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/**
* 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.hadoop.hive.ql.udf.generic;
import java.util.ArrayList;
import java.util.List;
import java.util.Collections;
import java.util.Random;
import org.apache.hadoop.hive.serde2.io.DoubleWritable;
import org.apache.hadoop.hive.serde2.objectinspector.primitive.DoubleObjectInspector;
/**
* A generic, re-usable histogram class that supports partial aggregations.
* The algorithm is a heuristic adapted from the following paper:
* Yael Ben-Haim and Elad Tom-Tov, "A streaming parallel decision tree algorithm",
* J. Machine Learning Research 11 (2010), pp. 849--872. Although there are no approximation
* guarantees, it appears to work well with adequate data and a large (e.g., 20-80) number
* of histogram bins.
*/
public class NumericHistogram {
/**
* The Coord class defines a histogram bin, which is just an (x,y) pair.
*/
static class Coord implements Comparable {
double x;
double y;
public int compareTo(Object other) {
return Double.compare(x, ((Coord) other).x);
}
};
// Class variables
private int nbins;
private int nusedbins;
private ArrayList bins;
private Random prng;
/**
* Creates a new histogram object. Note that the allocate() or merge()
* method must be called before the histogram can be used.
*/
public NumericHistogram() {
nbins = 0;
nusedbins = 0;
bins = null;
// init the RNG for breaking ties in histogram merging. A fixed seed is specified here
// to aid testing, but can be eliminated to use a time-based seed (which would
// make the algorithm non-deterministic).
prng = new Random(31183);
}
/**
* Resets a histogram object to its initial state. allocate() or merge() must be
* called again before use.
*/
public void reset() {
bins = null;
nbins = nusedbins = 0;
}
/**
* Returns the number of bins currently being used by the histogram.
*/
public int getUsedBins() {
return nusedbins;
}
/**
* Returns true if this histogram object has been initialized by calling merge()
* or allocate().
*/
public boolean isReady() {
return nbins != 0;
}
/**
* Returns a particular histogram bin.
*/
public Coord getBin(int b) {
return bins.get(b);
}
/**
* Sets the number of histogram bins to use for approximating data.
*
* @param num_bins Number of non-uniform-width histogram bins to use
*/
public void allocate(int num_bins) {
nbins = num_bins;
bins = new ArrayList();
nusedbins = 0;
}
/**
* Takes a serialized histogram created by the serialize() method and merges
* it with the current histogram object.
*
* @param other A serialized histogram created by the serialize() method
* @see #merge
*/
public void merge(List other, DoubleObjectInspector doi) {
if(other == null) {
return;
}
if(nbins == 0 || nusedbins == 0) {
// Our aggregation buffer has nothing in it, so just copy over 'other'
// by deserializing the ArrayList of (x,y) pairs into an array of Coord objects
nbins = (int) doi.get(other.get(0));
nusedbins = (other.size()-1)/2;
bins = new ArrayList(nusedbins);
for (int i = 1; i < other.size(); i+=2) {
Coord bin = new Coord();
bin.x = doi.get(other.get(i));
bin.y = doi.get(other.get(i+1));
bins.add(bin);
}
} else {
// The aggregation buffer already contains a partial histogram. Therefore, we need
// to merge histograms using Algorithm #2 from the Ben-Haim and Tom-Tov paper.
ArrayList tmp_bins = new ArrayList(nusedbins + (other.size()-1)/2);
// Copy all the histogram bins from us and 'other' into an overstuffed histogram
for (int i = 0; i < nusedbins; i++) {
Coord bin = new Coord();
bin.x = bins.get(i).x;
bin.y = bins.get(i).y;
tmp_bins.add(bin);
}
for (int j = 1; j < other.size(); j += 2) {
Coord bin = new Coord();
bin.x = doi.get(other.get(j));
bin.y = doi.get(other.get(j+1));
tmp_bins.add(bin);
}
Collections.sort(tmp_bins);
// Now trim the overstuffed histogram down to the correct number of bins
bins = tmp_bins;
nusedbins += (other.size()-1)/2;
trim();
}
}
/**
* Adds a new data point to the histogram approximation. Make sure you have
* called either allocate() or merge() first. This method implements Algorithm #1
* from Ben-Haim and Tom-Tov, "A Streaming Parallel Decision Tree Algorithm", JMLR 2010.
*
* @param v The data point to add to the histogram approximation.
*/
public void add(double v) {
// Binary search to find the closest bucket that v should go into.
// 'bin' should be interpreted as the bin to shift right in order to accomodate
// v. As a result, bin is in the range [0,N], where N means that the value v is
// greater than all the N bins currently in the histogram. It is also possible that
// a bucket centered at 'v' already exists, so this must be checked in the next step.
int bin = 0;
for(int l=0, r=nusedbins; l < r; ) {
bin = (l+r)/2;
if (bins.get(bin).x > v) {
r = bin;
} else {
if (bins.get(bin).x < v) {
l = ++bin;
} else {
break; // break loop on equal comparator
}
}
}
// If we found an exact bin match for value v, then just increment that bin's count.
// Otherwise, we need to insert a new bin and trim the resulting histogram back to size.
// A possible optimization here might be to set some threshold under which 'v' is just
// assumed to be equal to the closest bin -- if fabs(v-bins[bin].x) < THRESHOLD, then
// just increment 'bin'. This is not done now because we don't want to make any
// assumptions about the range of numeric data being analyzed.
if (bin < nusedbins && bins.get(bin).x == v) {
bins.get(bin).y++;
} else {
Coord newBin = new Coord();
newBin.x = v;
newBin.y = 1;
bins.add(bin, newBin);
// Trim the bins down to the correct number of bins.
if (++nusedbins > nbins) {
trim();
}
}
}
/**
* Trims a histogram down to 'nbins' bins by iteratively merging the closest bins.
* If two pairs of bins are equally close to each other, decide uniformly at random which
* pair to merge, based on a PRNG.
*/
private void trim() {
while(nusedbins > nbins) {
// Find the closest pair of bins in terms of x coordinates. Break ties randomly.
double smallestdiff = bins.get(1).x - bins.get(0).x;
int smallestdiffloc = 0, smallestdiffcount = 1;
for(int i = 1; i < nusedbins-1; i++) {
double diff = bins.get(i+1).x - bins.get(i).x;
if(diff < smallestdiff) {
smallestdiff = diff;
smallestdiffloc = i;
smallestdiffcount = 1;
} else {
if(diff == smallestdiff && prng.nextDouble() <= (1.0/++smallestdiffcount) ) {
smallestdiffloc = i;
}
}
}
// Merge the two closest bins into their average x location, weighted by their heights.
// The height of the new bin is the sum of the heights of the old bins.
// double d = bins[smallestdiffloc].y + bins[smallestdiffloc+1].y;
// bins[smallestdiffloc].x *= bins[smallestdiffloc].y / d;
// bins[smallestdiffloc].x += bins[smallestdiffloc+1].x / d *
// bins[smallestdiffloc+1].y;
// bins[smallestdiffloc].y = d;
double d = bins.get(smallestdiffloc).y + bins.get(smallestdiffloc+1).y;
Coord smallestdiffbin = bins.get(smallestdiffloc);
smallestdiffbin.x *= smallestdiffbin.y / d;
smallestdiffbin.x += bins.get(smallestdiffloc+1).x / d * bins.get(smallestdiffloc+1).y;
smallestdiffbin.y = d;
// Shift the remaining bins left one position
bins.remove(smallestdiffloc+1);
nusedbins--;
}
}
/**
* Gets an approximate quantile value from the current histogram. Some popular
* quantiles are 0.5 (median), 0.95, and 0.98.
*
* @param q The requested quantile, must be strictly within the range (0,1).
* @return The quantile value.
*/
public double quantile(double q) {
assert(bins != null && nusedbins > 0 && nbins > 0);
double sum = 0, csum = 0;
int b;
for(b = 0; b < nusedbins; b++) {
sum += bins.get(b).y;
}
for(b = 0; b < nusedbins; b++) {
csum += bins.get(b).y;
if(csum / sum >= q) {
if(b == 0) {
return bins.get(b).x;
}
csum -= bins.get(b).y;
double r = bins.get(b-1).x +
(q*sum - csum) * (bins.get(b).x - bins.get(b-1).x)/(bins.get(b).y);
return r;
}
}
return -1; // for Xlint, code will never reach here
}
/**
* In preparation for a Hive merge() call, serializes the current histogram object into an
* ArrayList of DoubleWritable objects. This list is deserialized and merged by the
* merge method.
*
* @return An ArrayList of Hadoop DoubleWritable objects that represents the current
* histogram.
* @see #merge
*/
public ArrayList serialize() {
ArrayList result = new ArrayList();
// Return a single ArrayList where the first element is the number of bins bins,
// and subsequent elements represent bins (x,y) pairs.
result.add(new DoubleWritable(nbins));
if(bins != null) {
for(int i = 0; i < nusedbins; i++) {
result.add(new DoubleWritable(bins.get(i).x));
result.add(new DoubleWritable(bins.get(i).y));
}
}
return result;
}
public int getNumBins() {
return bins == null ? 0 : bins.size();
}
}
