Eagle::LowerTriangular< N, value > Class Template Reference

A symmetric matrix stored in lower triangular form. More...

#include <elementary/eagle/Matrix.hpp>

Inheritance diagram for Eagle::LowerTriangular< N, value >:

Public Types
typedef Vector< 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< value, N *(N+1)/2 >
enum
	The number of elements in this array.
Public Types inherited from Eagle::FixedArray< value, N >
typedef FlattenedArray_t::value_type	Element_t
	The maximally reduced type of elements stored here.
typedef GetFixedArrayType< value >::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 value	value_type
	Export the type of the respective element value type.

Public Member Functions
	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 value &v, const Operator<' *'> &M)
	Computational constructor for scalar multiplication.
template<class T >
	LowerTriangular (const LowerTriangular< N, T > &LT)
	Construct from symmetric matrix of same size but different type.
template<class T >
constexpr	LowerTriangular (const std::initializer_list< T > &Init)
	Initialize from initializer list.
template<class T >
	LowerTriangular (const Vector< T, N *(N+1)/2 > &V)
	Construct symmetric matrix from compatible vector of possibly different type.
value &	operator() (dimension_t row, dimension_t column)
	read/write Element access
const value &	operator() (dimension_t row, dimension_t column) const
	readonly Element access
LowerTriangular< N-1, 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, 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< value, N *(N+1)/2 >
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 value &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 value &value)
	Self-division.
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.
void	set (const V &value)
	Assign all values to the same scalar.
constexpr	Vector ()
	Default constructor.
	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.
	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.
	Vector (const FixedArray< InputType, SIZE > &V)
	Type conversion constructor.
	Vector (const Indicable &I, const AnyType &)
	Construct from indicable object, i.e.
	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.
constexpr	Vector (const std::initializer_list< InputType > &Init)
	Construct from a initialization array.
	Vector (const value &a)
	Convenience Constructor: initialize the first element.
	Vector (const value &a, const value &b)
	Convenience Constructor: initialize the first two elements.
	Vector (const value &a, const value &b, const value &c)
	Convenience Constructor: initialize the first three elements.
	Vector (const value &a, const value &b, const value &c, const value &d)
	Convenience Constructor: initialize the first four elements.
	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.
	Vector (const Vector< InputType, SIZE > &V)
	Type conversion constructor.
Public Member Functions inherited from Eagle::FixedArray< value, 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.
template<class AType , class BType , OperatorID_t CompType>
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.
template<typename T , dimension_t M>
constexpr	FixedArray (const FixedArray< T, M > &F, const T &DefaultValue)
	Construct array from another array type of variable length.
template<typename T >
constexpr	FixedArray (const FixedArray< T, N > &F)
	Automatic type conversion function.
template<typename T , typename ConversionFunctor >
constexpr	FixedArray (const FixedArray< T, N > &F, const ConversionFunctor &CF, const FA_CONVERT &)
	Construct array from another array type of same length.
template<class InitType >
constexpr	FixedArray (const std::initializer_list< InitType > &Init)
	Construct from a initialization array.
constexpr	FixedArray (const value &a)
	Convenience Constructor: initialize the first element.
constexpr	FixedArray (const value &a, const value &b)
	Convenience Constructor: initialize the first two elements.
	FixedArray (const value &a, const value &b, const value &c)
	Convenience Constructor: initialize the first three elements.
constexpr	FixedArray (const value &a, const value &b, const value &c, const value &d)
	Convenience Constructor: initialize the first four elements.
constexpr	FixedArray (const value &a, const value &b, const value &c, const value &d, const value &e)
	Convenience Constructor: initialize the first five elements.
constexpr value &	get (int i)
	writable element access
constexpr const value &	get (int i) const
	read-only element access
template<int subsize, int offset>
constexpr const FixedArray< value, subsize > *	get_subarray () const
	Helper class for retrieve a subset of the current array.
constexpr const FixedArray< value, 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 value	getMax () const
	Compute the maximum element value of this array.
constexpr value	getMin () const
	Compute the maximum element value of this array.
template<typename T >
constexpr bool	operator!= (const FixedArray< T, N > &F) const
	Compare two arrays.
template<typename T >
constexpr bool	operator== (const FixedArray< T, N > &F) const
	Compare two arrays.
constexpr value &	operator[] (int i)
	writeable element access operator
constexpr const value &	operator[] (int i) const
	read-only element access operator
constexpr value *	ptr (int i=0) noexcept
	Return a pointer to the ith element, no range checking.
template<class Value >
constexpr void	set (const Value &x)
	Set all array elements to the same value.
void	setFromArray (const value *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.

Static Public Member Functions
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< value, N >
template<typename T , typename ConversionFunctor >
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
STATIC_CONSTEXPR_BEGIN	columns = N
	number of columns
STATIC_CONSTEXPR_BEGIN	rows = N
	number of rows

Static Public Attributes
static constexpr auto	MEMSIZE = sizeof(Base_t) / sizeof(value)
	The number of value elements occupied in memory due to alignment.
static constexpr auto	SIZE = Vector_t::SIZE
	The number of value elements, i.e. N*(N+1)/2.

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

Detailed Description

template<dimension_t N, class value>
class Eagle::LowerTriangular< N, value >

A symmetric matrix stored in lower triangular form.

For a 3x3 symmetric matrix (six independent components) we get the following layout:

0 1 3
1 2 4
3 4 5

and for a 4x4 symmetric matrix with ten components we get:

0 1 3 6
1 2 4 7
3 4 5 8
6 7 8 9

This layout ensures that the upper left submatrix of lower dimension is always contained in higher dimensional matrices. I.e. a matrix of type LowerTriangular<N> may always be casted to a matrix of type LowerTriangular<N-n> with n<N.