Class Maths

  • All Implemented Interfaces:
    RevisionHandler

    public class Maths
    extends java.lang.Object
    implements RevisionHandler
    Utility class.

    Adapted from the JAMA package.

    Version:
    $Revision: 1.3 $
    Author:
    The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz)
    • Field Summary

      Fields 
      Modifier and Type Field Description
      static int chisqDistribution
      Distribution type: chi-squared
      static double logPSI
      The constant - log( sqrt(2 pi) )
      static int normalDistribution
      Distribution type: noraml
      static double PSI
      The constant 1 / sqrt(2 pi)
      static int undefinedDistribution
      Distribution type: undefined
    • Constructor Summary

      Constructors 
      Constructor Description
      Maths()  
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      static double dchisq​(double x)
      Returns the density of the Chi-squared distribution.
      static double dchisq​(double x, double ncp)
      Returns the density of the noncentral Chi-squared distribution.
      static DoubleVector dchisq​(double x, DoubleVector ncp)
      Returns the density of the noncentral Chi-squared distribution.
      static double dchisqLog​(double x)
      Returns the log-density of the noncentral Chi-square distribution.
      static double dchisqLog​(double x, double ncp)
      Returns the log-density value of a noncentral Chi-square distribution.
      static DoubleVector dchisqLog​(double x, DoubleVector ncp)
      Returns the log-density of a set of noncentral Chi-squared distributions.
      static double dnorm​(double x)
      Returns the density of the standard normal.
      static double dnorm​(double x, double mean, double sd)
      Returns the density value of a standard normal.
      static DoubleVector dnorm​(double x, DoubleVector mean, double sd)
      Returns the density values of a set of normal distributions with different means.
      static double dnormLog​(double x)
      Returns the log-density of the standard normal.
      static double dnormLog​(double x, double mean, double sd)
      Returns the log-density value of a standard normal.
      static DoubleVector dnormLog​(double x, DoubleVector mean, double sd)
      Returns the log-density values of a set of normal distributions with different means.
      java.lang.String getRevision()
      Returns the revision string.
      static double hypot​(double a, double b)
      sqrt(a^2 + b^2) without under/overflow.
      static double pchisq​(double x)
      Returns the cumulative probability of the Chi-squared distribution
      static double pchisq​(double x, double ncp)
      Returns the cumulative probability of the noncentral Chi-squared distribution.
      static DoubleVector pchisq​(double x, DoubleVector ncp)
      Returns the cumulative probability of a set of noncentral Chi-squared distributions.
      static double pnorm​(double x)
      Returns the cumulative probability of the standard normal.
      static double pnorm​(double x, double mean, double sd)
      Returns the cumulative probability of a normal distribution.
      static DoubleVector pnorm​(double x, DoubleVector mean, double sd)
      Returns the cumulative probability of a set of normal distributions with different means.
      static DoubleVector rchisq​(int n, double ncp, java.util.Random random)
      Generates a sample of a Chi-square distribution.
      static DoubleVector rnorm​(int n, double mean, double sd, java.util.Random random)
      Generates a sample of a normal distribution.
      static double square​(double x)
      Returns the square of a value
      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Field Detail

      • logPSI

        public static final double logPSI
        The constant - log( sqrt(2 pi) )
        See Also:
        Constant Field Values
      • undefinedDistribution

        public static final int undefinedDistribution
        Distribution type: undefined
        See Also:
        Constant Field Values
      • normalDistribution

        public static final int normalDistribution
        Distribution type: noraml
        See Also:
        Constant Field Values
      • chisqDistribution

        public static final int chisqDistribution
        Distribution type: chi-squared
        See Also:
        Constant Field Values
    • Constructor Detail

      • Maths

        public Maths()
    • Method Detail

      • hypot

        public static double hypot​(double a,
                                   double b)
        sqrt(a^2 + b^2) without under/overflow.
      • square

        public static double square​(double x)
        Returns the square of a value
        Parameters:
        x -
        Returns:
        the square
      • pnorm

        public static double pnorm​(double x)
        Returns the cumulative probability of the standard normal.
        Parameters:
        x - the quantile
      • pnorm

        public static double pnorm​(double x,
                                   double mean,
                                   double sd)
        Returns the cumulative probability of a normal distribution.
        Parameters:
        x - the quantile
        mean - the mean of the normal distribution
        sd - the standard deviation of the normal distribution.
      • pnorm

        public static DoubleVector pnorm​(double x,
                                         DoubleVector mean,
                                         double sd)
        Returns the cumulative probability of a set of normal distributions with different means.
        Parameters:
        x - the vector of quantiles
        mean - the means of the normal distributions
        sd - the standard deviation of the normal distribution.
        Returns:
        the cumulative probability
      • dnorm

        public static double dnorm​(double x)
        Returns the density of the standard normal.
        Parameters:
        x - the quantile
        Returns:
        the density
      • dnorm

        public static double dnorm​(double x,
                                   double mean,
                                   double sd)
        Returns the density value of a standard normal.
        Parameters:
        x - the quantile
        mean - the mean of the normal distribution
        sd - the standard deviation of the normal distribution.
        Returns:
        the density
      • dnorm

        public static DoubleVector dnorm​(double x,
                                         DoubleVector mean,
                                         double sd)
        Returns the density values of a set of normal distributions with different means.
        Parameters:
        x - the quantile
        mean - the means of the normal distributions
        sd - the standard deviation of the normal distribution.
        Returns:
        the density
      • dnormLog

        public static double dnormLog​(double x)
        Returns the log-density of the standard normal.
        Parameters:
        x - the quantile
        Returns:
        the density
      • dnormLog

        public static double dnormLog​(double x,
                                      double mean,
                                      double sd)
        Returns the log-density value of a standard normal.
        Parameters:
        x - the quantile
        mean - the mean of the normal distribution
        sd - the standard deviation of the normal distribution.
        Returns:
        the density
      • dnormLog

        public static DoubleVector dnormLog​(double x,
                                            DoubleVector mean,
                                            double sd)
        Returns the log-density values of a set of normal distributions with different means.
        Parameters:
        x - the quantile
        mean - the means of the normal distributions
        sd - the standard deviation of the normal distribution.
        Returns:
        the density
      • rnorm

        public static DoubleVector rnorm​(int n,
                                         double mean,
                                         double sd,
                                         java.util.Random random)
        Generates a sample of a normal distribution.
        Parameters:
        n - the size of the sample
        mean - the mean of the normal distribution
        sd - the standard deviation of the normal distribution.
        random - the random stream
        Returns:
        the sample
      • pchisq

        public static double pchisq​(double x)
        Returns the cumulative probability of the Chi-squared distribution
        Parameters:
        x - the quantile
      • pchisq

        public static double pchisq​(double x,
                                    double ncp)
        Returns the cumulative probability of the noncentral Chi-squared distribution.
        Parameters:
        x - the quantile
        ncp - the noncentral parameter
      • pchisq

        public static DoubleVector pchisq​(double x,
                                          DoubleVector ncp)
        Returns the cumulative probability of a set of noncentral Chi-squared distributions.
        Parameters:
        x - the quantile
        ncp - the noncentral parameters
      • dchisq

        public static double dchisq​(double x)
        Returns the density of the Chi-squared distribution.
        Parameters:
        x - the quantile
        Returns:
        the density
      • dchisq

        public static double dchisq​(double x,
                                    double ncp)
        Returns the density of the noncentral Chi-squared distribution.
        Parameters:
        x - the quantile
        ncp - the noncentral parameter
      • dchisq

        public static DoubleVector dchisq​(double x,
                                          DoubleVector ncp)
        Returns the density of the noncentral Chi-squared distribution.
        Parameters:
        x - the quantile
        ncp - the noncentral parameters
      • dchisqLog

        public static double dchisqLog​(double x)
        Returns the log-density of the noncentral Chi-square distribution.
        Parameters:
        x - the quantile
        Returns:
        the density
      • dchisqLog

        public static double dchisqLog​(double x,
                                       double ncp)
        Returns the log-density value of a noncentral Chi-square distribution.
        Parameters:
        x - the quantile
        ncp - the noncentral parameter
        Returns:
        the density
      • dchisqLog

        public static DoubleVector dchisqLog​(double x,
                                             DoubleVector ncp)
        Returns the log-density of a set of noncentral Chi-squared distributions.
        Parameters:
        x - the quantile
        ncp - the noncentral parameters
      • rchisq

        public static DoubleVector rchisq​(int n,
                                          double ncp,
                                          java.util.Random random)
        Generates a sample of a Chi-square distribution.
        Parameters:
        n - the size of the sample
        ncp - the noncentral parameter
        random - the random stream
        Returns:
        the sample
      • getRevision

        public java.lang.String getRevision()
        Returns the revision string.
        Specified by:
        getRevision in interface RevisionHandler
        Returns:
        the revision