Matrix handling. More...

#include <matrice.hpp>

Inheritance diagram for Kadath::Matrice:

Public Member Functions
	Matrice (int size1, int size2)
	Standard constructor. More...

	Matrice (const Matrice &)
	Constructor by copy. More...

	Matrice (const Array< double > &tab)
	Constructor from a `Tbl`. More...

	~Matrice ()
	Destructor. More...

void	annule ()
	Sets all the coeficients of the `*std` to 0. More...

int	get_dim (int i) const
	Returns the dimension of the matrix. More...

Array< double > *	get_lu ()
	Returns a pointer on the `lu` decomposition. More...

Array< int > *	get_permute ()
	Returns a pointer on the permutation array. More...

const Array< double > &	get_array () const
	Returns the array of matrix elements. More...

Array< double > &	get_array ()
	Returns the array of matrix elements non const version. More...

void	operator= (double x)
	Sets all the element of `*std` to x. More...

void	operator= (const Matrice &)
	Assignement to another `Matrice`. More...

void	operator= (const Array< double > &)
	Assignement to an array. More...

double &	set (int i, int j)
	Read/write of a particuliar element. More...

void	copy_inside (int i, int j, const Matrice &so)
	Copies the elements of `so` inside the matrice, starting at the position . More...

double	operator() (int i, int j) const
	Read-only of a particuliar element. More...

void	set_band (int up, int low) const
	Calculate the band storage of `*std`. More...

void	set_lu () const
	Calculate the LU-representation, assuming the band-storage has been done. More...

Array< double >	solve (const Array< double > &sec_membre) const
	Solves the linear system represented by the matrix. More...

Array< double >	val_propre () const
	Returns the eigenvalues of the matrix, calculated using LAPACK. More...

Matrice	vect_propre () const
	Returns the eigenvectors of the matrix, calculated using LAPACK. More...

Matrice	transpose () const
	Computes the transpose matrix. More...

void	operator+= (const Matrice &)
	Operator +=. More...

void	operator+= (double)
	Operator +=. More...

void	operator-= (const Matrice &)
	Operator -=. More...

void	operator-= (double)
	Operator -=. More...

void	operator*= (double)
	Operator *=. More...

void	operator/= (double)
	Operator /=. More...

Private Member Functions
void	del_deriv ()
	Logical destructor : dellocates the memory of the various used representations. More...

Private Attributes
Dim_array	sizes
	`Dim_array` of dimension 2 containing the size of the matrix. More...

Array< double > *	std
	Pointer on the array of the standard representation. More...

int	ku
	Number of upper-diagonals in the band representation. More...

int	kl
	Number of lower-diagonals in the band representation. More...

Array< double > *	band
	Pointer on the array of the band representation of a square matrix. More...

Array< double > *	lu
	Pointer on the first array of the LU-representation. More...

Array< int > *	permute
	Pointer on the second array of the LU-representation. More...

Friends
ostream &	operator<< (ostream &, const Matrice &)
	Impression. More...

Matrice	operator+ (const Matrice &, const Matrice &)
	Operator + (binary version) More...

Matrice	operator- (const Matrice &, const Matrice &)
	Operator - (binary version) More...

Matrice	operator- (const Matrice &)
	Operator - (unitary version) More...

Matrice	operator* (const Matrice &, double)
	Operator*. More...

Matrice	operator* (double, const Matrice &)
	Operator*. More...

Matrice	operator* (const Matrice &, const Matrice &)
	Operator*. More...

Matrice	operator/ (const Matrice &, double)
	Operator/. More...

Detailed Description

Matrix handling.

The matrix can be stored in the usual way in std, in a band-way by band and on a LU-decomposition by the two arrays lu and permute. All the storage conventions are those af LAPACK which is used to make the LU-decomposition, the inversion and to compute the eigenvalues of the matrix. All those representations are redondant, that means that doing the LU-decomposition, for example, does NOT destroy previously calculated type of storage.

Definition at line 38 of file matrice.hpp.

Constructor & Destructor Documentation

◆ Matrice() [1/3]

Kadath::Matrice::Matrice	(	int	size1,
		int	size2
	)

Standard constructor.

Parameters

size1	[input] number of lines.
size2	[input] number of columns.

Definition at line 45 of file matrice.cpp.

References band, kl, ku, lu, permute, Kadath::Dim_array::set(), sizes, and std.

◆ Matrice() [2/3]

Kadath::Matrice::Matrice ( const Matrice & source )

Constructor by copy.

Definition at line 57 of file matrice.cpp.

References band, kl, ku, lu, permute, and std.

◆ Matrice() [3/3]

Kadath::Matrice::Matrice ( const Array< double > & tab )

Constructor from a Tbl.

Parameters

tab	[input] 2-dimension or 1-dimension array

If tab is a 1-dimension Tbl, a single-column matrix is created, otherwise *std is simply constructed by a Tbl copy of tab.

Definition at line 71 of file matrice.cpp.

References band, Kadath::Dim_array::get_ndim(), kl, ku, lu, permute, sizes, and std.

◆ ~Matrice()

Kadath::Matrice::~Matrice ( )

Destructor.

Definition at line 82 of file matrice.cpp.

References del_deriv(), and std.

Member Function Documentation

◆ annule()

void Kadath::Matrice::annule ( )

Sets all the coeficients of the *std to 0.

The other representations are destroyed.

Definition at line 37 of file matrice.cpp.

References del_deriv(), Kadath::Index::inc(), Kadath::Array< T >::set(), sizes, and std.

◆ copy_inside()

void Kadath::Matrice::copy_inside	(	int	i,
		int	j,
		const Matrice &	so
	)

Copies the elements of so inside the matrice, starting at the position $ (i,j) $ .

Definition at line 130 of file matrice.cpp.

References del_deriv(), Kadath::Index::inc(), Kadath::Array< T >::set(), Kadath::Index::set(), sizes, and std.

◆ del_deriv()

void Kadath::Matrice::del_deriv ( )

private

Logical destructor : dellocates the memory of the various used representations.

Deletes the (mutable) derived members: band, lu, permute

Definition at line 27 of file matrice.cpp.

References band, lu, and permute.

◆ get_array() [1/2]

Array<double>& Kadath::Matrice::get_array ( )

inline

Returns the array of matrix elements non const version.

Definition at line 116 of file matrice.hpp.

References std.

◆ get_array() [2/2]

const Array<double>& Kadath::Matrice::get_array ( ) const

inline

Returns the array of matrix elements.

Definition at line 114 of file matrice.hpp.

References std.

◆ get_dim()

int Kadath::Matrice::get_dim ( int i ) const

inline

Returns the dimension of the matrix.

Parameters

i	[input] if i =0 returns the number of lines and if i =2 returns the number of columns.

Definition at line 108 of file matrice.hpp.

References sizes.

◆ get_lu()

Array<double>* Kadath::Matrice::get_lu ( )

inline

Returns a pointer on the lu decomposition.

Definition at line 110 of file matrice.hpp.

References lu.

◆ get_permute()

Array<int>* Kadath::Matrice::get_permute ( )

inline

Returns a pointer on the permutation array.

Definition at line 112 of file matrice.hpp.

References permute.

◆ operator()()

double Kadath::Matrice::operator()	(	int	i,
		int	j
	)		const

Read-only of a particuliar element.

Parameters

j	[input] line coordinate.
i	[input] column coordinate.

Definition at line 144 of file matrice.cpp.

References Kadath::Index::set(), sizes, and std.

◆ operator*=()

void Kadath::Matrice::operator*= ( double x )

Operator *=.

Definition at line 400 of file matrice.cpp.

References std.

◆ operator+=() [1/2]

void Kadath::Matrice::operator+= ( const Matrice & a )

Operator +=.

Definition at line 380 of file matrice.cpp.

References std.

◆ operator+=() [2/2]

void Kadath::Matrice::operator+= ( double x )

Operator +=.

Definition at line 390 of file matrice.cpp.

References std.

◆ operator-=() [1/2]

void Kadath::Matrice::operator-= ( const Matrice & a )

Operator -=.

Definition at line 385 of file matrice.cpp.

References std.

◆ operator-=() [2/2]

void Kadath::Matrice::operator-= ( double x )

Operator -=.

Definition at line 395 of file matrice.cpp.

References std.

◆ operator/=()

void Kadath::Matrice::operator/= ( double x )

Operator /=.

Definition at line 405 of file matrice.cpp.

References std.

◆ operator=() [1/3]

void Kadath::Matrice::operator= ( const Array< double > & source )

Assignement to an array.

Definition at line 111 of file matrice.cpp.

References del_deriv(), Kadath::Array< T >::get_dimensions(), kl, ku, sizes, and std.

◆ operator=() [2/3]

void Kadath::Matrice::operator= ( const Matrice & source )

Assignement to another Matrice.

Definition at line 94 of file matrice.cpp.

References band, del_deriv(), kl, ku, lu, permute, sizes, and std.

◆ operator=() [3/3]

void Kadath::Matrice::operator= ( double x )

Sets all the element of *std to x.

The other representations are destroyed.

Definition at line 88 of file matrice.cpp.

References del_deriv(), and std.

◆ set()

double & Kadath::Matrice::set	(	int	i,
		int	j
	)

Read/write of a particuliar element.

This is done in *std and all the other representations are no longer valid.

Parameters

j	[input] line coordinate.
i	[input] column coordinate.

Definition at line 122 of file matrice.cpp.

References del_deriv(), Kadath::Array< T >::set(), Kadath::Index::set(), sizes, and std.

◆ set_band()

void Kadath::Matrice::set_band	(	int	up,
		int	low
	)		const

Calculate the band storage of *std.

Please note that this function does NOT check if *std represents a real band-matrix.

Parameters

up	[input] number of upper-diagonals.
low	[input] number of lower-diagonals.

Definition at line 165 of file matrice.cpp.

References band, kl, ku, Kadath::Array< T >::set(), and sizes.

◆ set_lu()

void Kadath::Matrice::set_lu ( ) const

Calculate the LU-representation, assuming the band-storage has been done.

The calculus is done using LAPACK.

Definition at line 192 of file matrice.cpp.

References band, kl, ku, lu, permute, Kadath::Array< T >::set_data(), sizes, and std.

◆ solve()

Array< double > Kadath::Matrice::solve ( const Array< double > & sec_membre ) const

Solves the linear system represented by the matrix.

The calculus assumes the the LU-decomposition has been done and is conducted using LAPACK.

Parameters

sec_membre [input] the right-hand side of the system.

Definition at line 221 of file matrice.cpp.

References band, Kadath::Array< T >::get_size(), kl, ku, lu, permute, Kadath::Array< T >::set_data(), and sizes.

◆ transpose()

Matrice Kadath::Matrice::transpose ( ) const

Computes the transpose matrix.

Definition at line 362 of file matrice.cpp.

References Kadath::Array< T >::get_dimensions(), Kadath::Index::set(), set(), sizes, and std.

◆ val_propre()

Array< double > Kadath::Matrice::val_propre ( ) const

Returns the eigenvalues of the matrix, calculated using LAPACK.

Returns: contains the real and the imaginary parts of the eigenvalues. The real parts are in Array<double> (0, *) and the imaginary parts in Array<double> (1, *).

Definition at line 253 of file matrice.cpp.

References Kadath::Index::inc(), Kadath::Array< T >::set(), Kadath::Dim_array::set(), and sizes.

◆ vect_propre()

Matrice Kadath::Matrice::vect_propre ( ) const

Returns the eigenvectors of the matrix, calculated using LAPACK.

Definition at line 308 of file matrice.cpp.

References Kadath::Index::inc(), set(), sizes, and std.

Friends And Related Function Documentation

◆ operator* [1/3]

Matrice operator*	(	const Matrice &	aa,
		const Matrice &	bb
	)

friend

Operator*.

Definition at line 442 of file matrice.cpp.

◆ operator* [2/3]

Matrice operator*	(	const Matrice &	a,
		double	x
	)

friend

Operator*.

Definition at line 430 of file matrice.cpp.

◆ operator* [3/3]

Matrice operator*	(	double	x,
		const Matrice &	a
	)

friend

Operator*.

Definition at line 436 of file matrice.cpp.

◆ operator+

Matrice operator+	(	const Matrice &	a,
		const Matrice &	b
	)

friend

Operator + (binary version)

Definition at line 411 of file matrice.cpp.

◆ operator- [1/2]

Matrice operator- ( const Matrice & a )

friend

Operator - (unitary version)

Definition at line 423 of file matrice.cpp.

◆ operator- [2/2]

Matrice operator-	(	const Matrice &	a,
		const Matrice &	b
	)

friend

Operator - (binary version)

Definition at line 417 of file matrice.cpp.

◆ operator/

Matrice operator/	(	const Matrice &	a,
		double	x
	)

friend

Operator/.

Definition at line 463 of file matrice.cpp.

◆ operator<<

ostream& operator<<	(	ostream &	flux,
		const Matrice &	source
	)

friend

Impression.

Definition at line 152 of file matrice.cpp.

Member Data Documentation

◆ band

Array<double>* Kadath::Matrice::band

mutableprivate

Pointer on the array of the band representation of a square matrix.

To be precise, $ A(i, j)$ is stored in band $[ku+1+i-j, j]$ for $\mathrm {max}(1, j-ku) \leq i \leq \mathrm{min} (n, j+kl)$ , n being the size of the matrix.

Definition at line 58 of file matrice.hpp.

◆ kl

int Kadath::Matrice::kl

mutableprivate

Number of lower-diagonals in the band representation.

Definition at line 50 of file matrice.hpp.

◆ ku

int Kadath::Matrice::ku

mutableprivate

Number of upper-diagonals in the band representation.

Definition at line 49 of file matrice.hpp.

◆ lu

Array<double>* Kadath::Matrice::lu

mutableprivate

Pointer on the first array of the LU-representation.

Definition at line 61 of file matrice.hpp.

◆ permute

Array<int>* Kadath::Matrice::permute

mutableprivate

Pointer on the second array of the LU-representation.

Definition at line 62 of file matrice.hpp.

◆ sizes

Dim_array Kadath::Matrice::sizes

private

Dim_array of dimension 2 containing the size of the matrix.

Definition at line 45 of file matrice.hpp.

◆ std

Array<double>* Kadath::Matrice::std

private

Pointer on the array of the standard representation.

Definition at line 46 of file matrice.hpp.

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

Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrice() [1/3]

◆ Matrice() [2/3]

◆ Matrice() [3/3]

◆ ~Matrice()

Member Function Documentation

◆ annule()

◆ copy_inside()

◆ del_deriv()

◆ get_array() [1/2]

◆ get_array() [2/2]

◆ get_dim()

◆ get_lu()

◆ get_permute()

◆ operator()()

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ set()

◆ set_band()

◆ set_lu()

◆ solve()

◆ transpose()

◆ val_propre()

◆ vect_propre()

Friends And Related Function Documentation

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+

◆ operator- [1/2]

◆ operator- [2/2]

◆ operator/

◆ operator<<

Member Data Documentation

◆ band

◆ kl

◆ ku

◆ lu

◆ permute

◆ sizes

◆ std