Public Member Functions
	SymmetricMatrix ()
	Empty constructor.
	SymmetricMatrix (long MatrixOrder, double InitValue=0.0)
	Constructor with parameters.
	SymmetricMatrix (FILE *File)
	Constructor with parameters.
	SymmetricMatrix (SymmetricMatrix &Instance)
	Copy constructor.
	~SymmetricMatrix ()
SymmetricMatrix &	operator= (SymmetricMatrix &Instance)
	Assignment operator '='.
SymmetricMatrix &	Equal (SymmetricMatrix &Instance)
	Assignment function.
	operator double *const ()
	Converts from SymmetricMatrix to doulbe*.
double &	operator() (long Row, long Col)
	Accesses the elements of the matrix.
double &	GetElement (unsigned long Row, unsigned long Column)
	Returns the element of the matrix through parameters row and column.
void	SetOrder (unsigned long MatrixOrder=0, double InitValue=0.0)
	Initializes the matrix order.
unsigned long	GetOrder ()
	Returns the matrix order.
unsigned long	GetNumberElements ()
	Returns the elements number of symmetric matrix.
long	SizeOf ()
	Returns the bytes number occupied by the symmetric matrix.
void	Reset (double Value=0.0)
	Reboots the elements of the matrix with a value determinate.
void	Reset (unsigned long NumEls, double Value=0.0)
	Reboots the elements of the matrix with a value determinate.
void	Identity ()
	Transforms the matrix to a identity matrix.
void	Insert (SymmetricMatrix &SubMatrix, long InitLine=0, long InitColumn=0)
	Inserts a symmetric sub-matrix from the parameters: rows and columns.
double	Maximum ()
	Returns the largest element of the symmetric matrix.
double	Minimum ()
	Returns the smallest element of the symmetric matrix.
double	EuclideanNorm ()
	Returns euclidean norm of the symmetric matrix.
void	Product (double *A, unsigned long N, double b=1.0)
double	OneNorm ()
	Returns the norm-1 of the symmetric matrix.
double	InfinityNorm ()
	Returns infinity norm of the symmetric matrix: norm-1 = inifinity norm.
SymmetricMatrix &	Chs ()
	Changes the signal of the symmetric matrix elements.
SymmetricMatrix &	operator- ()
	Changes the signal of the symmetric matrix elements.
SymmetricMatrix &	Add (SymmetricMatrix &A, SymmetricMatrix &B)
	Symmetric matrix addition.
SymmetricMatrix &	operator+= (SymmetricMatrix &B)
	Symmetric matrix addition.
SymmetricMatrix &	Add (SymmetricMatrix &B)
	Symmetric matrix addition.
SymmetricMatrix &	Add (SymmetricMatrix &B, unsigned long NumEls)
	Symmetric matrix addition.
void	AddMultiplicate (SymmetricMatrix &B, double scalar, unsigned long NumEls)
	Symmetric matrix addition and multiplication. It also resets B matrix.
SymmetricMatrix &	Subtract (SymmetricMatrix &A, SymmetricMatrix &B)
	Symmetric matrix subtraction.
SymmetricMatrix &	operator-= (SymmetricMatrix &B)
	Symmetric matrix subtraction.
SymmetricMatrix &	Subtract (SymmetricMatrix &B)
	Symmetric matrix subtraction.
SymmetricMatrix &	Add (double Scalar)
	Addition of a scalar in the symmetric matrix.
SymmetricMatrix &	operator+= (double Scalar)
	Addition of a scalar in the symmetric matrix.
SymmetricMatrix &	Subtract (double Scalar)
	Subtraction of a scalar of the symmetric matrix.
SymmetricMatrix &	operator-= (double Scalar)
	Subtraction of a scalar of the symmetric matrix.
SymmetricMatrix &	operator*= (double Scalar)
	Multiplication of a scalar by the symmetric matrix.
SymmetricMatrix &	Multiplicate (double Scalar)
	Multiplication of a scalar by the symmetric matrix.
void	Multiplicate (double X, double Y)
	Multiplies the symmetric matrix by a vector: x = A.y.
void	Multiplicate (double X, unsigned long Size, double Y)
	Multiplies the symmetric matrix by a vector: x = A.y.
void	Multiplicate (double A, unsigned long nlA, unsigned long ncA, double B, unsigned long nlB, unsigned long ncB)
	Multiplies two matrices (any double), yielding a symmetric matrix. AB = SymettricMatrix.
void	TripleProduct (Matrix &A, SymmetricMatrix &B)
	Triple product: "this = At * B * A".
void	TripleProduct (double *A, unsigned short NlinesA, unsigned short NcolsA, SymmetricMatrix &B)
	Triple product: "this = At * B * A".
double	ScalarProduct (SymmetricMatrix &B)
	Scalar product between symmetric matrices.
double	operator^ (SymmetricMatrix &B)
	Scalar product between symmetric matrices.
void	Save (FILE *File)
	Saves the matrix in a binary file.
void	Save (char Tabname, int Version, char Filename)
	Saves the symmetric matrix in the "acdp" database.
void	Restore (FILE *File)
	Reads the symmetric matrix from a binary file.
void	Restore (char Tabname, int Version, char Filename)
	Reads the symmetric matrix from the "acdp" database.
void	Print (FILE File, char Title, char *Format)
	Prints the matrix in ASCII format.
void	Print (FILE File=stdout, const char Message="", int NumMaxCols=5, int Mant=14, int Dec=7)
	Prints the matrix in ASCII format.
void	Print (FILE *File, int Mant, int Dec)
void	Free ()
	Fees memory area allocated for the matrix.
void	GaussSolver (double U, double B, double Precision)
	Method to solve system of linear equations.
void	GaussSolver ()
	Method to solve system of linear equations.
void	GaussSolver (double U, double B)
	Solves linear system by Gauss method - back substitution.
long	Jacobi (double U, double B, long NumberIterations, double &NormRes, double Precision=1e-4, ConvCriterion_E Crit=WEIGHT_RESIDUE, NormDS_E Norm=EUCLID)
	Jacobi's Iterative Method.
void	EigJacobi (SymmetricMatrix &B, double tol, SymmetricMatrix &eigv, Matrix &eigvec)
	Calculates the eigenvalues and eigenvectors of the generalized eigensystem: [A]{x} = {lambda}[B]{x} using the Jacobi method. Matrices A and B must be symmetrical and positive-definite. Matrix A is the one you are calling here in DS.
long	GaussSeidel (double U, double B, long NumberIterations, double &NormRes, double Precision=1e-4, ConvCriterion_E Crit=WEIGHT_RESIDUE, NormDS_E Norm=EUCLID)
	Gauss-Seidel iterative method.
long	SOR (double U, double B, long NumberIterations, double &NormRes, double Precision=1e-4, double Omega=1.81, ConvCriterion_E Crit=WEIGHT_RESIDUE, NormDS_E Norm=EUCLID)
	SOR (succesive over relaxation) iterative method.
long	CG (double U, double B, long MaxNumberIter, double &NormRes, double Precision=1e-4, ConvCriterion_E Crit=WEIGHT_RESIDUE, NormDS_E Norm=EUCLID)
	Standard conjugate gradient.
long	CGDiagonal (double U, double B, long MaxNumberIter, double &NormRes, double Precision=1e-4, ConvCriterion_E Crit=WEIGHT_RESIDUE, NormDS_E Norm=EUCLID)
	Conjugate gradient method with diagonal conditioned matrix.
long	CGPreConditionated (double U, double B, long MaxNumberIter, double &NormRes, double Precision=1e-4, double Omega=1.81, PreMatrix_E PreMatrix=SGS, ConvCriterion_E Crit=WEIGHT_RESIDUE, NormDS_E Norm=EUCLID)
	Preconditioned conjugate gradient method.
Protected Member Functions
void	FreeAuxVectors ()
	Frees the memory area to the auxiliary vectors.
void	Alloc (double InitValue=0.0)
	Allocates memory space to the matrix.
int	ConvCriteria (double U, double Un, double *b, double Prec, double Normb, ConvCriterion_E Crit, NormDS_E Norm, double &NormRes)
	Checks the convergence of iterative methods.
void	praux (double vetb, double vetx)
	Auxiliary function for gradient method with diagonal matrix.
void	fwdsubst (double vetx, double vetb, double omega)
	Auxiliary function for gradient method with preconditioning.
void	prodaux (double U, double Y, double cte)
	Runs product between the main diagonal of matrix and the element correspondent of the output 'vaux' vector provided by 'fwdsubst' function.
void	bcksubst (double vetx, double vetb, double omega)
	Thalot routine makes the step of back substitution of the system: 'ma' * 'vetaux' = 'vaux'.
void	prodfx (double z, double x, double Omega)
	Solve the system: z = F.x, where F is the upper triangular matrix.
double	norinfv (double *u, long dim)
	Calculates the infinity norm of the array.
double	scalv (double x, double y, unsigned long dim)
	Calculates the product scalar between two vectors.
double	normaev (double *u, long dim)
	Calculate the euclidean norm of a vector.
int	mgausimt (double mas, long neq, long step)
	Gaussian Elimination Method.
void	pmatbsa (double mcs, double ma, long nlina, long ncola, double *mbs)
	Calculates the matricial product. The product is performed according to mathematic formula below: Ci,j = At i,k * Bk,r * Ar,j.
void	promabs (double mc, double ma, double *mbs, long nlina, long ncola)
	Multiplies a matrix of the double type stored by rows by a symmetric matrix also of the double type stored in the shape supra-diagonal by rows.
void	solgasim (double vetx, double mas, double *vetb, long int neq)
	Resolves a system of linear equations by Gaussian Elimination Method.
Protected Attributes
unsigned long	PolyOrder
	Stores the order of matrix.
double *	d
	Auxiliary vector used in the methods to solve systems of equations.
double *	f
	Auxiliary vector used in the methods to solve systems of equations.
double *	g
	Auxiliary vector used in the methods to solve systems of equations.
double *	h
	Auxiliary vector used in the methods to solve systems of equations.
double *	SMatrix
	Elements of matrix stored in the vector.
DoublePtr_T *	PSLines
	Vector of pointers to the rows.
char	ExtraMemory [SizeExtraMemSM]
	Extra memory used in the memory alignment during allocation of class object.
Friends
SymmetricMatrix	operator+ (SymmetricMatrix &A, SymmetricMatrix &B)
	Symmetric matrix addition.
SymmetricMatrix	operator- (SymmetricMatrix &A, SymmetricMatrix &B)
	Symmetric matrix subtraction.
void	Multiplicate (Matrix &A, SymmetricMatrix &B, Matrix &C)
	Runs the operation of multiplication: A = B * C (A and C are full. B is symmetric).

Constructor & Destructor Documentation

SymmetricMatrix::SymmetricMatrix	(	long	MatrixOrder,
		double	InitValue = `0.0`
	)

Constructor with parameters.

Parameters:

[in]	MatrixOrder	- The order matrix.
[in]	InitValue	- The initial value to the matrix.

SymmetricMatrix::SymmetricMatrix ( FILE * File )

Constructor with parameters.

Creates the matrix through reading a ASCII data file.

Parameters:

[in] File - A binary file.

SymmetricMatrix::SymmetricMatrix ( SymmetricMatrix & Instance )

Copy constructor.

Parameters:

[in] Instance - symmetric matrix type.

SymmetricMatrix::~SymmetricMatrix ( )

.

Member Function Documentation

SymmetricMatrix & SymmetricMatrix::Add	(	SymmetricMatrix &	A,
		SymmetricMatrix &	B
	)

Symmetric matrix addition.

Ex.: C.Add(A, B).

Parameters:

[in]	A	- the symmetric matrix A to be summed.
[in]	B	- the symmetric matrix B to be summed.

Returns:: a Symmetric Matrix with the sum result of two matrices.

SymmetricMatrix & SymmetricMatrix::Add ( SymmetricMatrix & B )

Symmetric matrix addition.

Ex.: A.Add(B).

Parameters:

[in] B - a symmetric matrix to be sum.

Returns:: a Symmetric Matrix with the result of sum the operation "A.Add(B)."

SymmetricMatrix & SymmetricMatrix::Add	(	SymmetricMatrix &	B,
		unsigned long	NumEls
	)

Symmetric matrix addition.

Ex.: A.Add(B).

Parameters:

[in]	B	- a symmetric matrix to be sum.
[in]	NumEls	- Number of elements of both matrices.

Returns:: a Symmetric Matrix with the result of sum the operation "A.Add(B)."

SymmetricMatrix & SymmetricMatrix::Add ( double Scalar )

Addition of a scalar in the symmetric matrix.

Ex.: A.Add(10).

Parameters:

[in] Scalar - Scalar value to be added in the symmetric matrix.

Returns:: a Symmetric Matrix with the result of the sum of a symmetric matrix by a scalar.

void SymmetricMatrix::AddMultiplicate	(	SymmetricMatrix &	B,
		double	scalar,
		unsigned long	NumEls
	)

Symmetric matrix addition and multiplication. It also resets B matrix.

Ex.: A.Add(B).

Parameters:

[in]	B	- a symmetric matrix to be operated.
[in]	scalar	- A scalar value to be multiplied.
[in]	NumEls	- Number of elements of both matrices.

void SymmetricMatrix::Alloc ( double InitValue = 0.0 ) [protected]

Allocates memory space to the matrix.

Parameters:

[in] InitValue - Initial Value to set the elements of matrix.

void SymmetricMatrix::bcksubst	(	double *	vetx,
		double *	vetb,
		double	omega
	)		`[protected]`

Thalot routine makes the step of back substitution of the system: 'ma' * 'vetaux' = 'vaux'.

Parameters:

[in]	vetb.
[in]	omega.
[out]	vetx.

long SymmetricMatrix::CG	(	double *	U,
		double *	B,
		long	MaxNumberIter,
		double &	NormRes,
		double	Precision = `1e-4`,
		ConvCriterion_E	Crit = `WEIGHT_RESIDUE`,
		NormDS_E	Norm = `EUCLID`
	)

Standard conjugate gradient.

Parameters:

[in]	B	- double pointer to independent terms.
[in]	MaxNumberIter	- Maximum number of iterations.
[in]	NormRes	- the residue norm of solution.
[in]	Precision	- constant for the convergence test.
[in]	Crit	- convergence criterion.
[in]	Norm	- Norm type. 1 - Infinity norm 2 - Euclidean norm.
[out]	U	- double pointer to answer vector.

Returns:: a long type indicating if there was convergence.

long SymmetricMatrix::CGDiagonal	(	double *	U,
		double *	B,
		long	MaxNumberIter,
		double &	NormRes,
		double	Precision = `1e-4`,
		ConvCriterion_E	Crit = `WEIGHT_RESIDUE`,
		NormDS_E	Norm = `EUCLID`
	)

Conjugate gradient method with diagonal conditioned matrix.

Parameters:

[in]	B	- double pointer to independent terms.
[in]	MaxNumberIter	- Maximum number of iterations.
[in]	NormRes	- the residue norm of solution.
[in]	Precision	- constant for the convergence test.
[in]	Crit	- convergence criterion.
[in]	Norm	- Norm type. 1 - Infinity norm 2 - Euclidean norm.
[out]	U	- double pointer to answer vector.

Returns:: a long type indicating if there was convergence.

long SymmetricMatrix::CGPreConditionated	(	double *	U,
		double *	B,
		long	MaxNumberIter,
		double &	NormRes,
		double	Precision = `1e-4`,
		double	Omega = `1.81`,
		PreMatrix_E	PreMatrix = `SGS`,
		ConvCriterion_E	Crit = `WEIGHT_RESIDUE`,
		NormDS_E	Norm = `EUCLID`
	)

Preconditioned conjugate gradient method.

Parameters:

[in]	B	- double pointer to independent terms.
[in]	MaxNumberIter	- Maximum number of iterations.
[in]	NormRes	- the residue norm of solution.
[in]	Precision	- constant for the convergence test.
[in]	Omega	- parameter of relaxation.
[in]	PreMatrix	- It is a enum type that indicates the preconditioning matrix type.
[in]	Crit	- convergence criterion.
[in]	Norm	- Norm type. 1 - Infinity norm 2 - Euclidean norm.
[out]	U	- double pointer to answer vector.

Returns:: a long type indicating if there was convergence.

SymmetricMatrix & SymmetricMatrix::Chs ( )

Changes the signal of the symmetric matrix elements.

Ex.: A.Chs();

Returns:: a SymmetricMatrix object with the inverted signal.

int SymmetricMatrix::ConvCriteria	(	double *	U,
		double *	Un,
		double *	b,
		double	Prec,
		double	Normb,
		ConvCriterion_E	Crit,
		NormDS_E	Norm,
		double &	NormRes
	)		`[protected]`

Checks the convergence of iterative methods.

Parameters:

[in]	U	- pointer to vector operand.
[in]	b.
[in]	Prec.
[in]	Normb.
[in]	Crit.
[in]	Norm.
[in]	NormRes.
[out]	Un	- Pointer to vector that contains the result.

Returns:: 0 or 1.

void SymmetricMatrix::EigJacobi	(	SymmetricMatrix &	B,
		double	tol,
		SymmetricMatrix &	eigv,
		Matrix &	eigvec
	)

Calculates the eigenvalues and eigenvectors of the generalized eigensystem: [A]{x} = {lambda}[B]{x} using the Jacobi method. Matrices A and B must be symmetrical and positive-definite. Matrix A is the one you are calling here in DS.

Parameters:

[in]	B	- matrix of the right-hand side of the eigensystem
[in]	tol	- numerical tolerance
[out]	eigv	- Diagonal matrix with eigenvalues
[out]	eigvec	- matrix with eigenvectors

SymmetricMatrix & SymmetricMatrix::Equal ( SymmetricMatrix & Instance )

Assignment function.

Ex.: A.Equal(B);

Parameters:

[in] Instance - the symmetric matrix type.

Returns:: a object of the SymmetricMatrix.

double SymmetricMatrix::EuclideanNorm ( )

Returns euclidean norm of the symmetric matrix.

Returns:: a double type with the value of Euclidean Norm.

void SymmetricMatrix::fwdsubst	(	double *	vetx,
		double *	vetb,
		double	omega
	)		`[protected]`

Auxiliary function for gradient method with preconditioning.

Parameters:

[in]	vetb	- the residue vector.
[in]	omega.
[out]	vetx	- the answer vector.

long SymmetricMatrix::GaussSeidel	(	double *	U,
		double *	B,
		long	NumberIterations,
		double &	NormRes,
		double	Precision = `1e-4`,
		ConvCriterion_E	Crit = `WEIGHT_RESIDUE`,
		NormDS_E	Norm = `EUCLID`
	)

Gauss-Seidel iterative method.

Parameters:

[in]	B	- double pointer to independent terms.
[in]	NumberIterations	- number of iterations.
[in]	NormRes	- the residue norm of solution.
[in]	Precision	- precision desired.
[in]	Crit	- convergence criterion.
[in]	Norm	- Norm type. 1 - Infinity norm 2 - Euclidean norm.
[out]	U	- double pointer to answer vector.

Returns:: a long type indicating if there was convergence.

void SymmetricMatrix::GaussSolver	(	double *	U,
		double *	B,
		double	Precision
	)

Method to solve system of linear equations.

Gauss Elimination Method.

Parameters:

[in]	B	- double pointer to independent terms.
[in]	Precision.
[out]	U	- double pointer to answer vector.

void SymmetricMatrix::GaussSolver ( )

Method to solve system of linear equations.

Triangularization of the matrix by gauss method.

void SymmetricMatrix::GaussSolver	(	double *	U,
		double *	B
	)

Solves linear system by Gauss method - back substitution.

Parameters:

[in]	B	- double pointer to independent terms.
[out]	U	- double pointer to answer vector.

double & SymmetricMatrix::GetElement	(	unsigned long	Row,
		unsigned long	Column
	)

Returns the element of the matrix through parameters row and column.

Checks if (Row, Col) belongs the matrix.

Parameters:

[in]	Row	- the rows number of symmetric matrix.
[in]	Col	- the columns number of symmetric matrix.

Returns:: a double type contains a element of the symmetric matrix.

unsigned long SymmetricMatrix::GetNumberElements ( )

Returns the elements number of symmetric matrix.

Returns:: a unsigned long type with elements number.

unsigned long SymmetricMatrix::GetOrder ( )

Returns the matrix order.

Returns:: a long type with the matrix order.

double SymmetricMatrix::InfinityNorm ( )

Returns infinity norm of the symmetric matrix: norm-1 = inifinity norm.

Returns:: a double type with the value of Infinity Norm.

void SymmetricMatrix::Insert	(	SymmetricMatrix &	SubMatrix,
		long	InitLine = `0`,
		long	InitColumn = `0`
	)

Inserts a symmetric sub-matrix from the parameters: rows and columns.

Parameters:

[in]	SubMatrix	- Sub-Matrix to be inserted in the symmetric matrix.
[in]	InitLine	- The row where will be inserted the sub-matrix.
[in]	InitColumn	- The column where will be inserted the sub-matrix.

long SymmetricMatrix::Jacobi	(	double *	U,
		double *	B,
		long	NumberIterations,
		double &	NormRes,
		double	Precision = `1e-4`,
		ConvCriterion_E	Crit = `WEIGHT_RESIDUE`,
		NormDS_E	Norm = `EUCLID`
	)

Jacobi's Iterative Method.

Parameters:

[in]	U	- double pointer to answer vector.
[in]	B	- double pointer to independent terms.
[in]	NumberIterations	- number of iterations.
[in]	NormRes	- the residue norm of solution.
[in]	Precision	- precision desired.
[in]	Crit	- convergence criterion.
[in]	Norm	- Norm type. 1 - Infinity norm 2 - Euclidean norm.

Returns:: a long type indicating if there was convergence.

double SymmetricMatrix::Maximum ( )

Returns the largest element of the symmetric matrix.

Returns:: a double type that indicates the maximum value of the symmetric matrix.

int SymmetricMatrix::mgausimt	(	double *	mas,
		long	neq,
		long *	step
	)		`[protected]`

Gaussian Elimination Method.

Triangularize the system matrix according to gaussian elimination. The system matrix and symmetric are stored on the shape of the supra diagonal by rows. This routine returns a code informing whether obtained successful in the triangularization or not, in which case there was singularity of the system matrix preventing the continuation of the gauss method.

Parameters:

[in]	*mas	- system matrix.
[in]	neq	- number of equations
[in]	step	- 'k' step of the proccess of the 'forward elimination'

Returns:: an integer with value '0' or '1' indicating whether the method obtained successful.

double SymmetricMatrix::Minimum ( )

Returns the smallest element of the symmetric matrix.

Returns:: a double type that indicates the minimum value of the symmetric matrix.

SymmetricMatrix & SymmetricMatrix::Multiplicate ( double Scalar )

Multiplication of a scalar by the symmetric matrix.

Ex.: A.Multiplicate(1.5).

Parameters:

[in] Scalar - Scalar value to be multiplied by the symmetric matrix.

Returns:: a Symmetric Matrix with the result of the multiplication of a Symmetric Matrix by a scalar.

void SymmetricMatrix::Multiplicate	(	double *	X,
		double *	Y
	)

Multiplies the symmetric matrix by a vector: x = A.y.

Parameters:

[in]	Y	- The vector to be multiplies by the symmetric matrix.
[out]	X	- The resultant vector of product of a symmetric matrix by a vector.

void SymmetricMatrix::Multiplicate	(	double *	X,
		unsigned long	Size,
		double *	Y
	)

Multiplies the symmetric matrix by a vector: x = A.y.

Parameters:

[in]	Y	- The vector to be multiplies by the symmetric matrix.
[in]	Size	- The number of columns of the matrix and number of rows of the vector.
[out]	X	- The resultant vector of product of a symmetric matrix by a vector.

void SymmetricMatrix::Multiplicate	(	double *	A,
		unsigned long	nlA,
		unsigned long	ncA,
		double *	B,
		unsigned long	nlB,
		unsigned long	ncB
	)

Multiplies two matrices (any double*), yielding a symmetric matrix. A*B = SymettricMatrix.

Parameters:

[in]	A	- Given matrix.
[in]	nlA	- Number of lines of A.
[in]	ncA	- Number of columns of A.
[in]	B	- Another matrix.
[in]	nlB	- Number of lines of B.
[in]	ncB	- Number of columns of B.

double SymmetricMatrix::norinfv	(	double *	u,
		long	dim
	)		`[protected]`

Calculates the infinity norm of the array.

Parameters:

[in]	*u	- array of double.
[in]	dim	- dimension of the array u.

Returns:: a double - the infinity norm of an array.

double SymmetricMatrix::normaev	(	double *	u,
		long	dim
	)		`[protected]`

Calculate the euclidean norm of a vector.

Parameters:

[in]	*u	- the vector which will be calculated the euclidean norm.
[in]	dim	- dimension of vector u.

Returns:: a double - the value of the euclidean norm of a vector.

double SymmetricMatrix::OneNorm ( )

Returns the norm-1 of the symmetric matrix.

Returns:: a double type with the value of Norm 1.

SymmetricMatrix::operator double *const ( )

Converts from SymmetricMatrix to doulbe*.

Returns:: a pointer to double that stores the elements of the symmetric matrix.

double & SymmetricMatrix::operator()	(	long	Row,
		long	Col
	)

Accesses the elements of the matrix.

Parameters:

[in]	Row	- the rows number of symmetric matrix.
[in]	Col	- the columns number of symmetric matrix.

Returns:: a double type contains a element of the symmetric matrix.

SymmetricMatrix & SymmetricMatrix::operator*= ( double Scalar )

Multiplication of a scalar by the symmetric matrix.

Ex.: A *= 1.5.

Parameters:

[in] Scalar - Scalar value to be multiplied by the symmetric matrix.

Returns:: a Symmetric Matrix with the result of the multiplication of a Symmetric Matrix by a scalar.

SymmetricMatrix & SymmetricMatrix::operator+= ( SymmetricMatrix & B )

Symmetric matrix addition.

Ex.: A += B.

Parameters:

[in] B - a symmetric matrix to be sum.

Returns:: a Symmetric Matrix with the result of the operation "A += B".

SymmetricMatrix & SymmetricMatrix::operator+= ( double Scalar )

Addition of a scalar in the symmetric matrix.

Ex.: A += 10.

Parameters:

[in] Scalar - Scalar value to be added in the symmetric matrix.

Returns:: a Symmetric Matrix with the result of the sum of a Symmetric Matrix by a scalar.

SymmetricMatrix & SymmetricMatrix::operator- ( )

Changes the signal of the symmetric matrix elements.

Ex.: -A;

Returns:: a SymmetricMatrix object with the inverted signal.

SymmetricMatrix & SymmetricMatrix::operator-= ( SymmetricMatrix & B )

Symmetric matrix subtraction.

Ex.: A -= B.

Parameters:

[in] B - The symmetric matrix to be subtracted.

Returns:: a Symmetric Matrix with the result of the subtraction of operation "A -= B"

SymmetricMatrix & SymmetricMatrix::operator-= ( double Scalar )

Subtraction of a scalar of the symmetric matrix.

Ex.: A -= 10.

Parameters:

[in] Scalar - Scalar value to be subtracted in the symmetric matrix.

Returns:: a Symmetric Matrix with the result of the subtraction of a symmetric matrix by a scalar.

SymmetricMatrix & SymmetricMatrix::operator= ( SymmetricMatrix & Instance )

Assignment operator '='.

Ex.: A = B.

Parameters:

[in] - Instance - the symmetric matrix type.

Returns:: a object of the SymmetricMatrix.

double SymmetricMatrix::operator^ ( SymmetricMatrix & B )

Scalar product between symmetric matrices.

Ex.: r = A ^ B.

Parameters:

[in] B - The symmetric matrix to be multiplied.

Returns:: a double type with result of multiplication between two symmetric matrices.

void SymmetricMatrix::pmatbsa	(	double *	mcs,
		double *	ma,
		long	nlina,
		long	ncola,
		double *	mbs
	)		`[protected]`

Calculates the matricial product. The product is performed according to mathematic formula below: Ci,j = At i,k * Bk,r * Ar,j.

Considers that the second matrix is symmetric and pre-multiplies by the transposed of the first matrix resulting in the symmetric matrix stored in the shape supra-diagonal by rows, that is, performes the product CS = AT * BS * A.

Parameters:

[in]	*mcs	- pointer to the resulted matrix.
[in]	*ma	- pointer to the 'ma' matrix.
[in]	nlina	- number of rows of the 'ma' matrix.
[in]	ncola	- number of colums of the 'ma' matrix.
[out]	*mbs	- pointer to the symmetric matrix.

void SymmetricMatrix::praux	(	double *	vetb,
		double *	vetx
	)		`[protected]`

Auxiliary function for gradient method with diagonal matrix.

Parameters:

[in]	vetb.
[out]	vetx.

void SymmetricMatrix::Print	(	FILE *	File,
		char *	Title,
		char *	Format
	)

Prints the matrix in ASCII format.

Ex.: A.Print(File, "matrix1", "%7.2lf").

Parameters:

[in]	File	- the file where will be printed the matrix data.
[in]	Title	- this a header to indicate a operation type.
[in]	Format	- the data format to be printed.

void SymmetricMatrix::Print	(	FILE *	File = `stdout`,
		const char *	Message = `""`,
		int	NumMaxCols = `5`,
		int	Mant = `14`,
		int	Dec = `7`
	)

Prints the matrix in ASCII format.

Prints the band of matrix by row. Ex.: A.Print(File, "matrix1", 18, 7).

Parameters:

[in]	File	- the file where will be printed the symmetric matrix data. (the default is stdout)
[in]	Message	- Indicates the operation type that was run.
[in]	NumMaxCols	- the maximum value of columns that can printed by row.
[in]	Mant	- Indicates the space size that should have between columns.
[in]	Dec	- Indicates the size of the decimal part to be printed.

void SymmetricMatrix::Print	(	FILE *	File,
		int	Mant,
		int	Dec
	)

Prints the matrix in ASCII file to suitable format for SymmetricSparse(FILE *) constructor.

The format is following: matrix order and coeficients. 3 1.2 2.0 3.2 5.4 10.84 23.87

Parameters:

[in]	File	- the file where will be printed the symmetric matrix data. (the default is stdout)
[in]	Mant	- Indicates the space size that should have between columns.
[in]	Dec	- Indicates the size of the decimal part to be printed.

void SymmetricMatrix::prodaux	(	double *	U,
		double *	Y,
		double	cte
	)		`[protected]`

Runs product between the main diagonal of matrix and the element correspondent of the output 'vaux' vector provided by 'fwdsubst' function.

Parameters:

[in]	Y.
[in]	cte.
[out]	U.

void SymmetricMatrix::prodfx	(	double *	z,
		double *	x,
		double	Omega
	)		`[protected]`

Solve the system: z = F.x, where F is the upper triangular matrix.

Parameters:

[in]	x	- the upper triangular matrix.
[in]	omega.
[out]	z	- the result matrix.

void SymmetricMatrix::Product	(	double *	A,
		unsigned long	N,
		double	b = `1.0`
	)

@ brief: Array multiplication. The size of the array is not necessarily the same of A.

Ex.: C.Product(A, N).

Parameters:

[in]	A	- Array.
[in]	N	- Number of rows.
[in]	b	- Scalar value. the multiplication AtransposeA of a double A array.

void SymmetricMatrix::promabs	(	double *	mc,
		double *	ma,
		double *	mbs,
		long	nlina,
		long	ncola
	)		`[protected]`

Multiplies a matrix of the double type stored by rows by a symmetric matrix also of the double type stored in the shape supra-diagonal by rows.

param[out] *mc - pointer to the resulted matrix param[in] *ma - pointer to the 'ma' matrix param[in] *mbs - pointer to the symmetric matrix param[in] nlina - number of rows of the 'ma' matrix param[in] ncola - number of columns of the 'ma' matrix

void SymmetricMatrix::Reset ( double Value = 0.0 )

Reboots the elements of the matrix with a value determinate.

Parameters:

[in] Value - Used to initialize the elements of matrix.

void SymmetricMatrix::Reset	(	unsigned long	NumEls,
		double	Value = `0.0`
	)

Reboots the elements of the matrix with a value determinate.

Parameters:

[in]	NumEls	- Number of elements, to avoid calculating inside the function.
[in]	Value	- Used to initialize the elements of matrix.

void SymmetricMatrix::Restore ( FILE * File )

Reads the symmetric matrix from a binary file.

Ex.: A.Restore(File).

Parameters:

[in] File - the binary file where the symmetric matrix will read.

void SymmetricMatrix::Restore	(	char *	Tabname,
		int	Version,
		char *	Filename
	)

Reads the symmetric matrix from the "acdp" database.

Ex.: A.Restore("matrix1", 1, "matbda").

Parameters:

[in]	TabName	- the table name of the database to read matrix data.
[in]	Version	- the version of the read data.
[in]	Filename	- the database name.

void SymmetricMatrix::Save ( FILE * File )

Saves the matrix in a binary file.

Ex.: A.Save(File).

Parameters:

[in] File - the file to save the matrix data.

void SymmetricMatrix::Save	(	char *	Tabname,
		int	Version,
		char *	Filename
	)

Saves the symmetric matrix in the "acdp" database.

Ex.: A.Save("matrix1", 1, "matbda").

Parameters:

[in]	TabName	- the table name of the database to saved symmetric matrix data.
[in]	Version	- the version of the update data.
[in]	Filename	- Stores the database name.

double SymmetricMatrix::ScalarProduct ( SymmetricMatrix & B )

Scalar product between symmetric matrices.

Ex.: r = A.ScalarProduct(B).

Parameters:

[in] B - The symmetric matrix to be multiplied.

Returns:: a double type with result of multiplication between two symmetric matrices.

double SymmetricMatrix::scalv	(	double *	x,
		double *	y,
		unsigned long	dim
	)		`[protected]`

Calculates the product scalar between two vectors.

Parameters:

[in]	*x	- first vector.
[in]	*y	- second vector.
[in]	dim	- dimension of vector x and y.

Returns:: a double - the value of the product scalar between vectors x and y.

void SymmetricMatrix::SetOrder	(	unsigned long	MatrixOrder = `0`,
		double	InitValue = `0.0`
	)

Initializes the matrix order.

Parameters:

[in]	MatrixOrder	- The order matrix.
[in]	InitValue	- The initial value to the matrix.

long SymmetricMatrix::SizeOf ( )

Returns the bytes number occupied by the symmetric matrix.

Returns:: a long type with bytes total of the symmetric matrix.

void SymmetricMatrix::solgasim	(	double *	vetx,
		double *	mas,
		double *	vetb,
		long int	neq
	)		`[protected]`

Resolves a system of linear equations by Gaussian Elimination Method.

This method performing the modification of the independent terms according to the obted result in the mgausimt function and of the step of the 'back substitution'. This function allows the user solve a system with multiple vector of the load. The system matrix is of the symmetric type stored in the shape supra-diagonal by rows and is provided triangularized by mgausimt function.

Parameters:

[out]	*vetx	- pointer the answer vector.
[in]	*mas	- pointer to the system matrix.
[in]	*vetb	- pointer to the vector of independent terms.
[in]	neq	- number of equations.

long SymmetricMatrix::SOR	(	double *	U,
		double *	B,
		long	NumberIterations,
		double &	NormRes,
		double	Precision = `1e-4`,
		double	Omega = `1.81`,
		ConvCriterion_E	Crit = `WEIGHT_RESIDUE`,
		NormDS_E	Norm = `EUCLID`
	)

SOR (succesive over relaxation) iterative method.

Parameters:

[in]	B	- double pointer to independent terms.
[in]	NumberIterations	- Iterations number.
[in]	NormRes	- the residue norm of solution.
[in]	Precision	- constant for the convergence test.
[in]	Omega	- parameter of relaxation.
[in]	Crit	- convergence criterion.
[in]	Norm	- Norm type. 1 - Infinity norm 2 - Euclidean norm.
[out]	U	- double pointer to answer vector.

Returns:: a long type indicating if there was convergence.

SymmetricMatrix & SymmetricMatrix::Subtract	(	SymmetricMatrix &	A,
		SymmetricMatrix &	B
	)

Symmetric matrix subtraction.

Ex.: C.Subtract(A, B).

Parameters:

[in]	A.
[in]	B.

Returns:: a Symmetric Matrix with the result of the subtract of A by B.

SymmetricMatrix & SymmetricMatrix::Subtract ( SymmetricMatrix & B )

Symmetric matrix subtraction.

Ex.: A.Subtract(B).

Parameters:

[in] B - The symmetric matrix to be subtracted.

Returns:: a Symmetric Matrix with the result of the subtraction of operation "A.Subtract(B)"

SymmetricMatrix & SymmetricMatrix::Subtract ( double Scalar )

Subtraction of a scalar of the symmetric matrix.

Ex.: A.Subtract(10).

Parameters:

[in] Scalar - Scalar value to be subtracted in the symmetric matrix.

Returns:: a Symmetric Matrix with the result of the subtraction of a symmetric matrix by a scalar

void SymmetricMatrix::TripleProduct	(	Matrix &	A,
		SymmetricMatrix &	B
	)

Triple product: "this = At * B * A".

Parameters:

[in]	A	- the matrix to be multiplied.
[in]	B	- the symmetric matrix to be multiplied.

void SymmetricMatrix::TripleProduct	(	double *	A,
		unsigned short	NlinesA,
		unsigned short	NcolsA,
		SymmetricMatrix &	B
	)

Triple product: "this = At * B * A".

Parameters:

[in]	A	- the matrix to be multiplied.
[in]	B	- the symmetric matrix to be multiplied.

Friends And Related Function Documentation

void Multiplicate	(	Matrix &	A,
		SymmetricMatrix &	B,
		Matrix &	C
	)		`[friend]`

Runs the operation of multiplication: A = B * C (A and C are full. B is symmetric).

Parameters:

[in]	B	- the symmetric matrix to be multiplicated.
[in]	C	- the matrix to be multiplicated.
[out]	A	- the matrix that stores the result of multiplication.

SymmetricMatrix operator+	(	SymmetricMatrix &	A,
		SymmetricMatrix &	B
	)		`[friend]`

Symmetric matrix addition.

Ex.: C= A + B.

Parameters:

[in]	A	- the symmetric matrix A to be summed.
[in]	B	- the symmetric matrix B to be summed.

Returns:: a Symmetric Matrix with the sum result of two matrices.

SymmetricMatrix operator-	(	SymmetricMatrix &	A,
		SymmetricMatrix &	B
	)		`[friend]`

Symmetric matrix subtraction.

Ex.: C = A - B.

Parameters:

[in]	A.
[in]	B.

Returns:: a Symmetric Matrix with the result of the subtract of A by B.

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

include/ds/SymmetricMatrix.h
src/ds/SymmetricMatrix.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation