This class defines multi-dimensional (numeric) arrays. More...

#include "stir/Array.h"

Inheritance diagram for stir::Array< num_dimensions, elemT >:

[legend]

Public Types

typedef base_type::value_type	value_type
	typedefs such that we do not need to have `typename` wherever we use these types defined in the base class

typedef base_type::reference	reference

typedef base_type::const_reference	const_reference

typedef base_type::difference_type	difference_type

typedef base_type::size_type	size_type

typedef base_type::iterator	iterator

typedef base_type::const_iterator	const_iterator

typedefs for full_iterator support
Full iterators provide a 1-dimensional view on a multi-dimensional Array.
typedef elemT	full_value_type

typedef full_value_type *	full_pointer

typedef const full_value_type *	const_full_pointer

typedef full_value_type &	full_reference

typedef const full_value_type &	const_full_reference

typedef FullArrayIterator< typename base_type::iterator, typename Array< num_dimensions - 1, elemT >::full_iterator, elemT, full_reference, full_pointer >	full_iterator
	This defines an iterator type that iterates through all elements.

typedef FullArrayIterator< typename base_type::const_iterator, typename Array< num_dimensions - 1, elemT >::const_full_iterator, elemT, const_full_reference, const_full_pointer >	const_full_iterator
	As full_iterator, but for const objects.

Public Types inherited from stir::VectorWithOffset< Array< num_dimensions - 1, elemT > >
typedef size_t	size_type

typedef Array< num_dimensions - 1, elemT >	value_type

typedef value_type &	reference

typedef const value_type &	const_reference

typedef ptrdiff_t	difference_type

typedef Array< num_dimensions - 1, elemT > *	iterator

typedef Array< num_dimensions - 1, elemT > const *	const_iterator

typedef std::reverse_iterator< iterator >	reverse_iterator

typedef std::reverse_iterator< const_iterator >	const_reverse_iterator

Public Member Functions
	Array ()
	Construct an empty Array.

	Array (const IndexRange< num_dimensions > &)
	Construct an Array of given range of indices, elements are initialised to 0.

	Array (const IndexRange< num_dimensions > &range, shared_ptr< elemT[]> data_sptr)
	Construct an Array pointing to existing contiguous data. More...

	Array (const base_type &t)
	Construct an Array from an object of its base_type.

	Array (const self &t)
	Copy constructor.

	~Array () override
	virtual destructor, frees up any allocated memory

	Array (Array &&other) noexcept
	move constructor More...

Array &	operator= (Array other)
	assignment operator More...

IndexRange< num_dimensions >	get_index_range () const

size_t	size_all () const
	return the total number of elements in this array

virtual void	resize (const IndexRange< num_dimensions > &range)
	change the array to a new range of indices, new elements are set to 0 More...

virtual void	grow (const IndexRange< num_dimensions > &range)
	alias for resize()

elemT	sum () const
	return sum of all elements

elemT	sum_positive () const
	return sum of all positive elements

elemT	find_max () const
	return maximum of all the elements

elemT	find_min () const
	return minimum of all the elements

void	fill (const elemT &n)
	Fill elements with value `n`. More...

void	apply_lower_threshold (const elemT &l)
	Sets elements below value to the value.

void	apply_upper_threshold (const elemT &u)
	Sets elements above value to the value.

bool	is_regular () const
	checks if the index range is 'regular' More...

bool	get_regular_range (BasicCoordinate< num_dimensions, int > &min, BasicCoordinate< num_dimensions, int > &max) const
	find regular range, returns `false` if the range is not regular More...

Array< num_dimensions - 1, elemT > &	operator[] (int i)
	allow array-style access, read/write

const Array< num_dimensions - 1, elemT > &	operator[] (int i) const
	array access, read-only

elemT &	operator[] (const BasicCoordinate< num_dimensions, int > &c)
	allow array-style access given a BasicCoordinate to specify the indices, read/write

const elemT &	operator[] (const BasicCoordinate< num_dimensions, int > &c) const
	array access given a BasicCoordinate to specify the indices, read-only

template<typename elemT2 >
STIR_DEPRECATED void	axpby (const elemT2 a, const Array &x, const elemT2 b, const Array &y)

void	xapyb (const Array &x, const elemT a, const Array &y, const elemT b)
	set values of the array to xa+yb, where a and b are scalar

void	xapyb (const Array &x, const Array &a, const Array &y, const Array &b)
	set values of the array to xa+yb, where a and b are arrays

template<class T >
void	sapyb (const T &a, const Array &y, const T &b)
	set values of the array to selfa+yb where a and b are scalar or arrays

template<int num_dimensions, typename elemT>
	Array (Array< num_dimensions, elemT > &&other) noexcept

template<typename elemT2 >
void	axpby (const elemT2 a, const Array &x, const elemT2 b, const Array &y)

functions returning full_iterators
full_iterator	begin_all ()
	start value for iterating through all elements in the array, see full_iterator

const_full_iterator	begin_all () const
	start value for iterating through all elements in the (const) array, see full_iterator

const_full_iterator	begin_all_const () const
	start value for iterating through all elements in the array, see full_iterator

full_iterator	end_all ()
	end value for iterating through all elements in the array, see full_iterator

const_full_iterator	end_all () const
	end value for iterating through all elements in the (const) array, see full_iterator

const_full_iterator	end_all_const () const
	end value for iterating through all elements in the array, see full_iterator

indexed access with range checking (throw std:out_of_range)
Array< num_dimensions - 1, elemT > &	at (int i)

const Array< num_dimensions - 1, elemT > &	at (int i) const

elemT &	at (const BasicCoordinate< num_dimensions, int > &c)

const elemT &	at (const BasicCoordinate< num_dimensions, int > &c) const

access to the data via a pointer
bool	is_contiguous () const
	return if the array is contiguous in memory

elemT *	get_full_data_ptr ()
	member function for access to the data via a elemT* More...

const elemT *	get_const_full_data_ptr () const
	member function for access to the data via a const elemT* More...

void	release_full_data_ptr ()
	signal end of access to elemT* More...

void	release_const_full_data_ptr () const
	signal end of access to const elemT* More...

Public Member Functions inherited from stir::NumericVectorWithOffset< Array< num_dimensions - 1, elemT >, elemT >
	NumericVectorWithOffset (const VectorWithOffset< Array< num_dimensions - 1, elemT > > &t)
	Constructor from an object of this class' base_type.

	NumericVectorWithOffset (const NumericVectorWithOffset &t)
	Constructor from an object of this class' base_type.

	NumericVectorWithOffset (NumericVectorWithOffset &&other) noexcept
	move constructor More...

NumericVectorWithOffset &	operator= (const NumericVectorWithOffset &other)
	assignment

NumericVectorWithOffset	operator+ (const NumericVectorWithOffset &v) const
	adding vectors, element by element

NumericVectorWithOffset	operator+ (const elemT &v) const
	return a new vector with elements equal to the sum of the elements in the original and the `elemT`

NumericVectorWithOffset	operator- (const NumericVectorWithOffset &v) const
	subtracting vectors, element by element

NumericVectorWithOffset	operator- (const elemT &v) const
	return a new vector with elements equal to the difference of the elements in the original and the `elemT`

NumericVectorWithOffset	operator* (const NumericVectorWithOffset &v) const
	multiplying vectors, element by element

NumericVectorWithOffset	operator* (const elemT &v) const
	return a new vector with elements equal to the multiplication of the elements in the original and the `elemT`

NumericVectorWithOffset	operator/ (const NumericVectorWithOffset &v) const
	dividing vectors, element by element

NumericVectorWithOffset	operator/ (const elemT &v) const
	return a new vector with elements equal to the division of the elements in the original and the `elemT`

NumericVectorWithOffset &	operator+= (const NumericVectorWithOffset &v)
	adding elements of `v` to the current vector More...

NumericVectorWithOffset &	operator+= (const elemT &v)
	adding an `elemT` to the elements of the current vector

NumericVectorWithOffset &	operator-= (const NumericVectorWithOffset &v)
	subtracting elements of `v` from the current vector More...

NumericVectorWithOffset &	operator-= (const elemT &v)
	subtracting an `elemT` from the elements of the current vector

NumericVectorWithOffset &	operator*= (const NumericVectorWithOffset &v)
	multiplying elements of the current vector with elements of `v` More...

NumericVectorWithOffset &	operator*= (const elemT &v)
	multiplying the elements of the current vector with an `elemT`

NumericVectorWithOffset &	operator/= (const NumericVectorWithOffset &v)
	dividing all elements of the current vector by elements of `v` More...

NumericVectorWithOffset &	operator/= (const elemT &v)
	dividing the elements of the current vector by an `elemT`

STIR_DEPRECATED void	axpby (const elemT2 a, const NumericVectorWithOffset &x, const elemT2 b, const NumericVectorWithOffset &y)

void	axpby (const NUMBER2 a, const NumericVectorWithOffset &x, const NUMBER2 b, const NumericVectorWithOffset &y)

void	xapyb (const NumericVectorWithOffset &x, const elemT a, const NumericVectorWithOffset &y, const elemT b)
	set values of the array to xa+yb, where a and b are scalar

void	xapyb (const NumericVectorWithOffset &x, const NumericVectorWithOffset &a, const NumericVectorWithOffset &y, const NumericVectorWithOffset &b)
	set the values of the array to xa+yb, where a and b are vectors

void	sapyb (const T2 &a, const NumericVectorWithOffset &y, const T2 &b)
	set the values of the array to selfa+yb, where a and b are scalar or vectors

Public Member Functions inherited from stir::VectorWithOffset< Array< num_dimensions - 1, elemT > >
	VectorWithOffset ()
	Default constructor: creates a vector of length 0.

	VectorWithOffset (const int hsz)
	Construct a VectorWithOffset of given length (initialised with `T()`)

	VectorWithOffset (const int min_index, const int max_index)
	Construct a VectorWithOffset with offset `min_index` (initialised with `T()`)

STIR_DEPRECATED	VectorWithOffset (const int hsz, Array< num_dimensions - 1, elemT > const data_ptr, Array< num_dimensions - 1, elemT > const end_of_data_ptr)
	Construct a VectorWithOffset of given length pointing to existing data. More...

STIR_DEPRECATED	VectorWithOffset (const int min_index, const int max_index, Array< num_dimensions - 1, elemT > const data_ptr, Array< num_dimensions - 1, elemT > const end_of_data_ptr)
	Construct a VectorWithOffset with offset `min_index` pointing to existing data. More...

	VectorWithOffset (const int hsz, const Array< num_dimensions - 1, elemT > *const data_ptr)
	Construct a VectorWithOffset of given length from a bare pointer (copying data)

	VectorWithOffset (const int min_index, const int max_index, const Array< num_dimensions - 1, elemT > *const data_ptr)
	Construct a VectorWithOffset with offset `min_index` from a bare pointer (copying data)

	VectorWithOffset (const int min_index, const int max_index, shared_ptr< Array< num_dimensions - 1, elemT > []> data_sptr)
	Construct a VectorWithOffset sharing existing data. More...

	VectorWithOffset (const int sz, shared_ptr< Array< num_dimensions - 1, elemT > []> data_sptr)
	Construct a VectorWithOffset sharing existing data. More...

	VectorWithOffset (const VectorWithOffset &il)
	copy constructor

	VectorWithOffset (VectorWithOffset &&other) noexcept
	move constructor More...

virtual	~VectorWithOffset ()
	Destructor.

void	recycle ()
	Free all memory and make object as if default-constructed. More...

VectorWithOffset &	operator= (const VectorWithOffset &il)
	assignment operator with another vector More...

Array< num_dimensions - 1, elemT > &	operator[] (int i)
	allow array-style access, read/write More...

const Array< num_dimensions - 1, elemT > &	operator[] (int i) const
	array access, read-only More...

Array< num_dimensions - 1, elemT > &	at (int i)
	allow array-style access, read/write, but with range checking (throws std::out_of_range)

const Array< num_dimensions - 1, elemT > &	at (int i) const
	array access, read-only, but with range checking (throws std::out_of_range)

bool	empty () const
	checks if the vector is empty

void	fill (const Array< num_dimensions - 1, elemT > &n)
	fill elements with value n

void	apply_lower_threshold (const Array< num_dimensions - 1, elemT > &lower)
	Sets elements below value to the value.

void	apply_upper_threshold (const Array< num_dimensions - 1, elemT > &upper)
	Sets elements above value to the value.

int	get_length () const
	return number of elements in this vector More...

size_t	size () const
	return number of elements in this vector

int	get_min_index () const
	get value of first valid index

int	get_max_index () const
	get value of last valid index

void	set_offset (const int min_index)
	change value of starting index

void	set_min_index (const int min_index)
	identical to set_offset()

virtual void	grow (const int min_index, const int max_index)
	grow the range of the vector, new elements are set to `T()` More...

void	grow (const unsigned int new_size)
	grow the range of the vector from 0 to new_size-1, new elements are set to `T()`

virtual void	resize (const int min_index, const int max_index)
	change the range of the vector, new elements are set to `T()` More...

void	resize (const unsigned int new_size)
	change the range of the vector from 0 to new_size-1, new elements are set to `T()`

void	reserve (const int min_index, const int max_index)
	make the allocated range at least from min_index to max_index

void	reserve (const unsigned int new_size)
	make the allocated range at least from 0 to new_size-1

size_t	capacity () const
	get allocated size

bool	owns_memory_for_data () const
	check if this object owns the memory for the data More...

int	get_capacity_min_index () const
	get min_index within allocated range More...

int	get_capacity_max_index () const
	get max_index within allocated range More...

bool	operator== (const VectorWithOffset &iv) const

bool	operator!= (const VectorWithOffset &iv) const

Array< num_dimensions - 1, elemT > *	get_data_ptr ()
	member function for access to the data via a T* More...

const Array< num_dimensions - 1, elemT > *	get_const_data_ptr () const
	member function for access to the data via a const T* More...

void	release_data_ptr ()
	signal end of access to T* More...

void	release_const_data_ptr () const
	signal end of access to const T* More...

iterator	begin ()
	use to initialise an iterator to the first element of the vector

const_iterator	begin () const
	use to initialise an iterator to the first element of the (const) vector

iterator	end ()
	iterator 'past' the last element of the vector

const_iterator	end () const
	iterator 'past' the last element of the (const) vector

reverse_iterator	rbegin ()

const_reverse_iterator	rbegin () const

reverse_iterator	rend ()

const_reverse_iterator	rend () const

VectorWithOffset &	operator+= (const VectorWithOffset &v)
	adding elements of `v` to the current vector

VectorWithOffset &	operator-= (const VectorWithOffset &v)
	subtracting elements of `v` from the current vector

VectorWithOffset &	operator*= (const VectorWithOffset &v)
	multiplying elements of the current vector with elements of `v`

VectorWithOffset &	operator/= (const VectorWithOffset &v)
	dividing all elements of the current vector by elements of `v`

VectorWithOffset	operator+ (const VectorWithOffset &v) const
	adding vectors, element by element

VectorWithOffset	operator- (const VectorWithOffset &v) const
	subtracting vectors, element by element

VectorWithOffset	operator* (const VectorWithOffset &v) const
	multiplying vectors, element by element

VectorWithOffset	operator/ (const VectorWithOffset &v) const
	dividing vectors, element by element

Friends
template<int num_dimensions2, class elemT2 >
class	Array

void	swap (Array &first, Array &second)
	Swap content/members of 2 objects.

Additional Inherited Members
Protected Member Functions inherited from stir::VectorWithOffset< Array< num_dimensions - 1, elemT > >
void	check_state () const
	Called internally to see if all variables are consistent. More...

void	init (const int min_index, const int max_index, Array< num_dimensions - 1, elemT > *const data_ptr, bool copy_data)
	change vector with new index range and point to `data_ptr` More...

Protected Attributes inherited from stir::VectorWithOffset< Array< num_dimensions - 1, elemT > >
Array< num_dimensions - 1, elemT > *	num
	pointer to (*this)[0] (taking get_min_index() into account that is).

Detailed Description

template<int num_dimensions, typename elemT>
class stir::Array< num_dimensions, elemT >

This class defines multi-dimensional (numeric) arrays.

This class implements multi-dimensional arrays which can have 'irregular' ranges. See IndexRange for a description of the ranges. Normal numeric operations are defined. In addition, two types of iterators are defined, one which iterators through the outer index, and one which iterates through all elements of the array.

Array inherits its numeric operators from NumericVectorWithOffset. In particular this means that operator+= etc. potentially grow the object. However, as grow() is a virtual function, Array::grow is called, which initialises new elements first to 0.

Constructor & Destructor Documentation

◆ Array() [1/2]

template<int num_dimensions, typename elemT>

stir::Array< num_dimensions, elemT >::Array	(	const IndexRange< num_dimensions > &	range,
		shared_ptr< elemT[]>	data_sptr
	)

inline

Construct an Array pointing to existing contiguous data.

data_sptr should point to a contiguous block of correct size. The constructed Array will essentially be a "view" of the data_sptr.get() block. Therefore, any modifications to the array will modify the data at data_sptr.get(). This will be true until the Array is resized.

The C-array data_ptr will be accessed with the last dimension running fastest ("row-major" order).

◆ Array() [2/2]

template<int num_dimensions, typename elemT>

stir::Array< num_dimensions, elemT >::Array ( Array< num_dimensions, elemT > && other )

noexcept

move constructor

implementation uses the copy-and-swap idiom, see e.g. https://stackoverflow.com/a/3279550

Member Function Documentation

◆ operator=()

template<int num_dimensions, typename elemT>

Array< num_dimensions, elemT > & stir::Array< num_dimensions, elemT >::operator= ( Array< num_dimensions, elemT > other )

assignment operator

implementation uses the copy-and-swap idiom, see e.g. https://stackoverflow.com/a/3279550

◆ resize()

template<int num_dimensions, typename elemT >

void stir::Array< num_dimensions, elemT >::resize ( const IndexRange< num_dimensions > & range )

inlinevirtual

change the array to a new range of indices, new elements are set to 0

Current behaviour is that when resizing to a smaller array, the same memory will be used. However, when growing any of the dimensions, a new Array will be allocated and the data copied.

If the array points to an existing block of data, resizing is therefore problematic. When growing the array, the resized array will no longer point to the original block of data.

Referenced by stir::SegmentBySinogram< elemT >::resize(), stir::SegmentByView< elemT >::resize(), and stir::ColsherFilter::set_up().

◆ fill()

template<int num_dimensions, typename elemT>

void stir::Array< num_dimensions, elemT >::fill ( const elemT & n )

inline

Fill elements with value n.

hides VectorWithOffset::fill

Referenced by stir::PoissonLogLikelihoodWithLinearModelForMeanAndListModeDataWithProjMatrixByBin< TargetT >::actual_subsets_are_approximately_balanced(), stir::PoissonLogLikelihoodWithLinearModelForMeanAndProjData< TargetT >::actual_subsets_are_approximately_balanced(), stir::QuadraticPrior< float >::compute_gradient(), stir::LogcoshPrior< elemT >::compute_gradient(), stir::RelativeDifferencePrior< elemT >::compute_gradient(), stir::PLSPrior< elemT >::compute_gradient(), stir::BackProjectorByBin::get_output(), stir::make_det_pair_data(), stir::QuadraticPrior< float >::parabolic_surrogate_curvature(), stir::LogcoshPrior< elemT >::parabolic_surrogate_curvature(), stir::convert_array_Tests::run_tests(), stir::warp_imageTests::run_tests(), stir::zoom_imageTests::run_tests(), stir::SeparableMetzArrayFilterTests::run_tests(), stir::ProjDataInMemoryTests::run_tests(), stir::stir_mathTests::run_tests(), stir::SeparableMetzArrayFilter< num_dimensions, elemT >::SeparableMetzArrayFilter(), stir::ColsherFilter::set_up(), stir::ecat::BinNormalisationFromECAT8::set_up(), stir::truncate_end_planes(), stir::ScatterEstimation::upsample_and_fit_scatter_estimate(), and stir::BackProjectorByBinUsingInterpolation::use_piecewise_linear_interpolation().

◆ is_regular()

template<int num_dimensions, typename elemT >

bool stir::Array< num_dimensions, elemT >::is_regular ( ) const

inline

checks if the index range is 'regular'

Implementation note: this works by calling get_index_range().is_regular(). We cannot rely on remembering if it was a regular range at construction (or even resizing) time as resize() could have been called on an element of the array. Checking for this would involve a performance penalty on operator[], which is definitely not a good idea.

Referenced by stir::absolute_max_eigenvector_using_power_method(), stir::apply_array_function_on_1st_index(), stir::apply_array_functions_on_each_index(), stir::in_place_apply_array_function_on_1st_index(), stir::Array< 2, float >::is_regular(), stir::matrix_transpose(), and stir::truncate_rim().

◆ get_regular_range()

template<int num_dimensions, typename elemT >

bool stir::Array< num_dimensions, elemT >::get_regular_range	(	BasicCoordinate< num_dimensions, int > &	min,
		BasicCoordinate< num_dimensions, int > &	max
	)		const

find regular range, returns false if the range is not regular

See also: class IndexRange for a definition of (ir)regular ranges

Referenced by stir::ITKOutputFileFormat::actual_write_to_file(), stir::apply_array_functions_on_each_index(), stir::VoxelsOnCartesianGrid< elemT >::grow_z_range(), stir::interpolate_line(), stir::maximum_location_per_slice(), stir::NonseparableConvolutionUsingRealDFTImageFilter< elemT >::NonseparableConvolutionUsingRealDFTImageFilter(), stir::ArrayFilterUsingRealDFTWithPadding< 2, float >::set_kernel(), stir::ProjMatrixByBinUsingSolidAngle::set_up(), stir::ProjMatrixByBinWithPositronRange::set_up(), stir::ProjMatrixByBinSinglePhoton::set_up(), and stir::ProjMatrixByDenselUsingRayTracing::set_up().

◆ axpby()

template<int num_dimensions, typename elemT>

template<typename elemT2 >

STIR_DEPRECATED void stir::Array< num_dimensions, elemT >::axpby	(	const elemT2	a,
		const Array< num_dimensions, elemT > &	x,
		const elemT2	b,
		const Array< num_dimensions, elemT > &	y
	)

inline

Deprecated:: a*x+b*y (use xapyb)

◆ get_full_data_ptr()

template<int num_dimensions, typename elemT >

elemT * stir::Array< num_dimensions, elemT >::get_full_data_ptr ( )

inline

member function for access to the data via a elemT*

If is_contiguous() is false, calls error(). Otherwise, return a elemT* to the first element of the array.

Use only in emergency cases...

To prevent invalidating the safety checks (and making reimplementation more difficult), NO manipulation with the array is allowed between the pairs get_full_data_ptr() and release_full_data_ptr() and get_const_full_data_ptr() and release_const_full_data_ptr(). (This is checked with assert() in DEBUG mode.)

Referenced by stir::detail::read_data_1d().

◆ get_const_full_data_ptr()

template<int num_dimensions, typename elemT >

const elemT * stir::Array< num_dimensions, elemT >::get_const_full_data_ptr ( ) const

inline

member function for access to the data via a const elemT*

If is_contiguous() is false, calls error(). Otherwise, return a const elemT* to the first element of the array.

Use get_const_full_data_ptr() when you are not going to modify the data.

See also: get_full_data_ptr()

Referenced by stir::detail::write_data_1d().

◆ release_full_data_ptr()

template<int num_dimensions, typename elemT >

void stir::Array< num_dimensions, elemT >::release_full_data_ptr ( )

inline

signal end of access to elemT*

This has to be used when access to the elemT* returned by get_full_data_ptr() is finished. It updates the Array with any changes you made, and allows access to the other member functions again.

See also: get_full_data_ptr()

Referenced by stir::detail::read_data_1d().

◆ release_const_full_data_ptr()

template<int num_dimensions, typename elemT >

void stir::Array< num_dimensions, elemT >::release_const_full_data_ptr ( ) const

inline

signal end of access to const elemT*

This has to be used when access to the const elemT* returned by get_const_full_data_ptr() is finished. It allows access to the other member functions again.

See also: get_const_full_data_ptr()

Referenced by stir::detail::write_data_1d().

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

/home/sirfuser/devel/STIRdistrib/STIR/src/include/stir/Array.h
/home/sirfuser/devel/STIRdistrib/STIR/src/include/stir/Array.inl

Public Types

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

template<int num_dimensions, typename elemT> class stir::Array< num_dimensions, elemT >

Constructor & Destructor Documentation

◆ Array() [1/2]

◆ Array() [2/2]

Member Function Documentation

◆ operator=()

◆ resize()

◆ fill()

◆ is_regular()

◆ get_regular_range()

◆ axpby()

◆ get_full_data_ptr()

◆ get_const_full_data_ptr()

◆ release_full_data_ptr()

◆ release_const_full_data_ptr()

template<int num_dimensions, typename elemT>
class stir::Array< num_dimensions, elemT >