Documentation

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

Frobenius-norm-based sparse shape.

Sparse shape uses a Tensor of Frobenius norms to describe the magnitude of the data contained in tiles of an Array object. Because tiles may have an arbitrary size, screening of tiles uses scaled (per-element) Frobenius norms obtained by dividing the tile's Frobenius norm by the tile volume (=its number of elements):

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

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. Note that such scaled Frobenius norms no longer have the properties of the Frobenius norms such as the submiltiplicativity.

All constructors will zero out tiles whose scaled norms are below the threshold. The screening threshold is accessed via SparseShape:::threshold() ; it is the global, but not immutable. Thus it is possible to screen each operation separately, by changing the screening threshold between each operation.

Warning: If tile's scaled norm is below threshold, its scaled norm is set to to zero and thus lost forever. E.g. shape.scale(1e-10).scale(1e10) does not in general equal shape , whereas shape.scale(1e10).scale(1e-10) does.

Definition at line 74 of file sparse_shape.h.

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

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

using	index1_type = TA_1INDEX_TYPE

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

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

	SparseShape (const value_type &tile_norm, const TiledRange &trange)
	"Dense" Constructor More...

	SparseShape (const Tensor< value_type > &tile_norms, const TiledRange &trange, bool do_not_scale=false)
	"Dense" constructor More...

template<typename SparseNormSequence , typename = std::enable_if_t< TiledArray::detail::has_member_function_begin_anyreturn< std::decay_t<SparseNormSequence>>::value && TiledArray::detail::has_member_function_end_anyreturn< std::decay_t<SparseNormSequence>>::value>>
	SparseShape (const SparseNormSequence &tile_norms, const TiledRange &trange, bool do_not_scale=false)
	"Sparse" constructor More...

	SparseShape (World &world, const Tensor< value_type > &tile_norms, const TiledRange &trange, bool do_not_scale=false)
	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...

const Tensor< value_type > &	tile_norms () 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 Index1 , typename Index2 , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2>>>
SparseShape	update_block (const Index1 &lower_bound, const Index2 &upper_bound, const SparseShape &other) const
	Creates a copy of this with a sub-block updated with contents of another shape. More...

template<typename Index1 , typename Index2 , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2>>>
SparseShape	update_block (const std::initializer_list< Index1 > &lower_bound, const std::initializer_list< Index2 > &upper_bound, const SparseShape &other) const
	Creates a copy of this with a sub-block updated with contents of another shape. More...

template<typename PairRange , typename = std::enable_if_t<detail::is_gpair_range_v<PairRange>>>
SparseShape	update_block (const PairRange &bounds, const SparseShape &other) const
	Creates a copy of this with a sub-block updated with contents of another shape. More...

template<typename Index , typename = std::enable_if_t<std::is_integral_v<Index>>>
SparseShape	update_block (const std::initializer_list< std::initializer_list< Index >> &bounds, const SparseShape &other) const
	Creates a copy of this with a sub-block updated with contents of another shape. More...

bool	operator== (const SparseShape< T > &other) const
	Bitwise comparison. More...

template<typename Index1 , typename Index2 , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2>>>
SparseShape	block (const Index1 &lower_bound, const Index2 &upper_bound) const
	Create a copy of a sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2>>>
SparseShape	block (const std::initializer_list< Index1 > &lower_bound, const std::initializer_list< Index2 > &upper_bound) const
	Create a copy of a sub-block of the shape. More...

template<typename PairRange , typename = std::enable_if_t<detail::is_gpair_range_v<PairRange>>>
SparseShape	block (const PairRange &bounds) const
	Create a copy of a sub-block of the shape. More...

template<typename Index , typename = std::enable_if_t<std::is_integral_v<Index>>>
SparseShape	block (const std::initializer_list< std::initializer_list< Index >> &bounds) const
	Create a copy of a sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2> && detail::is_numeric_v<Scalar>>>
SparseShape	block (const Index1 &lower_bound, const Index2 &upper_bound, const Scalar factor) const
	Create a scaled sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2> && detail::is_numeric_v<Scalar>>>
SparseShape	block (const std::initializer_list< Index1 > &lower_bound, const std::initializer_list< Index2 > &upper_bound, const Scalar factor) const
	Create a scaled sub-block of the shape. More...

template<typename PairRange , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && detail::is_gpair_range_v<PairRange>>>
SparseShape	block (const PairRange &bounds, const Scalar factor) const
	Create a scaled sub-block of the shape. More...

template<typename Index , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && std::is_integral_v<Index>>>
SparseShape	block (const std::initializer_list< std::initializer_list< Index >> &bounds, const Scalar factor) const
	Create a scaled sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2>>>
SparseShape	block (const Index1 &lower_bound, const Index2 &upper_bound, const Permutation &perm) const
	Create a permuted sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2>>>
SparseShape	block (const std::initializer_list< Index1 > &lower_bound, const std::initializer_list< Index2 > &upper_bound, const Permutation &perm) const
	Create a permuted sub-block of the shape. More...

template<typename PairRange , typename = std::enable_if_t<detail::is_gpair_range_v<PairRange>>>
SparseShape	block (const PairRange &bounds, const Permutation &perm) const
	Create a permuted sub-block of the shape. More...

template<typename Index , typename = std::enable_if_t<std::is_integral_v<Index>>>
SparseShape	block (const std::initializer_list< std::initializer_list< Index >> &bounds, const Permutation &perm) const
	Create a permuted sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2> && detail::is_numeric_v<Scalar>>>
SparseShape	block (const Index1 &lower_bound, const Index2 &upper_bound, const Scalar factor, const Permutation &perm) const
	Create a permuted scaled sub-block of the shape. More...

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2> && detail::is_numeric_v<Scalar>>>
SparseShape	block (const std::initializer_list< Index1 > &lower_bound, const std::initializer_list< Index2 > &upper_bound, const Scalar factor, const Permutation &perm) const
	Create a permuted scaled sub-block of the shape. More...

template<typename PairRange , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && detail::is_gpair_range_v<PairRange>>>
SparseShape	block (const PairRange &bounds, const Scalar factor, const Permutation &perm) const
	Create a permuted scaled sub-block of the shape. More...

template<typename Index , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && std::is_integral_v<Index>>>
SparseShape	block (const std::initializer_list< std::initializer_list< Index >> &bounds, const Scalar factor, const Permutation &perm) const
	Create a permuted scaled sub-block of the shape. More...

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

template<typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar>>>
SparseShape_	scale (const Scalar 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

template<typename Archive , typename std::enable_if< madness::archive::is_input_archive< Archive >::value >::type * = nullptr>
void	serialize (const Archive &ar)

template<typename Archive , typename std::enable_if< madness::archive::is_output_archive< Archive >::value >::type * = nullptr>
void	serialize (const Archive &ar) 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...

Member Typedef Documentation

◆ index1_type

template<typename T >

using TiledArray::SparseShape< T >::index1_type = TA_1INDEX_TYPE

Definition at line 78 of file sparse_shape.h.

◆ size_type

template<typename T >

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

Size type.

Definition at line 81 of file sparse_shape.h.

◆ SparseShape_

template<typename T >

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

This object type.

Definition at line 76 of file sparse_shape.h.

◆ value_type

template<typename T >

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

The norm value type.

Definition at line 77 of file sparse_shape.h.

Constructor & Destructor Documentation

◆ SparseShape() [1/7]

template<typename T >

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

inline

Default constructor.

Construct a shape with no data.

Definition at line 274 of file sparse_shape.h.

◆ SparseShape() [2/7]

template<typename T >

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

inline

"Dense" Constructor

This constructor set the tile norms to the same value.

Parameters

tile_norm	the value of the (per-element) norm for every tile
trange	The tiled range of the tensor

Note: this ctor does not scale tile norms; if tile_norm is less than the threshold then all tile norms are set to zero

Definition at line 284 of file sparse_shape.h.

◆ SparseShape() [3/7]

template<typename T >

TiledArray::SparseShape< T >::SparseShape	(	const Tensor< value_type > &	tile_norms,
		const TiledRange &	trange,
		bool	do_not_scale = `false`
	)

inline

"Dense" constructor

This constructor will scale the tile norms, i.e. multiply each tile norm by the inverse of its volume.

Parameters

tile_norms	The Frobenius norm of tiles by default
trange	The tiled range of the tensor
do_not_scale	if true, assume that the tile norms in `tile_norms` are already scaled

Definition at line 299 of file sparse_shape.h.

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◆ SparseShape() [4/7]

template<typename T >

template<typename SparseNormSequence , typename = std::enable_if_t< TiledArray::detail::has_member_function_begin_anyreturn< std::decay_t<SparseNormSequence>>::value && TiledArray::detail::has_member_function_end_anyreturn< std::decay_t<SparseNormSequence>>::value>>

TiledArray::SparseShape< T >::SparseShape	(	const SparseNormSequence &	tile_norms,
		const TiledRange &	trange,
		bool	do_not_scale = `false`
	)

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 scaled by the inverse of the corresponding tile's volumes.

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
do_not_scale	if true, assume that the tile norms in `tile_norms` are already scaled

Definition at line 333 of file sparse_shape.h.

◆ SparseShape() [5/7]

template<typename T >

TiledArray::SparseShape< T >::SparseShape	(	World &	world,
		const Tensor< value_type > &	tile_norms,
		const TiledRange &	trange,
		bool	do_not_scale = `false`
	)

inline

Collective "dense" constructor.

This constructor uses tile norms given as a dense tensor. The tile norms are max-reduced across all processes (via an all reduce). Next, the norms are scaled by the inverse of the corresponding tile's volumes.

Parameters

world	The world where the shape will live
tile_norms	The Frobenius norm of tiles by default; expected to contain nonzeros for this rank's subset of tiles, or be replicated.
trange	The tiled range of the tensor
do_not_scale	if true, assume that the tile norms in `tile_norms` are already scaled

Definition at line 369 of file sparse_shape.h.

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◆ SparseShape() [6/7]

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 scaled to per-element norms by dividing each norm by the tile's volume. Lastly, the norms are max-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; expected to contain nonzeros for this rank's subset of tiles, or be replicated.
trange	The tiled range of the tensor

Definition at line 405 of file sparse_shape.h.

◆ SparseShape() [7/7]

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 416 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 1179 of file sparse_shape.h.

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◆ add() [2/6]

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 1240 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 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 1274 of file sparse_shape.h.

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◆ add() [4/6]

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 1208 of file sparse_shape.h.

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◆ add() [5/6]

template<typename T >

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

inline

Definition at line 1363 of file sparse_shape.h.

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◆ add() [6/6]

template<typename T >

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

inline

Definition at line 1299 of file sparse_shape.h.

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◆ block() [1/16]

template<typename T >

template<typename Index1 , typename Index2 , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2>>>

SparseShape TiledArray::SparseShape< T >::block	(	const Index1 &	lower_bound,
		const Index2 &	upper_bound
	)		const

inline

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

Template Parameters

Index1	An integral range type
Index2	An integral range type

Parameters

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

Definition at line 829 of file sparse_shape.h.

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◆ block() [2/16]

template<typename T >

template<typename Index1 , typename Index2 , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2>>>

SparseShape TiledArray::SparseShape< T >::block	(	const Index1 &	lower_bound,
		const Index2 &	upper_bound,
		const Permutation &	perm
	)		const

inline

Create a permuted sub-block of the shape.

Template Parameters

Index1	An integral range type
Index2	An integral range type

Parameters

lower_bound	The lower bound of the sub-block
upper_bound	The upper bound of the sub-block
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 965 of file sparse_shape.h.

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◆ block() [3/16]

template<typename T >

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2> && detail::is_numeric_v<Scalar>>>

SparseShape TiledArray::SparseShape< T >::block	(	const Index1 &	lower_bound,
		const Index2 &	upper_bound,
		const Scalar	factor
	)		const

inline

Create a scaled sub-block of the shape.

Template Parameters

Index1	An integral range type
Index2	An integral range type
Scalar	A numeric type

Note: expression abs(Scalar) 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
factor	the scaling factor

Definition at line 890 of file sparse_shape.h.

◆ block() [4/16]

template<typename T >

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2> && detail::is_numeric_v<Scalar>>>

SparseShape TiledArray::SparseShape< T >::block	(	const Index1 &	lower_bound,
		const Index2 &	upper_bound,
		const Scalar	factor,
		const Permutation &	perm
	)		const

inline

Create a permuted scaled sub-block of the shape.

Template Parameters

Index1	An integral range type
Index2	An integral range type
Scalar	A numeric type

Note: expression abs(Scalar) 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
factor	the scaling factor
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 1029 of file sparse_shape.h.

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◆ block() [5/16]

template<typename T >

template<typename PairRange , typename = std::enable_if_t<detail::is_gpair_range_v<PairRange>>>

SparseShape TiledArray::SparseShape< T >::block ( const PairRange & bounds ) const

inline

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

Template Parameters

PairRange Type representing a range of generalized pairs (see TiledArray::detail::is_gpair_v )

Parameters

bounds The {lower,upper} bounds of the sub-block

Definition at line 859 of file sparse_shape.h.

◆ block() [6/16]

template<typename T >

template<typename PairRange , typename = std::enable_if_t<detail::is_gpair_range_v<PairRange>>>

SparseShape TiledArray::SparseShape< T >::block	(	const PairRange &	bounds,
		const Permutation &	perm
	)		const

inline

Create a permuted sub-block of the shape.

Template Parameters

PairRange Type representing a range of generalized pairs (see TiledArray::detail::is_gpair_v )

Parameters

bounds	A range of {lower,upper} bounds for each dimension
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 995 of file sparse_shape.h.

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◆ block() [7/16]

template<typename T >

template<typename PairRange , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && detail::is_gpair_range_v<PairRange>>>

SparseShape TiledArray::SparseShape< T >::block	(	const PairRange &	bounds,
		const Scalar	factor
	)		const

inline

Create a scaled sub-block of the shape.

Template Parameters

PairRange	Type representing a range of generalized pairs (see TiledArray::detail::is_gpair_v )
Scalar	A numeric type

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

Parameters

bounds	A range of {lower,upper} bounds for each dimension
factor	the scaling factor

Definition at line 929 of file sparse_shape.h.

◆ block() [8/16]

template<typename T >

template<typename PairRange , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && detail::is_gpair_range_v<PairRange>>>

SparseShape TiledArray::SparseShape< T >::block	(	const PairRange &	bounds,
		const Scalar	factor,
		const Permutation &	perm
	)		const

inline

Create a permuted scaled sub-block of the shape.

Template Parameters

PairRange	Type representing a range of generalized pairs (see TiledArray::detail::is_gpair_v )
Scalar	A numeric type

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

Parameters

bounds	A range of {lower,upper} bounds for each dimension
factor	the scaling factor
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 1068 of file sparse_shape.h.

◆ block() [9/16]

template<typename T >

template<typename Index1 , typename Index2 , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< Index1 > &	lower_bound,
		const std::initializer_list< Index2 > &	upper_bound
	)		const

inline

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

Template Parameters

Index1	An integral type
Index2	An integral type

Parameters

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

Definition at line 845 of file sparse_shape.h.

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◆ block() [10/16]

template<typename T >

template<typename Index1 , typename Index2 , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< Index1 > &	lower_bound,
		const std::initializer_list< Index2 > &	upper_bound,
		const Permutation &	perm
	)		const

inline

Create a permuted sub-block of the shape.

Template Parameters

Index1	An integral type
Index2	An integral type

Parameters

lower_bound	The lower bound of the sub-block
upper_bound	The upper bound of the sub-block
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 981 of file sparse_shape.h.

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◆ block() [11/16]

template<typename T >

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2> && detail::is_numeric_v<Scalar>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< Index1 > &	lower_bound,
		const std::initializer_list< Index2 > &	upper_bound,
		const Scalar	factor
	)		const

inline

Create a scaled sub-block of the shape.

Template Parameters

Index1	An integral type
Index2	An integral type
Scalar	A numeric type

Note: expression abs(Scalar) 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 911 of file sparse_shape.h.

◆ block() [12/16]

template<typename T >

template<typename Index1 , typename Index2 , typename Scalar , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2> && detail::is_numeric_v<Scalar>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< Index1 > &	lower_bound,
		const std::initializer_list< Index2 > &	upper_bound,
		const Scalar	factor,
		const Permutation &	perm
	)		const

inline

Create a permuted scaled sub-block of the shape.

Template Parameters

Index1	An integral type
Index2	An integral type
Scalar	A numeric type

Note: expression abs(Scalar) 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
factor	the scaling factor
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 1050 of file sparse_shape.h.

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◆ block() [13/16]

template<typename T >

template<typename Index , typename = std::enable_if_t<std::is_integral_v<Index>>>

SparseShape TiledArray::SparseShape< T >::block ( const std::initializer_list< std::initializer_list< Index >> & bounds ) const

inline

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

Template Parameters

Index An integral type

Parameters

bounds A range of {lower,upper} bounds for each dimension

Definition at line 870 of file sparse_shape.h.

◆ block() [14/16]

template<typename T >

template<typename Index , typename = std::enable_if_t<std::is_integral_v<Index>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< std::initializer_list< Index >> &	bounds,
		const Permutation &	perm
	)		const

inline

Create a permuted sub-block of the shape.

Template Parameters

Index An integral type

Parameters

bounds	A range of {lower,upper} bounds for each dimension
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 1007 of file sparse_shape.h.

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◆ block() [15/16]

template<typename T >

template<typename Index , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && std::is_integral_v<Index>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< std::initializer_list< Index >> &	bounds,
		const Scalar	factor
	)		const

inline

Create a scaled sub-block of the shape.

Template Parameters

Index	An integral type
Scalar	A numeric type

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

Parameters

bounds	A range of {lower,upper} bounds for each dimension
factor	the scaling factor

Definition at line 946 of file sparse_shape.h.

◆ block() [16/16]

template<typename T >

template<typename Index , typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar> && std::is_integral_v<Index>>>

SparseShape TiledArray::SparseShape< T >::block	(	const std::initializer_list< std::initializer_list< Index >> &	bounds,
		const Scalar	factor,
		const Permutation &	perm
	)		const

inline

Create a permuted scaled sub-block of the shape.

Template Parameters

Index	An integral type
Scalar	A numeric type

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

Parameters

bounds	A range of {lower,upper} bounds for each dimension
factor	the scaling factor
perm	permutation to apply

Note: permutation is not fused into construction

Definition at line 1089 of file sparse_shape.h.

◆ data()

template<typename T >

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

inline

Data accessor.

Returns: A const reference to the Tensor object that stores the scaled (per-element) Frobenius norms of tiles

Definition at line 528 of file sparse_shape.h.

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◆ empty()

template<typename T >

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

inline

Initialization check.

Returns: true when this shape has been initialized.

Definition at line 549 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 1459 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 1557 of file sparse_shape.h.

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◆ is_dense()

template<typename T >

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

inlinestaticconstexpr

Check density.

Returns: true

Definition at line 463 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 455 of file sparse_shape.h.

◆ 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 555 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 1392 of file sparse_shape.h.

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◆ mult() [2/4]

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 1421 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 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 1439 of file sparse_shape.h.

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◆ mult() [4/4]

template<typename T >

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

inline

Definition at line 1404 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 431 of file sparse_shape.h.

◆ operator==()

template<typename T >

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

inline

Bitwise comparison.

Parameters

other a SparseShape object

Returns: true if this object and other object are bitwise identical

Definition at line 697 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 (scaled) norm of the tile at index

Definition at line 489 of file sparse_shape.h.

◆ 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 1102 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 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 1150 of file sparse_shape.h.

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◆ scale() [2/2]

template<typename T >

template<typename Scalar , typename = std::enable_if_t<detail::is_numeric_v<Scalar>>>

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

inline

Scale shape.

Construct a new scaled shape as:

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

Template Parameters

Scalar A numeric type

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

Parameters

factor The scaling factor

Returns: A new, scaled shape

Definition at line 1120 of file sparse_shape.h.

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◆ serialize() [1/2]

template<typename T >

template<typename Archive , typename std::enable_if< madness::archive::is_input_archive< Archive >::value >::type * = nullptr>

void TiledArray::SparseShape< T >::serialize ( const Archive & ar )

inline

Definition at line 1566 of file sparse_shape.h.

◆ serialize() [2/2]

template<typename T >

template<typename Archive , typename std::enable_if< madness::archive::is_output_archive< Archive >::value >::type * = nullptr>

void TiledArray::SparseShape< T >::serialize ( const Archive & ar ) const

inline

Definition at line 1579 of file sparse_shape.h.

◆ 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 468 of file sparse_shape.h.

◆ subt() [1/6]

template<typename T >

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

inline

Definition at line 1369 of file sparse_shape.h.

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◆ subt() [2/6]

template<typename T >

template<typename Factor >

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

inline

Definition at line 1376 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 Permutation &	perm
	)		const

inline

Definition at line 1381 of file sparse_shape.h.

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◆ subt() [4/6]

template<typename T >

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

inline

Definition at line 1371 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 1386 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 1388 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 476 of file sparse_shape.h.

◆ 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 481 of file sparse_shape.h.

◆ tile_norms()

template<typename T >

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

inline

Data accessor.

Returns: A const reference to the Tensor object that stores the Frobenius norms of tiles

Definition at line 534 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 scaled the output norms will be identically scaled, e.g. when Op is an identity operation the output SparseShape data will have the same values as this.

Definition at line 504 of file sparse_shape.h.

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◆ update_block() [1/4]

template<typename T >

template<typename Index1 , typename Index2 , typename = std::enable_if_t<detail::is_integral_range_v<Index1> && detail::is_integral_range_v<Index2>>>

SparseShape TiledArray::SparseShape< T >::update_block	(	const Index1 &	lower_bound,
		const Index2 &	upper_bound,
		const SparseShape< T > &	other
	)		const

inline

Creates a copy of this with a sub-block updated with contents of another shape.

Template Parameters

Index1	An integral range type
Index2	An integral range 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 sub-block defined by lower_bound and upper_bound contains the data result_tile_norms of other.

Definition at line 593 of file sparse_shape.h.

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◆ update_block() [2/4]

template<typename T >

template<typename PairRange , typename = std::enable_if_t<detail::is_gpair_range_v<PairRange>>>

SparseShape TiledArray::SparseShape< T >::update_block	(	const PairRange &	bounds,
		const SparseShape< T > &	other
	)		const

inline

Creates a copy of this with a sub-block updated with contents of another shape.

Template Parameters

PairRange Type representing a range of generalized pairs (see TiledArray::detail::is_gpair_v )

Parameters

bounds	The {lower,upper} bounds of the sub-block
other	The shape that will be used to update the sub-block

Returns: A new sparse shape object where the sub-block defined by lower_bound and upper_bound contains the data result_tile_norms of other.

Definition at line 651 of file sparse_shape.h.

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◆ update_block() [3/4]

template<typename T >

template<typename Index1 , typename Index2 , typename = std::enable_if_t<std::is_integral_v<Index1> && std::is_integral_v<Index2>>>

SparseShape TiledArray::SparseShape< T >::update_block	(	const std::initializer_list< Index1 > &	lower_bound,
		const std::initializer_list< Index2 > &	upper_bound,
		const SparseShape< T > &	other
	)		const

inline

Creates a copy of this with a sub-block updated with contents of another shape.

Template Parameters

Index1	An integral type
Index2	An integral 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 sub-block defined by lower_bound and upper_bound contains the data result_tile_norms of other.

Definition at line 632 of file sparse_shape.h.

◆ update_block() [4/4]

template<typename T >

template<typename Index , typename = std::enable_if_t<std::is_integral_v<Index>>>

SparseShape TiledArray::SparseShape< T >::update_block	(	const std::initializer_list< std::initializer_list< Index >> &	bounds,
		const SparseShape< T > &	other
	)		const

inline

Creates a copy of this with a sub-block updated with contents of another shape.

Template Parameters

Index An integral type

Parameters

bounds	The {lower,upper} bounds of the sub-block
other	The shape that will be used to update the sub-block

Returns: A new sparse shape object where the sub-block defined by lower_bound and upper_bound contains the data result_tile_norms of other.

Definition at line 686 of file sparse_shape.h.

◆ 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 445 of file sparse_shape.h.

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

TiledArray/sparse_shape.h

Documentation

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

Public Types

Public Member Functions

Static Public Member Functions

Member Typedef Documentation

◆ index1_type

◆ size_type

◆ SparseShape_

◆ value_type

Constructor & Destructor Documentation

◆ SparseShape() [1/7]

◆ SparseShape() [2/7]

◆ SparseShape() [3/7]

◆ SparseShape() [4/7]

◆ SparseShape() [5/7]

◆ SparseShape() [6/7]

◆ SparseShape() [7/7]

Member Function Documentation

◆ add() [1/6]

◆ add() [2/6]

◆ add() [3/6]

◆ add() [4/6]

◆ add() [5/6]

◆ add() [6/6]

◆ block() [1/16]

◆ block() [2/16]

◆ block() [3/16]

◆ block() [4/16]

◆ block() [5/16]

◆ block() [6/16]

◆ block() [7/16]

◆ block() [8/16]

◆ block() [9/16]

◆ block() [10/16]

◆ block() [11/16]

◆ block() [12/16]

◆ block() [13/16]

◆ block() [14/16]

◆ block() [15/16]

◆ block() [16/16]

◆ 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==()

◆ operator[]()

◆ perm()

◆ scale() [1/2]

◆ scale() [2/2]

◆ serialize() [1/2]

◆ serialize() [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]

◆ tile_norms()

◆ transform()

◆ update_block() [1/4]

◆ update_block() [2/4]

◆ update_block() [3/4]

◆ update_block() [4/4]

◆ validate()

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