Namespaces
namespace	mpi

namespace	solver
	Namespace containing linear system solvers.

Classes
struct	ASTNode

struct	avx2_t

class	CacheInfo

class	Derivate
	A 2D aligned matrix for numerical derivatives. More...

class	DerivateND
	A multi-dimensional aligned tensor for numerical derivatives. More...

class	GemmKernelBig

class	GemmKernelBigger

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

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

class	Parser

class	SpectalChebyshev
	Placeholder Chebyshev spectral method class. More...

class	SpectralFFT
	Fast Fourier Transform (FFT) implementation using Cooley–Tukey algorithm. More...

class	Tensor
	Multi-dimensional tensor class with fixed rank and SIMD support. More...

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

Enumerations
enum class	ASTNodeType { Number , Symbol , BinaryOp , UnaryOp , FunctionCall , Subscript , Superscript , Derivative , Integral , TensorSymbol }

Functions
template<typename Container >
Container	richardson_derivative_container (const Container &plus_h, const Container &minus_h, const Container &plus_half_h, const Container &minus_half_h, double h)
	Richardson extrapolation for vectors or containers.

template<typename T >
T	richardson_derivative (const T &plus_h, const T &minus_h, const T &plus_half_h, const T &minus_half_h, double h)
	Richardson extrapolation for scalar values.

template<typename T >
T GemmKernelBigger< T >::blockA_packed[MC *KC]	__attribute__ ((aligned(64)))

template<typename T >
T GemmKernelBigger< T >::blockB_packed[NC *KC]	__attribute__ ((aligned(64)))

template<typename T >
Vector< T >	add_vec (const Vector< T > &a, const Vector< T > &b)

template<typename T >
Vector< T >	sub_vec (const Vector< T > &a, const Vector< T > &b)

template<typename T >
Vector< T >	scl_vec (const Vector< T > &a, T scalar)

template<typename T >
T	norm1_vec (const Vector< T > &a)

template<typename T >
T	norm2_vec (const Vector< T > &a)

template<typename T >
T	normInf_vec (const Vector< T > &a)

template<typename T >
T	dot_vec (const Vector< T > &a, const Vector< T > &b)

template<typename T >
T	cosine_vec (const Vector< T > &a, const Vector< T > &b)

template<typename T >
Vector< T >	lerp_vec (const Vector< T > &a, const Vector< T > &b, T t)

template<typename T >
Vector< T >	linear_combination_vec (const std::vector< Vector< T > > &u, const std::vector< T > &coef)

template<typename T >
Vector< T >	cross_vec (const Vector< T > &a, const Vector< T > &b)

template<typename T >
Matrix< T >	add_mat (const Matrix< T > &A, const Matrix< T > &B)

template<typename T >
Matrix< T >	sub_mat (const Matrix< T > &A, const Matrix< T > &B)

template<typename T >
Matrix< T >	scl_mat (const Matrix< T > &A, T scalar)

template<typename T >
Matrix< T >	lerp_mat (const Matrix< T > &A, const Matrix< T > &B, T t)

template<typename T >
Matrix< T >	mul_mat (const Matrix< T > &A, const Matrix< T > &B)

template<typename T >
Matrix< T >	transpose_mat (const Matrix< T > &A)

template<typename T >
Matrix< T >	trace_mat (const Matrix< T > &A)

template<typename T >
Vector< T >	mul_vec (const Matrix< T > &A, const Vector< T > &x)

template<typename T >
Matrix< T >	inverse_mat (const Matrix< T > &A)

template<typename T >
T	det_mat (const Matrix< T > &A)

template<typename T >
size_t	rank_mat (const Matrix< T > &A)

template<typename K , std::size_t Rank>
Tensor< K, Rank >	transpose_tensor (const Tensor< K, Rank > &T)

template<typename K , size_t R1, size_t R2>
Tensor< K, R1+R2 >	mul_tensor (const Tensor< K, R1 > &A, const Tensor< K, R2 > &B)

template<size_t I, size_t J, typename K , std::size_t Rank>
Tensor< K, Rank - 2 >	contract_tensor (const Tensor< K, Rank > &T)

template<typename T >
Vector< T >	gauss_solve (const Matrix< T > &A, const Vector< T > &b)

template<typename T >
Vector< T >	jacobi_solve (const Matrix< T > &A, const Vector< T > &b, T tol=1e-6, int max_iter=1000)

template<typename T >
void	row_echelon (Matrix< T > &A, Vector< T > *b=nullptr, T eps=T(1e-12))

template<typename K >
void	centered_derivative (const Derivate< K > &input, Derivate< K > &output, size_t axis, K dx)

template<typename K >
void	centered_derivative_order4 (const Derivate< K > &input, Derivate< K > &output, size_t axis, K dx)

template<typename K , size_t Rank>
void	centered_derivative (const DerivateND< K, Rank > &input, DerivateND< K, Rank > &output, size_t axis, K dx)

template<typename K , size_t Rank>
void	centered_derivative_order4 (const DerivateND< K, Rank > &input, DerivateND< K, Rank > &output, size_t axis, K dx)

template<typename T >
void	forwardFFT (tensorium::Vector< std::complex< T > > &data)

template<typename T >
void	backwardFFT (tensorium::Vector< std::complex< T > > &data)

template<typename T >
void	backwardFFP (tensorium::Vector< std::complex< T > > &data)

template<typename T >
tensorium::Tensor< T, 2 >	inv_mat_tensor (const tensorium::Tensor< T, 2 > &g)

template<typename T >
Matrix< T >	tensor_to_matrix (const Tensor< T, 2 > &tensor)

template<typename T >
Tensor< T, 2 >	matrix_to_tensor (const Matrix< T > &mat)

template<typename T , typename MetricFunc >
tensorium_RG::ChristoffelSym< T >	compute_christoffel (const tensorium::Vector< T > &X, T h, const tensorium::Tensor< T, 2 > &g, const tensorium::Tensor< T, 2 > &g_inv, MetricFunc &&metric_generator)

template<typename T >
void	generate_metric (const tensorium_RG::Metric< T > &metric, const Vector< T > &X, Tensor< T, 2 > &g)

template<typename T >
tensorium::Tensor< T, 4 >	compute_riemann_tensor (const tensorium::Vector< T > &X, T h, const tensorium_RG::Metric< T > &metric)

template<typename T >
void	print_riemann_tensor (const tensorium::Tensor< T, 4 > &R)

template<typename T >
Tensor< T, 2 >	contract_riemann_to_ricci (const Tensor< T, 4 > &R, const Tensor< T, 2 > &ginv)

template<typename T >
T	compute_ricci_scalar (const Tensor< T, 2 > &Ricci, const Tensor< T, 2 > &ginv)

template<typename T >
void	print_ricci_tensor (const Tensor< T, 2 > &R)

template<typename T >
void	print_ricci_scalar (const Tensor< T, 2 > &Ricci, const Tensor< T, 2 > &g_inv)

template<typename T >
T	compute_conformal_factor (const tensorium_RG::Metric< T > &metric, const Tensor< T, 2 > &gamma)

template<typename T >
Tensor< T, 2 >	compute_conformal_metric (const tensorium_RG::Metric< T > &metric, const Tensor< T, 2 > &gamma, T chi)

template<typename T >
void	compute_christoffel_3D (const Tensor< T, 2 > &gamma_tilde, const Tensor< T, 3 > &dgamma_tilde, const Tensor< T, 2 > &gamma_tilde_inv, Tensor< T, 3 > &Christoffel)

template<typename T >
tensorium_RG::BSSN< T >	setup_BSSN_grid (const Vector< T > &X, const tensorium_RG::Metric< T > &metric, T dx, T dy, T dz)

void	print_ast (const std::shared_ptr< ASTNode > &node, int indent=0)

Enumeration Type Documentation

◆ ASTNodeType

enum class tensorium::ASTNodeType

strong

Enumerator
Number
Symbol
BinaryOp
UnaryOp
FunctionCall
Subscript
Superscript
Derivative
Integral
TensorSymbol

Function Documentation

◆ attribute() [1/2]

template<typename T >

T GemmKernelBigger< T >::blockA_packed[MC *KC] tensorium::__attribute__ ( (aligned(64)) )

◆ attribute() [2/2]

template<typename T >

T GemmKernelBigger< T >::blockB_packed[NC *KC] tensorium::__attribute__ ( (aligned(64)) )

◆ add_mat()

template<typename T >

Matrix< T > tensorium::add_mat	(	const Matrix< T > &	A,
		const Matrix< T > &	B )

◆ add_vec()

template<typename T >

Vector< T > tensorium::add_vec	(	const Vector< T > &	a,
		const Vector< T > &	b )

◆ backwardFFP()

template<typename T >

void tensorium::backwardFFP ( tensorium::Vector< std::complex< T > > & data )

inline

References tensorium::SpectralFFT< T >::backward().

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◆ backwardFFT()

template<typename T >

void tensorium::backwardFFT ( tensorium::Vector< std::complex< T > > & data )

inline

References tensorium::SpectralFFT< T >::backward().

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◆ centered_derivative() [1/2]

template<typename K >

void tensorium::centered_derivative	(	const Derivate< K > &	input,
		Derivate< K > &	output,
		size_t	axis,
		K	dx )

inline

◆ centered_derivative() [2/2]

template<typename K , size_t Rank>

void tensorium::centered_derivative	(	const DerivateND< K, Rank > &	input,
		DerivateND< K, Rank > &	output,
		size_t	axis,
		K	dx )

inline

◆ centered_derivative_order4() [1/2]

template<typename K >

void tensorium::centered_derivative_order4	(	const Derivate< K > &	input,
		Derivate< K > &	output,
		size_t	axis,
		K	dx )

inline

References centered_derivative_order4().

Referenced by centered_derivative_order4().

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◆ centered_derivative_order4() [2/2]

template<typename K , size_t Rank>

void tensorium::centered_derivative_order4	(	const DerivateND< K, Rank > &	input,
		DerivateND< K, Rank > &	output,
		size_t	axis,
		K	dx )

inline

◆ compute_christoffel()

template<typename T , typename MetricFunc >

tensorium_RG::ChristoffelSym< T > tensorium::compute_christoffel	(	const tensorium::Vector< T > &	X,
		T	h,
		const tensorium::Tensor< T, 2 > &	g,
		const tensorium::Tensor< T, 2 > &	g_inv,
		MetricFunc &&	metric_generator )

References X().

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◆ compute_christoffel_3D()

template<typename T >

void tensorium::compute_christoffel_3D	(	const Tensor< T, 2 > &	gamma_tilde,
		const Tensor< T, 3 > &	dgamma_tilde,
		const Tensor< T, 2 > &	gamma_tilde_inv,
		Tensor< T, 3 > &	Christoffel )

inline

References tensorium_RG::BSSNChristoffel< T >::compute().

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◆ compute_conformal_factor()

template<typename T >

T tensorium::compute_conformal_factor	(	const tensorium_RG::Metric< T > &	metric,
		const Tensor< T, 2 > &	gamma )

inline

References gamma.

◆ compute_conformal_metric()

template<typename T >

Tensor< T, 2 > tensorium::compute_conformal_metric	(	const tensorium_RG::Metric< T > &	metric,
		const Tensor< T, 2 > &	gamma,
		T	chi )

inline

References chi, and gamma.

◆ compute_ricci_scalar()

template<typename T >

T tensorium::compute_ricci_scalar	(	const Tensor< T, 2 > &	Ricci,
		const Tensor< T, 2 > &	ginv )

inline

References tensorium_RG::RicciTensor< T >::compute_ricci_scalar().

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◆ compute_riemann_tensor()

template<typename T >

tensorium::Tensor< T, 4 > tensorium::compute_riemann_tensor	(	const tensorium::Vector< T > &	X,
		T	h,
		const tensorium_RG::Metric< T > &	metric )

inline

References tensorium_RG::RiemannTensor< T >::compute(), and X().

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◆ contract_riemann_to_ricci()

template<typename T >

Tensor< T, 2 > tensorium::contract_riemann_to_ricci	(	const Tensor< T, 4 > &	R,
		const Tensor< T, 2 > &	ginv )

inline

References tensorium_RG::RicciTensor< T >::contract_to_ricci().

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◆ contract_tensor()

template<size_t I, size_t J, typename K , std::size_t Rank>

Tensor< K, Rank - 2 > tensorium::contract_tensor ( const Tensor< K, Rank > & T )

◆ cosine_vec()

template<typename T >

T tensorium::cosine_vec	(	const Vector< T > &	a,
		const Vector< T > &	b )

◆ cross_vec()

template<typename T >

Vector< T > tensorium::cross_vec	(	const Vector< T > &	a,
		const Vector< T > &	b )

◆ det_mat()

template<typename T >

T tensorium::det_mat ( const Matrix< T > & A )

◆ dot_vec()

template<typename T >

T tensorium::dot_vec	(	const Vector< T > &	a,
		const Vector< T > &	b )

◆ forwardFFT()

template<typename T >

void tensorium::forwardFFT ( tensorium::Vector< std::complex< T > > & data )

inline

References tensorium::SpectralFFT< T >::forward().

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◆ gauss_solve()

template<typename T >

Vector< T > tensorium::gauss_solve	(	const Matrix< T > &	A,
		const Vector< T > &	b )

◆ generate_metric()

template<typename T >

void tensorium::generate_metric	(	const tensorium_RG::Metric< T > &	metric,
		const Vector< T > &	X,
		Tensor< T, 2 > &	g )

References X().

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◆ inv_mat_tensor()

template<typename T >

tensorium::Tensor< T, 2 > tensorium::inv_mat_tensor ( const tensorium::Tensor< T, 2 > & g )

References matrix_to_tensor(), and tensor_to_matrix().

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◆ inverse_mat()

template<typename T >

Matrix< T > tensorium::inverse_mat ( const Matrix< T > & A )

◆ jacobi_solve()

template<typename T >

Vector< T > tensorium::jacobi_solve	(	const Matrix< T > &	A,
		const Vector< T > &	b,
		T	tol = 1e-6,
		int	max_iter = 1000 )

References tensorium::solver::Jacobi< K >::solve().

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◆ lerp_mat()

template<typename T >

Matrix< T > tensorium::lerp_mat	(	const Matrix< T > &	A,
		const Matrix< T > &	B,
		T	t )

◆ lerp_vec()

template<typename T >

Vector< T > tensorium::lerp_vec	(	const Vector< T > &	a,
		const Vector< T > &	b,
		T	t )

◆ linear_combination_vec()

template<typename T >

Vector< T > tensorium::linear_combination_vec	(	const std::vector< Vector< T > > &	u,
		const std::vector< T > &	coef )

◆ matrix_to_tensor()

template<typename T >

Tensor< T, 2 > tensorium::matrix_to_tensor ( const Matrix< T > & mat )

Referenced by inv_mat_tensor().

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◆ mul_mat()

template<typename T >

Matrix< T > tensorium::mul_mat	(	const Matrix< T > &	A,
		const Matrix< T > &	B )

Referenced by main().

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◆ mul_tensor()

template<typename K , size_t R1, size_t R2>

Tensor< K, R1+R2 > tensorium::mul_tensor	(	const Tensor< K, R1 > &	A,
		const Tensor< K, R2 > &	B )

inline

◆ mul_vec()

template<typename T >

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

◆ norm1_vec()

template<typename T >

T tensorium::norm1_vec ( const Vector< T > & a )

◆ norm2_vec()

template<typename T >

T tensorium::norm2_vec ( const Vector< T > & a )

◆ normInf_vec()

template<typename T >

T tensorium::normInf_vec ( const Vector< T > & a )

◆ print_ast()

void tensorium::print_ast	(	const std::shared_ptr< ASTNode > &	node,
		int	indent = 0 )

inline

References print_ast().

Referenced by print_ast().

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◆ print_ricci_scalar()

template<typename T >

void tensorium::print_ricci_scalar	(	const Tensor< T, 2 > &	Ricci,
		const Tensor< T, 2 > &	g_inv )

inline

References tensorium_RG::RicciTensor< T >::print_ricci_scalar().

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◆ print_ricci_tensor()

template<typename T >

void tensorium::print_ricci_tensor ( const Tensor< T, 2 > & R )

inline

References tensorium_RG::RicciTensor< T >::print_componentwise().

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◆ print_riemann_tensor()

template<typename T >

void tensorium::print_riemann_tensor ( const tensorium::Tensor< T, 4 > & R )

inline

References tensorium_RG::RiemannTensor< T >::print_componentwise().

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◆ rank_mat()

template<typename T >

size_t tensorium::rank_mat ( const Matrix< T > & A )

◆ richardson_derivative()

template<typename T >

T tensorium::richardson_derivative	(	const T &	plus_h,
		const T &	minus_h,
		const T &	plus_half_h,
		const T &	minus_half_h,
		double	h )

inline

Richardson extrapolation for scalar values.

Template Parameters

T	Scalar type.

Parameters

plus_h	f(x + h)
minus_h	f(x - h)
plus_half_h	f(x + h/2)
minus_half_h	f(x - h/2)
h	Step size.

Returns: Richardson-extrapolated scalar derivative.

Referenced by tensorium_RG::RiemannTensor< T >::compute().

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◆ richardson_derivative_container()

template<typename Container >

Container tensorium::richardson_derivative_container	(	const Container &	plus_h,
		const Container &	minus_h,
		const Container &	plus_half_h,
		const Container &	minus_half_h,
		double	h )

inline

Richardson extrapolation for vectors or containers.

Template Parameters

Container Vector-like container type.

Parameters

plus_h	f(x + h)
minus_h	f(x - h)
plus_half_h	f(x + h/2)
minus_half_h	f(x - h/2)
h	Step size.

Returns: Richardson-extrapolated derivative.

◆ row_echelon()

template<typename T >

void tensorium::row_echelon	(	Matrix< T > &	A,
		Vector< T > *	b = nullptr,
		T	eps = T(1e-12) )

inline

References tensorium::solver::Gauss< K >::raw_row_echelon().

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◆ scl_mat()

template<typename T >

Matrix< T > tensorium::scl_mat	(	const Matrix< T > &	A,
		T	scalar )

◆ scl_vec()

template<typename T >

Vector< T > tensorium::scl_vec	(	const Vector< T > &	a,
		T	scalar )

◆ setup_BSSN_grid()

template<typename T >

tensorium_RG::BSSN< T > tensorium::setup_BSSN_grid	(	const Vector< T > &	X,
		const tensorium_RG::Metric< T > &	metric,
		T	dx,
		T	dy,
		T	dz )

inline

References X().

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◆ sub_mat()

template<typename T >

Matrix< T > tensorium::sub_mat	(	const Matrix< T > &	A,
		const Matrix< T > &	B )

◆ sub_vec()

template<typename T >

Vector< T > tensorium::sub_vec	(	const Vector< T > &	a,
		const Vector< T > &	b )

◆ tensor_to_matrix()

template<typename T >

Matrix< T > tensorium::tensor_to_matrix ( const Tensor< T, 2 > & tensor )

References tensorium::Tensor< K, Rank >::dimensions.

Referenced by inv_mat_tensor().

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◆ trace_mat()

template<typename T >

Matrix< T > tensorium::trace_mat ( const Matrix< T > & A )

◆ transpose_mat()

template<typename T >

Matrix< T > tensorium::transpose_mat ( const Matrix< T > & A )

◆ transpose_tensor()

template<typename K , std::size_t Rank>

Tensor< K, Rank > tensorium::transpose_tensor ( const Tensor< K, Rank > & T )

References tensorium::Tensor< K, Rank >::transpose_simd().

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Namespaces

Classes

Enumerations

Functions

Enumeration Type Documentation

◆ ASTNodeType

Function Documentation

◆ __attribute__() [1/2]

◆ __attribute__() [2/2]

◆ add_mat()

◆ add_vec()

◆ backwardFFP()

◆ backwardFFT()

◆ centered_derivative() [1/2]

◆ centered_derivative() [2/2]

◆ centered_derivative_order4() [1/2]

◆ centered_derivative_order4() [2/2]

◆ compute_christoffel()

◆ compute_christoffel_3D()

◆ compute_conformal_factor()

◆ compute_conformal_metric()

◆ compute_ricci_scalar()

◆ compute_riemann_tensor()

◆ contract_riemann_to_ricci()

◆ contract_tensor()

◆ cosine_vec()

◆ cross_vec()

◆ det_mat()

◆ dot_vec()

◆ forwardFFT()

◆ gauss_solve()

◆ generate_metric()

◆ inv_mat_tensor()

◆ inverse_mat()

◆ jacobi_solve()

◆ lerp_mat()

◆ lerp_vec()

◆ linear_combination_vec()

◆ matrix_to_tensor()

◆ mul_mat()

◆ mul_tensor()

◆ mul_vec()

◆ norm1_vec()

◆ norm2_vec()

◆ normInf_vec()

◆ print_ast()

◆ print_ricci_scalar()

◆ print_ricci_tensor()

◆ print_riemann_tensor()

◆ rank_mat()

◆ richardson_derivative()

◆ richardson_derivative_container()

◆ row_echelon()

◆ scl_mat()

◆ scl_vec()

◆ setup_BSSN_grid()

◆ sub_mat()

◆ sub_vec()

◆ tensor_to_matrix()

◆ trace_mat()

◆ transpose_mat()

◆ transpose_tensor()

◆ attribute() [1/2]

◆ attribute() [2/2]