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The Waikato Environment for Knowledge Analysis (WEKA), a machine learning workbench. This version represents the developer version, the "bleeding edge" of development, you could say. New functionality gets added to this version.

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/*
 * This software is a cooperative product of The MathWorks and the National
 * Institute of Standards and Technology (NIST) which has been released to the
 * public domain. Neither The MathWorks nor NIST assumes any responsibility
 * whatsoever for its use by other parties, and makes no guarantees, expressed
 * or implied, about its quality, reliability, or any other characteristic.
 */

/*
 * Maths.java
 * Copyright (C) 1999 The Mathworks and NIST
 *
 */

package weka.core.matrix;

import weka.core.RevisionHandler;
import weka.core.RevisionUtils;
import weka.core.Statistics;

import java.util.Random;

/**
 * Utility class.
 * 

* Adapted from the JAMA package. * * @author The Mathworks and NIST * @author Fracpete (fracpete at waikato dot ac dot nz) * @version $Revision: 5953 $ */ public class Maths implements RevisionHandler { /** The constant 1 / sqrt(2 pi) */ public static final double PSI = 0.3989422804014327028632; /** The constant - log( sqrt(2 pi) ) */ public static final double logPSI = -0.9189385332046726695410; /** Distribution type: undefined */ public static final int undefinedDistribution = 0; /** Distribution type: noraml */ public static final int normalDistribution = 1; /** Distribution type: chi-squared */ public static final int chisqDistribution = 2; /** * sqrt(a^2 + b^2) without under/overflow. */ public static double hypot(double a, double b) { double r; if (Math.abs(a) > Math.abs(b)) { r = b/a; r = Math.abs(a)*Math.sqrt(1+r*r); } else if (b != 0) { r = a/b; r = Math.abs(b)*Math.sqrt(1+r*r); } else { r = 0.0; } return r; } /** * Returns the square of a value * @param x * @return the square */ public static double square( double x ) { return x * x; } /* methods for normal distribution */ /** * Returns the cumulative probability of the standard normal. * @param x the quantile */ public static double pnorm( double x ) { return Statistics.normalProbability( x ); } /** * Returns the cumulative probability of a normal distribution. * @param x the quantile * @param mean the mean of the normal distribution * @param sd the standard deviation of the normal distribution. */ public static double pnorm( double x, double mean, double sd ) { if( sd <= 0.0 ) throw new IllegalArgumentException("standard deviation <= 0.0"); return pnorm( (x - mean) / sd ); } /** * Returns the cumulative probability of a set of normal distributions * with different means. * @param x the vector of quantiles * @param mean the means of the normal distributions * @param sd the standard deviation of the normal distribution. * @return the cumulative probability */ public static DoubleVector pnorm( double x, DoubleVector mean, double sd ) { DoubleVector p = new DoubleVector( mean.size() ); for( int i = 0; i < mean.size(); i++ ) { p.set( i, pnorm(x, mean.get(i), sd) ); } return p; } /** Returns the density of the standard normal. * @param x the quantile * @return the density */ public static double dnorm( double x ) { return Math.exp( - x * x / 2. ) * PSI; } /** Returns the density value of a standard normal. * @param x the quantile * @param mean the mean of the normal distribution * @param sd the standard deviation of the normal distribution. * @return the density */ public static double dnorm( double x, double mean, double sd ) { if( sd <= 0.0 ) throw new IllegalArgumentException("standard deviation <= 0.0"); return dnorm( (x - mean) / sd ); } /** Returns the density values of a set of normal distributions with * different means. * @param x the quantile * @param mean the means of the normal distributions * @param sd the standard deviation of the normal distribution. * @return the density */ public static DoubleVector dnorm( double x, DoubleVector mean, double sd ) { DoubleVector den = new DoubleVector( mean.size() ); for( int i = 0; i < mean.size(); i++ ) { den.set( i, dnorm(x, mean.get(i), sd) ); } return den; } /** Returns the log-density of the standard normal. * @param x the quantile * @return the density */ public static double dnormLog( double x ) { return logPSI - x * x / 2.; } /** Returns the log-density value of a standard normal. * @param x the quantile * @param mean the mean of the normal distribution * @param sd the standard deviation of the normal distribution. * @return the density */ public static double dnormLog( double x, double mean, double sd ) { if( sd <= 0.0 ) throw new IllegalArgumentException("standard deviation <= 0.0"); return - Math.log(sd) + dnormLog( (x - mean) / sd ); } /** Returns the log-density values of a set of normal distributions with * different means. * @param x the quantile * @param mean the means of the normal distributions * @param sd the standard deviation of the normal distribution. * @return the density */ public static DoubleVector dnormLog( double x, DoubleVector mean, double sd ) { DoubleVector denLog = new DoubleVector( mean.size() ); for( int i = 0; i < mean.size(); i++ ) { denLog.set( i, dnormLog(x, mean.get(i), sd) ); } return denLog; } /** * Generates a sample of a normal distribution. * @param n the size of the sample * @param mean the mean of the normal distribution * @param sd the standard deviation of the normal distribution. * @param random the random stream * @return the sample */ public static DoubleVector rnorm( int n, double mean, double sd, Random random ) { if( sd < 0.0) throw new IllegalArgumentException("standard deviation < 0.0"); if( sd == 0.0 ) return new DoubleVector( n, mean ); DoubleVector v = new DoubleVector( n ); for( int i = 0; i < n; i++ ) v.set( i, (random.nextGaussian() + mean) / sd ); return v; } /* methods for Chi-square distribution */ /** Returns the cumulative probability of the Chi-squared distribution * @param x the quantile */ public static double pchisq( double x ) { double xh = Math.sqrt( x ); return pnorm( xh ) - pnorm( -xh ); } /** Returns the cumulative probability of the noncentral Chi-squared * distribution. * @param x the quantile * @param ncp the noncentral parameter */ public static double pchisq( double x, double ncp ) { double mean = Math.sqrt( ncp ); double xh = Math.sqrt( x ); return pnorm( xh - mean ) - pnorm( -xh - mean ); } /** Returns the cumulative probability of a set of noncentral Chi-squared * distributions. * @param x the quantile * @param ncp the noncentral parameters */ public static DoubleVector pchisq( double x, DoubleVector ncp ) { int n = ncp.size(); DoubleVector p = new DoubleVector( n ); double mean; double xh = Math.sqrt( x ); for( int i = 0; i < n; i++ ) { mean = Math.sqrt( ncp.get(i) ); p.set( i, pnorm( xh - mean ) - pnorm( -xh - mean ) ); } return p; } /** Returns the density of the Chi-squared distribution. * @param x the quantile * @return the density */ public static double dchisq( double x ) { if( x == 0.0 ) return Double.POSITIVE_INFINITY; double xh = Math.sqrt( x ); return dnorm( xh ) / xh; } /** Returns the density of the noncentral Chi-squared distribution. * @param x the quantile * @param ncp the noncentral parameter */ public static double dchisq( double x, double ncp ) { if( ncp == 0.0 ) return dchisq( x ); double xh = Math.sqrt( x ); double mean = Math.sqrt( ncp ); return (dnorm( xh - mean ) + dnorm( -xh - mean)) / (2 * xh); } /** Returns the density of the noncentral Chi-squared distribution. * @param x the quantile * @param ncp the noncentral parameters */ public static DoubleVector dchisq( double x, DoubleVector ncp ) { int n = ncp.size(); DoubleVector d = new DoubleVector( n ); double xh = Math.sqrt( x ); double mean; for( int i = 0; i < n; i++ ) { mean = Math.sqrt( ncp.get(i) ); if( ncp.get(i) == 0.0 ) d.set( i, dchisq( x ) ); else d.set( i, (dnorm( xh - mean ) + dnorm( -xh - mean)) / (2 * xh) ); } return d; } /** Returns the log-density of the noncentral Chi-square distribution. * @param x the quantile * @return the density */ public static double dchisqLog( double x ) { if( x == 0.0) return Double.POSITIVE_INFINITY; double xh = Math.sqrt( x ); return dnormLog( xh ) - Math.log( xh ); } /** Returns the log-density value of a noncentral Chi-square distribution. * @param x the quantile * @param ncp the noncentral parameter * @return the density */ public static double dchisqLog( double x, double ncp ) { if( ncp == 0.0 ) return dchisqLog( x ); double xh = Math.sqrt( x ); double mean = Math.sqrt( ncp ); return Math.log( dnorm( xh - mean ) + dnorm( -xh - mean) ) - Math.log(2 * xh); } /** Returns the log-density of a set of noncentral Chi-squared * distributions. * @param x the quantile * @param ncp the noncentral parameters */ public static DoubleVector dchisqLog( double x, DoubleVector ncp ) { DoubleVector dLog = new DoubleVector( ncp.size() ); double xh = Math.sqrt( x ); double mean; for( int i = 0; i < ncp.size(); i++ ) { mean = Math.sqrt( ncp.get(i) ); if( ncp.get(i) == 0.0 ) dLog.set( i, dchisqLog( x ) ); else dLog.set( i, Math.log( dnorm( xh - mean ) + dnorm( -xh - mean) ) - Math.log(2 * xh) ); } return dLog; } /** * Generates a sample of a Chi-square distribution. * @param n the size of the sample * @param ncp the noncentral parameter * @param random the random stream * @return the sample */ public static DoubleVector rchisq( int n, double ncp, Random random ) { DoubleVector v = new DoubleVector( n ); double mean = Math.sqrt( ncp ); double x; for( int i = 0; i < n; i++ ) { x = random.nextGaussian() + mean; v.set( i, x * x ); } return v; } /** * Returns the revision string. * * @return the revision */ public String getRevision() { return RevisionUtils.extract("$Revision: 5953 $"); } }





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