MATRIX2 Class Reference

A general 2x2 matrix. More...

#include <Matrix2.h>

Public Member Functions
	MATRIX2 (const REAL *array)
	Constructs a matrix from an array. More...
	MATRIX2 (REAL m00, REAL m01, REAL m10, REAL m11)
	Constructs a matrix from 4 values. More...
	MATRIX2 (const MATRIX2 &source)
	MATRIX2 (const MATRIXN &m)
	MATRIX2 (const SHAREDMATRIXN &m)
	MATRIX2 (const CONST_SHAREDMATRIXN &m)
unsigned	size () const
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 2x2 matrix.
MATRIX2 &	invert ()
	Inverts this matrix.
MATRIX2	inverse () const
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.
ORIGIN2	get_row (unsigned i) const
	Gets the specified row of the matrix. More...
ORIGIN2	get_column (unsigned i) const
	Gets the specified column of the matrix. More...
void	set_identity ()
	Sets this matrix to identity.
void	set_zero ()
	Sets this matrix to zero.
ORIGIN2	mult (const ORIGIN2 &v) const
	Multiplies this matrix by a vector and returns the result in a new vector.
ORIGIN2	transpose_mult (const ORIGIN2 &v) const
	Multiplies the transpose of this matrix by a vector and returns the result in a new vector.
MATRIX2	mult (const MATRIX2 &m) const
	Multiplies this matrix by another 2x2 matrix.
MATRIX2	transpose_mult (const MATRIX2 &m) const
	Multiplies the transpose of this matrix by a matrix and returns the result in a new matrix.
MATRIX2	transpose_mult_transpose (const MATRIX2 &m) const
	Multiplies the transpose of this matrix by the transpose of a matrix and returns the result in a new matrix.
MATRIX2	mult_transpose (const MATRIX2 &m) const
	Multiplies this matrix by the transpose of a matrix and returns the result in a new matrix.
MATRIX2 &	operator= (const MATRIX2 &source)
	Copies a matrix to this one.
MATRIX2 &	operator= (const MATRIXN &source)
	Copies a matrix to this one.
MATRIX2 &	operator= (const SHAREDMATRIXN &source)
	Copies a matrix to this one.
MATRIX2 &	operator= (const CONST_SHAREDMATRIXN &source)
	Copies a matrix to this one.
MATRIX2 &	operator+= (const MATRIX2 &m)
	Adds m to this in place.
MATRIX2 &	operator-= (const MATRIX2 &m)
	Subtracts m from this in place.
MATRIX2 &	operator*= (const MATRIX2 &m)
MATRIX2 &	operator*= (REAL scalar)
	Multiplies this matrix by a scalar in place.
MATRIX2 &	operator/= (REAL scalar)
ORIGIN2	operator* (const ORIGIN2 &o) const
MATRIX2	operator+ (const MATRIX2 &m) const
MATRIX2	operator- (const MATRIX2 &m) const
MATRIX2	operator* (const MATRIX2 &m) const
MATRIX2	operator* (REAL scalar) const
MATRIX2	operator/ (REAL scalar) const
MATRIX2	operator- () const
	Returns the negation of this matrix.
unsigned	leading_dim () const
unsigned	inc () const
const REAL &	xx () const
const REAL &	yx () const
const REAL &	xy () const
const REAL &	yy () const
REAL &	xx ()
REAL &	yx ()
REAL &	xy ()
REAL &	yy ()
REAL &	operator() (unsigned i, unsigned j)
const REAL &	operator() (unsigned i, unsigned j) const
MATRIX2 &	resize (unsigned rows, unsigned columns, bool preserve=false)
const REAL *	data (unsigned i) const
REAL *	data (unsigned i)
const REAL *	data () const
	Gets a constant pointer to the beginning of the matrix array.
REAL *	data ()
	Gets a 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<>
ORIGIN2 &	get_column (unsigned i, ORIGIN2 &result) const
	Gets the specified column of the matrix.
template<>
ORIGIN2 &	get_row (unsigned i, ORIGIN2 &result) const
	Gets the specified row of the matrix. More...
template<>
MATRIX2 &	set_column (unsigned i, const ORIGIN2 &o)
	Sets the specified column of the matrix. More...
template<>
MATRIX2 &	set_row (unsigned i, const ORIGIN2 &o)
	Sets the specified row of the matrix. More...

Static Public Member Functions
static MATRIX2	invert (const MATRIX2 &m)
	Determines the inverse of the given matrix.
static MATRIX2	rot_Z (REAL angle)
	Returns the rotation matrix of the specified angle around the Z axis.
static MATRIX2	transpose (const MATRIX2 &m)
	Determines the transpose of this matrix.
static bool	valid_rotation (const MATRIX2 &R)
static MATRIX2	identity ()
static MATRIX2	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 general 2x2 matrix.

Constructor & Destructor Documentation

MATRIX2::MATRIX2

(

const REAL *

array

)

Constructs a matrix from an array.

Parameters

array

an array of 4 REAL values in column-major format

MATRIX2::MATRIX2	(	REAL	m00,
		REAL	m01,
		REAL	m10,
		REAL	m11
	)

Constructs a matrix from 4 values.

The resulting matrix will appear as follows:
m00 m01
m10 m11

Member Function Documentation

CONST_COLUMN_ITERATOR MATRIX2::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& MATRIX2::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

ORIGIN2 MATRIX2::get_column

(

unsigned

i

)

const

Gets the specified column of the matrix.

Parameters

i	the 0-index of the column

Referenced by get_column().

template<>

ORIGIN2& MATRIX2::get_row	(	unsigned	i,
		ORIGIN2 &	result
	)		const

Gets the specified row of the matrix.

Parameters

i	the 0-index of the row

References get_row().

ORIGIN2 MATRIX2::get_row

(

unsigned

i

)

const

Gets the specified row of the matrix.

Parameters

i	the 0-index of the row

Referenced by get_row().

template<class M >

M& MATRIX2::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& MATRIX2::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& MATRIX2::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& MATRIX2::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& MATRIX2::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& MATRIX2::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& MATRIX2::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<>

MATRIX2& MATRIX2::set_column	(	unsigned	i,
		const ORIGIN2 &	o
	)

Sets the specified column of the matrix.

Parameters

i	the 0-index of the column
o	a 2D vector

template<>

MATRIX2& MATRIX2::set_row	(	unsigned	i,
		const ORIGIN2 &	o
	)

Sets the specified row of the matrix.

Parameters

i	the 0-index of the row
o	a 2D vector

Note

the number of columns of this must be three!

template<class M >

MATRIXX& MATRIX2::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

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

• /home/drum/Ravelin.new/include/Ravelin/Matrix2.h
• /home/drum/Ravelin.new/src/Matrix2.cpp