//******************************************************************************
//
// File: XYZSeries.java
// Package: edu.rit.numeric
// Unit: Class edu.rit.numeric.XYZSeries
//
// This Java source file is copyright (C) 2011 by Alan Kaminsky. All rights
// reserved. For further information, contact the author, Alan Kaminsky, at
// ark@cs.rit.edu.
//
// This Java source file is part of the Parallel Java Library ("PJ"). PJ is free
// software; you can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// PJ is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
// A PARTICULAR PURPOSE. See the GNU General Public License for more details.
//
// A copy of the GNU General Public License is provided in the file gpl.txt. You
// may also obtain a copy of the GNU General Public License on the World Wide
// Web at http://www.gnu.org/licenses/gpl.html.
//
//******************************************************************************
package edu.rit.numeric;
import java.io.PrintStream;
import java.io.PrintWriter;
/**
* Class XYZSeries is the abstract base class for a series of (x,y,z)
* triples of real values (type double).
*
* @author Alan Kaminsky
* @version 20-Jul-2011
*/
public abstract class XYZSeries
{
// Exported helper classes.
/**
* Class XYZSeries.Regression holds the results of a regression on an
* {@linkplain XYZSeries}. The x and y values are the data
* points; each z value is the standard deviation of the measurement
* error in the corresponding y value, assuming the measurement error
* distribution is a zero-mean Gaussian.
*
* @author Alan Kaminsky
* @version 16-Mar-2010
*/
public static class Regression
{
/**
* Intercept a.
*/
public final double a;
/**
* Slope b.
*/
public final double b;
/**
* Variance in the estimate of a.
*/
public final double var_a;
/**
* Variance in the estimate of b.
*/
public final double var_b;
/**
* Covariance in the estimates of a and b.
*/
public final double cov_ab;
/**
* Coefficient of correlation between the uncertainty in a and
* the uncertainty in b.
*/
public final double r_ab;
/**
* Chi-square merit function of the fit between the model (this
* Regression object) and the data (original XYZSeries object).
*/
public final double chi2;
/**
* Significance of χ2.
*/
public final double significance;
/**
* Construct a new Regression object.
*/
private Regression
(double a,
double b,
double var_a,
double var_b,
double cov_ab,
double r_ab,
double chi2,
double significance)
{
this.a = a;
this.b = b;
this.var_a = var_a;
this.var_b = var_b;
this.cov_ab = cov_ab;
this.r_ab = r_ab;
this.chi2 = chi2;
this.significance = significance;
}
}
/**
* Class XYZSeries.XSeriesView provides a series view of the X values in an
* XYZ series.
*
* @author Alan Kaminsky
* @version 12-Jun-2007
*/
private static class XSeriesView
extends Series
{
private XYZSeries outer;
public XSeriesView
(XYZSeries outer)
{
this.outer = outer;
}
public int length()
{
return outer.length();
}
public double x
(int i)
{
return outer.x (i);
}
}
/**
* Class XYZSeries.YSeriesView provides a series view of the Y values in an
* XYZ series.
*
* @author Alan Kaminsky
* @version 12-Jun-2007
*/
private static class YSeriesView
extends Series
{
private XYZSeries outer;
public YSeriesView
(XYZSeries outer)
{
this.outer = outer;
}
public int length()
{
return outer.length();
}
public double x
(int i)
{
return outer.y (i);
}
}
/**
* Class XYZSeries.ZSeriesView provides a series view of the Z values in an
* XYZ series.
*
* @author Alan Kaminsky
* @version 12-Jun-2007
*/
private static class ZSeriesView
extends Series
{
private XYZSeries outer;
public ZSeriesView
(XYZSeries outer)
{
this.outer = outer;
}
public int length()
{
return outer.length();
}
public double x
(int i)
{
return outer.z (i);
}
}
/**
* Class XYZSeries.XYSeriesView provides an XY series view of the X and Y
* values in an XYZ series.
*
* @author Alan Kaminsky
* @version 13-Oct-2007
*/
private static class XYSeriesView
extends XYSeries
{
private XYZSeries outer;
public XYSeriesView
(XYZSeries outer)
{
this.outer = outer;
}
public int length()
{
return outer.length();
}
public double x
(int i)
{
return outer.x (i);
}
public double y
(int i)
{
return outer.y (i);
}
}
// Exported constructors.
/**
* Construct a new XYZ series.
*/
public XYZSeries()
{
}
// Exported operations.
/**
* Returns the number of values in this series.
*
* @return Length.
*/
public abstract int length();
/**
* Determine if this series is empty.
*
* @return True if this series is empty (length = 0), false otherwise.
*/
public boolean isEmpty()
{
return length() == 0;
}
/**
* Returns the given X value in this series.
*
* @param i Index.
*
* @return The X value in this series at index i.
*
* @exception ArrayIndexOutOfBoundsException
* (unchecked exception) Thrown if i is not in the range
* 0 .. length()-1.
*/
public abstract double x
(int i);
/**
* Returns the given Y value in this series.
*
* @param i Index.
*
* @return The Y value in this series at index i.
*
* @exception ArrayIndexOutOfBoundsException
* (unchecked exception) Thrown if i is not in the range
* 0 .. length()-1.
*/
public abstract double y
(int i);
/**
* Returns the given Z value in this series.
*
* @param i Index.
*
* @return The Z value in this series at index i.
*
* @exception ArrayIndexOutOfBoundsException
* (unchecked exception) Thrown if i is not in the range
* 0 .. length()-1.
*/
public abstract double z
(int i);
/**
* Returns the minimum X value in this series.
*
* @return Minimum X value.
*/
public double minX()
{
int n = length();
double result = Double.POSITIVE_INFINITY;
for (int i = 0; i < n; ++ i)
{
result = Math.min (result, x(i));
}
return result;
}
/**
* Returns the maximum X value in this series.
*
* @return Maximum X value.
*/
public double maxX()
{
int n = length();
double result = Double.NEGATIVE_INFINITY;
for (int i = 0; i < n; ++ i)
{
result = Math.max (result, x(i));
}
return result;
}
/**
* Returns the minimum Y value in this series.
*
* @return Minimum Y value.
*/
public double minY()
{
int n = length();
double result = Double.POSITIVE_INFINITY;
for (int i = 0; i < n; ++ i)
{
result = Math.min (result, y(i));
}
return result;
}
/**
* Returns the maximum Y value in this series.
*
* @return Maximum Y value.
*/
public double maxY()
{
int n = length();
double result = Double.NEGATIVE_INFINITY;
for (int i = 0; i < n; ++ i)
{
result = Math.max (result, y(i));
}
return result;
}
/**
* Returns the minimum Z value in this series.
*
* @return Minimum Z value.
*/
public double minZ()
{
int n = length();
double result = Double.POSITIVE_INFINITY;
for (int i = 0; i < n; ++ i)
{
result = Math.min (result, z(i));
}
return result;
}
/**
* Returns the maximum Z value in this series.
*
* @return Maximum Z value.
*/
public double maxZ()
{
int n = length();
double result = Double.NEGATIVE_INFINITY;
for (int i = 0; i < n; ++ i)
{
result = Math.max (result, z(i));
}
return result;
}
/**
* Returns the linear regression of the (x,y) values in this XYZ
* series. Each z value is the standard deviation of the measurement
* error in the corresponding y value, assuming the measurement error
* distribution is a zero-mean Gaussian. The linear function
* y = a + bx is fitted to the
* data. The return value is a {@linkplain Regression Regression} object
* containing the intercept a, the slope b, and various
* statistics.
*
* @return Regression.
*/
public Regression linearRegression()
{
// Accumulate sums.
int n = length();
double Sx = 0.0;
double Sy = 0.0;
double S = 0.0;
for (int i = 0; i < n; ++ i)
{
double sigma_i = z(i);
double sigma2_i = sigma_i*sigma_i;
Sx += x(i)/sigma2_i;
Sy += y(i)/sigma2_i;
S += 1.0/sigma2_i;
}
double Sx_over_S = Sx/S;
// Calculate b.
double b = 0.0;
double Stt = 0.0;
for (int i = 0; i < n; ++ i)
{
double sigma_i = z(i);
double t_i = (x(i) - Sx_over_S)/sigma_i;
b += t_i*y(i)/sigma_i;
Stt += t_i*t_i;
}
b /= Stt;
// Calculate other model parameters.
double a = (Sy - Sx*b)/S;
double var_a = (1.0 + Sx*Sx/S/Stt)/S;
double var_b = 1.0/Stt;
double cov_ab = -Sx/S/Stt;
double r_ab = cov_ab/Math.sqrt(var_a)/Math.sqrt(var_b);
// Calculate chi^2.
double chi2 = 0.0;
for (int i = 0; i < n; ++ i)
{
double d = (y(i) - a - b*x(i))/z(i);
chi2 += d*d;
}
double significance = Statistics.chiSquarePvalue (n - 2, chi2);
// Return results.
return new Regression
(a, b, var_a, var_b, cov_ab, r_ab, chi2, significance);
}
/**
* Returns a {@linkplain Series} view of the X values in this XYZ series.
*
* Note: The returned Series object is backed by this XYZ series
* object. Changing the contents of this XYZ series object will change the
* contents of the returned Series object.
*
* @return Series of X values.
*/
public Series xSeries()
{
return new XSeriesView (this);
}
/**
* Returns a {@linkplain Series} view of the Y values in this XYZ series.
*
* Note: The returned Series object is backed by this XYZ series
* object. Changing the contents of this XYZ series object will change the
* contents of the returned Series object.
*
* @return Series of Y values.
*/
public Series ySeries()
{
return new YSeriesView (this);
}
/**
* Returns a {@linkplain Series} view of the Z values in this XYZ series.
*
* Note: The returned Series object is backed by this XYZ series
* object. Changing the contents of this XYZ series object will change the
* contents of the returned Series object.
*
* @return Series of Z values.
*/
public Series zSeries()
{
return new ZSeriesView (this);
}
/**
* Returns an {@linkplain XYSeries} view of the X and Y values in this XYZ
* series.
*
* Note: The returned XYSeries object is backed by this XYZ series
* object. Changing the contents of this XYZ series object will change the
* contents of the returned Series object.
*
* @return Series of X and Y values.
*/
public XYSeries xySeries()
{
return new XYSeriesView (this);
}
/**
* Print this XYZ series on the standard output. Each line of output
* consists of the index, the x value, the y value, and the
* z value, separated by tabs.
*/
public void print()
{
print (System.out);
}
/**
* Print this XYZ series on the given print stream. Each line of output
* consists of the index, the x value, the y value, and the
* z value, separated by tabs.
*
* @param theStream Print stream.
*/
public void print
(PrintStream theStream)
{
int n = length();
for (int i = 0; i < n; ++ i)
{
theStream.print (i);
theStream.print ('\t');
theStream.print (x(i));
theStream.print ('\t');
theStream.print (y(i));
theStream.print ('\t');
theStream.println (z(i));
}
}
/**
* Print this XYZ series on the given print writer. Each line of output
* consists of the index, the x value, the y value, and the
* z value, separated by tabs.
*
* @param theWriter Print writer.
*/
public void print
(PrintWriter theWriter)
{
int n = length();
for (int i = 0; i < n; ++ i)
{
theWriter.print (i);
theWriter.print ('\t');
theWriter.print (x(i));
theWriter.print ('\t');
theWriter.print (y(i));
theWriter.print ('\t');
theWriter.println (z(i));
}
}
}
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