2D matrix, struct implementation. More...

Public Member Functions
	mat2 (mat2 m)
	Copy constructor. Initializes components of a 2D matrix with components of the specified matrix. More...

	mat2 (double xx, double xy, double yx, double yy)
	Initializes 2D matrix structure with the specified components. More...

	mat2 (double component)
	Initializes 2D with the specified component. More...

	mat2 (vec2 xrow, vec2 yrow)
	Initializes 2D matrix structure with the specified rows. 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...

mat2	NormalizedEuclidean ()
	Returns this matrix normalized with Euclidean norm. More...

mat2	NormalizedForbenius ()
	Returns this matrix normalized with Euclidean norm. More...

mat2	Normalized1 ()
	Returns this matrix normalized with 1 norm. More...

mat2	NormalizedInfinity ()
	Returns this matrix normalized with infinity norm. More...

vec2	Solve (vec2 b)
	Returns solution of system of equations with the current system matrix and the specified right-hand sides. More...

mat2	Add (mat2 a)
	Returns sum of the current matrix and the specified matrix. More...

mat2	Subtract (mat2 a)
	Returns difference between the current matrix and the specified matrix. More...

mat2	MultiplyRight (mat2 b)
	Right-multiplies the current 2D matrix with the specified matrix and returns the product. More...

mat2	MultiplyLeft (mat2 b)
	Left-multiplies the current 2D matrix with the specified matrix and returns the product. More...

vec2	Multiply (vec2 b)
	Right-multiplies the current 2D matrix with the specified 2D vector and returns the product. More...

mat2	Multiply (double b)
	Multiplies the current 2D matrix with the specified scalar and returns the product. More...

override string	ToString ()
	Returns a string representation of this 2D matrix. More...

void	Read ()
	Reads this 2D matrix components from a console. More...

void	Read (string name)
	Reads this 2D matrix components from a console. More...

Static Public Member Functions
static mat2	Copy (mat2 m)
	Returns a copy of the specified 2D matrix. More...

static void	Negate (mat2 m, ref mat2 res)
	Negates the specified 2D matrix and stores its copy in the resulting matrix. More...

static int	EigenSystem2d (mat2 a, ref mat2 eigenvec, ref vec2 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 mat2	operator+ (mat2 m)
	Unary plus for 2D matrices, returns the operand. More...

static mat2	operator- (mat2 a)
	Unary negation for 2D matrices, returns the negative operand. More...

static mat2	operator+ (mat2 a, mat2 b)
	Matrix addition in 2D. More...

static mat2	operator- (mat2 a, mat2 b)
	Matrix subtraction in 2D. More...

static mat2	operator* (mat2 a, mat2 b)
	Matrix multiplication in 2D. More...

static vec2	operator* (mat2 a, vec2 b)
	Matrix with vector multiplication in 2D. More...

static mat2	operator* (mat2 a, double b)
	Product of a 2D matrix by a scalar. More...

static mat2	operator* (double a, mat2 b)
	Product of a 2D matrix by a scalar. More...

static mat2	operator/ (mat2 a, double b)
	Division of a 2D matrix by a scalar. More...

static bool	operator== (mat2 a, mat2 b)
	Vector comparison. More...

static bool	operator!= (mat2 a, mat2 b)
	Vector comparison, returns true if vectors are different. More...

static void	Example ()
	A short example of how to use mat2 and vec2 structs. More...

Public Attributes
double	xx

double	xy

double	yx

double	yy

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

vec2	rowx `[get, set]`
	Gets or sets the x-row of the 2D matrix. More...

vec2	rowy `[get, set]`
	Gets or sets the y-row of the 2D matrix. More...

vec2	columnx `[get, set]`
	Gets or sets the x-column of the 2D matrix. More...

vec2	columny `[get, set]`
	Gets or sets the y-column of the 2D 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...

mat2	Transpose `[get]`
	Gets transpose of the current matrix. More...

mat2	T `[get]`
	Gets transpose of the current matrix. More...

mat2	Inverse `[get]`
	Gets inverse of the current matrix. More...

mat2	Inv `[get]`
	Gets inverse of the current matrix. More...

Detailed Description

2D 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.mat2.mat2 ( mat2 m )

inline

Copy constructor. Initializes components of a 2D matrix with components of the specified matrix.

Parameters

m	Matrix whose components are copied to the initialized matrix.

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

IG.Num.mat2.mat2	(	double	xx,
		double	xy,
		double	yx,
		double	yy
	)

inline

Initializes 2D matrix structure with the specified components.

IG.Num.mat2.mat2 ( double component )

inline

Initializes 2D with the specified component.

Parameters

component Value that is assigned to all matrix components.

IG.Num.mat2.mat2	(	vec2	xrow,
		vec2	yrow
	)

inline

Initializes 2D matrix structure with the specified rows.

References IG.Num.vec2.x, and IG.Num.vec2.y.

Member Function Documentation

void IG.Num.mat2.Zero ( )

inline

Sets components of the vector to 0.0.

void IG.Num.mat2.Set ( double comp )

inline

Sets components of the vector to the specified value.

override int IG.Num.mat2.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.mat2.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 mat2) and has equal elements as the current matrix.

Overrides the object.Equals(object) method.

mat2 IG.Num.mat2.NormalizedEuclidean ( )

inline

Returns this matrix normalized with Euclidean norm.

mat2 IG.Num.mat2.NormalizedForbenius ( )

inline

Returns this matrix normalized with Euclidean norm.

mat2 IG.Num.mat2.Normalized1 ( )

inline

Returns this matrix normalized with 1 norm.

mat2 IG.Num.mat2.NormalizedInfinity ( )

inline

Returns this matrix normalized with infinity norm.

vec2 IG.Num.mat2.Solve ( vec2 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

mat2 IG.Num.mat2.Add ( mat2 a )

inline

Returns sum of the current matrix and the specified matrix.

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

Referenced by IG.Num.mat2.operator+().

mat2 IG.Num.mat2.Subtract ( mat2 a )

inline

Returns difference between the current matrix and the specified matrix.

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

Referenced by IG.Num.mat2.operator-().

mat2 IG.Num.mat2.MultiplyRight ( mat2 b )

inline

Right-multiplies the current 2D matrix with the specified matrix and returns the product.

Parameters

b	Right-hand side factor of multiplication.

Returns: this*b

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

Referenced by IG.Num.mat2.MultiplyLeft(), and IG.Num.mat2.operator*().

mat2 IG.Num.mat2.MultiplyLeft ( mat2 b )

inline

Left-multiplies the current 2D matrix with the specified matrix and returns the product.

Parameters

b	Left-hand side factor of multiplication.

Returns: b*this

References IG.Num.mat2.MultiplyRight().

vec2 IG.Num.mat2.Multiply ( vec2 b )

inline

Right-multiplies the current 2D matrix with the specified 2D vector and returns the product.

Parameters

b	Right-hand side factor of multiplication.

Returns: this*b

References IG.Num.vec2.x, and IG.Num.vec2.y.

Referenced by IG.Num.mat2.operator*(), and IG.Num.mat2.operator/().

mat2 IG.Num.mat2.Multiply ( double b )

inline

Multiplies the current 2D matrix with the specified scalar and returns the product.

Parameters

b	Factor of multiplication.

Returns: this*b

static mat2 IG.Num.mat2.Copy ( mat2 m )

inlinestatic

Returns a copy of the specified 2D matrix.

Parameters

m	Matrix whose copy is returned.

Referenced by IG.Num.mat2.operator+().

static void IG.Num.mat2.Negate	(	mat2	m,
		ref mat2	res
	)

inlinestatic

Negates the specified 2D 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.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

Referenced by IG.Num.Matrix2d.Negate().

static int IG.Num.mat2.EigenSystem2d	(	mat2	a,
		ref mat2	eigenvec,
		ref vec2	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.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

Referenced by IG.Num.Matrix2d.EigenSystem2d().

static mat2 IG.Num.mat2.operator+ ( mat2 m )

inlinestatic

Unary plus for 2D matrices, returns the operand.

References IG.Num.mat2.Copy().

static mat2 IG.Num.mat2.operator- ( mat2 a )

inlinestatic

Unary negation for 2D matrices, returns the negative operand.

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

static mat2 IG.Num.mat2.operator+	(	mat2	a,
		mat2	b
	)

inlinestatic

Matrix addition in 2D.

References IG.Num.mat2.Add().

static mat2 IG.Num.mat2.operator-	(	mat2	a,
		mat2	b
	)

inlinestatic

Matrix subtraction in 2D.

References IG.Num.mat2.Subtract().

static mat2 IG.Num.mat2.operator*	(	mat2	a,
		mat2	b
	)

inlinestatic

Matrix multiplication in 2D.

References IG.Num.mat2.MultiplyRight().

static vec2 IG.Num.mat2.operator*	(	mat2	a,
		vec2	b
	)

inlinestatic

Matrix with vector multiplication in 2D.

References IG.Num.mat2.Multiply().

static mat2 IG.Num.mat2.operator*	(	mat2	a,
		double	b
	)

inlinestatic

Product of a 2D matrix by a scalar.

References IG.Num.mat2.Multiply().

static mat2 IG.Num.mat2.operator*	(	double	a,
		mat2	b
	)

inlinestatic

Product of a 2D matrix by a scalar.

References IG.Num.mat2.Multiply().

static mat2 IG.Num.mat2.operator/	(	mat2	a,
		double	b
	)

inlinestatic

Division of a 2D matrix by a scalar.

References IG.Num.mat2.Multiply().

static bool IG.Num.mat2.operator==	(	mat2	a,
		mat2	b
	)

inlinestatic

Vector comparison.

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

static bool IG.Num.mat2.operator!=	(	mat2	a,
		mat2	b
	)

inlinestatic

Vector comparison, returns true if vectors are different.

References IG.Num.mat2.xx, IG.Num.mat2.xy, IG.Num.mat2.yx, and IG.Num.mat2.yy.

override string IG.Num.mat2.ToString ( )

inline

Returns a string representation of this 2D matrix.

void IG.Num.mat2.Read ( )

inline

Reads this 2D matrix components from a console.

Referenced by IG.Num.mat2.Example(), and IG.Num.Matrix2d.Read().

void IG.Num.mat2.Read ( string name )

inline

Reads this 2D 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.mat2.Example ( )

inlinestatic

A short example of how to use mat2 and vec2 structs.

References IG.Num.A, IG.Num.mat2.Determinant, IG.Num.mat2.Inv, IG.Num.mat2.Inverse, IG.Lib.UtilConsole.Read(), IG.Num.vec2.Read(), IG.Num.mat2.Read(), and IG.Num.mat2.T.

Member Data Documentation

double IG.Num.mat2.xx

Referenced by IG.Num.mat2.Add(), IG.Num.mat2.EigenSystem2d(), IG.Num.Func2dVectorFormBase.Hessian(), IG.Num.mat2.mat2(), IG.Num.mat2.MultiplyRight(), IG.Num.mat2.Negate(), IG.Num.mat2.operator!=(), IG.Num.mat2.operator-(), IG.Num.mat2.operator==(), and IG.Num.mat2.Subtract().

double IG.Num.mat2.xy

Referenced by IG.Num.mat2.Add(), IG.Num.mat2.EigenSystem2d(), IG.Num.Func2dVectorFormBase.Hessian(), IG.Num.mat2.mat2(), IG.Num.mat2.MultiplyRight(), IG.Num.mat2.Negate(), IG.Num.mat2.operator!=(), IG.Num.mat2.operator-(), IG.Num.mat2.operator==(), and IG.Num.mat2.Subtract().

double IG.Num.mat2.yx

Referenced by IG.Num.mat2.Add(), IG.Num.mat2.EigenSystem2d(), IG.Num.mat2.mat2(), IG.Num.mat2.MultiplyRight(), IG.Num.mat2.Negate(), IG.Num.mat2.operator!=(), IG.Num.mat2.operator-(), IG.Num.mat2.operator==(), and IG.Num.mat2.Subtract().

double IG.Num.mat2.yy

Referenced by IG.Num.mat2.Add(), IG.Num.mat2.EigenSystem2d(), IG.Num.Func2dVectorFormBase.Hessian(), IG.Num.mat2.mat2(), IG.Num.mat2.MultiplyRight(), IG.Num.mat2.Negate(), IG.Num.mat2.operator!=(), IG.Num.mat2.operator-(), IG.Num.mat2.operator==(), and IG.Num.mat2.Subtract().

Property Documentation

double IG.Num.mat2.this[int i, int j]

getset

Index operator.

Parameters

i	Component index.
j	Component index.

Returns: The specified component of a 2D vector.

vec2 IG.Num.mat2.rowx

getset

Gets or sets the x-row of the 2D matrix.

vec2 IG.Num.mat2.rowy

getset

Gets or sets the y-row of the 2D matrix.

vec2 IG.Num.mat2.columnx

getset

Gets or sets the x-column of the 2D matrix.

vec2 IG.Num.mat2.columny

getset

Gets or sets the y-column of the 2D matrix.

double IG.Num.mat2.NormForbenius

get

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

double IG.Num.mat2.NormEuclidean

get

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

double IG.Num.mat2.Norm

get

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

double IG.Num.mat2.Norm1

get

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

double IG.Num.mat2.NormInfinity

get

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

double IG.Num.mat2.Determinant

get

Gets matrix determinant.

Referenced by IG.Num.mat2.Example().

double IG.Num.mat2.Det

get

Gets matrix determinant.

double IG.Num.mat2.Trace

get

Gets matrix trace (sum of diagonal elements).

mat2 IG.Num.mat2.Transpose

get

Gets transpose of the current matrix.

mat2 IG.Num.mat2.T

get

Gets transpose of the current matrix.

Referenced by IG.Num.mat2.Example().

mat2 IG.Num.mat2.Inverse

get

Gets inverse of the current matrix.

Referenced by IG.Num.mat2.Example().

mat2 IG.Num.mat2.Inv

get

Gets inverse of the current matrix.

Referenced by IG.Num.mat2.Example().

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

igbase/numeric/geometry/Matrix2D.cs

Public Member Functions

Static Public Member Functions

Public Attributes

Properties

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation