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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.stat.ranking;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Iterator;
import java.util.List;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.NotANumberException;
import org.apache.commons.math3.random.RandomDataGenerator;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.util.FastMath;
/**
* Ranking based on the natural ordering on doubles.
* NaNs are treated according to the configured {@link NaNStrategy} and ties
* are handled using the selected {@link TiesStrategy}.
* Configuration settings are supplied in optional constructor arguments.
* Defaults are {@link NaNStrategy#FAILED} and {@link TiesStrategy#AVERAGE},
* respectively. When using {@link TiesStrategy#RANDOM}, a
* {@link RandomGenerator} may be supplied as a constructor argument.
* Examples:
*
*
* Input data: (20, 17, 30, 42.3, 17, 50, Double.NaN, Double.NEGATIVE_INFINITY, 17)
* NaNStrategy TiesStrategy
* rank(data)
* default (NaNs maximal)
* default (ties averaged)
* (5, 3, 6, 7, 3, 8, 9, 1, 3)
*
* default (NaNs maximal)
* MINIMUM
* (5, 2, 6, 7, 2, 8, 9, 1, 2)
*
* MINIMAL
* default (ties averaged)
* (6, 4, 7, 8, 4, 9, 1.5, 1.5, 4)
*
* REMOVED
* SEQUENTIAL
* (5, 2, 6, 7, 3, 8, 1, 4)
*
* MINIMAL
* MAXIMUM
* (6, 5, 7, 8, 5, 9, 2, 2, 5)
*
* @since 2.0
*/
public class NaturalRanking implements RankingAlgorithm {
/** default NaN strategy */
public static final NaNStrategy DEFAULT_NAN_STRATEGY = NaNStrategy.FAILED;
/** default ties strategy */
public static final TiesStrategy DEFAULT_TIES_STRATEGY = TiesStrategy.AVERAGE;
/** NaN strategy - defaults to NaNs maximal */
private final NaNStrategy nanStrategy;
/** Ties strategy - defaults to ties averaged */
private final TiesStrategy tiesStrategy;
/** Source of random data - used only when ties strategy is RANDOM */
private final RandomDataGenerator randomData;
/**
* Create a NaturalRanking with default strategies for handling ties and NaNs.
*/
public NaturalRanking() {
super();
tiesStrategy = DEFAULT_TIES_STRATEGY;
nanStrategy = DEFAULT_NAN_STRATEGY;
randomData = null;
}
/**
* Create a NaturalRanking with the given TiesStrategy.
*
* @param tiesStrategy the TiesStrategy to use
*/
public NaturalRanking(TiesStrategy tiesStrategy) {
super();
this.tiesStrategy = tiesStrategy;
nanStrategy = DEFAULT_NAN_STRATEGY;
randomData = new RandomDataGenerator();
}
/**
* Create a NaturalRanking with the given NaNStrategy.
*
* @param nanStrategy the NaNStrategy to use
*/
public NaturalRanking(NaNStrategy nanStrategy) {
super();
this.nanStrategy = nanStrategy;
tiesStrategy = DEFAULT_TIES_STRATEGY;
randomData = null;
}
/**
* Create a NaturalRanking with the given NaNStrategy and TiesStrategy.
*
* @param nanStrategy NaNStrategy to use
* @param tiesStrategy TiesStrategy to use
*/
public NaturalRanking(NaNStrategy nanStrategy, TiesStrategy tiesStrategy) {
super();
this.nanStrategy = nanStrategy;
this.tiesStrategy = tiesStrategy;
randomData = new RandomDataGenerator();
}
/**
* Create a NaturalRanking with TiesStrategy.RANDOM and the given
* RandomGenerator as the source of random data.
*
* @param randomGenerator source of random data
*/
public NaturalRanking(RandomGenerator randomGenerator) {
super();
this.tiesStrategy = TiesStrategy.RANDOM;
nanStrategy = DEFAULT_NAN_STRATEGY;
randomData = new RandomDataGenerator(randomGenerator);
}
/**
* Create a NaturalRanking with the given NaNStrategy, TiesStrategy.RANDOM
* and the given source of random data.
*
* @param nanStrategy NaNStrategy to use
* @param randomGenerator source of random data
*/
public NaturalRanking(NaNStrategy nanStrategy,
RandomGenerator randomGenerator) {
super();
this.nanStrategy = nanStrategy;
this.tiesStrategy = TiesStrategy.RANDOM;
randomData = new RandomDataGenerator(randomGenerator);
}
/**
* Return the NaNStrategy
*
* @return returns the NaNStrategy
*/
public NaNStrategy getNanStrategy() {
return nanStrategy;
}
/**
* Return the TiesStrategy
*
* @return the TiesStrategy
*/
public TiesStrategy getTiesStrategy() {
return tiesStrategy;
}
/**
* Rank data using the natural ordering on Doubles, with
* NaN values handled according to nanStrategy and ties
* resolved using tiesStrategy.
*
* @param data array to be ranked
* @return array of ranks
* @throws NotANumberException if the selected {@link NaNStrategy} is {@code FAILED}
* and a {@link Double#NaN} is encountered in the input data
*/
public double[] rank(double[] data) {
// Array recording initial positions of data to be ranked
IntDoublePair[] ranks = new IntDoublePair[data.length];
for (int i = 0; i < data.length; i++) {
ranks[i] = new IntDoublePair(data[i], i);
}
// Recode, remove or record positions of NaNs
List nanPositions = null;
switch (nanStrategy) {
case MAXIMAL: // Replace NaNs with +INFs
recodeNaNs(ranks, Double.POSITIVE_INFINITY);
break;
case MINIMAL: // Replace NaNs with -INFs
recodeNaNs(ranks, Double.NEGATIVE_INFINITY);
break;
case REMOVED: // Drop NaNs from data
ranks = removeNaNs(ranks);
break;
case FIXED: // Record positions of NaNs
nanPositions = getNanPositions(ranks);
break;
case FAILED:
nanPositions = getNanPositions(ranks);
if (nanPositions.size() > 0) {
throw new NotANumberException();
}
break;
default: // this should not happen unless NaNStrategy enum is changed
throw new MathInternalError();
}
// Sort the IntDoublePairs
Arrays.sort(ranks);
// Walk the sorted array, filling output array using sorted positions,
// resolving ties as we go
double[] out = new double[ranks.length];
int pos = 1; // position in sorted array
out[ranks[0].getPosition()] = pos;
List tiesTrace = new ArrayList();
tiesTrace.add(ranks[0].getPosition());
for (int i = 1; i < ranks.length; i++) {
if (Double.compare(ranks[i].getValue(), ranks[i - 1].getValue()) > 0) {
// tie sequence has ended (or had length 1)
pos = i + 1;
if (tiesTrace.size() > 1) { // if seq is nontrivial, resolve
resolveTie(out, tiesTrace);
}
tiesTrace = new ArrayList();
tiesTrace.add(ranks[i].getPosition());
} else {
// tie sequence continues
tiesTrace.add(ranks[i].getPosition());
}
out[ranks[i].getPosition()] = pos;
}
if (tiesTrace.size() > 1) { // handle tie sequence at end
resolveTie(out, tiesTrace);
}
if (nanStrategy == NaNStrategy.FIXED) {
restoreNaNs(out, nanPositions);
}
return out;
}
/**
* Returns an array that is a copy of the input array with IntDoublePairs
* having NaN values removed.
*
* @param ranks input array
* @return array with NaN-valued entries removed
*/
private IntDoublePair[] removeNaNs(IntDoublePair[] ranks) {
if (!containsNaNs(ranks)) {
return ranks;
}
IntDoublePair[] outRanks = new IntDoublePair[ranks.length];
int j = 0;
for (int i = 0; i < ranks.length; i++) {
if (Double.isNaN(ranks[i].getValue())) {
// drop, but adjust original ranks of later elements
for (int k = i + 1; k < ranks.length; k++) {
ranks[k] = new IntDoublePair(
ranks[k].getValue(), ranks[k].getPosition() - 1);
}
} else {
outRanks[j] = new IntDoublePair(
ranks[i].getValue(), ranks[i].getPosition());
j++;
}
}
IntDoublePair[] returnRanks = new IntDoublePair[j];
System.arraycopy(outRanks, 0, returnRanks, 0, j);
return returnRanks;
}
/**
* Recodes NaN values to the given value.
*
* @param ranks array to recode
* @param value the value to replace NaNs with
*/
private void recodeNaNs(IntDoublePair[] ranks, double value) {
for (int i = 0; i < ranks.length; i++) {
if (Double.isNaN(ranks[i].getValue())) {
ranks[i] = new IntDoublePair(
value, ranks[i].getPosition());
}
}
}
/**
* Checks for presence of NaNs in ranks.
*
* @param ranks array to be searched for NaNs
* @return true iff ranks contains one or more NaNs
*/
private boolean containsNaNs(IntDoublePair[] ranks) {
for (int i = 0; i < ranks.length; i++) {
if (Double.isNaN(ranks[i].getValue())) {
return true;
}
}
return false;
}
/**
* Resolve a sequence of ties, using the configured {@link TiesStrategy}.
* The input ranks array is expected to take the same value
* for all indices in tiesTrace. The common value is recoded
* according to the tiesStrategy. For example, if ranks = <5,8,2,6,2,7,1,2>,
* tiesTrace = <2,4,7> and tiesStrategy is MINIMUM, ranks will be unchanged.
* The same array and trace with tiesStrategy AVERAGE will come out
* <5,8,3,6,3,7,1,3>.
*
* @param ranks array of ranks
* @param tiesTrace list of indices where ranks is constant
* -- that is, for any i and j in TiesTrace, ranks[i] == ranks[j]
*
*/
private void resolveTie(double[] ranks, List tiesTrace) {
// constant value of ranks over tiesTrace
final double c = ranks[tiesTrace.get(0)];
// length of sequence of tied ranks
final int length = tiesTrace.size();
switch (tiesStrategy) {
case AVERAGE: // Replace ranks with average
fill(ranks, tiesTrace, (2 * c + length - 1) / 2d);
break;
case MAXIMUM: // Replace ranks with maximum values
fill(ranks, tiesTrace, c + length - 1);
break;
case MINIMUM: // Replace ties with minimum
fill(ranks, tiesTrace, c);
break;
case RANDOM: // Fill with random integral values in [c, c + length - 1]
Iterator iterator = tiesTrace.iterator();
long f = FastMath.round(c);
while (iterator.hasNext()) {
// No advertised exception because args are guaranteed valid
ranks[iterator.next()] =
randomData.nextLong(f, f + length - 1);
}
break;
case SEQUENTIAL: // Fill sequentially from c to c + length - 1
// walk and fill
iterator = tiesTrace.iterator();
f = FastMath.round(c);
int i = 0;
while (iterator.hasNext()) {
ranks[iterator.next()] = f + i++;
}
break;
default: // this should not happen unless TiesStrategy enum is changed
throw new MathInternalError();
}
}
/**
* Setsdata[i] = value for each i in tiesTrace.
*
* @param data array to modify
* @param tiesTrace list of index values to set
* @param value value to set
*/
private void fill(double[] data, List tiesTrace, double value) {
Iterator iterator = tiesTrace.iterator();
while (iterator.hasNext()) {
data[iterator.next()] = value;
}
}
/**
* Set ranks[i] = Double.NaN for each i in nanPositions.
*
* @param ranks array to modify
* @param nanPositions list of index values to set to Double.NaN
*/
private void restoreNaNs(double[] ranks, List nanPositions) {
if (nanPositions.size() == 0) {
return;
}
Iterator iterator = nanPositions.iterator();
while (iterator.hasNext()) {
ranks[iterator.next().intValue()] = Double.NaN;
}
}
/**
* Returns a list of indexes where ranks is NaN.
*
* @param ranks array to search for NaNs
* @return list of indexes i such that ranks[i] = NaN
*/
private List getNanPositions(IntDoublePair[] ranks) {
ArrayList out = new ArrayList();
for (int i = 0; i < ranks.length; i++) {
if (Double.isNaN(ranks[i].getValue())) {
out.add(Integer.valueOf(i));
}
}
return out;
}
/**
* Represents the position of a double value in an ordering.
* Comparable interface is implemented so Arrays.sort can be used
* to sort an array of IntDoublePairs by value. Note that the
* implicitly defined natural ordering is NOT consistent with equals.
*/
private static class IntDoublePair implements Comparable {
/** Value of the pair */
private final double value;
/** Original position of the pair */
private final int position;
/**
* Construct an IntDoublePair with the given value and position.
* @param value the value of the pair
* @param position the original position
*/
public IntDoublePair(double value, int position) {
this.value = value;
this.position = position;
}
/**
* Compare this IntDoublePair to another pair.
* Only the values are compared.
*
* @param other the other pair to compare this to
* @return result of Double.compare(value, other.value)
*/
public int compareTo(IntDoublePair other) {
return Double.compare(value, other.value);
}
// N.B. equals() and hashCode() are not implemented; see MATH-610 for discussion.
/**
* Returns the value of the pair.
* @return value
*/
public double getValue() {
return value;
}
/**
* Returns the original position of the pair.
* @return position
*/
public int getPosition() {
return position;
}
}
}