de.lmu.ifi.dbs.elki.data
Class ParameterizationFunction

java.lang.Object
  de.lmu.ifi.dbs.elki.logging.AbstractLoggable
      de.lmu.ifi.dbs.elki.data.AbstractDatabaseObject
          de.lmu.ifi.dbs.elki.data.NumberVector<V,N>
              de.lmu.ifi.dbs.elki.data.RealVector<DoubleVector,Double>
                  de.lmu.ifi.dbs.elki.data.DoubleVector
                      de.lmu.ifi.dbs.elki.data.ParameterizationFunction

All Implemented Interfaces:

WekaObject<WekaNumericAttribute>, DatabaseObject, FeatureVector<DoubleVector,Double>, SpatialComparable, SpatialObject, Loggable

public class ParameterizationFunction
extends DoubleVector

A parameterization function decribes all lines in a d-dimensional feature space intersecting in one point p. A single line in d-dimensional space is uniquely determined by a translation vector p and (d-1) angles alpha_i belonging to the normal vector n.

Author:

Elke Achtert

Nested Class Summary

static class

ParameterizationFunction.ExtremumType Available types for the global extremum.

Field Summary

private double[]	alphaExtremum Holds the alpha values of the global extremum.
static double	DELTA A small number to handle numbers near 0 as 0.
private ParameterizationFunction.ExtremumType	extremumType Holds the type of the global extremum.

Fields inherited from class de.lmu.ifi.dbs.elki.data.NumberVector

ATTRIBUTE_SEPARATOR

Fields inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debug

Constructor Summary

ParameterizationFunction(double[] p)
Provides a new parameterization function decribing all lines in a d-dimensional feature space intersecting in one point p.

Method Summary

private double	determineAlphaMax(int n, double[] alpha_max, HyperBoundingBox interval) Determines the n-th alpha value where this function has a maximum in the specified interval.
private double	determineAlphaMin(int n, double[] alpha_min, HyperBoundingBox interval) Determines the n-th alpha value where this function has a minimum in the specified interval.
HyperBoundingBox	determineAlphaMinMax(HyperBoundingBox interval) Determines the alpha values where this function has a minumum and maximum value in the given interval.
private void	determineGlobalExtremum() Determines the global extremum of this parameterization function.
private void	determineGlobalExtremumType() Determines the type od the global extremum.
private double	extremum_alpha_n(int n, double[] alpha) Determines the value for alpha_n where this function has a (local) extremum.
private ParameterizationFunction.ExtremumType	extremumType(int n, double[] alpha_extreme, HyperBoundingBox interval) Returns the type of the extremum at the specified alpha values.
double	function(double[] alpha) Computes the function value at alpha.
double[]	getGlobalAlphaExtremum() Returns the alpha values of the extremum point in interval [(0,...,0), (Pi,...
double	getGlobalExtremum() Returns the global extremum of this function in interval [0,...
ParameterizationFunction.ExtremumType	getGlobalExtremumType() Returns the type of the global extremum in interval [0,...
DoubleVector	newInstance(double[] values) Returns a new RealVector of N for the given values.
private double	sinusProduct(int start, int end, double[] alpha) Computes the product of all sinus values of the specified angles from start to end index.
String	toString() Returns a string representation of the object.
String	toString(int offset) Returns a string representation of the object with the specified offset.

Methods inherited from class de.lmu.ifi.dbs.elki.data.DoubleVector

getColumnVector, getDimensionality, getRowVector, getValue, multiplicate, negativeVector, nullVector, plus, randomInstance, randomInstance

Methods inherited from class de.lmu.ifi.dbs.elki.data.NumberVector

equals, getAttributes, getMax, getMin, newInstance

Methods inherited from class de.lmu.ifi.dbs.elki.data.AbstractDatabaseObject

getID, setID

Methods inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debugFine, debugFiner, debugFinest, exception, message, progress, progress, progress, verbose, verbose, warning

Methods inherited from class java.lang.Object

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

Methods inherited from interface de.lmu.ifi.dbs.elki.data.DatabaseObject

getID, setID

Methods inherited from interface de.lmu.ifi.dbs.elki.index.tree.spatial.SpatialObject

getID

Field Detail

DELTA

public static final double DELTA

A small number to handle numbers near 0 as 0.

See Also:

Constant Field Values

alphaExtremum

private double[] alphaExtremum

Holds the alpha values of the global extremum.

extremumType

private ParameterizationFunction.ExtremumType extremumType

Holds the type of the global extremum.

Constructor Detail

ParameterizationFunction

public ParameterizationFunction(double[] p)

Provides a new parameterization function decribing all lines in a d-dimensional feature space intersecting in one point p.

Parameters:

p - the values of the point p

Method Detail

newInstance

public DoubleVector newInstance(double[] values)

Description copied from class: RealVector

Returns a new RealVector of N for the given values.

Overrides:

newInstance in class DoubleVector

Parameters:

values - the values of the featureVector

Returns:

a new DoubleVector with the specified values

See Also:

RealVector.newInstance(double[])

function

public double function(double[] alpha)

Computes the function value at alpha.

Parameters:

alpha - the values of the d-1 angles

Returns:

the function value at alpha

determineAlphaMinMax

public HyperBoundingBox determineAlphaMinMax(HyperBoundingBox interval)

Determines the alpha values where this function has a minumum and maximum value in the given interval.

Parameters:

interval - the hyper bounding box defining the interval

Returns:

he alpha values where this function has a minumum and maximum value in the given interval

extremumType

private ParameterizationFunction.ExtremumType extremumType(int n,
                                                           double[] alpha_extreme,
                                                           HyperBoundingBox interval)

Returns the type of the extremum at the specified alpha values.

Parameters:

n - the index until the alpha values are computed

alpha_extreme - the already computed alpha values

interval - the hyper bounding box defining the interval in which the extremum occurs

Returns:

the type of the extremum at the specified alpha_values

determineAlphaMin

private double determineAlphaMin(int n,
                                 double[] alpha_min,
                                 HyperBoundingBox interval)

Determines the n-th alpha value where this function has a minimum in the specified interval.

Parameters:

n - the index of the alpha value to be determined

alpha_min - the already computed alpha values

interval - the hyper bounding box defining the interval

Returns:

the n-th alpha value where this function has a minimum in the specified interval

determineAlphaMax

private double determineAlphaMax(int n,
                                 double[] alpha_max,
                                 HyperBoundingBox interval)

Determines the n-th alpha value where this function has a maximum in the specified interval.

Parameters:

n - the index of the alpha value to be determined

alpha_max - the already computed alpha values

interval - the hyper bounding box defining the interval

Returns:

the n-th alpha value where this function has a minimum in the specified interval

getGlobalAlphaExtremum

public double[] getGlobalAlphaExtremum()

Returns the alpha values of the extremum point in interval [(0,...,0), (Pi,...,Pi)].

Returns:

the alpha values of the extremum

getGlobalExtremum

public double getGlobalExtremum()

Returns the global extremum of this function in interval [0,...,Pi)^d-1.

Returns:

the global extremum

getGlobalExtremumType

public ParameterizationFunction.ExtremumType getGlobalExtremumType()

Returns the type of the global extremum in interval [0,...,Pi)^d-1.

Returns:

the type of the global extremum

toString

public String toString()

Returns a string representation of the object.

Specified by:

toString in interface FeatureVector<DoubleVector,Double>

Overrides:

toString in class DoubleVector

Returns:

a string representation of the object.

See Also:

FeatureVector.toString()

toString

public String toString(int offset)

Returns a string representation of the object with the specified offset.

Parameters:

offset - the offset of the string representation

Returns:

a string representation of the object.

sinusProduct

private double sinusProduct(int start,
                            int end,
                            double[] alpha)

Computes the product of all sinus values of the specified angles from start to end index.

Parameters:

start - the index to start

end - the index to end

alpha - the array of angles

Returns:

the product of all sinus values of the specified angles from start to end index

determineGlobalExtremum

private void determineGlobalExtremum()

Determines the global extremum of this parameterization function.

determineGlobalExtremumType

private void determineGlobalExtremumType()

Determines the type od the global extremum.

extremum_alpha_n

private double extremum_alpha_n(int n,
                                double[] alpha)

Determines the value for alpha_n where this function has a (local) extremum.

Parameters:

n - the index of the angle

alpha - the already determined alpha_values for the extremum

Returns:

the value for alpha_n where this function has a (local) extremum