#include <elementary/eagle/Christoffel.hpp>

Inheritance diagram for Eagle::Christoffel< Dims, Value >:

Public Member Functions
TVector_t	operator() (const TVector_t &v, const TVector_t &w) const
	Compute $u^a = \Gamma^a_{bc} v^b w^c \$. It can be written using the curvature-1-forms:$ \Gamma^a_{bc} w^c \equiv \Gamma^a_b w $, thus $u = (\Gamma^a_b \|\_ w) v^b$ .

Value &	operator() (int a, int b, int C)
	Return $\Gamma_{bc}^a$ .

const Value &	operator() (int a, int b, int C) const
	Return $\Gamma_{ab}^c$ .

Public Member Functions inherited from Eagle::LowerTriangular< Dims, Row< Dims, Value > >
	LowerTriangular ()
	Constructor, does not initialize anything.

	LowerTriangular (const LowerTriangular &LT)
	Copy constructor.

	LowerTriangular (const LowerTriangular &LT, const LowerTriangular &RT, const Operator<'+'> &A)
	Computational constructor for adding two types.

	LowerTriangular (const LowerTriangular &LT, const LowerTriangular &RT, const Operator<'-'> &A)
	Computational constructor for adding two types.

	LowerTriangular (const LowerTriangular &LT, const Row< Dims, Value > &v, const Operator<' *'> &M)
	Computational constructor for scalar multiplication.

	LowerTriangular (const LowerTriangular< N, T > &LT)
	Construct from symmetric matrix of same size but different type.

constexpr	LowerTriangular (const std::initializer_list< T > &Init)
	Initialize from initializer list.

	LowerTriangular (const Vector< T, N *(N+1)/2 > &V)
	Construct symmetric matrix from compatible vector of possibly different type.

Row< Dims, Value > &	operator() (dimension_t row, dimension_t column)
	read/write Element access

const Row< Dims, Value > &	operator() (dimension_t row, dimension_t column) const
	readonly Element access

LowerTriangular< N-1, Row< Dims, Value > > &	submatrix ()
	Due to the special layout of the LowerTriangular matrix class, retrieving a writeable reference to the lower dimensional submatrix is a possible operation and without runtime costs.

const LowerTriangular< N-1, Row< Dims, Value > > &	submatrix () const
	Due to the special layout of the LowerTriangular matrix class, retrieving a reference to the lower dimensional submatrix is a no-cost operation.

Public Member Functions inherited from Eagle::Vector< T, n >
Base_t &	fixed_array ()
	Provide access to the base class, writable.

const Base_t &	fixed_array () const
	Provide access to the base class, read-only.

Vector &	*operator=** (const T &value)
	Self-multiplication.

Vector &	operator+= (const Vector &v)
	Self-addition.

Vector	operator- () const
	Unary minus.

Vector &	operator-= (const Vector &v)
	Self-subtraction.

Vector &	operator/= (const T &value)
	Self-division.

template<class scalar >
Assignment< Vector, 0 >	operator= (const scalar &x)
	Assign first element with scalar and use consecutive comma expressions for assignment of further elements As such a Vector may be assigned as.

Vector &	operator= (const Vector &src)
	Assignment operator.

template<class V >
void	set (const V &value)
	Assign all values to the same scalar.

constexpr	Vector ()
	Default constructor.

template<class AType , class BType , int CompType>
	Vector (const FixedArray< AType, n > &l, const FixedArray< BType, n > &r, const Operator< CompType > &Op)
	Computational constructor for binary operations on two fixed arrays, calls the Operator's ternary() member function for each element.

template<class AType , class ScalarType , int CompType>
	Vector (const FixedArray< AType, n > &l, const Operator< CompType > &, const ScalarType &scalar)
	Computational constructor from vector with scalar, calls the Operator's ternary() member function for each element and the scalar as its 3rd argument.

template<typename InputType >
	Vector (const FixedArray< InputType, SIZE > &V)
	Type conversion constructor.

template<typename Indicable >
	Vector (const Indicable &I, const AnyType &)
	Construct from indicable object, i.e.

template<class AType , class ScalarType , int CompType>
	Vector (const Operator< CompType > &, const ScalarType &scalar, const FixedArray< AType, n > &v)
	Computational constructor from scalar with vector calls the Operator's ternary() member function for each element and the scalar as its 2nd argument.

template<typename InputType >
constexpr	Vector (const std::initializer_list< InputType > &Init)
	Construct from a initialization array.

	Vector (const T &a)
	Convenience Constructor: initialize the first element.

	Vector (const T &a, const T &b)
	Convenience Constructor: initialize the first two elements.

	Vector (const T &a, const T &b, const T &c)
	Convenience Constructor: initialize the first three elements.

	Vector (const T &a, const T &b, const T &c, const T &d)
	Convenience Constructor: initialize the first four elements.

template<int CompType>
	Vector (const Vector &l, const Vector &r, const Operator< CompType > &)
	Computational constructor for binary operations on two vectors calls the Operator's ternary() member function for each element.

	Vector (const Vector &NV, const Sub &, const Sub &)
	Computational constructor for unary minus.

constexpr	Vector (const Vector &v)
	Copy constructor.

	Vector (const Vector &v, const Operator<'-'> &)
	Unitary minus computational constructor Applies the unitary minus to each element.

template<typename InputType >
	Vector (const Vector< InputType, SIZE > &V)
	Type conversion constructor.

Public Member Functions inherited from Eagle::FixedArray< T, n >
void	expandMinMax (FixedArray &MinValues, FixedArray &MaxValues) const
	Expand a range given by MinValues,MaxValues to include the values of this array, done per component.

constexpr	FixedArray () noexcept
	Default constructor.

constexpr	FixedArray (const FixedArray< AType, N > &l, const FixedArray< BType, N > &r, const Operator< CompType > &)
	Computational constructor for binary operations on two fixed arrays, calls the Operator's ternary() member function for each element.

constexpr	FixedArray (const FixedArray< T, M > &F, const T &DefaultValue)
	Construct array from another array type of variable length.

constexpr	FixedArray (const FixedArray< T, N > &F)
	Automatic type conversion function.

constexpr	FixedArray (const FixedArray< T, N > &F, const ConversionFunctor &CF, const FA_CONVERT &)
	Construct array from another array type of same length.

constexpr	FixedArray (const std::initializer_list< InitType > &Init)
	Construct from a initialization array.

constexpr	FixedArray (const T &a)
	Convenience Constructor: initialize the first element.

constexpr	FixedArray (const T &a, const T &b)
	Convenience Constructor: initialize the first two elements.

	FixedArray (const T &a, const T &b, const T &c)
	Convenience Constructor: initialize the first three elements.

constexpr	FixedArray (const T &a, const T &b, const T &c, const T &d)
	Convenience Constructor: initialize the first four elements.

constexpr	FixedArray (const T &a, const T &b, const T &c, const T &d, const T &e)
	Convenience Constructor: initialize the first five elements.

constexpr T &	get (int i)
	writable element access

constexpr const T &	get (int i) const
	read-only element access

constexpr const FixedArray< T, subsize > *	get_subarray () const
	Helper class for retrieve a subset of the current array.

constexpr const FixedArray< T, SIZE-1 > &	get_subdim () const
	Mainly introduced because of Interpolate::operator[].

const FixedArray_t &	getFixedArray () const noexcept
	convenience function for base classes

FixedArray_t &	getFixedArray () noexcept
	convenience function for base classes

constexpr T	getMax () const
	Compute the maximum element value of this array.

constexpr T	getMin () const
	Compute the maximum element value of this array.

constexpr bool	operator!= (const FixedArray< T, N > &F) const
	Compare two arrays.

constexpr bool	operator== (const FixedArray< T, N > &F) const
	Compare two arrays.

constexpr T &	operator[] (int i)
	writeable element access operator

constexpr const T &	operator[] (int i) const
	read-only element access operator

constexpr T *	ptr (int i=0) noexcept
	Return a pointer to the ith element, no range checking.

constexpr void	set (const Value &x)
	Set all array elements to the same value.

void	setFromArray (const T *x, int length=SIZE, int offset=0)
	Set all array elements to an array's element value.

void	sort (FixedArray< int, N > &I) const
	Sort the elements of an array into the index array.

Additional Inherited Members
Public Types inherited from Eagle::LowerTriangular< Dims, Row< Dims, Value > >
typedef Vector< Row< Dims, Value >, N *(N+1)/2 >	Base_t
	The (vectorial) base class.

typedef Base_t::Vector_t	Vector_t
	The compatible vector class.

Public Types inherited from Eagle::Vector< T, n >
enum
	The number of elements in this array.

Public Types inherited from Eagle::FixedArray< T, n >
typedef FlattenedArray_t::value_type	Element_t
	The maximally reduced type of elements stored here.

typedef GetFixedArrayType< T >::result_t	ElementAsFixedArray_t
	Element type as fixed array, if it is convertible to a fixed array.

typedef FixedArray	FixedArray_t
	Exporting the type definition of this array cass type.

typedef FixedArrayFlattener< FixedArrayOfElements_t >	FixedArrayFlattener_t
	Internal helper class.

typedef FixedArray< ElementAsFixedArray_t, N >	FixedArrayOfElements_t
	If the value is derived from a fixed array type itself, then the FixedArrayOfElements_t is an FixedArray<FixedArray<>> type.

typedef FixedArrayFlattener_t::result_t	FlattenedArray_t
	Reduction of this array type, if it is nested, to an flattened type which contains elementary types.

typedef T	value_type
	Export the type of the respective element value type.

Static Public Member Functions inherited from Eagle::LowerTriangular< Dims, Row< Dims, Value > >
static constexpr dimension_t	mem_index (dimension_t row, dimension_t column)
	Retrieve the linear index from row/column indices.

Static Public Member Functions inherited from Eagle::FixedArray< T, n >
static constexpr FixedArray	convert (const FixedArray< T, N > &F, const ConversionFunctor &CF)
	Perform a type conversion on a given fixed array into another basis type:

static constexpr dimension_t	size ()
	The number of elements here.

Public Attributes inherited from Eagle::LowerTriangular< Dims, Row< Dims, Value > >
STATIC_CONSTEXPR_BEGIN	columns
	number of columns

STATIC_CONSTEXPR_BEGIN	rows
	number of rows

Static Public Attributes inherited from Eagle::LowerTriangular< Dims, Row< Dims, Value > >
static constexpr auto	MEMSIZE
	The number of value elements occupied in memory due to alignment.

static constexpr auto	SIZE
	The number of value elements, i.e. N*(N+1)/2.

Protected Attributes inherited from Eagle::FixedArray< T, n >
T	data [SIZE]
	The actual data values, intentional no-initialization for data member, which increases performance on vector creation.

Detailed Description

template<int Dims, class Value>
class Eagle::Christoffel< Dims, Value >

Christoffel symbols.

Member Function Documentation

◆ operator()()

template<int Dims, class Value >

TVector_t Eagle::Christoffel< Dims, Value >::operator()	(	const TVector_t &	v,
		const TVector_t &	w
	)		const

inline

Compute $u^a = \Gamma^a_{bc} v^b w^c \$. It can be written using the curvature-1-forms:$ \Gamma^a_{bc} w^c \equiv \Gamma^a_b w $, thus $u = (\Gamma^a_b |\_ w) v^b$ .

Todo:: Make use of symmetry $\Gamma^a_{bc} = \Gamma^a_{cb}$ , add special case v==w.

References Eagle::Vector< T, n >::set().

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ operator()()