Ell Sparse Block Matrix format. More...

Public Member Functions
	EllSparseBlockMat ()=default
	default constructor does nothing

	EllSparseBlockMat (int num_block_rows, int num_block_cols, int num_blocks_per_line, int num_different_blocks, int n)
	Allocate storage.

template<class other_real_type , template< class > class Other_Vector>
	EllSparseBlockMat (const EllSparseBlockMat< other_real_type, Other_Vector > &src)

int	total_num_rows () const
	total number of rows is `num_rowsnleft_size*right_size`

int	total_num_cols () const
	total number of columns is `num_colsnleft_size*right_size`

dg::SparseMatrix< int, real_type, thrust::host_vector >	asCuspMatrix () const
	Convert to a sparse matrix.

template<class value_type >
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.

template<class value_type >
void	symv (SharedVectorTag, CudaTag, value_type alpha, const value_type x, value_type beta, value_type y) const

void	set_default_range ()
	Set `right_range[0] = 0, right_range[1] = right_size`

void	set_right_size (int new_right_size)
	Set `right_size = new_right_size; set_default_range();`

void	set_left_size (int new_left_size)
	Set `left_size = new_left_size;`

void	display (std::ostream &os=std::cout, bool show_data=false) const
	Display internal data to a stream.

template<class value_type >
void	launch_multiply_kernel (SerialTag, value_type alpha, const value_type x_ptr, value_type beta, value_type y_ptr) const

Public Attributes
Vector< real_type >	data
	The data array is of size nnnum_different_blocks and contains the blocks. The first block is contained in the first n*n elements, then comes the next block, etc.

Vector< int >	cols_idx
	is of size num_rows*num_blocks_per_line and contains the column indices % n into the vector

Vector< int >	data_idx
	has the same size as cols_idx and contains indices into the data array, i.e. the block number

Vector< int >	right_range
	range (can be used to apply the matrix to only part of the right rows

int	num_rows
	number of block rows, each row contains blocks

int	num_cols
	number of block columns

int	blocks_per_line
	number of blocks in each line

int	n
	each block has size n*n

int	left_size
	size of the left Kronecker delta

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

Static Public Attributes
static constexpr int	invalid_index = -1

Friends
template<class other_real_type , template< class > class Other_Vector>
class	EllSparseBlockMat

Detailed Description

template<class real_type, template< class > class Vector>
struct dg::EllSparseBlockMat< real_type, Vector >

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() [1/3]

template<class real_type , template< class > class Vector>

dg::EllSparseBlockMat< real_type, Vector >::EllSparseBlockMat ( )

default

default constructor does nothing

◆ EllSparseBlockMat() [2/3]

template<class real_type , template< class > class Vector>

dg::EllSparseBlockMat< real_type, Vector >::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

◆ EllSparseBlockMat() [3/3]

template<class real_type , template< class > class Vector>

template<class other_real_type , template< class > class Other_Vector>

dg::EllSparseBlockMat< real_type, Vector >::EllSparseBlockMat ( const EllSparseBlockMat< other_real_type, Other_Vector > & src )

inline

Member Function Documentation

◆ asCuspMatrix()

template<class real_type , template< class > class Vector>

dg::SparseMatrix< int, real_type, thrust::host_vector > dg::EllSparseBlockMat< real_type, Vector >::asCuspMatrix ( ) const

Convert to a sparse matrix.

Returns: The matrix in sparse matrix format

◆ display()

template<class real_type , template< class > class Vector>

void dg::EllSparseBlockMat< real_type, Vector >::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

◆ launch_multiply_kernel()

template<class real_type , template< class > class Vector>

template<class value_type >

void dg::EllSparseBlockMat< real_type, Vector >::launch_multiply_kernel	(	SerialTag	,
		value_type	alpha,
		const value_type *	x_ptr,
		value_type	beta,
		value_type *	y_ptr ) const

◆ set_default_range()

template<class real_type , template< class > class Vector>

void dg::EllSparseBlockMat< real_type, Vector >::set_default_range ( )

inline

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

◆ set_left_size()

template<class real_type , template< class > class Vector>

void dg::EllSparseBlockMat< real_type, Vector >::set_left_size ( int new_left_size )

inline

Set left_size = new_left_size;

◆ set_right_size()

template<class real_type , template< class > class Vector>

void dg::EllSparseBlockMat< real_type, Vector >::set_right_size ( int new_right_size )

inline

Set right_size = new_right_size; set_default_range();

◆ symv() [1/2]

template<class real_type , template< class > class Vector>

template<class value_type >

void dg::EllSparseBlockMat< real_type, Vector >::symv	(	SharedVectorTag	,
		CudaTag	,
		value_type	alpha,
		const value_type *	x,
		value_type	beta,
		value_type *	y ) const

inline

◆ symv() [2/2]

template<class real_type , template< class > class Vector>

template<class value_type >

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

inline

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

Template Parameters

value_type value_type = real_type*value_type must be possible

◆ total_num_cols()

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::total_num_cols ( ) const

inline

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

◆ total_num_rows()

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::total_num_rows ( ) const

inline

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

Friends And Related Symbol Documentation

◆ EllSparseBlockMat

template<class real_type , template< class > class Vector>

template<class other_real_type , template< class > class Other_Vector>

friend class EllSparseBlockMat

friend

Member Data Documentation

◆ blocks_per_line

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::blocks_per_line

number of blocks in each line

◆ cols_idx

template<class real_type , template< class > class Vector>

Vector<int> dg::EllSparseBlockMat< real_type, Vector >::cols_idx

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

◆ data

template<class real_type , template< class > class Vector>

Vector<real_type> dg::EllSparseBlockMat< real_type, Vector >::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 real_type , template< class > class Vector>

Vector<int> dg::EllSparseBlockMat< real_type, Vector >::data_idx

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

◆ invalid_index

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::invalid_index = -1

staticconstexpr

Value used to pad the rows of the cols_idx array The data_idx must always be valid

◆ left_size

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::left_size

size of the left Kronecker delta

◆ n

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::n

each block has size n*n

◆ num_cols

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::num_cols

number of block columns

◆ num_rows

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::num_rows

number of block rows, each row contains blocks

◆ right_range

template<class real_type , template< class > class Vector>

Vector<int> dg::EllSparseBlockMat< real_type, Vector >::right_range

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

◆ right_size

template<class real_type , template< class > class Vector>

int dg::EllSparseBlockMat< real_type, Vector >::right_size

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

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

backend/sparseblockmat.h
backend/sparseblockmat_cpu_kernels.h

Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ EllSparseBlockMat() [1/3]

◆ EllSparseBlockMat() [2/3]

◆ EllSparseBlockMat() [3/3]

Member Function Documentation

◆ asCuspMatrix()

◆ display()

◆ launch_multiply_kernel()

◆ set_default_range()

◆ set_left_size()

◆ set_right_size()

◆ symv() [1/2]

◆ symv() [2/2]

◆ total_num_cols()

◆ total_num_rows()

Friends And Related Symbol Documentation

◆ EllSparseBlockMat

Member Data Documentation

◆ blocks_per_line

◆ cols_idx

◆ data

◆ data_idx

◆ invalid_index

◆ left_size

◆ n

◆ num_cols

◆ num_rows

◆ right_range

◆ right_size