Arbitrary sparse shape. More...

#include <sparse_shape.h>

Public Types
typedef SparseShape< T >	SparseShape_
	This object type. More...

typedef T	value_type
	The norm value type. More...

typedef Tensor< value_type >::size_type	size_type
	Size type. More...

Public Member Functions
	SparseShape ()
	Default constructor. More...

	SparseShape (const Tensor< value_type > &tile_norms, const TiledRange &trange)
	Constructor. More...

template<typename SparseNormSequence >
	SparseShape (const SparseNormSequence &tile_norms, const TiledRange &trange)
	"Sparse" constructor More...

	SparseShape (World &world, const Tensor< value_type > &tile_norms, const TiledRange &trange)
	Collective "dense" constructor. More...

template<typename SparseNormSequence >
	SparseShape (World &world, const SparseNormSequence &tile_norms, const TiledRange &trange)
	Collective "sparse" constructor. More...

	SparseShape (const SparseShape< T > &other)
	Copy constructor. More...

SparseShape< T > &	operator= (const SparseShape< T > &other)
	Copy assignment operator. More...

bool	validate (const Range &range) const
	Validate shape range. More...

template<typename Index >
bool	is_zero (const Index &i) const
	Check that a tile is zero. More...

float	sparsity () const
	Sparsity of the shape. More...

template<typename Index >
value_type	operator[] (const Index &index) const
	Tile norm accessor. More...

template<typename Op >
SparseShape_	transform (Op &&op) const
	Transform the norm tensor with an operation. More...

const Tensor< value_type > &	data () const
	Data accessor. More...

bool	empty () const
	Initialization check. More...

SparseShape_	mask (const SparseShape_ &mask_shape) const
	Compute union of two shapes. More...

template<typename Index >
SparseShape	update_block (const Index &lower_bound, const Index &upper_bound, const SparseShape &other) const
	Update sub-block of shape. More...

template<typename Index >
SparseShape	block (const Index &lower_bound, const Index &upper_bound) const
	Create a copy of a sub-block of the shape. More...

template<typename Index , typename Factor >
SparseShape	block (const Index &lower_bound, const Index &upper_bound, const Factor factor) const
	Create a scaled sub-block of the shape. More...

template<typename Index >
SparseShape	block (const Index &lower_bound, const Index &upper_bound, const Permutation &perm) const
	Create a copy of a sub-block of the shape. More...

template<typename Index , typename Factor >
SparseShape	block (const Index &lower_bound, const Index &upper_bound, const Factor factor, const Permutation &perm) const
	Create a copy of a sub-block of the shape. More...

SparseShape_	perm (const Permutation &perm) const
	Create a permuted shape of this shape. More...

template<typename Factor >
SparseShape_	scale (const Factor factor) const
	Scale shape. More...

template<typename Factor >
SparseShape_	scale (const Factor factor, const Permutation &perm) const
	Scale and permute shape. More...

SparseShape_	add (const SparseShape_ &other) const
	Add shapes. More...

SparseShape_	add (const SparseShape_ &other, const Permutation &perm) const
	Add and permute shapes. More...

template<typename Factor >
SparseShape_	add (const SparseShape_ &other, const Factor factor) const
	Add and scale shapes. More...

template<typename Factor >
SparseShape_	add (const SparseShape_ &other, const Factor factor, const Permutation &perm) const
	Add, scale, and permute shapes. More...

SparseShape_	add (value_type value) const

SparseShape_	add (const value_type value, const Permutation &perm) const

SparseShape_	subt (const SparseShape_ &other) const

SparseShape_	subt (const SparseShape_ &other, const Permutation &perm) const

template<typename Factor >
SparseShape_	subt (const SparseShape_ &other, const Factor factor) const

template<typename Factor >
SparseShape_	subt (const SparseShape_ &other, const Factor factor, const Permutation &perm) const

SparseShape_	subt (const value_type value) const

SparseShape_	subt (const value_type value, const Permutation &perm) const

SparseShape_	mult (const SparseShape_ &other) const

SparseShape_	mult (const SparseShape_ &other, const Permutation &perm) const

template<typename Factor >
SparseShape_	mult (const SparseShape_ &other, const Factor factor) const

template<typename Factor >
SparseShape_	mult (const SparseShape_ &other, const Factor factor, const Permutation &perm) const

template<typename Factor >
SparseShape_	gemm (const SparseShape_ &other, const Factor factor, const math::GemmHelper &gemm_helper) const

template<typename Factor >
SparseShape_	gemm (const SparseShape_ &other, const Factor factor, const math::GemmHelper &gemm_helper, const Permutation &perm) const

Static Public Member Functions
static constexpr bool	is_dense ()
	Check density. More...

static value_type	threshold ()
	Threshold accessor. More...

static void	threshold (const value_type thresh)
	Set threshold to `thresh`. More...

Detailed Description

template<typename T>
class TiledArray::SparseShape< T >

Arbitrary sparse shape.

Sparse shape uses a Tensor of Frobenius norms to estimate the magnitude of the data contained in tiles of an Array object. Because tiles may have an arbitrary size, the norm data is normalized, internally, by dividing the norms by the number of elements in each tile.

${\rm{shape}}_{ij...} = \frac{\|A_{ij...}\|}{N_i N_j ...}$

where $ij...$ are tile indices, $\|A_{ij}\|$ is norm of tile $ij...$ , and $N_i N_j ...$ is the product of tile $ij...$ in each dimension.

Template Parameters

T	The sparse element value type

Note: Scaling operations, such as SparseShape<T>::scale , SparseShape<T>::gemm , etc. accept generic scaling factors; internally (modulus of) the scaling factor is first converted to T, then used (see SparseShape<T>::to_abs_factor).

Definition at line 55 of file sparse_shape.h.

Member Typedef Documentation

◆ size_type

template<typename T>

typedef Tensor<value_type>::size_type TiledArray::SparseShape< T >::size_type

Size type.

Definition at line 60 of file sparse_shape.h.

◆ SparseShape_

template<typename T>

typedef SparseShape<T> TiledArray::SparseShape< T >::SparseShape_

This object type.

Definition at line 57 of file sparse_shape.h.

◆ value_type

template<typename T>

typedef T TiledArray::SparseShape< T >::value_type

The norm value type.

Definition at line 58 of file sparse_shape.h.

Constructor & Destructor Documentation

◆ SparseShape() [1/6]

template<typename T>

TiledArray::SparseShape< T >::SparseShape ( )

inline

Default constructor.

Construct a shape with no data.

Definition at line 210 of file sparse_shape.h.

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◆ SparseShape() [2/6]

template<typename T>

TiledArray::SparseShape< T >::SparseShape	(	const Tensor< value_type > &	tile_norms,
		const TiledRange &	trange
	)

inline

Constructor.

This constructor will normalize the tile norm, where the normalization constant for each tile is the inverse of the number of elements in the tile.

Parameters

tile_norms	The Frobenius norm of tiles
trange	The tiled range of the tensor

Definition at line 219 of file sparse_shape.h.

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◆ SparseShape() [3/6]

template<typename T>

template<typename SparseNormSequence >

TiledArray::SparseShape< T >::SparseShape	(	const SparseNormSequence &	tile_norms,
		const TiledRange &	trange
	)

inline

"Sparse" constructor

This constructor uses tile norms given as a sparse tensor, represented as a sequence of {index,value_type} data. The tile norms are normalized to per-element norms by dividing each norm by the number of elements in the corresponding tile.

Template Parameters

SparseNormSequence the sequence of std::pair<index,value_type> objects, where index is a directly-addressable sequence indices.

Parameters

tile_norms	The Frobenius norm of tiles
trange	The tiled range of the tensor

Definition at line 240 of file sparse_shape.h.

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◆ SparseShape() [4/6]

template<typename T>

TiledArray::SparseShape< T >::SparseShape	(	World &	world,
		const Tensor< value_type > &	tile_norms,
		const TiledRange &	trange
	)

inline

Collective "dense" constructor.

This constructor uses tile norms given as a dense tensor. The tile norms data are summed across all processes (via an all reduce). Next, the norms are converted to per-element norms by dividing each norm by the number of elements in the corresponding tile.

Parameters

world	The world where the shape will live
tile_norms	The Frobenius norm of tiles
trange	The tiled range of the tensor

Definition at line 271 of file sparse_shape.h.

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◆ SparseShape() [5/6]

template<typename T>

template<typename SparseNormSequence >

TiledArray::SparseShape< T >::SparseShape	(	World &	world,
		const SparseNormSequence &	tile_norms,
		const TiledRange &	trange
	)

inline

Collective "sparse" constructor.

This constructor uses tile norms given as a sparse tensor, represented as a sequence of {index,value_type} data. The tile norms are normalized to per-element norms by dividing each norm by the number of elements in the corresponding tile. Lastly, he norms are sum-reduced across all processors.

Template Parameters

SparseNormSequence the sequence of std::pair<index,value_type> objects, where index is a directly-addressable sequence of integers.

Parameters

world	The world where the shape will live
tile_norms	The Frobenius norm of tiles
trange	The tiled range of the tensor

Definition at line 298 of file sparse_shape.h.

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◆ SparseShape() [6/6]

template<typename T>

TiledArray::SparseShape< T >::SparseShape ( const SparseShape< T > & other )

inline

Copy constructor.

Shallow copy of other.

Parameters

other The other shape object to be copied

Definition at line 309 of file sparse_shape.h.

Member Function Documentation

◆ add() [1/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::add ( const SparseShape_ & other ) const

inline

Add shapes.

Construct a new sum of shapes as:

${(\rm{result})}_{ij...} = (\rm{this})_{ij...} + (\rm{other})_{ij...}$

Parameters

other The shape to be added to this shape

Returns: A sum of shapes

Definition at line 701 of file sparse_shape.h.

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◆ add() [2/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::add	(	const SparseShape_ &	other,
		const Permutation &	perm
	)		const

inline

Add and permute shapes.

Construct a new sum of shapes as:

${(\rm{result})}_{ji...} = \rm{perm}(i,j) (\rm{this})_{ij...} + (\rm{other})_{ij...}$

Parameters

other	The shape to be added to this shape
perm	The permutation that is applied to the result

Returns: the new shape, equals this + other

Definition at line 732 of file sparse_shape.h.

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◆ add() [3/6]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::add	(	const SparseShape_ &	other,
		const Factor	factor
	)		const

inline

Add and scale shapes.

Construct a new sum of shapes as:

${(\rm{result})}_{ij...} = |(\rm{factor})| ((\rm{this})_{ij...} + (\rm{other})_{ij...})$

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Parameters

other	The shape to be added to this shape
factor	The scaling factor

Returns: A scaled sum of shapes

Definition at line 767 of file sparse_shape.h.

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◆ add() [4/6]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::add	(	const SparseShape_ &	other,
		const Factor	factor,
		const Permutation &	perm
	)		const

inline

Add, scale, and permute shapes.

Construct a new sum of shapes as:

${(\rm{result})}_{ij...} = |(\rm{factor})| ((\rm{this})_{ij...} + (\rm{other})_{ij...})$

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Parameters

other	The shape to be added to this shape
factor	The scaling factor
perm	The permutation that is applied to the result

Returns: A scaled and permuted sum of shapes

Definition at line 804 of file sparse_shape.h.

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◆ add() [5/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::add ( value_type value ) const

inline

Definition at line 831 of file sparse_shape.h.

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◆ add() [6/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::add	(	const value_type	value,
		const Permutation &	perm
	)		const

inline

Definition at line 891 of file sparse_shape.h.

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◆ block() [1/4]

template<typename T>

template<typename Index >

SparseShape TiledArray::SparseShape< T >::block	(	const Index &	lower_bound,
		const Index &	upper_bound
	)		const

inline

Create a copy of a sub-block of the shape.

Template Parameters

Index The upper and lower bound array type

Parameters

lower_bound	The lower bound of the sub-block
upper_bound	The upper bound of the sub-block

Definition at line 530 of file sparse_shape.h.

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◆ block() [2/4]

template<typename T>

template<typename Index , typename Factor >

SparseShape TiledArray::SparseShape< T >::block	(	const Index &	lower_bound,
		const Index &	upper_bound,
		const Factor	factor
	)		const

inline

Create a scaled sub-block of the shape.

Template Parameters

Index	The upper and lower bound array type
Factor	The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Parameters

lower_bound	The lower bound of the sub-block
upper_bound	The upper bound of the sub-block

Definition at line 565 of file sparse_shape.h.

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◆ block() [3/4]

template<typename T>

template<typename Index >

SparseShape TiledArray::SparseShape< T >::block	(	const Index &	lower_bound,
		const Index &	upper_bound,
		const Permutation &	perm
	)		const

inline

Create a copy of a sub-block of the shape.

Parameters

lower_bound	The lower bound of the sub-block
upper_bound	The upper bound of the sub-block

Definition at line 600 of file sparse_shape.h.

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◆ block() [4/4]

template<typename T>

template<typename Index , typename Factor >

SparseShape TiledArray::SparseShape< T >::block	(	const Index &	lower_bound,
		const Index &	upper_bound,
		const Factor	factor,
		const Permutation &	perm
	)		const

inline

Create a copy of a sub-block of the shape.

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Parameters

lower_bound	The lower bound of the sub-block
upper_bound	The upper bound of the sub-block

Definition at line 614 of file sparse_shape.h.

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◆ data()

template<typename T>

const Tensor<value_type>& TiledArray::SparseShape< T >::data ( ) const

inline

Data accessor.

Returns: A reference to the Tensor object that stores shape data

Definition at line 414 of file sparse_shape.h.

◆ empty()

template<typename T>

bool TiledArray::SparseShape< T >::empty ( ) const

inline

Initialization check.

Returns: true when this shape has been initialized.

Definition at line 419 of file sparse_shape.h.

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◆ gemm() [1/2]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::gemm	(	const SparseShape_ &	other,
		const Factor	factor,
		const math::GemmHelper &	gemm_helper
	)		const

inline

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Definition at line 1041 of file sparse_shape.h.

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◆ gemm() [2/2]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::gemm	(	const SparseShape_ &	other,
		const Factor	factor,
		const math::GemmHelper &	gemm_helper,
		const Permutation &	perm
	)		const

inline

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Definition at line 1130 of file sparse_shape.h.

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◆ is_dense()

template<typename T>

static constexpr bool TiledArray::SparseShape< T >::is_dense ( )

inlinestatic

Check density.

Returns: true

Definition at line 348 of file sparse_shape.h.

◆ is_zero()

template<typename T>

template<typename Index >

bool TiledArray::SparseShape< T >::is_zero ( const Index & i ) const

inline

Check that a tile is zero.

Template Parameters

Index The type of the index

Returns: false

Definition at line 340 of file sparse_shape.h.

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◆ mask()

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::mask ( const SparseShape_ & mask_shape ) const

inline

Compute union of two shapes.

Parameters

mask	The input shape, hard zeros are used to mask the output.

Returns: A shape that is masked by the mask.

Definition at line 425 of file sparse_shape.h.

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◆ mult() [1/4]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::mult ( const SparseShape_ & other ) const

inline

Definition at line 978 of file sparse_shape.h.

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◆ mult() [2/4]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::mult	(	const SparseShape_ &	other,
		const Permutation &	perm
	)		const

inline

Definition at line 990 of file sparse_shape.h.

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◆ mult() [3/4]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::mult	(	const SparseShape_ &	other,
		const Factor	factor
	)		const

inline

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Definition at line 1006 of file sparse_shape.h.

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◆ mult() [4/4]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::mult	(	const SparseShape_ &	other,
		const Factor	factor,
		const Permutation &	perm
	)		const

inline

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Definition at line 1022 of file sparse_shape.h.

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◆ operator=()

template<typename T>

SparseShape<T>& TiledArray::SparseShape< T >::operator= ( const SparseShape< T > & other )

inline

Copy assignment operator.

Shallow copy of other.

Parameters

other The other shape object to be copied

Returns: A reference to this object.

Definition at line 319 of file sparse_shape.h.

◆ operator[]()

template<typename T>

template<typename Index >

value_type TiledArray::SparseShape< T >::operator[] ( const Index & index ) const

inline

Tile norm accessor.

Template Parameters

Index The index type

Parameters

index The index of the tile norm to retrieve

Returns: The norm of the tile at index

Definition at line 374 of file sparse_shape.h.

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◆ perm()

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::perm ( const Permutation & perm ) const

inline

Create a permuted shape of this shape.

Parameters

perm	The permutation to be applied

Returns: A new, permuted shape

Definition at line 624 of file sparse_shape.h.

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◆ scale() [1/2]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::scale ( const Factor factor ) const

inline

Scale shape.

Construct a new scaled shape as:

${(\rm{result})}_{ij...} = |(\rm{factor})| (\rm{this})_{ij...}$

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Parameters

factor The scaling factor

Returns: A new, scaled shape

Definition at line 640 of file sparse_shape.h.

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◆ scale() [2/2]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::scale	(	const Factor	factor,
		const Permutation &	perm
	)		const

inline

Scale and permute shape.

Compute a new scaled shape is computed as:

${(\rm{result})}_{ji...} = \rm{perm}(j,i) |(\rm{factor})| (\rm{this})_{ij...}$

Template Parameters

Factor The scaling factor type

Note: expression abs(Factor) must be well defined (by default, std::abs will be used)

Parameters

factor	The scaling factor
perm	The permutation that will be applied to this tensor.

Returns: A new, scaled-and-permuted shape

Definition at line 672 of file sparse_shape.h.

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◆ sparsity()

template<typename T>

float TiledArray::SparseShape< T >::sparsity ( ) const

inline

Sparsity of the shape.

Returns: The fraction of tiles that are zero.

Definition at line 353 of file sparse_shape.h.

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◆ subt() [1/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::subt ( const SparseShape_ & other ) const

inline

Definition at line 897 of file sparse_shape.h.

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◆ subt() [2/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::subt	(	const SparseShape_ &	other,
		const Permutation &	perm
	)		const

inline

Definition at line 901 of file sparse_shape.h.

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◆ subt() [3/6]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::subt	(	const SparseShape_ &	other,
		const Factor	factor
	)		const

inline

Definition at line 906 of file sparse_shape.h.

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◆ subt() [4/6]

template<typename T>

template<typename Factor >

SparseShape_ TiledArray::SparseShape< T >::subt	(	const SparseShape_ &	other,
		const Factor	factor,
		const Permutation &	perm
	)		const

inline

Definition at line 911 of file sparse_shape.h.

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◆ subt() [5/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::subt ( const value_type value ) const

inline

Definition at line 917 of file sparse_shape.h.

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◆ subt() [6/6]

template<typename T>

SparseShape_ TiledArray::SparseShape< T >::subt	(	const value_type	value,
		const Permutation &	perm
	)		const

inline

Definition at line 921 of file sparse_shape.h.

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◆ threshold() [1/2]

template<typename T>

static value_type TiledArray::SparseShape< T >::threshold ( )

inlinestatic

Threshold accessor.

Returns: The current threshold

Definition at line 361 of file sparse_shape.h.

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◆ threshold() [2/2]

template<typename T>

static void TiledArray::SparseShape< T >::threshold ( const value_type thresh )

inlinestatic

Set threshold to thresh.

Parameters

thresh The new threshold

Definition at line 366 of file sparse_shape.h.

◆ transform()

template<typename T>

template<typename Op >

SparseShape_ TiledArray::SparseShape< T >::transform ( Op && op ) const

inline

Transform the norm tensor with an operation.

Returns: A deep copy of the norms of the object having performed the operation Op.
Op should take a const ref to a Tensor<T> and return a Tensor<T> Since the input tile norms have already been normalized the output norms will avoid normalization, which is neccesary for correct behavior.
One example is when Op is an identity operation the output SparseShape data will have the same values as this.

Definition at line 389 of file sparse_shape.h.

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◆ update_block()

template<typename T>

template<typename Index >

SparseShape TiledArray::SparseShape< T >::update_block	(	const Index &	lower_bound,
		const Index &	upper_bound,
		const SparseShape< T > &	other
	)		const

inline

Update sub-block of shape.

Update a sub-block shape information with another shape object.

Template Parameters

Index The bound index type

Parameters

lower_bound	The lower bound of the sub-block to be updated
upper_bound	The upper bound of the sub-block to be updated
other	The shape that will be used to update the sub-block

Returns: A new sparse shape object where the specified sub-block contains the data result_tile_norms of other.

Definition at line 460 of file sparse_shape.h.

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◆ validate()

template<typename T>

bool TiledArray::SparseShape< T >::validate ( const Range & range ) const

inline

Validate shape range.

Returns: true when range matches the range of this shape

Definition at line 329 of file sparse_shape.h.

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

TiledArray/sparse_shape.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename T> class TiledArray::SparseShape< T >

Member Typedef Documentation

◆ size_type

◆ SparseShape_

◆ value_type

Constructor & Destructor Documentation

◆ SparseShape() [1/6]

◆ SparseShape() [2/6]

◆ SparseShape() [3/6]

◆ SparseShape() [4/6]

◆ SparseShape() [5/6]

◆ SparseShape() [6/6]

Member Function Documentation

◆ add() [1/6]

◆ add() [2/6]

◆ add() [3/6]

◆ add() [4/6]

◆ add() [5/6]

◆ add() [6/6]

◆ block() [1/4]

◆ block() [2/4]

◆ block() [3/4]

◆ block() [4/4]

◆ data()

◆ empty()

◆ gemm() [1/2]

◆ gemm() [2/2]

◆ is_dense()

◆ is_zero()

◆ mask()

◆ mult() [1/4]

◆ mult() [2/4]

◆ mult() [3/4]

◆ mult() [4/4]

◆ operator=()

◆ operator[]()

◆ perm()

◆ scale() [1/2]

◆ scale() [2/2]

◆ sparsity()

◆ subt() [1/6]

◆ subt() [2/6]

◆ subt() [3/6]

◆ subt() [4/6]

◆ subt() [5/6]

◆ subt() [6/6]

◆ threshold() [1/2]

◆ threshold() [2/2]

◆ transform()

◆ update_block()

◆ validate()

template<typename T>
class TiledArray::SparseShape< T >