edu.stanford.math.plex4.utility

Class MathUtility

java.lang.Object

edu.stanford.math.plex4.utility.MathUtility

public class MathUtility
extends java.lang.Object

This class contains various static utility functions relating to math.

Author:

Andrew Tausz

Constructor Summary

Constructors

Constructor and Description
MathUtility()

Method Summary

Methods

Modifier and Type	Method and Description
static double	absApproximation(double x, double M)
static double	dotProduct(double[] a, double[] b)
static long	euclideanGcd(long a, long b)
static int	floorLog2(int input) This function returns the floor of the base-2 logarithm of the input.
static double	gaussianDensity(double x) This function evaluates the standard gaussian density with mean 0 and variance 1.
static double	gaussianDensity(double x, double mean, double standardDeviation) This function evaluates the 1-dimensional gaussian density function with specified mean and standard deviation.
static double	greatCircleDistance(double[] x, double[] y) This function returns the great circle distance between two points on the unit sphere given their rectangular coordinates.
static double	greatCircleDistance(double latitude1, double longitude1, double latitude2, double longitude2) This function returns the great circle distance (geodesic distance) between two points on the unit sphere.
static double	huberPenaltyFunction(double x, double M) This function computes the Huber penalty function of an input.
static double	maxApproximation(double x, double y, double M)
static int	maxLog2(int input)
static int	minLog2(int input)
static int[]	modularInverses(int p) This function returns the multiplicative inverses of the integers [0, 1, ..., p-1] in mod p arithmetic.
static int	signum(double l)
static int	signum(long l)

Methods inherited from class java.lang.Object

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

Constructor Detail

MathUtility

public MathUtility()

Method Detail

euclideanGcd

public static long euclideanGcd(long a,
                long b)

signum

public static int signum(long l)

signum

public static int signum(double l)

modularInverses

public static int[] modularInverses(int p)

This function returns the multiplicative inverses of the integers [0, 1, ..., p-1] in mod p arithmetic. Note that the 0-th index is simply set to 0 for convenience so that the inverse of n is in the n-th component of the returned array. TODO: This is an inefficient way to compute the inverses (it was inherited from the original Plex implementation). It should be rewritten.

Parameters:

p -

Returns:

an array containing the multiplicative inverses in the field Z/pZ

floorLog2

public static int floorLog2(int input)

This function returns the floor of the base-2 logarithm of the input. The input must be strictly positive.

Parameters:

input - the input argument

Returns:

the floor of the base-2 logarithm of the input

minLog2

public static int minLog2(int input)

maxLog2

public static int maxLog2(int input)

greatCircleDistance

public static double greatCircleDistance(double latitude1,
                         double longitude1,
                         double latitude2,
                         double longitude2)

This function returns the great circle distance (geodesic distance) between two points on the unit sphere.

Parameters:

latitude1 - the latitude of the first point

longitude1 - the longitude of the first point

latitude2 - the latitude of the second point

longitude2 - the longitude of the second point

Returns:

the geodesic distance between the two input points

greatCircleDistance

public static double greatCircleDistance(double[] x,
                         double[] y)

This function returns the great circle distance between two points on the unit sphere given their rectangular coordinates.

Parameters:

x - the first point

y - the second point

Returns:

the distance between x and y along the unit sphere

huberPenaltyFunction

public static double huberPenaltyFunction(double x,
                          double M)

This function computes the Huber penalty function of an input. The Huber penalty function is equal to x^2 for |x| <= M, and linear for |x| > M.

Parameters:

x - the value at which to compute the Huber penalty function

M - the parameter which determines the linear/quadratic region

Returns:

The Huber penalty function at x

absApproximation

public static double absApproximation(double x,
                      double M)

maxApproximation

public static double maxApproximation(double x,
                      double y,
                      double M)

gaussianDensity

public static double gaussianDensity(double x)

This function evaluates the standard gaussian density with mean 0 and variance 1.

Parameters:

x - the point to evaluate at

Returns:

the standard normal density evaluated at x

gaussianDensity

public static double gaussianDensity(double x,
                     double mean,
                     double standardDeviation)

This function evaluates the 1-dimensional gaussian density function with specified mean and standard deviation.

Parameters:

x - the point to evaluate at

mean - the mean of the distribution

standardDeviation - the standard deviation of the distribution

Returns:

the gaussian density evaluated at x

dotProduct

public static double dotProduct(double[] a,
                double[] b)