Implementation of a 3D symmetric matrix. More...

#include <MatrixSymmetric.h>

Public Member Functions
	operator Matrix3D () const
	Casting operator; casts MatrixSymmetric3D to Matrix3D. More...

	MatrixSymmetric3D ()
	Default constructor. More...

	MatrixSymmetric3D (Mdouble xx, Mdouble xy, Mdouble xz, Mdouble yy, Mdouble yz, Mdouble zz)
	Alternative constructor, with all (6) elements as arguments. More...

void	setZero ()
	Sets all elements to zero. More...

Mdouble	trace () const
	Returns the MEAN of the diagonal elements (i.e. the trace divided by three). More...

MatrixSymmetric3D	operator+ (const MatrixSymmetric3D &A) const
	Matrix addition. More...

MatrixSymmetric3D	operator- (const MatrixSymmetric3D &A) const
	Matrix substraction. More...

MatrixSymmetric3D	operator+ (Mdouble a) const
	Scalar addition. More...

MatrixSymmetric3D	operator- (Mdouble a) const
	Scalar substraction. More...

MatrixSymmetric3D	operator* (Mdouble a) const
	Scalar multiplication. More...

MatrixSymmetric3D	operator/ (Mdouble a) const
	Scalar division. More...

MatrixSymmetric3D &	operator+= (const MatrixSymmetric3D &A)
	Matrix addition. More...

MatrixSymmetric3D &	operator-= (const MatrixSymmetric3D &A)
	Matrix substraction. More...

MatrixSymmetric3D &	operator/= (Mdouble a)
	Scalar division. More...

MatrixSymmetric3D	inverse () const
	Computes the inverse of a matrix; exits if the inverse doesn't exist. More...

MatrixSymmetric3D	getCylindricalTensorField (const Vec3D &p) const
	Returns the matrix in cylindrical coordinates. More...

Static Public Member Functions
static MatrixSymmetric3D	square (const MatrixSymmetric3D &A)
	Calculates the pointwise square. More...

static MatrixSymmetric3D	sqrt (const MatrixSymmetric3D &A)
	Calculates the pointwise square root. More...

static MatrixSymmetric3D	selfDyadic (const Vec3D &a)
	Calculates the dyadic product of a Vec3D with itself: \(a \otimes a\). More...

static MatrixSymmetric3D	symmetrisedDyadic (const Vec3D &a, const Vec3D &b)
	Calculates the symmetrised dyadic product of two Vec3D: \( \frac{1}{2}(a \otimes b + b \otimes a) \). More...

static MatrixSymmetric3D	inverse (const MatrixSymmetric3D &A)
	Computes the inverse of a matrix; exits if the inverse doesn't exist. More...

static Mdouble	determinant (const MatrixSymmetric3D &A)
	Computes the determinant of a matrix. More...

Public Attributes
Mdouble	XX
	The six distinctive matrix elements. More...

Mdouble	XY

Mdouble	XZ

Mdouble	YY

Mdouble	YZ

Mdouble	ZZ

Friends
Vec3D	operator* (const MatrixSymmetric3D &A, const Vec3D &b)
	Vector multiplication. More...

std::ostream &	operator<< (std::ostream &os, const MatrixSymmetric3D &A)
	Add elements to an ostream. More...

std::istream &	operator>> (std::istream &is, MatrixSymmetric3D &A)
	Add elements to an istream. More...

Detailed Description

Implementation of a 3D symmetric matrix.

Constructor & Destructor Documentation

◆ MatrixSymmetric3D() [1/2]

MatrixSymmetric3D::MatrixSymmetric3D ( )

Default constructor.

Default constructor

 {
     setZero();
 }

References setZero().

Referenced by operator*(), operator+(), operator-(), operator/(), selfDyadic(), sqrt(), square(), and symmetrisedDyadic().

◆ MatrixSymmetric3D() [2/2]

MatrixSymmetric3D::MatrixSymmetric3D	(	Mdouble	xx,
		Mdouble	xy,
		Mdouble	xz,
		Mdouble	yy,
		Mdouble	yz,
		Mdouble	zz
	)

Alternative constructor, with all (6) elements as arguments.

Alternative constructor, lets you define all (6) elements

Parameters

[in]	xx	initializer for an element of the matrix
[in]	xy	initializer for an element of the matrix
[in]	xz	initializer for an element of the matrix
[in]	yy	initializer for an element of the matrix
[in]	yz	initializer for an element of the matrix
[in]	zz	initializer for an element of the matrix

 {
     XX = xx;
     XY = xy;
     XZ = xz;
     YY = yy;
     YZ = yz;
     ZZ = zz;
 }

References XX, xy, XY, XZ, YY, YZ, and ZZ.

Member Function Documentation

◆ determinant()

Mdouble MatrixSymmetric3D::determinant ( const MatrixSymmetric3D & A )

static

Computes the determinant of a matrix.

 {
     return 1. / (A.XX * (A.YY * A.ZZ - A.YZ * A.YZ)
                  + A.XY * (A.YZ * A.XZ - A.XY * A.ZZ)
                  + A.XZ * (A.XY * A.YZ - A.YY * A.XZ));
 }

Referenced by inverse().

◆ getCylindricalTensorField()

MatrixSymmetric3D MatrixSymmetric3D::getCylindricalTensorField ( const Vec3D & p ) const

Returns the matrix in cylindrical coordinates.

Todo:: implement MatrixSymmetric3D::getCylindricalTensorField

Transforms the (Cartesian) vector to cylindrical coordinates. See https://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates

Returns: Transformed vector

 {
 //    //define sin(A)=y/r, cos(A)=x/r
 //    Mdouble r = std::sqrt(p.X*p.X+p.Y*p.Y);
 //    Mdouble s = p.Y/r;
 //    Mdouble c = p.X/r;
 //    if (r==0) {
 //        s=0;
 //        c=1;
 //    }
     return *this;
 }

Referenced by CGFields::StandardFields::setCylindricalFields().

◆ inverse() [1/2]

MatrixSymmetric3D MatrixSymmetric3D::inverse ( ) const

Computes the inverse of a matrix; exits if the inverse doesn't exist.

Used for inverting matrices like the inertia tensor.

Parameters

[in] A Matrix that should be inverted.

Returns: Inverse of matrix A.

 {
     MatrixSymmetric3D result;
     Mdouble det = MatrixSymmetric3D::determinant(*this);
     logger.assert_debug(det != 0,
                   "determinant is not zero"); //should be replaced by the condition number or sth. like fabs(det)>1e-5*norm.
     result.XX = (YY * ZZ - YZ * YZ) * det;
     result.XY = -(XY * ZZ - XZ * YZ) * det;
     result.XZ = (XY * YZ - XZ * YY) * det;
     result.YY = (XX * ZZ - XZ * XZ) * det;
     result.YZ = -(XX * YZ - XZ * XY) * det;
     result.ZZ = (XX * YY - XY * XY) * det;
     return result;
 }

References determinant(), logger, XX, XY, XZ, YY, YZ, and ZZ.

Referenced by BaseParticle::setInertia().

◆ inverse() [2/2]

MatrixSymmetric3D MatrixSymmetric3D::inverse ( const MatrixSymmetric3D & A )

static

Computes the inverse of a matrix; exits if the inverse doesn't exist.

Used for inverting matrices like the inertia tensor.

Parameters

[in] A Matrix that should be inverted.

Returns: Inverse of matrix A.

 {
     return A.inverse();
 }

Referenced by ClumpParticle::ClumpParticle(), ClumpParticle::computeMass(), BaseParticle::getAngularMomentum(), BaseParticle::getInertia(), ClumpParticle::rotateTensorOfInertia(), and ClumpParticle::setInitInertia().

◆ operator Matrix3D()

MatrixSymmetric3D::operator Matrix3D ( ) const

explicit

Casting operator; casts MatrixSymmetric3D to Matrix3D.

This operator casts a MatrixSymmetric3D object to a Matrix3D object when needed.

Returns: The output is a symmetric matrix of type Matrix3D.

 {
     return {XX, XY, XZ, XY, YY, YZ, XZ, YZ, ZZ};
 }

References XX, XY, XZ, YY, and YZ.

◆ operator*()

MatrixSymmetric3D MatrixSymmetric3D::operator* ( Mdouble a ) const

Scalar multiplication.

Scalar multiplication

Parameters

[in] a the scalar

Returns: The multiplication result

 {
     return MatrixSymmetric3D(XX * a, XY * a, XZ * a,
                              YY * a, YZ * a, ZZ * a);
 }

References a, MatrixSymmetric3D(), XX, XY, XZ, YY, YZ, and ZZ.

◆ operator+() [1/2]

MatrixSymmetric3D MatrixSymmetric3D::operator+ ( const MatrixSymmetric3D & A ) const

Matrix addition.

Addition of symmetric 3D matrices

Parameters

[in] A symmetric matrix to be added

Returns: Result of the addition

 {
     return MatrixSymmetric3D(XX + A.XX, XY + A.XY, XZ + A.XZ, YY + A.YY, YZ + A.YZ, ZZ + A.ZZ);
 }

References MatrixSymmetric3D(), XX, XY, XZ, YY, YZ, and ZZ.

◆ operator+() [2/2]

MatrixSymmetric3D MatrixSymmetric3D::operator+ ( Mdouble a ) const

Scalar addition.

Addition of a scalar

Parameters

[in] a scalar to be added

Returns: Result of the addition

 {
     return MatrixSymmetric3D(XX + a, XY + a, XZ + a, YY + a, YZ + a, ZZ + a);
 }

References a, MatrixSymmetric3D(), XX, XY, XZ, YY, YZ, and ZZ.

◆ operator+=()

MatrixSymmetric3D & MatrixSymmetric3D::operator+= ( const MatrixSymmetric3D & A )

Matrix addition.

Matrix addition

Parameters

[in] A the matrix to be added to this one

Returns: (reference to) this matrix, i.e. the result of the addition

 {
     XX += A.XX;
     XY += A.XY;
     XZ += A.XZ;
     YY += A.YY;
     YZ += A.YZ;
     ZZ += A.ZZ;
     return *this;
 }

References XX, XY, XZ, YY, YZ, and ZZ.

◆ operator-() [1/2]

MatrixSymmetric3D MatrixSymmetric3D::operator- ( const MatrixSymmetric3D & A ) const

Matrix substraction.

Substraction of symmetric 3D matrices

Parameters

[in] A symmetric matrix to be subtracted

Returns: Result of the substraction

 {
     return MatrixSymmetric3D(XX - A.XX, XY - A.XY, XZ - A.XZ, YY - A.YY, YZ - A.YZ, ZZ - A.ZZ);
 }

References MatrixSymmetric3D(), XX, XY, XZ, YY, YZ, and ZZ.

◆ operator-() [2/2]

MatrixSymmetric3D MatrixSymmetric3D::operator- ( Mdouble a ) const

Scalar substraction.

Substraction of a scalar

Parameters

[in] a scalar to be subtracted

Returns: Result of the substraction

 {
     return MatrixSymmetric3D(XX - a, XY - a, XZ - a, YY - a, YZ - a, ZZ - a);
 }

References a, MatrixSymmetric3D(), XX, XY, XZ, YY, YZ, and ZZ.

◆ operator-=()

MatrixSymmetric3D & MatrixSymmetric3D::operator-= ( const MatrixSymmetric3D & A )

Matrix substraction.

Matrix substraction

Parameters

[in] A the matrix to be subtracted

Returns: (reference to) this matrix, which is the result of the substraction

 {
     XX -= A.XX;
     XY -= A.XY;
     XZ -= A.XZ;
     YY -= A.YY;
     YZ -= A.YZ;
     ZZ -= A.ZZ;
     return *this;
 }

References XX, XY, XZ, YY, YZ, and ZZ.

◆ operator/()

MatrixSymmetric3D MatrixSymmetric3D::operator/ ( Mdouble a ) const

Scalar division.

Scalar division

Parameters

[in] a the scalar to be divided by

Returns: The division result

 {
     return MatrixSymmetric3D(XX / a, XY / a, XZ / a, YY / a, YZ / a, ZZ / a);
 }

References a, MatrixSymmetric3D(), XX, XY, XZ, YY, YZ, and ZZ.

◆ operator/=()

MatrixSymmetric3D & MatrixSymmetric3D::operator/= ( Mdouble a )

Scalar division.

Scalar division

Parameters

[in] a the scalar to be divided by

Returns: (reference to) this matrix, which is the result of the division

 {
     XX /= a;
     XY /= a;
     XZ /= a;
     YY /= a;
     YZ /= a;
     ZZ /= a;
     return *this;
 }

References a, XX, XY, XZ, YY, YZ, and ZZ.

◆ selfDyadic()

MatrixSymmetric3D MatrixSymmetric3D::selfDyadic ( const Vec3D & a )

static

Calculates the dyadic product of a Vec3D with itself: \(a \otimes a\).

Calculates the dyadic product of a 3D vector with itself, which (obviously) results in a symmetric 3D matrix. NB: this is a STATIC function!

Parameters

[in] a the 3D vector

Returns: the resulting symmetric 3D matrix.

 {
     return MatrixSymmetric3D(a.X * a.X, a.X * a.Y, a.X * a.Z, a.Y * a.Y, a.Y * a.Z, a.Z * a.Z);
 }

References a, and MatrixSymmetric3D().

Referenced by CGFields::DisplacementField::setFields(), and CGFields::StandardFields::setFields().

◆ setZero()

void MatrixSymmetric3D::setZero ( )

Sets all elements to zero.

Sets all elements of the symmetric matrix to 0.

 {
     XX = XY = XZ = YY = YZ = ZZ = 0.0;
 }

References XX, XY, XZ, YY, YZ, and ZZ.

Referenced by MatrixSymmetric3D(), BaseParticle::setInfiniteInertia(), CGFields::DisplacementField::setZero(), CGFields::OrientationField::setZero(), and CGFields::StandardFields::setZero().

◆ sqrt()

MatrixSymmetric3D MatrixSymmetric3D::sqrt ( const MatrixSymmetric3D & A )

static

Calculates the pointwise square root.

Pointwise square roots the matrix, i.e. takes the sq. root of each element. NB: this is a STATIC function!

Parameters

[in] A The matrix to be pointwise square rooted

Returns: Resulting matrix

 {
     return MatrixSymmetric3D(std::sqrt(A.XX), std::sqrt(A.XY), std::sqrt(A.XZ), std::sqrt(A.YY), std::sqrt(A.YZ),
                              std::sqrt(A.ZZ));
 }

References MatrixSymmetric3D(), and sqrt().

◆ square()

MatrixSymmetric3D MatrixSymmetric3D::square ( const MatrixSymmetric3D & A )

static

Calculates the pointwise square.

Pointwise squares the matrix, i.e. takes the square of each element. NB: is a STATIC function!

Parameters

[in] A The matrix to be pointwise squared

Returns: Resulting matrix

 {
     return MatrixSymmetric3D(mathsFunc::square(A.XX), mathsFunc::square(A.XY), mathsFunc::square(A.XZ),
                              mathsFunc::square(A.YY), mathsFunc::square(A.YZ), mathsFunc::square(A.ZZ));
 }

References MatrixSymmetric3D(), and mathsFunc::square().

Referenced by CGFields::DisplacementField::getSquared(), CGFields::OrientationField::getSquared(), and CGFields::StandardFields::getSquared().

◆ symmetrisedDyadic()

MatrixSymmetric3D MatrixSymmetric3D::symmetrisedDyadic	(	const Vec3D &	a,
		const Vec3D &	b
	)

static

Calculates the symmetrised dyadic product of two Vec3D: \( \frac{1}{2}(a \otimes b + b \otimes a) \).

Calculates the dyadic product of two 3D vectors, and 'symmetrises' the resulting matrix by taking the average of each pair of opposing non-diagonal elements. NB: this is a STATIC function!

Parameters

[in]	a	the first 3D vector
[in]	b	the second 3D vector

Returns: the resulting symmetric 3D matrix

 {
     return MatrixSymmetric3D(a.X * b.X, 0.5 * (a.X * b.Y + b.X * a.Y), 0.5 * (a.X * b.Z + b.X * a.Z), a.Y * b.Y,
                              0.5 * (a.Y * b.Z + b.Y * a.Z), a.Z * b.Z);
 }

References a, b, and MatrixSymmetric3D().

◆ trace()

Mdouble MatrixSymmetric3D::trace ( ) const

Returns the MEAN of the diagonal elements (i.e. the trace divided by three).

Returns the MEAN of the diagonal matrix elements, which is technically the trace divided by the number of diagonal elements.

Returns: The mean of the diagonal elements.

 {
     return (XX + YY + ZZ) / 3;
 }

References XX, YY, and ZZ.

Friends And Related Function Documentation

◆ operator*

Vec3D operator*	(	const MatrixSymmetric3D &	A,
		const Vec3D &	b
	)

friend

Vector multiplication.

Multiplication of a symmetric 3D matrix with a vector (global operator, friend of this class)

Parameters

[in]	A	the matrix
[in]	b	the vector

Returns: The multiplication result

 {
     return Vec3D(A.XX * b.X + A.XY * b.Y + A.XZ * b.Z,
                  A.XY * b.X + A.YY * b.Y + A.YZ * b.Z,
                  A.XZ * b.X + A.YZ * b.Y + A.ZZ * b.Z);
 }

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const MatrixSymmetric3D &	A
	)

friend

Add elements to an ostream.

Adds all elements of a symmetric 3D matrix to an ostream

Parameters

[in,out]	os	output stream
[in]	A	the matrix

Returns: (reference to) output stream with matrix elements added

 {
     os << A.XX << ' ' << A.XY << ' ' << A.XZ << " " << A.YY << ' ' << A.YZ << " " << A.ZZ;
     return os;
 }

◆ operator>>

std::istream& operator>>	(	std::istream &	is,
		MatrixSymmetric3D &	A
	)

friend

Add elements to an istream.

Reads the elements of a symmetric 3D matrix from an istream

Parameters

[in,out]	is	input stream,
[out]	A	the matrix

Returns: (reference to) input stream from with matrix elements were read

 {
     is >> A.XX >> A.XY >> A.XZ >> A.YY >> A.YZ >> A.ZZ;
     return is;
 }

Member Data Documentation

◆ XX

Mdouble MatrixSymmetric3D::XX

◆ XY

Mdouble MatrixSymmetric3D::XY

Referenced by ChangingTOIParticle::actionsAfterTimeStep(), ClumpParticle::angularAccelerateClumpIterative(), SuperQuadricParticle::computeMass(), inverse(), MatrixSymmetric3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), Quaternion::rotateInverseInertiaTensor(), CGFields::OrientationField::setFields(), ChangingTOIParticle::setupInitialConditions(), and setZero().

◆ XZ

Mdouble MatrixSymmetric3D::XZ

Referenced by ChangingTOIParticle::actionsAfterTimeStep(), ClumpParticle::angularAccelerateClumpIterative(), SuperQuadricParticle::computeMass(), inverse(), MatrixSymmetric3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), Quaternion::rotateInverseInertiaTensor(), CGFields::OrientationField::setFields(), ChangingTOIParticle::setupInitialConditions(), and setZero().

◆ YY

◆ YZ

Mdouble MatrixSymmetric3D::YZ

Referenced by ChangingTOIParticle::actionsAfterTimeStep(), ClumpParticle::angularAccelerateClumpIterative(), SuperQuadricParticle::computeMass(), inverse(), MatrixSymmetric3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), Quaternion::rotateInverseInertiaTensor(), CGFields::OrientationField::setFields(), ChangingTOIParticle::setupInitialConditions(), and setZero().

◆ ZZ

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ MatrixSymmetric3D() [1/2]

◆ MatrixSymmetric3D() [2/2]

Member Function Documentation

◆ determinant()

◆ getCylindricalTensorField()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ operator Matrix3D()

◆ operator*()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ selfDyadic()

◆ setZero()

◆ sqrt()

◆ square()

◆ symmetrisedDyadic()

◆ trace()

Friends And Related Function Documentation

◆ operator*

◆ operator<<

◆ operator>>

Member Data Documentation

◆ XX

◆ XY

◆ XZ

◆ YY

◆ YZ

◆ ZZ