Symmetric diagonal matrix. More...

#include <matrix.h>

Public Member Functions
	SymDiaMatrix ()
	Empty constructor. More...

	SymDiaMatrix (int n)
	Size constructor. More...

	SymDiaMatrix (int n, const iArrayView id, const cArrayView v)
	Data constructor. More...

	SymDiaMatrix (SymDiaMatrix const &A)
	Copy constructor. More...

	SymDiaMatrix (SymDiaMatrix &&A)
	Move constructor. More...

template<class Functor >
SymDiaMatrix &	populate (unsigned d, Functor f)
	Plain symmetrical populator. More...

	~SymDiaMatrix ()

void	drop ()
	Free all fields, set dimensions to zero. More...

int	diag (int i) const
	Diagonal index. More...

size_t	size () const
	Matrix dimension. More...

int	bandwidth () const
	Bandwidth. More...

bool	is_compatible (SymDiaMatrix const &B) const
	Check compatibility of matrices. More...

SymDiaMatrix const &	operator= (SymDiaMatrix &&A)

SymDiaMatrix const &	operator= (SymDiaMatrix const &A)

SymDiaMatrix const &	operator+= (SymDiaMatrix const &B)

SymDiaMatrix const &	operator-= (SymDiaMatrix const &B)

cArray	dot (const cArrayView B, MatrixTriangle triangle=both, bool parallelize=false) const
	Dot product. More...

cArray	lowerSolve (const cArrayView b) const
	Back-substitution (lower). More...

cArray	upperSolve (const cArrayView b) const
	Back-substitution (upper). More...

SymDiaMatrix	kron (SymDiaMatrix const &B) const
	Kronecker product. More...

void	link (std::string name)
	Link matrix to a disk file. More...

std::string	linkedto () const
	Return the name of the linked disk file. More...

cArray	toPaddedRows () const
	Zero-pad rows. More...

cArray	toPaddedCols () const
	Zero-pad columns. More...

CooMatrix	tocoo (MatrixTriangle triangle=both) const
	Convert matrix part to CooMatrix. More...

RowMatrix< Complex >	torow (MatrixTriangle triangle=both) const
	Convert matrix part to RowMatrix. More...


iArray const &	diag () const
	Diagonal indices. More...

iArray &	diag ()


cArrayView	main_diagonal () const
	Main diagonal. More...

cArrayView	main_diagonal ()


cArray const &	data () const
	Data pointer. More...

cArray &	data ()


Complex const *	dptr (int i) const
	Pointer to diagonal data. More...

Complex *	dptr (int i)


bool	hdfload ()
	Load from file. More...

bool	hdfload (std::string name)


bool	hdfsave () const
	Save data to file. More...

bool	hdfsave (std::string name, bool docompress=false, int consec=10) const

Friends
std::ostream &	operator<< (std::ostream &out, SymDiaMatrix const &A)
	Output to a text stream. More...

Detailed Description

A multi-diagonal matrix is a sparse matrix of the structure

\[ A = \pmatrix { \ast & \dots & \ast & & & \cr \vdots & \ddots & & \ddots & & \cr \ast & & \ddots & & \ddots & \cr & \ddots & & \ddots & & \ast \cr & & \ddots & & \ddots & \vdots \cr & & & \ast & \dots & \ast \cr } \ , \]

i.e. it is banded, with nonzero elements only near to the diagonal. Some of the diagonals may be identically zero. This class holds all nonzero main and upper diagonals (lower diagonals are not necessary in the symmetric case). The diagonal storage has several advantages:

Matrix-vector multiplication can be vectorized, in contrast to the CSR-matrix-vector multiplication which requires a strongly irregular memory access.
Matrix-matrix multiplication conserves the DIA structure, with just a simple increase of bandwidth. It holds that the bandwidth of the matrix C = AB is equal to the sum of the bandwidths of the factors decreased by one.

Constructor & Destructor Documentation

SymDiaMatrix::SymDiaMatrix ( )

SymDiaMatrix::SymDiaMatrix ( int n )

SymDiaMatrix::SymDiaMatrix	(	int	n,
		const iArrayView	id,
		const cArrayView	v
	)

Parameters

n	Size of the matrix.
id	Identifyiers of the diagonals (positive integers expected).
v	Stacked (and padded if ncessary) diagonals.

SymDiaMatrix::SymDiaMatrix ( SymDiaMatrix const & A )

SymDiaMatrix::SymDiaMatrix ( SymDiaMatrix && A )

SymDiaMatrix::~SymDiaMatrix ( )

inline

Member Function Documentation

int SymDiaMatrix::bandwidth ( ) const

inline

Return the bandwidth of the matrix, i.e. number of all (upper, main an lower) diagonals that would have to be stored in a full banded-matrix format.

cArray const& SymDiaMatrix::data ( ) const

inline

Return direct-access data pointer.

cArray& SymDiaMatrix::data ( )

inline

iArray const& SymDiaMatrix::diag ( ) const

inline

Return array of indices of the stored diagonals. These are always only main and upper diagonals, so all numbers are non-negative. The array is sorted and begins with zero. Its length is always larger than zero.

iArray& SymDiaMatrix::diag ( )

inline

int SymDiaMatrix::diag ( int i ) const

inline

Return diagonal index for of i-th stored diagonal. The zero-th stored diagonal is always the main diagonal (= 0), but it doesn't have to hold for next diagonals.

cArray SymDiaMatrix::dot	(	const cArrayView	B,
		MatrixTriangle	triangle = `both`,
		bool	parallelize = `false`
	)		const

This is a key member of the structure, defining e.g. the speed of conjugate gradients and evaluation of the scattering amplitudes.

Parameters

B	Dense matrix. It is supposed to be stored by columns and to have dimensions n times k, where n is the column count of (this) matrix. Also, though only a view of the array is required, it is assumed that B is actually rArray, i.e. that it is aligned with the alignment 2sizeof(T).
triangle	Whether to use only the upper or only the lower or both triangles of the othwerwise symmetric matrix.
parallelize	Whether to use OpenMP to parallelize the SpMV operation.

Complex const* SymDiaMatrix::dptr ( int i ) const

inline

Parameters

i	Index of the diagonal in the "idiag_" array. The maximal value is thus less then the number stored diagonals.

Complex* SymDiaMatrix::dptr ( int i )

inline

void SymDiaMatrix::drop ( )

inline

bool SymDiaMatrix::hdfload ( )

inline

Load the matrix from a HDF5 file created by the routine hdfsave.

Returns: True on successful read, false otherwise (mostly when doesn't exist).

bool SymDiaMatrix::hdfload ( std::string name )

bool SymDiaMatrix::hdfsave ( ) const

inline

Save the matrix to the HDF5 file as a set of four datasets:

idiag - identifiers of (positive) diagonals that contain nonzeros,
n - single number containing size of the matrix (rows or columns)
x - concatenated diagonal elements (interleaved complex values)
zero_blocks - information on the compression of the "x" array, see NumberArray::compress.

Returns: True on successful write, false otherwise.

bool SymDiaMatrix::hdfsave	(	std::string	name,
		bool	docompress = `false`,
		int	consec = `10`
	)		const

bool SymDiaMatrix::is_compatible ( SymDiaMatrix const & B ) const

Check that the matrix B has the same dimensions as *this matrix and also that they keep the same diagonals. Such matrices can be very effectively summed and subtracted – just by doing the operation on the stored element arrays.

SymDiaMatrix SymDiaMatrix::kron ( SymDiaMatrix const & B ) const

Compute Kronecker product with other matrix.

void SymDiaMatrix::link ( std::string name )

std::string SymDiaMatrix::linkedto ( ) const

inline

cArray SymDiaMatrix::lowerSolve ( const cArrayView b ) const

Assume the matrix is normalized lower-triangular (i.e. has unit main diagonal and zero upper triangle) and do the triangular solve.

Parameters

b	Right hand side of the triangular system.

cArrayView SymDiaMatrix::main_diagonal ( ) const

inline

Return direct-access view of the main diagonal.

cArrayView SymDiaMatrix::main_diagonal ( )

inline

SymDiaMatrix const & SymDiaMatrix::operator+= ( SymDiaMatrix const & B )

SymDiaMatrix const & SymDiaMatrix::operator-= ( SymDiaMatrix const & B )

SymDiaMatrix const & SymDiaMatrix::operator= ( SymDiaMatrix && A )

SymDiaMatrix const & SymDiaMatrix::operator= ( SymDiaMatrix const & A )

template<class Functor >

SymDiaMatrix& SymDiaMatrix::populate	(	unsigned	d,
		Functor	f
	)

inline

Given a functor of the signature

Complex (*) (int, int);

the function will call the functor with row and column number of every element that is to be set.

Parameters

d	How many upper diagonals to populate. The main diagonal will be populated always.
f	The functor that will compute the matrix elements.

size_t SymDiaMatrix::size ( ) const

inline

Return row/column count. The matrix is symmetric and so both counts are equal.

CooMatrix SymDiaMatrix::tocoo ( MatrixTriangle triangle = both ) const

cArray SymDiaMatrix::toPaddedCols ( ) const

Pad rows with zeros as in toPaddedRows, then concatenate columns and return as a single array.

cArray SymDiaMatrix::toPaddedRows ( ) const

Pad rows with zeros as below:

\[ \left( \matrix { \ast & \ast & & & \cr \ast & \ast & \ast & & \cr \ast & \ast & \ast & \ast & \cr \ast & \ast & \ast & \ast & \ast \cr & \ast & \ast & \ast & \ast \cr & & \ast & \ast & \ast \cr & & & \ast & \ast \cr } \right) \longrightarrow \matrix { 0 & 0 & 0 \cr & 0 & 0 \cr & & 0 \cr & & . \cr & & . \cr & & . \cr & & . \cr } \left( \matrix { \ast & \ast & & & \cr \ast & \ast & \ast & & \cr \ast & \ast & \ast & \ast & \cr \ast & \ast & \ast & \ast & \ast \cr & \ast & \ast & \ast & \ast \cr & & \ast & \ast & \ast \cr & & & \ast & \ast \cr } \right) \matrix { . & & \cr . & & \cr . & & \cr . & & \cr 0 & & \cr 0 & 0 & \cr 0 & 0 & 0 \cr } \longrightarrow \matrix { 0 & 0 & 0 & \ast & \ast \cr 0 & 0 & \ast & \ast & \ast \cr 0 & \ast & \ast & \ast & \ast \cr \ast & \ast & \ast & \ast & \ast \cr \ast & \ast & \ast & \ast & 0 \cr \ast & \ast & \ast & 0 & 0 \cr \ast & \ast & 0 & 0 & 0 \cr } \]

Then concatenate rows and return as a single array.

RowMatrix< Complex > SymDiaMatrix::torow ( MatrixTriangle triangle = both ) const

cArray SymDiaMatrix::upperSolve ( const cArrayView b ) const

Assume the matrix is normalized upper-triangular (i.e. has unit main diagonal and zero lower triangle) and do the triangular solve.

Parameters

b	Right hand side of the triangular system.

Friends And Related Function Documentation

std::ostream& operator<<	(	std::ostream &	out,
		SymDiaMatrix const &	A
	)

friend

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

src/matrix.h
src/matrix.cpp

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation