001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.stat.ranking;
019
020 import java.util.ArrayList;
021 import java.util.Arrays;
022 import java.util.Iterator;
023 import java.util.List;
024
025 import org.apache.commons.math.exception.MathInternalError;
026 import org.apache.commons.math.random.RandomData;
027 import org.apache.commons.math.random.RandomDataImpl;
028 import org.apache.commons.math.random.RandomGenerator;
029 import org.apache.commons.math.util.FastMath;
030
031
032 /**
033 * <p> Ranking based on the natural ordering on doubles.</p>
034 * <p>NaNs are treated according to the configured {@link NaNStrategy} and ties
035 * are handled using the selected {@link TiesStrategy}.
036 * Configuration settings are supplied in optional constructor arguments.
037 * Defaults are {@link NaNStrategy#MAXIMAL} and {@link TiesStrategy#AVERAGE},
038 * respectively. When using {@link TiesStrategy#RANDOM}, a
039 * {@link RandomGenerator} may be supplied as a constructor argument.</p>
040 * <p>Examples:
041 * <table border="1" cellpadding="3">
042 * <tr><th colspan="3">
043 * Input data: (20, 17, 30, 42.3, 17, 50, Double.NaN, Double.NEGATIVE_INFINITY, 17)
044 * </th></tr>
045 * <tr><th>NaNStrategy</th><th>TiesStrategy</th>
046 * <th><code>rank(data)</code></th>
047 * <tr>
048 * <td>default (NaNs maximal)</td>
049 * <td>default (ties averaged)</td>
050 * <td>(5, 3, 6, 7, 3, 8, 9, 1, 3)</td></tr>
051 * <tr>
052 * <td>default (NaNs maximal)</td>
053 * <td>MINIMUM</td>
054 * <td>(5, 2, 6, 7, 2, 8, 9, 1, 2)</td></tr>
055 * <tr>
056 * <td>MINIMAL</td>
057 * <td>default (ties averaged)</td>
058 * <td>(6, 4, 7, 8, 4, 9, 1.5, 1.5, 4)</td></tr>
059 * <tr>
060 * <td>REMOVED</td>
061 * <td>SEQUENTIAL</td>
062 * <td>(5, 2, 6, 7, 3, 8, 1, 4)</td></tr>
063 * <tr>
064 * <td>MINIMAL</td>
065 * <td>MAXIMUM</td>
066 * <td>(6, 5, 7, 8, 5, 9, 2, 2, 5)</td></tr></table></p>
067 *
068 * @since 2.0
069 * @version $Revision: 1061496 $ $Date: 2011-01-20 21:32:16 +0100 (jeu. 20 janv. 2011) $
070 */
071 public class NaturalRanking implements RankingAlgorithm {
072
073 /** default NaN strategy */
074 public static final NaNStrategy DEFAULT_NAN_STRATEGY = NaNStrategy.MAXIMAL;
075
076 /** default ties strategy */
077 public static final TiesStrategy DEFAULT_TIES_STRATEGY = TiesStrategy.AVERAGE;
078
079 /** NaN strategy - defaults to NaNs maximal */
080 private final NaNStrategy nanStrategy;
081
082 /** Ties strategy - defaults to ties averaged */
083 private final TiesStrategy tiesStrategy;
084
085 /** Source of random data - used only when ties strategy is RANDOM */
086 private final RandomData randomData;
087
088 /**
089 * Create a NaturalRanking with default strategies for handling ties and NaNs.
090 */
091 public NaturalRanking() {
092 super();
093 tiesStrategy = DEFAULT_TIES_STRATEGY;
094 nanStrategy = DEFAULT_NAN_STRATEGY;
095 randomData = null;
096 }
097
098 /**
099 * Create a NaturalRanking with the given TiesStrategy.
100 *
101 * @param tiesStrategy the TiesStrategy to use
102 */
103 public NaturalRanking(TiesStrategy tiesStrategy) {
104 super();
105 this.tiesStrategy = tiesStrategy;
106 nanStrategy = DEFAULT_NAN_STRATEGY;
107 randomData = new RandomDataImpl();
108 }
109
110 /**
111 * Create a NaturalRanking with the given NaNStrategy.
112 *
113 * @param nanStrategy the NaNStrategy to use
114 */
115 public NaturalRanking(NaNStrategy nanStrategy) {
116 super();
117 this.nanStrategy = nanStrategy;
118 tiesStrategy = DEFAULT_TIES_STRATEGY;
119 randomData = null;
120 }
121
122 /**
123 * Create a NaturalRanking with the given NaNStrategy and TiesStrategy.
124 *
125 * @param nanStrategy NaNStrategy to use
126 * @param tiesStrategy TiesStrategy to use
127 */
128 public NaturalRanking(NaNStrategy nanStrategy, TiesStrategy tiesStrategy) {
129 super();
130 this.nanStrategy = nanStrategy;
131 this.tiesStrategy = tiesStrategy;
132 randomData = new RandomDataImpl();
133 }
134
135 /**
136 * Create a NaturalRanking with TiesStrategy.RANDOM and the given
137 * RandomGenerator as the source of random data.
138 *
139 * @param randomGenerator source of random data
140 */
141 public NaturalRanking(RandomGenerator randomGenerator) {
142 super();
143 this.tiesStrategy = TiesStrategy.RANDOM;
144 nanStrategy = DEFAULT_NAN_STRATEGY;
145 randomData = new RandomDataImpl(randomGenerator);
146 }
147
148
149 /**
150 * Create a NaturalRanking with the given NaNStrategy, TiesStrategy.RANDOM
151 * and the given source of random data.
152 *
153 * @param nanStrategy NaNStrategy to use
154 * @param randomGenerator source of random data
155 */
156 public NaturalRanking(NaNStrategy nanStrategy,
157 RandomGenerator randomGenerator) {
158 super();
159 this.nanStrategy = nanStrategy;
160 this.tiesStrategy = TiesStrategy.RANDOM;
161 randomData = new RandomDataImpl(randomGenerator);
162 }
163
164 /**
165 * Return the NaNStrategy
166 *
167 * @return returns the NaNStrategy
168 */
169 public NaNStrategy getNanStrategy() {
170 return nanStrategy;
171 }
172
173 /**
174 * Return the TiesStrategy
175 *
176 * @return the TiesStrategy
177 */
178 public TiesStrategy getTiesStrategy() {
179 return tiesStrategy;
180 }
181
182 /**
183 * Rank <code>data</code> using the natural ordering on Doubles, with
184 * NaN values handled according to <code>nanStrategy</code> and ties
185 * resolved using <code>tiesStrategy.</code>
186 *
187 * @param data array to be ranked
188 * @return array of ranks
189 */
190 public double[] rank(double[] data) {
191
192 // Array recording initial positions of data to be ranked
193 IntDoublePair[] ranks = new IntDoublePair[data.length];
194 for (int i = 0; i < data.length; i++) {
195 ranks[i] = new IntDoublePair(data[i], i);
196 }
197
198 // Recode, remove or record positions of NaNs
199 List<Integer> nanPositions = null;
200 switch (nanStrategy) {
201 case MAXIMAL: // Replace NaNs with +INFs
202 recodeNaNs(ranks, Double.POSITIVE_INFINITY);
203 break;
204 case MINIMAL: // Replace NaNs with -INFs
205 recodeNaNs(ranks, Double.NEGATIVE_INFINITY);
206 break;
207 case REMOVED: // Drop NaNs from data
208 ranks = removeNaNs(ranks);
209 break;
210 case FIXED: // Record positions of NaNs
211 nanPositions = getNanPositions(ranks);
212 break;
213 default: // this should not happen unless NaNStrategy enum is changed
214 throw new MathInternalError();
215 }
216
217 // Sort the IntDoublePairs
218 Arrays.sort(ranks);
219
220 // Walk the sorted array, filling output array using sorted positions,
221 // resolving ties as we go
222 double[] out = new double[ranks.length];
223 int pos = 1; // position in sorted array
224 out[ranks[0].getPosition()] = pos;
225 List<Integer> tiesTrace = new ArrayList<Integer>();
226 tiesTrace.add(ranks[0].getPosition());
227 for (int i = 1; i < ranks.length; i++) {
228 if (Double.compare(ranks[i].getValue(), ranks[i - 1].getValue()) > 0) {
229 // tie sequence has ended (or had length 1)
230 pos = i + 1;
231 if (tiesTrace.size() > 1) { // if seq is nontrivial, resolve
232 resolveTie(out, tiesTrace);
233 }
234 tiesTrace = new ArrayList<Integer>();
235 tiesTrace.add(ranks[i].getPosition());
236 } else {
237 // tie sequence continues
238 tiesTrace.add(ranks[i].getPosition());
239 }
240 out[ranks[i].getPosition()] = pos;
241 }
242 if (tiesTrace.size() > 1) { // handle tie sequence at end
243 resolveTie(out, tiesTrace);
244 }
245 if (nanStrategy == NaNStrategy.FIXED) {
246 restoreNaNs(out, nanPositions);
247 }
248 return out;
249 }
250
251 /**
252 * Returns an array that is a copy of the input array with IntDoublePairs
253 * having NaN values removed.
254 *
255 * @param ranks input array
256 * @return array with NaN-valued entries removed
257 */
258 private IntDoublePair[] removeNaNs(IntDoublePair[] ranks) {
259 if (!containsNaNs(ranks)) {
260 return ranks;
261 }
262 IntDoublePair[] outRanks = new IntDoublePair[ranks.length];
263 int j = 0;
264 for (int i = 0; i < ranks.length; i++) {
265 if (Double.isNaN(ranks[i].getValue())) {
266 // drop, but adjust original ranks of later elements
267 for (int k = i + 1; k < ranks.length; k++) {
268 ranks[k] = new IntDoublePair(
269 ranks[k].getValue(), ranks[k].getPosition() - 1);
270 }
271 } else {
272 outRanks[j] = new IntDoublePair(
273 ranks[i].getValue(), ranks[i].getPosition());
274 j++;
275 }
276 }
277 IntDoublePair[] returnRanks = new IntDoublePair[j];
278 System.arraycopy(outRanks, 0, returnRanks, 0, j);
279 return returnRanks;
280 }
281
282 /**
283 * Recodes NaN values to the given value.
284 *
285 * @param ranks array to recode
286 * @param value the value to replace NaNs with
287 */
288 private void recodeNaNs(IntDoublePair[] ranks, double value) {
289 for (int i = 0; i < ranks.length; i++) {
290 if (Double.isNaN(ranks[i].getValue())) {
291 ranks[i] = new IntDoublePair(
292 value, ranks[i].getPosition());
293 }
294 }
295 }
296
297 /**
298 * Checks for presence of NaNs in <code>ranks.</code>
299 *
300 * @param ranks array to be searched for NaNs
301 * @return true iff ranks contains one or more NaNs
302 */
303 private boolean containsNaNs(IntDoublePair[] ranks) {
304 for (int i = 0; i < ranks.length; i++) {
305 if (Double.isNaN(ranks[i].getValue())) {
306 return true;
307 }
308 }
309 return false;
310 }
311
312 /**
313 * Resolve a sequence of ties, using the configured {@link TiesStrategy}.
314 * The input <code>ranks</code> array is expected to take the same value
315 * for all indices in <code>tiesTrace</code>. The common value is recoded
316 * according to the tiesStrategy. For example, if ranks = <5,8,2,6,2,7,1,2>,
317 * tiesTrace = <2,4,7> and tiesStrategy is MINIMUM, ranks will be unchanged.
318 * The same array and trace with tiesStrategy AVERAGE will come out
319 * <5,8,3,6,3,7,1,3>.
320 *
321 * @param ranks array of ranks
322 * @param tiesTrace list of indices where <code>ranks</code> is constant
323 * -- that is, for any i and j in TiesTrace, <code> ranks[i] == ranks[j]
324 * </code>
325 */
326 private void resolveTie(double[] ranks, List<Integer> tiesTrace) {
327
328 // constant value of ranks over tiesTrace
329 final double c = ranks[tiesTrace.get(0)];
330
331 // length of sequence of tied ranks
332 final int length = tiesTrace.size();
333
334 switch (tiesStrategy) {
335 case AVERAGE: // Replace ranks with average
336 fill(ranks, tiesTrace, (2 * c + length - 1) / 2d);
337 break;
338 case MAXIMUM: // Replace ranks with maximum values
339 fill(ranks, tiesTrace, c + length - 1);
340 break;
341 case MINIMUM: // Replace ties with minimum
342 fill(ranks, tiesTrace, c);
343 break;
344 case RANDOM: // Fill with random integral values in [c, c + length - 1]
345 Iterator<Integer> iterator = tiesTrace.iterator();
346 long f = FastMath.round(c);
347 while (iterator.hasNext()) {
348 ranks[iterator.next()] =
349 randomData.nextLong(f, f + length - 1);
350 }
351 break;
352 case SEQUENTIAL: // Fill sequentially from c to c + length - 1
353 // walk and fill
354 iterator = tiesTrace.iterator();
355 f = FastMath.round(c);
356 int i = 0;
357 while (iterator.hasNext()) {
358 ranks[iterator.next()] = f + i++;
359 }
360 break;
361 default: // this should not happen unless TiesStrategy enum is changed
362 throw new MathInternalError();
363 }
364 }
365
366 /**
367 * Sets<code>data[i] = value</code> for each i in <code>tiesTrace.</code>
368 *
369 * @param data array to modify
370 * @param tiesTrace list of index values to set
371 * @param value value to set
372 */
373 private void fill(double[] data, List<Integer> tiesTrace, double value) {
374 Iterator<Integer> iterator = tiesTrace.iterator();
375 while (iterator.hasNext()) {
376 data[iterator.next()] = value;
377 }
378 }
379
380 /**
381 * Set <code>ranks[i] = Double.NaN</code> for each i in <code>nanPositions.</code>
382 *
383 * @param ranks array to modify
384 * @param nanPositions list of index values to set to <code>Double.NaN</code>
385 */
386 private void restoreNaNs(double[] ranks, List<Integer> nanPositions) {
387 if (nanPositions.size() == 0) {
388 return;
389 }
390 Iterator<Integer> iterator = nanPositions.iterator();
391 while (iterator.hasNext()) {
392 ranks[iterator.next().intValue()] = Double.NaN;
393 }
394
395 }
396
397 /**
398 * Returns a list of indexes where <code>ranks</code> is <code>NaN.</code>
399 *
400 * @param ranks array to search for <code>NaNs</code>
401 * @return list of indexes i such that <code>ranks[i] = NaN</code>
402 */
403 private List<Integer> getNanPositions(IntDoublePair[] ranks) {
404 ArrayList<Integer> out = new ArrayList<Integer>();
405 for (int i = 0; i < ranks.length; i++) {
406 if (Double.isNaN(ranks[i].getValue())) {
407 out.add(Integer.valueOf(i));
408 }
409 }
410 return out;
411 }
412
413 /**
414 * Represents the position of a double value in an ordering.
415 * Comparable interface is implemented so Arrays.sort can be used
416 * to sort an array of IntDoublePairs by value. Note that the
417 * implicitly defined natural ordering is NOT consistent with equals.
418 */
419 private static class IntDoublePair implements Comparable<IntDoublePair> {
420
421 /** Value of the pair */
422 private final double value;
423
424 /** Original position of the pair */
425 private final int position;
426
427 /**
428 * Construct an IntDoublePair with the given value and position.
429 * @param value the value of the pair
430 * @param position the original position
431 */
432 public IntDoublePair(double value, int position) {
433 this.value = value;
434 this.position = position;
435 }
436
437 /**
438 * Compare this IntDoublePair to another pair.
439 * Only the <strong>values</strong> are compared.
440 *
441 * @param other the other pair to compare this to
442 * @return result of <code>Double.compare(value, other.value)</code>
443 */
444 public int compareTo(IntDoublePair other) {
445 return Double.compare(value, other.value);
446 }
447
448 /**
449 * Returns the value of the pair.
450 * @return value
451 */
452 public double getValue() {
453 return value;
454 }
455
456 /**
457 * Returns the original position of the pair.
458 * @return position
459 */
460 public int getPosition() {
461 return position;
462 }
463 }
464 }