MathUtil (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

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de.lmu.ifi.dbs.elki.math
Class MathUtil

java.lang.Object
  de.lmu.ifi.dbs.elki.math.MathUtil

public final class MathUtil
extends Object
extends Object

A collection of math related utility functions.

Field Summary
`(package private) static double[]`	`ERFAPP_A` Coefficients for erf approximation.
`(package private) static double[]`	`ERFAPP_B` Coefficients for erf approximation.
`(package private) static double[]`	`ERFAPP_C` Coefficients for erf approximation.
`(package private) static double[]`	`ERFAPP_D` Coefficients for erf approximation.
`(package private) static double[]`	`ERFAPP_P` Coefficients for erf approximation.
`(package private) static double[]`	`ERFAPP_Q` Coefficients for erf approximation.
`(package private) static double[]`	`ERFINV_A` Coefficients for erfinv approximation, rational version
`(package private) static double[]`	`ERFINV_B` Coefficients for erfinv approximation, rational version
`(package private) static double[]`	`ERFINV_C` Coefficients for erfinv approximation, rational version
`(package private) static double[]`	`ERFINV_D` Coefficients for erfinv approximation, rational version
`(package private) static double[]`	`LANCZOS` LANCZOS-Coefficients for Gamma approximation.
`(package private) static double`	`NUM_PRECISION` Numerical precision to use
`static double`	`ONE_BY_SQRTPI` Precomputed value of 1 / sqrt(pi)
`(package private) static double`	`P_HIGH` Treshold for switching nethods for erfinv approximation
`(package private) static double`	`P_LOW` Treshold for switching nethods for erfinv approximation
`static double`	`SQRT2` Square root of 2.
`static double`	`SQRTHALF` Square root of 0.5 == 1 / Sqrt(2)
`static double`	`SQRTTWOPI` Squre root of two times Pi.
`static double`	`TWOPI` Two times Pi.

Constructor Summary
`private`	`MathUtil()` Fake constructor for static class.

Method Summary
`static double`	`approximateBinomialCoefficient(int n, int k)` Binomial coefficent, also known as "n choose k")
`static double`	`approximateFactorial(int n)` Compute the Factorial of n, often written as `c!`
`static long`	`binomialCoefficient(long n, long k)` Binomial coefficient, also known as "n choose k".
`static double`	`cosineSimilarity(Vector v1, Vector v2)` Compute the cosine similarity for two vectors.
`static double`	`deg2rad(double deg)` Convert Degree to Radians
`static double`	`erf(double x)` Error function for Gaussian distributions = Normal distributions.
`static double`	`erfc(double x)` Complementary error function for Gaussian distributions = Normal distributions.
`static double`	`erfinv(double x)` Inverse error function.
`static BigInteger`	`factorial(BigInteger n)` Compute the Factorial of n, often written as `c!`
`static long`	`factorial(int n)` Compute the Factorial of n, often written as `c!`
`static double`	`hypotenuse(double a, double b)` Computes the square root of the sum of the squared arguments without under or overflow.
`static double`	`latlngDistance(double lat1, double lon1, double lat2, double lon2)` Compute the approximate on-earth-surface distance of two points.
`static double`	`logGamma(double x)` Compute logGamma.
`static double`	`mahalanobisDistance(Matrix weightMatrix, Vector o1_minus_o2)` Compute the Mahalanobis distance using the given weight matrix
`static double`	`normalCDF(double x, double mu, double sigma)` Cumulative probability density function (CDF) of a normal distribution.
`static double`	`normalPDF(double x, double mu, double sigma)` Probability density function of the normal distribution.
`static double`	`normalProbit(double x, double mu, double sigma)` Inverse cumulative probability density function (probit) of a normal distribution.
`static double`	`pearsonCorrelationCoefficient(double[] x, double[] y)` Provides the Pearson product-moment correlation coefficient for two FeatureVectors.
`static double`	`pearsonCorrelationCoefficient(NumberVector<?,?> x, NumberVector<?,?> y)` Provides the Pearson product-moment correlation coefficient for two FeatureVectors.
`static double`	`rad2deg(double rad)` Radians to Degree
`static double[]`	`randomDoubleArray(int len)` Produce an array of random numbers in [0:1]
`static double[]`	`randomDoubleArray(int len, Random r)` Produce an array of random numbers in [0:1]
`static double`	`regularizedGammaP(double a, double x)` Returns the regularized gamma function P(a, x).
`static double`	`regularizedGammaQ(double a, double x)` Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
`static double`	`standardNormalProbit(double d)` Approximate the inverse error function for normal distributions.
`static long`	`sumFirstIntegers(long i)` Compute the sum of the i first integers.
`static double`	`weightedPearsonCorrelationCoefficient(double[] x, double[] y, double[] weights)` Provides the Pearson product-moment correlation coefficient for two FeatureVectors.
`static double`	`weightedPearsonCorrelationCoefficient(NumberVector<?,?> x, NumberVector<?,?> y, double[] weights)` Provides the Pearson product-moment correlation coefficient for two FeatureVectors.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

TWOPI

public static final double TWOPI

Two times Pi.

See Also:: Constant Field Values

SQRTTWOPI

public static final double SQRTTWOPI

Squre root of two times Pi.

SQRT2

public static final double SQRT2

Square root of 2.

SQRTHALF

public static final double SQRTHALF

Square root of 0.5 == 1 / Sqrt(2)

ONE_BY_SQRTPI

public static final double ONE_BY_SQRTPI

Precomputed value of 1 / sqrt(pi)