MatrixKernel provides specialized SIMD-accelerated matrix multiplication routines for statically-sized square matrices. More...

#include <MatrixKernel.hpp>

Inheritance diagram for tensorium::MatrixKernel< K >:

Collaboration diagram for tensorium::MatrixKernel< K >:

Public Types
using	Simd = simd::SimdTraits<K, DefaultISA>

using	reg = typename Simd::reg

Public Types inherited from tensorium::Matrix< K, true >
using	Simd

using	reg

Public Member Functions
	MatrixKernel (const Matrix< K, true > &m)
	Construct a MatrixKernel from a column-major matrix.

	MatrixKernel (const Matrix< K, false > &m)
	Construct a MatrixKernel from a row-major matrix by copying elements.

	MatrixKernel (size_t r, size_t c)
	Construct an empty column-major matrix kernel of size (r × c).

Matrix< K >	mul_mat2x2 (const MatrixKernel< K > &B) const
	Multiply two 2×2 matrices using SIMD.

Matrix< K >	mul_mat3x3 (const MatrixKernel< K > &B) const
	Multiply two 3×3 matrices using SIMD.

Matrix< K >	mul_mat4x4 (const MatrixKernel< K > &B) const
	Multiply two 4×4 matrices using SIMD.

Matrix< K >	mul_mat8x8 (const MatrixKernel< K > &B) const
	Multiply two 8×8 matrices using SIMD.

Matrix< K >	mul_mat16x16 (const MatrixKernel< K > &B) const
	Multiply two 16×16 matrices using SIMD with FMADD accumulation. This function splits each row into two registers (low/high).

Matrix< K >	mul_mat32x32 (const MatrixKernel< K > &B) const
	Multiply two 32×32 matrices using SIMD. Each row is split into two registers (16 elements each).

Matrix< K >	mul_mat64x64 (const MatrixKernel< K > &B) const
	Multiply two 64×64 matrices using SIMD. Each row is split into 4 SIMD registers (4×16 elements). Vectorized FMADD chaining is used for performance.

Public Member Functions inherited from tensorium::Matrix< K, true >
	Matrix (size_t r, size_t c)
	Construct a matrix of size r × c, initialized with zeros.

size_t	index (size_t i, size_t j) const

size_t	size () const
	Return the total number of elements.

K &	operator() (size_t i, size_t j)
	Element access (mutable)

const K &	operator() (size_t i, size_t j) const

void	print () const
	Print the matrix to stdout.

void	swap_rows (size_t i, size_t j)
	Swap two rows of the matrix.

Vector< T >	operator* (const Vector< T > &v) const
	Multiply matrix by a vector (naïve fallback)

void	add (const Matrix &m)
	In-place matrix addition: this += m.

void	sub (const Matrix &m)
	In-place matrix subtraction: this -= m.

void	scl (K a)
	In-place scalar multiplication: this *= a.

void	lerp (const Matrix< K > &A, const Matrix< K > &B, K alpha)
	Linearly interpolate between two matrices: this = (1 - α) * A + α * B.

Matrix	_mul_mat (const Matrix< K > &mat) const
	Multiply matrix by another matrix using optimized SIMD path.

Vector< T >	mul_vec (const Vector< T > &x) const
	Multiply matrix by a vector using SIMD.

Matrix< K >	transpose () const
	Returns the transpose \( A^T \) of the matrix (column-major layout)

Matrix< K >	trace () const
	Returns the trace of a square matrix as a 1×1 matrix.

Matrix< K >	inverse () const
	Compute the inverse of the matrix using Gauss–Jordan elimination.

K	det () const
	Compute the determinant using Gaussian elimination.

size_t	rank (K eps=K(1e-6)) const
	Compute the numerical rank of the matrix.

Additional Inherited Members
Public Attributes inherited from tensorium::Matrix< K, true >
size_t	rows

size_t	cols

aligned_vector< K >	data

size_t	block_size

bool	iscolumn

size_t	simd_width

Detailed Description

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

MatrixKernel provides specialized SIMD-accelerated matrix multiplication routines for statically-sized square matrices.

This class inherits from a column-major Matrix<K, true> and offers optimized kernels for specific square sizes (2x2, 3x3, ..., 64x64), using AVX/SIMD intrinsics for high performance. The kernels exploit register-level blocking and FMADD chaining.

Template Parameters

K	Scalar type (float, double, etc.)

Member Typedef Documentation

◆ reg

template<typename K >

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

◆ Simd

template<typename K >

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

Constructor & Destructor Documentation

◆ MatrixKernel() [1/3]

template<typename K >

tensorium::MatrixKernel< K >::MatrixKernel ( const Matrix< K, true > & m )

inline

Construct a MatrixKernel from a column-major matrix.

Parameters

m	Source matrix.

◆ MatrixKernel() [2/3]

template<typename K >

tensorium::MatrixKernel< K >::MatrixKernel ( const Matrix< K, false > & m )

inline

Construct a MatrixKernel from a row-major matrix by copying elements.

Parameters

m	Source matrix.

References tensorium::Matrix< K, RowMajor >::cols, and tensorium::Matrix< K, RowMajor >::rows.

◆ MatrixKernel() [3/3]

template<typename K >

tensorium::MatrixKernel< K >::MatrixKernel	(	size_t	r,
		size_t	c )

inline

Construct an empty column-major matrix kernel of size (r × c).

Member Function Documentation

◆ mul_mat16x16()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat16x16 ( const MatrixKernel< K > & B ) const

inline

Multiply two 16×16 matrices using SIMD with FMADD accumulation. This function splits each row into two registers (low/high).

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

References tensorium::Matrix< K, true >::data, and tensorium::Matrix< K, RowMajor >::data.

◆ mul_mat2x2()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat2x2 ( const MatrixKernel< K > & B ) const

inline

Multiply two 2×2 matrices using SIMD.

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

References tensorium::Matrix< K, RowMajor >::data.

◆ mul_mat32x32()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat32x32 ( const MatrixKernel< K > & B ) const

inline

Multiply two 32×32 matrices using SIMD. Each row is split into two registers (16 elements each).

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

References tensorium::Matrix< K, true >::data, and tensorium::Matrix< K, RowMajor >::data.

◆ mul_mat3x3()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat3x3 ( const MatrixKernel< K > & B ) const

inline

Multiply two 3×3 matrices using SIMD.

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

◆ mul_mat4x4()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat4x4 ( const MatrixKernel< K > & B ) const

inline

Multiply two 4×4 matrices using SIMD.

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

References tensorium::Matrix< K, true >::data, and tensorium::Matrix< K, RowMajor >::data.

◆ mul_mat64x64()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat64x64 ( const MatrixKernel< K > & B ) const

inline

Multiply two 64×64 matrices using SIMD. Each row is split into 4 SIMD registers (4×16 elements). Vectorized FMADD chaining is used for performance.

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

References tensorium::Matrix< K, true >::data, and tensorium::Matrix< K, RowMajor >::data.

◆ mul_mat8x8()

template<typename K >

Matrix< K > tensorium::MatrixKernel< K >::mul_mat8x8 ( const MatrixKernel< K > & B ) const

inline

Multiply two 8×8 matrices using SIMD.

Parameters

B	Right-hand matrix.

Returns: Result of multiplication.

References tensorium::Matrix< K, true >::data, and tensorium::Matrix< K, RowMajor >::data.

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

includes/Tensorium/Core/MatrixKernels/MatrixKernel.hpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ reg

◆ Simd

Constructor & Destructor Documentation

◆ MatrixKernel() [1/3]

◆ MatrixKernel() [2/3]

◆ MatrixKernel() [3/3]

Member Function Documentation

◆ mul_mat16x16()

◆ mul_mat2x2()

◆ mul_mat32x32()

◆ mul_mat3x3()

◆ mul_mat4x4()

◆ mul_mat64x64()

◆ mul_mat8x8()