MR::SymMatrix3< T > Struct Template Reference

#include <MRSymMatrix3.h>

Public Types
using	ValueType = T

Public Member Functions
constexpr	SymMatrix3 () noexcept=default
template<typename U >
constexpr	SymMatrix3 (const SymMatrix3< U > &m)
constexpr T	trace () const noexcept
	computes trace of the matrix
constexpr T	normSq () const noexcept
	computes the squared norm of the matrix, which is equal to the sum of 9 squared elements
constexpr T	det () const noexcept
	computes determinant of the matrix
constexpr SymMatrix3< T >	inverse () const noexcept
	computes inverse matrix
constexpr SymMatrix3< T >	inverse (T det) const noexcept
	computes inverse matrix given determinant of this
SymMatrix3 &	operator+= (const SymMatrix3< T > &b)
SymMatrix3 &	operator-= (const SymMatrix3< T > &b)
SymMatrix3 &	operator*= (T b)
SymMatrix3 &	operator/= (T b)
Vector3< T >	eigens (Matrix3< T > *eigenvectors=nullptr) const
Vector3< T >	eigenvector (T eigenvalue) const
	computes not-unit eigenvector corresponding to a not-repeating eigenvalue
SymMatrix3< T >	pseudoinverse (T tol=std::numeric_limits< T >::epsilon(), int *rank=nullptr, Vector3< T > *space=nullptr) const

Static Public Member Functions
static constexpr SymMatrix3	identity () noexcept
static constexpr SymMatrix3	diagonal (T diagVal) noexcept

Public Attributes
T	xx = 0
	zero matrix by default
T	xy = 0
T	xz = 0
T	yy = 0
T	yz = 0
T	zz = 0

Related Symbols
(Note that these are not member symbols.)
template<typename T >
Vector3< T >	operator* (const SymMatrix3< T > &a, const Vector3< T > &b)
	x = a * b
template<typename T >
SymMatrix3< T >	outerSquare (const Vector3< T > &a)
	x = a * a^T
template<typename T >
SymMatrix3< T >	outerSquare (T k, const Vector3< T > &a)
	x = k * a * a^T
template<typename T >
SymMatrix3< T >	crossSquare (const Vector3< T > &a)

Detailed Description

template<typename T>
struct MR::SymMatrix3< T >

symmetric 3x3 matrix

Member Typedef Documentation

ValueType

template<typename T >

using MR::SymMatrix3< T >::ValueType = T

Constructor & Destructor Documentation

SymMatrix3() [1/2]

template<typename T >

MR::SymMatrix3< T >::SymMatrix3 ( )

constexprdefaultnoexcept

SymMatrix3() [2/2]

template<typename T >

template<typename U >

MR::SymMatrix3< T >::SymMatrix3 ( const SymMatrix3< U > & m )

inlineexplicitconstexpr

Member Function Documentation

det()

template<typename T >

T MR::SymMatrix3< T >::det ( ) const

constexprnoexcept

computes determinant of the matrix

diagonal()

template<typename T >

static constexpr SymMatrix3 MR::SymMatrix3< T >::diagonal ( T diagVal )

inlinestaticconstexprnoexcept

eigens()

template<typename T >

Vector3< T > MR::SymMatrix3< T >::eigens

(

Matrix3< T > *

eigenvectors = nullptr

)

const

returns eigenvalues of the matrix in ascending order (diagonal matrix L), and optionally returns corresponding unit eigenvectors in the rows of orthogonal matrix V, M*V^T = V^T*L; M = V^T*L*V

eigenvector()

template<typename T >

Vector3< T > MR::SymMatrix3< T >::eigenvector

(

T

eigenvalue

)

const

computes not-unit eigenvector corresponding to a not-repeating eigenvalue

identity()

template<typename T >

static constexpr SymMatrix3 MR::SymMatrix3< T >::identity ( )

inlinestaticconstexprnoexcept

inverse() [1/2]

template<typename T >

SymMatrix3< T > MR::SymMatrix3< T >::inverse ( ) const

inlineconstexprnoexcept

computes inverse matrix

inverse() [2/2]

template<typename T >

SymMatrix3< T > MR::SymMatrix3< T >::inverse ( T det ) const

constexprnoexcept

computes inverse matrix given determinant of this

normSq()

template<typename T >

T MR::SymMatrix3< T >::normSq ( ) const

constexprnoexcept

computes the squared norm of the matrix, which is equal to the sum of 9 squared elements

operator*=()

template<typename T >

SymMatrix3 & MR::SymMatrix3< T >::operator*= ( T b )

inline

operator+=()

template<typename T >

SymMatrix3 & MR::SymMatrix3< T >::operator+= ( const SymMatrix3< T > & b )

inline

operator-=()

template<typename T >

SymMatrix3 & MR::SymMatrix3< T >::operator-= ( const SymMatrix3< T > & b )

inline

operator/=()

template<typename T >

SymMatrix3 & MR::SymMatrix3< T >::operator/= ( T b )

inline

pseudoinverse()

template<typename T >

SymMatrix3< T > MR::SymMatrix3< T >::pseudoinverse	(	T	tol = std::numeric_limits< T >::epsilon(),
		int *	rank = nullptr,
		Vector3< T > *	space = nullptr ) const

for not-degenerate matrix returns just inverse matrix, otherwise returns degenerate matrix, which performs inversion on not-kernel subspace;

Parameters

tol	relative epsilon-tolerance for too small number detection
rank	optional output for this matrix rank according to given tolerance
space	rank=1: unit direction of solution line, rank=2: unit normal to solution plane, rank=3: zero vector

trace()

template<typename T >

T MR::SymMatrix3< T >::trace ( ) const

inlineconstexprnoexcept

computes trace of the matrix

Friends And Related Symbol Documentation

crossSquare()

template<typename T >

SymMatrix3< T > crossSquare ( const Vector3< T > & a )

related

computes a matrix that gives double application of a cross product with given vector M x = [ a, [a, x] ] https://en.wikipedia.org/wiki/Cross_product#Alternative_ways_to_compute

operator*()

template<typename T >

Vector3< T > operator* ( const SymMatrix3< T > & a, const Vector3< T > & b )

related

x = a * b

outerSquare() [1/2]

template<typename T >

SymMatrix3< T > outerSquare ( const Vector3< T > & a )

related

x = a * a^T

outerSquare() [2/2]

template<typename T >

SymMatrix3< T > outerSquare ( T k, const Vector3< T > & a )

related

x = k * a * a^T

Member Data Documentation

xx

template<typename T >

T MR::SymMatrix3< T >::xx = 0

zero matrix by default

xy

template<typename T >

T MR::SymMatrix3< T >::xy = 0

xz

template<typename T >

T MR::SymMatrix3< T >::xz = 0

yy

template<typename T >

T MR::SymMatrix3< T >::yy = 0

yz

template<typename T >

T MR::SymMatrix3< T >::yz = 0

zz

template<typename T >

T MR::SymMatrix3< T >::zz = 0

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

• MRSymMatrix3.h