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-rw-r--r--src/main/java/org/apache/commons/math/stat/descriptive/rank/Max.java163
-rw-r--r--src/main/java/org/apache/commons/math/stat/descriptive/rank/Median.java55
-rw-r--r--src/main/java/org/apache/commons/math/stat/descriptive/rank/Min.java163
-rw-r--r--src/main/java/org/apache/commons/math/stat/descriptive/rank/Percentile.java497
-rw-r--r--src/main/java/org/apache/commons/math/stat/descriptive/rank/package.html20
5 files changed, 898 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/stat/descriptive/rank/Max.java b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Max.java
new file mode 100644
index 0000000..1b15750
--- /dev/null
+++ b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Max.java
@@ -0,0 +1,163 @@
+/*
+ * 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.math.stat.descriptive.rank;
+
+import java.io.Serializable;
+
+import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
+
+/**
+ * Returns the maximum of the available values.
+ * <p>
+ * <ul>
+ * <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
+ * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
+ * <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>,
+ * the result is <code>Double.POSITIVE_INFINITY.</code></li>
+ * </ul></p>
+* <p>
+ * <strong>Note that this implementation is not synchronized.</strong> If
+ * multiple threads access an instance of this class concurrently, and at least
+ * one of the threads invokes the <code>increment()</code> or
+ * <code>clear()</code> method, it must be synchronized externally.</p>
+ *
+ * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
+ */
+public class Max extends AbstractStorelessUnivariateStatistic implements Serializable {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = -5593383832225844641L;
+
+ /** Number of values that have been added */
+ private long n;
+
+ /** Current value of the statistic */
+ private double value;
+
+ /**
+ * Create a Max instance
+ */
+ public Max() {
+ n = 0;
+ value = Double.NaN;
+ }
+
+ /**
+ * Copy constructor, creates a new {@code Max} identical
+ * to the {@code original}
+ *
+ * @param original the {@code Max} instance to copy
+ */
+ public Max(Max original) {
+ copy(original, this);
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public void increment(final double d) {
+ if (d > value || Double.isNaN(value)) {
+ value = d;
+ }
+ n++;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public void clear() {
+ value = Double.NaN;
+ n = 0;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public double getResult() {
+ return value;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ public long getN() {
+ return n;
+ }
+
+ /**
+ * Returns the maximum of the entries in the specified portion of
+ * the input array, or <code>Double.NaN</code> if the designated subarray
+ * is empty.
+ * <p>
+ * Throws <code>IllegalArgumentException</code> if the array is null or
+ * the array index parameters are not valid.</p>
+ * <p>
+ * <ul>
+ * <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
+ * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
+ * <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>,
+ * the result is <code>Double.POSITIVE_INFINITY.</code></li>
+ * </ul></p>
+ *
+ * @param values the input array
+ * @param begin index of the first array element to include
+ * @param length the number of elements to include
+ * @return the maximum of the values or Double.NaN if length = 0
+ * @throws IllegalArgumentException if the array is null or the array index
+ * parameters are not valid
+ */
+ @Override
+ public double evaluate(final double[] values, final int begin, final int length) {
+ double max = Double.NaN;
+ if (test(values, begin, length)) {
+ max = values[begin];
+ for (int i = begin; i < begin + length; i++) {
+ if (!Double.isNaN(values[i])) {
+ max = (max > values[i]) ? max : values[i];
+ }
+ }
+ }
+ return max;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public Max copy() {
+ Max result = new Max();
+ copy(this, result);
+ return result;
+ }
+
+ /**
+ * Copies source to dest.
+ * <p>Neither source nor dest can be null.</p>
+ *
+ * @param source Max to copy
+ * @param dest Max to copy to
+ * @throws NullPointerException if either source or dest is null
+ */
+ public static void copy(Max source, Max dest) {
+ dest.setData(source.getDataRef());
+ dest.n = source.n;
+ dest.value = source.value;
+ }
+}
diff --git a/src/main/java/org/apache/commons/math/stat/descriptive/rank/Median.java b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Median.java
new file mode 100644
index 0000000..6e13b13
--- /dev/null
+++ b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Median.java
@@ -0,0 +1,55 @@
+/*
+ * 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.math.stat.descriptive.rank;
+
+import java.io.Serializable;
+
+
+/**
+ * Returns the median of the available values. This is the same as the 50th percentile.
+ * See {@link Percentile} for a description of the algorithm used.
+ * <p>
+ * <strong>Note that this implementation is not synchronized.</strong> If
+ * multiple threads access an instance of this class concurrently, and at least
+ * one of the threads invokes the <code>increment()</code> or
+ * <code>clear()</code> method, it must be synchronized externally.</p>
+ *
+ * @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $
+ */
+public class Median extends Percentile implements Serializable {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = -3961477041290915687L;
+
+ /**
+ * Default constructor.
+ */
+ public Median() {
+ super(50.0);
+ }
+
+ /**
+ * Copy constructor, creates a new {@code Median} identical
+ * to the {@code original}
+ *
+ * @param original the {@code Median} instance to copy
+ */
+ public Median(Median original) {
+ super(original);
+ }
+
+}
diff --git a/src/main/java/org/apache/commons/math/stat/descriptive/rank/Min.java b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Min.java
new file mode 100644
index 0000000..1c264c6
--- /dev/null
+++ b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Min.java
@@ -0,0 +1,163 @@
+/*
+ * 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.math.stat.descriptive.rank;
+
+import java.io.Serializable;
+
+import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
+
+/**
+ * Returns the minimum of the available values.
+ * <p>
+ * <ul>
+ * <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
+ * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
+ * <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>,
+ * the result is <code>Double.NEGATIVE_INFINITY.</code></li>
+ * </ul></p>
+ * <p>
+ * <strong>Note that this implementation is not synchronized.</strong> If
+ * multiple threads access an instance of this class concurrently, and at least
+ * one of the threads invokes the <code>increment()</code> or
+ * <code>clear()</code> method, it must be synchronized externally.</p>
+ *
+ * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
+ */
+public class Min extends AbstractStorelessUnivariateStatistic implements Serializable {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = -2941995784909003131L;
+
+ /**Number of values that have been added */
+ private long n;
+
+ /**Current value of the statistic */
+ private double value;
+
+ /**
+ * Create a Min instance
+ */
+ public Min() {
+ n = 0;
+ value = Double.NaN;
+ }
+
+ /**
+ * Copy constructor, creates a new {@code Min} identical
+ * to the {@code original}
+ *
+ * @param original the {@code Min} instance to copy
+ */
+ public Min(Min original) {
+ copy(original, this);
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public void increment(final double d) {
+ if (d < value || Double.isNaN(value)) {
+ value = d;
+ }
+ n++;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public void clear() {
+ value = Double.NaN;
+ n = 0;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public double getResult() {
+ return value;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ public long getN() {
+ return n;
+ }
+
+ /**
+ * Returns the minimum of the entries in the specified portion of
+ * the input array, or <code>Double.NaN</code> if the designated subarray
+ * is empty.
+ * <p>
+ * Throws <code>IllegalArgumentException</code> if the array is null or
+ * the array index parameters are not valid.</p>
+ * <p>
+ * <ul>
+ * <li>The result is <code>NaN</code> iff all values are <code>NaN</code>
+ * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
+ * <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>,
+ * the result is <code>Double.NEGATIVE_INFINITY.</code></li>
+ * </ul> </p>
+ *
+ * @param values the input array
+ * @param begin index of the first array element to include
+ * @param length the number of elements to include
+ * @return the minimum of the values or Double.NaN if length = 0
+ * @throws IllegalArgumentException if the array is null or the array index
+ * parameters are not valid
+ */
+ @Override
+ public double evaluate(final double[] values,final int begin, final int length) {
+ double min = Double.NaN;
+ if (test(values, begin, length)) {
+ min = values[begin];
+ for (int i = begin; i < begin + length; i++) {
+ if (!Double.isNaN(values[i])) {
+ min = (min < values[i]) ? min : values[i];
+ }
+ }
+ }
+ return min;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public Min copy() {
+ Min result = new Min();
+ copy(this, result);
+ return result;
+ }
+
+ /**
+ * Copies source to dest.
+ * <p>Neither source nor dest can be null.</p>
+ *
+ * @param source Min to copy
+ * @param dest Min to copy to
+ * @throws NullPointerException if either source or dest is null
+ */
+ public static void copy(Min source, Min dest) {
+ dest.setData(source.getDataRef());
+ dest.n = source.n;
+ dest.value = source.value;
+ }
+}
diff --git a/src/main/java/org/apache/commons/math/stat/descriptive/rank/Percentile.java b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Percentile.java
new file mode 100644
index 0000000..0c8a90f
--- /dev/null
+++ b/src/main/java/org/apache/commons/math/stat/descriptive/rank/Percentile.java
@@ -0,0 +1,497 @@
+/*
+ * 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.math.stat.descriptive.rank;
+
+import java.io.Serializable;
+import java.util.Arrays;
+
+import org.apache.commons.math.MathRuntimeException;
+import org.apache.commons.math.exception.util.LocalizedFormats;
+import org.apache.commons.math.stat.descriptive.AbstractUnivariateStatistic;
+import org.apache.commons.math.util.FastMath;
+
+/**
+ * Provides percentile computation.
+ * <p>
+ * There are several commonly used methods for estimating percentiles (a.k.a.
+ * quantiles) based on sample data. For large samples, the different methods
+ * agree closely, but when sample sizes are small, different methods will give
+ * significantly different results. The algorithm implemented here works as follows:
+ * <ol>
+ * <li>Let <code>n</code> be the length of the (sorted) array and
+ * <code>0 < p <= 100</code> be the desired percentile.</li>
+ * <li>If <code> n = 1 </code> return the unique array element (regardless of
+ * the value of <code>p</code>); otherwise </li>
+ * <li>Compute the estimated percentile position
+ * <code> pos = p * (n + 1) / 100</code> and the difference, <code>d</code>
+ * between <code>pos</code> and <code>floor(pos)</code> (i.e. the fractional
+ * part of <code>pos</code>). If <code>pos >= n</code> return the largest
+ * element in the array; otherwise</li>
+ * <li>Let <code>lower</code> be the element in position
+ * <code>floor(pos)</code> in the array and let <code>upper</code> be the
+ * next element in the array. Return <code>lower + d * (upper - lower)</code>
+ * </li>
+ * </ol></p>
+ * <p>
+ * To compute percentiles, the data must be at least partially ordered. Input
+ * arrays are copied and recursively partitioned using an ordering definition.
+ * The ordering used by <code>Arrays.sort(double[])</code> is the one determined
+ * by {@link java.lang.Double#compareTo(Double)}. This ordering makes
+ * <code>Double.NaN</code> larger than any other value (including
+ * <code>Double.POSITIVE_INFINITY</code>). Therefore, for example, the median
+ * (50th percentile) of
+ * <code>{0, 1, 2, 3, 4, Double.NaN}</code> evaluates to <code>2.5.</code></p>
+ * <p>
+ * Since percentile estimation usually involves interpolation between array
+ * elements, arrays containing <code>NaN</code> or infinite values will often
+ * result in <code>NaN<code> or infinite values returned.</p>
+ * <p>
+ * Since 2.2, Percentile implementation uses only selection instead of complete
+ * sorting and caches selection algorithm state between calls to the various
+ * {@code evaluate} methods when several percentiles are to be computed on the same data.
+ * This greatly improves efficiency, both for single percentile and multiple
+ * percentiles computations. However, it also induces a need to be sure the data
+ * at one call to {@code evaluate} is the same as the data with the cached algorithm
+ * state from the previous calls. Percentile does this by checking the array reference
+ * itself and a checksum of its content by default. If the user already knows he calls
+ * {@code evaluate} on an immutable array, he can save the checking time by calling the
+ * {@code evaluate} methods that do <em>not</em>
+ * </p>
+ * <p>
+ * <strong>Note that this implementation is not synchronized.</strong> If
+ * multiple threads access an instance of this class concurrently, and at least
+ * one of the threads invokes the <code>increment()</code> or
+ * <code>clear()</code> method, it must be synchronized externally.</p>
+ *
+ * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
+ */
+public class Percentile extends AbstractUnivariateStatistic implements Serializable {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = -8091216485095130416L;
+
+ /** Minimum size under which we use a simple insertion sort rather than Hoare's select. */
+ private static final int MIN_SELECT_SIZE = 15;
+
+ /** Maximum number of partitioning pivots cached (each level double the number of pivots). */
+ private static final int MAX_CACHED_LEVELS = 10;
+
+ /** Determines what percentile is computed when evaluate() is activated
+ * with no quantile argument */
+ private double quantile = 0.0;
+
+ /** Cached pivots. */
+ private int[] cachedPivots;
+
+ /**
+ * Constructs a Percentile with a default quantile
+ * value of 50.0.
+ */
+ public Percentile() {
+ this(50.0);
+ }
+
+ /**
+ * Constructs a Percentile with the specific quantile value.
+ * @param p the quantile
+ * @throws IllegalArgumentException if p is not greater than 0 and less
+ * than or equal to 100
+ */
+ public Percentile(final double p) {
+ setQuantile(p);
+ cachedPivots = null;
+ }
+
+ /**
+ * Copy constructor, creates a new {@code Percentile} identical
+ * to the {@code original}
+ *
+ * @param original the {@code Percentile} instance to copy
+ */
+ public Percentile(Percentile original) {
+ copy(original, this);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public void setData(final double[] values) {
+ if (values == null) {
+ cachedPivots = null;
+ } else {
+ cachedPivots = new int[(0x1 << MAX_CACHED_LEVELS) - 1];
+ Arrays.fill(cachedPivots, -1);
+ }
+ super.setData(values);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public void setData(final double[] values, final int begin, final int length) {
+ if (values == null) {
+ cachedPivots = null;
+ } else {
+ cachedPivots = new int[(0x1 << MAX_CACHED_LEVELS) - 1];
+ Arrays.fill(cachedPivots, -1);
+ }
+ super.setData(values, begin, length);
+ }
+
+ /**
+ * Returns the result of evaluating the statistic over the stored data.
+ * <p>
+ * The stored array is the one which was set by previous calls to
+ * </p>
+ * @param p the percentile value to compute
+ * @return the value of the statistic applied to the stored data
+ */
+ public double evaluate(final double p) {
+ return evaluate(getDataRef(), p);
+ }
+
+ /**
+ * Returns an estimate of the <code>p</code>th percentile of the values
+ * in the <code>values</code> array.
+ * <p>
+ * Calls to this method do not modify the internal <code>quantile</code>
+ * state of this statistic.</p>
+ * <p>
+ * <ul>
+ * <li>Returns <code>Double.NaN</code> if <code>values</code> has length
+ * <code>0</code></li>
+ * <li>Returns (for any value of <code>p</code>) <code>values[0]</code>
+ * if <code>values</code> has length <code>1</code></li>
+ * <li>Throws <code>IllegalArgumentException</code> if <code>values</code>
+ * is null or p is not a valid quantile value (p must be greater than 0
+ * and less than or equal to 100) </li>
+ * </ul></p>
+ * <p>
+ * See {@link Percentile} for a description of the percentile estimation
+ * algorithm used.</p>
+ *
+ * @param values input array of values
+ * @param p the percentile value to compute
+ * @return the percentile value or Double.NaN if the array is empty
+ * @throws IllegalArgumentException if <code>values</code> is null
+ * or p is invalid
+ */
+ public double evaluate(final double[] values, final double p) {
+ test(values, 0, 0);
+ return evaluate(values, 0, values.length, p);
+ }
+
+ /**
+ * Returns an estimate of the <code>quantile</code>th percentile of the
+ * designated values in the <code>values</code> array. The quantile
+ * estimated is determined by the <code>quantile</code> property.
+ * <p>
+ * <ul>
+ * <li>Returns <code>Double.NaN</code> if <code>length = 0</code></li>
+ * <li>Returns (for any value of <code>quantile</code>)
+ * <code>values[begin]</code> if <code>length = 1 </code></li>
+ * <li>Throws <code>IllegalArgumentException</code> if <code>values</code>
+ * is null, or <code>start</code> or <code>length</code>
+ * is invalid</li>
+ * </ul></p>
+ * <p>
+ * See {@link Percentile} for a description of the percentile estimation
+ * algorithm used.</p>
+ *
+ * @param values the input array
+ * @param start index of the first array element to include
+ * @param length the number of elements to include
+ * @return the percentile value
+ * @throws IllegalArgumentException if the parameters are not valid
+ *
+ */
+ @Override
+ public double evaluate( final double[] values, final int start, final int length) {
+ return evaluate(values, start, length, quantile);
+ }
+
+ /**
+ * Returns an estimate of the <code>p</code>th percentile of the values
+ * in the <code>values</code> array, starting with the element in (0-based)
+ * position <code>begin</code> in the array and including <code>length</code>
+ * values.
+ * <p>
+ * Calls to this method do not modify the internal <code>quantile</code>
+ * state of this statistic.</p>
+ * <p>
+ * <ul>
+ * <li>Returns <code>Double.NaN</code> if <code>length = 0</code></li>
+ * <li>Returns (for any value of <code>p</code>) <code>values[begin]</code>
+ * if <code>length = 1 </code></li>
+ * <li>Throws <code>IllegalArgumentException</code> if <code>values</code>
+ * is null , <code>begin</code> or <code>length</code> is invalid, or
+ * <code>p</code> is not a valid quantile value (p must be greater than 0
+ * and less than or equal to 100)</li>
+ * </ul></p>
+ * <p>
+ * See {@link Percentile} for a description of the percentile estimation
+ * algorithm used.</p>
+ *
+ * @param values array of input values
+ * @param p the percentile to compute
+ * @param begin the first (0-based) element to include in the computation
+ * @param length the number of array elements to include
+ * @return the percentile value
+ * @throws IllegalArgumentException if the parameters are not valid or the
+ * input array is null
+ */
+ public double evaluate(final double[] values, final int begin,
+ final int length, final double p) {
+
+ test(values, begin, length);
+
+ if ((p > 100) || (p <= 0)) {
+ throw MathRuntimeException.createIllegalArgumentException(
+ LocalizedFormats.OUT_OF_BOUNDS_QUANTILE_VALUE, p);
+ }
+ if (length == 0) {
+ return Double.NaN;
+ }
+ if (length == 1) {
+ return values[begin]; // always return single value for n = 1
+ }
+ double n = length;
+ double pos = p * (n + 1) / 100;
+ double fpos = FastMath.floor(pos);
+ int intPos = (int) fpos;
+ double dif = pos - fpos;
+ double[] work;
+ int[] pivotsHeap;
+ if (values == getDataRef()) {
+ work = getDataRef();
+ pivotsHeap = cachedPivots;
+ } else {
+ work = new double[length];
+ System.arraycopy(values, begin, work, 0, length);
+ pivotsHeap = new int[(0x1 << MAX_CACHED_LEVELS) - 1];
+ Arrays.fill(pivotsHeap, -1);
+ }
+
+ if (pos < 1) {
+ return select(work, pivotsHeap, 0);
+ }
+ if (pos >= n) {
+ return select(work, pivotsHeap, length - 1);
+ }
+ double lower = select(work, pivotsHeap, intPos - 1);
+ double upper = select(work, pivotsHeap, intPos);
+ return lower + dif * (upper - lower);
+ }
+
+ /**
+ * Select the k<sup>th</sup> smallest element from work array
+ * @param work work array (will be reorganized during the call)
+ * @param pivotsHeap set of pivot index corresponding to elements that
+ * are already at their sorted location, stored as an implicit heap
+ * (i.e. a sorted binary tree stored in a flat array, where the
+ * children of a node at index n are at indices 2n+1 for the left
+ * child and 2n+2 for the right child, with 0-based indices)
+ * @param k index of the desired element
+ * @return k<sup>th</sup> smallest element
+ */
+ private double select(final double[] work, final int[] pivotsHeap, final int k) {
+
+ int begin = 0;
+ int end = work.length;
+ int node = 0;
+
+ while (end - begin > MIN_SELECT_SIZE) {
+
+ final int pivot;
+ if ((node < pivotsHeap.length) && (pivotsHeap[node] >= 0)) {
+ // the pivot has already been found in a previous call
+ // and the array has already been partitioned around it
+ pivot = pivotsHeap[node];
+ } else {
+ // select a pivot and partition work array around it
+ pivot = partition(work, begin, end, medianOf3(work, begin, end));
+ if (node < pivotsHeap.length) {
+ pivotsHeap[node] = pivot;
+ }
+ }
+
+ if (k == pivot) {
+ // the pivot was exactly the element we wanted
+ return work[k];
+ } else if (k < pivot) {
+ // the element is in the left partition
+ end = pivot;
+ node = Math.min(2 * node + 1, pivotsHeap.length); // the min is here to avoid integer overflow
+ } else {
+ // the element is in the right partition
+ begin = pivot + 1;
+ node = Math.min(2 * node + 2, pivotsHeap.length); // the min is here to avoid integer overflow
+ }
+
+ }
+
+ // the element is somewhere in the small sub-array
+ // sort the sub-array using insertion sort
+ insertionSort(work, begin, end);
+ return work[k];
+
+ }
+
+ /** Select a pivot index as the median of three
+ * @param work data array
+ * @param begin index of the first element of the slice
+ * @param end index after the last element of the slice
+ * @return the index of the median element chosen between the
+ * first, the middle and the last element of the array slice
+ */
+ int medianOf3(final double[] work, final int begin, final int end) {
+
+ final int inclusiveEnd = end - 1;
+ final int middle = begin + (inclusiveEnd - begin) / 2;
+ final double wBegin = work[begin];
+ final double wMiddle = work[middle];
+ final double wEnd = work[inclusiveEnd];
+
+ if (wBegin < wMiddle) {
+ if (wMiddle < wEnd) {
+ return middle;
+ } else {
+ return (wBegin < wEnd) ? inclusiveEnd : begin;
+ }
+ } else {
+ if (wBegin < wEnd) {
+ return begin;
+ } else {
+ return (wMiddle < wEnd) ? inclusiveEnd : middle;
+ }
+ }
+
+ }
+
+ /**
+ * Partition an array slice around a pivot
+ * <p>
+ * Partitioning exchanges array elements such that all elements
+ * smaller than pivot are before it and all elements larger than
+ * pivot are after it
+ * </p>
+ * @param work data array
+ * @param begin index of the first element of the slice
+ * @param end index after the last element of the slice
+ * @param pivot initial index of the pivot
+ * @return index of the pivot after partition
+ */
+ private int partition(final double[] work, final int begin, final int end, final int pivot) {
+
+ final double value = work[pivot];
+ work[pivot] = work[begin];
+
+ int i = begin + 1;
+ int j = end - 1;
+ while (i < j) {
+ while ((i < j) && (work[j] >= value)) {
+ --j;
+ }
+ while ((i < j) && (work[i] <= value)) {
+ ++i;
+ }
+
+ if (i < j) {
+ final double tmp = work[i];
+ work[i++] = work[j];
+ work[j--] = tmp;
+ }
+ }
+
+ if ((i >= end) || (work[i] > value)) {
+ --i;
+ }
+ work[begin] = work[i];
+ work[i] = value;
+ return i;
+
+ }
+
+ /**
+ * Sort in place a (small) array slice using insertion sort
+ * @param work array to sort
+ * @param begin index of the first element of the slice to sort
+ * @param end index after the last element of the slice to sort
+ */
+ private void insertionSort(final double[] work, final int begin, final int end) {
+ for (int j = begin + 1; j < end; j++) {
+ final double saved = work[j];
+ int i = j - 1;
+ while ((i >= begin) && (saved < work[i])) {
+ work[i + 1] = work[i];
+ i--;
+ }
+ work[i + 1] = saved;
+ }
+ }
+
+ /**
+ * Returns the value of the quantile field (determines what percentile is
+ * computed when evaluate() is called with no quantile argument).
+ *
+ * @return quantile
+ */
+ public double getQuantile() {
+ return quantile;
+ }
+
+ /**
+ * Sets the value of the quantile field (determines what percentile is
+ * computed when evaluate() is called with no quantile argument).
+ *
+ * @param p a value between 0 < p <= 100
+ * @throws IllegalArgumentException if p is not greater than 0 and less
+ * than or equal to 100
+ */
+ public void setQuantile(final double p) {
+ if (p <= 0 || p > 100) {
+ throw MathRuntimeException.createIllegalArgumentException(
+ LocalizedFormats.OUT_OF_BOUNDS_QUANTILE_VALUE, p);
+ }
+ quantile = p;
+ }
+
+ /**
+ * {@inheritDoc}
+ */
+ @Override
+ public Percentile copy() {
+ Percentile result = new Percentile();
+ copy(this, result);
+ return result;
+ }
+
+ /**
+ * Copies source to dest.
+ * <p>Neither source nor dest can be null.</p>
+ *
+ * @param source Percentile to copy
+ * @param dest Percentile to copy to
+ * @throws NullPointerException if either source or dest is null
+ */
+ public static void copy(Percentile source, Percentile dest) {
+ dest.setData(source.getDataRef());
+ if (source.cachedPivots != null) {
+ System.arraycopy(source.cachedPivots, 0, dest.cachedPivots, 0, source.cachedPivots.length);
+ }
+ dest.quantile = source.quantile;
+ }
+
+}
diff --git a/src/main/java/org/apache/commons/math/stat/descriptive/rank/package.html b/src/main/java/org/apache/commons/math/stat/descriptive/rank/package.html
new file mode 100644
index 0000000..c69107b
--- /dev/null
+++ b/src/main/java/org/apache/commons/math/stat/descriptive/rank/package.html
@@ -0,0 +1,20 @@
+<html>
+<!--
+ 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.
+ -->
+ <!-- $Revision: 480440 $ $Date: 2006-11-29 08:14:12 +0100 (mer. 29 nov. 2006) $ -->
+ <body>Summary statistics based on ranks.</body>
+</html>