Simple matrix class for performing fast operations on matrices of sizes known at compile-time. More...

#include <elementary/eagle/Matrix.hpp>

Inheritance diagram for Eagle::Matrix< R, C, Value >:

Public Types
using	Matrix_t = Matrix
	Matrix type.

Public Types inherited from Eagle::Vector< Value, R *C >
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
constexpr const Matrix_t &	matrix () const
	yield matrix here, useful for derived classes.

Constructors
constexpr	Matrix ()
	Default constructor.

constexpr	Matrix (const Matrix &M)
	Copy constructor.

constexpr	Matrix (const Base_t &V)
	Construct matrix from linear vector.

template<class T >
constexpr	Matrix (const std::array< T, 16 > &Init)
	Construct matrix from initializer list.

Public Member Functions inherited from Eagle::Vector< Value, R *C >
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.

Related Symbols
(Note that these are not member symbols.)
template<int N, class value >
void	UnsortedEigenVectors (LowerTriangular< N, value > &A, Quadratic< N, value > &RRmatrix, Row< N, value > &E, double precision=1E-10)
	Eigenvalues and eigenvectors of a real symmetric matrix.

Arithmetic operations
typedef Operator<' *'>	Mult
	Computational constructor argument for multiplicative operations.

typedef Operator<'~'>	TransposeOperation
	Computational constructor argument for transpose operations.

constexpr	Matrix (const Matrix &A, const Value &V, const Operator<' *'> &M)
	Computational constructor for multiplying matrix by scalar.

constexpr	Matrix (const Value &V, const Matrix &A, const Operator<' *'> &M)
	Computational constructor for multiplying scalar by matrix.

constexpr	Matrix (const Matrix &A, const Value &V, const Operator<'/'> &Op)
	Computational constructor for dividing matrix by scalar.

constexpr	Matrix (const Matrix &A, const Matrix &B, const Operator<'+'> &Op)
	Computational constructor for matrix addition.

constexpr	Matrix (const Matrix &A, const Matrix &B, const Operator<'-'> &Op)
	Computational constructor for matrix subtraction.

template<class AType , class BType , OperatorID_t CompType>
constexpr	Matrix (const FixedArray< AType, R C > &l, const FixedArray< BType, R C > &r, const Operator< CompType > &Op)
	Generic computational constructor for two arrays of size compatible with the matrix.

template<class Type >
constexpr	Matrix (const FixedArray< Type, R *C > &Data)
	Explicit constructor from arbitrary compatible type.

template<class ValueType , OperatorID_t CompType>
constexpr	Matrix (const FixedArray< ValueType, R > &l, const Operator< CompType > &Op, const Value &scalar)
	Generic computational constructor for vector/scalar operations.

template<class ValueType , OperatorID_t CompType>
constexpr	Matrix (const Operator< CompType > &Op, const Value &scalar, const FixedArray< ValueType, R > &l)
	Generic computational constructor for scalar/vector operations.

constexpr	Matrix (const Matrix &A, const Operator<'-'> &Op)
	Computational constructor for unary minus.

template<dimension_t M, class ValueA , class ValueB >
constexpr	Matrix (const Matrix< R, M, ValueA > &A, const Matrix< M, C, ValueB > &B, const Operator<' *'> &)
	Matrix multiplication .

template<dimension_t M, class ValueA , class ValueB >
constexpr	Matrix (const Matrix< R, M, ValueA > &A, const Matrix< C, M, ValueB > &B, const Operator<' *','~'> &)
	Transposed matrix multiplication $A B^{\tau}$ .

template<dimension_t M>
constexpr	Matrix (const Matrix< R, M, Value > &A, const Matrix< C, M, Value > &B, const Mult &, const TransposeOperation &)
	Matrix multiplication with transpose of matrix B.

template<dimension_t M>
constexpr	Matrix (const Matrix< M, R, Value > &A, const Matrix< M, C, Value > &B, const TransposeOperation &, const Mult &)
	Matrix multiplication with transpose of matrix A.

constexpr	Matrix (const Matrix< R, C, Value > &A, const LowerTriangular< C, Value > &B, const Mult &)
	Matrix multiplication where B is a symmetric matrix stored in lower triangular form.

constexpr	Matrix (const Matrix< C, R, Value > &A, const LowerTriangular< C, Value > &B, const TransposeOperation &, const Mult &)
	Matrix multiplication where B is a symmetric matrix stored in lower triangular form.

constexpr const Column< R, Value > &	column (int i) const
	Return the ith column of this matrix.

constexpr Column< R, Value > &	column (int i)
	Return the ith column of this matrix, writeable.

constexpr Value &	operator() (dimension_t row, dimension_t column)
	Access element for writing.

constexpr const Value &	operator() (dimension_t row, dimension_t column) const
	Element access operation for reading.

constexpr Row_t	row (dimension_t rowNr)
	Return writable reference to the ith row of this matrix.

constexpr const Row_t	row (dimension_t rowNr) const
	Return read-only reference to the ith row of this matrix.

constexpr const auto	operator[] (dimension_t r) const
	Allow nested access to matrix elements via bracket operator.

constexpr auto &	operator[] (dimension_t r)
	Allow nested access to matrix elements via bracket operator.

constexpr Matrix	operator+ (const Matrix &A, const Matrix &B)
	Add matrices.

template<dimension_t M>
constexpr Matrix	operator* (const Matrix< R, M, Value > &A, const Matrix< M, C, Value > &B)
	Matrix product.

template<dimension_t M, class ValueA , class ValueB >
constexpr Matrix	matrix_mult (const Matrix< R, M, ValueA > &A, const Matrix< M, C, ValueB > &B)
	Matrix product, version as function.

template<dimension_t M, class ValueA , class ValueB >
constexpr Matrix	matrix_mult_transp (const Matrix< R, M, ValueA > &A, const Matrix< C, M, ValueB > &B)
	Transposed matrix product, version as function.

Additional Inherited Members
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.

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 R, dimension_t C, class Value>
class Eagle::Matrix< R, C, Value >

Simple matrix class for performing fast operations on matrices of sizes known at compile-time.

All operations are implemented as inline functions using computational constructors, such that simple operations don't require any temporaries. However, advanced techniques like expression templates are not employed here, so complex operations may require temporary objects. The intentional use are small, fast operations with compile time check of operational consistency.

Parameters

R	rows
C	columns

The layout is given as (column,row) indexing according to a matrix A as

$A = \begin{pmatrix} A_{0,0} & \dots & A_{c-1,0} \\ &\dots& \\ A_{0,r-1} & \dots & A_{c-1,r-1} \end{pmatrix}$

. The elements are stored compatible with OpenGL, see e.g. https://www.geeks3d.com/20141114/glsl-4x4-matrix-mat4-fields/ . A Matrix is therefore a collection of columns and is like an array of column vectors. A column can be referenced without copy and can be modified (in contrast to rows, which requires a copy).

Be alert that initialization from an initializer list looks transposed, see the

See also: Matrix.cpp text example:
Matrix<4,4, double> mat =

{0,1,2,3,

4,5,6,7,

8,9,10,11,

12,13,14,15

};

Eagle::Matrix
Simple matrix class for performing fast operations on matrices of sizes known at compile-time.
Definition Matrix.hpp:440

is the matrix
$A = \begin{pmatrix} 0 & 4 & 8 & 12 \\ 1 & 5 & 9 & 13 \\ 2 & 6 & 10 & 14 \\ 3 & 7 & 11 & 15 \\ \end{pmatrix}$
.; LowerTriangular, Matrix, Row, Column

Constructor & Destructor Documentation

◆ Matrix() [1/6]

template<dimension_t R, dimension_t C, class Value >

template<dimension_t M, class ValueA , class ValueB >

constexpr Eagle::Matrix< R, C, Value >::Matrix	(	const Matrix< R, M, ValueA > &	A,
		const Matrix< M, C, ValueB > &	B,
		const Operator<' *'> &
	)

inlineconstexpr

Matrix multiplication $ A B$ .

@TODO Test matrix multiplication!!! @TODO Optimize for row-wise contraction!

$M_{rc} = \Sigma_m A_{rm} B_{mc}$

◆ Matrix() [2/6]

template<dimension_t R, dimension_t C, class Value >

template<dimension_t M, class ValueA , class ValueB >

constexpr Eagle::Matrix< R, C, Value >::Matrix	(	const Matrix< R, M, ValueA > &	A,
		const Matrix< C, M, ValueB > &	B,
		const Operator<' *','~'> &
	)

inlineconstexpr

Transposed matrix multiplication $A B^{\tau}$ .

@TODO Test matrix multiplication!!! @TODO Optimize for row-wise contraction!

$M_{rc} = \Sigma_m A_{rm} B_{cm}$

◆ Matrix() [3/6]

template<dimension_t R, dimension_t C, class Value >

template<dimension_t M>

constexpr Eagle::Matrix< R, C, Value >::Matrix	(	const Matrix< R, M, Value > &	A,
		const Matrix< C, M, Value > &	B,
		const Mult &	,
		const TransposeOperation &
	)

inlineconstexpr

Matrix multiplication $ A B^t$ with transpose of matrix B.

Todo:: This code is UNTESTED! Verify before usage!

◆ Matrix() [4/6]

template<dimension_t R, dimension_t C, class Value >

template<dimension_t M>

constexpr Eagle::Matrix< R, C, Value >::Matrix	(	const Matrix< M, R, Value > &	A,
		const Matrix< M, C, Value > &	B,
		const TransposeOperation &	,
		const Mult &
	)

inlineconstexpr

Matrix multiplication $ A^t B$ with transpose of matrix A.

Todo:: This code is UNTESTED! Verify before usage!

◆ Matrix() [5/6]

template<dimension_t R, dimension_t C, class Value >

constexpr Eagle::Matrix< R, C, Value >::Matrix	(	const Matrix< R, C, Value > &	A,
		const LowerTriangular< C, Value > &	B,
		const Mult &
	)

inlineconstexpr

Matrix multiplication $ A B$ where B is a symmetric matrix stored in lower triangular form.

@TODO Optimize for symmetries on the operation!

◆ Matrix() [6/6]

template<dimension_t R, dimension_t C, class Value >

constexpr Eagle::Matrix< R, C, Value >::Matrix	(	const Matrix< C, R, Value > &	A,
		const LowerTriangular< C, Value > &	B,
		const TransposeOperation &	,
		const Mult &
	)

inlineconstexpr

Matrix multiplication $ A^t B$ where B is a symmetric matrix stored in lower triangular form.

@TODO Optimize for symmetries on the operation!

Member Function Documentation

◆ operator()()

template<dimension_t R, dimension_t C, class Value >

constexpr Value & Eagle::Matrix< R, C, Value >::operator()	(	dimension_t	row,
		dimension_t	column
	)

inlineconstexpr

Access element for writing.

The memory layout is set up according to

M[ i+j*ROWS ] = M[i][j].

such that linear access to the elements works through the comma assignment operator:

Matrix<3,4,double>      A;
 
A = 1,0,0,
    0,1,0,
    0,0,1,
    0,0,0;

References Eagle::Matrix< R, C, Value >::column(), and Eagle::Matrix< R, C, Value >::row().

◆ row() [1/2]

template<dimension_t R, dimension_t C, class Value >

constexpr Row_t Eagle::Matrix< R, C, Value >::row ( dimension_t rowNr )

inlineconstexpr

Return writable reference to the ith row of this matrix.

Note that the result is not a vectorized vector (and thus not of type Row<>), because it is possibly not aligned as required by a vectorized vector.

Referenced by Eagle::Quadratic< N, Value >::GaussDecompose(), Eagle::Matrix< R, C, Value >::operator()(), and Eagle::Matrix< R, C, Value >::operator()().

◆ row() [2/2]

template<dimension_t R, dimension_t C, class Value >

constexpr const Row_t Eagle::Matrix< R, C, Value >::row ( dimension_t rowNr ) const

inlineconstexpr

Return read-only reference to the ith row of this matrix.

Note that the result is not a vectorized vector (and thus not of type Row<>), because it is possibly not aligned as required by a vectorized vector.

Public Types

Public Member Functions

Related Symbols

Arithmetic operations

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/6]

◆ Matrix() [2/6]

◆ Matrix() [3/6]

◆ Matrix() [4/6]

◆ Matrix() [5/6]

◆ Matrix() [6/6]

Member Function Documentation

◆ operator()()

◆ row() [1/2]

◆ row() [2/2]