Matrix3D Class Reference

Implementation of a 3D matrix. More...

#include <Matrix.h>

Public Member Functions
	Matrix3D ()
	default constructor More...
	Matrix3D (const Mdouble xx, const Mdouble xy, const Mdouble xz, const Mdouble yx, const Mdouble yy, const Mdouble yz, const Mdouble zx, const Mdouble zy, const Mdouble zz)
	Alternative constructor, which let you define all elements. More...
void	setZero ()
	Sets all elements to zero. More...
double	trace () const
	Mean of the diagonal elements. More...
Matrix3D	operator+ (const Matrix3D &A) const
	Matrix addition. More...
Matrix3D	operator- (const Matrix3D &A) const
	Matrix subtraction. More...
Matrix3D	operator+ (const Mdouble a) const
	Scalar addition. More...
Matrix3D	operator- (const Mdouble a) const
	Scalar subtraction. More...
Matrix3D	operator* (const Mdouble a) const
	Scalar multiplication. More...
Vec3D	operator* (const Vec3D &a) const
	Vector multiplication. More...
Matrix3D	operator* (const Matrix3D &a) const
	Matrix multiplication. More...
Matrix3D	operator/ (const Mdouble a) const
	Scalar division. More...
Matrix3D &	operator+= (const Matrix3D &A)
	Matrix addition. More...
Matrix3D &	operator-= (const Matrix3D &A)
	Matrix substraction. More...
Matrix3D &	operator/= (const Mdouble a)
	Scalar division. More...

Static Public Member Functions
static Matrix3D	square (const Matrix3D &A)
	Calculates the pointwise square. More...
static Matrix3D	sqrt (const Matrix3D &A)
	Calculates the pointwise square root. More...
static Matrix3D	dyadic (const Vec3D &a, const Vec3D &b)
	Calculates the dyadic product of a two Vec3D: \(a \otimes b\). More...
static Matrix3D	cross (const Vec3D &a, const Matrix3D &b)
	'Special' cross product; CP of vector with each column of a matrix More...

Public Attributes
Mdouble	XX
	all nine matrix elements More...
Mdouble	XY
Mdouble	XZ
Mdouble	YX
Mdouble	YY
Mdouble	YZ
Mdouble	ZX
Mdouble	ZY
Mdouble	ZZ

Friends
std::ostream &	operator<< (std::ostream &os, const Matrix3D &A)
	Add elements to ostream. More...
std::istream &	operator>> (std::istream &is, Matrix3D &A)
	Add elements to istream. More...

Detailed Description

Implementation of a 3D matrix.

Definition at line 36 of file Matrix.h.

Constructor & Destructor Documentation

Matrix3D::Matrix3D

(

)

default constructor

default constructor, which is empty (i.e., only creates the object)

Definition at line 32 of file Matrix.cc.

Referenced by cross(), dyadic(), operator*(), operator+(), operator-(), operator/(), sqrt(), and square().

{
}

Matrix3D::Matrix3D	(	const Mdouble	xx,
		const Mdouble	xy,
		const Mdouble	xz,
		const Mdouble	yx,
		const Mdouble	yy,
		const Mdouble	yz,
		const Mdouble	zx,
		const Mdouble	zy,
		const Mdouble	zz
	)

Alternative constructor, which let you define all elements.

Alternative constructor. Let's you specify ALL 9 elements of the 3x3 matrix.

Parameters

[in]

[all]

xx/xy/xz /yx/yy/yz /zx/zy/zz are all nine elements (left-to-right, top-to-bottom) of the 3D matrix.

Definition at line 42 of file Matrix.cc.

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    XX = xx;
    XY = xy;
    XZ = xz;
    YX = yx;
    YY = yy;
    YZ = yz;
    ZX = zx;
    ZY = zy;
    ZZ = zz;
}

Member Function Documentation

Matrix3D Matrix3D::cross ( const Vec3D &  a, const Matrix3D &  B  )

static

'Special' cross product; CP of vector with each column of a matrix

Returns a matrix, who's columns are the inner product of a given vector with the corresponding columns of a given matrix

Parameters

[in]	a	vector
[in]	B	matrix

Returns

Resulting matrix

Definition at line 299 of file Matrix.cc.

References Matrix3D(), Vec3D::X, XX, XY, XZ, Vec3D::Y, YX, YY, YZ, Vec3D::Z, ZX, ZY, and ZZ.

{
    return Matrix3D(
                    a.Y * B.ZX - a.Z * B.YX, a.Y * B.ZY - a.Z * B.YY, a.Y * B.ZZ - a.Z * B.YZ,
                    a.Z * B.XX - a.X * B.ZX, a.Z * B.XY - a.X * B.ZY, a.Z * B.XZ - a.X * B.ZZ,
                    a.X * B.YX - a.Y * B.XX, a.X * B.YY - a.Y * B.XY, a.X * B.YZ - a.Y * B.XZ);
}

Matrix3D Matrix3D::dyadic ( const Vec3D &  a, const Vec3D &  b  )

static

Calculates the dyadic product of a two Vec3D: \(a \otimes b\).

Dyadic product of two vectors

Parameters

[in]	a	first vector
[in]	b	second vector

Returns

Resulting matrix

Definition at line 285 of file Matrix.cc.

References Matrix3D(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

{
    return Matrix3D(a.X * b.X, a.X * b.Y, a.X * b.Z,
                    a.Y * b.X, a.Y * b.Y, a.Y * b.Z,
                    a.Z * b.X, a.Z * b.Y, a.Z * b.Z);
}

Matrix3D Matrix3D::operator*

(

const Mdouble

a

)

const

Scalar multiplication.

Multiplication with scalar

Parameters

[in]

a

Scalar to be multiplied with

Returns

resulting matrix

Definition at line 127 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX * a, XY * a, XZ * a,
                    YX * a, YY * a, YZ * a,
                    ZX * a, ZY * a, ZZ * a);
}

Vec3D Matrix3D::operator*

(

const Vec3D &

a

)

const

Vector multiplication.

Multiplication with vector

Parameters

[in]

a

Vector to be multiplied with

Returns

Resulting vector

Definition at line 139 of file Matrix.cc.

References Vec3D::X, XX, XY, XZ, Vec3D::Y, YX, YY, YZ, Vec3D::Z, ZX, ZY, and ZZ.

{
    return Vec3D(XX * a.X + XY * a.Y + XZ * a.Z,
                 YX * a.X + YY * a.Y + YZ * a.Z,
                 ZX * a.X + ZY * a.Y + ZZ * a.Z);
}

Matrix3D Matrix3D::operator*

(

const Matrix3D &

a

)

const

Matrix multiplication.

Definition at line 146 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX * a.XX + XY * a.YX + XZ * a.ZX,
                    YX * a.XX + YY * a.YX + YZ * a.ZX,
                    ZX * a.XX + ZY * a.YX + ZZ * a.ZX,
                    XX * a.XY + XY * a.YY + XZ * a.ZY,
                    YX * a.XY + YY * a.YY + YZ * a.ZY,
                    ZX * a.XY + ZY * a.YY + ZZ * a.ZY,
                    XX * a.XZ + XY * a.YZ + XZ * a.ZZ,
                    YX * a.XZ + YY * a.YZ + YZ * a.ZZ,
                    ZX * a.XZ + ZY * a.YZ + ZZ * a.ZZ
                    );
}

Matrix3D Matrix3D::operator+

(

const Matrix3D &

A

)

const

Matrix addition.

Addition of this matrix with given one

Parameters

[in]

A

Matrix to be added

Returns

resulting matrix

Definition at line 78 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX + A.XX, XY + A.XY, XZ + A.XZ,
                    YX + A.YX, YY + A.YY, YZ + A.YZ,
                    ZX + A.ZX, ZY + A.ZY, ZZ + A.ZZ);
}

Matrix3D Matrix3D::operator+

(

const Mdouble

a

)

const

Scalar addition.

Addition of scalar

Parameters

[in]

a

Scalar to be added

Returns

resulting matrix

Definition at line 103 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX + a, XY + a, XZ + a,
                    YX + a, YY + a, YZ + a,
                    ZX + a, ZY + a, ZZ + a);
}

Matrix3D & Matrix3D::operator+=

(

const Matrix3D &

A

)

Matrix addition.

Adds all elements of a given matrix to its own

Parameters

[in]

A

3D matrix to be added

Returns

(reference to) resulting (this) matrix

Definition at line 203 of file Matrix.cc.

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

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

Matrix3D Matrix3D::operator-

(

const Matrix3D &

A

)

const

Matrix subtraction.

Substraction of given matrix from this one

Parameters

[in]

A

Matrix to be substracted

Returns

resulting matrix

Definition at line 91 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX - A.XX, XY - A.XY, XZ - A.XZ,
                    YX - A.YX, YY - A.YY, YZ - A.YZ,
                    ZX - A.ZX, ZY - A.ZY, ZZ - A.ZZ);
}

Matrix3D Matrix3D::operator-

(

const Mdouble

a

)

const

Scalar subtraction.

Substraction of scalar

Parameters

[in]

a

Scalar to be substracted

Returns

resulting matrix

Definition at line 115 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX - a, XY - a, XZ - a,
                    YX - a, YY - a, YZ - a,
                    ZX - a, ZY - a, ZZ - a);
}

Matrix3D & Matrix3D::operator-=

(

const Matrix3D &

A

)

Matrix substraction.

Substract all elements of a given matrix from its own

Parameters

[in]

A

3D matrix to be substracted

Returns

(reference to) resulting (this) matrix

Definition at line 222 of file Matrix.cc.

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

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

Matrix3D Matrix3D::operator/

(

const Mdouble

a

)

const

Scalar division.

Division by a scalar

Parameters

[in]

a

scalar to be divided by

Returns

resulting matrix

Definition at line 165 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(XX / a, XY / a, XZ / a,
                    YX / a, YY / a, YZ / a,
                    ZX / a, ZY / a, ZZ / a);
}

Matrix3D & Matrix3D::operator/=

(

const Mdouble

a

)

Scalar division.

Division by a scalar

Parameters

[in]

a

scalar to be divided by

Returns

(reference to) resulting (this) matrix

Definition at line 241 of file Matrix.cc.

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

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

void Matrix3D::setZero

(

)

Sets all elements to zero.

Sets all elements to zero.

Definition at line 58 of file Matrix.cc.

References XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    XX = XY = XZ = YX = YY = YZ = ZX = ZY = ZZ = 0.0;
}

Matrix3D Matrix3D::sqrt ( const Matrix3D &  A )

static

Calculates the pointwise square root.

Takes the square root of all the elements in given matrix

Parameters

[in]

A

Matrix to be pointwise square rooted

Returns

Resulting matrix

Definition at line 272 of file Matrix.cc.

References Matrix3D(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(std::sqrt(A.XX), std::sqrt(A.XY), std::sqrt(A.XZ),
                    std::sqrt(A.YX), std::sqrt(A.YY), std::sqrt(A.YZ),
                    std::sqrt(A.ZX), std::sqrt(A.ZY), std::sqrt(A.ZZ));
}

Matrix3D Matrix3D::square ( const Matrix3D &  A )

static

Calculates the pointwise square.

Squares all the elements in given matrix

Parameters

[in]

A

Matrix to be pointwise squared

Returns

Resulting matrix

Definition at line 260 of file Matrix.cc.

References Matrix3D(), mathsFunc::square(), XX, XY, XZ, YX, YY, YZ, ZX, ZY, and ZZ.

{
    return Matrix3D(mathsFunc::square(A.XX), mathsFunc::square(A.XY), mathsFunc::square(A.XZ),
                    mathsFunc::square(A.YX), mathsFunc::square(A.YY), mathsFunc::square(A.YZ),
                    mathsFunc::square(A.ZX), mathsFunc::square(A.ZY), mathsFunc::square(A.ZZ));
}

Mdouble Matrix3D::trace

(

)

const

Mean of the diagonal elements.

Returns the sum of the diagonal elements of the maxtrix, divided by the total number of diagonal elements.

Returns

resulting scalar

Definition at line 68 of file Matrix.cc.

References XX, YY, and ZZ.

{
    return (XX + YY + ZZ) / 3;
}

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  os, const Matrix3D &  A  )

friend

Add elements to ostream.

Adds all elements of a matrix to an ostream

Parameters

[out]	os	output stream
[in]	A	3D matrix

Returns

output stream with matrix elements added

Definition at line 178 of file Matrix.cc.

{
    os << A.XX << ' ' << A.XY << ' ' << A.XZ << ' '
        << A.YX << ' ' << A.YY << ' ' << A.YZ << ' '
        << A.ZX << ' ' << A.ZY << ' ' << A.ZZ;
    return os;
}

std::istream& operator>> ( std::istream &  is, Matrix3D &  A  )

friend

Add elements to istream.

Reads the elements of a matrix from an istream

Parameters

[in,out]	is	input stream
[out]	A	3D matrix

Returns

is input stream after the read operation.

Definition at line 192 of file Matrix.cc.

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

Member Data Documentation

Mdouble Matrix3D::XX

all nine matrix elements

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), square(), and trace().

Mdouble Matrix3D::XY

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble Matrix3D::XZ

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble Matrix3D::YX

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble Matrix3D::YY

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), square(), and trace().

Mdouble Matrix3D::YZ

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble Matrix3D::ZX

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble Matrix3D::ZY

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), and square().

Mdouble Matrix3D::ZZ

Definition at line 42 of file Matrix.h.

Referenced by cross(), Matrix3D(), operator*(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator<<(), operator>>(), setZero(), sqrt(), square(), and trace().

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

• Math/Matrix.h
• Math/Matrix.cc