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## weka.classifiers.functions.pace
Class Maths

    java.lang.Object
      weka.classifiers.functions.pace.Maths

    public class Maths

extends java.lang.Object

Class for some utility mathematical or statistical functions.

Version:
  $Revision: 1.2.2.1 $
Author:
  Yong Wang

Field Summary
`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
`Maths()`

Method Summary
`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.
`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

### PSI

    public static final double PSI

  The constant 1 / sqrt(2 pi)

  See Also:
    Constant Field Values

### 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

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