Epetra_SerialSymDenseMatrix: A class for constructing and using symmetric positive definite dense matrices. More...

#include <Epetra_SerialSymDenseMatrix.h>

Inheritance diagram for Epetra_SerialSymDenseMatrix:

Collaboration diagram for Epetra_SerialSymDenseMatrix:

Public Member Functions
void	CopyUPLOMat (bool Upper, double *A, int LDA, int NumRows)

Constructor/Destructor Methods
	Epetra_SerialSymDenseMatrix (void)
	Default constructor; defines a zero size object. More...

	Epetra_SerialSymDenseMatrix (Epetra_DataAccess CV, double *A, int LDA, int NumRowsCols)
	Set object values from two-dimensional array. More...

	Epetra_SerialSymDenseMatrix (const Epetra_SerialSymDenseMatrix &Source)
	Epetra_SerialSymDenseMatrix copy constructor.

virtual	~Epetra_SerialSymDenseMatrix ()
	Epetra_SerialSymDenseMatrix destructor.

Set Methods
int	Shape (int NumRowsCols)
	Set dimensions of a Epetra_SerialSymDenseMatrix object; init values to zero. More...

int	Reshape (int NumRowsCols)
	Reshape a Epetra_SerialSymDenseMatrix object. More...

void	SetLower ()
	Specify that the lower triangle of the this matrix should be used.

void	SetUpper ()
	Specify that the upper triangle of the this matrix should be used.

Query methods
bool	Upper () const
	Returns true if upper triangle of this matrix has and will be used.

char	UPLO () const
	Returns character value of UPLO used by LAPACK routines.

Mathematical Methods
int	Scale (double ScalarA)
	Inplace scalar-matrix product A = a A. More...

double	NormOne () const
	Computes the 1-Norm of the this matrix. More...

double	NormInf () const
	Computes the Infinity-Norm of the this matrix.

Deprecated methods (will be removed in later versions of this class)
double	OneNorm () const
	Computes the 1-Norm of the this matrix (identical to NormOne() method). More...

double	InfNorm () const
	Computes the Infinity-Norm of the this matrix (identical to NormInf() method).

Public Member Functions inherited from Epetra_SerialDenseMatrix
	Epetra_SerialDenseMatrix (bool set_object_label=true)
	Default constructor; defines a zero size object. More...

	Epetra_SerialDenseMatrix (int NumRows, int NumCols, bool set_object_label=true)
	Shaped constructor; defines a variable-sized object. More...

	Epetra_SerialDenseMatrix (Epetra_DataAccess CV, double *A_in, int LDA_in, int NumRows, int NumCols, bool set_object_label=true)
	Set object values from two-dimensional array. More...

	Epetra_SerialDenseMatrix (const Epetra_SerialDenseMatrix &Source)
	Epetra_SerialDenseMatrix copy constructor.

virtual	~Epetra_SerialDenseMatrix ()
	Epetra_SerialDenseMatrix destructor.

int	Shape (int NumRows, int NumCols)
	Set dimensions of a Epetra_SerialDenseMatrix object; init values to zero. More...

int	Reshape (int NumRows, int NumCols)
	Reshape a Epetra_SerialDenseMatrix object. More...

int	Multiply (char TransA, char TransB, double ScalarAB, const Epetra_SerialDenseMatrix &A, const Epetra_SerialDenseMatrix &B, double ScalarThis)
	Matrix-Matrix multiplication, this = ScalarThis*this + ScalarABAB. More...

int	Multiply (bool transA, const Epetra_SerialDenseMatrix &x, Epetra_SerialDenseMatrix &y)
	Matrix-Vector multiplication, y = A*x, where 'this' == A.

int	Multiply (char SideA, double ScalarAB, const Epetra_SerialSymDenseMatrix &A, const Epetra_SerialDenseMatrix &B, double ScalarThis)
	Matrix-Matrix multiplication with a symmetric matrix A. More...

int	Scale (double ScalarA)
	Inplace scalar-matrix product A = a A. More...

Epetra_SerialDenseMatrix &	operator= (const Epetra_SerialDenseMatrix &Source)
	Value copy from one matrix to another. More...

bool	operator== (const Epetra_SerialDenseMatrix &rhs) const
	Comparison operator. More...

bool	operator!= (const Epetra_SerialDenseMatrix &rhs) const
	Inequality operator. More...

Epetra_SerialDenseMatrix &	operator+= (const Epetra_SerialDenseMatrix &Source)
	Add one matrix to another. More...

double &	operator() (int RowIndex, int ColIndex)
	Element access function. More...

const double &	operator() (int RowIndex, int ColIndex) const
	Element access function. More...

double *	operator[] (int ColIndex)
	Column access function. More...

const double *	operator[] (int ColIndex) const
	Column access function. More...

int	Random ()
	Set matrix values to random numbers. More...

int	M () const
	Returns row dimension of system.

int	N () const
	Returns column dimension of system.

double *	A () const
	Returns pointer to the this matrix.

double *	A ()
	Returns pointer to the this matrix.

int	LDA () const
	Returns the leading dimension of the this matrix.

Epetra_DataAccess	CV () const
	Returns the data access mode of the this matrix.

virtual void	Print (std::ostream &os) const
	Print service methods; defines behavior of ostream << operator.

virtual int	SetUseTranspose (bool UseTranspose_in)
	If set true, transpose of this operator will be applied. More...

virtual int	Apply (const Epetra_SerialDenseMatrix &X, Epetra_SerialDenseMatrix &Y)
	Returns the result of a Epetra_SerialDenseOperator applied to a Epetra_SerialDenseMatrix X in Y. More...

virtual int	ApplyInverse (const Epetra_SerialDenseMatrix &X, Epetra_SerialDenseMatrix &Y)
	Returns the result of a Epetra_SerialDenseOperator inverse applied to an Epetra_SerialDenseMatrix X in Y. More...

virtual const char *	Label () const
	Returns a character string describing the operator.

virtual bool	UseTranspose () const
	Returns the current UseTranspose setting.

virtual bool	HasNormInf () const
	Returns true if the this object can provide an approximate Inf-norm, false otherwise.

virtual int	RowDim () const
	Returns the row dimension of operator.

virtual int	ColDim () const
	Returns the column dimension of operator.

Public Member Functions inherited from Epetra_CompObject
Epetra_CompObject &	operator= (const Epetra_CompObject &src)

	Epetra_CompObject ()
	Basic Epetra_CompObject constuctor.

	Epetra_CompObject (const Epetra_CompObject &Source)
	Epetra_CompObject copy constructor.

virtual	~Epetra_CompObject ()
	Epetra_CompObject destructor.

void	SetFlopCounter (const Epetra_Flops &FlopCounter_in)
	Set the internal Epetra_Flops() pointer.

void	SetFlopCounter (const Epetra_CompObject &CompObject)
	Set the internal Epetra_Flops() pointer to the flop counter of another Epetra_CompObject.

void	UnsetFlopCounter ()
	Set the internal Epetra_Flops() pointer to 0 (no flops counted).

Epetra_Flops *	GetFlopCounter () const
	Get the pointer to the Epetra_Flops() object associated with this object, returns 0 if none.

void	ResetFlops () const
	Resets the number of floating point operations to zero for this multi-vector.

double	Flops () const
	Returns the number of floating point operations with this multi-vector.

void	UpdateFlops (int Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (long int Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (long long Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (double Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (float Flops_in) const
	Increment Flop count for this object.

Public Member Functions inherited from Epetra_Object
	Epetra_Object (int TracebackModeIn=-1, bool set_label=true)
	Epetra_Object Constructor. More...

	Epetra_Object (const char *const Label, int TracebackModeIn=-1)
	Epetra_Object Constructor. More...

	Epetra_Object (const Epetra_Object &Object)
	Epetra_Object Copy Constructor. More...

virtual	~Epetra_Object ()
	Epetra_Object Destructor. More...

virtual int	ReportError (const std::string Message, int ErrorCode) const
	Error reporting method.

virtual void	SetLabel (const char *const Label)
	Epetra_Object Label definition using char *. More...

Public Member Functions inherited from Epetra_SerialDenseOperator
virtual	~Epetra_SerialDenseOperator ()
	Destructor.

Public Member Functions inherited from Epetra_BLAS
	Epetra_BLAS (void)
	Epetra_BLAS Constructor. More...

	Epetra_BLAS (const Epetra_BLAS &BLAS)
	Epetra_BLAS Copy Constructor. More...

virtual	~Epetra_BLAS (void)
	Epetra_BLAS Destructor.

float	ASUM (const int N, const float *X, const int INCX=1) const
	Epetra_BLAS one norm function (SASUM).

double	ASUM (const int N, const double *X, const int INCX=1) const
	Epetra_BLAS one norm function (DASUM).

float	DOT (const int N, const float X, const float Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS dot product function (SDOT).

double	DOT (const int N, const double X, const double Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS dot product function (DDOT).

float	NRM2 (const int N, const float *X, const int INCX=1) const
	Epetra_BLAS norm function (SNRM2).

double	NRM2 (const int N, const double *X, const int INCX=1) const
	Epetra_BLAS norm function (DNRM2).

void	SCAL (const int N, const float ALPHA, float *X, const int INCX=1) const
	Epetra_BLAS vector scale function (SSCAL)

void	SCAL (const int N, const double ALPHA, double *X, const int INCX=1) const
	Epetra_BLAS vector scale function (DSCAL)

void	COPY (const int N, const float X, float Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector copy function (SCOPY)

void	COPY (const int N, const double X, double Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector scale function (DCOPY)

int	IAMAX (const int N, const float *X, const int INCX=1) const
	Epetra_BLAS arg maximum of absolute value function (ISAMAX)

int	IAMAX (const int N, const double *X, const int INCX=1) const
	Epetra_BLAS arg maximum of absolute value function (IDAMAX)

void	AXPY (const int N, const float ALPHA, const float X, float Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector update function (SAXPY)

void	AXPY (const int N, const double ALPHA, const double X, double Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector update function (DAXPY)

void	GEMV (const char TRANS, const int M, const int N, const float ALPHA, const float A, const int LDA, const float X, const float BETA, float *Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS matrix-vector multiply function (SGEMV)

void	GEMV (const char TRANS, const int M, const int N, const double ALPHA, const double A, const int LDA, const double X, const double BETA, double *Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS matrix-vector multiply function (DGEMV)

void	GEMM (const char TRANSA, const char TRANSB, const int M, const int N, const int K, const float ALPHA, const float A, const int LDA, const float B, const int LDB, const float BETA, float *C, const int LDC) const
	Epetra_BLAS matrix-matrix multiply function (SGEMM)

void	GEMM (const char TRANSA, const char TRANSB, const int M, const int N, const int K, const double ALPHA, const double A, const int LDA, const double B, const int LDB, const double BETA, double *C, const int LDC) const
	Epetra_BLAS matrix-matrix multiply function (DGEMM)

void	SYMM (const char SIDE, const char UPLO, const int M, const int N, const float ALPHA, const float A, const int LDA, const float B, const int LDB, const float BETA, float *C, const int LDC) const
	Epetra_BLAS symmetric matrix-matrix multiply function (SSYMM)

void	SYMM (const char SIDE, const char UPLO, const int M, const int N, const double ALPHA, const double A, const int LDA, const double B, const int LDB, const double BETA, double *C, const int LDC) const
	Epetra_BLAS matrix-matrix multiply function (DSYMM)

void	TRMM (const char SIDE, const char UPLO, const char TRANSA, const char DIAG, const int M, const int N, const float ALPHA, const float A, const int LDA, float B, const int LDB) const
	Epetra_BLAS triangular matrix-matrix multiply function (STRMM)

void	TRMM (const char SIDE, const char UPLO, const char TRANSA, const char DIAG, const int M, const int N, const double ALPHA, const double A, const int LDA, double B, const int LDB) const
	Epetra_BLAS triangular matrix-matrix multiply function (DTRMM)

void	SYRK (const char UPLO, const char TRANS, const int N, const int K, const float ALPHA, const float A, const int LDA, const float BETA, float C, const int LDC) const
	Eperta_BLAS symetric rank k funtion (ssyrk)

void	SYRK (const char UPLO, const char TRANS, const int N, const int K, const double ALPHA, const double A, const int LDA, const double BETA, double C, const int LDC) const
	Eperta_BLAS symetric rank k funtion (dsyrk)

Additional Inherited Members
Static Public Member Functions inherited from Epetra_Object
static void	SetTracebackMode (int TracebackModeValue)
	Set the value of the Epetra_Object error traceback report mode. More...

static int	GetTracebackMode ()
	Get the value of the Epetra_Object error report mode.

static std::ostream &	GetTracebackStream ()
	Get the output stream for error reporting.

Static Public Attributes inherited from Epetra_Object
static int	TracebackMode

Protected Member Functions inherited from Epetra_SerialDenseMatrix
void	CopyMat (const double Source, int Source_LDA, int NumRows, int NumCols, double Target, int Target_LDA, bool add=false)

void	CleanupData ()

Protected Member Functions inherited from Epetra_Object
std::string	toString (const int &x) const

std::string	toString (const long long &x) const

std::string	toString (const double &x) const

Protected Attributes inherited from Epetra_SerialDenseMatrix
int	M_

int	N_

bool	A_Copied_

Epetra_DataAccess	CV_

int	LDA_

double *	A_

bool	UseTranspose_

Protected Attributes inherited from Epetra_CompObject
Epetra_Flops *	FlopCounter_

Detailed Description

Epetra_SerialSymDenseMatrix: A class for constructing and using symmetric positive definite dense matrices.

The Epetra_SerialSymDenseMatrix class enables the construction and use of
real-valued, symmetric positive definite,
double-precision dense matrices.  It is built on the Epetra_SerialDenseMatrix class which
in turn is built on the
BLAS via the Epetra_BLAS class.

The Epetra_SerialSymDenseMatrix class is intended to provide full-featured support for solving linear and eigen system problems for symmetric positive definite matrices. It is written on top of BLAS and LAPACK and thus has excellent performance and numerical capabilities. Using this class, one can either perform simple factorizations and solves or apply all the tricks available in LAPACK to get the best possible solution for very ill-conditioned problems.

Epetra_SerialSymDenseMatrix vs. Epetra_LAPACK

The Epetra_LAPACK class provides access to most of the same functionality as Epetra_SerialSymDenseMatrix. The primary difference is that Epetra_LAPACK is a "thin" layer on top of LAPACK and Epetra_SerialSymDenseMatrix attempts to provide easy access to the more sophisticated aspects of solving dense linear and eigensystems.

When you should use Epetra_LAPACK: If you are simply looking for a convenient wrapper around the Fortran LAPACK routines and you have a well-conditioned problem, you should probably use Epetra_LAPACK directly.
When you should use Epetra_SerialSymDenseMatrix: If you want to (or potentially want to) solve ill-conditioned problems or want to work with a more object-oriented interface, you should probably use Epetra_SerialSymDenseMatrix.

Constructing Epetra_SerialSymDenseMatrix Objects

There are three Epetra_DenseMatrix constructors. The first constructs a zero-sized object which should be made to appropriate length using the Shape() or Reshape() functions and then filled with the [] or () operators. The second is a constructor that accepts user data as a 2D array, the third is a copy constructor. The second constructor has two data access modes (specified by the Epetra_DataAccess argument):

Copy mode - Allocates memory and makes a copy of the user-provided data. In this case, the user data is not needed after construction.
View mode - Creates a "view" of the user data. In this case, the user data is required to remain intact for the life of the object.

Warning: View mode is extremely dangerous from a data hiding perspective. Therefore, we strongly encourage users to develop code using Copy mode first and only use the View mode in a secondary optimization phase.

Extracting Data from Epetra_SerialSymDenseMatrix Objects

Once a Epetra_SerialSymDenseMatrix is constructed, it is possible to view the data via access functions.

Warning: Use of these access functions cam be extremely dangerous from a data hiding perspective.

Vector and Utility Functions

Once a Epetra_SerialSymDenseMatrix is constructed, several mathematical functions can be applied to the object. Specifically:

Multiplication.
Norms.

Counting floating point operations The Epetra_SerialSymDenseMatrix class has Epetra_CompObject as a base class. Thus, floating point operations are counted and accumulated in the Epetra_Flop object (if any) that was set using the SetFlopCounter() method in the Epetra_CompObject base class.

Constructor & Destructor Documentation

Epetra_SerialSymDenseMatrix::Epetra_SerialSymDenseMatrix ( void )

Default constructor; defines a zero size object.

Epetra_SerialSymDenseMatrix objects defined by the default constructor should be sized with the Shape() or Reshape() functions. Values should be defined by using the [] or ()operators.

Note: By default the active part of the matrix is assumed to be in the lower triangle. To set the upper part as active, call SetUpper(). See Detailed Description section for further discussion.

Epetra_SerialSymDenseMatrix::Epetra_SerialSymDenseMatrix	(	Epetra_DataAccess	CV,
		double *	A,
		int	LDA,
		int	NumRowsCols
	)

Set object values from two-dimensional array.

Parameters

In	Epetra_DataAccess - Enumerated type set to Copy or View.
In	A - Pointer to an array of double precision numbers. The first vector starts at A. The second vector starts at A+LDA, the third at A+2*LDA, and so on.
In	LDA - The "Leading Dimension", or stride between vectors in memory.
In	NumRowsCols - Number of rows and columns in object.

Note: By default the active part of the matrix is assumed to be in the lower triangle. To set the upper part as active, call SetUpper(). See Detailed Description section for further discussion.

Member Function Documentation

double Epetra_SerialSymDenseMatrix::NormOne ( ) const

virtual

Computes the 1-Norm of the this matrix.

Returns: Integer error code, set to 0 if successful.

Reimplemented from Epetra_SerialDenseMatrix.

Referenced by OneNorm().

double Epetra_SerialSymDenseMatrix::OneNorm ( ) const

inlinevirtual

Computes the 1-Norm of the this matrix (identical to NormOne() method).

Returns: Integer error code, set to 0 if successful.

Reimplemented from Epetra_SerialDenseMatrix.

References NormOne().

int Epetra_SerialSymDenseMatrix::Reshape ( int NumRowsCols )

inline

Reshape a Epetra_SerialSymDenseMatrix object.

Parameters

In	NumRowsCols - Number of rows and columns in object.

Allows user to define the dimensions of a Epetra_SerialSymDenseMatrix at any point. This function can be called at any point after construction. Any values that were previously in this object are copied into the new shape. If the new shape is smaller than the original, the upper left portion of the original matrix (the principal submatrix) is copied to the new matrix.

Returns: Integer error code, set to 0 if successful.

References Epetra_SerialDenseMatrix::Reshape().

int Epetra_SerialSymDenseMatrix::Scale ( double ScalarA )

Inplace scalar-matrix product A = a A.

Scale a matrix, entry-by-entry using the value ScalarA.  This method is sensitive to
the UPLO() parameter.

Parameters

ScalarA (In) Scalar to multiply with A.

Returns: Integer error code, set to 0 if successful.

int Epetra_SerialSymDenseMatrix::Shape ( int NumRowsCols )

inline

Set dimensions of a Epetra_SerialSymDenseMatrix object; init values to zero.

Parameters

In	NumRowsCols - Number of rows and columns in object.

Allows user to define the dimensions of a Epetra_DenseMatrix at any point. This function can be called at any point after construction. Any values that were previously in this object are destroyed and the resized matrix starts off with all zero values.

Returns: Integer error code, set to 0 if successful.

References Epetra_SerialDenseMatrix::Shape().

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

Epetra_SerialSymDenseMatrix.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation