Class Vector

java.lang.Object
  Vector

 class Vector
extends Object

This class introduces vectors and enables basic operations with them. The coordinates are stored as a field of Fractions.

Since:

2014-04-01

Version:

1.0

Author:

Pavel Sikora

Constructor Summary

Vector()
Constructs a null vector of dimension 0.

Vector(Fraction[] V, int d)
Constructs a vector from a field of Fractions.

Vector(int d)
Constructs a zero vector of a given dimension.

Vector(Point B)
Constructs a vector from a point (initial point will be the origin).

Vector(Point A, Point B)
Constructs a vector from two given points.

Method Summary

(package private) Vector	add(Vector A) Adds another vector to this vector.
(package private) Cyclometric	angleDirectionVectors(Vector W) Calculates the angle of two direction vectors of lines (the resulting angle will be from 0 to π/2).
(package private) Cyclometric	angleDirectionVectors(Vector W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of two direction vectors of lines (the resulting angle will be from 0 to π/2).
(package private) Cyclometric	angleNormalVectorDirectionVector(Vector W) Calculates the angle of a direction vector and a normal vector of lines (the resulting angle will be from 0 to π/2).
(package private) Cyclometric	angleNormalVectorDirectionVector(Vector W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of a direction vector and a normal vector of lines (the resulting angle will be from 0 to π/2).
(package private) Cyclometric	angleNormalVectors(Vector W) Calculates the angle of two normal vectors of lines (the resulting angle will be from 0 to π/2).
(package private) Cyclometric	angleNormalVectors(Vector W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of two normal vectors of lines (the resulting angle will be from 0 to π/2).
(package private) void	copy(Vector I) Copies another vector onto this vector.
(package private) static Vector[]	generateRandomParallelVectors(int DIM) Generates two random parallel vectors of given dimension.
(package private) static Vector[]	generateRandomPerpendicularVectors(int DIM) Generates two random perpendicular vectors of given dimension.
(package private) static Vector[]	generateRandomVectorsWithAngle30(int DIM) Generates two random vectors of given dimension whose angle is π/6.
(package private) static Vector[]	generateRandomVectorsWithAngle45(int DIM) Generates two random vectors of given dimension whose angle is π/4.
(package private) static Vector[]	generateRandomVectorsWithAngle60(int DIM) Generates two random vectors of given dimension whose angle is π/3.
(package private) static Vector[]	generateRandomVectorsWithGivenAngle(PiFraction angle, int DIM) Generates two random vectors, while the angle of the vectors will be one of 0, π/6, π/4, π/3, or π/2.
(package private) Fraction	get(int i) The getter of this class - returns the value of a given coordinate.
(package private) int	getDim() Gets the dimensions of the vector.
(package private) boolean	isEqual(Vector C) Checks if two vectors are equal.
(package private) boolean	isZeroVector() Checks whether or not this vector is a zero vector.
(package private) SquareRootFraction	length() Computes length of this vector.
(package private) SquareRootFraction	length(char label, boolean verbose) Computes length of this vector.
(package private) Vector	multiply(Fraction F) Multiplies this vector by a scalar.
(package private) Vector	opposite() Finds ppposite vector to this vector.
(package private) Vector	orthogonalComponent(Matrix W) Finds the orthogonal component of the vector onto a given difference space.
(package private) Vector	orthogonalComponent(Matrix W, boolean verbose) Finds the orthogonal component of the vector onto a given difference space.
(package private) Vector	orthogonalProjection(Matrix W) Finds the orthogonal projection of this vector onto a given difference space.
(package private) Vector	orthogonalProjection(Matrix W, boolean verbose) Finds the orthogonal projection of this vector onto a given difference space.
(package private) Fraction	scalarProduct(Vector F) Computes scalar product of two vectors.
(package private) SquareRootFraction	scalarProductNorm(Vector F) Computes scalar product of two vectors after normalizing them.
(package private) void	set(Fraction F, int i) The setter of this class - sets given coordinate to a given value.
(package private) Vector	subtract(Vector S) Subtracts another vector from this vector.
(package private) Matrix	toMatrixColumn() Converts the vector to a 1-column matrix.
(package private) Matrix	toMatrixRow() Converts the vector to a 1-row matrix.
(package private) String	toTeX() Prints this vector formatted as TeX code.
(package private) String	toText() Prints this vector formatted as text.

Methods inherited from class

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Vector

Vector()

Constructs a null vector of dimension 0.

Vector

Vector(Fraction[] V,
       int d)

Constructs a vector from a field of Fractions.

Parameters:

V - field of Fractions, containing the vector's coordinates

d - dimension of the vector, ie. number of its coordinates

Vector

Vector(int d)

Constructs a zero vector of a given dimension.

Parameters:

d - dimension of the vector, ie. number of its coordinates

Vector

Vector(Point B)

Constructs a vector from a point (initial point will be the origin).

Parameters:

B - terminal point

Throws:

UnsupportedOperationException - Throws an exception if the points don't have equal dimension.

Vector

Vector(Point A,
       Point B)

Constructs a vector from two given points.

Parameters:

A - initial point

B - terminal point

Throws:

UnsupportedOperationException - Throws an exception if the points don't have equal dimension.

Method Detail

add

Vector add(Vector A)

Adds another vector to this vector.

Parameters:

A - addend vector

Throws:

UnsupportedOperationException - Throws an exception if the vectors don't have equal dimension.

angleDirectionVectors

Cyclometric angleDirectionVectors(Vector W)

Calculates the angle of two direction vectors of lines (the resulting angle will be from 0 to π/2). This method doesn't “talk” (creates no text nor TeX output).

Parameters:

V - the other vector

Returns:

a Cyclometric that holds all information about the angle; most importantly, if the angle was any of 0, π/6, π/4, π/3, π/2, this value is marked together with double value in radians

angleDirectionVectors

Cyclometric angleDirectionVectors(Vector W,
                                  char firstLabel,
                                  char secondLabel,
                                  boolean verbose)

Calculates the angle of two direction vectors of lines (the resulting angle will be from 0 to π/2).

Parameters:

V - the other vector

verbose - determines, if the method “talks” (creates any text and TeX output)

Returns:

a Cyclometric that holds all information about the angle; most importantly, if the angle was any of 0, π/6, π/4, π/3, π/2, this value is marked together with double value in radians

angleNormalVectorDirectionVector

Cyclometric angleNormalVectorDirectionVector(Vector W)

Calculates the angle of a direction vector and a normal vector of lines (the resulting angle will be from 0 to π/2). This method doesn't “talk” (creates no text nor TeX output).

Parameters:

V - the other vector

Returns:

a Cyclometric that holds all information about the angle; most importantly, if the angle was any of 0, π/6, π/4, π/3, π/2, this value is marked together with double value in radians

angleNormalVectorDirectionVector

Cyclometric angleNormalVectorDirectionVector(Vector W,
                                             char firstLabel,
                                             char secondLabel,
                                             boolean verbose)

Calculates the angle of a direction vector and a normal vector of lines (the resulting angle will be from 0 to π/2).

Parameters:

V - the other vector

verbose - determines, if the method “talks” (creates any text and TeX output)

Returns:

a Cyclometric that holds all information about the angle; most importantly, if the angle was any of 0, π/6, π/4, π/3, π/2, this value is marked together with double value in radians

angleNormalVectors

Cyclometric angleNormalVectors(Vector W)

Calculates the angle of two normal vectors of lines (the resulting angle will be from 0 to π/2). This method doesn't “talk” (creates no text nor TeX output).

Parameters:

V - the other vector

Returns:

a Cyclometric that holds all information about the angle; most importantly, if the angle was any of 0, π/6, π/4, π/3, π/2, this value is marked together with double value in radians

angleNormalVectors

Cyclometric angleNormalVectors(Vector W,
                               char firstLabel,
                               char secondLabel,
                               boolean verbose)

Calculates the angle of two normal vectors of lines (the resulting angle will be from 0 to π/2).

Parameters:

V - the other vector

verbose - determines, if the method “talks” (creates any text and TeX output)

Returns:

a Cyclometric that holds all information about the angle; most importantly, if the angle was any of 0, π/6, π/4, π/3, π/2, this value is marked together with double value in radians

copy

void copy(Vector I)

Copies another vector onto this vector. This is the correct way of assigning vectors, not by =.

Parameters:

I - the image vector

generateRandomParallelVectors

static Vector[] generateRandomParallelVectors(int DIM)

Generates two random parallel vectors of given dimension.

Parameters:

DIM - dimension of the vectors

Returns:

vectors with desired angle

Throws:

UnsupportedOperationException - if DIM is zero

generateRandomPerpendicularVectors

static Vector[] generateRandomPerpendicularVectors(int DIM)

Generates two random perpendicular vectors of given dimension.

Returns:

vectors with desired angle

Throws:

UnsupportedOperationException - if DIM is zero

generateRandomVectorsWithAngle30

static Vector[] generateRandomVectorsWithAngle30(int DIM)

Generates two random vectors of given dimension whose angle is π/6.

Returns:

vectors with desired angle

Throws:

UnsupportedOperationException - if DIM is less than three

generateRandomVectorsWithAngle45

static Vector[] generateRandomVectorsWithAngle45(int DIM)

Generates two random vectors of given dimension whose angle is π/4.

Returns:

vectors with desired angle

Throws:

UnsupportedOperationException - if DIM is less than two

generateRandomVectorsWithAngle60

static Vector[] generateRandomVectorsWithAngle60(int DIM)

Generates two random vectors of given dimension whose angle is π/3.

Returns:

vectors with desired angle

Throws:

UnsupportedOperationException - if DIM is less than three

generateRandomVectorsWithGivenAngle

static Vector[] generateRandomVectorsWithGivenAngle(PiFraction angle,
                                                    int DIM)

Generates two random vectors, while the angle of the vectors will be one of 0, π/6, π/4, π/3, or π/2.

Parameters:

angle - the desired angle of vectors

Returns:

vectors with desired angle

Throws:

UnsupportedOperationException - if angle is none of 0, π/6, π/4, π/3, or π/2

get

Fraction get(int i)

The getter of this class - returns the value of a given coordinate.

Parameters:

i - the index of desired coordinate

Returns:

the ith coordinate value (a Fraction)

Throws:

IndexOutOfBoundsException - Throws an exception if the index isn't of <1,dimension of the vector>.

getDim

int getDim()

Gets the dimensions of the vector.

Returns:

dimension of the vector

isEqual

boolean isEqual(Vector C)

Checks if two vectors are equal.

Parameters:

C - comparand vector

Returns:

true if this vector is equal to the comparand, false otherwise

Throws:

UnsupportedOperationException - Throws an exception if the vectors don't have equal dimension.

isZeroVector

boolean isZeroVector()

Checks whether or not this vector is a zero vector.

Returns:

true if this vector is a zero vector or a null vector, false otherwise

length

SquareRootFraction length()

Computes length of this vector. This method doesn't “talk” (creates no text nor TeX output).

Returns:

length of this vector

length

SquareRootFraction length(char label,
                          boolean verbose)

Computes length of this vector.

Parameters:

label - label of the matrix

verbose - determines, if the method “talks” (creates any text and TeX output)

Returns:

length of this vector

multiply

Vector multiply(Fraction F)

Multiplies this vector by a scalar.

Parameters:

F - factor

Returns:

F-multiple of this vector

opposite

Vector opposite()

Finds ppposite vector to this vector.

Returns:

the opposite vector

orthogonalComponent

Vector orthogonalComponent(Matrix W)

Finds the orthogonal component of the vector onto a given difference space. This method doesn't “talk” (creates no text nor TeX output).

Parameters:

W - difference space onto which we project the vector

Returns:

the orthogonal component of this vector onto a given difference space

orthogonalComponent

Vector orthogonalComponent(Matrix W,
                           boolean verbose)

Finds the orthogonal component of the vector onto a given difference space.

Parameters:

W - difference space onto which we project the vector

verbose - determines, if the method “talks” (creates any text and TeX output)

Returns:

the orthogonal component of this vector onto a given difference space

orthogonalProjection

Vector orthogonalProjection(Matrix W)

Finds the orthogonal projection of this vector onto a given difference space. This method doesn't “talk” (creates no text nor TeX output).

Parameters:

W - difference space onto which we project the vector

Returns:

the orthogonal projection of this vector onto a given difference space

orthogonalProjection

Vector orthogonalProjection(Matrix W,
                            boolean verbose)

Finds the orthogonal projection of this vector onto a given difference space.

Parameters:

W - difference space onto which we project the vector

verbose - determines, if the method “talks” (creates any text and TeX output)

Returns:

the orthogonal projection of this vector onto a given difference space

scalarProduct

Fraction scalarProduct(Vector F)

Computes scalar product of two vectors.

Parameters:

F - factor vector

Throws:

UnsupportedOperationException - Throws an exception if the vectors don't have equal dimension.

scalarProductNorm

SquareRootFraction scalarProductNorm(Vector F)

Computes scalar product of two vectors after normalizing them.

Parameters:

F - factor vector

Throws:

UnsupportedOperationException - Throws an exception if the vectors don't have equal dimension.

set

void set(Fraction F,
         int i)

The setter of this class - sets given coordinate to a given value.

Parameters:

F - the ith coordinate desired value (a Fraction)

i - the index of desired coordinate

Throws:

IndexOutOfBoundsException - Throws an exception if the index isn't of <1,dimension of the vector>.

subtract

Vector subtract(Vector S)

Subtracts another vector from this vector.

Parameters:

S - subtrahend vector

Throws:

UnsupportedOperationException - Throws an exception if the vectors don't have equal dimension.

toMatrixColumn

Matrix toMatrixColumn()

Converts the vector to a 1-column matrix.

toMatrixRow

Matrix toMatrixRow()

Converts the vector to a 1-row matrix.

toTeX

String toTeX()

Prints this vector formatted as TeX code.

Returns:

TeX code for this vector

toText

String toText()

Prints this vector formatted as text.

Returns:

plain text description of this vector; it will begin with ( and end with )