3D matrix, struct implementation. More...

Public Member Functions
	mat3 (mat3 m)
	Copy constructor. Initializes components of a 3D matrix with components of the specified matrix. More...

	mat3 (double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz)
	Initializes 3D matrix structure with the specified components. More...

	mat3 (double component)
	Initializes 3D with the specified component. More...

	mat3 (vec3 xrow, vec3 yrow, vec3 zrow)
	Initializes 3D matrix structure with the specified components. More...

void	Zero ()
	Sets components of the vector to 0.0. More...

void	Set (double comp)
	Sets components of the vector to the specified value. More...

override int	GetHashCode ()
	Returns the hashRet code (hashRet function) of the current matrix. More...

override bool	Equals (Object obj)
	Returns a value indicating whether the specified object is equal to the current matrix. More...

mat3	NormalizedEuclidean ()
	Returns this matrix normalized with Euclidean norm. More...

mat3	NormalizedForbenius ()
	Returns this matrix normalized with Euclidean norm. More...

mat3	Normalized1 ()
	Returns this matrix normalized with 1 norm. More...

mat3	NormalizedInfinity ()
	Returns this matrix normalized with infinity norm. More...

vec3	Solve (vec3 b)
	Returns solution of system of equations with the current system matrix and the specified right-hand sides. More...

mat3	Add (mat3 a)
	Returns sum of the current matrix and the specified matrix. More...

mat3	Subtract (mat3 a)
	Returns difference between the current matrix and the specified matrix. More...

mat3	MultiplyRight (mat3 b)
	Right-multiplies the current 3D matrix with the specified matrix and returns the product. More...

mat3	MultiplyLeft (mat3 b)
	Left-multiplies the current 3D matrix with the specified matrix and returns the product. More...

vec3	Multiply (vec3 b)
	Right-multiplies the current 3D matrix with the specified 3D vector and returns the product. More...

mat3	Multiply (double b)
	Multiplies the current 3D matrix with the specified scalar and returns the product. More...

override string	ToString ()
	Returns a string representation of this 3D matrix. More...

void	Read ()
	Reads this 3D matrix components from a console. More...

void	Read (string name)
	Reads this 3D matrix components from a console. More...

Static Public Member Functions
static mat3	Copy (mat3 m)
	Returns a copy of the specified 3D matrix. More...

static void	Negate (mat3 m, ref mat3 res)
	Negates the specified 3D matrix and stores its copy in the resulting matrix. More...

static int	EigenSystem2d (mat3 a, ref mat3 eigenvec, ref vec3 eigenval)
	Calculates eigenvectors and eigenvalues of a 2x2 matrix a and stores eigenvectors to lines of eigenvec and eigenvalues to eigenval. eigenvec can be the same matrix as a. The number of different real eigenvalues is returned. Ref.: linalg.nb Not tested yet! More...

static mat3	operator+ (mat3 m)
	Unary plus for 3D matrices, returns the operand. More...

static mat3	operator- (mat3 a)
	Unary negation for 3D matrices, returns the negative operand. More...

static mat3	operator+ (mat3 a, mat3 b)
	Matrix addition in 3D. More...

static mat3	operator- (mat3 a, mat3 b)
	Matrix subtraction in 3D. More...

static mat3	operator* (mat3 a, mat3 b)
	Matrix multiplication in 3D. More...

static vec3	operator* (mat3 a, vec3 b)
	Matrix with vector multiplication in 3D. More...

static mat3	operator* (mat3 a, double b)
	Product of a 3D matrix by a scalar. More...

static mat3	operator* (double a, mat3 b)
	Product of a 3D matrix by a scalar. More...

static mat3	operator/ (mat3 a, double b)
	Division of a 3D matrix by a scalar. More...

static bool	operator== (mat3 a, mat3 b)
	Vector comparison. More...

static bool	operator!= (mat3 a, mat3 b)
	Vector comparison, returns true if vectors are different. More...

static void	Example ()
	A short example of how to use mat3 and vec3 structs. More...

Public Attributes
double	xx

double	xy

double	xz

double	yx

double	yy

double	yz

double	zx

double	zy

double	zz

Properties
double	this[int i, int j] `[get, set]`
	Index operator. More...

vec3	rowx `[get, set]`
	Gets or sets the x-row of the 3D matrix. More...

vec3	rowy `[get, set]`
	Gets or sets the y-row of the 3D matrix. More...

vec3	rowz `[get, set]`
	Gets or sets the z-row of the 3D matrix. More...

vec3	columnx `[get, set]`
	Gets or sets the x-column of the 3D matrix. More...

vec3	columny `[get, set]`
	Gets or sets the y-column of the 3D matrix. More...

vec3	columnz `[get, set]`
	Gets or sets the z-column of the 3D matrix. More...

double	NormForbenius `[get]`
	Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components. More...

double	NormEuclidean `[get]`
	Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components. More...

double	Norm `[get]`
	Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components. More...

double	Norm1 `[get]`
	Get the 1 norm of the matrix - maximum over columns of sum of absolute values of components. More...

double	NormInfinity `[get]`
	Get the infinity norm of the matrix - maximum over rows of sum of absolute values of components. More...

double	Determinant `[get]`
	Gets matrix determinant. More...

double	Det `[get]`
	Gets matrix determinant. More...

double	Trace `[get]`
	Gets matrix trace (sum of diagonal elements). More...

mat3	Transpose `[get]`
	Gets transpose of the current matrix. More...

mat3	T `[get]`
	Gets transpose of the current matrix. More...

mat3	Inverse `[get]`
	Gets inverse of the current matrix. More...

mat3	Inv `[get]`
	Gets inverse of the current matrix. More...

Detailed Description

3D matrix, struct implementation.

Name of this struct is not in line with conventions. This is intentional in order to prevent mistaking struct implementation for class interpretation.

$A Igor Jul08, Oct10;

Constructor & Destructor Documentation

IG.Num.mat3.mat3 ( mat3 m )

inline

Copy constructor. Initializes components of a 3D matrix with components of the specified matrix.

Parameters

m	Matrix whose components are copied to the initialized matrix.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

IG.Num.mat3.mat3	(	double	xx,
		double	xy,
		double	xz,
		double	yx,
		double	yy,
		double	yz,
		double	zx,
		double	zy,
		double	zz
	)

inline

Initializes 3D matrix structure with the specified components.

IG.Num.mat3.mat3 ( double component )

inline

Initializes 3D with the specified component.

Parameters

component Value that is assigned to all matrix components.

IG.Num.mat3.mat3	(	vec3	xrow,
		vec3	yrow,
		vec3	zrow
	)

inline

Initializes 3D matrix structure with the specified components.

References IG.Num.vec3.x, IG.Num.vec3.y, and IG.Num.vec3.z.

Member Function Documentation

void IG.Num.mat3.Zero ( )

inline

Sets components of the vector to 0.0.

void IG.Num.mat3.Set ( double comp )

inline

Sets components of the vector to the specified value.

override int IG.Num.mat3.GetHashCode ( )

inline

Returns the hashRet code (hashRet function) of the current matrix.

This method should be consistent with the MatrixBase.GetHashCode() method, which is standard for implementations of the IMatrix interface.

Two matrices that have the same equal all elements will produce the same hashRet codes.

Probability that two different matrixes will produce the same hashRet code is small but it exists.

Overrides the object.GetHashCode method.

override bool IG.Num.mat3.Equals ( Object obj )

inline

Returns a value indicating whether the specified object is equal to the current matrix.

True is returned if the object is of type mat3) and has equal elements as the current matrix.

Overrides the object.Equals(object) method.

mat3 IG.Num.mat3.NormalizedEuclidean ( )

inline

Returns this matrix normalized with Euclidean norm.

mat3 IG.Num.mat3.NormalizedForbenius ( )

inline

Returns this matrix normalized with Euclidean norm.

mat3 IG.Num.mat3.Normalized1 ( )

inline

Returns this matrix normalized with 1 norm.

mat3 IG.Num.mat3.NormalizedInfinity ( )

inline

Returns this matrix normalized with infinity norm.

vec3 IG.Num.mat3.Solve ( vec3 b )

inline

Returns solution of system of equations with the current system matrix and the specified right-hand sides.

Parameters

b	Vector of right-hand sides of equations.

Returns

mat3 IG.Num.mat3.Add ( mat3 a )

inline

Returns sum of the current matrix and the specified matrix.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

Referenced by IG.Num.mat3.operator+().

mat3 IG.Num.mat3.Subtract ( mat3 a )

inline

Returns difference between the current matrix and the specified matrix.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

Referenced by IG.Num.mat3.operator-().

mat3 IG.Num.mat3.MultiplyRight ( mat3 b )

inline

Right-multiplies the current 3D matrix with the specified matrix and returns the product.

Parameters

b	Right-hand side factor of multiplication.

Returns: this*b

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

Referenced by IG.Num.mat3.MultiplyLeft(), and IG.Num.mat3.operator*().

mat3 IG.Num.mat3.MultiplyLeft ( mat3 b )

inline

Left-multiplies the current 3D matrix with the specified matrix and returns the product.

Parameters

b	Left-hand side factor of multiplication.

Returns: b*this

References IG.Num.mat3.MultiplyRight().

vec3 IG.Num.mat3.Multiply ( vec3 b )

inline

Right-multiplies the current 3D matrix with the specified 3D vector and returns the product.

Parameters

b	Right-hand side factor of multiplication.

Returns: this*b

References IG.Num.vec3.x, IG.Num.vec3.y, and IG.Num.vec3.z.

Referenced by IG.Num.mat3.operator*(), and IG.Num.mat3.operator/().

mat3 IG.Num.mat3.Multiply ( double b )

inline

Multiplies the current 3D matrix with the specified scalar and returns the product.

Parameters

b	Factor of multiplication.

Returns: this*b

static mat3 IG.Num.mat3.Copy ( mat3 m )

inlinestatic

Returns a copy of the specified 3D matrix.

Parameters

m	Matrix whose copy is returned.

Referenced by IG.Num.mat3.operator+().

static void IG.Num.mat3.Negate	(	mat3	m,
		ref mat3	res
	)

inlinestatic

Negates the specified 3D matrix and stores its copy in the resulting matrix.

Parameters

m	Matrix to be negated.
res	Matrix where the result is stored.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

Referenced by IG.Num.Matrix3d.Negate().

static int IG.Num.mat3.EigenSystem2d	(	mat3	a,
		ref mat3	eigenvec,
		ref vec3	eigenval
	)

inlinestatic

Calculates eigenvectors and eigenvalues of a 2x2 matrix a and stores eigenvectors to lines of eigenvec and eigenvalues to eigenval. eigenvec can be the same matrix as a. The number of different real eigenvalues is returned. Ref.: linalg.nb Not tested yet!

Parameters

a	2D Matrix whose eigenvalues and eigenvectors are calculated.
eigenvec	Matrix where eigenvectors are stored as rows.
eigenval	Vector where eigenvalues are stored.

Returns: The number of different real eigenvalues.

$A Igor Aug08, Oct10;

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.yx, and IG.Num.mat3.yy.

Referenced by IG.Num.Matrix3d.EigenSystem2d().

static mat3 IG.Num.mat3.operator+ ( mat3 m )

inlinestatic

Unary plus for 3D matrices, returns the operand.

References IG.Num.mat3.Copy().

static mat3 IG.Num.mat3.operator- ( mat3 a )

inlinestatic

Unary negation for 3D matrices, returns the negative operand.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

static mat3 IG.Num.mat3.operator+	(	mat3	a,
		mat3	b
	)

inlinestatic

Matrix addition in 3D.

References IG.Num.mat3.Add().

static mat3 IG.Num.mat3.operator-	(	mat3	a,
		mat3	b
	)

inlinestatic

Matrix subtraction in 3D.

References IG.Num.mat3.Subtract().

static mat3 IG.Num.mat3.operator*	(	mat3	a,
		mat3	b
	)

inlinestatic

Matrix multiplication in 3D.

References IG.Num.mat3.MultiplyRight().

static vec3 IG.Num.mat3.operator*	(	mat3	a,
		vec3	b
	)

inlinestatic

Matrix with vector multiplication in 3D.

References IG.Num.mat3.Multiply().

static mat3 IG.Num.mat3.operator*	(	mat3	a,
		double	b
	)

inlinestatic

Product of a 3D matrix by a scalar.

References IG.Num.mat3.Multiply().

static mat3 IG.Num.mat3.operator*	(	double	a,
		mat3	b
	)

inlinestatic

Product of a 3D matrix by a scalar.

References IG.Num.mat3.Multiply().

static mat3 IG.Num.mat3.operator/	(	mat3	a,
		double	b
	)

inlinestatic

Division of a 3D matrix by a scalar.

References IG.Num.mat3.Multiply().

static bool IG.Num.mat3.operator==	(	mat3	a,
		mat3	b
	)

inlinestatic

Vector comparison.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

static bool IG.Num.mat3.operator!=	(	mat3	a,
		mat3	b
	)

inlinestatic

Vector comparison, returns true if vectors are different.

References IG.Num.mat3.xx, IG.Num.mat3.xy, IG.Num.mat3.xz, IG.Num.mat3.yx, IG.Num.mat3.yy, IG.Num.mat3.yz, IG.Num.mat3.zx, IG.Num.mat3.zy, and IG.Num.mat3.zz.

override string IG.Num.mat3.ToString ( )

inline

Returns a string representation of this 3D matrix.

void IG.Num.mat3.Read ( )

inline

Reads this 3D matrix components from a console.

Referenced by IG.Num.mat3.Example(), and IG.Num.Matrix3d.Read().

void IG.Num.mat3.Read ( string name )

inline

Reads this 3D matrix components from a console.

Parameters

name	Name of the matrix to be read; it is written as orientation to the user and can be null.

References IG.Lib.UtilConsole.Read().

static void IG.Num.mat3.Example ( )

inlinestatic

A short example of how to use mat3 and vec3 structs.

References IG.Num.A, IG.Num.mat3.Determinant, IG.Num.mat3.Inv, IG.Num.mat3.Inverse, IG.Lib.UtilConsole.Read(), IG.Num.vec3.Read(), IG.Num.mat3.Read(), and IG.Num.mat3.T.

Member Data Documentation

double IG.Num.mat3.xx

Referenced by IG.Num.mat3.Add(), IG.Num.mat3.EigenSystem2d(), IG.Num.Func3dVectorFormBase.Hessian(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.xy

Referenced by IG.Num.mat3.Add(), IG.Num.mat3.EigenSystem2d(), IG.Num.Func3dVectorFormBase.Hessian(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.xz

Referenced by IG.Num.mat3.Add(), IG.Num.Func3dVectorFormBase.Hessian(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.yx

Referenced by IG.Num.mat3.Add(), IG.Num.mat3.EigenSystem2d(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.yy

Referenced by IG.Num.mat3.Add(), IG.Num.mat3.EigenSystem2d(), IG.Num.Func3dVectorFormBase.Hessian(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.yz

Referenced by IG.Num.mat3.Add(), IG.Num.Func3dVectorFormBase.Hessian(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.zx

Referenced by IG.Num.mat3.Add(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.zy

Referenced by IG.Num.mat3.Add(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

double IG.Num.mat3.zz

Referenced by IG.Num.mat3.Add(), IG.Num.Func3dVectorFormBase.Hessian(), IG.Num.mat3.mat3(), IG.Num.mat3.MultiplyRight(), IG.Num.mat3.Negate(), IG.Num.mat3.operator!=(), IG.Num.mat3.operator-(), IG.Num.mat3.operator==(), and IG.Num.mat3.Subtract().

Property Documentation

double IG.Num.mat3.this[int i, int j]

getset

Index operator.

Parameters

i	Component index 1.
j	Component index 2.

Returns: The specified component of a 3D matrix.

vec3 IG.Num.mat3.rowx

getset

Gets or sets the x-row of the 3D matrix.

vec3 IG.Num.mat3.rowy

getset

Gets or sets the y-row of the 3D matrix.

vec3 IG.Num.mat3.rowz

getset

Gets or sets the z-row of the 3D matrix.

vec3 IG.Num.mat3.columnx

getset

Gets or sets the x-column of the 3D matrix.

vec3 IG.Num.mat3.columny

getset

Gets or sets the y-column of the 3D matrix.

vec3 IG.Num.mat3.columnz

getset

Gets or sets the z-column of the 3D matrix.

double IG.Num.mat3.NormForbenius

get

Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components.

double IG.Num.mat3.NormEuclidean

get

Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components.

double IG.Num.mat3.Norm

get

Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components.

double IG.Num.mat3.Norm1

get

Get the 1 norm of the matrix - maximum over columns of sum of absolute values of components.

double IG.Num.mat3.NormInfinity

get

Get the infinity norm of the matrix - maximum over rows of sum of absolute values of components.

double IG.Num.mat3.Determinant

get

Gets matrix determinant.

Referenced by IG.Num.mat3.Example().

double IG.Num.mat3.Det

get

Gets matrix determinant.

double IG.Num.mat3.Trace

get

Gets matrix trace (sum of diagonal elements).

mat3 IG.Num.mat3.Transpose

get

Gets transpose of the current matrix.

mat3 IG.Num.mat3.T

get

Gets transpose of the current matrix.

Referenced by IG.Num.mat3.Example().

mat3 IG.Num.mat3.Inverse

get

Gets inverse of the current matrix.

Referenced by IG.Num.mat3.Example().

mat3 IG.Num.mat3.Inv

get

Gets inverse of the current matrix.

Referenced by IG.Num.mat3.Example().

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

igbase/numeric/geometry/Matrix3D.cs

Public Member Functions

Static Public Member Functions

Public Attributes

Properties

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation