3x3 matrix with Quantity components More...

#include <Matrix3x3.hpp>

Public Member Functions
constexpr	Matrix ()
	Construct a zero matrix.

constexpr	Matrix (const Vector3< T > &col0, const Vector3< T > &col1, const Vector3< T > &col2)
	Construct from three column vectors.

constexpr	Matrix (T m00, T m01, T m02, T m10, T m11, T m12, T m20, T m21, T m22)
	Construct from individual components (row-major ordering)

constexpr Matrix	Transpose () const
	Compute the transpose of the matrix.

constexpr T	Trace () const
	Compute the trace of the matrix.

constexpr auto	Symmetric () const
	Compute the symmetric part of the matrix.

constexpr auto	Antisymmetric () const
	Compute the antisymmetric part of the matrix.

const T &	At (const int i, const int j) const
	Access element at row i, column j with bounds checking (0-based indexing)

T &	At (const int i, const int j)
	Access element at row i, column j with bounds checking (0-based indexing) - mutable version.

constexpr const T &	operator() (const int i, const int j) const
	Access element at row i, column j (0-based indexing) - no bounds checking.

constexpr T &	operator() (const int i, const int j)
	Access element at row i, column j (0-based indexing) - mutable version.

template<typename U >
constexpr auto	operator+ (const Matrix3x3< U > &other) const
	Matrix addition.

template<typename U >
constexpr auto	operator- (const Matrix3x3< U > &other) const
	Matrix subtraction.

constexpr auto	operator- () const
	Unary negation.

template<typename U >
constexpr auto	operator* (U scalar) const
	Scalar multiplication (matrix * scalar)

template<typename U >
constexpr auto	operator* (const Vector3< U > &v) const
	Matrix-vector multiplication: M * v.

template<typename U >
constexpr auto	operator* (const Matrix3x3< U > &other) const
	Matrix-matrix multiplication: A * B.

template<typename U >
constexpr Matrix &	operator+= (const Matrix3x3< U > &other)
	Addition assignment.

template<typename U >
constexpr Matrix &	operator-= (const Matrix3x3< U > &other)
	Subtraction assignment.

template<typename U >
constexpr Matrix &	operator*= (U scalar)
	Scalar multiplication assignment.

template<typename U >
constexpr bool	operator== (const Matrix3x3< U > &other) const
	Equality comparison.

template<typename U >
constexpr bool	operator!= (const Matrix3x3< U > &other) const
	Inequality comparison.

template<typename UnitT >
Matrix3x3< Quantity< UnitT > >	As () const
	Convert all components to a different unit of the same dimension.

Static Public Member Functions
static constexpr Matrix	Identity ()
	Create an identity matrix.

Public Attributes
Vector3< T >	x_basis

Vector3< T >	y_basis

Vector3< T >	z_basis

Friends
std::ostream &	operator<< (std::ostream &os, const Matrix &m)
	Stream insertion operator.

Detailed Description

template<typename T>
struct Phyth::Matrix< 3, 3, T >

3x3 matrix with Quantity components

Matrix3x3 stores three column vectors, enabling matrix-vector operations while preserving physical dimensions.

Template Parameters

T	Component type (must be a Quantity instantiation)

Example: Matrix3x3<Quantity<Meter>> m; // 3x3 matrix with meter components auto result = m * Vector3<Quantity<Meter>>(1.0_m, 0_m, 0_m);

Definition at line 27 of file Matrix3x3.hpp.

Constructor & Destructor Documentation

◆ Matrix() [1/3]

template<typename T >

constexpr Phyth::Matrix< 3, 3, T >::Matrix ( )

inlineconstexpr

Construct a zero matrix.

Initializes all elements to zero using Quantity's default constructor.

Definition at line 39 of file Matrix3x3.hpp.

◆ Matrix() [2/3]

template<typename T >

constexpr Phyth::Matrix< 3, 3, T >::Matrix	(	const Vector3< T > &	col0,
		const Vector3< T > &	col1,
		const Vector3< T > &	col2
	)

inlineconstexpr

Construct from three column vectors.

Parameters

col0	First column vector
col1	Second column vector
col2	Third column vector

Definition at line 49 of file Matrix3x3.hpp.

◆ Matrix() [3/3]

template<typename T >

constexpr Phyth::Matrix< 3, 3, T >::Matrix	(	T	m00,
		T	m01,
		T	m02,
		T	m10,
		T	m11,
		T	m12,
		T	m20,
		T	m21,
		T	m22
	)

inlineconstexpr

Construct from individual components (row-major ordering)

This constructor takes components in row-major order but stores them internally in column-major order.

Parameters

m00	Row 0, Col 0
m01	Row 0, Col 1
m02	Row 0, Col 2
m10	Row 1, Col 0
m11	Row 1, Col 1
m12	Row 1, Col 2
m20	Row 2, Col 0
m21	Row 2, Col 1
m22	Row 2, Col 2

Example: Matrix3x3 m(1, 2, 3, 4, 5, 6, 7, 8, 9); // m(1, 0) == 4, m(0, 1) == 2

Definition at line 75 of file Matrix3x3.hpp.

Member Function Documentation

◆ Antisymmetric()

template<typename T >

constexpr auto Phyth::Matrix< 3, 3, T >::Antisymmetric ( ) const

inlineconstexpr

Compute the antisymmetric part of the matrix.

Returns (M - M^T) / 2

Returns: Matrix3x3 Antisymmetric part

Example: auto anti = m.Antisymmetric(); // (m - m^T) / 2

Definition at line 157 of file Matrix3x3.hpp.

◆ As()

template<typename T >

template<typename UnitT >

Matrix3x3< Quantity< UnitT > > Phyth::Matrix< 3, 3, T >::As ( ) const

inline

Convert all components to a different unit of the same dimension.

Template Parameters

UnitT Target unit type

Returns: Matrix3x3<Quantity<UnitT>> Matrix with components converted to the new unit

Example: auto m_mm = m.as<Millimeter>();

Definition at line 444 of file Matrix3x3.hpp.

◆ At() [1/2]

template<typename T >

T & Phyth::Matrix< 3, 3, T >::At	(	const int	i,
		const int	j
	)

inline

Access element at row i, column j with bounds checking (0-based indexing) - mutable version.

Parameters

i	Row index (0, 1, 2)
j	Column index (0, 1, 2)

Returns: T& Element value

Exceptions

std::out_of_range if index is out of bounds

Example: m.at(0, 1) = 5; // Set element at row 0, column 1 to 5

Definition at line 195 of file Matrix3x3.hpp.

◆ At() [2/2]

template<typename T >

const T & Phyth::Matrix< 3, 3, T >::At	(	const int	i,
		const int	j
	)		const

inline

Access element at row i, column j with bounds checking (0-based indexing)

Parameters

i	Row index (0, 1, 2)
j	Column index (0, 1, 2)

Returns: const T& Element value

Exceptions

std::out_of_range if index is out of bounds

Example: auto val = m.at(1, 2); // Get element at row 1, column 2

Definition at line 172 of file Matrix3x3.hpp.

◆ Identity()

template<typename T >

static constexpr Matrix Phyth::Matrix< 3, 3, T >::Identity ( )

inlinestaticconstexpr

Create an identity matrix.

Returns a 3x3 identity matrix with ones on the diagonal and zeros elsewhere.

Returns: Matrix3x3 Identity matrix

Example: auto I = Matrix3x3<Quantity<Meter>>::Identity();

Definition at line 94 of file Matrix3x3.hpp.

◆ operator!=()

template<typename T >

template<typename U >

constexpr bool Phyth::Matrix< 3, 3, T >::operator!= ( const Matrix3x3 & other ) const

inlineconstexpr

Inequality comparison.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to compare against

Returns: true if any corresponding component differs

Example: if (m1 != m2) { ... }

Definition at line 430 of file Matrix3x3.hpp.

◆ operator()() [1/2]

template<typename T >

constexpr T & Phyth::Matrix< 3, 3, T >::operator()	(	const int	i,
		const int	j
	)

inlineconstexpr

Access element at row i, column j (0-based indexing) - mutable version.

Parameters

i	Row index (0, 1, 2)
j	Column index (0, 1, 2)

Returns: T& Element value

Note: Matrix is stored in column-major order internally

Warning: No bounds checking is performed. Use at() for safe access.

Example: m(0, 1) = 5; // Set element at row 0, column 1 to 5

Definition at line 239 of file Matrix3x3.hpp.

◆ operator()() [2/2]

template<typename T >

constexpr const T & Phyth::Matrix< 3, 3, T >::operator()	(	const int	i,
		const int	j
	)		const

inlineconstexpr

Access element at row i, column j (0-based indexing) - no bounds checking.

Parameters

i	Row index (0, 1, 2)
j	Column index (0, 1, 2)

Returns: const T& Element value

Note: Matrix is stored in column-major order internally

Warning: No bounds checking is performed. Use at() for safe access.

Example: auto val = m(1, 2); // Get element at row 1, column 2

Definition at line 220 of file Matrix3x3.hpp.

◆ operator*() [1/3]

template<typename T >

template<typename U >

constexpr auto Phyth::Matrix< 3, 3, T >::operator* ( const Matrix3x3 & other ) const

inlineconstexpr

Matrix-matrix multiplication: A * B.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to multiply with

Returns: Matrix3x3<decltype(*this * other.x_basis)> Product of the two matrices

Example: auto product = m1 * m2;

Definition at line 341 of file Matrix3x3.hpp.

◆ operator*() [2/3]

template<typename T >

template<typename U >

constexpr auto Phyth::Matrix< 3, 3, T >::operator* ( const Vector3 & v ) const

inlineconstexpr

Matrix-vector multiplication: M * v.

Template Parameters

U	Quantity type of the vector

Parameters

v	Vector to multiply with

Returns: auto Resulting vector

Example: auto v = m * Vector3<Quantity<Meter>>(1, 2, 3);

Definition at line 325 of file Matrix3x3.hpp.

◆ operator*() [3/3]

template<typename T >

template<typename U >

constexpr auto Phyth::Matrix< 3, 3, T >::operator* ( U scalar ) const

inlineconstexpr

Scalar multiplication (matrix * scalar)

Template Parameters

U	Scalar type

Parameters

scalar Scalar value to multiply with

Returns: Matrix3x3<decltype(x_basis * scalar)> Matrix scaled by scalar

Example: auto scaled = m * 2.0;

Definition at line 306 of file Matrix3x3.hpp.

◆ operator*=()

template<typename T >

template<typename U >

constexpr Matrix & Phyth::Matrix< 3, 3, T >::operator*= ( U scalar )

inlineconstexpr

Scalar multiplication assignment.

Template Parameters

U	Scalar type

Parameters

scalar Scalar value to multiply with

Returns: Matrix3x3& Reference to this matrix

Example: m *= 2.0;

Definition at line 397 of file Matrix3x3.hpp.

◆ operator+()

template<typename T >

template<typename U >

constexpr auto Phyth::Matrix< 3, 3, T >::operator+ ( const Matrix3x3 & other ) const

inlineconstexpr

Matrix addition.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to add

Returns: Matrix3x3<decltype(x_basis + other.x_basis)> Sum of the two matrices

Example: auto sum = m1 + m2;

Definition at line 256 of file Matrix3x3.hpp.

◆ operator+=()

template<typename T >

template<typename U >

constexpr Matrix & Phyth::Matrix< 3, 3, T >::operator+= ( const Matrix3x3 & other )

inlineconstexpr

Addition assignment.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to add

Returns: Matrix3x3& Reference to this matrix

Example: m += other;

Definition at line 361 of file Matrix3x3.hpp.

◆ operator-() [1/2]

template<typename T >

constexpr auto Phyth::Matrix< 3, 3, T >::operator- ( ) const

inlineconstexpr

Unary negation.

Returns: Matrix3x3 Negated matrix

Example: auto neg = -m;

Definition at line 291 of file Matrix3x3.hpp.

◆ operator-() [2/2]

template<typename T >

template<typename U >

constexpr auto Phyth::Matrix< 3, 3, T >::operator- ( const Matrix3x3 & other ) const

inlineconstexpr

Matrix subtraction.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to subtract

Returns: Matrix3x3<decltype(x_basis - other.x_basis)> Difference of the two matrices

Example: auto diff = m1 - m2;

Definition at line 275 of file Matrix3x3.hpp.

◆ operator-=()

template<typename T >

template<typename U >

constexpr Matrix & Phyth::Matrix< 3, 3, T >::operator-= ( const Matrix3x3 & other )

inlineconstexpr

Subtraction assignment.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to subtract

Returns: Matrix3x3& Reference to this matrix

Example: m -= other;

Definition at line 379 of file Matrix3x3.hpp.

◆ operator==()

template<typename T >

template<typename U >

constexpr bool Phyth::Matrix< 3, 3, T >::operator== ( const Matrix3x3 & other ) const

inlineconstexpr

Equality comparison.

Template Parameters

U	Quantity type of the other matrix

Parameters

other Matrix to compare against

Returns: true if all corresponding components are equal

Example: if (m1 == m2) { ... }

Definition at line 415 of file Matrix3x3.hpp.

◆ Symmetric()

template<typename T >

constexpr auto Phyth::Matrix< 3, 3, T >::Symmetric ( ) const

inlineconstexpr

Compute the symmetric part of the matrix.

Returns (M + M^T) / 2

Returns: Matrix3x3 Symmetric part

Example: auto sym = m.Symmetric(); // (m + m^T) / 2

Definition at line 143 of file Matrix3x3.hpp.

◆ Trace()

template<typename T >

constexpr T Phyth::Matrix< 3, 3, T >::Trace ( ) const

inlineconstexpr

Compute the trace of the matrix.

The trace is the sum of the diagonal elements: M[0][0] + M[1][1] + M[2][2]

Returns: T Sum of diagonal elements

Example: auto tr = m.Trace(); // m00 + m11 + m22

Definition at line 129 of file Matrix3x3.hpp.

◆ Transpose()

template<typename T >

constexpr Matrix Phyth::Matrix< 3, 3, T >::Transpose ( ) const

inlineconstexpr

Compute the transpose of the matrix.

Returns: Matrix3x3 Transposed matrix

Example: auto m = Matrix3x3(...); auto mT = m.Transpose();

Definition at line 111 of file Matrix3x3.hpp.

Friends And Related Symbol Documentation

◆ operator<<

template<typename T >

std::ostream & operator<<	(	std::ostream &	os,
		const Matrix< 3, 3, T > &	m
	)

friend

Stream insertion operator.

Parameters

os	Output stream
m	Matrix to output

Returns: std::ostream& Reference to the output stream

Example: std::cout << m << std::endl;

Definition at line 462 of file Matrix3x3.hpp.

Member Data Documentation

◆ x_basis

template<typename T >

Vector3<T> Phyth::Matrix< 3, 3, T >::x_basis

Definition at line 30 of file Matrix3x3.hpp.

◆ y_basis

template<typename T >

Vector3<T> Phyth::Matrix< 3, 3, T >::y_basis

Definition at line 31 of file Matrix3x3.hpp.

◆ z_basis

template<typename T >

Vector3<T> Phyth::Matrix< 3, 3, T >::z_basis

Definition at line 32 of file Matrix3x3.hpp.

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

include/Phyth/Tools/Matrix3x3.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/3]

◆ Matrix() [2/3]

◆ Matrix() [3/3]

Member Function Documentation

◆ Antisymmetric()

◆ As()

◆ At() [1/2]

◆ At() [2/2]

◆ Identity()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator==()

◆ Symmetric()

◆ Trace()

◆ Transpose()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ x_basis

◆ y_basis

◆ z_basis