This class creates and provides basic support for banded dense matrices of templated type. More...

#include <Teuchos_SerialBandDenseMatrix.hpp>

Inheritance diagram for Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >:

Public Types
typedef OrdinalType	ordinalType
	Typedef for ordinal type. More...

typedef ScalarType	scalarType
	Typedef for scalar type. More...

Public Types inherited from Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >
typedef details::GivensRotator < ScalarType >::c_type	rotg_c_type
	The type used for c in ROTG. More...

Public Member Functions
Constructor/Destructor methods.
	SerialBandDenseMatrix ()
	Default Constructor. More...

	SerialBandDenseMatrix (OrdinalType numRows, OrdinalType numCols, OrdinalType kl, OrdinalType ku, bool zeroOut=true)
	Shaped Constructor. More...

	SerialBandDenseMatrix (DataAccess CV, ScalarType *values, OrdinalType stride, OrdinalType numRows, OrdinalType numCols, OrdinalType kl, OrdinalType ku)
	Shaped Constructor with Values. More...

	SerialBandDenseMatrix (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Source, ETransp trans=Teuchos::NO_TRANS)
	Copy Constructor. More...

	SerialBandDenseMatrix (DataAccess CV, const SerialBandDenseMatrix< OrdinalType, ScalarType > &Source, OrdinalType numRows, OrdinalType numCols, OrdinalType startCol=0)
	Submatrix Copy Constructor. More...

virtual	~SerialBandDenseMatrix ()
	Destructor. More...

Shaping methods.
int	shape (OrdinalType numRows, OrdinalType numCols, OrdinalType kl, OrdinalType ku)
	Shape method for changing the size of a SerialBandDenseMatrix, initializing entries to zero. More...

int	shapeUninitialized (OrdinalType numRows, OrdinalType numCols, OrdinalType kl, OrdinalType ku)
	Same as `shape()` except leaves uninitialized. More...

int	reshape (OrdinalType numRows, OrdinalType numCols, OrdinalType kl, OrdinalType ku)
	Reshaping method for changing the size of a SerialBandDenseMatrix, keeping the entries. More...

Set methods.
SerialBandDenseMatrix < OrdinalType, ScalarType > &	operator= (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Source)
	Copies values from one matrix to another. More...

SerialBandDenseMatrix < OrdinalType, ScalarType > &	assign (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Source)
	Copies values from one matrix to another. More...

SerialBandDenseMatrix < OrdinalType, ScalarType > &	operator= (const ScalarType value)
	Set all values in the matrix to a constant value. More...

int	putScalar (const ScalarType value=Teuchos::ScalarTraits< ScalarType >::zero())
	Set all values in the matrix to a constant value. More...

int	random ()
	Set all values in the matrix to be random numbers. More...

Accessor methods.
ScalarType &	operator() (OrdinalType rowIndex, OrdinalType colIndex)
	Element access method (non-const). More...

const ScalarType &	operator() (OrdinalType rowIndex, OrdinalType colIndex) const
	Element access method (const). More...

ScalarType *	operator[] (OrdinalType colIndex)
	Column access method (non-const). More...

const ScalarType *	operator[] (OrdinalType colIndex) const
	Column access method (const). More...

ScalarType *	values () const
	Data array access method. More...

Mathematical methods.
SerialBandDenseMatrix < OrdinalType, ScalarType > &	operator+= (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Source)
	Add another matrix to this matrix. More...

SerialBandDenseMatrix < OrdinalType, ScalarType > &	operator-= (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Source)
	Subtract another matrix from this matrix. More...

SerialBandDenseMatrix < OrdinalType, ScalarType > &	operator*= (const ScalarType alpha)
	Scale `this` matrix by `alpha`; `this` = `alpha*this.` More...

int	scale (const ScalarType alpha)
	Scale `this` matrix by `alpha`; `this` = `alpha*this.` More...

int	scale (const SerialBandDenseMatrix< OrdinalType, ScalarType > &A)
	Point-wise scale `this` matrix by `A`; i.e. this(i,j) = A(i,j) More...

Comparison methods.
bool	operator== (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Operand) const
	Equality of two matrices. More...

bool	operator!= (const SerialBandDenseMatrix< OrdinalType, ScalarType > &Operand) const
	Inequality of two matrices. More...

Attribute methods.
OrdinalType	numRows () const
	Returns the row dimension of this matrix. More...

OrdinalType	numCols () const
	Returns the column dimension of this matrix. More...

OrdinalType	lowerBandwidth () const
	Returns the lower bandwidth of this matrix. More...

OrdinalType	upperBandwidth () const
	Returns the upper bandwidth of this matrix. More...

OrdinalType	stride () const
	Returns the stride between the columns of this matrix in memory. More...

bool	empty () const
	Returns whether this matrix is empty. More...

Norm methods.
ScalarTraits< ScalarType > ::magnitudeType	normOne () const
	Returns the 1-norm of the matrix. More...

ScalarTraits< ScalarType > ::magnitudeType	normInf () const
	Returns the Infinity-norm of the matrix. More...

ScalarTraits< ScalarType > ::magnitudeType	normFrobenius () const
	Returns the Frobenius-norm of the matrix. More...

I/O methods.
virtual std::ostream &	print (std::ostream &os) const
	Print method. Defines the behavior of the std::ostream << operator. More...

Public Member Functions inherited from Teuchos::CompObject
	CompObject ()
	Default constructor. More...

	CompObject (const CompObject &source)
	Copy Constructor. More...

virtual	~CompObject ()
	Destructor. More...

void	setFlopCounter (const Flops &FlopCounter)
	Set the internal Teuchos::Flops() pointer. More...

void	setFlopCounter (const CompObject &compObject)
	Set the internal Teuchos::Flops() pointer to the flop counter of another Teuchos::CompObject. More...

void	unsetFlopCounter ()
	Set the internal Teuchos::Flops() pointer to 0 (no flops counted). More...

Flops *	getFlopCounter () const
	Get the pointer to the Teuchos::Flops() object associated with this object, returns 0 if none. More...

void	resetFlops () const
	Resets the number of floating point operations to zero for this multi-std::vector. More...

double	getFlops () const
	Returns the number of floating point operations with this multi-std::vector. More...

void	updateFlops (int addflops) const
	Increment Flop count for this object. More...

void	updateFlops (long int addflops) const
	Increment Flop count for this object. More...

void	updateFlops (double addflops) const
	Increment Flop count for this object. More...

void	updateFlops (float addflops) const
	Increment Flop count for this object. More...

Public Member Functions inherited from Teuchos::BLAS< OrdinalType, ScalarType >
	BLAS (void)
	Default constructor. More...

	BLAS (const BLAS< OrdinalType, ScalarType > &)
	Copy constructor. More...

virtual	~BLAS (void)
	Destructor. More...

Public Member Functions inherited from Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >
	DefaultBLASImpl (void)
	Default constructor. More...

	DefaultBLASImpl (const DefaultBLASImpl< OrdinalType, ScalarType > &)
	Copy constructor. More...

virtual	~DefaultBLASImpl (void)
	Destructor. More...

template<typename alpha_type , typename A_type , typename x_type , typename beta_type >
void	GEMV (ETransp trans, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, const x_type x, const OrdinalType &incx, const beta_type beta, ScalarType *y, const OrdinalType &incy) const
	Performs the matrix-vector operation: `y` `<-` `alphaAx+betay` or `y` `<-` `alphaA'x+betay` where `A` is a general `m` by `n` matrix. More...

template<typename A_type >
void	TRMV (EUplo uplo, ETransp trans, EDiag diag, const OrdinalType &n, const A_type A, const OrdinalType &lda, ScalarType x, const OrdinalType &incx) const
	Performs the matrix-vector operation: `x` `<-` `Ax` or `x` `<-` `A'x` where `A` is a unit/non-unit `n` by `n` upper/lower triangular matrix. More...

template<typename alpha_type , typename x_type , typename y_type >
void	GER (const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const x_type x, const OrdinalType &incx, const y_type y, const OrdinalType &incy, ScalarType *A, const OrdinalType &lda) const
	Performs the rank 1 operation: `A` `<-` `alphaxy'+A`. More...

template<typename alpha_type , typename A_type , typename B_type , typename beta_type >
void	GEMM (ETransp transa, ETransp transb, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const alpha_type alpha, const A_type A, const OrdinalType &lda, const B_type B, const OrdinalType &ldb, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
	General matrix-matrix multiply. More...

void	SWAP (const OrdinalType &n, ScalarType const x, const OrdinalType &incx, ScalarType const y, const OrdinalType &incy) const
	Swap the entries of x and y. More...

template<typename alpha_type , typename A_type , typename B_type , typename beta_type >
void	SYMM (ESide side, EUplo uplo, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, const B_type B, const OrdinalType &ldb, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
	Performs the matrix-matrix operation: `C` `<-` `alphaAB+betaC` or `C` `<-` `alphaBA+betaC` where `A` is an `m` by `m` or `n` by `n` symmetric matrix and `B` is a general matrix. More...

template<typename alpha_type , typename A_type , typename beta_type >
void	SYRK (EUplo uplo, ETransp trans, const OrdinalType &n, const OrdinalType &k, const alpha_type alpha, const A_type A, const OrdinalType &lda, const beta_type beta, ScalarType C, const OrdinalType &ldc) const
	Performs the symmetric rank k operation: `C` <- `alphaAA'+betaC` or `C` <- `alphaA'A+betaC`, where `alpha` and `beta` are scalars, `C` is an `n` by `n` symmetric matrix and `A` is an `n` by `k` matrix in the first case or `k` by `n` matrix in the second case. More...

template<typename alpha_type , typename A_type >
void	TRMM (ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb) const
	Performs the matrix-matrix operation: `B` `<-` `alphaop`(A)B or `B` `<-` `alphaBop`(A) where `op(A)` is an unit/non-unit, upper/lower triangular matrix and `B` is a general matrix. More...

template<typename alpha_type , typename A_type >
void	TRSM (ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb) const
	Solves the matrix equations: `op(A)X=alphaB` or `Xop`(A)=alphaB where `X` and `B` are `m` by `n` matrices, `A` is a unit/non-unit, upper/lower triangular matrix and `op(A)` is `A` or `A'`. The matrix `X` is overwritten on `B`. More...

void	ROTG (ScalarType da, ScalarType db, rotg_c_type c, ScalarType s) const
	Computes a Givens plane rotation. More...

void	ROT (const OrdinalType &n, ScalarType dx, const OrdinalType &incx, ScalarType dy, const OrdinalType &incy, MagnitudeType c, ScalarType s) const
	Applies a Givens plane rotation. More...

void	SCAL (const OrdinalType &n, const ScalarType &alpha, ScalarType *x, const OrdinalType &incx) const
	Scale the vector `x` by the constant `alpha`. More...

void	COPY (const OrdinalType &n, const ScalarType x, const OrdinalType &incx, ScalarType y, const OrdinalType &incy) const
	Copy the vector `x` to the vector `y`. More...

template<typename alpha_type , typename x_type >
void	AXPY (const OrdinalType &n, const alpha_type alpha, const x_type x, const OrdinalType &incx, ScalarType y, const OrdinalType &incy) const
	Perform the operation: `y` `<-` `y+alpha*x`. More...

ScalarTraits< ScalarType > ::magnitudeType	ASUM (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
	Sum the absolute values of the entries of `x`. More...

template<typename x_type , typename y_type >
ScalarType	DOT (const OrdinalType &n, const x_type x, const OrdinalType &incx, const y_type y, const OrdinalType &incy) const
	Form the dot product of the vectors `x` and `y`. More...

ScalarTraits< ScalarType > ::magnitudeType	NRM2 (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
	Compute the 2-norm of the vector `x`. More...

OrdinalType	IAMAX (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
	Return the index of the element of `x` with the maximum magnitude. More...

Related Functions
(Note that these are not member functions.)
template<typename OrdinalType , typename ScalarType >
Teuchos::RCP < SerialBandDenseMatrix < OrdinalType, ScalarType > >	generalToBanded (const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &A, const OrdinalType kl, const OrdinalType ku, const bool factorFormat)
	A templated, non-member, helper function for converting a SerialDenseMatrix to a SerialBandDenseMatrix. More...

template<typename OrdinalType , typename ScalarType >
Teuchos::RCP < SerialDenseMatrix < OrdinalType, ScalarType > >	bandedToGeneral (const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > &AB)
	A templated, non-member, helper function for converting a SerialBandDenseMatrix to a SerialDenseMatrix. More...

Detailed Description

template<typename OrdinalType, typename ScalarType>
class Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >

This class creates and provides basic support for banded dense matrices of templated type.

The Teuchos_SerialBandDenseMatrix class enables the construction and use of banded dense matrices of templated type.

The Teuchos::SerialBandDenseMatrix class is intended to provide full-featured support for solving
linear and eigen system problems for banded 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.

<b>Teuchos::SerialBandDenseMatrix vs. Teuchos::LAPACK</b>

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

When you should use Teuchos::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 Teuchos::LAPACK directly.
When you should use Teuchos::SerialBandDenseMatrix: 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 Teuchos::SerialBandDenseMatrix.

Constructing Teuchos::SerialBandDenseMatrix Objects

There are three Teuchos::SerialBandDenseMatrix 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 Teuchos::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.

Format of the matrix A

The matrix A is stored as a banded matrix AB according to the LAPACK format. Consider using the non-member conversion routines generalToBanded and bandedToGeneral if the full Teuchos::SerialDenseMatrix is already in storage. However, it is more efficient to simply construct the Teuchos::SerialBandDenseMatrix with the desired parameters and use the provided matrix access operators to assign (legal) entries so that the full rectangular matrix does not need to be stored. A full description of the LAPACK banded format can be found at http://www.netlib.org/lapack/lug/node124.html. Briefly, the banded storage format of AB used internally is as follows:

The dimension of AB is KL+KU+1 by N, where KL and KU are the lower and upper bandwidths, respectively.
The entries are stored in a compressed format: AB(KU+i-j,j) = A(i,j) for max(0,j-KU)<=i<=min(M-1,j+KL).

Extracting Data from Teuchos::SerialBandDenseMatrix Objects

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

Multiplication.
Norms.

Definition at line 133 of file Teuchos_SerialBandDenseMatrix.hpp.

Member Typedef Documentation

template<typename OrdinalType, typename ScalarType>

typedef OrdinalType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::ordinalType

Typedef for ordinal type.

Definition at line 138 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

typedef ScalarType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::scalarType

Typedef for scalar type.

Definition at line 140 of file Teuchos_SerialBandDenseMatrix.hpp.

Constructor & Destructor Documentation

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::SerialBandDenseMatrix ( )

Default Constructor.

Creates a empty matrix of no dimension. The Shaping methods should be used to size this matrix. Values of this matrix should be set using the [], (), or = operators.

Definition at line 451 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::SerialBandDenseMatrix	(	OrdinalType	numRows,
		OrdinalType	numCols,
		OrdinalType	kl,
		OrdinalType	ku,
		bool	zeroOut = `true`
	)

Shaped Constructor.

Parameters

numRows	- Number of rows in matrix.
numCols	- Number of columns in matrix.
kl	- Lower bandwidth of matrix.
ku	- Upper bandwidth of matrix.
zeroOut	- Initializes values to 0 if true (default)

Creates a shaped matrix with numRows rows and numCols cols. All values are initialized to 0 when zeroOut is true. Values of this matrix should be set using the [] or the () operators.

Definition at line 465 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::SerialBandDenseMatrix	(	DataAccess	CV,
		ScalarType *	values,
		OrdinalType	stride,
		OrdinalType	numRows,
		OrdinalType	numCols,
		OrdinalType	kl,
		OrdinalType	ku
	)

Shaped Constructor with Values.

Parameters

CV	- Enumerated type set to Teuchos::Copy or Teuchos::View.
values	- Pointer to an array of ScalarType. The first column starts at `values`, the second at `values+stride`, etc.
stride	- The stride between the columns of the matrix in memory.
numRows	- Number of rows in matrix.
numCols	- Number of columns in matrix.
kl	- Lower bandwidth of matrix.
ku	- Upper bandwidth of matrix.

Definition at line 488 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::SerialBandDenseMatrix	(	const SerialBandDenseMatrix< OrdinalType, ScalarType > &	Source,
		ETransp	trans = `Teuchos::NO_TRANS`
	)

Copy Constructor.

Note: A deep copy of the Source transposed can be obtained if trans=Teuchos::TRANS, else a non-transposed copy of Source is made. There is no storage of the transpose state of the matrix within the SerialBandDenseMatrix class, so this information will not propogate to any operation performed on a matrix that has been copy constructed in transpose.

Definition at line 515 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::SerialBandDenseMatrix	(	DataAccess	CV,
		const SerialBandDenseMatrix< OrdinalType, ScalarType > &	Source,
		OrdinalType	numRows,
		OrdinalType	numCols,
		OrdinalType	startCol = `0`
	)

Submatrix Copy Constructor.

Parameters

CV	- Enumerated type set to Teuchos::Copy or Teuchos::View.
Source	- Reference to another dense matrix from which values are to be copied.
numRows	- The number of rows in this matrix.
numCols	- The number of columns in this matrix.
kl	- Lower bandwidth of matrix.
ku	- Upper bandwidth of matrix.
startRow	- The row of `Source` from which the submatrix copy should start.
startCol	- The column of `Source` from which the submatrix copy should start.

Creates a shaped matrix with numRows rows and numCols columns, which is a submatrix of Source. If startRow and startCol are not given, then the submatrix is the leading submatrix of Source. Otherwise, the (1,1) entry in the copied matrix is the (startRow, startCol) entry of Source.

Definition at line 569 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::~SerialBandDenseMatrix ( )

virtual

Destructor.

Definition at line 595 of file Teuchos_SerialBandDenseMatrix.hpp.

Member Function Documentation

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::shape	(	OrdinalType	numRows,
		OrdinalType	numCols,
		OrdinalType	kl,
		OrdinalType	ku
	)

Shape method for changing the size of a SerialBandDenseMatrix, initializing entries to zero.

Parameters

numRows	- The number of rows in this matrix.
numCols	- The number of columns in this matrix.
kl	- Lower bandwidth of matrix.
ku	- Upper bandwidth of matrix.

This method allows the user to define the dimensions of a SerialBandDenseMatrix at any point. This method can be called at any point after construction. Any values previously in this object will be destroyed and the resized matrix starts of with all zero values.

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

Definition at line 605 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::shapeUninitialized	(	OrdinalType	numRows,
		OrdinalType	numCols,
		OrdinalType	kl,
		OrdinalType	ku
	)

Same as shape() except leaves uninitialized.

Definition at line 623 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::reshape	(	OrdinalType	numRows,
		OrdinalType	numCols,
		OrdinalType	kl,
		OrdinalType	ku
	)

Reshaping method for changing the size of a SerialBandDenseMatrix, keeping the entries.

Parameters

numRows	- The number of rows in this matrix.
numCols	- The number of columns in this matrix.
kl	- Lower bandwidth of matrix.
ku	- Upper bandwidth of matrix.

This method allows the user to redefine the dimensions of a SerialBandDenseMatrix at any point. This method can be called at any point after construction. Any values previously in this object will be copied into the reshaped matrix.

Returns: Integer error code, set 0 if successful.

Definition at line 640 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

SerialBandDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator= ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & Source )

Copies values from one matrix to another.

The operator= copies the values from one existing SerialBandDenseMatrix to another. If Source is a view (i.e. CV = Teuchos::View), then this method will return a view. Otherwise, it will return a copy of Source. this object will be resized if it is not large enough to copy Source into.

Definition at line 703 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

SerialBandDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::assign ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & Source )

Copies values from one matrix to another.

The operator= copies the values from one existing SerialBandDenseMatrix to another if the dimension of both matrices are the same. If not, this matrix will be returned unchanged.

Definition at line 795 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

SerialBandDenseMatrix<OrdinalType, ScalarType>& Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator= ( const ScalarType value )

inline

Set all values in the matrix to a constant value.

Parameters

value - Value to use;

Definition at line 268 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::putScalar ( const ScalarType value = Teuchos::ScalarTraits<ScalarType>::zero() )

Set all values in the matrix to a constant value.

Parameters

value - Value to use; zero if none specified.

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

Definition at line 674 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::random ( )

Set all values in the matrix to be random numbers.

Definition at line 688 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

ScalarType & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator()	(	OrdinalType	rowIndex,
		OrdinalType	colIndex
	)

inline

Element access method (non-const).

Returns the element in the ith row and jth column if A(i,j) is specified, the expression A[j][i] will return the same element.

Returns: Element from the specified rowIndex row and colIndex column.

Warning: The validity of rowIndex and colIndex will only be checked if Teuchos is configured with –enable-teuchos-abc.

Definition at line 816 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

const ScalarType & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator()	(	OrdinalType	rowIndex,
		OrdinalType	colIndex
	)		const

inline

Element access method (const).

Returns the element in the ith row and jth column if A(i,j) is specified, the expression A[j][i] will return the same element.

Returns: Element from the specified rowIndex row and colIndex column.

Warning: The validity of rowIndex and colIndex will only be checked if Teuchos is configured with –enable-teuchos-abc.

Definition at line 825 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

ScalarType * Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator[] ( OrdinalType colIndex )

inline

Column access method (non-const).

Returns the pointer to the ScalarType array at the jth column if A[j] is specified, the expression A[j][i] will return the same element as A(i,j).

Returns: Pointer to the ScalarType array at the colIndex column ( values_+colIndex*stride_ ).

Warning: The validity of colIndex will only be checked if Teuchos is configured with –enable-teuchos-abc.

Definition at line 843 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

const ScalarType * Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator[] ( OrdinalType colIndex ) const

inline

Column access method (const).

Returns the pointer to the ScalarType array at the jth column if A[j] is specified, the expression A[j][i] will return the same element as A(i,j).

Returns: Pointer to the ScalarType array at the colIndex column ( values_+colIndex*stride_ ).

Warning: The validity of colIndex will only be checked if Teuchos is configured with –enable-teuchos-abc.

Definition at line 834 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

ScalarType* Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::values ( ) const

inline

Data array access method.

Returns: Pointer to the ScalarType data array contained in the object.

Definition at line 327 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

SerialBandDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator+= ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & Source )

Add another matrix to this matrix.

Add Source to this if the dimension of both matrices are the same. If not, this matrix will be returned unchanged.

Definition at line 769 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

SerialBandDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator-= ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & Source )

Subtract another matrix from this matrix.

Subtract Source from this if the dimension of both matrices are the same. If not, this matrix will be returned unchanged.

Definition at line 782 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

SerialBandDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator*= ( const ScalarType alpha )

Scale this matrix by alpha; *this = alpha**this.

Parameters

alpha Scalar to multiply this by.

Definition at line 950 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::scale ( const ScalarType alpha )

Scale this matrix by alpha; *this = alpha**this.

Parameters

alpha Scalar to multiply this by.

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

Definition at line 957 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::scale ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & A )

Point-wise scale this matrix by A; i.e. *this(i,j) *= A(i,j)

The values of *this matrix will be point-wise scaled by the values in A. If A and this matrix are not the same dimension this will be returned unchanged.

Parameters

B	Teuchos::SerialBandDenseMatrix used to perform element-wise scaling of this.

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

Definition at line 975 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

bool Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator== ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & Operand ) const

Equality of two matrices.

Returns: True if this matrix and Operand are of the same shape (rows and columns) and have the same entries, else False will be returned.

Definition at line 919 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

bool Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::operator!= ( const SerialBandDenseMatrix< OrdinalType, ScalarType > & Operand ) const

Inequality of two matrices.

Returns: True if this matrix and Operand of not of the same shape (rows and columns) or don't have the same entries, else False will be returned.

Definition at line 940 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::numRows ( ) const

inline

Returns the row dimension of this matrix.

Definition at line 391 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::numCols ( ) const

inline

Returns the column dimension of this matrix.

Definition at line 394 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::lowerBandwidth ( ) const

inline

Returns the lower bandwidth of this matrix.

Definition at line 397 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::upperBandwidth ( ) const

inline

Returns the upper bandwidth of this matrix.

Definition at line 400 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::stride ( ) const

inline

Returns the stride between the columns of this matrix in memory.

Definition at line 403 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::empty ( ) const

inline

Returns whether this matrix is empty.

Definition at line 406 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

ScalarTraits< ScalarType >::magnitudeType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::normOne ( ) const

Returns the 1-norm of the matrix.

Definition at line 856 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

ScalarTraits< ScalarType >::magnitudeType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::normInf ( ) const

Returns the Infinity-norm of the matrix.

Definition at line 880 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

ScalarTraits< ScalarType >::magnitudeType Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::normFrobenius ( ) const

Returns the Frobenius-norm of the matrix.

Definition at line 898 of file Teuchos_SerialBandDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >

std::ostream & Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >::print ( std::ostream & os ) const

virtual

Print method. Defines the behavior of the std::ostream << operator.

Definition at line 997 of file Teuchos_SerialBandDenseMatrix.hpp.

Friends And Related Function Documentation

template<typename OrdinalType , typename ScalarType >

Teuchos::RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > generalToBanded	(	const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &	A,
		const OrdinalType	kl,
		const OrdinalType	ku,
		const bool	factorFormat
	)

Parameters

A	- [in] SerialDenseMatrix to be converted
kl	- [in] Integer indicating desired lower bandwidth of band matrix.
ku	- [in] Integer indicating desired upper bandwidth of band matrix.
factorFormat	- [in] Bool indicating whether kl extra superdiagonals should be stored to be used by factorization.

Note: The syntax for calling this function is: Teuchos::SerialBandDenseMatrix<int,double> AB = Teuchos::generalToBanded<int,double>( A, kl, ku, true )

Definition at line 228 of file Teuchos_SerialDenseHelpers.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::RCP< SerialDenseMatrix< OrdinalType, ScalarType > > bandedToGeneral ( const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > & AB )

Parameters

A	- [in] SerialBandDenseMatrix to be converted

Note: The syntax for calling this function is: Teuchos::SerialDenseMatrix<int,double> A = Teuchos::bandedToGeneral<int,double>( AB )

Definition at line 264 of file Teuchos_SerialDenseHelpers.hpp.

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

Public Types

Public Member Functions

Related Functions

Detailed Description

template<typename OrdinalType, typename ScalarType> class Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename OrdinalType, typename ScalarType>
class Teuchos::SerialBandDenseMatrix< OrdinalType, ScalarType >