Matrix handling. More...

#include <matrice.h>

Public Member Functions
	Matrice (int size1, int size2)
	Standard constructor.
	Matrice (const Matrice &)
	Constructor by copy.
	Matrice (const Tbl &tab)
	Constructor from a `Tbl`.
	~Matrice ()
	Destructor.
int	get_etat () const
	Returns the logical state.
void	set_etat_qcq ()
	Sets the logical state to `ETATQCQ` (ordinary state).
void	set_etat_zero ()
	Sets the logical state to `ETATZERO` (zero).
void	set_etat_nondef ()
	Sets the logical state to `ETATNONDEF` (undefined state).
void	annule_hard ()
	Sets the logical state to `ETATQCQ` (undefined state).
int	get_dim (int i) const
	Returns the dimension of the matrix.
Tbl	get_array () const
	Returns the array of matrix elements.
void	operator= (double x)
	Sets all the element of `*std` to x.
void	operator= (const Matrice &)
	Assignement to another `Matrice`.
void	operator= (const Tbl &)
	Assignement to a `Tbl`.
double &	set (int j, int i)
	Read/write of a particuliar element.
double	operator() (int j, int i) const
	Read-only of a particuliar element.
void	set_band (int up, int low) const
	Calculate the band storage of `*std`.
void	set_lu () const
	Calculate the LU-representation, assuming the band-storage has been done.
Tbl	inverse (const Tbl &sec_membre) const
	Solves the linear system represented by the matrix.
Tbl	val_propre () const
	Returns the eigenvalues of the matrix, calculated using LAPACK.
Matrice	vect_propre () const
	Returns the eigenvectors of the matrix, calculated using LAPACK.
double	determinant () const
	Computes the determinant of the matrix, using LAPACK and the standard decomposition.
Matrice	transpose () const
	Computes the transpose matrix.
void	operator+= (const Matrice &)
	Addition of a `Matrice` to `this`.
void	operator+= (double)
	Addition of a `double` to `this`.
void	operator-= (const Matrice &)
	Subtraction of a `Matrice` to `this`.
void	operator-= (double)
	Subtraction of a `double` to `this`.
void	operator*= (double)
	Multiplication of `this` by a `double`.
void	operator/= (double)
	Division of `this` by a `double`.

Private Member Functions
void	del_t ()
	Logical destructor : dellocates the memory of the various used representations.
void	del_deriv ()
	Deletes the (mutable) derived members: band, lu, permute.

Private Attributes
int	etat
	logical state (ETATZERO, ETATQCQ or ETATNONDEF)
Tbl *	std
	Pointer on the array of the standard representation.
int	ku
	Number of upper-diagonals in the band representation.
int	kl
	Number of lower-diagonals in the band representation.
Tbl *	band
	Pointer on the array of the band representation of a square matrix.
Tbl *	lu
	Pointer on the first array of the LU-representation.
Itbl *	permute
	Pointer on the second array of the LU-representation.

Friends
ostream &	operator<< (ostream &flux, const Matrice &source)
	Display.
Matrice	operator+ (const Matrice &a, const Matrice &b)
	`Matrice` + `Matrice`
Matrice	operator- (const Matrice &a, const Matrice &b)
	`Matrice` - `Matrice`
Matrice	operator* (const Matrice &a, double x)
	`Matrice` * `double`
Matrice	operator* (double x, const Matrice &a)
	`double` * `Matrice`
Matrice	operator* (const Matrice &aa, const Matrice &bb)
	Matrix product.
Matrice	operator/ (const Matrice &a, double x)
	`Matrice` / `double`

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 152 of file matrice.h.

Constructor & Destructor Documentation

◆ Matrice() [1/3]

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

Standard constructor.

All the representations are set to ETATNONDEF.

Parameters

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

Definition at line 203 of file matrice.C.

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

◆ Matrice() [2/3]

Lorene::Matrice::Matrice ( const Matrice & source )

Constructor by copy.

Definition at line 214 of file matrice.C.

References band, etat, kl, ku, lu, Matrice(), permute, and std.

◆ Matrice() [3/3]

Lorene::Matrice::Matrice ( const Tbl & 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 228 of file matrice.C.

References band, etat, Lorene::Tbl::get_etat(), Lorene::Tbl::get_ndim(), Lorene::Tbl::get_taille(), kl, ku, lu, permute, std, and Lorene::Tbl::t.

◆ ~Matrice()

Lorene::Matrice::~Matrice ( )

Destructor.

Definition at line 255 of file matrice.C.

References del_t().

Member Function Documentation

◆ annule_hard()

void Lorene::Matrice::annule_hard ( )

Sets the logical state to ETATQCQ (undefined state).

And sets all the components to zero

Definition at line 193 of file matrice.C.

References del_deriv(), etat, and std.

◆ del_deriv()

void Lorene::Matrice::del_deriv ( )

private

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

Definition at line 164 of file matrice.C.

References band, lu, and permute.

◆ del_t()

void Lorene::Matrice::del_t ( )

private

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

Definition at line 156 of file matrice.C.

References del_deriv(), and std.

◆ determinant()

double Lorene::Matrice::determinant ( ) const

Computes the determinant of the matrix, using LAPACK and the standard decomposition.

Definition at line 560 of file matrice.C.

References get_dim(), and val_propre().

◆ get_array()

Tbl Lorene::Matrice::get_array ( ) const

inline

Returns the array of matrix elements.

Definition at line 251 of file matrice.h.

References std.

◆ get_dim()

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

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 260 of file matrice.C.

References std.

◆ get_etat()

int Lorene::Matrice::get_etat ( ) const

inline

Returns the logical state.

Definition at line 213 of file matrice.h.

References etat.

◆ inverse()

Tbl Lorene::Matrice::inverse ( const Tbl & 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 424 of file matrice.C.

References band, get_dim(), Lorene::Tbl::get_dim(), kl, ku, lu, permute, and Lorene::Tbl::t.

◆ operator()()

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

inline

Read-only of a particuliar element.

Parameters

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

Definition at line 290 of file matrice.h.

References etat, and std.

◆ operator*=()

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

Multiplication of this by a double.

Definition at line 622 of file matrice.C.

References std, and Lorene::x.

◆ operator+=() [1/2]

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

Addition of a Matrice to this.

Definition at line 602 of file matrice.C.

References Matrice(), and std.

◆ operator+=() [2/2]

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

Addition of a double to this.

Definition at line 612 of file matrice.C.

References std, and Lorene::x.

◆ operator-=() [1/2]

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

Subtraction of a Matrice to this.

Definition at line 607 of file matrice.C.

References Matrice(), and std.

◆ operator-=() [2/2]

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

Subtraction of a double to this.

Definition at line 617 of file matrice.C.

References std, and Lorene::x.

◆ operator/=()

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

Division of this by a double.

Definition at line 627 of file matrice.C.

References std, and Lorene::x.

◆ operator=() [1/3]

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

Assignement to another Matrice.

Definition at line 273 of file matrice.C.

References band, del_t(), etat, Lorene::Tbl::get_dim(), kl, ku, lu, Matrice(), permute, set_etat_nondef(), set_etat_qcq(), set_etat_zero(), and std.

◆ operator=() [2/3]

void Lorene::Matrice::operator= ( const Tbl & source )

Assignement to a Tbl.

Definition at line 306 of file matrice.C.

References del_t(), Lorene::Tbl::etat, Lorene::Tbl::get_dim(), set_etat_nondef(), set_etat_qcq(), set_etat_zero(), std, and Lorene::Tbl::t.

◆ operator=() [3/3]

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

Sets all the element of *std to x.

The other representations are set to ETATNONDEF.

Definition at line 265 of file matrice.C.

References set_etat_qcq(), set_etat_zero(), std, and Lorene::x.

◆ set()

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

inline

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 277 of file matrice.h.

References band, del_deriv(), etat, lu, and std.

◆ set_band()

void Lorene::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 364 of file matrice.C.

References band, kl, ku, and std.

◆ set_etat_nondef()

void Lorene::Matrice::set_etat_nondef ( )

Sets the logical state to ETATNONDEF (undefined state).

The state of of all the representations is now ETATNONDEF.

Definition at line 187 of file matrice.C.

References del_deriv(), etat, and std.

◆ set_etat_qcq()

void Lorene::Matrice::set_etat_qcq ( )

Sets the logical state to ETATQCQ (ordinary state).

The state of *std is now ETATQCQ and the one of all the other representations is ETATNONDEF.

Definition at line 175 of file matrice.C.

References del_deriv(), etat, and std.

◆ set_etat_zero()

void Lorene::Matrice::set_etat_zero ( )

Sets the logical state to ETATZERO (zero).

The state of *std is now ETATZERO and the one of all the other representations is ETATNONDEF.

Definition at line 181 of file matrice.C.

References del_deriv(), etat, and std.

◆ set_lu()

void Lorene::Matrice::set_lu ( ) const

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

The calculus is done using LAPACK.

Definition at line 392 of file matrice.C.

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

◆ transpose()

Matrice Lorene::Matrice::transpose ( ) const

Computes the transpose matrix.

Definition at line 578 of file matrice.C.

References etat, Matrice(), set(), set_etat_qcq(), set_etat_zero(), and std.

◆ val_propre()

Tbl Lorene::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 Tbl (0, *) and the imaginary parts in Tbl (1, *).

Definition at line 457 of file matrice.C.

References etat, get_dim(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), and std.

◆ vect_propre()

Matrice Lorene::Matrice::vect_propre ( ) const

Returns the eigenvectors of the matrix, calculated using LAPACK.

Definition at line 507 of file matrice.C.

References etat, get_dim(), Matrice(), set(), set_etat_qcq(), and std.

◆ operator* [1/3]

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

friend

Matrice * double

Definition at line 646 of file matrice.C.

References Matrice(), std, and Lorene::x.

◆ operator* [2/3]

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

friend

Matrix product.

Definition at line 658 of file matrice.C.

References Lorene::Tbl::get_dim(), get_etat(), Matrice(), set(), set_etat_qcq(), set_etat_zero(), and std.

◆ operator* [3/3]

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

friend

double * Matrice

Definition at line 652 of file matrice.C.

References Matrice(), std, and Lorene::x.

◆ operator+

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

friend

Matrice + Matrice

Definition at line 634 of file matrice.C.

References Matrice(), and std.

◆ operator-

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

friend

Matrice - Matrice

Definition at line 640 of file matrice.C.

References Matrice(), and std.

◆ operator/

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

friend

Matrice / double

Definition at line 693 of file matrice.C.

References Matrice(), std, and Lorene::x.

◆ operator<<

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

friend

Display.

Definition at line 330 of file matrice.C.

References band, Lorene::Tbl::get_dim(), Lorene::Tbl::get_etat(), kl, ku, lu, Matrice(), and std.

Member Data Documentation

◆ band

Tbl* Lorene::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 170 of file matrice.h.

◆ etat

int Lorene::Matrice::etat

private

logical state (ETATZERO, ETATQCQ or ETATNONDEF)

Definition at line 156 of file matrice.h.

◆ kl

int Lorene::Matrice::kl

mutableprivate

Number of lower-diagonals in the band representation.

Definition at line 162 of file matrice.h.

◆ ku

int Lorene::Matrice::ku

mutableprivate

Number of upper-diagonals in the band representation.

Definition at line 161 of file matrice.h.

◆ lu

Tbl* Lorene::Matrice::lu

mutableprivate

Pointer on the first array of the LU-representation.

Definition at line 173 of file matrice.h.

◆ permute

Itbl* Lorene::Matrice::permute

mutableprivate

Pointer on the second array of the LU-representation.

Definition at line 174 of file matrice.h.

◆ std

Tbl* Lorene::Matrice::std

private

Pointer on the array of the standard representation.

Definition at line 158 of file matrice.h.

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_hard()

◆ del_deriv()

◆ del_t()

◆ determinant()

◆ get_array()

◆ get_dim()

◆ get_etat()

◆ inverse()

◆ 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_etat_nondef()

◆ set_etat_qcq()

◆ set_etat_zero()

◆ set_lu()

◆ transpose()

◆ val_propre()

◆ vect_propre()

Friends And Related Symbol Documentation

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+

◆ operator-

◆ operator/

◆ operator<<

Member Data Documentation

◆ band

◆ etat

◆ kl

◆ ku

◆ lu

◆ permute

◆ std