A 3x3 matrix. More...

Public Member Functions
	Matrix3 (const Any &any)
	Must be in one of the following forms: More...

	Matrix3 (DoNotInitialize dni)

	Matrix3 ()
	Initial values are undefined for performance. More...

	Matrix3 (class BinaryInput &b)

	Matrix3 (const float aafEntry[3][3])

	Matrix3 (const Matrix3 &rkMatrix)

	Matrix3 (float fEntry00, float fEntry01, float fEntry02, float fEntry10, float fEntry11, float fEntry12, float fEntry20, float fEntry21, float fEntry22)

	Matrix3 (const class Quat &q)
	Constructs a matrix from a quaternion. More...

Vector3	column (int c) const

void	deserialize (class BinaryInput &b)

float	determinant () const

float	diffOneNorm (const Matrix3 &y) const

void	eigenSolveSymmetric (float afEigenvalue[3], Vector3 akEigenvector[3]) const
	eigensolver, matrix must be symmetric More...

float	frobeniusNorm () const

bool	fuzzyEq (const Matrix3 &b) const

bool	inverse (Matrix3 &rkInverse, float fTolerance=1e-06) const

Matrix3	inverse (float fTolerance=1e-06) const

bool	is3DRotationDilation () const
	Returns true if the rows are orthogonal, have the same length, and the determinant is greater than zero. More...

bool	isOrthonormal () const
	Returns true if the rows and column L2 norms are 1.0 and the rows are orthogonal. More...

bool	isRightHanded () const
	Returns true if column(0).cross(column(1)).dot(column(2)) > 0. More...

float	l1Norm () const

float	lInfNorm () const

	operator const float * () const

	operator float * ()

bool	operator!= (const Matrix3 &rkMatrix) const

Matrix3	operator* (const Matrix3 &rkMatrix) const
	Matrix-matrix multiply. More...

Vector3	operator* (const Vector3 &v) const
	matrix * vector [3x3 * 3x1 = 3x1] More...

Matrix3	operator* (float fScalar) const
	matrix * scalar More...

Matrix3 &	operator*= (const Matrix3 &rkMatrix)
	Matrix-matrix multiply. More...

Matrix3 &	operator*= (float k)

Matrix3	operator+ (const Matrix3 &rkMatrix) const

Matrix3 &	operator+= (const Matrix3 &rkMatrix)

Matrix3	operator- (const Matrix3 &rkMatrix) const

Matrix3	operator- () const

Matrix3 &	operator-= (const Matrix3 &rkMatrix)

Matrix3 &	operator/= (float k)

Matrix3 &	operator= (const Matrix3 &rkMatrix)

bool	operator== (const Matrix3 &rkMatrix) const

float *	operator[] (int iRow)
	Member access, allows use of construct mat[r][c] More...

const float *	operator[] (int iRow) const

void	orthonormalize ()
	Gram-Schmidt orthonormalization (applied to columns of rotation matrix) More...

void	polarDecomposition (Matrix3 &R, Matrix3 &S) const
	Polar decomposition of a matrix. More...

void	qDUDecomposition (Matrix3 &rkQ, Vector3 &rkD, Vector3 &rkU) const
	orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12) More...

const Vector3 &	row (int r) const

void	serialize (class BinaryOutput &b) const

void	set (float fEntry00, float fEntry01, float fEntry02, float fEntry10, float fEntry11, float fEntry12, float fEntry20, float fEntry21, float fEntry22)
	Sets all elements. More...

void	setColumn (int iCol, const Vector3 &vector)

void	setRow (int iRow, const Vector3 &vector)

void	singularValueComposition (const Matrix3 &rkL, const Vector3 &rkS, const Matrix3 &rkR)
	singular value decomposition More...

void	singularValueDecomposition (Matrix3 &rkL, Vector3 &rkS, Matrix3 &rkR) const
	singular value decomposition More...

float	spectralNorm () const
	Matrix norms. More...

float	squaredFrobeniusNorm () const

Any	toAny () const

void	toAxisAngle (Vector3 &rkAxis, float &rfRadians) const
	matrix must be orthonormal More...

bool	toEulerAnglesXYZ (float &rfYAngle, float &rfPAngle, float &rfRAngle) const
	The matrix must be orthonormal. More...

bool	toEulerAnglesXZY (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool	toEulerAnglesYXZ (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool	toEulerAnglesYZX (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool	toEulerAnglesZXY (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool	toEulerAnglesZYX (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

String	toString () const

Matrix3	transpose () const

Static Public Member Functions
static Matrix3	diagonal (float e00, float e11, float e22)

static Matrix3	fromAxisAngle (const Vector3 &rkAxis, float fRadians)

static Matrix3	fromColumns (const Vector3 &c0, const Vector3 &c1, const Vector3 &c2)

static Matrix3	fromDiagonal (const Vector3 &d)

static Matrix3	fromEulerAnglesXYZ (float fYAngle, float fPAngle, float fRAngle)

static Matrix3	fromEulerAnglesXZY (float fYAngle, float fPAngle, float fRAngle)

static Matrix3	fromEulerAnglesYXZ (float fYAngle, float fPAngle, float fRAngle)

static Matrix3	fromEulerAnglesYZX (float fYAngle, float fPAngle, float fRAngle)

static Matrix3	fromEulerAnglesZXY (float fYAngle, float fPAngle, float fRAngle)

static Matrix3	fromEulerAnglesZYX (float fYAngle, float fPAngle, float fRAngle)

static Matrix3	fromRows (const Vector3 &r0, const Vector3 &r1, const Vector3 &r2)

static Matrix3	fromUnitAxisAngle (const Vector3 &rkAxis, float fRadians)
	Assumes that rkAxis has unit length. More...

static const Matrix3 &	identity ()

static void	mul (const Matrix3 &A, const Matrix3 &B, Matrix3 &out)
	Optimized implementation of out = A * B. More...

static void	tensorProduct (const Vector3 &rkU, const Vector3 &rkV, Matrix3 &rkProduct)

static void	transpose (const Matrix3 &A, Matrix3 &out)
	Optimized implementation of out = A.transpose(). More...

static const Matrix3 &	zero ()

Static Public Attributes
static const float	EPSILON

Protected Member Functions
bool	qLAlgorithm (float afDiag[3], float afSubDiag[3])

void	tridiagonal (float afDiag[3], float afSubDiag[3])

Static Protected Member Functions
static void	bidiagonalize (Matrix3 &kA, Matrix3 &kL, Matrix3 &kR)

static void	golubKahanStep (Matrix3 &kA, Matrix3 &kL, Matrix3 &kR)

static float	maxCubicRoot (float afCoeff[3])

Static Protected Attributes
static const float	ms_fSvdEpsilon

static const int	ms_iSvdMaxIterations

Friends
Vector3	operator* (const Vector3 &rkVector, const Matrix3 &rkMatrix)
	vector * matrix [1x3 * 3x3 = 1x3] More...

Matrix3	operator* (double fScalar, const Matrix3 &rkMatrix)
	scalar * matrix More...

Matrix3	operator* (float fScalar, const Matrix3 &rkMatrix)

Matrix3	operator* (int fScalar, const Matrix3 &rkMatrix)

Detailed Description

A 3x3 matrix.

Do not subclass. Data is unitializd when default constructed.

Constructor & Destructor Documentation

◆ Matrix3() [1/8]

G3D::Matrix3::Matrix3 ( const Any & any )

Must be in one of the following forms:

◆ Matrix3() [2/8]

G3D::Matrix3::Matrix3 ( DoNotInitialize dni )

inline

◆ Matrix3() [3/8]

G3D::Matrix3::Matrix3 ( )

inline

Initial values are undefined for performance.

See also: Matrix3::zero, Matrix3::identity, Matrix3::fromAxisAngle, etc.

Referenced by diagonal(), and fromDiagonal().

◆ Matrix3() [4/8]

G3D::Matrix3::Matrix3 ( class BinaryInput & b )

◆ Matrix3() [5/8]

G3D::Matrix3::Matrix3 ( const float aafEntry[3][3] )

◆ Matrix3() [6/8]

G3D::Matrix3::Matrix3 ( const Matrix3 & rkMatrix )

◆ Matrix3() [7/8]

G3D::Matrix3::Matrix3	(	float	fEntry00,
		float	fEntry01,
		float	fEntry02,
		float	fEntry10,
		float	fEntry11,
		float	fEntry12,
		float	fEntry20,
		float	fEntry21,
		float	fEntry22
	)

◆ Matrix3() [8/8]

G3D::Matrix3::Matrix3 ( const class Quat & q )

Constructs a matrix from a quaternion.

Referenced Code: Graphics Gems II, p. 351–354

Referenced Code: Implementation from Watt and Watt, pg 362

Member Function Documentation

◆ bidiagonalize()

static void G3D::Matrix3::bidiagonalize	(	Matrix3 &	kA,
		Matrix3 &	kL,
		Matrix3 &	kR
	)

staticprotected

◆ column()

Vector3 G3D::Matrix3::column ( int c ) const

Referenced by G3D::CoordinateFrame::getHeading(), G3D::CoordinateFrame::leftVector(), G3D::CoordinateFrame::lookVector(), G3D::CoordinateFrame::rightVector(), and G3D::CoordinateFrame::upVector().

◆ deserialize()

void G3D::Matrix3::deserialize ( class BinaryInput & b )

◆ determinant()

float G3D::Matrix3::determinant ( ) const

Referenced by G3D::determinant(), and G3D::CoordinateFrame::pointToObjectSpace().

◆ diagonal()

static Matrix3 G3D::Matrix3::diagonal	(	float	e00,
		float	e11,
		float	e22
	)

inlinestatic

◆ diffOneNorm()

float G3D::Matrix3::diffOneNorm ( const Matrix3 & y ) const

◆ eigenSolveSymmetric()

void G3D::Matrix3::eigenSolveSymmetric	(	float	afEigenvalue[3],
		Vector3	akEigenvector[3]
	)		const

eigensolver, matrix must be symmetric

◆ frobeniusNorm()

float G3D::Matrix3::frobeniusNorm ( ) const

◆ fromAxisAngle()

static Matrix3 G3D::Matrix3::fromAxisAngle	(	const Vector3 &	rkAxis,
		float	fRadians
	)

static

See also: fromUnitAxisAngle

Referenced by G3D::Matrix4::pitchDegrees(), G3D::Matrix4::rollDegrees(), and G3D::Matrix4::yawDegrees().

◆ fromColumns()

static Matrix3 G3D::Matrix3::fromColumns	(	const Vector3 &	c0,
		const Vector3 &	c1,
		const Vector3 &	c2
	)

inlinestatic

◆ fromDiagonal()

static Matrix3 G3D::Matrix3::fromDiagonal ( const Vector3 & d )

inlinestatic

◆ fromEulerAnglesXYZ()

static Matrix3 G3D::Matrix3::fromEulerAnglesXYZ	(	float	fYAngle,
		float	fPAngle,
		float	fRAngle
	)

static

◆ fromEulerAnglesXZY()

static Matrix3 G3D::Matrix3::fromEulerAnglesXZY	(	float	fYAngle,
		float	fPAngle,
		float	fRAngle
	)

static

◆ fromEulerAnglesYXZ()

static Matrix3 G3D::Matrix3::fromEulerAnglesYXZ	(	float	fYAngle,
		float	fPAngle,
		float	fRAngle
	)

static

◆ fromEulerAnglesYZX()

static Matrix3 G3D::Matrix3::fromEulerAnglesYZX	(	float	fYAngle,
		float	fPAngle,
		float	fRAngle
	)

static

◆ fromEulerAnglesZXY()

static Matrix3 G3D::Matrix3::fromEulerAnglesZXY	(	float	fYAngle,
		float	fPAngle,
		float	fRAngle
	)

static

◆ fromEulerAnglesZYX()

static Matrix3 G3D::Matrix3::fromEulerAnglesZYX	(	float	fYAngle,
		float	fPAngle,
		float	fRAngle
	)

static

◆ fromRows()

static Matrix3 G3D::Matrix3::fromRows	(	const Vector3 &	r0,
		const Vector3 &	r1,
		const Vector3 &	r2
	)

inlinestatic

◆ fromUnitAxisAngle()

static Matrix3 G3D::Matrix3::fromUnitAxisAngle	(	const Vector3 &	rkAxis,
		float	fRadians
	)

static

Assumes that rkAxis has unit length.

◆ fuzzyEq()

bool G3D::Matrix3::fuzzyEq ( const Matrix3 & b ) const

◆ golubKahanStep()

static void G3D::Matrix3::golubKahanStep	(	Matrix3 &	kA,
		Matrix3 &	kL,
		Matrix3 &	kR
	)

staticprotected

◆ identity()

static const Matrix3& G3D::Matrix3::identity ( )

static

Referenced by G3D::Matrix4::translation().

◆ inverse() [1/2]

bool G3D::Matrix3::inverse	(	Matrix3 &	rkInverse,
		float	fTolerance = `1e-06`
	)		const

◆ inverse() [2/2]

Matrix3 G3D::Matrix3::inverse ( float fTolerance = 1e-06 ) const

◆ is3DRotationDilation()

bool G3D::Matrix3::is3DRotationDilation ( ) const

Returns true if the rows are orthogonal, have the same length, and the determinant is greater than zero.

◆ isOrthonormal()

bool G3D::Matrix3::isOrthonormal ( ) const

Returns true if the rows and column L2 norms are 1.0 and the rows are orthogonal.

◆ isRightHanded()

bool G3D::Matrix3::isRightHanded ( ) const

Returns true if column(0).cross(column(1)).dot(column(2)) > 0.

◆ l1Norm()

float G3D::Matrix3::l1Norm ( ) const

◆ lInfNorm()

float G3D::Matrix3::lInfNorm ( ) const

◆ maxCubicRoot()

static float G3D::Matrix3::maxCubicRoot ( float afCoeff[3] )

staticprotected

◆ mul()

static void G3D::Matrix3::mul	(	const Matrix3 &	A,
		const Matrix3 &	B,
		Matrix3 &	out
	)

inlinestatic

Optimized implementation of out = A * B.

It is safe (but slow) to call with A, B, and out possibly pointer equal to one another.

◆ operator const float *()

G3D::Matrix3::operator const float * ( ) const

inline

◆ operator float *()

G3D::Matrix3::operator float * ( )

inline

◆ operator!=()

bool G3D::Matrix3::operator!= ( const Matrix3 & rkMatrix ) const

◆ operator*() [1/3]

Matrix3 G3D::Matrix3::operator* ( const Matrix3 & rkMatrix ) const

Matrix-matrix multiply.

◆ operator*() [2/3]

Vector3 G3D::Matrix3::operator* ( const Vector3 & v ) const

inline

matrix * vector [3x3 * 3x1 = 3x1]

◆ operator*() [3/3]

Matrix3 G3D::Matrix3::operator* ( float fScalar ) const

matrix * scalar

◆ operator*=() [1/2]

Matrix3& G3D::Matrix3::operator*= ( const Matrix3 & rkMatrix )

Matrix-matrix multiply.

◆ operator*=() [2/2]

Matrix3& G3D::Matrix3::operator*= ( float k )

◆ operator+()

Matrix3 G3D::Matrix3::operator+ ( const Matrix3 & rkMatrix ) const

◆ operator+=()

Matrix3& G3D::Matrix3::operator+= ( const Matrix3 & rkMatrix )

◆ operator-() [1/2]

Matrix3 G3D::Matrix3::operator- ( const Matrix3 & rkMatrix ) const

◆ operator-() [2/2]

Matrix3 G3D::Matrix3::operator- ( ) const

◆ operator-=()

Matrix3& G3D::Matrix3::operator-= ( const Matrix3 & rkMatrix )

◆ operator/=()

Matrix3& G3D::Matrix3::operator/= ( float k )

◆ operator=()

Matrix3& G3D::Matrix3::operator= ( const Matrix3 & rkMatrix )

inline

◆ operator==()

bool G3D::Matrix3::operator== ( const Matrix3 & rkMatrix ) const

◆ operator[]() [1/2]

float* G3D::Matrix3::operator[] ( int iRow )

inline

Member access, allows use of construct mat[r][c]

◆ operator[]() [2/2]

const float* G3D::Matrix3::operator[] ( int iRow ) const

inline

◆ orthonormalize()

void G3D::Matrix3::orthonormalize ( )

Gram-Schmidt orthonormalization (applied to columns of rotation matrix)

◆ polarDecomposition()

void G3D::Matrix3::polarDecomposition	(	Matrix3 &	R,
		Matrix3 &	S
	)		const

Polar decomposition of a matrix.

Based on pseudocode from Nicholas J Higham, "Computing the Polar Decomposition – with Applications Siam Journal of Science and Statistical Computing, Vol 7, No. 4, October 1986.

Decomposes A into R*S, where R is orthogonal and S is symmetric.

Ken Shoemake's "Matrix animation and polar decomposition" in Proceedings of the conference on Graphics interface '92 seems to be better known in the world of graphics, but Higham's version uses a scaling constant that can lead to faster convergence than Shoemake's when the initial matrix is far from orthogonal.

◆ qDUDecomposition()

void G3D::Matrix3::qDUDecomposition	(	Matrix3 &	rkQ,
		Vector3 &	rkD,
		Vector3 &	rkU
	)		const

orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12)

◆ qLAlgorithm()

bool G3D::Matrix3::qLAlgorithm	(	float	afDiag[3],
		float	afSubDiag[3]
	)

protected

◆ row()

const Vector3& G3D::Matrix3::row ( int r ) const

◆ serialize()

void G3D::Matrix3::serialize ( class BinaryOutput & b ) const

◆ set()

void G3D::Matrix3::set	(	float	fEntry00,
		float	fEntry01,
		float	fEntry02,
		float	fEntry10,
		float	fEntry11,
		float	fEntry12,
		float	fEntry20,
		float	fEntry21,
		float	fEntry22
	)

Sets all elements.

◆ setColumn()

void G3D::Matrix3::setColumn	(	int	iCol,
		const Vector3 &	vector
	)

◆ setRow()

void G3D::Matrix3::setRow	(	int	iRow,
		const Vector3 &	vector
	)

◆ singularValueComposition()

void G3D::Matrix3::singularValueComposition	(	const Matrix3 &	rkL,
		const Vector3 &	rkS,
		const Matrix3 &	rkR
	)

singular value decomposition

◆ singularValueDecomposition()

void G3D::Matrix3::singularValueDecomposition	(	Matrix3 &	rkL,
		Vector3 &	rkS,
		Matrix3 &	rkR
	)		const

singular value decomposition

◆ spectralNorm()

float G3D::Matrix3::spectralNorm ( ) const

Matrix norms.

◆ squaredFrobeniusNorm()

float G3D::Matrix3::squaredFrobeniusNorm ( ) const

◆ tensorProduct()

static void G3D::Matrix3::tensorProduct	(	const Vector3 &	rkU,
		const Vector3 &	rkV,
		Matrix3 &	rkProduct
	)

static

◆ toAny()

Any G3D::Matrix3::toAny ( ) const

◆ toAxisAngle()

void G3D::Matrix3::toAxisAngle	(	Vector3 &	rkAxis,
		float &	rfRadians
	)		const

matrix must be orthonormal

◆ toEulerAnglesXYZ()

bool G3D::Matrix3::toEulerAnglesXYZ	(	float &	rfYAngle,
		float &	rfPAngle,
		float &	rfRAngle
	)		const

The matrix must be orthonormal.

The decomposition is yaw*pitch*roll where yaw is rotation about the Up vector, pitch is rotation about the right axis, and roll is rotation about the Direction axis.

◆ toEulerAnglesXZY()

bool G3D::Matrix3::toEulerAnglesXZY	(	float &	rfYAngle,
		float &	rfPAngle,
		float &	rfRAngle
	)		const

◆ toEulerAnglesYXZ()

bool G3D::Matrix3::toEulerAnglesYXZ	(	float &	rfYAngle,
		float &	rfPAngle,
		float &	rfRAngle
	)		const

◆ toEulerAnglesYZX()

bool G3D::Matrix3::toEulerAnglesYZX	(	float &	rfYAngle,
		float &	rfPAngle,
		float &	rfRAngle
	)		const

◆ toEulerAnglesZXY()

bool G3D::Matrix3::toEulerAnglesZXY	(	float &	rfYAngle,
		float &	rfPAngle,
		float &	rfRAngle
	)		const

◆ toEulerAnglesZYX()

bool G3D::Matrix3::toEulerAnglesZYX	(	float &	rfYAngle,
		float &	rfPAngle,
		float &	rfRAngle
	)		const

◆ toString()

String G3D::Matrix3::toString ( ) const

◆ transpose() [1/2]

static void G3D::Matrix3::transpose	(	const Matrix3 &	A,
		Matrix3 &	out
	)

inlinestatic

Optimized implementation of out = A.transpose().

It is safe (but slow) to call with A and out possibly pointer equal to one another.

Note that A.transpose() * v can be computed more efficiently as v * A.

Referenced by G3D::CoordinateFrame::inverse(), and transpose().

◆ transpose() [2/2]

Matrix3 G3D::Matrix3::transpose ( ) const

◆ tridiagonal()

void G3D::Matrix3::tridiagonal	(	float	afDiag[3],
		float	afSubDiag[3]
	)

protected

◆ zero()

static const Matrix3& G3D::Matrix3::zero ( )

static

Friends And Related Function Documentation

◆ operator* [1/4]

Vector3 operator*	(	const Vector3 &	rkVector,
		const Matrix3 &	rkMatrix
	)

friend

vector * matrix [1x3 * 3x3 = 1x3]

◆ operator* [2/4]

Matrix3 operator*	(	double	fScalar,
		const Matrix3 &	rkMatrix
	)

friend

scalar * matrix

◆ operator* [3/4]

Matrix3 operator*	(	float	fScalar,
		const Matrix3 &	rkMatrix
	)

friend

◆ operator* [4/4]

Matrix3 operator*	(	int	fScalar,
		const Matrix3 &	rkMatrix
	)

friend

Member Data Documentation

◆ EPSILON

const float G3D::Matrix3::EPSILON

static

◆ ms_fSvdEpsilon

const float G3D::Matrix3::ms_fSvdEpsilon

staticprotected

◆ ms_iSvdMaxIterations

const int G3D::Matrix3::ms_iSvdMaxIterations

staticprotected

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Static Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix3() [1/8]

◆ Matrix3() [2/8]

◆ Matrix3() [3/8]

◆ Matrix3() [4/8]

◆ Matrix3() [5/8]

◆ Matrix3() [6/8]

◆ Matrix3() [7/8]

◆ Matrix3() [8/8]

Member Function Documentation

◆ bidiagonalize()

◆ column()

◆ deserialize()

◆ determinant()

◆ diagonal()

◆ diffOneNorm()

◆ eigenSolveSymmetric()

◆ frobeniusNorm()

◆ fromAxisAngle()

◆ fromColumns()

◆ fromDiagonal()

◆ fromEulerAnglesXYZ()

◆ fromEulerAnglesXZY()

◆ fromEulerAnglesYXZ()

◆ fromEulerAnglesYZX()

◆ fromEulerAnglesZXY()

◆ fromEulerAnglesZYX()

◆ fromRows()

◆ fromUnitAxisAngle()

◆ fuzzyEq()

◆ golubKahanStep()

◆ identity()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ is3DRotationDilation()

◆ isOrthonormal()

◆ isRightHanded()

◆ l1Norm()

◆ lInfNorm()

◆ maxCubicRoot()

◆ mul()

◆ operator const float *()

◆ operator float *()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ orthonormalize()

◆ polarDecomposition()

◆ qDUDecomposition()

◆ qLAlgorithm()

◆ row()

◆ serialize()

◆ set()

◆ setColumn()

◆ setRow()

◆ singularValueComposition()

◆ singularValueDecomposition()

◆ spectralNorm()

◆ squaredFrobeniusNorm()