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 (const Mdouble xx, const Mdouble xy, const Mdouble xz, const Mdouble yy, const Mdouble yz, const 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+ (const Mdouble a) const
	Scalar addition. More...

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

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

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

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

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

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

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.

Definition at line 36 of file MatrixSymmetric.h.

Constructor & Destructor Documentation

MatrixSymmetric3D::MatrixSymmetric3D ( )

Default constructor.

Default constructor

Definition at line 42 of file MatrixSymmetric.cc.

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

43 {

44 }

MatrixSymmetric3D::MatrixSymmetric3D	(	const Mdouble	xx,
		const Mdouble	xy,
		const Mdouble	xz,
		const Mdouble	yy,
		const Mdouble	yz,
		const 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

Definition at line 55 of file MatrixSymmetric.cc.

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

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

Member Function Documentation

MatrixSymmetric3D::operator Matrix3D ( ) const

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.

Definition at line 34 of file MatrixSymmetric.cc.

References XY, XZ, and YZ.

 {
     return Matrix3D(XX, XY, XZ, XY, YY, YZ, XZ, YZ, ZZ);
 }

MatrixSymmetric3D MatrixSymmetric3D::operator* ( const Mdouble a ) const

Scalar multiplication.

Scalar multiplication

Parameters

[in] a the scalar

Returns: The multiplication result

Definition at line 142 of file MatrixSymmetric.cc.

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

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

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

Definition at line 88 of file MatrixSymmetric.cc.

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

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

MatrixSymmetric3D MatrixSymmetric3D::operator+ ( const Mdouble a ) const

Scalar addition.

Addition of a scalar

Parameters

[in] a scalar to be added

Returns: Result of the addition

Definition at line 108 of file MatrixSymmetric.cc.

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

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

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

Definition at line 187 of file MatrixSymmetric.cc.

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

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

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

Matrix substraction.

Substraction of symmetric 3D matrices

Parameters

[in] A symmetric matrix to be substracted

Returns: Result of the substraction

Definition at line 98 of file MatrixSymmetric.cc.

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

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

MatrixSymmetric3D MatrixSymmetric3D::operator- ( const Mdouble a ) const

Scalar substraction.

Substraction of a scalar

Parameters

[in] a scalar to be substracted

Returns: Result of the substraction

Definition at line 118 of file MatrixSymmetric.cc.

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

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

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

Matrix substraction.

Matrix substraction

Parameters

[in] A the matrix to be substracted

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

Definition at line 203 of file MatrixSymmetric.cc.

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

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

MatrixSymmetric3D MatrixSymmetric3D::operator/ ( const Mdouble a ) const

Scalar division.

Scalar division

Parameters

[in] a the scalar to be divided by

Returns: The division result

Definition at line 153 of file MatrixSymmetric.cc.

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

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

MatrixSymmetric3D & MatrixSymmetric3D::operator/= ( const 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

Definition at line 219 of file MatrixSymmetric.cc.

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

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

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.

Definition at line 259 of file MatrixSymmetric.cc.

References MatrixSymmetric3D(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

 {
     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);
 }

void MatrixSymmetric3D::setZero ( )

Sets all elements to zero.

Sets all elements of the symmetric matrix to 0.

Definition at line 68 of file MatrixSymmetric.cc.

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

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

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

Definition at line 247 of file MatrixSymmetric.cc.

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

 {
     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));
 }

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

Definition at line 236 of file MatrixSymmetric.cc.

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

 {
     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));
 }

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

Definition at line 273 of file MatrixSymmetric.cc.

References MatrixSymmetric3D(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

 {
     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);
 }

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.

Definition at line 78 of file MatrixSymmetric.cc.

References XX, YY, and ZZ.

 {
     return (XX + YY + ZZ) / 3;
 }

Friends And Related Function Documentation

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

Definition at line 130 of file MatrixSymmetric.cc.

 {
     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);
 }

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

Definition at line 164 of file MatrixSymmetric.cc.

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

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

Definition at line 176 of file MatrixSymmetric.cc.

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

Member Data Documentation

Mdouble MatrixSymmetric3D::XX

The six distinctive matrix elements.

Definition at line 42 of file MatrixSymmetric.h.

Referenced by MatrixSymmetric3D(), operator*(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), square(), and trace().

Mdouble MatrixSymmetric3D::XY

Definition at line 42 of file MatrixSymmetric.h.

Referenced by MatrixSymmetric3D(), operator*(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble MatrixSymmetric3D::XZ

Definition at line 42 of file MatrixSymmetric.h.

Referenced by MatrixSymmetric3D(), operator*(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble MatrixSymmetric3D::YY

Definition at line 42 of file MatrixSymmetric.h.

Referenced by MatrixSymmetric3D(), operator*(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), square(), and trace().

Mdouble MatrixSymmetric3D::YZ

Definition at line 42 of file MatrixSymmetric.h.

Referenced by MatrixSymmetric3D(), operator*(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble MatrixSymmetric3D::ZZ

Definition at line 42 of file MatrixSymmetric.h.

Referenced by MatrixSymmetric3D(), operator*(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), square(), and trace().

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

Math/MatrixSymmetric.h
Math/MatrixSymmetric.cc

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation