MATRIX3 Class Reference

A 3x3 matrix that may be used for orientation, inertia tensors, etc. More...

#include <Matrix3.h>

Public Member Functions
	MATRIX3 (const MATRIX3 &source)
	MATRIX3 (const REAL *array)
	Constructs a matrix from an array. More...
	MATRIX3 (const QUAT &q)
	MATRIX3 (const AANGLE &a)
	MATRIX3 (REAL, REAL, REAL, REAL, REAL, REAL, REAL, REAL, REAL)
	Constructs a matrix from a set of values.
MATRIX3 &	operator= (const QUAT &q)
MATRIX3 &	operator= (const AANGLE &a)
	MATRIX3 (const MATRIXN &m)
	MATRIX3 (const SHAREDMATRIXN &m)
	MATRIX3 (const CONST_SHAREDMATRIXN &m)
REAL	norm_inf () const
	Computes the l-infinity norm of this matrix.
unsigned	rows () const
unsigned	columns () const
bool	is_symmetric (REAL tolerance) const
	Checks whether this matrix is symmetric.
bool	orthonormalize ()
	Makes the matrix orthonormal using Gram-Schmidt orthogonalization.
bool	is_orthonormal () const
	Determines whether this is an orthonormal matrix.
REAL	det () const
	Calculates the determinant for a 3x3 matrix.
MATRIX3 &	invert ()
	Inverts this matrix.
const REAL &	xx () const
REAL &	xx ()
const REAL &	xy () const
REAL &	xy ()
const REAL &	xz () const
REAL &	xz ()
const REAL &	yx () const
REAL &	yx ()
const REAL &	yy () const
REAL &	yy ()
const REAL &	yz () const
REAL &	yz ()
const REAL &	zx () const
REAL &	zx ()
const REAL &	zy () const
REAL &	zy ()
const REAL &	zz () const
REAL &	zz ()
MATRIX3	inverse () const
void	set_rot_X (REAL angle)
	Sets this matrix to the rotation matrix of the specified angle around the X axis.
void	set_rot_Y (REAL angle)
	Sets this matrix to the rotation matrix of the specified angle around the Y axis.
void	set_rot_Z (REAL angle)
	Sets this matrix to the rotation matrix of the specified angle around the Z axis.
void	transpose ()
	Sets this matrix to its transpose.
MATRIX3 &	set_zero (unsigned m, unsigned n)
MATRIX3 &	set_identity ()
	Sets this matrix to identity.
MATRIX3 &	set_zero ()
ORIGIN3	transpose_mult (const ORIGIN3 &v) const
	Multiplies the transpose of this matrix by a vector and returns the result in a new vector.
ORIGIN3	mult (const ORIGIN3 &v) const
	Multiplies this matrix by a vector and returns the result in a new vector.
MATRIX3	mult (const MATRIX3 &m) const
	Multiplies this matrix by a matrix and returns the result in a new matrix.
MATRIX3	transpose_mult (const MATRIX3 &m) const
	Multiplies the transpose of this matrix by a matrix and returns the result in a new matrix.
MATRIX3	mult_transpose (const MATRIX3 &m) const
	Multiplies this matrix by a transposed matrix and returns the result in a new matrix.
MATRIX3	transpose_mult_transpose (const MATRIX3 &m) const
	Multiplies the transpose of this matrix by a transposed matrix and returns the result in a new matrix.
MATRIX3 &	operator= (const MATRIX3 &source)
	Copies a matrix to this one.
MATRIX3 &	operator= (const MATRIXN &source)
	Copies a matrix to this one.
MATRIX3 &	operator= (const SHAREDMATRIXN &source)
	Copies a matrix to this one.
MATRIX3 &	operator= (const CONST_SHAREDMATRIXN &source)
	Copies a matrix to this one.
MATRIX3 &	operator+= (const MATRIX3 &m)
	Adds m to this in place.
MATRIX3 &	operator-= (const MATRIX3 &m)
	Subtracts m from this in place.
MATRIX3 &	operator*= (REAL scalar)
	Multiplies this matrix by a scalar in place.
MATRIX3 &	operator/= (REAL scalar)
MATRIX3	operator+ (const MATRIX3 &m) const
MATRIX3	operator- (const MATRIX3 &m) const
MATRIX3	operator* (REAL scalar) const
MATRIX3	operator/ (REAL scalar) const
MATRIX3	operator- () const
	Returns the negation of this matrix.
MATRIX3	operator* (const MATRIX3 &m) const
ORIGIN3	operator* (const ORIGIN3 &v) const
unsigned	leading_dim () const
unsigned	inc () const
ORIGIN3	get_column (unsigned i) const
	Gets the specified column of the matrix. More...
ORIGIN3	get_row (unsigned i) const
	Gets the specified row of the matrix. More...
REAL &	operator() (unsigned i, unsigned j)
const REAL &	operator() (unsigned i, unsigned j) const
MATRIX3 &	resize (unsigned rows, unsigned columns, bool preserve=false)
const REAL *	data (unsigned i) const
REAL *	data (unsigned i)
unsigned	size () const
	Gets the total number of elements in this matrix.
const REAL *	data () const
	Gets constant pointer to the beginning of the matrix array.
REAL *	data ()
	Gets pointer to the beginning of the matrix array.
CONST_COLUMN_ITERATOR	block_column_iterator_begin (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end) const
	This file consists of general routines for constant matrices. More...
CONST_COLUMN_ITERATOR	block_column_iterator_end (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end) const
	Gets a column iterator to a block.
CONST_ROW_ITERATOR	block_row_iterator_begin (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end) const
	Gets a row iterator to a block.
CONST_ROW_ITERATOR	block_row_iterator_end (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end) const
	Gets a row iterator to a block.
template<class V >
V &	get_row (unsigned row, V &v) const
template<class V >
V &	get_column (unsigned column, V &v) const
template<class T , class U >
U &	transpose_mult_transpose (const T &x, U &y, REAL alpha=(REAL) 1.0, REAL beta=(REAL) 0.0) const
	Does the operation y = beta*y + alpha*this'*x'.
template<class T , class U >
U &	mult_transpose (const T &x, U &y, REAL alpha=(REAL) 1.0, REAL beta=(REAL) 0.0) const
	Does the operation y = beta*y + alpha*this*x'.
template<class T , class U >
U &	transpose_mult (const T &x, U &y, REAL alpha=(REAL) 1.0, REAL beta=(REAL) 0.0) const
	Does the operation y = beta*y + alpha*this'*x.
template<class T , class U >
U &	mult (const T &x, U &y, REAL alpha=(REAL) 1.0, REAL beta=(REAL) 0.0) const
	Does the operation y = beta*y + alpha*this*x.
template<class M >
M &	get_sub_mat (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end, M &m, Transposition trans=eNoTranspose) const
	Gets the specified sub matrix. More...
template<class ForwardIterator , class M >
M &	select_columns (ForwardIterator col_start, ForwardIterator col_end, M &m) const
	Gets a submatrix of columns (not necessarily a block) More...
template<class M >
M &	select_columns (std::vector< bool > &col_select, M &m) const
	Gets a submatrix of columns (not necessarily a block) More...
template<class ForwardIterator , class M >
M &	select_rows (ForwardIterator row_start, ForwardIterator row_end, M &m) const
	Gets a submatrix of rows (not necessarily a block) More...
template<class M >
M &	select_rows (std::vector< bool > &row_select, M &m) const
	Gets a submatrix of rows (not necessarily a block) More...
template<class ForwardIterator1 , class ForwardIterator2 , class X >
X &	select (ForwardIterator1 row_start, ForwardIterator1 row_end, ForwardIterator2 col_start, ForwardIterator2 col_end, X &m) const
	Gets a submatrix (not necessarily a block) More...
template<class X >
X &	select (const std::vector< bool > &rows, const std::vector< bool > &cols, X &m) const
	Gets a submatrix (not necessarily a block)
template<class M >
M &	select_square (const std::vector< bool > &indices, M &result) const
	Gets a square submatrix (not necessarily a block)
template<class ForwardIterator , class M >
M &	select_square (ForwardIterator start, ForwardIterator end, M &m) const
CONST_COLUMN_ITERATOR	column_iterator_begin () const
	Get an iterator to the beginning.
CONST_COLUMN_ITERATOR	column_iterator_end () const
	Get an iterator to the end.
CONST_ROW_ITERATOR	row_iterator_begin () const
	Get an iterator to the beginning.
CONST_ROW_ITERATOR	row_iterator_end () const
	Get an iterator to the end.
COLUMN_ITERATOR	block_column_iterator_begin (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end)
	Gets a column iterator to a block.
COLUMN_ITERATOR	block_column_iterator_end (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end)
	Gets a column iterator to a block.
ROW_ITERATOR	block_row_iterator_begin (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end)
	Gets a row iterator to a block.
ROW_ITERATOR	block_row_iterator_end (unsigned row_start, unsigned row_end, unsigned col_start, unsigned col_end)
	Gets a row iterator to a block.
template<class V >
MATRIXX &	set_row (unsigned row, const V &v)
template<class V >
MATRIXX &	set_column (unsigned column, const V &v)
template<class M >
MATRIXX &	set_sub_mat (unsigned row_start, unsigned col_start, const M &m, Transposition trans=eNoTranspose)
	Sets the specified sub matrix. More...
ROW_ITERATOR	row_iterator_begin ()
	Get an iterator to the beginning (iterates column by column)
ROW_ITERATOR	row_iterator_end ()
	Get an iterator to the end.
COLUMN_ITERATOR	column_iterator_begin ()
	Get an iterator to the beginning (iterates column by column)
COLUMN_ITERATOR	column_iterator_end ()
	Get an iterator to the end.
template<>
MATRIX3 &	set_column (unsigned i, const ORIGIN3 &o)
	Sets the specified column of the matrix. More...
template<>
ORIGIN3 &	get_column (unsigned i, ORIGIN3 &result) const
	Gets the specified column of the matrix.
template<>
MATRIX3 &	set_row (unsigned i, const ORIGIN3 &o)
	Sets the specified row of the matrix. More...
template<>
ORIGIN3 &	get_row (unsigned i, ORIGIN3 &result) const
	Gets the specified row of the matrix. More...

Static Public Member Functions
static VECTOR3	calc_differential (const MATRIX3 &R1, const MATRIX3 &R2)
	Calculates the differential between two rotations.
static MATRIX3	invert (const MATRIX3 &m)
	Determines the inverse of the given matrix.
static MATRIX3	rot_X (REAL angle)
	Returns the rotation matrix of the specified angle around the X axis.
static MATRIX3	rot_Y (REAL angle)
	Returns the rotation matrix of the specified angle around the Y axis.
static MATRIX3	rot_Z (REAL angle)
	Returns the rotation matrix of the specified angle around the Z axis.
static MATRIX3	skew_symmetric (REAL a, REAL b, REAL c)
	Constructs a skew-symmetric matrix from the given values. More...
static MATRIX3	skew_symmetric (const ORIGIN3 &o)
	Constructs a skew-symmetric matrix from the given values. More...
static MATRIX3	skew_symmetric (const VECTOR3 &v)
	Constructs a skew-symmetric matrix from the given values. More...
static VECTOR3	inverse_skew_symmetric (const MATRIX3 &R)
	Constructs the vector from a skew-symmetric matrix.
static MATRIX3	transpose (const MATRIX3 &m)
	Determines the transpose of this matrix.
static bool	valid_rotation (const MATRIX3 &R)
	Checks whether this matrix represents a valid rotation for a right-handed coordinate system.
static bool	valid_rotation_scale (const MATRIX3 &R)
	Checks whether this matrix represents a valid rotation and scale for a right-handed coordinate system.
static MATRIX3	identity ()
static MATRIX3	zero ()
template<class V , class U , class W >
static W &	diag_mult (const V &d, const U &v, W &result)
	Determines the transpose of a matrix and stores the result in a given matrix. More...

Detailed Description

A 3x3 matrix that may be used for orientation, inertia tensors, etc.

Constructor & Destructor Documentation

MATRIX3::MATRIX3

(

const REAL *

array

)

Constructs a matrix from an array.

Parameters

array

an array of 9 REAL values in row-major format

Member Function Documentation

CONST_COLUMN_ITERATOR MATRIX3::block_column_iterator_begin ( unsigned  row_start, unsigned  row_end, unsigned  col_start, unsigned  col_end  ) const

inline

This file consists of general routines for constant matrices.

Gets a column iterator to a block

template<class V , class U , class W >

static W& MATRIX3::diag_mult ( const V &  d, const U &  v, W &  result  )

inlinestatic

Determines the transpose of a matrix and stores the result in a given matrix.

Multiplies the diagonal matrix formed from d by the vector v

ORIGIN3 MATRIX3::get_column

(

unsigned

i

)

const

Gets the specified column of the matrix.

Parameters

i	the 0-index of the column

Referenced by calc_differential(), get_column(), and valid_rotation_scale().

template<>

ORIGIN3& MATRIX3::get_row	(	unsigned	i,
		ORIGIN3 &	result
	)		const

Gets the specified row of the matrix.

Parameters

i	the 0-index of the row

References get_row().

ORIGIN3 MATRIX3::get_row

(

unsigned

i

)

const

Gets the specified row of the matrix.

Parameters

i	the 0-index of the row

Referenced by FIXEDJOINT::evaluate_constraints(), and get_row().

template<class M >

M& MATRIX3::get_sub_mat ( unsigned  row_start, unsigned  row_end, unsigned  col_start, unsigned  col_end, M &  m, Transposition  trans = eNoTranspose  ) const

inline

Gets the specified sub matrix.

Parameters

row_start	the row to start (inclusive)
row_end	the row to end (exclusive)
col_start	the column to start (inclusive)
col_end	the column to end (exclusive)
transpose	determines whether to store the transpose of the submatrix into m

Returns

a (row_end - row_start) x (col_end - col_start) sized matrix

template<class ForwardIterator1 , class ForwardIterator2 , class X >

X& MATRIX3::select ( ForwardIterator1  row_start, ForwardIterator1  row_end, ForwardIterator2  col_start, ForwardIterator2  col_end, X &  m  ) const

inline

Gets a submatrix (not necessarily a block)

Parameters

row_start	an iterator pointing to the beginning of a container of row indices (container need not be sorted)
row_end	an iterator pointing to the end of a container of row indices (container need not be sorted)
col_start	an iterator pointing to the beginning of a container of column indices (container need not be sorted)
col_end	an iterator pointing to the end of a container of column indices (container need not be sorted)
M	contains the submatrix on return

template<class ForwardIterator , class M >

M& MATRIX3::select_columns ( ForwardIterator  col_start, ForwardIterator  col_end, M &  m  ) const

inline

Gets a submatrix of columns (not necessarily a block)

Parameters

col_start	an iterator pointing to the beginning of a container of column indices (container need not be sorted)
col_end	an iterator pointing to the end of a container of column indices (container need not be sorted)
M	contains the submatrix on return

template<class M >

M& MATRIX3::select_columns ( std::vector< bool > &  col_select, M &  m  ) const

inline

Gets a submatrix of columns (not necessarily a block)

Parameters

col_select	a vector of bools; if the entry is true in the vector, the column is selected
M	contains the submatrix on return

template<class ForwardIterator , class M >

M& MATRIX3::select_rows ( ForwardIterator  row_start, ForwardIterator  row_end, M &  m  ) const

inline

Gets a submatrix of rows (not necessarily a block)

Parameters

row_start	an iterator pointing to the beginning of a container of row indices (container need not be sorted)
row_end	an iterator pointing to the end of a container of row indices (container need not be sorted)
M	contains the submatrix on return

template<class M >

M& MATRIX3::select_rows ( std::vector< bool > &  row_select, M &  m  ) const

inline

Gets a submatrix of rows (not necessarily a block)

Parameters

row_select	a vector of bools; if the entry is true in the vector, the row is selected
M	contains the submatrix on return

template<class ForwardIterator , class M >

M& MATRIX3::select_square ( ForwardIterator  start, ForwardIterator  end, M &  m  ) const

inline

Parameters

start	an iterator pointing to the beginning of a container of row/column indices (container need not be sorted)
end	an iterator pointing to the end of a container of row/column indices (container need not be sorted)
M	contains the submatrix on return

template<>

MATRIX3& MATRIX3::set_column	(	unsigned	i,
		const ORIGIN3 &	o
	)

Sets the specified column of the matrix.

Parameters

i	the 0-index of the column
o	a 3D vector

template<>

MATRIX3& MATRIX3::set_row	(	unsigned	i,
		const ORIGIN3 &	o
	)

Sets the specified row of the matrix.

Parameters

i	the 0-index of the row
o	a 3D vector

Note

the number of columns of this must be three!

template<class M >

MATRIXX& MATRIX3::set_sub_mat ( unsigned  row_start, unsigned  col_start, const M &  m, Transposition  trans = eNoTranspose  )

inline

Sets the specified sub matrix.

Parameters

row_start	the row to start (inclusive)
col_start	the column to start (inclusive)
m	the source matrix
transpose	determines whether the m is to be transposed

Note

fails assertion if m is too large to insert into this

MATRIX3 MATRIX3::skew_symmetric ( REAL  x, REAL  y, REAL  z  )

static

Constructs a skew-symmetric matrix from the given values.

The skew symmetric matrix generated will be: | 0 -z y | | z 0 -x | | -y x 0 |

Referenced by PLANARJOINT::calc_constraint_jacobian(), REVOLUTEJOINT::calc_constraint_jacobian(), SPHERICALJOINT::calc_constraint_jacobian(), MOVINGTRANSFORM3::calc_transform(), POSE3::dot_spatial_transform_to_matrix2(), SPATIAL_RB_INERTIA::inverse_mult(), TRANSFORM3::inverse_transform(), SPATIAL_RB_INERTIA::mult(), SPATIAL_AB_INERTIA::operator+(), SPATIAL_RB_INERTIA::operator+(), SPATIAL_RB_INERTIA::operator-(), SPATIAL_AB_INERTIA::operator=(), skew_symmetric(), POSE3::spatial_transform_to_matrix(), POSE3::spatial_transform_to_matrix2(), SPATIAL_RB_INERTIA::to_matrix(), SPATIAL_RB_INERTIA::to_PD_matrix(), SPATIAL_AB_INERTIA::to_rb_inertia(), and TRANSFORM3::transform().

MATRIX3 MATRIX3::skew_symmetric ( const ORIGIN3 &  v )

static

Constructs a skew-symmetric matrix from the given values.

The skew symmetric matrix generated will be: | 0 -v.z() v.y() | | v.z() 0 -v.x() | | -v.y() v.x() 0 |

References skew_symmetric().

MATRIX3 MATRIX3::skew_symmetric ( const VECTOR3 &  v )

static

Constructs a skew-symmetric matrix from the given values.

The skew symmetric matrix generated will be: | 0 -v.z() v.y() | | v.z() 0 -v.x() | | -v.y() v.x() 0 |

References skew_symmetric().

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

• /home/drum/Ravelin.new/include/Ravelin/Matrix3.h
• /home/drum/Ravelin.new/src/Matrix3.cpp