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.
Matrix &	operator+= (const Matrix &m)
Matrix &	operator-= (const Matrix &m)
Matrix &	operator*= (K alpha)

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.

References block_size, cols, data, detect_optimal_block_size(), and rows.

Referenced by _mul_mat(), add(), det(), inverse(), lerp(), operator*=(), operator+=(), operator-=(), rank(), sub(), trace(), and transpose().

Here is the call graph for this function:

Here is the caller graph for this function:

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 cols, data, Matrix(), and rows.

Referenced by tensorium::mul_mat(), and tensorium::operator*().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 _MM_HINT_T0, _mm_prefetch, cols, data, Matrix(), rows, simd_width, and size().

Referenced by tensorium::add_mat(), tensorium::operator+(), and operator+=().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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(), cols, det(), Matrix(), operator()(), rows, simd_width, and swap_rows().

Referenced by det(), and tensorium::det_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ index()

template<typename K, bool RowMajor = false>

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

inline

References cols, and rows.

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

Here is the caller graph for this function:

◆ 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(), cols, Matrix(), operator()(), rows, and swap_rows().

Referenced by tensorium_RG::__attribute__(), tensorium::inv_mat_tensor(), tensorium::inverse_mat(), tensorium_RG::Metric< T >::invert_metric_tensor(), and tensorium_RG::Metric< T >::invert_spatial_metric().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 cols, data, Matrix(), rows, simd_width, and size().

Referenced by tensorium::lerp_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 cols, rows, and tensorium::Vector< K >::size().

Referenced by tensorium::mul_vec().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 data, and index().

Referenced by det(), inverse(), and trace().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 data, and index().

Here is the call graph for this function:

◆ 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 cols, rows, and tensorium::Vector< K >::size().

Here is the call graph for this function:

◆ operator*=()

template<typename K, bool RowMajor = false>

Matrix & tensorium::Matrix< K, RowMajor >::operator*= ( K alpha )

inline

References Matrix(), and scl().

Here is the call graph for this function:

◆ operator+=()

template<typename K, bool RowMajor = false>

Matrix & tensorium::Matrix< K, RowMajor >::operator+= ( const Matrix< K, RowMajor > & m )

inline

References add(), and Matrix().

Here is the call graph for this function:

◆ operator-=()

template<typename K, bool RowMajor = false>

Matrix & tensorium::Matrix< K, RowMajor >::operator-= ( const Matrix< K, RowMajor > & m )

inline

References Matrix(), and sub().

Here is the call graph for this function:

◆ print()

template<typename K, bool RowMajor = false>

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

inline

Print the matrix to stdout.

References cols, and 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(), cols, Matrix(), rows, and swap_rows().

Referenced by tensorium::rank_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ scl()

template<typename K, bool RowMajor = false>

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

inline

In-place scalar multiplication: this *= a.

References _MM_HINT_T0, _mm_prefetch, data, simd_width, and size().

Referenced by tensorium::operator*(), operator*=(), and tensorium::scl_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ size()

template<typename K, bool RowMajor = false>

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

inline

Return the total number of elements.

References cols, and rows.

Referenced by add(), lerp(), scl(), and sub().

Here is the caller graph for this function:

◆ 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 _MM_HINT_T0, _mm_prefetch, cols, data, Matrix(), rows, simd_width, and size().

Referenced by tensorium::operator-(), operator-=(), and tensorium::sub_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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(), cols, and rows.

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

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 cols, Matrix(), operator()(), and rows.

Referenced by tensorium::trace_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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 cols, Matrix(), and rows.

Referenced by tensorium::transpose_mat().

Here is the call graph for this function:

Here is the caller graph for this function:

Member Data Documentation

◆ block_size

template<typename K, bool RowMajor = false>

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

Referenced by Matrix().

◆ cols

template<typename K, bool RowMajor = false>

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

◆ data

template<typename K, bool RowMajor = false>

aligned_vector<K> tensorium::Matrix< K, RowMajor >::data

Referenced by _mul_mat(), add(), lerp(), Matrix(), tensorium::MatrixKernel< K >::mul_mat16x16(), tensorium::MatrixKernel< K >::mul_mat2x2(), tensorium::MatrixKernel< K >::mul_mat32x32(), tensorium::MatrixKernel< K >::mul_mat4x4(), tensorium::MatrixKernel< K >::mul_mat64x64(), tensorium::MatrixKernel< K >::mul_mat8x8(), operator()(), operator()(), scl(), and sub().

◆ 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 add(), det(), lerp(), scl(), and 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*()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ print()

◆ rank()

◆ scl()

◆ size()

◆ sub()

◆ swap_rows()

◆ trace()

◆ transpose()

Member Data Documentation

◆ block_size

◆ cols

◆ data

◆ iscolumn

◆ rows

◆ simd_width