tensorium::DerivateND< K, Rank > Class Template Reference

A multi-dimensional aligned tensor for numerical derivatives. More...

#include <Derivate.hpp>

Collaboration diagram for tensorium::DerivateND< K, Rank >:

Public Types
using	reg = typename Simd::reg
using	reg = typename Simd::reg

Public Member Functions
	DerivateND (const std::array< size_t, Rank > &dims)
	Construct a tensor with a given shape.
size_t	flatten_index (const std::array< size_t, Rank > &indices) const
K &	operator() (const std::array< size_t, Rank > &indices)
	Mutable access to a tensor element.
const K &	operator() (const std::array< size_t, Rank > &indices) const
	Const access to a tensor element.
size_t	size () const
	Total number of elements in the tensor.
	__attribute__ ((always_inline, hot, flatten)) inline void centered_derivative(const DerivateND< K
	Compute second-order centered derivative along an axis.
	for (int i=Rank - 2;i >=0;--i) strides[i]
	for (size_t flat=0;flat< total;flat+=simd_width)
	__attribute__ ((always_inline, hot, flatten)) inline void centered_derivative_order4_rank(const DerivateND< K
	Compute fourth-order centered derivative along an axis.
	for (int i=Rank - 2;i >=0;--i) strides[i]
	for (size_t flat=0;flat< total;flat+=W)

Public Attributes
std::array< size_t, Rank >	shape = input.shape
aligned_vector< K >	data
size_t	block_size
Rank &	input
Rank DerivateND< K, Rank > &	output
Rank DerivateND< K, Rank > size_t	axis
Rank DerivateND< K, Rank > size_t K dx	const
const size_t	simd_width = Simd::width
const auto &	shape = input.shape
const size_t	total = input.size()
const K	inv_2dx = K(1) / (K(2) * dx)
const reg	inv2dx = Simd::set1(inv_2dx)
std::array< size_t, Rank >	strides
	strides [Rank - 1] = 1
const size_t	stride_axis = strides[axis]
const size_t	dim_axis = shape[axis]
constexpr size_t	W = Simd::width
const K	inv_12dx = K(1) / (K(12) * dx)
const reg	inv = Simd::set1(inv_12dx)

Detailed Description

template<typename K, size_t Rank>
class tensorium::DerivateND< K, Rank >

A multi-dimensional aligned tensor for numerical derivatives.

Template Parameters

K	Scalar type.
Rank	Tensor rank (dimensionality).

Member Typedef Documentation

reg [1/2]

template<typename K, size_t Rank>

using tensorium::DerivateND< K, Rank >::reg = typename Simd::reg

reg [2/2]

template<typename K, size_t Rank>

using tensorium::DerivateND< K, Rank >::reg = typename Simd::reg

Constructor & Destructor Documentation

DerivateND()

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::DerivateND ( const std::array< size_t, Rank > & dims )

inline

Construct a tensor with a given shape.

Parameters

dims	Tensor dimensions.

References block_size, data, detect_optimal_block_size(), and shape.

Referenced by __attribute__().

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Member Function Documentation

__attribute__() [1/2]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::__attribute__

(

(always_inline, hot, flatten)

)

const

Compute second-order centered derivative along an axis.

Parameters

input	Input tensor.
output	Output tensor.
axis	Axis to differentiate.
dx	Grid spacing.

__attribute__() [2/2]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::__attribute__

(

(always_inline, hot, flatten)

)

const

Compute fourth-order centered derivative along an axis.

Parameters

input	Input tensor.
output	Output tensor.
axis	Axis to differentiate.
dx	Grid spacing.

References axis, DerivateND(), input, and output.

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flatten_index()

template<typename K, size_t Rank>

size_t tensorium::DerivateND< K, Rank >::flatten_index ( const std::array< size_t, Rank > & indices ) const

inline

References shape.

Referenced by operator()(), and operator()().

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for() [1/4]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::for

(

int

i = Rank - 2;i >=0;--i

)

References axis, dim_axis, shape, stride_axis, and strides.

for() [2/4]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::for

(

int

i = Rank - 2;i >=0;--i

)

References shape, and strides.

for() [3/4]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::for ( )

inline

References dim_axis, input, inv2dx, inv_2dx, output, simd_width, stride_axis, and total.

for() [4/4]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::for ( )

inline

References dim_axis, input, inv, inv_12dx, output, stride_axis, total, and W.

operator()() [1/2]

template<typename K, size_t Rank>

K & tensorium::DerivateND< K, Rank >::operator() ( const std::array< size_t, Rank > & indices )

inline

Mutable access to a tensor element.

Parameters

indices

Multi-index.

Returns

Reference to the element.

References data, and flatten_index().

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operator()() [2/2]

template<typename K, size_t Rank>

const K & tensorium::DerivateND< K, Rank >::operator() ( const std::array< size_t, Rank > & indices ) const

inline

Const access to a tensor element.

Parameters

indices

Multi-index.

Returns

Const reference to the element.

References data, and flatten_index().

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size()

template<typename K, size_t Rank>

size_t tensorium::DerivateND< K, Rank >::size ( ) const

inline

Total number of elements in the tensor.

Returns

Total size.

References data.

Member Data Documentation

axis

template<typename K, size_t Rank>

Rank DerivateND< K, Rank > size_t tensorium::DerivateND< K, Rank >::axis

Referenced by __attribute__(), and for().

block_size

template<typename K, size_t Rank>

size_t tensorium::DerivateND< K, Rank >::block_size

Referenced by DerivateND().

const

template<typename K, size_t Rank>

Rank DerivateND< K, Rank > size_t K dx tensorium::DerivateND< K, Rank >::const

Initial value:

{
        using Simd = simd::SimdTraits<K, DefaultISA>

data

template<typename K, size_t Rank>

aligned_vector<K> tensorium::DerivateND< K, Rank >::data

Referenced by DerivateND(), operator()(), operator()(), and size().

dim_axis

template<typename K, size_t Rank>

const size_t tensorium::DerivateND< K, Rank >::dim_axis = shape[axis]

Referenced by for(), for(), and for().

input

template<typename K, size_t Rank>

Rank & tensorium::DerivateND< K, Rank >::input

Referenced by __attribute__(), for(), and for().

inv

template<typename K, size_t Rank>

const reg tensorium::DerivateND< K, Rank >::inv = Simd::set1(inv_12dx)

Referenced by for().

inv2dx

template<typename K, size_t Rank>

const reg tensorium::DerivateND< K, Rank >::inv2dx = Simd::set1(inv_2dx)

Referenced by for().

inv_12dx

template<typename K, size_t Rank>

const K tensorium::DerivateND< K, Rank >::inv_12dx = K(1) / (K(12) * dx)

Referenced by for().

inv_2dx

template<typename K, size_t Rank>

const K tensorium::DerivateND< K, Rank >::inv_2dx = K(1) / (K(2) * dx)

Referenced by for().

output

template<typename K, size_t Rank>

Rank DerivateND< K, Rank > & tensorium::DerivateND< K, Rank >::output

Referenced by __attribute__(), for(), and for().

shape [1/2]

template<typename K, size_t Rank>

const auto& tensorium::DerivateND< K, Rank >::shape = input.shape

shape [2/2]

template<typename K, size_t Rank>

const auto & tensorium::DerivateND< K, Rank >::shape = input.shape

Referenced by DerivateND(), flatten_index(), and for().

simd_width

template<typename K, size_t Rank>

const size_t tensorium::DerivateND< K, Rank >::simd_width = Simd::width

Referenced by for().

stride_axis

template<typename K, size_t Rank>

const size_t tensorium::DerivateND< K, Rank >::stride_axis = strides[axis]

Referenced by for(), for(), and for().

strides [1/2]

template<typename K, size_t Rank>

tensorium::DerivateND< K, Rank >::strides[Rank - 1] = 1

strides [2/2]

template<typename K, size_t Rank>

std::array< size_t, Rank > tensorium::DerivateND< K, Rank >::strides

Referenced by for().

total

template<typename K, size_t Rank>

const size_t tensorium::DerivateND< K, Rank >::total = input.size()

Referenced by for(), and for().

W

template<typename K, size_t Rank>

size_t tensorium::DerivateND< K, Rank >::W = Simd::width

constexpr

Referenced by for().

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

• includes/Tensorium/Core/Derivate.hpp