SMatrix Class Reference

SMatrix, square matrix class definition. More...

#include <SMatrix.h>

Inheritance diagram for SMatrix:

Public Member Functions
	SMatrix (int dim_i=1)
	Default initialisation, matrix dimension is dim_i, all elements are zero.
	SMatrix (int dim_i, complex< double > diag)
	Creates a diagonal matrix with dimension dim_i.
	SMatrix (int dim_i, const complex< double > *Mtab_i)
	Creates a matrix from array, read order from left to right.
	SMatrix (int dim_i, double real, double imag)
	Creates a matrix from real and imaginary arrays.
	SMatrix (const SMatrix &m)
	Constructor by copy.
	~SMatrix ()
	Destructor.
int	getdim () const
	Send matrix dimension (dim).
void	redim (int ndim)
	Modify the matrix dimension.
void	setdiag (complex< double > diag)
	Creates a diagonal matrix, which all elements = diag.
void	setdiag (complex< double > *tab_diag)
	Transform the matrix in a diagonal matrix one, which all elements = array tab_diag.
void	print (const char *option="") const
	Output matrix as C code, ONLY for matlab mexPrintf(), cout<<SMatrix instead.
void	decompositionLU (SMatrix &L, SMatrix &U)
	LU decomposition.
void	decompositionCholesky (SMatrix &L, SMatrix &U)
	Cholesky decomposition.
void	SolveCrout (Ket b, Ket &x, SMatrix Lm, SMatrix Um)
	Solve linear system using Crout Method.
void	SolveSOR (Ket b, Ket &x)
	Solve linear system using SOR Method.
void	SolveGaussSeidel (Ket b, Ket &x)
	Solve linear system using Gauss Seidel Method.
complex< double >	getdetformal () const
	Calculate the determinant (formal mode).
complex< double >	getdet () const
	Calculate the determinant with LU decomposition.
complex< double >	gettrace () const
	Calculate the matrix trace.
double	getnorm () const
	Calculate the matrix norm.
double	getmax (double a[], int n) const
	Get the maximum value.
SMatrix	gettransposed () const
	Calculate the matrix transposed.
SMatrix	gethermitiantransposed () const
	Calculate the conjugate transposed.
SMatrix	getreducedmatrix (int row, int col) const
	Return a matrix without row i and column j.
SMatrix	getinversedformal () const
	Calculate the inversed matrix (formal mode).
SMatrix	getinversed () const
	Calculate the inversed matrix.
SMatrix	getabsmatrix () const
	Return matrix with the abs of all elements.
SMatrix	getexpm () const
	Calculate the matrix exponential using Pade algoritm (see Matlab for documentation).
complex< double > &	operator() (int i, int j)
	Acces to matrix elements.
complex< double >	operator() (int i, int j) const
	Read/Write matrix elements.
const SMatrix &	operator= (const SMatrix &m)
	Affectation operator.
SMatrix	operator+ (const SMatrix &m) const
	Addition operator.
SMatrix	operator- (const SMatrix &m) const
	Soustraction operator.
SMatrix	operator* (const SMatrix &m) const
	Multiplication operator.
SMatrix	operator/ (const SMatrix &m) const
	Division operator.
Friends
EXPORTED_FUNCTION SMatrix	operator* (complex< double > a, const SMatrix &m)
	Scalar complex - matrix multiplication.
EXPORTED_FUNCTION SMatrix	operator* (double a, const SMatrix &m)
	Scalar double - matrix multiplication.
EXPORTED_FUNCTION SMatrix	operator* (const SMatrix &m, complex< double > a)
	Matrix - scalar complex multiplication.
EXPORTED_FUNCTION SMatrix	operator* (const SMatrix &m, double a)
	Matrix - scalar double multiplication.
EXPORTED_FUNCTION SMatrix	operator* (complex< double > a, const SMatrix *m)
	Scalar complex - matrix pointer multiplication.
EXPORTED_FUNCTION SMatrix	operator/ (const SMatrix &m, double a)
	Matrix - scalar double division.
EXPORTED_FUNCTION SMatrix	operator/ (const SMatrix &m, complex< double > a)
	Matrix - scalar complex division.
EXPORTED_FUNCTION std::ostream &	operator<< (std::ostream &out, const SMatrix &m)
	Write to a flux, allow cout<<matrix; .

Detailed Description

SMatrix, square matrix class definition.

SMatrix is the square matrix base class for linear algebra operations. This class is composed by basical matrix operations, like trace, determinant, etc... You can also find numerical methods like LU decomposition, direct and interactives methods to solve linear systems. This class provides a user friend interface for load, create and get information from matrices, this is the mother class of Quantum Operators (QOperator).

Constructor & Destructor Documentation

SMatrix::SMatrix ( int dim_i = 1 )

Default initialisation, matrix dimension is dim_i, all elements are zero.

To create a matrix with all elements 0, you need to pass a valid dimension (dim_i > 0).

Parameters:

dim_i

Matrix row = column dimension.

SMatrix::SMatrix	(	int	dim_i,
		complex< double >	diag
	)

Creates a diagonal matrix with dimension dim_i.

To create a diagonal matrix, you pass the matrix dimension and the non zero element that will be put in the diagonal.

Parameters:

	dim_i	Matrix row = column dimension.
	diag	Complex number with double precision that will be put in the diagonal.

SMatrix::SMatrix	(	int	dim_i,
		const complex< double > *	Mtab_i
	)

Creates a matrix from array, read order from left to right.

To create a matrix from a complex<double> array that contains matrix data, you pass the matrix dimension and the data array.

Parameters:

	dim_i	Matrix row = column dimension.
	Mtab_i	Complex double precision array with all data. The data is put from left to right, in other words we fix the row and change columns.

SMatrix::SMatrix	(	int	dim_i,
		double *	real,
		double *	imag
	)

Creates a matrix from real and imaginary arrays.

SMatrix::SMatrix ( const SMatrix & m )

Constructor by copy.

Allow you to do that: SMatrix A(B), where B is a SMatrix.

Parameters:

m

Matrix to be copied.

SMatrix::~SMatrix ( )

Destructor.

Destroy all matrix array elements.

Member Function Documentation

void SMatrix::decompositionCholesky	(	SMatrix &	L,
		SMatrix &	U
	)

Cholesky decomposition.

To elaborate a Cholesky decomposition, you need to pass the lower and upper matrices to be elaborated.

Parameters:

	L	Lower matrix
	U	Upper matrix

Returns:: Returns L and U with the correct data.

void SMatrix::decompositionLU	(	SMatrix &	L,
		SMatrix &	U
	)

LU decomposition.

To decompose your matrix into a lower and upper triangular matrix product, you pass to SMatrix L (lower), SMatrix U (upper).

Parameters:

	L	Lower matrix to be passed.
	U	Upper matrix to be passed.

Returns:: Returns L and U with the correct data.

SMatrix SMatrix::getabsmatrix ( ) const

Return matrix with the abs of all elements.

Returns:: Returns the matrix with all abs elements.

complex< double > SMatrix::getdet ( ) const

Calculate the determinant with LU decomposition.

Returns:: Returns the matrix determinant, using LU decomposition.

complex< double > SMatrix::getdetformal ( ) const

Calculate the determinant (formal mode).

Returns:: Returns the matrix determinant.

int SMatrix::getdim ( ) const [inline]

Send matrix dimension (dim).

SMatrix SMatrix::getexpm ( ) const

Calculate the matrix exponential using Pade algoritm (see Matlab for documentation).

Returns:: Returns the matrix exponential using Pade algorithm.

SMatrix SMatrix::gethermitiantransposed ( ) const

Calculate the conjugate transposed.

Returns:: Returns the transposed conjugate matrix.

SMatrix SMatrix::getinversed ( ) const

Calculate the inversed matrix.

Returns:: Returns the matrix inversed using LAPACK++ libraries if avaiable.

SMatrix SMatrix::getinversedformal ( ) const

Calculate the inversed matrix (formal mode).

Returns:: Returns the matrix inversed.

double SMatrix::getmax	(	double	a[],
		int	n
	)			const

Get the maximum value.

Returns:: Returns the maximum from an array.

Parameters:

	a	Your array.
	n	Array dimension.

double SMatrix::getnorm ( ) const

Calculate the matrix norm.

Returns:: Returns the matrix norm = bigger row abs sum (Matlab norm('A',inf)).

SMatrix SMatrix::getreducedmatrix	(	int	row,
		int	col
	)			const

Return a matrix without row i and column j.

Parameters:

	row	Row to be removed.
	col	Column to be removed.

Returns:: Returns the reduced matrix.

complex< double > SMatrix::gettrace ( ) const

Calculate the matrix trace.

Returns:: Returns the matrix trace.

SMatrix SMatrix::gettransposed ( ) const

Calculate the matrix transposed.

Returns:: Returns the transposed matrix.

complex<double> SMatrix::operator()	(	int	i,
		int	j
	)			const `[inline]`

Read/Write matrix elements.

complex<double>& SMatrix::operator()	(	int	i,
		int	j
	)			`[inline]`

Acces to matrix elements.

SMatrix SMatrix::operator* ( const SMatrix & m ) const

Multiplication operator.

Allow you to multiply 2 or more operators, i.e: A = A*B*...*C;

Returns:: Returns the matrix multiplication.

SMatrix SMatrix::operator+ ( const SMatrix & m ) const

Addition operator.

Allow you to sum 2 or more operators, i.e: A = A + B + ... + C;

Returns:: Returns the matrix sum.

SMatrix SMatrix::operator- ( const SMatrix & m ) const

Soustraction operator.

Allow you to subtracte 2 or more operators, i.e: A = A - B - ... - C;

Returns:: Returns the matrix subtraction.

SMatrix SMatrix::operator/ ( const SMatrix & m ) const

Division operator.

Allow you to divide 2 or more operators, i.e: A = A/B/.../C;

Returns:: Returns the matrix division.

const SMatrix & SMatrix::operator= ( const SMatrix & m )

Affectation operator.

Allow you to use the = operator, i.e: SMatrix A(2); SMatrix B(2); A = B;

void SMatrix::print ( const char * option = "" ) const

Output matrix as C code, ONLY for matlab mexPrintf(), cout<<SMatrix instead.

You can output matrix using this command i.e.: SMatrix A(...); A.print(); or A.print("expo");

Parameters:

option

If you pass the option "expo" all matrix elements will be showed with the exponential notation, else data will be showed as doubles.

Returns:: Return the matrix output.

void SMatrix::redim ( int ndim )

Modify the matrix dimension.

To modify the dimension of a matrix, you pass the new dimension.

Parameters:

ndim

New matrix dimension.

void SMatrix::setdiag ( complex< double > * tab_diag )

Transform the matrix in a diagonal matrix one, which all elements = array tab_diag.

To create a diagonal matrix, you need to pass a complex array that will be put in the diagonal.

Parameters:

tab_diag

Complex array that contains the elements to be put in the diagonal.

Returns:: Modify you matrix data.

void SMatrix::setdiag ( complex< double > diag )

Creates a diagonal matrix, which all elements = diag.

To create a diagonal matrix, you need to pass a complex number to be put in the diagonal.

Parameters:

diag

Complex number to be put in the diagonal.

Returns:: Modify your matrix data.

void SMatrix::SolveCrout	(	Ket	b,
		Ket &	x,
		SMatrix	Lm,
		SMatrix	Um
	)

Solve linear system using Crout Method.

To solve a linear system A*x=b, you pass b and an empty x, you also need to pass the LU matrix from A.

Parameters:

	b	The know vector.
	x	The solution vector.
	Lm	The lower triangular matrix.
	Um	The upper triangular matrix.

Returns:: Return x with the solution.

void SMatrix::SolveGaussSeidel	(	Ket	b,
		Ket &	x
	)

Solve linear system using Gauss Seidel Method.

To solve a linear system A*x=b, you pass b and an empty x.

Parameters:

	b	The know vector.
	x	The solution vector.

Returns:: Return x with the solution.

void SMatrix::SolveSOR	(	Ket	b,
		Ket &	x
	)

Solve linear system using SOR Method.

To solve a linear system A*x=b, you pass b and an empty x.

Parameters:

	b	The know vector.
	x	The solution vector.

Returns:: Return x with the solution.

Friends And Related Function Documentation

EXPORTED_FUNCTION SMatrix operator*	(	complex< double >	a,
		const SMatrix *	m
	)			`[friend]`

Scalar complex - matrix pointer multiplication.

EXPORTED_FUNCTION SMatrix operator*	(	const SMatrix &	m,
		double	a
	)			`[friend]`

Matrix - scalar double multiplication.

EXPORTED_FUNCTION SMatrix operator*	(	const SMatrix &	m,
		complex< double >	a
	)			`[friend]`

Matrix - scalar complex multiplication.

EXPORTED_FUNCTION SMatrix operator*	(	double	a,
		const SMatrix &	m
	)			`[friend]`

Scalar double - matrix multiplication.

EXPORTED_FUNCTION SMatrix operator*	(	complex< double >	a,
		const SMatrix &	m
	)			`[friend]`

Scalar complex - matrix multiplication.

EXPORTED_FUNCTION SMatrix operator/	(	const SMatrix &	m,
		complex< double >	a
	)			`[friend]`

Matrix - scalar complex division.

EXPORTED_FUNCTION SMatrix operator/	(	const SMatrix &	m,
		double	a
	)			`[friend]`

Matrix - scalar double division.

EXPORTED_FUNCTION std::ostream& operator<<	(	std::ostream &	out,
		const SMatrix &	m
	)			`[friend]`

Write to a flux, allow cout<<matrix; .

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

SMatrix Class Reference

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation