| /* |
| * 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; |
| |
| import static org.apache.datasketches.BoundsOnBinomialProportions.approximateLowerBoundOnP; |
| import static org.apache.datasketches.BoundsOnBinomialProportions.approximateUpperBoundOnP; |
| |
| /** |
| * This class is used to compute the bounds on the estimate of the ratio <i>|B| / |A|</i>, where: |
| * <ul> |
| * <li><i>|A|</i> is the unknown size of a set <i>A</i> of unique identifiers.</li> |
| * <li><i>|B|</i> is the unknown size of a subset <i>B</i> of <i>A</i>.</li> |
| * <li><i>a</i> = <i>|S<sub>A</sub>|</i> is the observed size of a sample of <i>A</i> |
| * that was obtained by Bernoulli sampling with a known inclusion probability <i>f</i>.</li> |
| * <li><i>b</i> = <i>|S<sub>A</sub> ∩ B|</i> is the observed size of a subset |
| * of <i>S<sub>A</sub></i>.</li> |
| * </ul> |
| * |
| * @author Kevin Lang |
| */ |
| public final class BoundsOnRatiosInSampledSets { |
| private static final double NUM_STD_DEVS = 2.0; //made a constant to simplify interface. |
| |
| private BoundsOnRatiosInSampledSets() {} |
| |
| /** |
| * Return the approximate lower bound based on a 95% confidence interval |
| * @param a See class javadoc |
| * @param b See class javadoc |
| * @param f the inclusion probability used to produce the set with size <i>a</i> and should |
| * generally be less than 0.5. Above this value, the results not be reliable. |
| * When <i>f</i> = 1.0 this returns the estimate. |
| * @return the approximate upper bound |
| */ |
| public static double getLowerBoundForBoverA(final long a, final long b, final double f) { |
| checkInputs(a, b, f); |
| if (a == 0) { return 0.0; } |
| if (f == 1.0) { return (double) b / a; } |
| return approximateLowerBoundOnP(a, b, NUM_STD_DEVS * hackyAdjuster(f)); |
| } |
| |
| /** |
| * Return the approximate upper bound based on a 95% confidence interval |
| * @param a See class javadoc |
| * @param b See class javadoc |
| * @param f the inclusion probability used to produce the set with size <i>a</i>. |
| * @return the approximate lower bound |
| */ |
| public static double getUpperBoundForBoverA(final long a, final long b, final double f) { |
| checkInputs(a, b, f); |
| if (a == 0) { return 1.0; } |
| if (f == 1.0) { return (double) b / a; } |
| return approximateUpperBoundOnP(a, b, NUM_STD_DEVS * hackyAdjuster(f)); |
| } |
| |
| /** |
| * Return the estimate of b over a |
| * @param a See class javadoc |
| * @param b See class javadoc |
| * @return the estimate of b over a |
| */ |
| public static double getEstimateOfBoverA(final long a, final long b) { |
| checkInputs(a, b, 0.3); |
| if (a == 0) { return 0.5; } |
| return (double) b / a; |
| } |
| |
| /** |
| * Return the estimate of A. See class javadoc. |
| * @param a See class javadoc |
| * @param f the inclusion probability used to produce the set with size <i>a</i>. |
| * @return the approximate lower bound |
| */ |
| public static double getEstimateOfA(final long a, final double f) { |
| checkInputs(a, 1, f); |
| return a / f; |
| } |
| |
| /** |
| * Return the estimate of B. See class javadoc. |
| * @param b See class javadoc |
| * @param f the inclusion probability used to produce the set with size <i>b</i>. |
| * @return the approximate lower bound |
| */ |
| public static double getEstimateOfB(final long b, final double f) { |
| checkInputs(b + 1, b, f); |
| return b / f; |
| } |
| |
| /** |
| * This hackyAdjuster is tightly coupled with the width of the confidence interval normally |
| * specified with number of standard deviations. To simplify this interface the number of |
| * standard deviations has been fixed to 2.0, which corresponds to a confidence interval of |
| * 95%. |
| * @param f the inclusion probability used to produce the set with size <i>a</i>. |
| * @return the hacky Adjuster |
| */ |
| private static double hackyAdjuster(final double f) { |
| final double tmp = Math.sqrt(1.0 - f); |
| return (f <= 0.5) ? tmp : tmp + (0.01 * (f - 0.5)); |
| } |
| |
| static void checkInputs(final long a, final long b, final double f) { |
| if ( ( (a - b) | (a) | (b) ) < 0) { //if any group goes negative |
| throw new SketchesArgumentException( |
| "a must be >= b and neither a nor b can be < 0: a = " + a + ", b = " + b); |
| } |
| if ((f > 1.0) || (f <= 0.0)) { |
| throw new SketchesArgumentException("Required: ((f <= 1.0) && (f > 0.0)): " + f); |
| } |
| } |
| |
| } |