src/main/java/org/apache/datasketches/quantilescommon/QuantilesUtil.java

/*
 * 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.datasketches.quantilescommon;

import static java.lang.Math.log;
import static java.lang.Math.pow;
import static org.apache.datasketches.quantilescommon.QuantileSearchCriteria.INCLUSIVE;

import java.util.Objects;

import org.apache.datasketches.common.SketchesArgumentException;
import org.apache.datasketches.common.Util;

/**
 * Utilities for the quantiles sketches.
 *
 * @author Lee Rhodes
 */
public final class QuantilesUtil {

  private QuantilesUtil() {}

  /**
   * Checks that the given normalized rank: <i>0 &le; nRank &le; 1.0</i>.
   * @param nRank the given normalized rank.
   */
  public static final void checkNormalizedRankBounds(final double nRank) {
    if ((nRank < 0.0) || (nRank > 1.0)) {
      throw new SketchesArgumentException(
          "A normalized rank must be >= 0 and <= 1.0: " + nRank);
    }
  }

  /**
   * Checks the sequential validity of the given array of double values.
   * They must be unique, monotonically increasing and not NaN.
   * @param values the given array of double values
   */
  public static final void checkDoublesSplitPointsOrder(final double[] values) {
    Objects.requireNonNull(values);
    final int len = values.length;
    if (len == 1 && Double.isNaN(values[0])) {
      throw new SketchesArgumentException(
        "Values must be unique, monotonically increasing and not NaN.");
    }
    for (int j = 0; j < len - 1; j++) {
      if (values[j] < values[j + 1]) { continue; }
      throw new SketchesArgumentException(
          "Values must be unique, monotonically increasing and not NaN.");
    }
  }

  /**
   * Checks the sequential validity of the given array of float values.
   * They must be unique, monotonically increasing and not NaN.
   * @param values the given array of double values
   */
  public static final void checkFloatsSplitPointsOrder(final float[] values) {
    Objects.requireNonNull(values);
    final int len = values.length;
    if (len == 1 && Float.isNaN(values[0])) {
      throw new SketchesArgumentException(
        "Values must be unique, monotonically increasing and not NaN.");
    }
    for (int j = 0; j < len - 1; j++) {
      if (values[j] < values[j + 1]) { continue; }
      throw new SketchesArgumentException(
          "Values must be unique, monotonically increasing and not NaN.");
    }
  }

  /**
   * Returns an array of (<i>num</i> + 1) values that define equally sized intervals between 0.0, inclusive, and 1.0,
   * inclusive. The end points 0.0 and 1.0 are part of the returned array.
   *
   * <p>For example, if num == 2, three values will be returned: 0.0, .5, and 1, where the two equally sized regions
   * are {0.0,0.5}, and {0.5, 1.0}.</p>
   * @param num the total number of equally sized intervals between 0.0, inclusive and 1.0, inclusive.
   * Must be 1 or greater.
   * @return a double array of values that define (num + 1) equally sized intervals between 0.0, inclusive and 1.0,
   * inclusive.
   * @throws IllegalArgumentException if <i>num</i> is less than 1.
   */
  public static double[] equallySpacedDoubles(final int num) {
    if (num < 1) { throw new IllegalArgumentException("num must be >= 1"); }
    final double[] out = new double[num + 1];
    out[0] = 0.0;
    out[num] = 1.0;
    final double delta = 1.0 / num;
    for (int i = 1; i < num; i++) { out[i] = i * delta; }
    return out;
  }

  /**
   * Returns an array of (<i>num</i> + 1) longs that define, approximately, equally spaced intervals between the given
   * <i>max</i>, inclusive, and <i>min</i>, inclusive. The end points <i>max</i> and <i>min</i> are part of the
   * returned array. Because the range of the values may not exactly divide into <i>num</i> intervals,
   * the size of these intervals may vary by plus or minus one.
   * @param min the lowest positive valued (or zero) number of the range
   * @param max the highest positive valued number of the range.  <i>max</i> must be greater than <i>min</i>
   * @param num Number of requested intervals. Must be greater or equal to one, and less than or equal to
   * <i>max - min</i>.
   *
   * @return an array of (<i>num</i> + 1) longs that are approximately equally spaced between the given min and max.
   */
  public static long[] equallySpacedLongs(final long min, final long max, final int num) {
    if (num < 1 || min < 0 || max < 1 || (min >= max) || num > (max - min)) {
      throw new SketchesArgumentException(
          "Improper inputs: n < 1, min < 0, max < 1, min >= max, or n > (max - min)");
    }
    final long span = (max - min);
    final double[] splits = equallySpacedDoubles(num);
    final int len = num + 1;
    final long[] out = new long[len];
    long prev = -1L;
    for (int i = 0; i < len; i++) {
      long cur = Math.round(splits[i] * span);
      if (cur == prev) { cur++; } else { prev = cur; }
      out[i] = min + cur;
    }
    return out;
  }

  /**
   * Returns a float array of evenly spaced values between value1, inclusive, and value2 inclusive.
   * If value2 &gt; value1, the resulting sequence will be increasing.
   * If value2 &lt; value1, the resulting sequence will be decreasing.
   * @param value1 will be in index 0 of the returned array
   * @param value2 will be in the highest index of the returned array
   * @param num the total number of values including value1 and value2. Must be 2 or greater.
   * @return a float array of evenly spaced values between value1, inclusive, and value2 inclusive.
   */
  public static float[] evenlySpacedFloats(final float value1, final float value2, final int num) {
    if (num < 2) {
      throw new SketchesArgumentException("num must be >= 2");
    }
    final float[] out = new float[num];
    out[0] = value1;
    out[num - 1] = value2;
    if (num == 2) { return out; }

    final float delta = (value2 - value1) / (num - 1);

    for (int i = 1; i < num - 1; i++) { out[i] = i * delta + value1; }
    return out;
  }

  /**
   * Returns a double array of evenly spaced values between value1, inclusive, and value2 inclusive.
   * If value2 &gt; value1, the resulting sequence will be increasing.
   * If value2 &lt; value1, the resulting sequence will be decreasing.
   * @param value1 will be in index 0 of the returned array
   * @param value2 will be in the highest index of the returned array
   * @param num the total number of values including value1 and value2. Must be 2 or greater.
   * @return a float array of evenly spaced values between value1, inclusive, and value2 inclusive.
   */
  public static double[] evenlySpacedDoubles(final double value1, final double value2, final int num) {
    if (num < 2) {
      throw new SketchesArgumentException("num must be >= 2");
    }
    final double[] out = new double[num];
    out[0] = value1;
    out[num - 1] = value2;
    if (num == 2) { return out; }

    final double delta = (value2 - value1) / (num - 1);

    for (int i = 1; i < num - 1; i++) { out[i] = i * delta + value1; }
    return out;
  }

  /**
   * Returns a double array of values between min and max inclusive where the log of the
   * returned values are evenly spaced.
   * If value2 &gt; value1, the resulting sequence will be increasing.
   * If value2 &lt; value1, the resulting sequence will be decreasing.
   * @param value1 will be in index 0 of the returned array, and must be greater than zero.
   * @param value2 will be in the highest index of the returned array, and must be greater than zero.
   * @param num the total number of values including value1 and value2. Must be 2 or greater
   * @return a double array of exponentially spaced values between value1 and value2 inclusive.
   */
  public static double[] evenlyLogSpaced(final double value1, final double value2, final int num) {
    if (num < 2) {
      throw new SketchesArgumentException("num must be >= 2");
    }
    if (value1 <= 0 || value2 <= 0) {
      throw new SketchesArgumentException("value1 and value2 must be > 0.");
    }

    final double[] arr = evenlySpacedDoubles(log(value1) / Util.LOG2, log(value2) / Util.LOG2, num);
    for (int i = 0; i < arr.length; i++) { arr[i] = pow(2.0,arr[i]); }
    return arr;
  }

  /** used in search to improve rounding over a wide dynamic range */
  public static final double tailRoundingFactor = 1e7;

  /**
   * Computes the closest Natural Rank from a given Normalized Rank
   * @param normalizedRank the given normalized rank
   * @param totalN the total N
   * @param searchCrit the search criterion.
   * @return the closest Natural Rank from a given Normalized Rank
   */
  public static double getNaturalRank(
      final double normalizedRank,
      final long totalN,
      final QuantileSearchCriteria searchCrit) {
    double naturalRank = (normalizedRank * totalN);
    if (totalN <= tailRoundingFactor) {
      naturalRank = Math.round(naturalRank * tailRoundingFactor) / tailRoundingFactor;
    }
    return (searchCrit == INCLUSIVE) ? (long)Math.ceil(naturalRank) : (long)Math.floor(naturalRank);
  }

}