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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.
/*
* 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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