &yy_a, Value const &zz_a)
	Add values to diagonal of xyzMatrix. More...
template<typename U >
xyzMatrix &	add_diagonal (xyzVector< U > const &diag_a)
	Add xyzVector to diagonal of xyzMatrix. More...
xyzMatrix &	subtract_diagonal (Value const &xx_a, Value const &yy_a, Value const &zz_a)
	Subtract values from diagonal of xyzMatrix. More...
template<typename U >
xyzMatrix &	subtract_diagonal (xyzVector< U > const &diag_a)
	Subtract xyzVector from diagonal of xyzMatrix. More...
xyzMatrix &	transpose ()
	Transpose. More...
template<typename U >
xyzMatrix &	right_multiply_by (xyzMatrix< U > const &m)
	Right multiply by xyzMatrix. More...
template<typename U >
xyzMatrix &	right_multiply_by_transpose (xyzMatrix< U > const &m)
	Right multiply by transpose xyzMatrix. More...
template<typename U >
xyzMatrix &	left_multiply_by (xyzMatrix< U > const &m)
	Left multiply by xyzMatrix. More...
template<typename U >
xyzMatrix &	left_multiply_by_transpose (xyzMatrix< U > const &m)
	Left multiply by transpose xyzMatrix. More...
Vector	col_x () const
	Column x. More...
xyzMatrix &	col_x (Vector const &v)
	Column x assignment. More...
Vector	col_y () const
	Column y. More...
xyzMatrix &	col_y (Vector const &v)
	Column y assignment. More...
Vector	col_z () const
	Column z. More...
xyzMatrix &	col_z (Vector const &v)
	Column z assignment. More...
Vector	col (int const i) const
	Column( i ): 1-based index. More...
xyzMatrix &	col (int const i, Vector const &v)
	Column( i, xyzVector ) assignment: 1-base index. More...
Vector	row_x () const
	Row x. More...
xyzMatrix &	row_x (Vector const &v)
	Row x assignment. More...
Vector	row_y () const
	Row y. More...
xyzMatrix &	row_y (Vector const &v)
	Row y assignment. More...
Vector	row_z () const
	Row z. More...
xyzMatrix &	row_z (Vector const &v)
	Row z assignment. More...
Vector	row (int const i) const
	Row ( i ): 1-based index. More...
xyzMatrix &	row (int const i, Vector const &v)
	Row ( i, xyzVector ) assignment: 1-based index. More...
Value const &	xx () const
	Value xx const. More...
Value &	xx ()
	Value xx. More...
Value const &	xy () const
	Value xy const. More...
Value &	xy ()
	Value xy. More...
Value const &	xz () const
	Value xz const. More...
Value &	xz ()
	Value xz. More...
Value const &	yx () const
	Value yx const. More...
Value &	yx ()
	Value yx. More...
Value const &	yy () const
	Value yy const. More...
Value &	yy ()
	Value yy. More...
Value const &	yz () const
	Value yz const. More...
Value &	yz ()
	Value yz. More...
Value const &	zx () const
	Value zx const. More...
Value &	zx ()
	Value zx. More...
Value const &	zy () const
	Value zy const. More...
Value &	zy ()
	Value zy. More...
Value const &	zz () const
	Value zz const. More...
Value &	zz ()
	Value zz. More...
Value const &	operator() (int const i, int const j) const
	xyzMatrix( i, j ) const: 1-based index More...
Value &	operator() (int const i, int const j)
	xyzMatrix( i, j ): 1-based index More...
void	xx (Value const &xx_a)
	xx assignment More...
void	xy (Value const &xy_a)
	xy assignment More...
void	xz (Value const &xz_a)
	xz assignment More...
void	yx (Value const &yx_a)
	yx assignment More...
void	yy (Value const &yy_a)
	yy assignment More...
void	yz (Value const &yz_a)
	yz assignment More...
void	zx (Value const &zx_a)
	zx assignment More...
void	zy (Value const &zy_a)
	zy assignment More...
void	zz (Value const &zz_a)
	zz assignment More...
bool	is_zero () const
	Is zero? More...
bool	is_identity () const
	Is identity? More...
Value	det () const
	Determinant. More...
Value	trace () const
	Trace. More...
xyzMatrix	transposed () const
	Transposed copy. More...
xyzMatrix< T >	inverse () const
void	show (std::ostream &output=std::cout) const
	Show. More...

Static Public Member Functions
static xyzMatrix	cols (Value const &xx_a, Value const &yx_a, Value const &zx_a, Value const &xy_a, Value const &yy_a, Value const &zy_a, Value const &xz_a, Value const &yz_a, Value const &zz_a)
	Column-ordered value named constructor. More...
template<typename U >
static ColsPointer< U >	cols (U const *cp)
	Pointer to contiguous column-ordered values named constructor/assignment. More...
template<typename U >
static ColPointers< U >	cols (U const *xp, U const *yp, U const *zp)
	Pointers to contiguous columns named constructor/assignment. More...
template<typename U >
static xyzMatrix	cols_constructor (U const *xp, U const *yp, U const *zp)
	Pointers to contiguous columns named constructor. More...
template<typename U >
static ColVectors< U >	cols (xyzVector< U > const &col_x, xyzVector< U > const &col_y, xyzVector< U > const &col_z)
	Column vectors named constructor/assignment. More...
template<typename U >
static xyzMatrix	cols_constructor (xyzVector< U > const &col_x, xyzVector< U > const &col_y, xyzVector< U > const &col_z)
	xyzVector columns named constructor More...
static xyzMatrix	rows (Value const &xx_a, Value const &xy_a, Value const &xz_a, Value const &yx_a, Value const &yy_a, Value const &yz_a, Value const &zx_a, Value const &zy_a, Value const &zz_a)
	Row-ordered value named constructor. More...
template<typename U >
static RowsPointer< U >	rows (U const *rp)
	Pointer to contiguous row-ordered values named constructor/assignment. More...
template<typename U >
static RowPointers< U >	rows (U const *xp, U const *yp, U const *zp)
	Pointers to contiguous rows named constructor/assignment. More...
template<typename U >
static xyzMatrix	rows_constructor (U const *xp, U const *yp, U const *zp)
	Pointers to contiguous rows named constructor. More...
template<typename U >
static RowVectors< U >	rows (xyzVector< U > const &row_x, xyzVector< U > const &row_y, xyzVector< U > const &row_z)
	Row vectors named constructor/assignment. More...
template<typename U >
static xyzMatrix	rows_constructor (xyzVector< U > const &row_x, xyzVector< U > const &row_y, xyzVector< U > const &row_z)
	xyzVector rows named constructor More...
static xyzMatrix	diag (Value const &xx_a, Value const &yy_a, Value const &zz_a)
	Diagonal value named constructor. More...
template<typename U >
static xyzMatrix	diag (xyzVector< U > const &diag_a)
	Diagonal xyzVector named constructor. More...
static xyzMatrix	identity ()
	Identity xyzMatrix named constructor. More...
static xyzMatrix const &	I ()
	Identity xyzMatrix for expressions. More...

Private Member Functions
	xyzMatrix (Value const &xx_a, Value const &xy_a, Value const &xz_a, Value const &yx_a, Value const &yy_a, Value const &yz_a, Value const &zx_a, Value const &zy_a, Value const &zz_a)
	Row-ordered value constructor. More...

Private Attributes
Value	xx_
	Elements of the 3x3 matrix. More...
Value	xy_
Value	xz_
Value	yx_
Value	yy_
Value	yz_
Value	zx_
Value	zy_
Value	zz_

Friends
template<typename >
class	xyzMatrix
xyzVector< T >	operator* (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector More...
xyzVector< T >	product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector product More...
xyzVector< T > &	inplace_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix * xyzVector in-place product More...
xyzVector< T >	transpose_product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix^T * xyzVector product More...
xyzVector< T > &	inplace_transpose_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix^T * xyzVector in-place transpose product More...
xyzMatrix< T >	outer_product (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector xyzVector outer product More...
xyzMatrix< T >	projection_matrix (xyzVector< T > const &v)
	geometric center More...
xyzMatrix< T >	rotation_matrix (xyzVector< T > const &axis, T const &theta)
	Rotation matrix for rotation about an axis by an angle in radians. More...
xyzVector< T >	rotation_axis (xyzMatrix< T > const &R, T &theta)
	Transformation from rotation matrix to helical axis of rotation. More...
xyzVector< T >	eigenvalue_jacobi (xyzMatrix< T > const &a, T const &tol)
	Classic Jacobi algorithm for the eigenvalues of a real symmetric matrix. More...
xyzVector< T >	eigenvector_jacobi (xyzMatrix< T > const &a, T const &tol, xyzMatrix< T > &J)
	Classic Jacobi algorithm for the eigenvalues and eigenvectors of a real symmetric matrix. More...
xyzMatrix< T >	inverse (xyzMatrix< T > const &a)
xyzMatrix	operator+ (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix + xyzMatrix More...
xyzMatrix	operator+ (xyzMatrix const &m, Value const &t)
	xyzMatrix + Value More...
xyzMatrix	operator+ (Value const &t, xyzMatrix const &m)
	Value + xyzMatrix. More...
xyzMatrix	operator- (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix - xyzMatrix More...
xyzMatrix	operator- (xyzMatrix const &m, Value const &t)
	xyzMatrix - Value More...
xyzMatrix	operator- (Value const &t, xyzMatrix const &m)
	Value - xyzMatrix. More...
xyzMatrix	operator* (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix * xyzMatrix More...
xyzMatrix	operator* (xyzMatrix const &m, Value const &t)
	xyzMatrix * Value More...
xyzMatrix	operator* (Value const &t, xyzMatrix const &m)
	Value * xyzMatrix. More...
xyzMatrix	operator/ (xyzMatrix const &m, Value const &t)
	xyzMatrix / Value More...
bool	operator== (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix == xyzMatrix More...
bool	operator!= (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix != xyzMatrix More...
bool	operator< (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix < xyzMatrix More...
bool	operator<= (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix <= xyzMatrix More...
bool	operator>= (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix >= xyzMatrix More...
bool	operator> (xyzMatrix const &a, xyzMatrix const &b)
	xyzMatrix > xyzMatrix More...
bool	operator== (xyzMatrix const &m, Value const &t)
	xyzMatrix == Value More...
bool	operator!= (xyzMatrix const &m, Value const &t)
	xyzMatrix != Value More...
bool	operator< (xyzMatrix const &m, Value const &t)
	xyzMatrix < Value More...
bool	operator<= (xyzMatrix const &m, Value const &t)
	xyzMatrix <= Value More...
bool	operator>= (xyzMatrix const &m, Value const &t)
	xyzMatrix >= Value More...
bool	operator> (xyzMatrix const &m, Value const &t)
	xyzMatrix > Value More...
bool	operator== (Value const &t, xyzMatrix const &m)
	Value == xyzMatrix. More...
bool	operator!= (Value const &t, xyzMatrix const &m)
	Value != xyzMatrix. More...
bool	operator< (Value const &t, xyzMatrix const &m)
	Value < xyzMatrix. More...
bool	operator<= (Value const &t, xyzMatrix const &m)
	Value <= xyzMatrix. More...
bool	operator>= (Value const &t, xyzMatrix const &m)
	Value >= xyzMatrix. More...
bool	operator> (Value const &t, xyzMatrix const &m)
	Value > xyzMatrix. More...

Detailed Description

template<typename>
class numeric::xyzMatrix< typename >

xyzMatrix: Fast 3x3 xyz matrix template

Member Typedef Documentation

template<typename >

typedef T const* numeric::xyzMatrix< typename >::const_pointer

template<typename >

typedef T const& numeric::xyzMatrix< typename >::const_reference

template<typename >

typedef T const* numeric::xyzMatrix< typename >::ConstPointer

template<typename >

typedef T const& numeric::xyzMatrix< typename >::ConstReference

template<typename >

typedef T* numeric::xyzMatrix< typename >::Pointer

template<typename >

typedef T* numeric::xyzMatrix< typename >::pointer

template<typename >

typedef T& numeric::xyzMatrix< typename >::Reference

template<typename >

typedef T& numeric::xyzMatrix< typename >::reference

template<typename >

typedef T numeric::xyzMatrix< typename >::Value

template<typename >

typedef T numeric::xyzMatrix< typename >::value_type

template<typename >

typedef xyzVector< T > numeric::xyzMatrix< typename >::Vector

Constructor & Destructor Documentation

template<typename >

numeric::xyzMatrix< typename >::xyzMatrix ( )

inline

Default constructor.

Note

Values are uninitialized for efficiency

Referenced by numeric::xyzMatrix< T >::cols(), numeric::xyzMatrix< T >::cols_constructor(), numeric::xyzMatrix< T >::diag(), numeric::xyzMatrix< T >::identity(), numeric::xyzMatrix< T >::rows(), numeric::xyzMatrix< T >::rows_constructor(), and numeric::xyzMatrix< T >::transposed().

template<typename >

numeric::xyzMatrix< typename >::xyzMatrix ( xyzMatrix< typename > const &  m )

inline

Copy constructor.

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( xyzMatrix< U > const &  m )

inline

Copy constructor.

template<typename >

numeric::xyzMatrix< typename >::xyzMatrix ( Value const &  t )

inlineexplicit

Uniform value constructor.

template<typename >

numeric::xyzMatrix< typename >::~xyzMatrix ( )

inline

Destructor.

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( ColsPointer< U > const &  c )

inline

Pointer to contiguous column-ordered values constructor.

See also

cols

Note

The cols named constructor/assignment provides a simple wrapper interface

Constructor usage: xyzMatrix m( xyzMatrix::cols( cols_pointer ) )

Assignment usage: m = xyzMatrix::cols( cols_pointer )

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( ColPointers< U > const &  c )

inline

Pointers to contiguous columns constructor.

See also

cols

Note

The cols named constructor/assignment provides a simple wrapper interface

Constructor usage: xyzMatrix m( xyzMatrix::cols( x_col_pointer, y_col_pointer, z_col_pointer ) )

Assignment usage: m = xyzMatrix::cols( x_col_pointer, y_col_pointer, z_col_pointer )

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( ColVectors< U > const &  c )

inline

Columns constructor.

See also

cols

Note

The cols named constructor/assignment provides a simple wrapper interface

Constructor usage: xyzMatrix m( xyzMatrix::cols( x_col_vector, y_col_vector, z_col_vector ) )

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( RowsPointer< U > const &  r )

inline

Pointer to contiguous row-ordered values constructor.

See also

rows

Note

The rows named constructor/assignment provides a simple wrapper interface

Constructor usage: xyzMatrix m( xyzMatrix::rows( rows_pointer ) )

Assignment usage: m = xyzMatrix::rows( rows_pointer )

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( RowPointers< U > const &  r )

inline

Pointers to contiguous rows constructor.

See also

rows

Note

The rows named constructor/assignment provides a simple wrapper interface

Constructor usage: xyzMatrix m( xyzMatrix::rows( x_row_pointer, y_row_pointer, z_row_pointer ) )

Assignment usage: m = xyzMatrix::rows( x_row_pointer, y_row_pointer, z_row_pointer )

template<typename >

template<typename U >

numeric::xyzMatrix< typename >::xyzMatrix ( RowVectors< U > const &  r )

inline

Rows constructor.

See also

rows

Note

The rows named constructor/assignment provides a simple wrapper interface

Constructor usage: xyzMatrix m( xyzMatrix::rows( x_row_vector, y_row_vector, z_row_vector ) )

template<typename >

numeric::xyzMatrix< typename >::xyzMatrix ( Value const &  xx_a, Value const &  xy_a, Value const &  xz_a, Value const &  yx_a, Value const &  yy_a, Value const &  yz_a, Value const &  zx_a, Value const &  zy_a, Value const &  zz_a  )

inlineprivate

Row-ordered value constructor.

Note

Client code uses named constructors that specify the value order explicitly

Member Function Documentation

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::add_diagonal ( Value const &  xx_a, Value const &  yy_a, Value const &  zz_a  )

inline

Add values to diagonal of xyzMatrix.

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::add_diagonal ( xyzVector< U > const &  diag_a )

inline

Add xyzVector to diagonal of xyzMatrix.

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::clear ( )

inline

Clear.

template<typename >

Vector numeric::xyzMatrix< typename >::col ( int const  i ) const

inline

Column( i ): 1-based index.

Referenced by numeric::first_principal_component(), and numeric::principal_components_and_eigenvalues().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::col ( int const  i, Vector const &  v  )

inline

Column( i, xyzVector ) assignment: 1-base index.

template<typename >

Vector numeric::xyzMatrix< typename >::col_x ( ) const

inline

Column x.

Referenced by check_for_contacts(), numeric::xyzMatrix< T >::cols(), numeric::xyzTransform< numeric::Real >::distance_squared(), numeric::xyzTransform< numeric::Real >::from_four_points(), and numeric::principal_components_and_eigenvalues().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::col_x ( Vector const &  v )

inline

Column x assignment.

template<typename >

Vector numeric::xyzMatrix< typename >::col_y ( ) const

inline

Column y.

Referenced by check_for_contacts(), numeric::xyzMatrix< T >::cols(), and numeric::xyzTransform< numeric::Real >::distance_squared().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::col_y ( Vector const &  v )

inline

Column y assignment.

template<typename >

Vector numeric::xyzMatrix< typename >::col_z ( ) const

inline

Column z.

Referenced by check_for_contacts(), numeric::xyzMatrix< T >::cols(), and numeric::xyzTransform< numeric::Real >::distance_squared().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::col_z ( Vector const &  v )

inline

Column z assignment.

template<typename >

static xyzMatrix numeric::xyzMatrix< typename >::cols ( Value const &  xx_a, Value const &  yx_a, Value const &  zx_a, Value const &  xy_a, Value const &  yy_a, Value const &  zy_a, Value const &  xz_a, Value const &  yz_a, Value const &  zz_a  )

inlinestatic

Column-ordered value named constructor.

Note

Constructor usage: xyzMatrix m( xyzMatrix::cols( xx_a, yx_a, zx_a, xy_a, yy_a, zy_a, xz_a, yz_a, zz_a ) )

Assignment usage: m = xyzMatrix::cols( xx_a, yx_a, zx_a, xy_a, yy_a, zy_a, xz_a, yz_a, zz_a )

Referenced by numeric::random::random_rotation(), basic::sampling::orientations::Quaternion::rotation_matrix(), and slice_ellipsoid_envelope().

template<typename >

template<typename U >

static ColsPointer< U > numeric::xyzMatrix< typename >::cols ( U const *  cp )

inlinestatic

Pointer to contiguous column-ordered values named constructor/assignment.

Warning

No way to check that argument points to nine contiguous values

Note

Constructor usage: xyzMatrix m( xyzMatrix::cols( cols_pointer ) )

Assignment usage: m = xyzMatrix::cols( cols_pointer )

template<typename >

template<typename U >

static ColPointers< U > numeric::xyzMatrix< typename >::cols ( U const *  xp, U const *  yp, U const *  zp  )

inlinestatic

Pointers to contiguous columns named constructor/assignment.

Warning

No way to check that arguments each point to three contiguous values

Note

Constructor usage: xyzMatrix m( xyzMatrix::cols( x_col_pointer, y_col_pointer, z_col_pointer ) )

Assignment usage: m = xyzMatrix::cols( x_col_pointer, y_col_pointer, z_col_pointer )

template<typename >

template<typename U >

static ColVectors< U > numeric::xyzMatrix< typename >::cols ( xyzVector< U > const &  col_x, xyzVector< U > const &  col_y, xyzVector< U > const &  col_z  )

inlinestatic

Column vectors named constructor/assignment.

Note

Constructor usage: xyzMatrix m( xyzMatrix::cols( x_col_vector, y_col_vector, z_col_vector ) )

Assignment usage: m = xyzMatrix::cols( x_col_vector, y_col_vector, z_col_vector )

template<typename >

template<typename U >

static xyzMatrix numeric::xyzMatrix< typename >::cols_constructor ( U const *  xp, U const *  yp, U const *  zp  )

inlinestatic

Pointers to contiguous columns named constructor.

Warning

No way to check that arguments each point to three contiguous values

Note

Can be faster than cols() construction due to return value optimization

Constructor usage: xyzMatrix m( xyzMatrix::cols_constructor( x_col_pointer, y_col_pointer, z_col_pointer ) )

template<typename >

template<typename U >

static xyzMatrix numeric::xyzMatrix< typename >::cols_constructor ( xyzVector< U > const &  col_x, xyzVector< U > const &  col_y, xyzVector< U > const &  col_z  )

inlinestatic

xyzVector columns named constructor

Note

Can be faster than cols() construction due to return value optimization

Constructor usage: xyzMatrix m( xyzMatrix::cols_constructor( x_col_vector, y_col_vector, z_col_vector ) )

template<typename >

Value numeric::xyzMatrix< typename >::det ( ) const

inline

Determinant.

Referenced by numeric::inverse().

template<typename >

static xyzMatrix numeric::xyzMatrix< typename >::diag ( Value const &  xx_a, Value const &  yy_a, Value const &  zz_a  )

inlinestatic

Diagonal value named constructor.

Note

diag refers to a diagonal matrix

template<typename >

template<typename U >

static xyzMatrix numeric::xyzMatrix< typename >::diag ( xyzVector< U > const &  diag_a )

inlinestatic

Diagonal xyzVector named constructor.

Note

diag refers to a diagonal matrix

template<typename >

static xyzMatrix const& numeric::xyzMatrix< typename >::I ( )

inlinestatic

Identity xyzMatrix for expressions.

Note

identity() named constructor can be faster for construction

Returns reference to function-local static object so can be used in construction of global objects

template<typename >

static xyzMatrix numeric::xyzMatrix< typename >::identity ( )

inlinestatic

Identity xyzMatrix named constructor.

Note

Can be faster than I() for construction due to return value optimization

Referenced by numeric::alignVectorSets(), and numeric::fourier::SHT::idx_to_rot().

template<typename >

xyzMatrix< T > numeric::xyzMatrix< typename >::inverse ( ) const

inline

template<typename >

bool numeric::xyzMatrix< typename >::is_identity ( ) const

inline

Is identity?

template<typename >

bool numeric::xyzMatrix< typename >::is_zero ( ) const

inline

Is zero?

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::left_multiply_by ( xyzMatrix< U > const &  m )

inline

Left multiply by xyzMatrix.

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::left_multiply_by_transpose ( xyzMatrix< U > const &  m )

inline

Left multiply by transpose xyzMatrix.

Referenced by numeric::eigenvalue_jacobi(), and numeric::eigenvector_jacobi().

template<typename >

Value const& numeric::xyzMatrix< typename >::operator() ( int const  i, int const  j  ) const

inline

xyzMatrix( i, j ) const: 1-based index

template<typename >

Value& numeric::xyzMatrix< typename >::operator() ( int const  i, int const  j  )

inline

xyzMatrix( i, j ): 1-based index

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator*= ( xyzMatrix< U > const &  m )

inline

*= xyzMatrix

Note

Same as right_multiply_by( xyzMatrix )

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::operator*= ( Value const &  t )

inline

*= Value

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator+= ( xyzMatrix< U > const &  m )

inline

+= xyzMatrix

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::operator+= ( Value const &  t )

inline

+= Value

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator-= ( xyzMatrix< U > const &  m )

inline

-= xyzMatrix

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::operator-= ( Value const &  t )

inline

-= Value

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::operator/= ( Value const &  t )

inline

/= Value

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( xyzMatrix< typename > const &  m )

inline

Copy assignment.

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( xyzMatrix< U > const &  m )

inline

Copy assignment.

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( ColsPointer< U > const &  c )

inline

Assignment from pointer to contiguous column-ordered values.

Note

Use via named assignment wrapper: m = xyzMatrix::cols( pointer )

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( RowsPointer< U > const &  r )

inline

Assignment from pointer to contiguous row-ordered values.

Note

Use via named assignment wrapper: m = xyzMatrix::rows( pointer )

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( ColPointers< U > const &  c )

inline

Assignment from pointers to contiguous columns.

Note

Use via named assignment wrapper: m = xyzMatrix::cols( pointer, pointer, pointer )

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( RowPointers< U > const &  r )

inline

Assignment from pointers to contiguous rows.

Note

Use via named assignment wrapper: m = xyzMatrix::rows( pointer, pointer, pointer )

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( ColVectors< U > const &  c )

inline

xyzVector columns assignment

Note

Use via named assignment wrapper: m = xyzMatrix::cols( xyzVector, xyzVector, xyzVector )

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( RowVectors< U > const &  r )

inline

xyzVector rows assignment

Note

Use via named assignment wrapper: m = xyzMatrix::rows( xyzVector, xyzVector, xyzVector )

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::operator= ( Value const &  t )

inline

= Value

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::right_multiply_by ( xyzMatrix< U > const &  m )

inline

Right multiply by xyzMatrix.

Note

Same as *= xyzMatrix

Referenced by numeric::eigenvalue_jacobi(), and numeric::eigenvector_jacobi().

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::right_multiply_by_transpose ( xyzMatrix< U > const &  m )

inline

Right multiply by transpose xyzMatrix.

template<typename >

Vector numeric::xyzMatrix< typename >::row ( int const  i ) const

inline

Row ( i ): 1-based index.

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::row ( int const  i, Vector const &  v  )

inline

Row ( i, xyzVector ) assignment: 1-based index.

template<typename >

Vector numeric::xyzMatrix< typename >::row_x ( ) const

inline

Row x.

Referenced by numeric::xyzMatrix< T >::rows().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::row_x ( Vector const &  v )

inline

Row x assignment.

template<typename >

Vector numeric::xyzMatrix< typename >::row_y ( ) const

inline

Row y.

Referenced by numeric::xyzMatrix< T >::rows().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::row_y ( Vector const &  v )

inline

Row y assignment.

template<typename >

Vector numeric::xyzMatrix< typename >::row_z ( ) const

inline

Row z.

Referenced by numeric::xyzMatrix< T >::rows().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::row_z ( Vector const &  v )

inline

Row z assignment.

template<typename >

static xyzMatrix numeric::xyzMatrix< typename >::rows ( Value const &  xx_a, Value const &  xy_a, Value const &  xz_a, Value const &  yx_a, Value const &  yy_a, Value const &  yz_a, Value const &  zx_a, Value const &  zy_a, Value const &  zz_a  )

inlinestatic

Row-ordered value named constructor.

Note

Constructor usage: xyzMatrix m( xyzMatrix::rows( xx_a, xy_a, xz_a, yx_a, yy_a, yz_a, zx_a, zy_a, zz_a ) )

Assignment usage: m = xyzMatrix::rows( xx_a, xy_a, xz_a, yx_a, yy_a, yz_a, zx_a, zy_a, zz_a )

Referenced by numeric::urs_Quat::asR(), numeric::FArray_to_xyzmatrix(), numeric::UniformRotationSampler::get(), numeric::x_rotation_matrix(), numeric::y_rotation_matrix(), and numeric::z_rotation_matrix().

template<typename >

template<typename U >

static RowsPointer< U > numeric::xyzMatrix< typename >::rows ( U const *  rp )

inlinestatic

Pointer to contiguous row-ordered values named constructor/assignment.

Warning

No way to check that argument points to nine contiguous values

Note

Constructor usage: xyzMatrix m( xyzMatrix::rows( rows_pointer ) )

Assignment usage: m = xyzMatrix::rows( rows_pointer )

template<typename >

template<typename U >

static RowPointers< U > numeric::xyzMatrix< typename >::rows ( U const *  xp, U const *  yp, U const *  zp  )

inlinestatic

Pointers to contiguous rows named constructor/assignment.

Warning

No way to check that arguments each point to three contiguous values

Note

Constructor usage: xyzMatrix m( xyzMatrix::rows( x_row_pointer, y_row_pointer, z_row_pointer ) )

Assignment usage: m = xyzMatrix::rows( x_row_pointer, y_row_pointer, z_row_pointer )

template<typename >

template<typename U >

static RowVectors< U > numeric::xyzMatrix< typename >::rows ( xyzVector< U > const &  row_x, xyzVector< U > const &  row_y, xyzVector< U > const &  row_z  )

inlinestatic

Row vectors named constructor/assignment.

Note

Constructor usage: xyzMatrix m( xyzMatrix::rows( x_row_vector, y_row_vector, z_row_vector ) )

Assignment usage: m = xyzMatrix::rows( x_row_vector, y_row_vector, z_row_vector )

template<typename >

template<typename U >

static xyzMatrix numeric::xyzMatrix< typename >::rows_constructor ( U const *  xp, U const *  yp, U const *  zp  )

inlinestatic

Pointers to contiguous rows named constructor.

Warning

No way to check that arguments each point to three contiguous values

Note

Can be faster than rows() construction due to return value optimization

Constructor usage: xyzMatrix m( xyzMatrix::rows_constructor( x_row_pointer, y_row_pointer, z_row_pointer ) )

Referenced by numeric::HomogeneousTransform< double >::rotation_matrix().

template<typename >

template<typename U >

static xyzMatrix numeric::xyzMatrix< typename >::rows_constructor ( xyzVector< U > const &  row_x, xyzVector< U > const &  row_y, xyzVector< U > const &  row_z  )

inlinestatic

xyzVector rows named constructor

Note

Can be faster than rows() construction due to return value optimization

Constructor usage: xyzMatrix m( xyzMatrix::rows_constructor( x_row_vector, y_row_vector, z_row_vector ) )

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::set_diagonal ( Value const &  xx_a, Value const &  yy_a, Value const &  zz_a  )

inline

set diagonal of xyzMatrix from value

Note

Resets the diagonal of the matrix only (diagonal refers to diagonal entries of a matrix)

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::set_diagonal ( xyzVector< U > const &  diag_a )

inline

Set diagonal of xyzMatrix from xyzVector.

Note

Resets the diagonal of the matrix only (diagonal refers to diagonal

template<typename >

void numeric::xyzMatrix< typename >::show ( std::ostream &  output = std::cout ) const

inline

Show.

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::subtract_diagonal ( Value const &  xx_a, Value const &  yy_a, Value const &  zz_a  )

inline

Subtract values from diagonal of xyzMatrix.

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::subtract_diagonal ( xyzVector< U > const &  diag_a )

inline

Subtract xyzVector from diagonal of xyzMatrix.

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::to_diag ( Value const &  xx_a, Value const &  yy_a, Value const &  zz_a  )

inline

Set to diagonal xyzMatrix from value.

Note

Resets the entire matrix (diag refers to a diagonal matrix)

template<typename >

template<typename U >

xyzMatrix& numeric::xyzMatrix< typename >::to_diag ( xyzVector< U > const &  diag_a )

inline

Set to diagonal xyzMatrix from xyzVector.

Note

Resets the entire matrix (diag refers to a diagonal matrix)

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::to_identity ( )

inline

Set to the identity xyzMatrix.

Referenced by numeric::eigenvector_jacobi(), numeric::jacobi_rotation(), and numeric::BodyPosition< typename >::to_identity().

template<typename >

Value numeric::xyzMatrix< typename >::trace ( ) const

inline

Trace.

Referenced by numeric::rotation_angle(), numeric::rotation_axis(), numeric::xyzTransform< numeric::Real >::rotation_cosine(), and numeric::xyzTransform< numeric::Real >::rotation_sine().

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::transpose ( )

inline

Transpose.

Referenced by numeric::BodyPosition< typename >::invert().

template<typename >

xyzMatrix numeric::xyzMatrix< typename >::transposed ( ) const

inline

Transposed copy.

Referenced by numeric::xyzTransform< numeric::Real >::inv_xform(), numeric::xyzTransform< numeric::Real >::inverse(), and numeric::xyzTransform< numeric::Real >::operator~().

template<typename >

Value const& numeric::xyzMatrix< typename >::xx ( ) const

inline

Value xx const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzTransform< numeric::Real >::xx(), and numeric::xyzmatrix_to_FArray().

template<typename >

Value& numeric::xyzMatrix< typename >::xx ( )

inline

Value xx.

template<typename >

void numeric::xyzMatrix< typename >::xx ( Value const &  xx_a )

inline

xx assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::xy ( ) const

inline

Value xy const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzTransform< numeric::Real >::xy(), and numeric::xyzmatrix_to_FArray().

template<typename >

Value& numeric::xyzMatrix< typename >::xy ( )

inline

Value xy.

template<typename >

void numeric::xyzMatrix< typename >::xy ( Value const &  xy_a )

inline

xy assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::xz ( ) const

inline

Value xz const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::xz().

template<typename >

Value& numeric::xyzMatrix< typename >::xz ( )

inline

Value xz.

template<typename >

void numeric::xyzMatrix< typename >::xz ( Value const &  xz_a )

inline

xz assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::yx ( ) const

inline

Value yx const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::yx().

template<typename >

Value& numeric::xyzMatrix< typename >::yx ( )

inline

Value yx.

template<typename >

void numeric::xyzMatrix< typename >::yx ( Value const &  yx_a )

inline

yx assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::yy ( ) const

inline

Value yy const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::yy().

template<typename >

Value& numeric::xyzMatrix< typename >::yy ( )

inline

Value yy.

template<typename >

void numeric::xyzMatrix< typename >::yy ( Value const &  yy_a )

inline

yy assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::yz ( ) const

inline

Value yz const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::yz().

template<typename >

Value& numeric::xyzMatrix< typename >::yz ( )

inline

Value yz.

template<typename >

void numeric::xyzMatrix< typename >::yz ( Value const &  yz_a )

inline

yz assignment

template<typename >

xyzMatrix& numeric::xyzMatrix< typename >::zero ( )

inline

Set to the zero xyzMatrix.

Referenced by app.pyrosetta_toolkit.window_modules.scorefunction.ScoreFxnControl.ScoreFxnControl::saveAS(), and app.pyrosetta_toolkit.window_modules.scorefunction.ScoreFxnControl.ScoreFxnControl::updateScoreandTerms().

template<typename >

Value const& numeric::xyzMatrix< typename >::zx ( ) const

inline

Value zx const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::zx().

template<typename >

Value& numeric::xyzMatrix< typename >::zx ( )

inline

Value zx.

template<typename >

void numeric::xyzMatrix< typename >::zx ( Value const &  zx_a )

inline

zx assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::zy ( ) const

inline

Value zy const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::zy().

template<typename >

Value& numeric::xyzMatrix< typename >::zy ( )

inline

Value zy.

template<typename >

void numeric::xyzMatrix< typename >::zy ( Value const &  zy_a )

inline

zy assignment

template<typename >

Value const& numeric::xyzMatrix< typename >::zz ( ) const

inline

Value zz const.

Referenced by numeric::alignVectorSets(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::xyzTransform< numeric::Real >::from_euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), numeric::operator>>(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::EulerAngles< typename >::to_rotation_matrix(), numeric::urs_Quat::urs_Quat(), numeric::xyzmatrix_to_FArray(), and numeric::xyzTransform< numeric::Real >::zz().

template<typename >

Value& numeric::xyzMatrix< typename >::zz ( )

inline

Value zz.

template<typename >

void numeric::xyzMatrix< typename >::zz ( Value const &  zz_a )

inline

zz assignment

Friends And Related Function Documentation

template<typename >

xyzVector< T > eigenvalue_jacobi ( xyzMatrix< T > const &  a, T const &  tol  )

friend

Classic Jacobi algorithm for the eigenvalues of a real symmetric matrix.

Note

Use eigenvector_jacobi if eigenvectors are also desired

template<typename >

xyzVector< T > eigenvector_jacobi ( xyzMatrix< T > const &  a, T const &  tol, xyzMatrix< T > &  J  )

friend

Classic Jacobi algorithm for the eigenvalues and eigenvectors of a real symmetric matrix.

Note

Use eigenvalue_jacobi if eigenvectors are not desired

template<typename >

xyzVector< T >& inplace_product ( xyzMatrix< T > const &  m, xyzVector< T > &  v  )

friend

xyzMatrix * xyzVector in-place product

Note

Input xyzVector is modified

template<typename >

xyzVector< T >& inplace_transpose_product ( xyzMatrix< T > const &  m, xyzVector< T > &  v  )

friend

xyzMatrix^T * xyzVector in-place transpose product

Note

Input xyzVector is modified

template<typename >

xyzMatrix< T > inverse ( xyzMatrix< T > const &  a )

friend

template<typename >

bool operator!= ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix != xyzMatrix

template<typename >

bool operator!= ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix != Value

template<typename >

bool operator!= ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value != xyzMatrix.

template<typename >

xyzVector< T > operator* ( xyzMatrix< T > const &  m, xyzVector< T > const &  v  )

friend

xyzMatrix * xyzVector

Note

Same as product( xyzMatrix, xyzVector )

template<typename >

xyzMatrix operator* ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix * xyzMatrix

template<typename >

xyzMatrix operator* ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix * Value

template<typename >

xyzMatrix operator* ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value * xyzMatrix.

template<typename >

xyzMatrix operator+ ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix + xyzMatrix

template<typename >

xyzMatrix operator+ ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix + Value

template<typename >

xyzMatrix operator+ ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value + xyzMatrix.

template<typename >

xyzMatrix operator- ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix - xyzMatrix

template<typename >

xyzMatrix operator- ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix - Value

template<typename >

xyzMatrix operator- ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value - xyzMatrix.

template<typename >

xyzMatrix operator/ ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix / Value

template<typename >

bool operator< ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix < xyzMatrix

template<typename >

bool operator< ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix < Value

template<typename >

bool operator< ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value < xyzMatrix.

template<typename >

bool operator<= ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix <= xyzMatrix

template<typename >

bool operator<= ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix <= Value

template<typename >

bool operator<= ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value <= xyzMatrix.

template<typename >

bool operator== ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix == xyzMatrix

template<typename >

bool operator== ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix == Value

template<typename >

bool operator== ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value == xyzMatrix.

template<typename >

bool operator> ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix > xyzMatrix

template<typename >

bool operator> ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix > Value

template<typename >

bool operator> ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value > xyzMatrix.

template<typename >

bool operator>= ( xyzMatrix< typename > const &  a, xyzMatrix< typename > const &  b  )

friend

xyzMatrix >= xyzMatrix

template<typename >

bool operator>= ( xyzMatrix< typename > const &  m, Value const &  t  )

friend

xyzMatrix >= Value

template<typename >

bool operator>= ( Value const &  t, xyzMatrix< typename > const &  m  )

friend

Value >= xyzMatrix.

template<typename >

xyzMatrix< T > outer_product ( xyzVector< T > const &  a, xyzVector< T > const &  b  )

friend

xyzVector xyzVector outer product

template<typename >

xyzVector< T > product ( xyzMatrix< T > const &  m, xyzVector< T > const &  v  )

friend

xyzMatrix * xyzVector product

Note

Same as xyzMatrix * xyzVector

template<typename >

xyzMatrix< T > projection_matrix ( xyzVector< T > const &  v )

friend

geometric center

Note

compute the geometric center of a list of points Projection matrix onto the line through a vector

template<typename >

xyzVector< T > rotation_axis ( xyzMatrix< T > const &  R, T &  theta  )

friend

Transformation from rotation matrix to helical axis of rotation.

Note

Input matrix must be orthogonal

Angle of rotation is also returned

Orientation of axis chosen so that the angle of rotation is non-negative [0,pi]

template<typename >

xyzMatrix< T > rotation_matrix ( xyzVector< T > const &  axis, T const &  theta  )

friend

Rotation matrix for rotation about an axis by an angle in radians.

template<typename >

xyzVector< T > transpose_product ( xyzMatrix< T > const &  m, xyzVector< T > const &  v  )

friend

xyzMatrix^T * xyzVector product

template<typename >

template<typename >

friend class xyzMatrix

friend

Member Data Documentation

template<typename >

Value numeric::xyzMatrix< typename >::xx_

private

Elements of the 3x3 matrix.

Referenced by numeric::xyzMatrix< T >::add_diagonal(), numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_x(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_x(), numeric::xyzMatrix< T >::set_diagonal(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::subtract_diagonal(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::trace(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::xx(), and numeric::xyzMatrix< T >::zero().

template<typename >

Value numeric::xyzMatrix< typename >::xy_

private

Referenced by numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_y(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_x(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::transpose(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::xy(), and numeric::xyzMatrix< T >::zero().

template<typename >

Value numeric::xyzMatrix< typename >::xz_

private

Referenced by numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_z(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_x(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::transpose(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::xz(), and numeric::xyzMatrix< T >::zero().

template<typename >

Value numeric::xyzMatrix< typename >::yx_

private

Referenced by numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_x(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_y(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::transpose(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::yx(), and numeric::xyzMatrix< T >::zero().

template<typename >

Value numeric::xyzMatrix< typename >::yy_

private

Referenced by numeric::xyzMatrix< T >::add_diagonal(), numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_y(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_y(), numeric::xyzMatrix< T >::set_diagonal(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::subtract_diagonal(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::trace(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::yy(), and numeric::xyzMatrix< T >::zero().

template<typename >

Value numeric::xyzMatrix< typename >::yz_

private

Referenced by numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_z(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_y(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::transpose(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::yz(), and numeric::xyzMatrix< T >::zero().

template<typename >

Value numeric::xyzMatrix< typename >::zx_

private

Referenced by numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_x(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_z(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::transpose(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::zero(), and numeric::xyzMatrix< T >::zx().

template<typename >

Value numeric::xyzMatrix< typename >::zy_

private

Referenced by numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_y(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_z(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::transpose(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::zero(), and numeric::xyzMatrix< T >::zy().

template<typename >

Value numeric::xyzMatrix< typename >::zz_

private

Referenced by numeric::xyzMatrix< T >::add_diagonal(), numeric::xyzMatrix< T >::clear(), numeric::xyzMatrix< T >::col(), numeric::xyzMatrix< T >::col_z(), numeric::xyzMatrix< T >::det(), numeric::eigenvalue_jacobi(), numeric::eigenvector_jacobi(), numeric::inplace_product(), numeric::inplace_transpose_product(), numeric::inverse(), numeric::xyzMatrix< T >::is_identity(), numeric::xyzMatrix< T >::is_zero(), numeric::xyzMatrix< T >::left_multiply_by(), numeric::xyzMatrix< T >::left_multiply_by_transpose(), numeric::xyzMatrix< T >::operator()(), numeric::operator*(), numeric::xyzMatrix< T >::operator*=(), numeric::xyzMatrix< T >::operator+=(), numeric::xyzMatrix< T >::operator-=(), numeric::xyzMatrix< T >::operator/=(), numeric::xyzMatrix< T >::operator=(), numeric::product(), numeric::xyzMatrix< T >::right_multiply_by(), numeric::xyzMatrix< T >::right_multiply_by_transpose(), numeric::rotation_axis(), numeric::rotation_matrix(), numeric::xyzMatrix< T >::row(), numeric::xyzMatrix< T >::row_z(), numeric::xyzMatrix< T >::set_diagonal(), numeric::xyzMatrix< T >::show(), numeric::xyzMatrix< T >::subtract_diagonal(), numeric::xyzMatrix< T >::to_diag(), numeric::xyzMatrix< T >::to_identity(), numeric::xyzMatrix< T >::trace(), numeric::transpose_product(), numeric::xyzMatrix< T >::transposed(), numeric::xyzMatrix< T >::zero(), and numeric::xyzMatrix< T >::zz().

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

• src/numeric/xyzMatrix.fwd.hh
• src/numeric/xyzMatrix.hh