dg::EllSparseBlockMat< value_type > Struct Template Reference

Ell Sparse Block Matrix format. More...

Public Member Functions
	EllSparseBlockMat ()=default
	default constructor does nothing More...
	EllSparseBlockMat (int num_block_rows, int num_block_cols, int num_blocks_per_line, int num_different_blocks, int n)
	Allocate storage. More...
int	total_num_rows () const
	total number of rows is num_rows*n*left_size*right_size More...
int	total_num_cols () const
	total number of columns is num_cols*n*left_size*right_size More...
cusp::coo_matrix< int, value_type, cusp::host_memory >	asCuspMatrix () const
	Convert to a cusp coordinate sparse matrix. More...
void	symv (SharedVectorTag, SerialTag, value_type alpha, const value_type *RESTRICT x, value_type beta, value_type *RESTRICT y) const
	Apply the matrix to a vector. More...
void	set_default_range ()
	Set right_range[0] = 0, right_range[1] = right_size More...
void	set_right_size (int new_right_size)
	Set right_size = new_right_size; set_default_range(); More...
void	set_left_size (int new_left_size)
	Set left_size = new_left_size; More...
void	display (std::ostream &os=std::cout, bool show_data=false) const
	Display internal data to a stream. More...

Public Attributes
thrust::host_vector< value_type >	data
	The data array is of size n*n*num_different_blocks and contains the blocks. The first block is contained in the first n*n elements, then comes the next block, etc. More...
thrust::host_vector< int >	cols_idx
	is of size num_rows*num_blocks_per_line and contains the column indices % n into the vector More...
thrust::host_vector< int >	data_idx
	has the same size as cols_idx and contains indices into the data array, i.e. the block number More...
thrust::host_vector< int >	right_range
	range (can be used to apply the matrix to only part of the right rows More...
int	num_rows
	number of block rows, each row contains blocks More...
int	num_cols
	number of block columns More...
int	blocks_per_line
	number of blocks in each line More...
int	n
	each block has size n*n More...
int	left_size
	size of the left Kronecker delta More...
int	right_size
	size of the right Kronecker delta (is e.g 1 for a x - derivative) More...

Detailed Description

template<class value_type>
struct dg::EllSparseBlockMat< value_type >

Ell Sparse Block Matrix format.

The basis of this format is the ell sparse matrix format, i.e. a format where the number of entries per line is fixed. The clue is that instead of a values array we use an index array with indices into a data array that contains the actual blocks. This safes storage if the number of nonrecurrent blocks is small. The indices and blocks are those of a one-dimensional problem. When we want to apply the matrix to a multidimensional vector we can multiply it by Kronecker deltas of the form

\[ M = \begin{pmatrix} B & C & & & & \\ A & B & C & & & \\ & A & B & C & & \\ & & A & B & C & \\ & & &...& & \end{pmatrix}\rightarrow \text{data} = ( A, B, C, 0)\quad \text{cols_idx} = ( 0,0,1,0,1,2,1,2,3,2,3,4,...) \quad \text{data_idx} = ( 3,1,2,0,1,2,0,1,2,0,1,2,...)\]

where \(A,\ B,\ C,\ 0\) are \(n\times n\) block matrices. The 0 is used for padding in order to keep the number of elements per line constant as 3 (in this example blocks_per_line=3, num_different_blocks=4). The matrix M has num_rows rows and num_cols columns of blocks.

\[ 1_\mathrm{left}\otimes M \otimes 1_\mathrm{right}\]

where \( 1\) are diagonal matrices of variable size and \( M\) is our one-dimensional matrix.

Constructor & Destructor Documentation

EllSparseBlockMat() [1/2]

template<class value_type >

dg::EllSparseBlockMat< value_type >::EllSparseBlockMat ( )

default

default constructor does nothing

EllSparseBlockMat() [2/2]

template<class value_type >

dg::EllSparseBlockMat< value_type >::EllSparseBlockMat ( int  num_block_rows, int  num_block_cols, int  num_blocks_per_line, int  num_different_blocks, int  n  )

inline

Allocate storage.

Initializes left_size = right_size = 1, right_range[0] = 0 and right_range[1] = 1, data(num_different_blocks*n*n), cols_idx( num_block_rows*num_blocks_per_line), data_idx(cols_idx.size())

Parameters

num_block_rows	number of rows num_rows. Each row contains blocks.
num_block_cols	number of columns num_cols.
num_blocks_per_line	number of blocks in each line blocks_per_line
num_different_blocks	number of nonrecurrent blocks
n	each block is of size nxn

Member Function Documentation

asCuspMatrix()

template<class value_type >

cusp::coo_matrix< int, value_type, cusp::host_memory > dg::EllSparseBlockMat< value_type >::asCuspMatrix

(

)

const

Convert to a cusp coordinate sparse matrix.

Returns

The matrix in coo sparse matrix format

display()

template<class value_type >

void dg::EllSparseBlockMat< value_type >::display	(	std::ostream &	os = std::cout,
		bool	show_data = false
	)		const

Display internal data to a stream.

Parameters

os	the output stream
show_data	if true, displays the whole data vector

set_default_range()

template<class value_type >

void dg::EllSparseBlockMat< value_type >::set_default_range ( )

inline

Set right_range[0] = 0, right_range[1] = right_size

set_left_size()

template<class value_type >

void dg::EllSparseBlockMat< value_type >::set_left_size ( int  new_left_size )

inline

Set left_size = new_left_size;

set_right_size()

template<class value_type >

void dg::EllSparseBlockMat< value_type >::set_right_size ( int  new_right_size )

inline

Set right_size = new_right_size; set_default_range();

symv()

template<class value_type >

void dg::EllSparseBlockMat< value_type >::symv	(	SharedVectorTag	,
		SerialTag	,
		value_type	alpha,
		const value_type *RESTRICT	x,
		value_type	beta,
		value_type *RESTRICT	y
	)		const

Apply the matrix to a vector.

\[ y= \alpha M x + \beta y\]

Parameters

alpha	multiplies input
x	input
beta	premultiplies output
y	output may not alias input

total_num_cols()

template<class value_type >

int dg::EllSparseBlockMat< value_type >::total_num_cols ( ) const

inline

total number of columns is num_cols*n*left_size*right_size

total_num_rows()

template<class value_type >

int dg::EllSparseBlockMat< value_type >::total_num_rows ( ) const

inline

total number of rows is num_rows*n*left_size*right_size

Member Data Documentation

blocks_per_line

template<class value_type >

int dg::EllSparseBlockMat< value_type >::blocks_per_line

number of blocks in each line

cols_idx

template<class value_type >

thrust::host_vector<int> dg::EllSparseBlockMat< value_type >::cols_idx

is of size num_rows*num_blocks_per_line and contains the column indices % n into the vector

data

template<class value_type >

thrust::host_vector<value_type> dg::EllSparseBlockMat< value_type >::data

The data array is of size n*n*num_different_blocks and contains the blocks. The first block is contained in the first n*n elements, then comes the next block, etc.

data_idx

template<class value_type >

thrust::host_vector<int> dg::EllSparseBlockMat< value_type >::data_idx

has the same size as cols_idx and contains indices into the data array, i.e. the block number

left_size

template<class value_type >

int dg::EllSparseBlockMat< value_type >::left_size

size of the left Kronecker delta

n

template<class value_type >

int dg::EllSparseBlockMat< value_type >::n

each block has size n*n

num_cols

template<class value_type >

int dg::EllSparseBlockMat< value_type >::num_cols

number of block columns

num_rows

template<class value_type >

int dg::EllSparseBlockMat< value_type >::num_rows

number of block rows, each row contains blocks

right_range

template<class value_type >

thrust::host_vector<int> dg::EllSparseBlockMat< value_type >::right_range

range (can be used to apply the matrix to only part of the right rows

right_size

template<class value_type >

int dg::EllSparseBlockMat< value_type >::right_size

size of the right Kronecker delta (is e.g 1 for a x - derivative)

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

• backend/sparseblockmat.h