RWSymBandMat< TypeT > Class Template Reference
[Sparse Matrices]

Encapsulates a symmetric band matrix. More...

#include <rw/lapack/sbndmat.h>

Public Member Functions
	RWSymBandMat ()
	RWSymBandMat (const RWSymBandMat< TypeT > &A)
	RWSymBandMat (unsigned n, unsigned nAgain, unsigned hb)
	RWSymBandMat (const RWMathVec< TypeT > &vd, unsigned n, unsigned nAgain, unsigned hb)
	RWSymBandMat (const RWSymBandMat< double > &re, const RWSymBandMat< double > &im)
unsigned	rows () const
unsigned	cols () const
unsigned	bandwidth () const
unsigned	halfBandwidth () const
unsigned	lowerBandwidth () const
unsigned	upperBandwidth () const
TypeT	val (int i, int j) const
TypeT	set (int i, int j, TypeT x)
RWRORef< TypeT >	ref (int i, int j)
TypeT	bcval (int i, int j) const
TypeT	bcset (int i, int j, TypeT x)
RWRORef< TypeT >	bcref (int i, int j)
RWSymBandMat< TypeT >	leadingSubmatrix (int k)
RWMathVec< TypeT >	diagonal (int j=0) const
RWMathVec< TypeT >	bcdiagonal (int j=0) const
RWSymBandMat< TypeT > &	reference (RWSymBandMat< TypeT > &m)
void	zero ()
RWSymBandMat< TypeT >	copy () const
RWSymBandMat< TypeT >	deepCopy () const
void	deepenShallowCopy ()
RWMathVec< TypeT >	dataVec ()
TypeT *	data ()
void	resize (unsigned m, unsigned n)
void	resize (unsigned n, unsigned nAgain, unsigned halfWidth)
void	scanFrom (std::istream &)
void	printOn (std::ostream &) const
void	restoreFrom (RWvistream &)
void	saveOn (RWvostream &) const
void	restoreFrom (RWFile &)
void	saveOn (RWFile &) const
unsigned	binaryStoreSize () const
RWRORef< TypeT >	operator() (int i, int j)
TypeT	operator() (int i, int j) const
bool	operator== (const RWSymBandMat< TypeT > &X)
bool	operator!= (const RWSymBandMat< TypeT > &X)
RWSymBandMat< TypeT > &	operator= (const RWSymBandMat< TypeT > &A)
RWSymBandMat< TypeT > &	operator+= (const RWSymBandMat< TypeT > &m)
RWSymBandMat< TypeT > &	operator-= (const RWSymBandMat< TypeT > &m)
RWSymBandMat< TypeT > &	operator*= (const RWSymBandMat< TypeT > &m)
RWSymBandMat< TypeT > &	operator*= (TypeT)
RWSymBandMat< TypeT > &	operator/= (const RWSymBandMat< TypeT > &m)
RWSymBandMat< TypeT > &	operator/= (TypeT)
Related Functions
(Note that these are not member functions.)
template<class TypeT >
RWSymBandMat< TypeT >	operator- (const RWSymBandMat< TypeT > &)
template<class TypeT >
RWSymBandMat< TypeT >	operator+ (const RWSymBandMat< TypeT > &)
template<class TypeT >
RWSymBandMat< TypeT >	operator* (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &)
template<class TypeT >
RWSymBandMat< TypeT >	operator/ (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &)
template<class TypeT >
RWSymBandMat< TypeT >	operator+ (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &)
template<class TypeT >
RWSymBandMat< TypeT >	operator- (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &)
template<class TypeT >
RWSymBandMat< TypeT >	operator* (const RWSymBandMat< TypeT > &A, TypeT x)
template<class TypeT >
RWSymBandMat< TypeT >	operator* (TypeT x, const RWSymBandMat< TypeT > &A)
template<class TypeT >
RWSymBandMat< TypeT >	operator/ (const RWSymBandMat< TypeT > &A, TypeT x)
template<class TypeT >
std::ostream &	operator<< (std::ostream &s, const RWSymBandMat< TypeT > &m)
template<class TypeT >
std::istream &	operator>> (std::istream &s, RWSymBandMat< TypeT > &m)
template<class TypeT >
RWSymBandMat< TypeT >	transpose (const RWSymBandMat< TypeT > &)
template<class TypeT >
RWMathVec< TypeT >	product (const RWSymBandMat< TypeT > &A, const RWMathVec< TypeT > &x)
template<class TypeT >
RWMathVec< TypeT >	product (const RWMathVec< TypeT > &x, const RWSymBandMat< TypeT > &A)
template<class TypeT >
RWSymBandMat< typename rw_numeric_traits< TypeT > ::norm_type >	abs (const RWSymBandMat< TypeT > &A)
RWSymBandMat< DComplex >	conj (const RWSymBandMat< DComplex > &A)
RWSymBandMat< double >	real (const RWSymBandMat< DComplex > &A)
RWSymBandMat< double >	imag (const RWSymBandMat< DComplex > &A)
RWSymBandMat< double >	norm (const RWSymBandMat< DComplex > &A)
RWSymBandMat< double >	arg (const RWSymBandMat< DComplex > &A)
double	minValue (const RWSymBandMat< double > &A)
double	maxValue (const RWSymBandMat< double > &A)
float	minValue (const RWSymBandMat< float > &A)
float	maxValue (const RWSymBandMat< float > &A)
template<class TypeT >
RWSymBandMat< TypeT >	toSymBandMat (const RWBandMat< TypeT > &A)

Detailed Description

template<class TypeT>
class RWSymBandMat< TypeT >

The class RWSymBandMat<T> encapsulates symmetric band matrices. A symmetric banded matrix is symmetric, and nonzero only near the diagonal. Specifically, if h is the half bandwidth, then any entries for which $ i-j > h $ or $ j-i > h $ are defined to be 0; in addition, an entry $A_{ij} = A_{ji}$ .

Synopsis

 #include <rw/lapack/sbndmat.h>
 
 RWSymBandMat<double> d;

Example

 #include <rw/lapack/sbndmat.h>
 
 int main()
 {
     RWSymBandMat<float> SB(4,4,1);
     SB.diagonal(-1) = -1;
     SB.diagonal( ) = 0;
     SB.diagonal( 1) = 1;
 }

Storage Scheme

As an example of the storage scheme, consider the following 9 x 9 matrix with a half bandwidth of two:

$\begin{bmatrix} & A_{11} & A_{12} & A_{13} & 0 & 0 & 0 & 0 & 0 & 0 \\ & A_{12} & A_{22} & A_{23} & A_{24} & 0 & 0 & 0 & 0 & 0 \\ & A_{13} & A_{23} & A_{33} & A_{34} & A_{35} & 0 & 0 & 0 & 0 \\ & 0 & A_{24} & A_{34} & A_{44} & A_{45} & A_{46} & 0 & 0 & 0 \\ & 0 & 0 & A_{35} & A_{45} & A_{55} & A_{56} & A_{57} & 0 & 0 \\ & 0 & 0 & 0 & A_{46} & A_{56} & A_{66} & A_{67} & A_{68} & 0 \\ & 0 & 0 & 0 & 0 & A_{57} & A_{67} & A_{77} & A_{78} & A_{79} \\ & 0 & 0 & 0 & 0 & 0 & A_{68} & A_{78} & A_{88} & A_{89} \\ & 0 & 0 & 0 & 0 & 0 & 0 & A_{79} & A_{89} & A_{99} \\ \end{bmatrix}$

The upper triangle is stored column by column. For convenience, there are some unused locations left in the vector of data. These are indicated as XXX in the following illustration of the storage vector:

[ XXX XXX A₁₁ XXX A₁₂ A₂₂ A₁₃ A₂₃ A₃₃ A₂₄ A₃₄ A₄₄ A₃₅ A₄₅ A₅₅ A₄₆ A₅₆ A₆₆ A₅₇ A₆₇ A₇₇ A₆₈ A₇₈ A₈₈ A₇₉ A₈₉ A₉₉ ]

The mapping between the array and storage vector is as follows:

$A(i + 1, j + 1) \to \left\{ \begin{array}{l l} \text{vec}[i + \text{halfwidth} + j*\text{halfwidth}] & \quad \text{if } j \geq i \\ \text{vec}[j + \text{halfwidth} + i*\text{halfwidth}] & \quad \text{if } j < i \\ \end{array} \right.$

Constructor & Destructor Documentation

template<class TypeT>

RWSymBandMat< TypeT >::RWSymBandMat ( )

Default constructor. Builds a matrix of size 0 x 0. This constructor is necessary to declare a matrix with no explicit constructor or to declare an array of matrices.

template<class TypeT>

RWSymBandMat< TypeT >::RWSymBandMat ( const RWSymBandMat< TypeT > & A )

Build a copy of its argument, A. Note that the new matrix references A's data. To construct a matrix with its own copy of the data, you can use either the copy() or deepenShallowCopy() member functions.

template<class TypeT>

RWSymBandMat< TypeT >::RWSymBandMat	(	unsigned	n,
		unsigned	nAgain,
		unsigned	hb
	)

Defines an uninitialized matrix of size n x nAgain with half bandwidth hb.

template<class TypeT>

RWSymBandMat< TypeT >::RWSymBandMat	(	const RWMathVec< TypeT > &	vd,
		unsigned	n,
		unsigned	nAgain,
		unsigned	hb
	)

Constructs an n x nAgain matrix with half bandwidth hb using the data in the passed vector. This data must be stored in the format described in the Storage Scheme section. The resultant matrix references the data in vector vd.

template<class TypeT>

RWSymBandMat< TypeT >::RWSymBandMat	(	const RWSymBandMat< double > &	re,
		const RWSymBandMat< double > &	im
	)

Constructs a complex matrix from the real and imaginary parts supplied. If no imaginary part is supplied, it is assumed to be 0.

Member Function Documentation

template<class TypeT>

unsigned RWSymBandMat< TypeT >::bandwidth ( ) const [inline]

Returns the bandwidth of the matrix. The bandwidth is twice the half bandwidth plus 1 for the main diagonal.

template<class TypeT>

RWMathVec<TypeT> RWSymBandMat< TypeT >::bcdiagonal ( int j = 0 ) const

Returns a reference to the j ^th diagonal of the matrix, after doing bounds checking. The main diagonal is indexed by 0, diagonals in the upper triangle are indexed with positive integers, diagonals in the lower triangle are indexed with negative integers.

template<class TypeT>

RWRORef<TypeT> RWSymBandMat< TypeT >::bcref	(	int	i,
		int	j
	)

Returns a reference to the ij ^th element of the matrix, after doing bounds checking.

template<class TypeT>

TypeT RWSymBandMat< TypeT >::bcset	(	int	i,
		int	j,
		TypeT	x
	)

Sets the ij ^th element of the matrix equal to x, after doing bounds checking.

template<class TypeT>

TypeT RWSymBandMat< TypeT >::bcval	(	int	i,
		int	j
	)			const

Returns the value of the ij ^th element of the matrix, after doing bounds checking.

template<class TypeT>

unsigned RWSymBandMat< TypeT >::binaryStoreSize ( ) const

Returns the number of bytes that it would take to write the matrix to a file using saveOn().

template<class TypeT>

unsigned RWSymBandMat< TypeT >::cols ( ) const [inline]

Returns the number of columns in the matrix.

template<class TypeT>

RWSymBandMat<TypeT> RWSymBandMat< TypeT >::copy ( ) const

Creates a copy of this matrix with distinct data. The stride of the data vector in the new matrix is guaranteed to be 1.

template<class TypeT>

TypeT* RWSymBandMat< TypeT >::data ( void ) [inline]

Returns a pointer to the first item of data in the vector storing the matrix's data. You can use this (with caution!) to pass the matrix's data to C or FORTRAN subroutines. Be aware that the stride of the data vector may not be 1.

template<class TypeT>

RWMathVec<TypeT> RWSymBandMat< TypeT >::dataVec ( ) [inline]

Returns the matrix's data vector. This is where the explicitly stored entries in the matrix are kept.

template<class TypeT>

RWSymBandMat<TypeT> RWSymBandMat< TypeT >::deepCopy ( ) const [inline]

Creates a copy of this matrix with distinct data. The stride of the data vector in the new matrix is guaranteed to be 1.

template<class TypeT>

void RWSymBandMat< TypeT >::deepenShallowCopy ( ) [inline]

Ensures that the data in the matrix is not shared by any other matrix or vector. Also ensure that the stride in the data vector is equal to 1. If necessary, a new copy of the data vector is made.

template<class TypeT >

RWMathVec< TypeT > RWSymBandMat< TypeT >::diagonal ( int j = 0 ) const [inline]

Returns a reference to the j ^th diagonal of the matrix. The main diagonal is indexed by 0, diagonals in the upper triangle are indexed with positive integers, and diagonals in the lower triangle are indexed with negative integers. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK is defined when the header file is read. The member function bcdiagonal() does the same thing with guaranteed bounds checking.

template<class TypeT>

unsigned RWSymBandMat< TypeT >::halfBandwidth ( ) const [inline]

Returns the half bandwidth of the matrix.

template<class TypeT>

RWSymBandMat<TypeT> RWSymBandMat< TypeT >::leadingSubmatrix ( int k )

Returns the k x k upper left corner of the matrix. The submatrix and the matrix share the same data.

template<class TypeT>

unsigned RWSymBandMat< TypeT >::lowerBandwidth ( ) const [inline]

Returns the lower bandwidth of the matrix.

template<class TypeT>

bool RWSymBandMat< TypeT >::operator!= ( const RWSymBandMat< TypeT > & X ) [inline]

Two matrices are considered equal if they have the same size and their elements are all exactly the same. Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.

template<class TypeT >

TypeT RWSymBandMat< TypeT >::operator()	(	int	i,
		int	j
	)			const `[inline]`

Accesses the ij ^th element. Using this operator is equivalent to calling the val() member function. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK is defined before including the header file.

template<class TypeT >

RWRORef< TypeT > RWSymBandMat< TypeT >::operator()	(	int	i,
		int	j
	)			`[inline]`

Returns a reference to the ij ^th element of the matrix. Using this operator is equivalent to calling the ref() member function. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK is defined before including the header file.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator*= ( TypeT )

Performs the indicated operation on each element of the matrix.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator*= ( const RWSymBandMat< TypeT > & m )

Performs element-by-element arithmetic on the data in the matrices.

Note:: operator*=() does element-by-element multiplication, not inner product style matrix multiplication. You can use the product() global function to do matrix-matrix inner product multiplication.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator+= ( const RWSymBandMat< TypeT > & m )

Performs element-by-element arithmetic on the data in the matrices.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator-= ( const RWSymBandMat< TypeT > & m )

Performs element-by-element arithmetic on the data in the matrices.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator/= ( TypeT )

Performs the indicated operation on each element of the matrix.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator/= ( const RWSymBandMat< TypeT > & m )

Performs element-by-element arithmetic on the data in the matrices.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator= ( const RWSymBandMat< TypeT > & A )

Sets the matrix elements equal to the elements of A. The two matrices must be the same size. To make the matrix reference the same data as A, use the reference() member function.

template<class TypeT>

bool RWSymBandMat< TypeT >::operator== ( const RWSymBandMat< TypeT > & X )

Two matrices are considered equal if they have the same size and their elements are all exactly the same. Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.

template<class TypeT>

void RWSymBandMat< TypeT >::printOn ( std::ostream & ) const

Prints the matrix to an output stream in human readable format.

template<class TypeT >

RWRORef< TypeT > RWSymBandMat< TypeT >::ref	(	int	i,
		int	j
	)			`[inline]`

Returns a reference to the ij ^th element of the matrix. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK is defined when the header file is read. The member function bcref() does the same thing with guaranteed bounds checking.

template<class TypeT>

RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::reference ( RWSymBandMat< TypeT > & m )

Makes this matrix a reference to the argument matrix. The two matrices share the same data. The matrices do not have to be the same size before calling reference(). To copy a matrix into another of the same size, use the operator=() member operator.

template<class TypeT>

void RWSymBandMat< TypeT >::resize	(	unsigned	n,
		unsigned	nAgain,
		unsigned	halfWidth
	)

Resizes the matrix or changes both its size and half bandwidth. Any new entries in the matrix are set to 0. Both arguments must be the same.

template<class TypeT>

void RWSymBandMat< TypeT >::resize	(	unsigned	m,
		unsigned	n
	)

Resizes the matrix or changes both its size and half bandwidth. Any new entries in the matrix are set to 0. Both arguments must be the same.

template<class TypeT>

void RWSymBandMat< TypeT >::restoreFrom ( RWFile & )

Reads in a matrix from an RWFile. The matrix must have been stored to the file using the saveOn() member function.

template<class TypeT>

void RWSymBandMat< TypeT >::restoreFrom ( RWvistream & )

Reads in a matrix from an RWvistream, the Rogue Wave virtual input stream class. The matrix must have been stored to the stream using the saveOn() member function.

template<class TypeT>

unsigned RWSymBandMat< TypeT >::rows ( ) const [inline]

Returns the number of rows in the matrix.

template<class TypeT>

void RWSymBandMat< TypeT >::saveOn ( RWFile & ) const

Stores a matrix to an RWFile. The matrix can be read using the restoreFrom() member function.

template<class TypeT>

void RWSymBandMat< TypeT >::saveOn ( RWvostream & ) const

Stores a matrix to an RWvostream, the Rogue Wave virtual output stream class. The matrix can be read using the restoreFrom() member function.

template<class TypeT>

void RWSymBandMat< TypeT >::scanFrom ( std::istream & )

Reads a matrix from an input stream. The format of the matrix is the same as the format output by the printOn() member function: first the half bandwidth, followed by the matrix itself. Below is a sample matrix showing the format. Note that extra white space and text preceding the bandwidth specification are ignored. Only the symmetric part of the relevant band of the matrix is used.

 1  5x5
 [
   3  7  0  0  0
   7  2  2  0  0
   0  2  8  9  0
   0  0  9  8  7
   0  0  0  7  8
 ]

template<class TypeT >

TypeT RWSymBandMat< TypeT >::set	(	int	i,
		int	j,
		TypeT	x
	)			`[inline]`

Sets the ij ^th element of the matrix equal to x. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK is defined when the header file is read. The member function bcset() does the same thing with guaranteed bounds checking.

template<class TypeT>

unsigned RWSymBandMat< TypeT >::upperBandwidth ( ) const [inline]

Returns the upper bandwidth of the matrix.

template<class TypeT >

TypeT RWSymBandMat< TypeT >::val	(	int	i,
		int	j
	)			const `[inline]`

Returns the value of the ij ^th element of the matrix. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK is defined when the header file is read. The member function bcval() does the same thing with guaranteed bounds checking.

template<class TypeT>

void RWSymBandMat< TypeT >::zero ( ) [inline]

Sets every element of the matrix to 0.

Friends And Related Function Documentation

template<class TypeT >

RWSymBandMat< typename rw_numeric_traits< TypeT >::norm_type > abs ( const RWSymBandMat< TypeT > & A ) [related]

Returns a matrix whose entries are the absolute value of the argument. The absolute value of a complex number is considered to be the sum of the absolute values of its real and imaginary parts. To get the norm of a complex matrix, you can use the norm() function.

template<class TypeT>

RWSymBandMat< double > arg ( const RWSymBandMat< DComplex > & A ) [related]

Returns a matrix where each element is the argument of the corresponding element in the matrix A.

template<class TypeT>

RWSymBandMat< DComplex > conj ( const RWSymBandMat< DComplex > & A ) [related]

Returns a matrix where each element is the complex conjugate of the corresponding element in the matrix A.

template<class TypeT>

RWSymBandMat< double > imag ( const RWSymBandMat< DComplex > & A ) [related]

Returns a matrix where each element is the imaginary part of the corresponding element in the matrix A.

template<class TypeT>

float maxValue ( const RWSymBandMat< float > & A ) [related]

Returns the maximum entry in the matrix.

template<class TypeT>

double maxValue ( const RWSymBandMat< double > & A ) [related]

Returns the maximum entry in the matrix.

template<class TypeT>

float minValue ( const RWSymBandMat< float > & A ) [related]

Returns the minimum entry in the matrix.

template<class TypeT>

double minValue ( const RWSymBandMat< double > & A ) [related]

Returns the minimum entry in the matrix.

template<class TypeT>

RWSymBandMat< double > norm ( const RWSymBandMat< DComplex > & A ) [related]

Returns a matrix where each element is the norm (magnitude) of the corresponding element in the matrix A.

template<class TypeT >

RWSymBandMat< TypeT > operator*	(	TypeT	x,
		const RWSymBandMat< TypeT > &	A
	)			`[related]`

Performs element-by-element operations on the arguments.

template<class TypeT >

RWSymBandMat< TypeT > operator*	(	const RWSymBandMat< TypeT > &	A,
		TypeT	x
	)			`[related]`

Performs element-by-element operations on the arguments.

template<class TypeT >

RWSymBandMat< TypeT > operator*	(	const RWSymBandMat< TypeT > &	,
		const RWSymBandMat< TypeT > &
	)			`[related]`

Performs element-by-element operation on the arguments. To do inner product matrix multiplication, you can use the product() global function.

template<class TypeT >

RWSymBandMat< TypeT > operator+	(	const RWSymBandMat< TypeT > &	,
		const RWSymBandMat< TypeT > &
	)			`[related]`

Performs element-by-element operation on the arguments.

template<class TypeT >

RWSymBandMat< TypeT > operator+ ( const RWSymBandMat< TypeT > & ) [related]

Unary plus operator. Returns a copy of the matrix.

template<class TypeT >

RWSymBandMat< TypeT > operator-	(	const RWSymBandMat< TypeT > &	,
		const RWSymBandMat< TypeT > &
	)			`[related]`

Performs element-by-element operation on the arguments. ;

template<class TypeT >

RWSymBandMat< TypeT > operator- ( const RWSymBandMat< TypeT > & ) [related]

Unary minus operator. Returns a copy of matrix's negation.

template<class TypeT >

RWSymBandMat< TypeT > operator/	(	const RWSymBandMat< TypeT > &	A,
		TypeT	x
	)			`[related]`

Performs element-by-element operations on the arguments.

template<class TypeT >

RWSymBandMat< TypeT > operator/	(	const RWSymBandMat< TypeT > &	,
		const RWSymBandMat< TypeT > &
	)			`[related]`

Performs element-by-element operation on the arguments. ;

template<class TypeT >

std::ostream & operator<<	(	std::ostream &	s,
		const RWSymBandMat< TypeT > &	m
	)			`[related]`

Writes the matrix to the stream. This is equivalent to calling the printOn() member function.

template<class TypeT >

std::istream & operator>>	(	std::istream &	s,
		RWSymBandMat< TypeT > &	m
	)			`[related]`

Reads the matrix from the stream. This is equivalent to calling the scanFrom() member function.

template<class TypeT >

RWMathVec< TypeT > product	(	const RWMathVec< TypeT > &	x,
		const RWSymBandMat< TypeT > &	A
	)			`[related]`

Returns the inner product (matrix-vector product) of x and A. This is equal to the product of A transpose and x.

template<class TypeT >

RWMathVec< TypeT > product	(	const RWSymBandMat< TypeT > &	A,
		const RWMathVec< TypeT > &	x
	)			`[related]`

Returns the inner product (matrix-vector product) of A and x.

template<class TypeT>

RWSymBandMat< double > real ( const RWSymBandMat< DComplex > & A ) [related]

Returns a matrix where each element is the real part of the corresponding element in the matrix A.

template<class TypeT >

RWSymBandMat< TypeT > toSymBandMat ( const RWBandMat< TypeT > & A ) [related]

Extracts the symmetric part of a banded matrix. The symmetric part of the banded matrix A is $(A + A^{T})/2$ .

template<class TypeT >

RWSymBandMat< TypeT > transpose ( const RWSymBandMat< TypeT > & ) [related]

Returns the transpose of the argument matrix.

SourcePro® C++ API Reference Guide

RWSymBandMat< TypeT > Class Template Reference [Sparse Matrices]

Public Member Functions

Related Functions

Detailed Description

template<class TypeT> class RWSymBandMat< TypeT >

Synopsis

Example

Storage Scheme

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

RWSymBandMat< TypeT > Class Template Reference
[Sparse Matrices]

template<class TypeT>
class RWSymBandMat< TypeT >