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/*
* Copyright 2013 Brian Tjaden
*
* This file is part of Rockhopper.
*
* Rockhopper 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
* any later version.
*
* Rockhopper 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.
*
* You should have received a copy of the GNU General Public License
* (in the file gpl.txt) along with Rockhopper.
* If not, see <http://www.gnu.org/licenses/>.
*/
import java.util.ArrayList;
import java.util.Collections;
public class SmoothDistribution {
/********************************************
********** INSTANCE VARIABLES **********
********************************************/
private ArrayList<Integer> data;
private double bandwidth;
private int BIN_SIZE;
private int minimum;
private int maximum;
private double pseudocount;
private ArrayList<Integer> histogram;
private ArrayList<Double> histogramNormalized;
private ArrayList<Integer> values;
private ArrayList<Double> smoothed;
private ArrayList<Double> smoothedNormalized;
/**************************************
********** CONSTRUCTORS **********
**************************************/
public SmoothDistribution(ArrayList<Integer> data) {
this(data, 1.0, 1);
}
public SmoothDistribution(ArrayList<Integer> data, double bandwidth, int BIN_SIZE) {
this(data, bandwidth, BIN_SIZE, Collections.min(data), Collections.max(data));
}
public SmoothDistribution(ArrayList<Integer> data, double bandwidth, int BIN_SIZE, int minimum, int maximum) {
this.data = data;
this.minimum = minimum;
this.maximum = maximum;
this.bandwidth = bandwidth;
this.BIN_SIZE = BIN_SIZE;
this.pseudocount = 0.0;
generateHistogram();
smoothData();
normalize();
}
/*************************************************
********** PUBLIC INSTANCE METHODS **********
*************************************************/
/**
* Get smoothed value at point "x".
*/
public double getSmoothedValue(double x) {
if (x < this.minimum) return this.pseudocount;
if (x > this.maximum) return this.pseudocount;
int index = binarySearch(values, x, 0, values.size()-1);
// If "x" is not in our discrete distribution, the index may be off by 1.
// For example, if our distribution includes 4,5,6,7 and x=5.3, we
// may return index 1 (corresponding to 5) or index 2 (corresponding to 6).
if (index > 0) {
if (Math.abs(x - values.get(index)) > Math.abs(x - values.get(index-1)))
return Math.max(smoothedNormalized.get(index-1), this.pseudocount);
}
if (index < smoothedNormalized.size()-1) {
if (Math.abs(x - values.get(index)) > Math.abs(x - values.get(index+1)))
return Math.max(smoothedNormalized.get(index+1), this.pseudocount);
}
return Math.max(smoothedNormalized.get(index), this.pseudocount);
}
/**
* Set the pseudocount for this distribution.
*/
public void setPseudocount(double pseudocount) {
this.pseudocount = pseudocount;
}
/**
* Returns a String representation of this smoothed distribution.
*/
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append("VALUES" + "\t" + "SMOOTHED" + "\t" + "NORMALIZED" + "\n");
for (int i=0; i<smoothedNormalized.size(); i++) {
sb.append(values.get(i) + "\t" + histogram.get(i) + "\t" + histogramNormalized.get(i) + "\t" + smoothedNormalized.get(i) + "\n");
}
return sb.toString();
}
/**************************************************
********** PRIVATE INSTANCE METHODS **********
**************************************************/
/**
* Generate histogram of data.
*/
private void generateHistogram() {
this.histogram = new ArrayList<Integer>();
this.histogramNormalized = new ArrayList<Double>();
for (int i=this.minimum; i<=maximum; i+=BIN_SIZE) {
histogram.add(0);
histogramNormalized.add(0.0);
}
for (int i=0; i<data.size(); i++) {
if (data.get(i) < minimum) histogram.set(0, histogram.get(0) + 1);
else if (data.get(i) > maximum) histogram.set(histogram.size()-1, histogram.get(histogram.size()-1) + 1);
else histogram.set((data.get(i)-minimum)/BIN_SIZE, histogram.get((data.get(i)-minimum)/BIN_SIZE) + 1);
}
for (int i=0; i<histogram.size(); i++) histogramNormalized.set(i, histogram.get(i) / (double)data.size());
}
/**
* Generate smooth distibution of data (based on Epanechnikov kernel).
*/
private void smoothData() {
values = new ArrayList<Integer>();
smoothed = new ArrayList<Double>();
int i = this.minimum;
while (i <= this.maximum) { // Compute weighted value for index i
double sum = 0.0;
for (int j=0; j<data.size(); j++) {
if (Math.abs(i - data.get(j)) <= this.bandwidth) {
double u = (i - data.get(j)) / this.bandwidth;
sum += (3.0/4.0) * (1.0 - u*u);
}
}
values.add(i);
smoothed.add(sum / (data.size() * this.bandwidth));
i += this.BIN_SIZE;
}
}
/**
* Determine pseudocounts and normalize distribution so it sums to 1.0.
*/
private void normalize() {
smoothedNormalized = new ArrayList<Double>();
double sum = 0.0;
for (int i=0; i<smoothed.size(); i++) sum += smoothed.get(i);
double min = Double.MAX_VALUE;
for (int i=0; i<smoothed.size(); i++) {
double normalizedValue = smoothed.get(i) / sum;
smoothedNormalized.add(normalizedValue);
if ((normalizedValue > 0) && (normalizedValue < min)) min = normalizedValue;
}
this.pseudocount = min / 10.0;
}
/**
* Perform a binary search for the specified value.
*/
private int binarySearch(ArrayList<Integer> a, double value, int lo, int hi) {
if (hi <= lo) return lo;
int mid = lo + (hi-lo)/2;
if (a.get(mid) > value) return binarySearch(a, value, lo, mid-1);
if (a.get(mid) < value) return binarySearch(a, value, mid+1, hi);
return mid;
}
/*************************************
********** MAIN METHOD **********
*************************************/
public static void main(String[] args) {
System.err.println("\nThe SmoothDistribution application cannot be executed from the command line. It must be instantiated from another Java application. It takes a set of data and generates a smoothed version of the data distribution based on the Epanechnikov kernel. Smoothing occurs at each point over an interval [-bandwidth,bandwidth]. The BIN_SIZE indicates how big each BIN_SIZE should be.\n");
}
}
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