Class Subspace

java.lang.Object
  Subspace

 class Subspace
extends Object

This is the computational core of the package. It introduces subspaces and enables basic operations with them, using all the other classes for that.

Since:

2014-04-01

Version:

1.0

Author:

Pavel Sikora

Constructor Summary

Subspace()
Constructs a null subspace.

Subspace(Matrix A)
Constructs a subspace given in general form.

Subspace(Point[] points, Vector[] vectors)
Constructs a subspace given in parametric form (ie. from at least one point and potentially some vectors).

Method Summary

(package private) Cyclometric	angle(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of any two subspaces using the most efficient method.
(package private) Cyclometric	angleHyperplaneHyperplane(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of two hyperplanes.
(package private) Cyclometric	angleLineAny(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of a line and any other subspace.
(package private) Cyclometric	angleLineHyperplane(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of a line and a hyperplane.
(package private) Cyclometric	angleLineLine(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of two lines, ie. one-dimensional subspaces.
(package private) Cyclometric	angleUniversal(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the angle of two subspaces.
(package private) void	beautifyGeneral() Multiplies individual equations by such numbers that their coefficients will be smallest possible integers.
(package private) void	beautifyParametric() Multiplies individual vectors by such numbers that their coefficients will be smallest possible integers.
(package private) void	copy(Subspace S) Copies the subspace.
(package private) String	describe(char label) Properly describes the subspace.
(package private) SquareRootFraction	distance(Subspace W) Calculates the distance of any two subspaces using the most efficient method.
(package private) SquareRootFraction	distance(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the distance of any two subspaces using the most efficient method.
(package private) SquareRootFraction	distanceFromParallelSubspace(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the distance of the subspace from a parallel subspace.
(package private) SquareRootFraction	distancePointAny(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the distance of a point from any subspace.
(package private) SquareRootFraction	distancePointHyperplane(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the distance of a point from a hyperplane.
(package private) SquareRootFraction	distancePointPoint(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the distance of two points.
(package private) SquareRootFraction	distanceUniversalUsingGram(Subspace W, char firstLabel, char secondLabel, boolean verbose) Calculates the distance of any two subspaces using Gram determinant.
(package private) static Subspace	generateRandomGeneralSubspace(int dim, int DIM) Generates a random subspace in general form.
(package private) static Subspace	generateRandomHyperplane(int DIM) Generates a random hyperplane in general form.
(package private) static Subspace	generateRandomHyperplaneWithIntegerNorm(int DIM) Generates a random hyperplane in general form.
(package private) static Subspace	generateRandomParametricSubspace(int dim, int DIM) Generates a random subspace in parametric form.
(package private) static Subspace[]	generateRandomSubspacesWithGivenAngle(int dim1, int dim2, int DIM, PiFraction angle) Generates two random subspaces in parametric form.
(package private) static Subspace[]	generateRandomSubspacesWithGivenDistance(int dim1, int dim2, int DIM, Fraction dist) Generates two random subspaces in general form.
(package private) Matrix	getAugMatrix() Returns the augmented matrix of equation system generating this subspace.
(package private) int	getDim() Returns the dimension of the subspace.
(package private) int	getDIM() Returns the dimension of the whole space (number of variables).
(package private) int	getDim(boolean verbose) Returns the dimension of the subspace.
(package private) int	getDim(boolean verbose, char label) Returns the dimension of the subspace.
(package private) boolean	getOriginalForm() Makes clear if the subspace was originally input in general or in parametric form
(package private) Matrix	getVecMatrix() Returns the matrix of direction vectors (in rows).
(package private) void	checkGeneralForm() Checks if general form is already available; if it's not, it gets it.
(package private) void	checkGeneralForm(char label, boolean verbose) Checks if general form is already available; if it's not, it gets it.
(package private) void	checkParametricForm() Checks if parametric form is already available; if it's not, it gets it.
(package private) void	checkParametricForm(char label, boolean verbose) Checks if parametric form is already available; if it's not, it gets it.
(package private) Subspace	intersectionDiffSpace(Subspace W, char firstLabel, char secondLabel, boolean verbose, boolean noPriorKnowledge) Finds intersection of difference spaces of two subspaces.
(package private) boolean	intersects(Subspace W) Checks, if this subspace intersects with the other.
(package private) boolean	intersects(Subspace W, char firstLabel, char secondLabel, boolean verbose) Checks, if this subspace intersects with the other.
(package private) boolean	isGeneralFormAvailable() Confirms if the general form is available.
(package private) boolean	isNull() Checks, if this subspace is a null space.
(package private) boolean	isParallel(Subspace W) Checks, if this subspace is parallel to the other.
(package private) boolean	isParallel(Subspace W, boolean verbose) Checks, if this subspace is parallel to the other.
(package private) boolean	isParametricFormAvailable() Confirms if the parametric form is available.
(package private) Subspace	orthogonalSupplement(char label, boolean verbose) Finds orthogonal supplement to a subspace.
(package private) String	toTeXGeneral() Prints general form of this subspace formatted as TeX code.
(package private) String	toTeXGeneral(char variable) Prints general form of this subspace formatted as TeX code.
(package private) String	toTeXParametric() Prints parametric form of this subspace formatted as TeX code.
(package private) String	toTextGeneral() Prints general form of this subspace formatted as text.
(package private) String	toTextGeneral(boolean verbose) Prints general form of this subspace formatted as text.
(package private) String	toTextGeneral(boolean verbose, char variable) Prints general form of this subspace formatted as text.
(package private) String	toTextParametric() Prints parametric form of this subspace formatted as text.
(package private) String	toTextParametric(boolean verbose) Prints parametric form of this subspace formatted as text.

Methods inherited from class

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

Constructor Detail

Subspace

Subspace()

Constructs a null subspace.

Subspace

Subspace(Matrix A)

Constructs a subspace given in general form.

Parameters:

A - augmented matrix of equation system generating this subspace

Throws:

UnsupportedOperationException - Throws an exception if the equation system is not solvable, and thus cannot generate a subspace.

Subspace

Subspace(Point[] points,
         Vector[] vectors)

Constructs a subspace given in parametric form (ie. from at least one point and potentially some vectors).

Parameters:

A - augmented matrix of equation system generating this subspace

Throws:

IndexOutOfBoundsException - Throws an exception if no reference point was given.

Method Detail

angle

Cyclometric angle(Subspace W,
                  char firstLabel,
                  char secondLabel,
                  boolean verbose)

Calculates the angle of any two subspaces using the most efficient method.

Parameters:

W - the other subspace

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

Throws:

IllegalArgumentException - Throws an exception if the two subspaces do not come from the same space, ie. they have a different DIM.

angleHyperplaneHyperplane

Cyclometric angleHyperplaneHyperplane(Subspace W,
                                      char firstLabel,
                                      char secondLabel,
                                      boolean verbose)

Calculates the angle of two hyperplanes.

Parameters:

W - the other hyperplane

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

Throws:

IllegalArgumentException - Throws an exception if any of the two subspaces is not a hyperplane in fact.

angleLineAny

Cyclometric angleLineAny(Subspace W,
                         char firstLabel,
                         char secondLabel,
                         boolean verbose)

Calculates the angle of a line and any other subspace.

Parameters:

W - the other subspace

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

Throws:

IllegalArgumentException - Throws an exception if this subspaces is not a line.

angleLineHyperplane

Cyclometric angleLineHyperplane(Subspace W,
                                char firstLabel,
                                char secondLabel,
                                boolean verbose)

Calculates the angle of a line and a hyperplane.

Parameters:

W - the hyperplane

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

Throws:

IllegalArgumentException - Throws an exception if this subspaces is not a line or W is not a hyperplane.

angleLineLine

Cyclometric angleLineLine(Subspace W,
                          char firstLabel,
                          char secondLabel,
                          boolean verbose)

Calculates the angle of two lines, ie. one-dimensional subspaces.

Parameters:

W - the other line

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

Throws:

IllegalArgumentException - Throws an exception if any of the two subspaces is not a line in fact.

angleUniversal

Cyclometric angleUniversal(Subspace W,
                           char firstLabel,
                           char secondLabel,
                           boolean verbose)

Calculates the angle of two subspaces.

Parameters:

W - the other subspace

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

beautifyGeneral

void beautifyGeneral()

Multiplies individual equations by such numbers that their coefficients will be smallest possible integers.

beautifyParametric

void beautifyParametric()

Multiplies individual vectors by such numbers that their coefficients will be smallest possible integers.

copy

void copy(Subspace S)

Copies the subspace.

Parameters:

S - subspace to be copied

describe

String describe(char label)

Properly describes the subspace.

Returns:

type of the subspace (null space, point, line, plane, n-dimensional space, hyperplane, whole space)

distance

SquareRootFraction distance(Subspace W)

Calculates the distance of any two subspaces using the most efficient method. This method doesn't “talk” (creates no text nor TeX output).

Parameters:

W - the other subspace

Returns:

the distance of the given subspaces

Throws:

IllegalArgumentException - Throws an exception if the two subspaces do not come from the same space, ie. they have a different DIM

distance

SquareRootFraction distance(Subspace W,
                            char firstLabel,
                            char secondLabel,
                            boolean verbose)

Calculates the distance of any two subspaces using the most efficient method.

Parameters:

W - the other subspace

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

Returns:

the distance of the given subspaces

Throws:

IllegalArgumentException - Throws an exception if the two subspaces do not come from the same space, ie. they have a different DIM

distanceFromParallelSubspace

SquareRootFraction distanceFromParallelSubspace(Subspace W,
                                                char firstLabel,
                                                char secondLabel,
                                                boolean verbose)

Calculates the distance of the subspace from a parallel subspace.

Parameters:

W - the other subspace, parallel to this one

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

Returns:

the distance of this subspace from the parallel subspace

distancePointAny

SquareRootFraction distancePointAny(Subspace W,
                                    char firstLabel,
                                    char secondLabel,
                                    boolean verbose)

Calculates the distance of a point from any subspace.

Parameters:

W - any subspace

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

Returns:

the distance of the point from the given subspace

Throws:

IllegalArgumentException - Throws an exception if this subspace is not a point.

distancePointHyperplane

SquareRootFraction distancePointHyperplane(Subspace W,
                                           char firstLabel,
                                           char secondLabel,
                                           boolean verbose)

Calculates the distance of a point from a hyperplane.

Parameters:

W - the hyperplane

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

Returns:

the distance of the point from the hyperplane

Throws:

IllegalArgumentException - Throws an exception if this subspace is not a point or W is not a hyperplane.

distancePointPoint

SquareRootFraction distancePointPoint(Subspace W,
                                      char firstLabel,
                                      char secondLabel,
                                      boolean verbose)

Calculates the distance of two points.

Parameters:

W - the other point

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

Returns:

the distance of the points

Throws:

IllegalArgumentException - Throws an exception if one of the spaces is not a point.

distanceUniversalUsingGram

SquareRootFraction distanceUniversalUsingGram(Subspace W,
                                              char firstLabel,
                                              char secondLabel,
                                              boolean verbose)

Calculates the distance of any two subspaces using Gram determinant.

Parameters:

W - the other subspace

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

Returns:

the distance of the given subspaces

generateRandomGeneralSubspace

static Subspace generateRandomGeneralSubspace(int dim,
                                              int DIM)

Generates a random subspace in general form.

Parameters:

dim - dimension of the subspace (must be from [0, DIM))

DIM - dimension of the superspace

Throws:

IndexOutOfBoundsException - throws an exception if dim is not from [0, DIM)

generateRandomHyperplane

static Subspace generateRandomHyperplane(int DIM)

Generates a random hyperplane in general form.

Parameters:

DIM - dimension of the superspace (ie. a number of variables)

generateRandomHyperplaneWithIntegerNorm

static Subspace generateRandomHyperplaneWithIntegerNorm(int DIM)

Generates a random hyperplane in general form. The length of the normal vector of the hyperplane will be an integer.

Parameters:

DIM - dimension of the superspace (ie. a number of variables)

generateRandomParametricSubspace

static Subspace generateRandomParametricSubspace(int dim,
                                                 int DIM)

Generates a random subspace in parametric form.

Parameters:

dim - dimension of the subspace (must be from [0, DIM))

DIM - dimension of the superspace

Throws:

IndexOutOfBoundsException - throws an exception if dim is not from [0, DIM)

generateRandomSubspacesWithGivenAngle

static Subspace[] generateRandomSubspacesWithGivenAngle(int dim1,
                                                        int dim2,
                                                        int DIM,
                                                        PiFraction angle)

Generates two random subspaces in parametric form. The subspaces satisfy that their angle is a given number.

Parameters:

dim1 - dimension of the first subspace (must be from [0, DIM))

dim2 - dimension of the second subspace (must be from [0, DIM))

DIM - dimension of the superspace

angle - angle of the subspaces

Throws:

IndexOutOfBoundsException - throws an exception if dim1 or dim2 is not from [0, DIM)

generateRandomSubspacesWithGivenDistance

static Subspace[] generateRandomSubspacesWithGivenDistance(int dim1,
                                                           int dim2,
                                                           int DIM,
                                                           Fraction dist)

Generates two random subspaces in general form. The subspaces satisfy that their distance is a given number.

Parameters:

dim1 - dimension of the first subspace (must be from [0, DIM))

dim2 - dimension of the second subspace (must be from [0, DIM))

DIM - dimension of the superspace

dist - distance of the subspaces

Throws:

IndexOutOfBoundsException - throws an exception if dim1 or dim2 is not from [0, DIM)

getAugMatrix

Matrix getAugMatrix()

Returns the augmented matrix of equation system generating this subspace.

Returns:

augmented matrix

getDim

int getDim()

Returns the dimension of the subspace.

Returns:

dimension of the subspace

getDIM

int getDIM()

Returns the dimension of the whole space (number of variables).

Returns:

dimension of the whole space

getDim

int getDim(boolean verbose)

Returns the dimension of the subspace. This method could also output the whole process of computing the dimension into text and tex files.

Parameters:

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

Returns:

dimension of the subspace

getDim

int getDim(boolean verbose,
           char label)

Returns the dimension of the subspace. This method could also output the whole process of computing the dimension into text and tex files.

Parameters:

label - label of the subspace

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

Returns:

dimension of the subspace

getOriginalForm

boolean getOriginalForm()

Makes clear if the subspace was originally input in general or in parametric form

Returns:

true if subspace was generally input in general form, false if the original form was parametric

getVecMatrix

Matrix getVecMatrix()

Returns the matrix of direction vectors (in rows).

Returns:

matrix of direction vectors

checkGeneralForm

void checkGeneralForm()

Checks if general form is already available; if it's not, it gets it. This method doesn't “talk” (creates no text nor TeX output).

checkGeneralForm

void checkGeneralForm(char label,
                      boolean verbose)

Checks if general form is already available; if it's not, it gets it.

Parameters:

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

checkParametricForm

void checkParametricForm()

Checks if parametric form is already available; if it's not, it gets it. This method doesn't “talk” (creates no text nor TeX output).

checkParametricForm

void checkParametricForm(char label,
                         boolean verbose)

Checks if parametric form is already available; if it's not, it gets it.

Parameters:

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

intersectionDiffSpace

Subspace intersectionDiffSpace(Subspace W,
                               char firstLabel,
                               char secondLabel,
                               boolean verbose,
                               boolean noPriorKnowledge)

Finds intersection of difference spaces of two subspaces.

Parameters:

W - the other subspace

Returns:

the intersection of the difference spaces

intersects

boolean intersects(Subspace W)

Checks, if this subspace intersects with the other. This method doesn't “talk” (creates no text nor TeX output).

Parameters:

W - the other subspace

Returns:

true, if the subspaces intersect, false otherwise

intersects

boolean intersects(Subspace W,
                   char firstLabel,
                   char secondLabel,
                   boolean verbose)

Checks, if this subspace intersects with the other.

Parameters:

W - the other subspace

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

Returns:

true, if the subspaces intersect, false otherwise

isGeneralFormAvailable

boolean isGeneralFormAvailable()

Confirms if the general form is available.

Returns:

true if general form is available, false otherwise

isNull

boolean isNull()

Checks, if this subspace is a null space.

Returns:

true, if dim < 0; false otherwise

isParallel

boolean isParallel(Subspace W)

Checks, if this subspace is parallel to the other. This method doesn't “talk” (creates no text nor TeX output).

Parameters:

W - the other subspace

Returns:

true, if the subspaces are parallel, false otherwise

isParallel

boolean isParallel(Subspace W,
                   boolean verbose)

Checks, if this subspace is parallel to the other.

Parameters:

W - the other subspace

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

Returns:

true, if the subspaces are parallel, false otherwise

isParametricFormAvailable

boolean isParametricFormAvailable()

Confirms if the parametric form is available.

Returns:

true if parametric form is available, false otherwise

orthogonalSupplement

Subspace orthogonalSupplement(char label,
                              boolean verbose)

Finds orthogonal supplement to a subspace.

Parameters:

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

Returns:

the orthogonal supplement to this subspace

toTeXGeneral

String toTeXGeneral()

Prints general form of this subspace formatted as TeX code.

Returns:

string formatted to general form

toTeXGeneral

String toTeXGeneral(char variable)

Prints general form of this subspace formatted as TeX code.

Parameters:

variable - label of the variables

Returns:

string formatted to general form

toTeXParametric

String toTeXParametric()

Prints parametric form of this subspace formatted as TeX code.

Returns:

string formatted to parametric form

toTextGeneral

String toTextGeneral()

Prints general form of this subspace formatted as text.

Returns:

indented string formatted to general form

toTextGeneral

String toTextGeneral(boolean verbose)

Prints general form of this subspace formatted as text.

Parameters:

verbose - determines if the output will be indented

Returns:

string formatted to general form

toTextGeneral

String toTextGeneral(boolean verbose,
                     char variable)

Prints general form of this subspace formatted as text.

Parameters:

verbose - determines if the output will be indented

variable - label of the variables

Returns:

string formatted to general form

toTextParametric

String toTextParametric()

Prints parametric form of this subspace formatted as text.

Returns:

string formatted to parametric form containing also “x_i = ”

toTextParametric

String toTextParametric(boolean verbose)

Prints parametric form of this subspace formatted as text.

Parameters:

verbose - determines if the result shall contain full output (containing “x_i = ”) = true; or short output (omitting “x_i = ”) = false

Returns:

string formatted to parametric form