Basic class for a 2D or 3D map. More...

#include <vectorsMatrices.hh>

Public Member Functions
Mapping< F, DimY, DimX >	adjugate () const
	Returns the adjugate of the matrix (only valid for square matrices) [f \mbox{adj}(M) = M^{-1}\det(M) \f]. More...

Point< F, DimY >	column (const uint i) const
	Returns a column of the matrix. More...

F	determinant () const
	Returns the determinant of the matrix (only valid for square matrices) More...

std::ostream &	info (std::ostream &os) const

Mapping< F, DimX, DimY >	inverse () const
	Returns the inverse of the matrix. More...

	Mapping ()
	Default constructor. More...

	Mapping (const Mapping< F, DimY, DimX > &m)
	Copy constructor. More...

template<class H >
	Mapping (const Mapping< H, DimY, DimX > &m)
	Constructor. More...

	Mapping (const Point< F, DimY > first)
	Constructor for a 1D. More...

	Mapping (const Point< F, DimY > first, const Point< F, DimY > second)
	Constructor for a 2D mapping. More...

	Mapping (const Point< F, DimY > first, const Point< F, DimY > second, const Point< F, DimY > third)
	Constructor for a 3D mapping. More...

	Mapping (const UnitNd< DimY > &n)
	Constructor for rotation. More...

template<class... FieldTs>
	Mapping (FieldTs... data)
	Constructor with variadic templates. More...

template<class G >
	Mapping (G x)
	Constructor. More...

template<class H >
Point< H, DimY >	mapPoint (const Point< H, DimX > &b) const

template<class H >
void	mapTranspose (const Point< H, DimY > &y, Point< H, DimX > &x) const
	Computes x = A^T y. More...

template<class H , class J , uint dimy, uint dimx>
void	operator() (const Point< H, dimy > &y, Point< J, dimx > &x) const
	Application operator. More...

F &	operator() (uint i, uint j)
	Returns an entry of the matrix (for read / write access) More...

const F &	operator() (uint i, uint j) const
	Returns an entry of the matrix. More...

template<class G >
Mapping< typename Combtype< G, F >::type, DimY, DimX >	operator* (const G n) const
	Scaling operator. More...

template<class G , uint DimZ>
Mapping< typename Combtype< G, F >::type, DimY, DimZ >	operator* (const Mapping< G, DimX, DimZ > &m) const
	Multiplication operator. More...

template<class H >
Point< typename Combtype< F, H >::type, DimY >	operator* (const Point< H, DimX > &p) const
	Returns a mapped Point. More...

Mapping< F, DimY, DimX > &	operator*= (const F n)
	Scaling operator. More...

Mapping< F, DimY, DimX > &	operator*= (const Mapping< F, DimY, DimX > &m)
	Multiplication operator ( this = operator()(this, m); ) More...

Mapping< F, DimY, DimX > &	operator+= (const Mapping< F, DimY, DimX > &M)
	Addition operator. More...

Mapping< F, DimY, DimY >	prodTranspose () const
	Returns the product with the transpose of the matrix. More...

void	rank1Product (const Point< F, DimX > x, const Point< F, DimY > y)
	Computes x y^T and adds the result to the matrix. More...

Mapping< F, DimY, DimX > &	scaleCols (const Point< F, DimX > &s)
	Scales the columns with the respective entries in `s`. More...

Mapping< F, DimY, DimX > &	scaleRows (const Point< F, DimY > &s)
	Scales the rows with the respective entries in `s`. More...

Mapping< F, DimY-1, DimX-1 >	subMatrix (uint i, uint j) const
	Returns the submatrix where the ith and jth column are erased. More...

F	trace () const
	Returns the trace (only valid for square matrices) More...

Mapping< F, DimX, DimY >	transpose () const
	Returns the transpose of the matrix. More...

void	zeros ()
	Fills the matrix with zeros. More...

Private Member Functions
const uint	lin_ (uint i, uint j) const
	index in stack array of entry (i,j) of row-based matrix More...

Private Attributes
F	data_ [DimX *DimY]
	entries of the matrix More...

Detailed Description

template<class F, uint DimY, uint DimX = DimY>
class concepts::Mapping< F, DimY, DimX >

Basic class for a 2D or 3D map.

The template parameters make it possible to use this class for real or complex values. The main use is to represent linear maps in 2D or 3D.

Test:: test::MappingTest

Author: Philipp Frauenfelder, 2001

Definition at line 313 of file vectorsMatrices.hh.

Constructor & Destructor Documentation

◆ Mapping() [1/9]

template<class F , uint DimY, uint DimX = DimY>

concepts::Mapping< F, DimY, DimX >::Mapping ( )

inline

Default constructor.

The elements of the matrix are left uninitialized.

Definition at line 318 of file vectorsMatrices.hh.

◆ Mapping() [2/9]

template<class F , uint DimY, uint DimX = DimY>

concepts::Mapping< F, DimY, DimX >::Mapping ( const Mapping< F, DimY, DimX > & m )

inline

Copy constructor.

Definition at line 321 of file vectorsMatrices.hh.

◆ Mapping() [3/9]

template<class F , uint DimY, uint DimX = DimY>

template<class H >

concepts::Mapping< F, DimY, DimX >::Mapping ( const Mapping< H, DimY, DimX > & m )

inline

Constructor.

Useful to generate a Mapping<Cmplx,DimX,DimY> out of a Mapping<Real,DimX,DimY>.

Precondition: F has a function F.operator=(H)

Definition at line 331 of file vectorsMatrices.hh.

◆ Mapping() [4/9]

template<class F , uint DimY, uint DimX = DimY>

template<class G >

concepts::Mapping< F, DimY, DimX >::Mapping ( G x )

inline

Constructor.

All elements are initialized to x.

Definition at line 344 of file vectorsMatrices.hh.

◆ Mapping() [5/9]

template<class F , uint DimY, uint DimX = DimY>

template<class... FieldTs>

concepts::Mapping< F, DimY, DimX >::Mapping ( FieldTs... data )

inline

Constructor with variadic templates.

Can be sed to construct matrices of any size by giving the entries as parameters, e.g. Mapping<Real,2,2>(1.,2.,3.,4.) creates a 2x2 matrix, while Mapping<Real,2,2>(1.,2.,3.) will produce an assertion as the number of entries (i.e. 3) mismatches the dimension 2x2.

Note: The flag MappingConstructorHack has to be set to 1 considering Py++ with C++11 standard

Definition at line 359 of file vectorsMatrices.hh.

◆ Mapping() [6/9]

template<class F , uint DimY, uint DimX = DimY>

concepts::Mapping< F, DimY, DimX >::Mapping ( const Point< F, DimY > first )

Constructor for a 1D.

Parameters

first First column of the matrix

◆ Mapping() [7/9]

template<class F , uint DimY, uint DimX = DimY>

concepts::Mapping< F, DimY, DimX >::Mapping	(	const Point< F, DimY >	first,
		const Point< F, DimY >	second
	)

Constructor for a 2D mapping.

Parameters

first	First column of the matrix
second	Second column of the matrix

◆ Mapping() [8/9]

template<class F , uint DimY, uint DimX = DimY>

concepts::Mapping< F, DimY, DimX >::Mapping	(	const Point< F, DimY >	first,
		const Point< F, DimY >	second,
		const Point< F, DimY >	third
	)

Constructor for a 3D mapping.

Parameters

first	First column of the matrix
second	Second column of the matrix
third	Third column of the matrix

◆ Mapping() [9/9]

template<class F , uint DimY, uint DimX = DimY>

concepts::Mapping< F, DimY, DimX >::Mapping ( const UnitNd< DimY > & n )

Constructor for rotation.

Parameters

n	Normal vector of the rotation

Member Function Documentation

◆ adjugate()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimX> concepts::Mapping< F, DimY, DimX >::adjugate ( ) const

Returns the adjugate of the matrix (only valid for square matrices) [f \mbox{adj}(M) = M^{-1}\det(M) \f].

◆ column()

template<class F , uint DimY, uint DimX = DimY>

Point<F, DimY> concepts::Mapping< F, DimY, DimX >::column ( const uint i ) const

Returns a column of the matrix.

◆ determinant()

template<class F , uint DimY, uint DimX = DimY>

F concepts::Mapping< F, DimY, DimX >::determinant ( ) const

Returns the determinant of the matrix (only valid for square matrices)

◆ info()

template<class F , uint DimY, uint DimX = DimY>

std::ostream& concepts::Mapping< F, DimY, DimX >::info ( std::ostream & os ) const

◆ inverse()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimX, DimY> concepts::Mapping< F, DimY, DimX >::inverse ( ) const

Returns the inverse of the matrix.

◆ lin_()

template<class F , uint DimY, uint DimX = DimY>

const uint concepts::Mapping< F, DimY, DimX >::lin_	(	uint	i,
		uint	j
	)		const

inlineprivate

index in stack array of entry (i,j) of row-based matrix

Definition at line 524 of file vectorsMatrices.hh.

◆ mapPoint()

template<class F , uint DimY, uint DimX = DimY>

template<class H >

Point<H, DimY> concepts::Mapping< F, DimY, DimX >::mapPoint ( const Point< H, DimX > & b ) const

inline

Definition at line 459 of file vectorsMatrices.hh.

◆ mapTranspose()

template<class F , uint DimY, uint DimX>

template<class H >

void concepts::Mapping< F, DimY, DimX >::mapTranspose	(	const Point< H, DimY > &	y,
		Point< H, DimX > &	x
	)		const

inline

Computes x = A^T y.

Parameters

H	can be F or any more general class that can operate on instances of F.

Definition at line 540 of file vectorsMatrices.hh.

◆ operator()() [1/3]

template<class F , uint DimY, uint DimX>

template<class H , class J , uint dimy, uint dimx>

void concepts::Mapping< F, DimY, DimX >::operator()	(	const Point< H, dimy > &	y,
		Point< J, dimx > &	x
	)		const

Application operator.

Computes x = A y where A is the matrix. If the dimensions do not match the matrix A is extended by the identity matrix.

Definition at line 557 of file vectorsMatrices.hh.

◆ operator()() [2/3]

template<class F , uint DimY, uint DimX = DimY>

F& concepts::Mapping< F, DimY, DimX >::operator()	(	uint	i,
		uint	j
	)

inline

Returns an entry of the matrix (for read / write access)

Definition at line 446 of file vectorsMatrices.hh.

◆ operator()() [3/3]

template<class F , uint DimY, uint DimX = DimY>

const F& concepts::Mapping< F, DimY, DimX >::operator()	(	uint	i,
		uint	j
	)		const

inline

Returns an entry of the matrix.

Definition at line 437 of file vectorsMatrices.hh.

◆ operator*() [1/3]

template<class F , uint DimY, uint DimX = DimY>

template<class G >

Mapping<typename Combtype<G,F>::type, DimY, DimX> concepts::Mapping< F, DimY, DimX >::operator* ( const G n ) const

Scaling operator.

◆ operator*() [2/3]

template<class F , uint DimY, uint DimX = DimY>

template<class G , uint DimZ>

Mapping<typename Combtype<G,F>::type, DimY, DimZ> concepts::Mapping< F, DimY, DimX >::operator* ( const Mapping< G, DimX, DimZ > & m ) const

Multiplication operator.

◆ operator*() [3/3]

template<class F , uint DimY, uint DimX>

template<class H >

Point< typename Combtype< F, H >::type, DimY > concepts::Mapping< F, DimY, DimX >::operator* ( const Point< H, DimX > & p ) const

Returns a mapped Point.

Definition at line 531 of file vectorsMatrices.hh.

◆ operator*=() [1/2]

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimX>& concepts::Mapping< F, DimY, DimX >::operator*= ( const F n )

Scaling operator.

◆ operator*=() [2/2]

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimX>& concepts::Mapping< F, DimY, DimX >::operator*= ( const Mapping< F, DimY, DimX > & m )

Multiplication operator ( *this = operator()(*this, m); )

◆ operator+=()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimX>& concepts::Mapping< F, DimY, DimX >::operator+= ( const Mapping< F, DimY, DimX > & M )

Addition operator.

◆ prodTranspose()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimY> concepts::Mapping< F, DimY, DimX >::prodTranspose ( ) const

Returns the product with the transpose of the matrix.

◆ rank1Product()

template<class F , uint DimY, uint DimX = DimY>

void concepts::Mapping< F, DimY, DimX >::rank1Product	(	const Point< F, DimX >	x,
		const Point< F, DimY >	y
	)

Computes x y^T and adds the result to the matrix.

◆ scaleCols()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimX>& concepts::Mapping< F, DimY, DimX >::scaleCols ( const Point< F, DimX > & s )

Scales the columns with the respective entries in s.

◆ scaleRows()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY, DimX>& concepts::Mapping< F, DimY, DimX >::scaleRows ( const Point< F, DimY > & s )

Scales the rows with the respective entries in s.

◆ subMatrix()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimY-1, DimX-1> concepts::Mapping< F, DimY, DimX >::subMatrix	(	uint	i,
		uint	j
	)		const

Returns the submatrix where the ith and jth column are erased.

◆ trace()

template<class F , uint DimY, uint DimX = DimY>

F concepts::Mapping< F, DimY, DimX >::trace ( ) const

Returns the trace (only valid for square matrices)

◆ transpose()

template<class F , uint DimY, uint DimX = DimY>

Mapping<F, DimX, DimY> concepts::Mapping< F, DimY, DimX >::transpose ( ) const

Returns the transpose of the matrix.

◆ zeros()

template<class F , uint DimY, uint DimX = DimY>

void concepts::Mapping< F, DimY, DimX >::zeros ( )

inline

Fills the matrix with zeros.

Definition at line 497 of file vectorsMatrices.hh.

Member Data Documentation

◆ data_

template<class F , uint DimY, uint DimX = DimY>

F concepts::Mapping< F, DimY, DimX >::data_[DimX *DimY]

private

entries of the matrix

Definition at line 521 of file vectorsMatrices.hh.

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

basics/vectorsMatrices.hh

concepts::Mapping< F, DimY, DimX > Class Template Reference

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<class F, uint DimY, uint DimX = DimY> class concepts::Mapping< F, DimY, DimX >

Constructor & Destructor Documentation

◆ Mapping() [1/9]

◆ Mapping() [2/9]

◆ Mapping() [3/9]

◆ Mapping() [4/9]

◆ Mapping() [5/9]

◆ Mapping() [6/9]

◆ Mapping() [7/9]

◆ Mapping() [8/9]

◆ Mapping() [9/9]

Member Function Documentation

◆ adjugate()

◆ column()

◆ determinant()

◆ info()

◆ inverse()

◆ lin_()

◆ mapPoint()

◆ mapTranspose()

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=()

◆ prodTranspose()

◆ rank1Product()

◆ scaleCols()

◆ scaleRows()

◆ subMatrix()

◆ trace()

◆ transpose()

◆ zeros()

Member Data Documentation

◆ data_

template<class F, uint DimY, uint DimX = DimY>
class concepts::Mapping< F, DimY, DimX >