tensorium::solver::Gauss< K > Class Template Reference

Direct Gaussian elimination solver with SIMD acceleration. More...

#include <LinearSolver.hpp>

Collaboration diagram for tensorium::solver::Gauss< K >:

Public Types
using	SimdT = simd::SimdTraits<K, DefaultISA>
using	regT = typename SimdT::reg

Public Member Functions
size_t	rows () const
	__attribute__ ((always_inline, hot, flatten)) static inline Vector< K > solve(const Matrix< K > &A_in
	Solve the linear system \( Ax = b \).
	assert (n==A_in.cols &&n==b_in.size())
Vector< K >	x (n)
aligned_vector< K >	rowi (n)
aligned_vector< K >	rowj (n)
	for (size_t i=0;i< n;++i)
	for (size_t ii=n;ii-- > 0;)

Static Public Member Functions
static void	raw_row_echelon (Matrix< K > &A, Vector< K > *b=nullptr, K eps=1e-12)

Public Attributes
size_t	block_size
aligned_vector< K >	data
const Vector< K > &	b_in
const size_t	n = A_in.rows
if(n >=1024) return Jacobi< K > Matrix< K >	M = A_in
Vector< K >	B = b_in
const size_t	W = SimdT::width
return	x

Detailed Description

template<typename K>
class tensorium::solver::Gauss< K >

Direct Gaussian elimination solver with SIMD acceleration.

This solver uses LU-style elimination with partial pivoting. For large systems ( \( n \geq 1024 \)), it redirects to Jacobi.

Template Parameters

K	Scalar type (must be floating-point)

Member Typedef Documentation

regT

template<typename K >

using tensorium::solver::Gauss< K >::regT = typename SimdT::reg

SimdT

template<typename K >

using tensorium::solver::Gauss< K >::SimdT = simd::SimdTraits<K, DefaultISA>

Member Function Documentation

__attribute__()

template<typename K >

tensorium::solver::Gauss< K >::__attribute__

(

(always_inline, hot, flatten)

)

const &

Solve the linear system \( Ax = b \).

Performs Gaussian elimination followed by back-substitution. Uses unrolled and SIMD-optimized loops for performance.

Parameters

A_in	Input matrix \( A \in \mathbb{R}^{n \times n} \)
b_in	Right-hand side vector \( b \in \mathbb{R}^n \)

Returns

Solution vector \( x \in \mathbb{R}^n \)

Exceptions

std::runtime_error

if matrix is singular or ill-conditioned

assert()

template<typename K >

tensorium::solver::Gauss< K >::assert

(

n

= =A_in.cols &&n==b_in.size()

)

Referenced by tensorium::solver::Gauss< K >::raw_row_echelon().

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for() [1/2]

template<typename K >

tensorium::solver::Gauss< K >::for ( )

inline

References MathsUtils::_abs(), MathsUtils::_swap(), tensorium::solver::Gauss< K >::B, tensorium::solver::Gauss< K >::M, tensorium::solver::Gauss< K >::n, tensorium::solver::Gauss< K >::rowi(), tensorium::solver::Gauss< K >::rowj(), UNROLL, and tensorium::solver::Gauss< K >::W.

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for() [2/2]

template<typename K >

tensorium::solver::Gauss< K >::for ( size_t ii = n; ii--, 0;  )

inline

References tensorium::solver::Gauss< K >::B, tensorium::solver::Gauss< K >::M, tensorium::solver::Gauss< K >::n, tensorium::solver::Gauss< K >::rowi(), tensorium::solver::Gauss< K >::W, and tensorium::solver::Gauss< K >::x.

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raw_row_echelon()

template<typename K >

static void tensorium::solver::Gauss< K >::raw_row_echelon ( Matrix< K > & A, Vector< K > * b = nullptr, K eps = 1e-12 )

inlinestatic

References MathsUtils::_abs(), MathsUtils::_swap(), tensorium::solver::Gauss< K >::assert(), tensorium::Matrix< K, RowMajor >::cols, tensorium::solver::Gauss< K >::n, tensorium::Matrix< K, RowMajor >::rows, and tensorium::Matrix< K, RowMajor >::swap_rows().

Referenced by tensorium::row_echelon().

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rowi()

template<typename K >

aligned_vector< K > tensorium::solver::Gauss< K >::rowi

(

n

)

Referenced by tensorium::solver::Gauss< K >::for(), and tensorium::solver::Gauss< K >::for().

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rowj()

template<typename K >

aligned_vector< K > tensorium::solver::Gauss< K >::rowj

(

n

)

Referenced by tensorium::solver::Gauss< K >::for().

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rows()

template<typename K >

size_t tensorium::solver::Gauss< K >::rows

(

)

const

x()

template<typename K >

Vector< K > tensorium::solver::Gauss< K >::x

(

n

)

Member Data Documentation

B

template<typename K >

Vector<K> tensorium::solver::Gauss< K >::B = b_in

Referenced by tensorium::solver::Gauss< K >::for(), and tensorium::solver::Gauss< K >::for().

b_in

template<typename K >

const Vector<K>& tensorium::solver::Gauss< K >::b_in

Initial value:

{
        static_assert(std::is_floating_point<K>::value, "")

block_size

template<typename K >

size_t tensorium::solver::Gauss< K >::block_size

data

template<typename K >

aligned_vector<K> tensorium::solver::Gauss< K >::data

M

template<typename K >

if (n >= 1024) return Jacobi<K> Matrix<K> tensorium::solver::Gauss< K >::M = A_in

Referenced by tensorium::solver::Gauss< K >::for(), and tensorium::solver::Gauss< K >::for().

n

template<typename K >

const size_t tensorium::solver::Gauss< K >::n = A_in.rows

Referenced by tensorium::solver::Gauss< K >::for(), tensorium::solver::Gauss< K >::for(), and tensorium::solver::Gauss< K >::raw_row_echelon().

W

template<typename K >

const size_t tensorium::solver::Gauss< K >::W = SimdT::width

Referenced by tensorium::solver::Gauss< K >::for(), and tensorium::solver::Gauss< K >::for().

x

template<typename K >

return tensorium::solver::Gauss< K >::x

Referenced by tensorium::solver::Gauss< K >::for().

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

• includes/Tensorium/Core/LinearSolver.hpp