Tiny Vector class template. More...

#include <tiny_algebra.hpp>

Public Types
typedef Intern::DataTypeExtractor< ValueType >::MyDataType	DataType
	The basic data type buried in the lowest level of the vector. More...

typedef T_	ValueType
	the value type of the vector More...

Public Member Functions
CUDA_HOST_DEVICE	Vector ()
	default constructor More...

template<typename Tx_ >
CUDA_HOST_DEVICE	Vector (const std::initializer_list< Tx_ > &x)
	Initializer list constructor. More...

template<int sx_>
CUDA_HOST_DEVICE	Vector (const Vector< T_, n_, sx_ > &x)
	copy constructor More...

CUDA_HOST_DEVICE	Vector (DataType value)
	value-assignment constructor More...

template<int m_, int sma_, int sna_, int sx_>
CUDA_HOST_DEVICE Vector &	add_mat_vec_mult (const Matrix< T_, n_, m_, sma_, sna_ > &a, const Vector< T_, m_, sx_ > &x, DataType alpha=DataType(1))
	Adds the result of a matrix-vector product onto this vector. More...

template<int mm_, int nn_, int ma_, int na_, int sna_, int sma_, int nx_, int sx_>
CUDA_HOST_DEVICE Vector &	add_mat_vec_mult_n (const Matrix< T_, ma_, na_, sma_, sna_ > &a, const Vector< T_, nx_, sx_ > &x, DataType alpha=DataType(1))
	Adds the result of a matrix-vector product onto this vector. More...

template<int m_, int sma_, int sna_, int sx_>
CUDA_HOST_DEVICE Vector &	add_vec_mat_mult (const Vector< T_, m_, sx_ > &x, const Matrix< T_, m_, n_, sma_, sna_ > &a, DataType alpha=DataType(1))
	Adds the result of a vector-matrix product onto this vector. More...

template<int nn_, int mm_, int mx_, int smx_, int ma_, int na_, int sma_, int sna_>
CUDA_HOST_DEVICE Vector &	add_vec_mat_mult_n (const Vector< T_, mx_, smx_ > &x, const Matrix< T_, ma_, na_, sma_, sna_ > &a, DataType alpha=DataType(1))
	Adds the result of a vector-matrix product onto this vector. More...

template<int snx_>
CUDA_HOST_DEVICE Vector &	axpy (DataType alpha, const Vector< T_, n_, snx_ > &x)
	Adds another scaled vector onto this vector. More...

template<int nn_, int nx_, int snx_>
CUDA_HOST_DEVICE Vector &	axpy_n (DataType alpha, const Vector< T_, nx_, snx_ > &x)
	Adds the first nn_ entries of another scaled vector onto this vector. More...

template<typename Tx_ , int sx_>
CUDA_HOST_DEVICE void	convert (const Vector< Tx_, n_, sx_ > &x)
	conversion operator More...

template<int snx_>
CUDA_HOST_DEVICE void	copy (const Vector< T_, n_, snx_ > &x)
	Copies a vector. More...

template<int nn_, int nx_, int snx_>
CUDA_HOST_DEVICE void	copy_n (const Vector< T_, nx_, snx_ > &x)
	Copies the first nn_ entries of a vector. More...

CUDA_HOST_DEVICE void	format (DataType alpha=DataType(0))
	Formats the vector. More...

template<int nn_>
CUDA_HOST_DEVICE void	format_n (DataType alpha=DataType(0))
	Formats the first nn_ entries of the vector. More...

CUDA_HOST_DEVICE Vector &	negate ()
	Negates the vector, i.e. effectively multiplies all components by -1. More...

template<int nn_>
CUDA_HOST_DEVICE Vector &	negate_n ()
	Negates the first nn_ entries of this vector. More...

CUDA_HOST_DEVICE DataType	norm_euclid () const
	Computes the euclid norm of this vector. More...

template<int nn_>
CUDA_HOST_DEVICE DataType	norm_euclid_n () const
	Computes the euclid norm of first nn_ entries of this vector. More...

CUDA_HOST_DEVICE DataType	norm_euclid_sqr () const
	Computes the squared euclid norm of this vector. More...

template<int nn_>
CUDA_HOST_DEVICE DataType	norm_euclid_sqr_n () const
	Computes the squared euclid norm of first nn_ entries of this vector. More...

CUDA_HOST_DEVICE DataType	norm_l1 () const
	Computes the l1-norm of this vector. More...

template<int nn_>
CUDA_HOST_DEVICE DataType	norm_l1_n () const
	Computes the l1-norm of the first nn_ entries of this vector. More...

CUDA_HOST_DEVICE DataType	norm_max () const
	Computes the max-norm of this vector. More...

template<int nn_>
CUDA_HOST_DEVICE DataType	norm_max_n () const
	Computes the max-norm of the vector. More...

CUDA_HOST_DEVICE Vector &	normalize ()
	Normalizes this vector. More...

template<int nn_>
CUDA_HOST_DEVICE Vector &	normalize_n ()
	Normalizes the first nn_ entries of this vector. More...

CUDA_HOST_DEVICE bool	normalized () const
	Return if the vector is normalized. More...

CUDA_HOST_DEVICE T_ &	operator() (int i)
	Access operator. More...

CUDA_HOST_DEVICE const T_ &	operator() (int i) const
	Access operator. More...

template<int sx_>
CUDA_HOST_DEVICE Vector &	operator*= (const Vector< T_, n_, sx_ > &x)
	element-wise-multiply operator More...

CUDA_HOST_DEVICE Vector &	operator*= (DataType alpha)
	scalar-multiply operator More...

template<int sx_>
CUDA_HOST_DEVICE Vector &	operator+= (const Vector< T_, n_, sx_ > &x)
	vector-add operator More...

template<int sx_>
CUDA_HOST_DEVICE Vector &	operator-= (const Vector< T_, n_, sx_ > &x)
	vector-subtract operator More...

template<typename Tx_ >
CUDA_HOST_DEVICE Vector &	operator= (const std::initializer_list< Tx_ > &x)
	Initializer list assignment operator. More...

template<int sx_>
CUDA_HOST_DEVICE Vector &	operator= (const Vector< T_, n_, sx_ > &x)
	copy-assignment operator More...

CUDA_HOST_DEVICE Vector &	operator= (DataType value)
	value-assignment operator More...

CUDA_HOST_DEVICE T_ &	operator[] (int i)
	Access operator. More...

CUDA_HOST_DEVICE const T_ &	operator[] (int i) const
	Access operator. More...

CUDA_HOST_DEVICE void	scale (DataType alpha)
	Scales the vector. More...

template<int nn_>
CUDA_HOST_DEVICE void	scale_n (DataType alpha)
	Scales the first nn_ entries of the vector. More...

template<int sna_, int snb_>
CUDA_HOST_DEVICE Vector &	set_convex (DataType alpha, const Vector< T_, n_, sna_ > &a, const Vector< T_, n_, snb_ > &b)
	Sets this vector to the convex combination of two other vectors. More...

template<int nn_, int na_, int nb_, int sna_, int snb_>
CUDA_HOST_DEVICE Vector &	set_convex_n (DataType alpha, const Vector< T_, na_, sna_ > &a, const Vector< T_, nb_, snb_ > &b)
	Sets the first nn_ entries of this vector to the convex combination of two other vectors. More...

template<int m_, int sma_, int sna_, int sx_>
CUDA_HOST_DEVICE Vector &	set_mat_vec_mult (const Matrix< T_, n_, m_, sma_, sna_ > &a, const Vector< T_, m_, sx_ > &x)
	Sets this vector to the result of a matrix-vector product. More...

template<int mm_, int nn_, int ma_, int na_, int sna_, int sma_, int nx_, int sx_>
CUDA_HOST_DEVICE Vector &	set_mat_vec_mult_n (const Matrix< T_, ma_, na_, sma_, sna_ > &a, const Vector< T_, nx_, sx_ > &x)
	Sets the first nn_ entries of this vector to the result of a matrix-vector product with the first mm_ entries of another vector. More...

template<int m_, int sma_, int sna_, int sx_>
CUDA_HOST_DEVICE Vector &	set_vec_mat_mult (const Vector< T_, m_, sx_ > &x, const Matrix< T_, m_, n_, sma_, sna_ > &a)
	Sets this vector to the result of a vector-matrix product. More...

template<int nn_, int mm_, int mx_, int smx_, int ma_, int na_, int sma_, int sna_>
CUDA_HOST_DEVICE Vector &	set_vec_mat_mult_n (const Vector< T_, mx_, smx_ > &x, const Matrix< T_, ma_, na_, sma_, sna_ > &a)
	Sets the first mm_ entries of this vector to the result of a vector-matrix product with the first mm_ entries of another vector. More...

Static Public Member Functions
template<typename Tx_ , int sx_>
static CUDA_HOST_DEVICE Vector	convert_new (const Vector< Tx_, n_, sx_ > &x)
	convert function, not callable with non convertable inner type More...

static CUDA_HOST_DEVICE Vector	convert_new (Vector &&x)
	overload for moveable rvalue type More...

static CUDA_HOST_DEVICE Vector	null ()
	Returns a null-vector. More...

Public Attributes
T_	v [s_]
	actual vector data More...

Static Public Attributes
static constexpr int	n = n_
	the length of the vector More...

static constexpr int	s = s_
	the stride of the vector More...

Friends
CUDA_HOST friend std::ostream &	operator<< (std::ostream &lhs, const Vector &b)
	Tiny::Vector streaming operator. More...

Detailed Description

template<typename T_, int n_, int s_ = n_>
class FEAT::Tiny::Vector< T_, n_, s_ >

Tiny Vector class template.

This class template implements a vector whose value type and size is given at compile-time. The value type can be a primitive type, or some other object like (again) a Vector.

Template Parameters

T_	The value-type that the vector shall contain.
n_	The length of the vector. Must be > 0.
s_	The stride of the vector. Must be >= `n_`.

Author: Peter Zajac

Definition at line 52 of file tiny_algebra.hpp.

Member Typedef Documentation

◆ DataType

template<typename T_ , int n_, int s_ = n_>

typedef Intern::DataTypeExtractor<ValueType>::MyDataType FEAT::Tiny::Vector< T_, n_, s_ >::DataType

The basic data type buried in the lowest level of the vector.

Definition at line 222 of file tiny_algebra.hpp.

◆ ValueType

template<typename T_ , int n_, int s_ = n_>

typedef T_ FEAT::Tiny::Vector< T_, n_, s_ >::ValueType

the value type of the vector

Definition at line 220 of file tiny_algebra.hpp.

Constructor & Destructor Documentation

◆ Vector() [1/4]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE FEAT::Tiny::Vector< T_, n_, s_ >::Vector ( )

inline

default constructor

Definition at line 228 of file tiny_algebra.hpp.

Referenced by FEAT::Tiny::Vector< T_, n_, s_ >::null().

◆ Vector() [2/4]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE FEAT::Tiny::Vector< T_, n_, s_ >::Vector ( DataType value )

inlineexplicit

value-assignment constructor

Definition at line 233 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::value.

◆ Vector() [3/4]

template<typename T_ , int n_, int s_ = n_>

template<int sx_>

CUDA_HOST_DEVICE FEAT::Tiny::Vector< T_, n_, s_ >::Vector ( const Vector< T_, n_, sx_ > & x )

inline

copy constructor

Definition at line 243 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ Vector() [4/4]

template<typename T_ , int n_, int s_ = n_>

template<typename Tx_ >

CUDA_HOST_DEVICE FEAT::Tiny::Vector< T_, n_, s_ >::Vector ( const std::initializer_list< Tx_ > & x )

inlineexplicit

Initializer list constructor.

This operator allows to assign values to a new vector in a simple manner:

Tiny::Vector<double, 3> v1{0.1, 2.1, 7.3};

Tiny::Vector<double, 3> v2 = {0.1, 2.1, 7.3};

FEAT::Tiny::Vector

Tiny Vector class template.

Definition: tiny_algebra.hpp:52

Parameters

[in] x The initializer list whose elements are to be assigned.

Definition at line 285 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v, and XASSERTM.

Member Function Documentation

◆ add_mat_vec_mult()

template<typename T_ , int n_, int s_ = n_>

template<int m_, int sma_, int sna_, int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::add_mat_vec_mult	(	const Matrix< T_, n_, m_, sma_, sna_ > &	a,
		const Vector< T_, m_, sx_ > &	x,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the result of a matrix-vector product onto this vector.

Let y denote this vector, and let A denote the input matrix and x in the input vector, then this function computes:

\[ y \leftarrow y + \alpha\cdot A\cdot x \]

Parameters

[in]	a	The matrix for the product.
[in]	x	The (right) multiplicand vector for the product.
[in]	alpha	The scaling parameter for the product.

Returns: *this

Definition at line 861 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ add_mat_vec_mult_n()

template<typename T_ , int n_, int s_ = n_>

template<int mm_, int nn_, int ma_, int na_, int sna_, int sma_, int nx_, int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::add_mat_vec_mult_n	(	const Matrix< T_, ma_, na_, sma_, sna_ > &	a,
		const Vector< T_, nx_, sx_ > &	x,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the result of a matrix-vector product onto this vector.

Let y denote this vector, and let A denote the input matrix and x in the input vector, then this function computes:

\[ y \leftarrow y + \alpha\cdot A\cdot x \]

Template Parameters

mm_	The number of matrix rows to multiply; must be mm_ <= min(n_, ma_)
nn_	The number of matrix columns to multiply; must be nn_ <= min(nx_, na_)

Parameters

[in]	a	The matrix for the product.
[in]	x	The (right) multiplicand vector for the product.
[in]	alpha	The scaling parameter for the product.

Returns: *this

Definition at line 901 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ add_vec_mat_mult()

template<typename T_ , int n_, int s_ = n_>

template<int m_, int sma_, int sna_, int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::add_vec_mat_mult	(	const Vector< T_, m_, sx_ > &	x,
		const Matrix< T_, m_, n_, sma_, sna_ > &	a,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the result of a vector-matrix product onto this vector.

Let y denote this vector, and let x in the input vector and A denote the input matrix, then this function computes:

\[ y^\top \leftarrow y^\top + \alpha\cdot x^\top \cdot A \Longleftrightarrow y \leftarrow y + \alpha\cdot A^\top\cdot x \]

Parameters

[in]	x	The (left) multiplicand vector for the product.
[in]	a	The matrix for the product.
[in]	alpha	The scaling parameter for the product.

Returns: *this

Definition at line 940 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ add_vec_mat_mult_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_, int mm_, int mx_, int smx_, int ma_, int na_, int sma_, int sna_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::add_vec_mat_mult_n	(	const Vector< T_, mx_, smx_ > &	x,
		const Matrix< T_, ma_, na_, sma_, sna_ > &	a,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the result of a vector-matrix product onto this vector.

Let y denote this vector, and let x in the input vector and A denote the input matrix, then this function computes:

\[ y^\top \leftarrow y^\top + \alpha\cdot x^\top \cdot A \Longleftrightarrow y \leftarrow y + \alpha\cdot A^\top\cdot x \]

Template Parameters

nn_	The number of matrix columns to multiply; must be nn_ <= min(nx_, na_)
mm_	The number of matrix rows to multiply; must be mm_ <= min(n_, ma_)

Parameters

[in]	x	The (left) multiplicand vector for the product.
[in]	a	The matrix for the product.
[in]	alpha	The scaling parameter for the product.

Returns: *this

Definition at line 980 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ axpy()

template<typename T_ , int n_, int s_ = n_>

template<int snx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::axpy	(	DataType	alpha,
		const Vector< T_, n_, snx_ > &	x
	)

inline

Adds another scaled vector onto this vector.

Parameters

[in]	x	The vector to be added onto this vector.
[in]	alpha	The scaling parameter for the axpy.

Returns: *this

Definition at line 609 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ axpy_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_, int nx_, int snx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::axpy_n	(	DataType	alpha,
		const Vector< T_, nx_, snx_ > &	x
	)

inline

Adds the first nn_ entries of another scaled vector onto this vector.

Template Parameters

nn_	The number of elements to axpy; must be nn_ <= min(n_, nx_)

Parameters

[in]	x	The vector to be added onto this vector.
[in]	alpha	The scaling parameter for the axpy.

Returns: *this

Definition at line 631 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ convert()

template<typename T_ , int n_, int s_ = n_>

template<typename Tx_ , int sx_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::convert ( const Vector< Tx_, n_, sx_ > & x )

inline

conversion operator

Definition at line 340 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

Referenced by FEAT::Trafo::Isoparam::Evaluator< Trafo_, EvalPolicy_, degree_, Shape::Hypercube< 2 > >::prepare(), and FEAT::Trafo::Isoparam::Evaluator< Trafo_, EvalPolicy_, degree_, Shape::Hypercube< 3 > >::prepare().

◆ convert_new() [1/2]

template<typename T_ , int n_, int s_ = n_>

template<typename Tx_ , int sx_>

static CUDA_HOST_DEVICE Vector FEAT::Tiny::Vector< T_, n_, s_ >::convert_new ( const Vector< Tx_, n_, sx_ > & x )

inlinestatic

convert function, not callable with non convertable inner type

Definition at line 253 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ convert_new() [2/2]

template<typename T_ , int n_, int s_ = n_>

static CUDA_HOST_DEVICE Vector FEAT::Tiny::Vector< T_, n_, s_ >::convert_new ( Vector< T_, n_, s_ > && x )

inlinestatic

overload for moveable rvalue type

Definition at line 267 of file tiny_algebra.hpp.

◆ copy()

template<typename T_ , int n_, int s_ = n_>

template<int snx_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::copy ( const Vector< T_, n_, snx_ > & x )

inline

Copies a vector.

Parameters

[in] x The source vector to copy

Definition at line 388 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ copy_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_, int nx_, int snx_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::copy_n ( const Vector< T_, nx_, snx_ > & x )

inline

Copies the first nn_ entries of a vector.

Template Parameters

nn_	The number of elements to copy; must be nn_ <= min(n_, nx_)

Parameters

[in] x The source vector to copy the elements from

Definition at line 406 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ format()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::format ( DataType alpha = DataType(0) )

inline

Formats the vector.

Parameters

[in] alpha The value that the vector is to be set to.

Definition at line 465 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ format_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::format_n ( DataType alpha = DataType(0) )

inline

Formats the first nn_ entries of the vector.

Template Parameters

nn_	The number of elements to format; must be nn_ <= n_

Parameters

[in] alpha The value that the vector is to be set to.

Definition at line 483 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ negate()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::negate ( )

inline

Negates the vector, i.e. effectively multiplies all components by -1.

Returns: *this

Definition at line 573 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ negate_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::negate_n ( )

inline

Negates the first nn_ entries of this vector.

Template Parameters

nn_	The number of elements to negate; must be nn_ <= n_

Returns: *this

Definition at line 589 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ norm_euclid()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid ( ) const

inline

Computes the euclid norm of this vector.

Returns: The euclid norm of this vector

Definition at line 1048 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_sqr(), and FEAT::Math::sqrt().

Referenced by FEAT::Assembly::BurgersAssembler< DataType_, IndexType_, dim_ >::assemble_matrix(), FEAT::Assembly::BurgersAssembler< DataType_, IndexType_, dim_ >::assemble_scalar_matrix(), FEAT::Meshopt::ChartDistanceFunction< ElementalFunction_, Trafo_, RefCellTrafo_ >::compute_dist_add(), FEAT::Trafo::Standard::inverse_mapping(), FEAT::Tiny::Vector< T_, n_, s_ >::normalize(), FEAT::Tiny::Vector< T_, n_, s_ >::normalized(), FEAT::Assembly::BurgersAssemblyTaskBase< Job_, DataType_ >::prepare(), FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare(), and FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::project_point().

◆ norm_euclid_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_n ( ) const

inline

Computes the euclid norm of first nn_ entries of this vector.

Returns: The euclid norm of the vector.

Definition at line 1064 of file tiny_algebra.hpp.

References FEAT::Math::sqrt().

◆ norm_euclid_sqr()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_sqr ( ) const

inline

Computes the squared euclid norm of this vector.

Returns: The squared euclid norm of this vector.

Definition at line 1006 of file tiny_algebra.hpp.

References FEAT::Math::sqr(), and FEAT::Tiny::Vector< T_, n_, s_ >::v.

Referenced by FEAT::LAFEM::MeanFilterBlocked< DT_, IT_, BlockSize_ >::MeanFilterBlocked(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), FEAT::LAFEM::MeanFilterBlocked< DT_, IT_, BlockSize_ >::convert(), FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid(), FEAT::Tiny::Vector< T_, n_, s_ >::normalize(), FEAT::Trafo::InverseMapping< Trafo_, DataType_ >::unmap_point_by_newton(), and FEAT::Geometry::Atlas::Extrude< Mesh_, SubChart_ >::write().

◆ norm_euclid_sqr_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_sqr_n ( ) const

inline

Computes the squared euclid norm of first nn_ entries of this vector.

Returns: The squared euclid norm of the vector.

Definition at line 1027 of file tiny_algebra.hpp.

References FEAT::Math::sqr(), and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ norm_l1()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_l1 ( ) const

inline

Computes the l1-norm of this vector.

Returns: The l1-norm of this vector

Definition at line 1080 of file tiny_algebra.hpp.

References FEAT::Math::abs(), and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ norm_l1_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_l1_n ( ) const

inline

Computes the l1-norm of the first nn_ entries of this vector.

Returns: The l1-norm of the vector

Definition at line 1101 of file tiny_algebra.hpp.

References FEAT::Math::abs(), and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ norm_max()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_max ( ) const

inline

Computes the max-norm of this vector.

Returns: The max-norm of this vector

Definition at line 1122 of file tiny_algebra.hpp.

References FEAT::Math::abs(), FEAT::Math::max(), and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ norm_max_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Vector< T_, n_, s_ >::norm_max_n ( ) const

inline

Computes the max-norm of the vector.

Returns: The max-norm of the vector.

Definition at line 1143 of file tiny_algebra.hpp.

References FEAT::Math::abs(), FEAT::Math::max(), and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ normalize()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::normalize ( )

inline

Normalizes this vector.

Returns: *this

Definition at line 530 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid(), and FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_sqr().

Referenced by FEAT::Trafo::Standard::inverse_mapping(), and FEAT::Trafo::IsoSphere::Evaluator< Trafo_, EvalPolicy_, Shape::Vertex >::prepare().

◆ normalize_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::normalize_n ( )

inline

Normalizes the first nn_ entries of this vector.

Template Parameters

nn_	The number of elements to normalize; must be nn_ <= n_

Returns: *this

Definition at line 552 of file tiny_algebra.hpp.

References ASSERTM.

◆ normalized()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE bool FEAT::Tiny::Vector< T_, n_, s_ >::normalized ( ) const

inline

Return if the vector is normalized.

Definition at line 1169 of file tiny_algebra.hpp.

References FEAT::Math::abs(), FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid(), and FEAT::Math::pow().

◆ null()

template<typename T_ , int n_, int s_ = n_>

static CUDA_HOST_DEVICE Vector FEAT::Tiny::Vector< T_, n_, s_ >::null ( )

inlinestatic

Returns a null-vector.

Definition at line 1161 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::Vector().

◆ operator()() [1/2]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE T_ & FEAT::Tiny::Vector< T_, n_, s_ >::operator() ( int i )

inline

Access operator.

Parameters

[in] i The index of the vector component to be returned.

Returns: A (const) reference to the i-th entry of the vector.

Definition at line 354 of file tiny_algebra.hpp.

References ASSERTM, and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator()() [2/2]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE const T_ & FEAT::Tiny::Vector< T_, n_, s_ >::operator() ( int i ) const

inline

Access operator.

Parameters

[in] i The index of the vector component to be returned.

Returns: A (const) reference to the i-th entry of the vector.

Definition at line 361 of file tiny_algebra.hpp.

References ASSERTM, and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator*=() [1/2]

template<typename T_ , int n_, int s_ = n_>

template<int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator*= ( const Vector< T_, n_, sx_ > & x )

inline

element-wise-multiply operator

Definition at line 428 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator*=() [2/2]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator*= ( DataType alpha )

inline

scalar-multiply operator

Definition at line 417 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator+=()

template<typename T_ , int n_, int s_ = n_>

template<int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator+= ( const Vector< T_, n_, sx_ > & x )

inline

vector-add operator

Definition at line 439 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator-=()

template<typename T_ , int n_, int s_ = n_>

template<int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator-= ( const Vector< T_, n_, sx_ > & x )

inline

vector-subtract operator

Definition at line 450 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator=() [1/3]

template<typename T_ , int n_, int s_ = n_>

template<typename Tx_ >

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator= ( const std::initializer_list< Tx_ > & x )

inline

Initializer list assignment operator.

This operator allows to assign values to the vector in a simple manner:

Tiny::Vector<double, 3> v;

v = {0.1, 2.1, 7.3};

FEAT::Tiny::Vector::v

T_ v[s_]

actual vector data

Definition: tiny_algebra.hpp:225

Parameters

[in] x The initializer list whose elements are to be assigned.

Returns: *this

Definition at line 329 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v, and XASSERTM.

◆ operator=() [2/3]

template<typename T_ , int n_, int s_ = n_>

template<int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator= ( const Vector< T_, n_, sx_ > & x )

inline

copy-assignment operator

Definition at line 305 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator=() [3/3]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::operator= ( DataType value )

inline

value-assignment operator

Definition at line 294 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::value.

◆ operator[]() [1/2]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE T_ & FEAT::Tiny::Vector< T_, n_, s_ >::operator[] ( int i )

inline

Access operator.

Parameters

[in] i The index of the vector component to be returned.

Returns: A (const) reference to the i-th entry of the vector.

Definition at line 368 of file tiny_algebra.hpp.

References ASSERTM, and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ operator[]() [2/2]

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE const T_ & FEAT::Tiny::Vector< T_, n_, s_ >::operator[] ( int i ) const

inline

Access operator.

Parameters

[in] i The index of the vector component to be returned.

Returns: A (const) reference to the i-th entry of the vector.

Definition at line 375 of file tiny_algebra.hpp.

References ASSERTM, and FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ scale()

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::scale ( DataType alpha )

inline

Scales the vector.

Parameters

[in] alpha The value that the vector is to be scaled by

Definition at line 498 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ scale_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_>

CUDA_HOST_DEVICE void FEAT::Tiny::Vector< T_, n_, s_ >::scale_n ( DataType alpha )

inline

Scales the first nn_ entries of the vector.

Template Parameters

nn_	The number of elements to scale; must be nn_ <= n_

Parameters

[in] alpha The value that the vector is to be scaled by

Definition at line 516 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ set_convex()

template<typename T_ , int n_, int s_ = n_>

template<int sna_, int snb_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::set_convex	(	DataType	alpha,
		const Vector< T_, n_, sna_ > &	a,
		const Vector< T_, n_, snb_ > &	b
	)

inline

Sets this vector to the convex combination of two other vectors.

Let y denote this vector, then this function computes:

\[ y \leftarrow (1-\alpha)\cdot a + \alpha\cdot b \]

Parameters

[in]	alpha	The interpolation parameter for the convex combination. Should be 0 <= alpha <= 1
[in]	a	The first vector for the convex combination.
[in]	b	The second vector for the convex combination.

Returns: *this

Definition at line 658 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

Referenced by FEAT::Trafo::Isoparam::Evaluator< Trafo_, EvalPolicy_, degree_, Shape::Hypercube< 2 > >::prepare().

◆ set_convex_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_, int na_, int nb_, int sna_, int snb_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::set_convex_n	(	DataType	alpha,
		const Vector< T_, na_, sna_ > &	a,
		const Vector< T_, nb_, snb_ > &	b
	)

inline

Sets the first nn_ entries of this vector to the convex combination of two other vectors.

Let y denote this vector, then this function computes:

\[ y \leftarrow (1-\alpha)\cdot a + \alpha\cdot b \]

Template Parameters

nn_	The number of elements to combine; must be nn_ <= min(n_, na_, nb_)

Parameters

[in]	alpha	The interpolation parameter for the convex combination. Should be 0 <= alpha <= 1
[in]	a	The first vector for the convex combination.
[in]	b	The second vector for the convex combination.

Returns: *this

Definition at line 686 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::v.

◆ set_mat_vec_mult()

template<typename T_ , int n_, int s_ = n_>

template<int m_, int sma_, int sna_, int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::set_mat_vec_mult	(	const Matrix< T_, n_, m_, sma_, sna_ > &	a,
		const Vector< T_, m_, sx_ > &	x
	)

inline

Sets this vector to the result of a matrix-vector product.

Let y denote this vector, and let A denote the input matrix and x in the input vector, then this function computes:

\[ y \leftarrow A\cdot x \]

Parameters

[in]	a	The matrix for the product.
[in]	x	The (right) multiplicand vector for the product.

Returns: *this

Definition at line 712 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

Referenced by FEAT::VoxelAssembly::Kernel::burgers_velo_material_mat_assembly_kernel(), FEAT::Geometry::MeshExtruder< ConformalMesh< Shape::Hypercube< 2 >, 2, Coord_ > >::extrude_vertex_set(), and FEAT::Tiny::operator*().

◆ set_mat_vec_mult_n()

template<typename T_ , int n_, int s_ = n_>

template<int mm_, int nn_, int ma_, int na_, int sna_, int sma_, int nx_, int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::set_mat_vec_mult_n	(	const Matrix< T_, ma_, na_, sma_, sna_ > &	a,
		const Vector< T_, nx_, sx_ > &	x
	)

inline

Sets the first nn_ entries of this vector to the result of a matrix-vector product with the first mm_ entries of another vector.

This function effectively multiplies the upper left mm_ x nn_ block of the matrix a.

Template Parameters

mm_	The number of matrix rows to multiply; must be mm_ <= min(n_, ma_)
nn_	The number of matrix columns to multiply; must be nn_ <= min(nx_, na_)

Parameters

[in]	a	The matrix for the product.
[in]	x	The (right) multiplicand vector for the product.

Returns: *this

Definition at line 748 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ set_vec_mat_mult()

template<typename T_ , int n_, int s_ = n_>

template<int m_, int sma_, int sna_, int sx_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::set_vec_mat_mult	(	const Vector< T_, m_, sx_ > &	x,
		const Matrix< T_, m_, n_, sma_, sna_ > &	a
	)

inline

Sets this vector to the result of a vector-matrix product.

Let y denote this vector, and let x in the input vector and A denote the input matrix, then this function computes:

\[ y^\top \leftarrow x^\top \cdot A \Longleftrightarrow y \leftarrow A^\top\cdot x \]

Parameters

[in]	x	The (left) multiplicand vector for the product.
[in]	a	The matrix for the product.

Returns: *this

Definition at line 785 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

Referenced by FEAT::Tiny::operator*().

◆ set_vec_mat_mult_n()

template<typename T_ , int n_, int s_ = n_>

template<int nn_, int mm_, int mx_, int smx_, int ma_, int na_, int sma_, int sna_>

CUDA_HOST_DEVICE Vector & FEAT::Tiny::Vector< T_, n_, s_ >::set_vec_mat_mult_n	(	const Vector< T_, mx_, smx_ > &	x,
		const Matrix< T_, ma_, na_, sma_, sna_ > &	a
	)

inline

Sets the first mm_ entries of this vector to the result of a vector-matrix product with the first mm_ entries of another vector.

This function effectively multiplies the upper left mm_ x nn_ block of the matrix a.

Template Parameters

nn_	The number of matrix columns to multiply; must be nn_ <= min(nx_, na_)
mm_	The number of matrix rows to multiply; must be mm_ <= min(n_, ma_)

Parameters

[in]	x	The (left) multiplicand vector for the product.
[in]	a	The matrix for the product.

Returns: *this

Definition at line 821 of file tiny_algebra.hpp.

References ASSERTM, FEAT::Tiny::Vector< T_, n_, s_ >::v, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

Friends And Related Function Documentation

◆ operator<<

template<typename T_ , int n_, int s_ = n_>

CUDA_HOST friend std::ostream & operator<<	(	std::ostream &	lhs,
		const Vector< T_, n_, s_ > &	b
	)

friend

Tiny::Vector streaming operator.

Parameters

[in]	lhs	The target stream.
[in]	b	The vector to be streamed.

Definition at line 1180 of file tiny_algebra.hpp.

Member Data Documentation

◆ n

template<typename T_ , int n_, int s_ = n_>

constexpr int FEAT::Tiny::Vector< T_, n_, s_ >::n = n_

staticconstexpr

the length of the vector

Definition at line 215 of file tiny_algebra.hpp.

Referenced by FEAT::LAFEM::MeanFilterBlocked< DT_, IT_, BlockSize_ >::filter_cor(), FEAT::LAFEM::MeanFilterBlocked< DT_, IT_, BlockSize_ >::filter_rhs(), and FEAT::LAFEM::MeanFilterBlocked< DT_, IT_, BlockSize_ >::filter_sol().

◆ s

template<typename T_ , int n_, int s_ = n_>

constexpr int FEAT::Tiny::Vector< T_, n_, s_ >::s = s_

staticconstexpr

the stride of the vector

Definition at line 217 of file tiny_algebra.hpp.

◆ v

template<typename T_ , int n_, int s_ = n_>

T_ FEAT::Tiny::Vector< T_, n_, s_ >::v[s_]

actual vector data

Definition at line 225 of file tiny_algebra.hpp.

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

kernel/util/tiny_algebra.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ DataType

◆ ValueType

Constructor & Destructor Documentation

◆ Vector() [1/4]

◆ Vector() [2/4]

◆ Vector() [3/4]

◆ Vector() [4/4]

Member Function Documentation

◆ add_mat_vec_mult()

◆ add_mat_vec_mult_n()

◆ add_vec_mat_mult()

◆ add_vec_mat_mult_n()

◆ axpy()

◆ axpy_n()

◆ convert()

◆ convert_new() [1/2]

◆ convert_new() [2/2]

◆ copy()

◆ copy_n()

◆ format()

◆ format_n()

◆ negate()

◆ negate_n()

◆ norm_euclid()

◆ norm_euclid_n()

◆ norm_euclid_sqr()

◆ norm_euclid_sqr_n()

◆ norm_l1()

◆ norm_l1_n()

◆ norm_max()

◆ norm_max_n()

◆ normalize()

◆ normalize_n()

◆ normalized()

◆ null()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ scale()

◆ scale_n()

◆ set_convex()

◆ set_convex_n()

◆ set_mat_vec_mult()

◆ set_mat_vec_mult_n()

◆ set_vec_mat_mult()

◆ set_vec_mat_mult_n()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ n

◆ s

◆ v