dg::SparseTensor< container > Struct Template Reference

Class for 2x2 and 3x3 matrices sharing elements. More...

Public Types
using	container_type = container

Public Member Functions
	SparseTensor ()
	no value is set, Indices default to -1
template<class Topology >
	SparseTensor (const Topology &grid)
	Construct the unit tensor.
	SparseTensor (const container &copyable)
	Construct the unit tensor.
template<class Topology >
void	construct (const Topology &grid)
	Construct the unit tensor.
void	construct (const container &copyable)
	Construct the unit tensor.
template<class OtherContainer >
	SparseTensor (const SparseTensor< OtherContainer > &src)
	Type conversion from other value types.
int	idx (unsigned i, unsigned j) const
	read index into the values array at the given position
int &	idx (unsigned i, unsigned j)
	write index into the values array at the given position
const container &	value (size_t i, size_t j) const
	Read access the underlying container.
std::vector< container > &	values ()
	Return write access to the values array.
const std::vector< container > &	values () const
	Return read access to the values array.
SparseTensor	transpose () const
	Return the transpose of the currrent tensor.

Detailed Description

template<class container>
struct dg::SparseTensor< container >

Class for 2x2 and 3x3 matrices sharing elements.

This class enables shared access to stored containers. It contains a (dense) 3x3 matrix of integers that is automatically allocated. The integers represent a gather index into a stored array of containers. In this way duplicate entries are stored only once, which helps to avoid unnecessary memory accesses. For example an orthogonal metric is represented as follows

\[ \begin{pmatrix} g^{xx} & 0 & 0\\ 0 & g^{yy} & 0 \\ 0 & 0 & g^{zz} \end{pmatrix} \quad\rightarrow\quad \text{idx} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix} \quad \text{values} = \begin{pmatrix} 0 & g^{xx} & g^{yy} & g^{zz} \end{pmatrix} \]

which in code can be assembled as

dg::SparseTensor<dg::HVec> metric; // allocate 3x3 index matrix
metric.idx(0,0) = 1, metric.idx(0,1) = 0, metric.idx(0,2) = 0;
metric.idx(1,0) = 0, metric.idx(1,1) = 2, metric.idx(1,2) = 0;
metric.idx(2,0) = 0, metric.idx(2,1) = 0, metric.idx(2,2) = 3;
std::vector<dg::HVec> values( 4);
values[0] = dg::HVec( 100, 0);   // the zero element
values[1] = dg::HVec( 100, 20.); // construct gxx element
values[2] = dg::HVec( 100, 30.); // construct gyy element
values[3] = dg::HVec( 100, 1.); // construct gzz element
metric.values() = values;
// then we can for example use dg::tensor functions:
dg::HVec det = dg::tensor::determinant( metric);
CHECK( det == dg::HVec( 100, 20*30));
// the individual elements can be accessed via the access operator
dg::HVec gxx = metric.value(0,0);
CHECK( gxx == dg::HVec( 100, 20));

Template Parameters

container

must be default constructible and copyable.

See also

dg::tensor

Member Typedef Documentation

container_type

template<class container >

using dg::SparseTensor< container >::container_type = container

Constructor & Destructor Documentation

SparseTensor() [1/4]

template<class container >

dg::SparseTensor< container >::SparseTensor ( )

inline

no value is set, Indices default to -1

SparseTensor() [2/4]

template<class container >

template<class Topology >

dg::SparseTensor< container >::SparseTensor ( const Topology & grid )

inline

Construct the unit tensor.

Parameters

grid	used to create explicit zeroes (Index 0) and ones (Index 1)

SparseTensor() [3/4]

template<class container >

dg::SparseTensor< container >::SparseTensor ( const container & copyable )

inline

Construct the unit tensor.

Parameters

copyable

used to create explicit zeroes (Index 0) and ones (Index 1)

SparseTensor() [4/4]

template<class container >

template<class OtherContainer >

dg::SparseTensor< container >::SparseTensor ( const SparseTensor< OtherContainer > & src )

inline

Type conversion from other value types.

Template Parameters

OtherContainer

dg::assign must be callable for container and OtherContainer

Parameters

src	the source matrix to convert

Member Function Documentation

construct() [1/2]

template<class container >

void dg::SparseTensor< container >::construct ( const container & copyable )

inline

Construct the unit tensor.

Parameters

copyable

used to create explicit zeroes (Index 0) and ones (Index 1)

construct() [2/2]

template<class container >

template<class Topology >

void dg::SparseTensor< container >::construct ( const Topology & grid )

inline

Construct the unit tensor.

Parameters

grid	used to create explicit zeroes (Index 0) and ones (Index 1)

idx() [1/2]

template<class container >

int & dg::SparseTensor< container >::idx ( unsigned i, unsigned j )

inline

write index into the values array at the given position

use this and the values() member to assemble the tensor

Parameters

i	row index 0<=i<3
j	col index 0<=j<3

Returns

write access to value index to be set

idx() [2/2]

template<class container >

int dg::SparseTensor< container >::idx ( unsigned i, unsigned j ) const

inline

read index into the values array at the given position

Parameters

i	row index 0<=i<3
j	col index 0<=j<3

Returns

index into values array

transpose()

template<class container >

SparseTensor dg::SparseTensor< container >::transpose ( ) const

inline

Return the transpose of the currrent tensor.

Returns

swapped rows and columns

value()

template<class container >

const container & dg::SparseTensor< container >::value ( size_t i, size_t j ) const

inline

Read access the underlying container.

Returns

values[idx(i,j)] is returned.

Parameters

i	row index 0<=i<3
j	col index 0<=j<3

Note

If the indices (i,j) fall out of range or if the corresponding value index idx(i,j) falls out of range of the values array, the result is undefined

values() [1/2]

template<class container >

std::vector< container > & dg::SparseTensor< container >::values ( )

inline

Return write access to the values array.

Returns

write access to values array

values() [2/2]

template<class container >

const std::vector< container > & dg::SparseTensor< container >::values ( ) const

inline

Return read access to the values array.

Returns

read access to values array

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

• topology/tensor.h