agi.foundation

(agi.foundation.core-2024r3.jar)

Class SphericalDescriptiveStatistics

java.lang.Object

agi.foundation.SphericalDescriptiveStatistics

public final class SphericalDescriptiveStatistics
extends Object

Provides descriptive statistic methods suited for spherical data. Since the spherical surface is embedded in Cartesian space, the data set is provided as a list of UnitCartesian directions locating the data points on the unit sphere. The algorithms are based on the mathematics found in "Directional Statistics" by Mardia and Jupp.

Method Summary

Modifier and Type	Method and Description
static double	dispersionAboutPosition(List<UnitCartesian> dataList, UnitSpherical position) Calculates the dispersion about a given input position.
static UnitSpherical	meanDirection(List<UnitCartesian> dataList) Calculates the mean direction of a list of data.
static double	meanResultantLength(List<UnitCartesian> dataList) Calculates the mean resultant length of a list of data.
static Spherical	meanVector(List<UnitCartesian> dataList) Computes the mean vector.
static UnitSpherical	medianDirection(List<UnitCartesian> dataList) Calculates the median direction of the data by using a simplex heuristic optimizer.
static UnitSpherical	medianDirection(List<UnitCartesian> dataList, SphericalMedianCalculationMethod calculationMethod) Calculates the median direction of the data by using a simplex heuristic optimizer.
static UnitSpherical	medianDirection(List<UnitCartesian> dataList, SphericalMedianCalculationMethod calculationMethod, MultivariableFunctionSolverResults<MultivariableFunctionSolverIterationResults>[] results) Calculates the median direction of the data by using a simplex heuristic optimizer.
static Matrix3By3Symmetric	scatterMatrix(List<UnitCartesian> dataList) Calculates the scatter matrix based upon the input data.
static double	variance(List<UnitCartesian> dataList) Calculates the variance of a list of data.

Methods inherited from class java.lang.Object

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

Method Detail

meanVector

@Nonnull
public static Spherical meanVector(@Nonnull
                                             List<UnitCartesian> dataList)

Computes the mean vector.

Parameters:

dataList - The list of data to use to calculate the mean vector.

Returns:

The mean vector.

Throws:

ArgumentNullException - Thrown when dataList is null.

ArgumentException - Thrown when dataList is empty.

meanResultantLength

public static double meanResultantLength(@Nonnull
                                         List<UnitCartesian> dataList)

Calculates the mean resultant length of a list of data.

The output range is 0 ≤ R ≤ 1.

Parameters:

dataList - The list of data to use to calculate the mean resultant length.

Returns:

The mean resultant length.

meanDirection

@Nonnull
public static UnitSpherical meanDirection(@Nonnull
                                                    List<UnitCartesian> dataList)

Calculates the mean direction of a list of data.

Parameters:

dataList - The list of data to use to calculate the mean direction.

Returns:

The mean direction.

medianDirection

@Nonnull
public static UnitSpherical medianDirection(@Nonnull
                                                      List<UnitCartesian> dataList)

Calculates the median direction of the data by using a simplex heuristic optimizer. The calculation method of the optimizer defaults to SphericalMedianCalculationMethod.NORMALIZED_SPATIAL_MEDIAN which minimizes the normalized spatial median function.

Parameters:

dataList - The list of data to use to calculate the median direction.

Returns:

The median direction.

medianDirection

@Nonnull
public static UnitSpherical medianDirection(@Nonnull
                                                      List<UnitCartesian> dataList,
                                                      @Nonnull
                                                      SphericalMedianCalculationMethod calculationMethod)

Calculates the median direction of the data by using a simplex heuristic optimizer. The optimizer minimizes the normalized spatial median function or the embedded R^3 arc distance function to compute the median.

Parameters:

dataList - The list of data to use to calculate the median direction.

calculationMethod - The function to minimize in order to calculate the spherical median. See SphericalMedianCalculationMethod for more information.

Returns:

The median direction.

medianDirection

@Nonnull
public static UnitSpherical medianDirection(@Nonnull
                                                      List<UnitCartesian> dataList,
                                                      @Nonnull
                                                      SphericalMedianCalculationMethod calculationMethod,
                                                      @Nonnull
                                                      MultivariableFunctionSolverResults<MultivariableFunctionSolverIterationResults>[] results)

Calculates the median direction of the data by using a simplex heuristic optimizer. The optimizer minimizes the normalized spatial median function or the embedded R^3 arc distance function to compute the median.

Parameters:

dataList - The list of data to use to calculate the median direction.

calculationMethod - The function to minimize in order to calculate the spherical median. See SphericalMedianCalculationMethod for more information.

results - The results of the optimizer. This data structure contains any warnings from the optimizer.

Returns:

The median direction.

variance

public static double variance(@Nonnull
                              List<UnitCartesian> dataList)

Calculates the variance of a list of data.

The output range is 0 ≤ V ≤ 1.

Parameters:

dataList - The list of data to use to calculate the variance.

Returns:

The variance.

dispersionAboutPosition

public static double dispersionAboutPosition(@Nonnull
                                             List<UnitCartesian> dataList,
                                             @Nonnull
                                             UnitSpherical position)

Calculates the dispersion about a given input position.

Parameters:

dataList - The list of data to use to calculate the dispersion.

position - The position about which the dispersion should be calculated.

Returns:

The dispersion about the given input position.

scatterMatrix

@Nonnull
public static Matrix3By3Symmetric scatterMatrix(@Nonnull
                                                          List<UnitCartesian> dataList)

Calculates the scatter matrix based upon the input data.

Parameters:

dataList - The list of data to use to calculate the scatter matrix.

Returns:

The scatter matrix, presented in Cartesian space.