Aligned, SIMD-optimized mathematical vector class for scientific computing. More...

#include <Vector.hpp>

Collaboration diagram for tensorium::Vector< K >:

Public Member Functions
Constructors
	Vector (const std::vector< K > &vec)
	Construct from a standard vector.

Element Access
K &	operator[] (size_t i)

const K &	operator[] (size_t i) const

const K &	operator() (size_t i) const

K &	operator() (size_t i)

	Vector (size_t n)
	Construct an empty vector of size `n`.

	Vector (std::initializer_list< K > init)
	Construct from an initializer list.

	Vector (size_t n, K value)
	Construct a constant vector.

Iterators
auto	begin ()

auto	end ()

auto	begin () const

auto	end () const

Size and Resizing
size_t	size () const

void	resize (size_t n)

Debug and Utilities
void	print () const
	Print the vector to stdout.

Basic Operations
using	Simd = simd::SimdTraits<K, DefaultISA>

using	reg = typename Simd::reg

const Vector< float > &	b

const Vector< float > float	t

const size_t	simd_width = Simd::width

const size_t	n = a.size()

const reg	vt = Simd::set1(t)

const reg	vt1 = Simd::sub(Simd::set1(1.0f), vt)

size_t	i = 0

return	result

	__attribute__ ((always_inline, hot, flatten)) Vector< K > operator-(const Vector< K > &other) const
	Subtract two vectors.

	__attribute__ ((always_inline, hot, flatten)) inline void add(const Vector &v)
	Add another vector to this one (in-place).

	__attribute__ ((always_inline, hot, flatten)) inline void sub(const Vector &v)
	Subtract another vector from this one (in-place).

	__attribute__ ((always_inline, hot, flatten)) inline void scl(float a)
	Scale this vector by a scalar (in-place).

	__attribute__ ((always_inline, hot, flatten)) static inline Vector< float > linear_combination(const std
	Compute the linear combination of vectors with coefficients.

	__attribute__ ((always_inline, hot, flatten)) static inline Vector< float > lerp(const Vector< float > &a
	Linearly interpolate between two vectors.

Vector< float >	result (n)

	_mm_prefetch ((const char *)&a.data[0], _MM_HINT_T0)

	for (;i+7< n;i+=simd_width)

	for (;i< n;++i) result.data[i]

static Vector< K >	canonical (int index, K dx, K dy, K dz)

Advanced Operations
aligned_vector< K >	data = std::fma(u.data[2], v.data[0], -u.data[0] * v.data[2])
	Underlying aligned data storage (SIMD-friendly).

const Vector< float > &	v

const float	dot = u.dot(v)

const float	norm_u = u.norm_2()

const float	norm_v = v.norm_2()

__m128	uxy = _mm_set_ps(0.0f, u.data[0], u.data[2], u.data[1])

__m128	vxy = _mm_set_ps(0.0f, v.data[0], v.data[2], v.data[1])

r	data [0] = std::fma(u.data[1], v.data[2], -u.data[2] * v.data[1])

return	r

	__attribute__ ((always_inline, hot, flatten)) inline float dot(const Vector< float > &v) const
	Compute the dot product with another vector.

	__attribute__ ((always_inline, hot, flatten)) inline float norm_1() const
	Compute the 1-norm (sum of absolute values).

	__attribute__ ((always_inline, hot, flatten)) inline float norm_2() const
	Compute the 2-norm (Euclidean norm).

	__attribute__ ((always_inline, hot, flatten)) inline float norm_inf() const
	Compute the infinity norm (maximum absolute value).

	__attribute__ ((always_inline, hot, flatten)) static inline float angle_cos(const Vector< float > &u
	Compute the cosine of the angle between two vectors.

return	dot (norm_u *norm_v)

	__attribute__ ((always_inline, hot, flatten)) static inline Vector< float > cross_product(const Vector< float > &u
	Compute the cross product between two 3D vectors.

Vector< float >	r (3)

Detailed Description

template<typename K>
class tensorium::Vector< K >

Aligned, SIMD-optimized mathematical vector class for scientific computing.

This class implements a 1D container with SIMD-accelerated arithmetic operations including addition, subtraction, scalar multiplication, dot product, and various norms. It uses an aligned memory allocator and supports fused-multiply-add instructions via the architecture-dependent SimdTraits specialization.

This class is intended to be used in high-performance numerical computing, physics simulations, and linear algebra backends.

Template Parameters

K	Scalar type (typically float or double).

Member Typedef Documentation

◆ reg

template<typename K >

using tensorium::Vector< K >::reg = typename Simd::reg

◆ Simd

template<typename K >

using tensorium::Vector< K >::Simd = simd::SimdTraits<K, DefaultISA>

Constructor & Destructor Documentation

◆ Vector() [1/4]

template<typename K >

tensorium::Vector< K >::Vector ( const std::vector< K > & vec )

inline

Construct from a standard vector.

Parameters

vec	The std::vector used to initialize the data.

◆ Vector() [2/4]

template<typename K >

tensorium::Vector< K >::Vector ( size_t n )

inline

Construct an empty vector of size n.

Parameters

n	Number of elements.

◆ Vector() [3/4]

template<typename K >

tensorium::Vector< K >::Vector ( std::initializer_list< K > init )

inline

Construct from an initializer list.

Parameters

init	Initializer list.

◆ Vector() [4/4]

template<typename K >

tensorium::Vector< K >::Vector	(	size_t	n,
		K	value )

inline

Construct a constant vector.

Parameters

n	Number of elements.
value	Constant value to fill.

Member Function Documentation

◆ attribute() [1/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

inline

Compute the dot product with another vector.

Parameters

v	The other vector.

Returns: The scalar dot product.

References tensorium::Vector< K >::_mm_prefetch(), tensorium::Vector< K >::b, tensorium::Tensor< K, Rank >::data, tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::result, tensorium::Vector< K >::simd_width, tensorium::Vector< K >::size(), and tensorium::Vector< K >::v.

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◆ attribute() [2/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const

inline

Compute the 1-norm (sum of absolute values).

Returns: The L1 norm.

References MathsUtils::_fabs(), tensorium::Vector< K >::_mm_prefetch(), tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::result, tensorium::Vector< K >::simd_width, tensorium::Vector< K >::size(), and tensorium::Vector< K >::v.

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◆ attribute() [3/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const

inline

Compute the 2-norm (Euclidean norm).

Returns: The L2 norm.

References tensorium::Vector< K >::_mm_prefetch(), tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::result, tensorium::Vector< K >::simd_width, tensorium::Vector< K >::size(), and tensorium::Vector< K >::v.

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◆ attribute() [4/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const

inline

Compute the infinity norm (maximum absolute value).

Returns: The L∞ norm.

References MathsUtils::_fabs(), MathsUtils::_max(), tensorium::Vector< K >::_mm_prefetch(), tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::result, tensorium::Vector< K >::simd_width, tensorium::Vector< K >::size(), and tensorium::Vector< K >::v.

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◆ attribute() [5/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

inline

Add another vector to this one (in-place).

Parameters

v	The vector to add.

References tensorium::Vector< K >::_mm_prefetch(), tensorium::Tensor< K, Rank >::data, tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::simd_width, tensorium::Vector< K >::size(), and tensorium::Vector< K >::v.

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◆ attribute() [6/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) )

inline

Scale this vector by a scalar (in-place).

Parameters

a	The scalar value.

References tensorium::Vector< K >::_mm_prefetch(), tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::simd_width, and tensorium::Vector< K >::size().

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◆ attribute() [7/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

inline

Subtract another vector from this one (in-place).

Parameters

v	The vector to subtract.

References tensorium::Vector< K >::_mm_prefetch(), tensorium::Tensor< K, Rank >::data, tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::simd_width, tensorium::Vector< K >::size(), and tensorium::Vector< K >::v.

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◆ attribute() [8/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

Compute the cosine of the angle between two vectors.

Parameters

u	First vector.
v	Second vector.

Returns: Cosine of the angle between u and v.

◆ attribute() [9/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

Compute the cross product between two 3D vectors.

Parameters

u	First 3D vector.
v	Second 3D vector.

Returns: Resulting 3D vector.

References tensorium::Vector< K >::v.

◆ attribute() [10/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

Linearly interpolate between two vectors.

Parameters

a	First vector.
b	Second vector.
t	Interpolation factor (0 = a, 1 = b).

Returns: Interpolated vector.

◆ attribute() [11/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const

inline

Compute the linear combination of vectors with coefficients.

Parameters

u	List of vectors.
coefs	List of coefficients.

Returns: A vector representing the linear combination: sum(c_i * u_i).

References tensorium::Tensor< K, Rank >::data, tensorium::Vector< K >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::n, tensorium::Vector< K >::result, tensorium::Vector< K >::simd_width, and tensorium::Vector< K >::v.

◆ attribute() [12/12]

template<typename K >

tensorium::Vector< K >::__attribute__ ( (always_inline, hot, flatten) ) const &

inline

Subtract two vectors.

Parameters

other The vector to subtract.

Returns: A new Vector containing the difference.

References tensorium::Tensor< K, Rank >::data, tensorium::Vector< K >::data, tensorium::Vector< K >::i, and tensorium::Vector< K >::result.

◆ _mm_prefetch()

template<typename K >

tensorium::Vector< K >::_mm_prefetch	(	(const char *)&a.	data[0],
		_MM_HINT_T0	)

Referenced by tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), and tensorium::Vector< K >::__attribute__().

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◆ begin() [1/2]

template<typename K >

auto tensorium::Vector< K >::begin ( )

inline

References tensorium::Vector< K >::data.

◆ begin() [2/2]

template<typename K >

auto tensorium::Vector< K >::begin ( ) const

inline

References tensorium::Vector< K >::data.

◆ canonical()

template<typename K >

static Vector< K > tensorium::Vector< K >::canonical	(	int	index,
		K	dx,
		K	dy,
		K	dz )

inlinestatic

◆ dot()

template<typename K >

return tensorium::Vector< K >::dot ( norm_u * norm_v )

◆ end() [1/2]

template<typename K >

auto tensorium::Vector< K >::end ( )

inline

References tensorium::Vector< K >::data.

◆ end() [2/2]

template<typename K >

auto tensorium::Vector< K >::end ( ) const

inline

References tensorium::Vector< K >::data.

◆ for() [1/2]

template<typename K >

tensorium::Vector< K >::for ( )

inline

References tensorium::Vector< K >::b, tensorium::Tensor< K, Rank >::data, tensorium::Vector< K >::i, tensorium::Vector< K >::r, tensorium::Vector< K >::result, tensorium::Vector< K >::vt, and tensorium::Vector< K >::vt1.

◆ for() [2/2]

template<typename K >

tensorium::Vector< K >::for ( )

◆ operator()() [1/2]

template<typename K >

K & tensorium::Vector< K >::operator() ( size_t i )

inline

References tensorium::Vector< K >::data, and tensorium::Vector< K >::i.

◆ operator()() [2/2]

template<typename K >

const K & tensorium::Vector< K >::operator() ( size_t i ) const

inline

References tensorium::Vector< K >::data, and tensorium::Vector< K >::i.

◆ operator[]() [1/2]

template<typename K >

K & tensorium::Vector< K >::operator[] ( size_t i )

inline

References tensorium::Vector< K >::data, and tensorium::Vector< K >::i.

◆ operator[]() [2/2]

template<typename K >

const K & tensorium::Vector< K >::operator[] ( size_t i ) const

inline

References tensorium::Vector< K >::data, and tensorium::Vector< K >::i.

◆ print()

template<typename K >

void tensorium::Vector< K >::print ( ) const

inline

Print the vector to stdout.

References tensorium::Vector< K >::data, and tensorium::Vector< K >::size().

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◆ r()

template<typename K >

Vector< float > tensorium::Vector< K >::r ( 3 )

◆ resize()

template<typename K >

void tensorium::Vector< K >::resize ( size_t n )

inline

References tensorium::Vector< K >::data, tensorium::Vector< K >::n, and tensorium::Tensor< K, Rank >::resize().

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◆ result()

template<typename K >

Vector< float > tensorium::Vector< K >::result ( n )

◆ size()

template<typename K >

size_t tensorium::Vector< K >::size ( ) const

inline

References tensorium::Vector< K >::data.

Referenced by tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::SpectralFFT< T >::bit_reverse(), tensorium::Matrix< K, RowMajor >::mul_vec(), tensorium::Matrix< K, RowMajor >::operator*(), tensorium::Vector< K >::print(), tensorium::solver::Jacobi< K >::solve(), and tensorium::SpectralFFT< T >::transform_impl().

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Member Data Documentation

◆ b

template<typename K >

const Vector<float>& tensorium::Vector< K >::b

Referenced by tensorium::Vector< K >::__attribute__(), and tensorium::Vector< K >::for().

◆ data [1/2]

template<typename K >

r tensorium::Vector< K >::data = std::fma(u.data[2], v.data[0], -u.data[0] * v.data[2])

Underlying aligned data storage (SIMD-friendly).

◆ data [2/2]

template<typename K >

r tensorium::Vector< K >::data[2] = std::fma(u.data[1], v.data[2], -u.data[2] * v.data[1])

◆ dot

template<typename K >

const float tensorium::Vector< K >::dot = u.dot(v)

◆ i

template<typename K >

size_t tensorium::Vector< K >::i = 0

◆ n

template<typename K >

const size_t tensorium::Vector< K >::n = a.size()

Referenced by tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), and tensorium::Vector< K >::resize().

◆ norm_u

template<typename K >

const float tensorium::Vector< K >::norm_u = u.norm_2()

◆ norm_v

template<typename K >

const float tensorium::Vector< K >::norm_v = v.norm_2()

◆ r

template<typename K >

return tensorium::Vector< K >::r

Referenced by tensorium::Vector< K >::for().

◆ result

template<typename K >

return tensorium::Vector< K >::result

Referenced by tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), and tensorium::Vector< K >::for().

◆ simd_width

template<typename K >

const size_t tensorium::Vector< K >::simd_width = Simd::width

Referenced by tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), and tensorium::Vector< K >::__attribute__().

◆ t

template<typename K >

const Vector<float> float tensorium::Vector< K >::t

Initial value:

{
        if (a.size() != b.size())
            throw std::invalid_argument("Vector sizes do not match")

◆ uxy

template<typename K >

__m128 tensorium::Vector< K >::uxy = _mm_set_ps(0.0f, u.data[0], u.data[2], u.data[1])

◆ v

template<typename K >

const Vector< float > & tensorium::Vector< K >::v

Initial value:

{
        if (u.size() != v.size())
            throw std::invalid_argument("Vector sizes do not match")

Referenced by tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), tensorium::Vector< K >::__attribute__(), and tensorium::Vector< K >::__attribute__().

◆ vt

template<typename K >

const reg tensorium::Vector< K >::vt = Simd::set1(t)

Referenced by tensorium::Vector< K >::for().

◆ vt1

template<typename K >

const reg tensorium::Vector< K >::vt1 = Simd::sub(Simd::set1(1.0f), vt)

Referenced by tensorium::Vector< K >::for().

◆ vxy

template<typename K >

__m128 tensorium::Vector< K >::vxy = _mm_set_ps(0.0f, v.data[0], v.data[2], v.data[1])

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

includes/Tensorium/Core/Vector.hpp

Public Member Functions

Basic Operations

Advanced Operations

Detailed Description

Member Typedef Documentation

◆ reg

◆ Simd

Constructor & Destructor Documentation

◆ Vector() [1/4]

◆ Vector() [2/4]

◆ Vector() [3/4]

◆ Vector() [4/4]

Member Function Documentation

◆ __attribute__() [1/12]

◆ __attribute__() [2/12]

◆ __attribute__() [3/12]

◆ __attribute__() [4/12]

◆ __attribute__() [5/12]

◆ __attribute__() [6/12]

◆ __attribute__() [7/12]

◆ __attribute__() [8/12]

◆ __attribute__() [9/12]

◆ __attribute__() [10/12]

◆ __attribute__() [11/12]

◆ __attribute__() [12/12]

◆ _mm_prefetch()

◆ begin() [1/2]

◆ begin() [2/2]

◆ canonical()

◆ dot()

◆ end() [1/2]

◆ end() [2/2]

◆ for() [1/2]

◆ for() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ print()

◆ r()

◆ resize()

◆ result()

◆ size()

Member Data Documentation

◆ b

◆ data [1/2]

◆ data [2/2]

◆ dot

◆ i

◆ n

◆ norm_u

◆ norm_v

◆ r

◆ result

◆ simd_width

◆ t

◆ uxy

◆ v

◆ vt

◆ vt1

◆ vxy

◆ attribute() [1/12]

◆ attribute() [2/12]

◆ attribute() [3/12]

◆ attribute() [4/12]

◆ attribute() [5/12]

◆ attribute() [6/12]

◆ attribute() [7/12]

◆ attribute() [8/12]

◆ attribute() [9/12]

◆ attribute() [10/12]

◆ attribute() [11/12]

◆ attribute() [12/12]