High-performance aligned matrix class with SIMD support. More...

#include <Matrix.hpp>

Collaboration diagram for tensorium::Matrix< K, RowMajor >:

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

using	reg = typename Simd::reg

Public Member Functions
	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.

template<typename T >
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.

template<typename T >
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.

Public Attributes
size_t	rows

size_t	cols

aligned_vector< K >	data

size_t	block_size

bool	iscolumn

size_t	simd_width = Simd::width

Detailed Description

template<typename K, bool RowMajor = false>
class tensorium::Matrix< K, RowMajor >

High-performance aligned matrix class with SIMD support.

This class provides a dense matrix container with:

Aligned memory allocation for SIMD operations
Fast matrix arithmetic (add, sub, scale)
Optimized matrix-vector and matrix-matrix multiplication
Support for inversion, determinant, transpose, and rank

Template Parameters

K	Scalar type (float, double, etc.)

Member Typedef Documentation

◆ reg

template<typename K , bool RowMajor = false>

using tensorium::Matrix< K, RowMajor >::reg = typename Simd::reg

◆ Simd

template<typename K , bool RowMajor = false>

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

Constructor & Destructor Documentation

◆ Matrix()

template<typename K , bool RowMajor = false>

tensorium::Matrix< K, RowMajor >::Matrix	(	size_t	r,
		size_t	c )

inline

Construct a matrix of size r × c, initialized with zeros.

Member Function Documentation

◆ _mul_mat()

template<typename K , bool RowMajor = false>

Matrix tensorium::Matrix< K, RowMajor >::_mul_mat ( const Matrix< K > & mat ) const

inline

Multiply matrix by another matrix using optimized SIMD path.

Uses blocking and micro-kernels to avoid cache bottleneck with FMA/AVX units repartition. Fast-paths exist for 4×4, 8×8, and 16×16.

References tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::data, tensorium::GemmKernelBigger< T >::matmul(), and tensorium::Matrix< K, RowMajor >::rows.

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◆ add()

template<typename K , bool RowMajor = false>

void tensorium::Matrix< K, RowMajor >::add ( const Matrix< K, RowMajor > & m )

inline

In-place matrix addition: this += m.

References tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::data, tensorium::Matrix< K, RowMajor >::rows, tensorium::Matrix< K, RowMajor >::simd_width, and tensorium::Matrix< K, RowMajor >::size().

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◆ det()

template<typename K , bool RowMajor = false>

K tensorium::Matrix< K, RowMajor >::det ( ) const

inline

Compute the determinant using Gaussian elimination.

\[ \det A = \prod_{i=1}^n U_{ii} \quad \text{with } A = LU \]

References MathsUtils::_abs(), tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::det(), f(), tensorium::Matrix< K, RowMajor >::operator()(), tensorium::Matrix< K, RowMajor >::rows, tensorium::Matrix< K, RowMajor >::simd_width, and tensorium::Matrix< K, RowMajor >::swap_rows().

Referenced by tensorium::Matrix< K, RowMajor >::det().

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◆ index()

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::index	(	size_t	i,
		size_t	j ) const

inline

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

Referenced by tensorium::Matrix< K, RowMajor >::operator()(), and tensorium::Matrix< K, RowMajor >::operator()().

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◆ inverse()

template<typename K , bool RowMajor = false>

Matrix< K > tensorium::Matrix< K, RowMajor >::inverse ( ) const

inline

Compute the inverse of the matrix using Gauss–Jordan elimination.

Throws if the matrix is singular or not square. need to add a fallback for unsquare matrix if possible

References MathsUtils::_abs(), tensorium::Matrix< K, RowMajor >::cols, f(), tensorium::Matrix< K, RowMajor >::operator()(), tensorium::Matrix< K, RowMajor >::rows, and tensorium::Matrix< K, RowMajor >::swap_rows().

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◆ lerp()

template<typename K , bool RowMajor = false>

void tensorium::Matrix< K, RowMajor >::lerp	(	const Matrix< K > &	A,
		const Matrix< K > &	B,
		K	alpha )

inline

Linearly interpolate between two matrices: this = (1 - α) * A + α * B.

References alpha, tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::data, tensorium::Matrix< K, RowMajor >::rows, tensorium::Matrix< K, RowMajor >::simd_width, and tensorium::Matrix< K, RowMajor >::size().

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◆ mul_vec()

template<typename K , bool RowMajor = false>

template<typename T >

Vector< T > tensorium::Matrix< K, RowMajor >::mul_vec ( const Vector< T > & x ) const

inline

Multiply matrix by a vector using SIMD.

This is a faster alternative to operator* when available.

References tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::rows, and tensorium::Vector< K >::size().

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◆ operator()() [1/2]

template<typename K , bool RowMajor = false>

K & tensorium::Matrix< K, RowMajor >::operator()	(	size_t	i,
		size_t	j )

inline

Element access (mutable)

References tensorium::Matrix< K, RowMajor >::data, and tensorium::Matrix< K, RowMajor >::index().

Referenced by tensorium::Matrix< K, RowMajor >::det(), tensorium::Matrix< K, RowMajor >::inverse(), and tensorium::Matrix< K, RowMajor >::trace().

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◆ operator()() [2/2]

template<typename K , bool RowMajor = false>

const K & tensorium::Matrix< K, RowMajor >::operator()	(	size_t	i,
		size_t	j ) const

inline

References tensorium::Matrix< K, RowMajor >::data, and tensorium::Matrix< K, RowMajor >::index().

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◆ operator*()

template<typename K , bool RowMajor = false>

template<typename T >

Vector< T > tensorium::Matrix< K, RowMajor >::operator* ( const Vector< T > & v ) const

inline

Multiply matrix by a vector (naïve fallback)

\[ (Ax)_i = \sum_j A_{ij} x_j \]

References tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::rows, and tensorium::Vector< K >::size().

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◆ print()

template<typename K , bool RowMajor = false>

void tensorium::Matrix< K, RowMajor >::print ( ) const

inline

Print the matrix to stdout.

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

◆ rank()

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::rank ( K eps = K(1e-6) ) const

inline

Compute the numerical rank of the matrix.

Performs row echelon reduction and counts non-zero pivots.

References MathsUtils::_abs(), tensorium::Matrix< K, RowMajor >::cols, f(), tensorium::Matrix< K, RowMajor >::rows, and tensorium::Matrix< K, RowMajor >::swap_rows().

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◆ scl()

template<typename K , bool RowMajor = false>

void tensorium::Matrix< K, RowMajor >::scl ( K a )

inline

In-place scalar multiplication: this *= a.

References tensorium::Matrix< K, RowMajor >::data, tensorium::Matrix< K, RowMajor >::simd_width, and tensorium::Matrix< K, RowMajor >::size().

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◆ size()

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::size ( ) const

inline

Return the total number of elements.

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

Referenced by tensorium::Matrix< K, RowMajor >::add(), tensorium::Matrix< K, RowMajor >::lerp(), tensorium::Matrix< K, RowMajor >::scl(), and tensorium::Matrix< K, RowMajor >::sub().

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◆ sub()

template<typename K , bool RowMajor = false>

void tensorium::Matrix< K, RowMajor >::sub ( const Matrix< K, RowMajor > & m )

inline

In-place matrix subtraction: this -= m.

References tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::data, tensorium::Matrix< K, RowMajor >::rows, tensorium::Matrix< K, RowMajor >::simd_width, and tensorium::Matrix< K, RowMajor >::size().

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◆ swap_rows()

template<typename K , bool RowMajor = false>

void tensorium::Matrix< K, RowMajor >::swap_rows	(	size_t	i,
		size_t	j )

inline

Swap two rows of the matrix.

References MathsUtils::_swap(), tensorium::Matrix< K, RowMajor >::cols, and tensorium::Matrix< K, RowMajor >::rows.

Referenced by tensorium::Matrix< K, RowMajor >::det(), tensorium::Matrix< K, RowMajor >::inverse(), tensorium::Matrix< K, RowMajor >::rank(), and tensorium::solver::Gauss< K >::raw_row_echelon().

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◆ trace()

template<typename K , bool RowMajor = false>

Matrix< K > tensorium::Matrix< K, RowMajor >::trace ( ) const

inline

Returns the trace of a square matrix as a 1×1 matrix.

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

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◆ transpose()

template<typename K , bool RowMajor = false>

Matrix< K > tensorium::Matrix< K, RowMajor >::transpose ( ) const

inline

Returns the transpose \( A^T \) of the matrix (column-major layout)

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

Member Data Documentation

◆ block_size

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::block_size

◆ cols

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::cols

◆ data

◆ iscolumn

template<typename K , bool RowMajor = false>

bool tensorium::Matrix< K, RowMajor >::iscolumn

◆ rows

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::rows

◆ simd_width

template<typename K , bool RowMajor = false>

size_t tensorium::Matrix< K, RowMajor >::simd_width = Simd::width

Referenced by tensorium::Matrix< K, RowMajor >::add(), tensorium::Matrix< K, RowMajor >::det(), tensorium::Matrix< K, RowMajor >::lerp(), tensorium::Matrix< K, RowMajor >::scl(), and tensorium::Matrix< K, RowMajor >::sub().

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

includes/Tensorium/Core/Matrix.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ reg

◆ Simd

Constructor & Destructor Documentation

◆ Matrix()

Member Function Documentation

◆ _mul_mat()

◆ add()

◆ det()

◆ index()

◆ inverse()

◆ lerp()

◆ mul_vec()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ print()

◆ rank()

◆ scl()

◆ size()

◆ sub()

◆ swap_rows()

◆ trace()

◆ transpose()

Member Data Documentation

◆ block_size

◆ cols

◆ data

◆ iscolumn

◆ rows

◆ simd_width