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Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType > Class Template Reference

This class creates and provides basic support for symmetric, positive-definite dense matrices of templated type. More...

#include <Teuchos_SerialSymDenseMatrix.hpp>

Inheritance diagram for Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >:
Teuchos::CompObject Teuchos::Object Teuchos::BLAS< OrdinalType, ScalarType > Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >

List of all members.

Public Types

typedef OrdinalType ordinalType
 Typedef for ordinal type.
typedef ScalarType scalarType
 Typedef for scalar type.

Public Member Functions

Constructor/Destructor Methods
 SerialSymDenseMatrix ()
 Default constructor; defines a zero size object.
 SerialSymDenseMatrix (OrdinalType numRowsCols, bool zeroOut=true)
 Basic constructor; defines a matrix of numRowsCols size and (optionally) initializes it.
 SerialSymDenseMatrix (DataAccess CV, bool upper, ScalarType *values, OrdinalType stride, OrdinalType numRowsCols)
 Set object values from two-dimensional array.
 SerialSymDenseMatrix (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Source)
 Teuchos::SerialSymDenseMatrix copy constructor.
 SerialSymDenseMatrix (DataAccess CV, const SerialSymDenseMatrix< OrdinalType, ScalarType > &Source, OrdinalType numRowCols, OrdinalType startRowCol=0)
 Submatrix Copy Constructor.
virtual ~SerialSymDenseMatrix ()
 Teuchos::SerialSymDenseMatrix destructor.
Shaping Methods
int shape (OrdinalType numRowsCols)
 Set dimensions of a Teuchos::SerialSymDenseMatrix object; init values to zero.
int shapeUninitialized (OrdinalType numRowsCols)
 Set dimensions of a Teuchos::SerialSymDenseMatrix object; don't initialize values.
int reshape (OrdinalType numRowsCols)
 Reshape a Teuchos::SerialSymDenseMatrix object.
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.
Set methods.
SerialSymDenseMatrix
< OrdinalType, ScalarType > & 
operator= (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Source)
 Copies values from one matrix to another.
SerialSymDenseMatrix
< OrdinalType, ScalarType > & 
assign (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Source)
 Copies values from one matrix to another.
SerialSymDenseMatrix
< OrdinalType, ScalarType > & 
operator= (const ScalarType value)
 Set all values in the matrix to a constant value.
int putScalar (const ScalarType value=Teuchos::ScalarTraits< ScalarType >::zero(), bool fullMatrix=false)
 Set all values in the matrix to a constant value.
int random (const ScalarType bias=0.1 *Teuchos::ScalarTraits< ScalarType >::one())
 Set all values in the active area (upper/lower triangle) of this matrix to be random numbers.
Accessor methods.
ScalarType & operator() (OrdinalType rowIndex, OrdinalType colIndex)
 Element access method (non-const).
const ScalarType & operator() (OrdinalType rowIndex, OrdinalType colIndex) const
 Element access method (const).
ScalarType * values () const
 Returns the pointer to the ScalarType data array contained in the object.
Query methods
bool upper () const
 Returns true if upper triangular part of this matrix has and will be used.
char UPLO () const
 Returns character value of UPLO used by LAPACK routines.
Mathematical Methods
SerialSymDenseMatrix
< OrdinalType, ScalarType > & 
operator*= (const ScalarType alpha)
 Inplace scalar-matrix product A = alpha*A.
SerialSymDenseMatrix
< OrdinalType, ScalarType > & 
operator+= (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Source)
 Add another matrix to this matrix.
SerialSymDenseMatrix
< OrdinalType, ScalarType > & 
operator-= (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Source)
 Subtract another matrix from this matrix.
Comparison methods.
bool operator== (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Operand) const
 Equality of two matrices.
bool operator!= (const SerialSymDenseMatrix< OrdinalType, ScalarType > &Operand) const
 Inequality of two matrices.
Attribute methods.
OrdinalType numRows () const
 Returns the row dimension of this matrix.
OrdinalType numCols () const
 Returns the column dimension of this matrix.
OrdinalType stride () const
 Returns the stride between the columns of this matrix in memory.
bool empty () const
 Returns whether this matrix is empty.
Norm methods.
ScalarTraits< ScalarType >
::magnitudeType 
normOne () const
 Returns the 1-norm of the matrix.
ScalarTraits< ScalarType >
::magnitudeType 
normInf () const
 Returns the Infinity-norm of the matrix.
ScalarTraits< ScalarType >
::magnitudeType 
normFrobenius () const
 Returns the Frobenius-norm of the matrix.
I/O methods.
virtual void print (std::ostream &os) const
 Print method. Defines the behavior of the std::ostream << operator inherited from the Object class.

Related Functions

(Note that these are not member functions.)

template<typename OrdinalType , typename ScalarType >
void symMatTripleProduct (ETransp transw, const ScalarType alpha, const SerialSymDenseMatrix< OrdinalType, ScalarType > &A, const SerialDenseMatrix< OrdinalType, ScalarType > &W, SerialSymDenseMatrix< OrdinalType, ScalarType > &B)
 A templated, non-member, helper function for computing the matrix triple-product: B = alpha*W^T*A*W or B = alpha*W*A*W^T.

Detailed Description

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

This class creates and provides basic support for symmetric, positive-definite dense matrices of templated type.

The Teuchos_SerialSymDenseMatrix class enables the construction and use of symmetric, positive-definite, dense matrices of templated type.

The Teuchos::SerialSymDenseMatrix class is intended to provide full-featured support for solving linear and eigen system problems for symmetric positive-definite (SPD) 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.

Teuchos::SerialSymDenseMatrix vs. Teuchos::LAPACK

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

Constructing Teuchos::SerialSymDenseMatrix Objects

There are three Teuchos::SerialSymDenseMatrix 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):

  1. Copy mode - Allocates memory and makes a copy of the user-provided data. In this case, the user data is not needed after construction.
  2. 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 Teuchos::SerialSymDenseMatrix Objects

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

Examples:

DenseMatrix/cxx_main_sym.cpp.

Definition at line 121 of file Teuchos_SerialSymDenseMatrix.hpp.


Member Typedef Documentation

template<typename OrdinalType, typename ScalarType>
typedef OrdinalType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::ordinalType

Typedef for ordinal type.

Definition at line 126 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
typedef ScalarType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::scalarType

Typedef for scalar type.

Definition at line 128 of file Teuchos_SerialSymDenseMatrix.hpp.


Constructor & Destructor Documentation

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::SerialSymDenseMatrix ( )

Default constructor; defines a zero size object.

Teuchos::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 the lower triangular part. To set the upper part as active, call SetUpper(). See Detailed Description section for further discussion.

Definition at line 433 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::SerialSymDenseMatrix ( OrdinalType  numRowsCols,
bool  zeroOut = true 
)

Basic constructor; defines a matrix of numRowsCols size and (optionally) initializes it.

Parameters:
numRowsCols- Number of rows and columns in the matrix.
zeroOut- Initializes values to 0 if true (default)

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

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

Definition at line 438 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::SerialSymDenseMatrix ( DataAccess  CV,
bool  upper,
ScalarType *  values,
OrdinalType  stride,
OrdinalType  numRowsCols 
)

Set object values from two-dimensional array.

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

Definition at line 448 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::SerialSymDenseMatrix ( const SerialSymDenseMatrix< OrdinalType, ScalarType > &  Source)

Teuchos::SerialSymDenseMatrix copy constructor.

Definition at line 469 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::SerialSymDenseMatrix ( DataAccess  CV,
const SerialSymDenseMatrix< OrdinalType, ScalarType > &  Source,
OrdinalType  numRowCols,
OrdinalType  startRowCol = 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.
numRowCols- The number of rows and columns in this matrix.
startRowCol- The row and column of Source from which the submatrix copy should start.

Creates a shaped matrix with numRowCols rows and columns, which is a submatrix of Source. If startRowCol are not given, then the submatrix is the leading submatrix of Source.

Definition at line 477 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::~SerialSymDenseMatrix ( ) [virtual]

Teuchos::SerialSymDenseMatrix destructor.

Definition at line 496 of file Teuchos_SerialSymDenseMatrix.hpp.


Member Function Documentation

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::shape ( OrdinalType  numRowsCols)

Set dimensions of a Teuchos::SerialSymDenseMatrix object; init values to zero.

Parameters:
numRowsCols- Number of rows and columns in object.

Allows user to define the dimensions of a Teuchos::SerialSymDenseMatrix 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.

Definition at line 506 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::shapeUninitialized ( OrdinalType  numRowsCols)

Set dimensions of a Teuchos::SerialSymDenseMatrix object; don't initialize values.

Parameters:
numRowsCols- Number of rows and columns in object.

Allows user to define the dimensions of a Teuchos::SerialSymDenseMatrix at any point. This function can be called at any point after construction. Any values that were previously in this object are destroyed. The resized matrix has uninitialized values.

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

Definition at line 518 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::reshape ( OrdinalType  numRowsCols)

Reshape a Teuchos::SerialSymDenseMatrix object.

Parameters:
numRowsCols- Number of rows and columns in object.

Allows user to define the dimensions of a Teuchos::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.

Definition at line 529 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::setLower ( )

Specify that the lower triangle of the this matrix should be used.

Warning:
This may necessitate the matrix values be copied from the upper to lower portion of the matrix.

Definition at line 556 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::setUpper ( )

Specify that the upper triangle of the this matrix should be used.

Warning:
This may necessitate the matrix values be copied from the lower to upper portion of the matrix.

Definition at line 567 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
SerialSymDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::operator= ( const SerialSymDenseMatrix< OrdinalType, ScalarType > &  Source)

Copies values from one matrix to another.

The operator= copies the values from one existing SerialSymDenseMatrix 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 645 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
SerialSymDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::assign ( const SerialSymDenseMatrix< OrdinalType, ScalarType > &  Source)

Copies values from one matrix to another.

Copies the values from one existing SerialSymDenseMatrix to another if the dimension of both matrices are the same. If not, this matrix will be returned unchanged.

Definition at line 739 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
SerialSymDenseMatrix<OrdinalType, ScalarType>& Teuchos::SerialSymDenseMatrix< 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 264 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::putScalar ( const ScalarType  value = Teuchos::ScalarTraits<ScalarType>::zero(),
bool  fullMatrix = false 
)

Set all values in the matrix to a constant value.

Parameters:
value- Value to use; zero if none specified.
fullMatrix- set full matrix entries to value, not just active portion of symmetric matrix.
Returns:
Integer error code, set to 0 if successful.

Definition at line 578 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::random ( const ScalarType  bias = 0.1*Teuchos::ScalarTraits<ScalarType>::one())

Set all values in the active area (upper/lower triangle) of this matrix to be random numbers.

Note:
The diagonal will be the sum of the off diagonal elements, plus a bias, so the matrix is SPD.

Definition at line 611 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
ScalarType & Teuchos::SerialSymDenseMatrix< 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.

Returns:
Element from the specified rowIndex row and colIndex column.
Note:
If the requested element lies in the inactive part of the matrix, then A(j,i) will be returned.
Warning:
The validity of rowIndex and colIndex will only be checked if Teuchos is configured with --enable-teuchos-abc.

Definition at line 761 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
const ScalarType & Teuchos::SerialSymDenseMatrix< 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.

Returns:
Element from the specified rowIndex row and colIndex column.
Note:
If the requested element lies in the inactive part of the matrix, then A(j,i) will be returned.
Warning:
The validity of rowIndex and colIndex will only be checked if Teuchos is configured with --enable-teuchos-abc.

Definition at line 783 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
ScalarType* Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::values ( ) const [inline]

Returns the pointer to the ScalarType data array contained in the object.

Note:
The matrix values are only guaranteed to be stored in the active area of the matrix (upper/lower).

Definition at line 307 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::upper ( ) const [inline]

Returns true if upper triangular part of this matrix has and will be used.

Definition at line 315 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
char Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::UPLO ( ) const [inline]

Returns character value of UPLO used by LAPACK routines.

Definition at line 318 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
SerialSymDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::operator*= ( const ScalarType  alpha)

Inplace scalar-matrix product A = alpha*A.

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

Parameters:
alpha- Scalar to multiply with A.

Definition at line 708 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
SerialSymDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::operator+= ( const SerialSymDenseMatrix< 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 715 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
SerialSymDenseMatrix< OrdinalType, ScalarType > & Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::operator-= ( const SerialSymDenseMatrix< 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 727 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
bool Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::operator== ( const SerialSymDenseMatrix< OrdinalType, ScalarType > &  Operand) const

Equality of two matrices.

Returns:
True if this matrix and Operand are of the same shape (rows / columns) and have the same entries in the active (upper / lower triangular) area of the matrix, else False will be returned.

Definition at line 891 of file Teuchos_SerialSymDenseMatrix.hpp.

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

Inequality of two matrices.

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

Definition at line 911 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::numRows ( ) const [inline]

Returns the row dimension of this matrix.

Definition at line 368 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::numCols ( ) const [inline]

Returns the column dimension of this matrix.

Definition at line 371 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::stride ( ) const [inline]

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

Definition at line 374 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::empty ( ) const [inline]

Returns whether this matrix is empty.

Definition at line 377 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
ScalarTraits< ScalarType >::magnitudeType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::normOne ( ) const

Returns the 1-norm of the matrix.

Definition at line 809 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
ScalarTraits< ScalarType >::magnitudeType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::normInf ( ) const

Returns the Infinity-norm of the matrix.

Definition at line 815 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
ScalarTraits< ScalarType >::magnitudeType Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::normFrobenius ( ) const

Returns the Frobenius-norm of the matrix.

Definition at line 858 of file Teuchos_SerialSymDenseMatrix.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialSymDenseMatrix< OrdinalType, ScalarType >::print ( std::ostream &  os) const [virtual]

Print method. Defines the behavior of the std::ostream << operator inherited from the Object class.

Reimplemented from Teuchos::Object.

Definition at line 970 of file Teuchos_SerialSymDenseMatrix.hpp.


Friends And Related Function Documentation

template<typename OrdinalType , typename ScalarType >
void symMatTripleProduct ( ETransp  transw,
const ScalarType  alpha,
const SerialSymDenseMatrix< OrdinalType, ScalarType > &  A,
const SerialDenseMatrix< OrdinalType, ScalarType > &  W,
SerialSymDenseMatrix< OrdinalType, ScalarType > &  B 
) [related]

A templated, non-member, helper function for computing the matrix triple-product: B = alpha*W^T*A*W or B = alpha*W*A*W^T.

Parameters:
transw- [in] Compute B = alpha*W^T*A*W if transw = Teuchos::TRANS, else compute B = alpha*W*A*W^T if transw = Teuchos::NO_TRANS.
alpha- [in] The scaling factor.
A- [in] SerialSymDenseMatrix
W- [in] SerialDenseMatrix
B- [out] SerialSymDenseMatrix
Note:
The syntax for calling this function is: Teuchos::symMatTripleProduct<int,double>( Teuchos::TRANS, alpha, A, W, B )

Definition at line 72 of file Teuchos_SerialDenseHelpers.hpp.


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