From 6fbd7d73eb85bcbffd94292ce0951c16a8fdae44 Mon Sep 17 00:00:00 2001 From: Joe Ross Date: Thu, 12 Sep 2019 20:59:42 -0700 Subject: [PATCH 1/5] add asymmetric scale functions and some comparison results --- .../tdunning/math/stats/MergingDigest.java | 7 + .../tdunning/math/stats/ScaleFunction.java | 290 ++++++++++++++++++ .../math/stats/MergingDigestTest.java | 99 +++++- .../com/tdunning/math/stats/TDigestTest.java | 76 +++++ docs/asymmetric/README.md | 34 ++ docs/asymmetric/generate_plots.py | 104 +++++++ .../plots/merging/t_digest_figs_K_0q.png | Bin 0 -> 69879 bytes .../plots/merging/t_digest_figs_K_1.png | Bin 0 -> 66706 bytes .../plots/merging/t_digest_figs_K_2.png | Bin 0 -> 67808 bytes .../plots/merging/t_digest_figs_K_3.png | Bin 0 -> 64701 bytes .../plots/tree/t_digest_figs_K_0q.png | Bin 0 -> 64530 bytes .../plots/tree/t_digest_figs_K_1.png | Bin 0 -> 64491 bytes .../plots/tree/t_digest_figs_K_2.png | Bin 0 -> 67470 bytes .../plots/tree/t_digest_figs_K_3.png | Bin 0 -> 69632 bytes 14 files changed, 605 insertions(+), 5 deletions(-) create mode 100644 docs/asymmetric/README.md create mode 100644 docs/asymmetric/generate_plots.py create mode 100644 docs/asymmetric/plots/merging/t_digest_figs_K_0q.png create mode 100644 docs/asymmetric/plots/merging/t_digest_figs_K_1.png create mode 100644 docs/asymmetric/plots/merging/t_digest_figs_K_2.png create mode 100644 docs/asymmetric/plots/merging/t_digest_figs_K_3.png create mode 100644 docs/asymmetric/plots/tree/t_digest_figs_K_0q.png create mode 100644 docs/asymmetric/plots/tree/t_digest_figs_K_1.png create mode 100644 docs/asymmetric/plots/tree/t_digest_figs_K_2.png create mode 100644 docs/asymmetric/plots/tree/t_digest_figs_K_3.png diff --git a/core/src/main/java/com/tdunning/math/stats/MergingDigest.java b/core/src/main/java/com/tdunning/math/stats/MergingDigest.java index 6e1047ba..20e1bb83 100644 --- a/core/src/main/java/com/tdunning/math/stats/MergingDigest.java +++ b/core/src/main/java/com/tdunning/math/stats/MergingDigest.java @@ -214,6 +214,9 @@ public MergingDigest(double compression, int bufferSize, int size) { size = (int) Math.ceil(this.compression + sizeFudge); } + // yet more fudge + size += 20; + // ensure enough space in buffer (possibly again) if (bufferSize <= 2 * size) { bufferSize = 2 * size; @@ -240,6 +243,10 @@ public TDigest recordAllData() { return this; } + public void setUseAlternatingSort(boolean bool) { + useAlternatingSort = bool; + } + @Override void add(double x, int w, Centroid base) { add(x, w, base.data()); diff --git a/core/src/main/java/com/tdunning/math/stats/ScaleFunction.java b/core/src/main/java/com/tdunning/math/stats/ScaleFunction.java index 606eb825..8ffc97c3 100644 --- a/core/src/main/java/com/tdunning/math/stats/ScaleFunction.java +++ b/core/src/main/java/com/tdunning/math/stats/ScaleFunction.java @@ -122,6 +122,87 @@ public double normalizer(double compression, double n) { } }, + /** + * Generates cluster sizes proportional to sqrt(1-q) for q >= 1/2, and uniform cluster sizes for q < 1/2 by gluing + * the graph of the K_1 function to its tangent line at q=1/2. Changing the split point is possible. + */ + K_1_GLUED { + + double splitPoint = 0.5; + + @Override + public double k(double q, double compression, double n) { + if (q <= splitPoint) { + return (compression / (2 * Math.PI)) * (Math.asin(2 * splitPoint - 1) + + (q - splitPoint) / (Math.sqrt(splitPoint * (1 - splitPoint)))); + } else { + return compression * Math.asin(2 * q - 1) / (2 * Math.PI); + } + } + + @Override + public double k(double q, double normalizer) { + if (q <= splitPoint) { + return normalizer * (Math.asin(2 * splitPoint - 1) + + (q - splitPoint) / (Math.sqrt(splitPoint * (1 - splitPoint)))); + } else { + return normalizer * Math.asin(2 * q - 1); + } + } + + + @Override + public double q(double k, double compression, double n) { + if (k <= compression * Math.asin(2 * splitPoint - 1) / Math.PI / 2) { + double ww = k * Math.PI * 2 / compression - Math.asin(2 * splitPoint - 1); + return ww * Math.sqrt(splitPoint * (1 - splitPoint)) + splitPoint; + } else { + return (Math.sin(k * 2 * Math.PI / compression) + 1) / 2; + } + } + + @Override + public double q(double k, double normalizer) { + if (k <= normalizer * Math.asin(2 * splitPoint - 1) ) { + double ww = k / normalizer - Math.asin(2 * splitPoint - 1); + return ww * Math.sqrt(splitPoint * (1 - splitPoint)) + splitPoint; + } else { + return (Math.sin(k / normalizer) + 1) / 2; + } + } + + @Override + public double max(double q, double compression, double n) { + if (q <= 0) { + return 0; + } else if (q >= 1) { + return 0; + } else if (q <= splitPoint) { + return Math.sqrt(splitPoint * (1 - splitPoint)) * 2 * Math.PI / compression; + } else { + return 2 * Math.sin(Math.PI / compression) * Math.sqrt(q * (1 - q)); + } + } + + @Override + public double max(double q, double normalizer) { + if (q <= 0) { + return 0; + } else if (q >= 1) { + return 0; + } else if (q <= splitPoint) { + return Math.sqrt(splitPoint * (1 - splitPoint)) / normalizer; + } else { + return 2 * Math.sin(0.5 / normalizer) * Math.sqrt(q * (1 - q)); + } + } + + @Override + public double normalizer(double compression, double n) { + return compression / (2 * Math.PI); + } + }, + /** * Generates cluster sizes proportional to sqrt(q*(1-q)) but avoids computation of asin in the critical path by * using an approximate version. @@ -245,6 +326,100 @@ private double Z(double compression, double n) { } }, + /** + * Generates cluster sizes proportional to 1-q for q >= 1/2, and uniform cluster sizes for q < 1/2 by gluing + * the graph of the K_2 function to its tangent line at q=1/2. Changing the split point is possible. + */ + K_2_GLUED { + + double splitPoint = 0.5; // should be between 1e-15 and 1 - 1e-15 + + @Override + public double k(double q, double compression, double n) { + if (n <= 1) { + if (q <= 0) { + return -10; + } else if (q >= 1) { + return 10; + } else { + return 0; + } + } + if (q <= splitPoint) { + return (((q - splitPoint) / splitPoint / (1 - splitPoint)) + + Math.log(splitPoint / (1 - splitPoint))) * compression / Z(compression, n); + } else if (q == 1) { + return 2 * k((n - 1) / n, compression, n); + } else { + return compression * Math.log(q / (1 - q)) / Z(compression, n); + } + } + + @Override + public double k(double q, double normalizer) { + if (q <= splitPoint) { + return (((q - splitPoint) / splitPoint / (1 - splitPoint)) + + Math.log(splitPoint / (1 - splitPoint))) * normalizer; // fixed parens + } else if (q > 1 - 1e-15) { + // this will return something more extreme than q = (n-1)/n + return 2 * k(1 - 1e-15, normalizer); + } else { + return Math.log(q / (1 - q)) * normalizer; + } + } + + @Override + public double q(double k, double compression, double n) { //fixedher too + if (k <= compression * Math.log(splitPoint / (1 - splitPoint)) / Z(compression, n)) { + return splitPoint * (1 - splitPoint) * (k * Z(compression, n) / compression - + Math.log(splitPoint / (1 - splitPoint))) + splitPoint; + } else { + double w = Math.exp(k * Z(compression, n) / compression); + return w / (1 + w); + } + } + + @Override + public double q(double k, double normalizer) { + if (k <= Math.log(splitPoint / (1 - splitPoint)) * normalizer) { ///fixed whole thing + return splitPoint * (1 - splitPoint) * (k / normalizer - + Math.log(splitPoint / (1 - splitPoint))) + splitPoint; + } + else { + double w = Math.exp(k / normalizer); + return w / (1 + w); + } + } + + @Override + public double max(double q, double compression, double n) { + if (q <= splitPoint) { + return Z(compression, n) * splitPoint * (1 - splitPoint) / compression; + } + else { + return Z(compression, n) * q * (1 - q) / compression; + } + } + + @Override + public double max(double q, double normalizer) { + if (q <= splitPoint) { + return splitPoint * (1 - splitPoint) / normalizer; // changed to division. + } else { + return q * (1 - q) / normalizer; + } + } + + @Override + public double normalizer(double compression, double n) { + return compression / Z(compression, n); + } + + private double Z(double compression, double n) { + return 4 * Math.log(n / compression) + 24; + } + }, + /** * Generates cluster sizes proportional to min(q, 1-q). This makes tail error bounds tighter than for K_1 or K_2. * The use of a normalizing function results in a strictly bounded number of clusters no matter how many samples. @@ -318,6 +493,121 @@ private double Z(double compression, double n) { } }, + /** + * Generates cluster sizes proportional to 1-q for q >= 1/2, and uniform cluster sizes for q < 1/2 by gluing + * the graph of the K_3 function to its tangent line at q=1/2. + */ + K_3_GLUED { + @Override + public double k(double q, double compression, double n) { + if (q <= 0.5) { + return compression * (2 * q - 1) / Z(compression, n); + } else if (q > 1 - 0.9 / n) { + return 10 * k((n - 1) / n, compression, n); + } else { + return - compression * Math.log(2 * (1 - q)) / Z(compression, n); + } + } + + @Override + public double k(double q, double normalizer) { + if (q <= 0.5) { + return normalizer * (2 * q - 1); + } else if (q > 1 - 1e-15) { + return 10 * k(1 - 1e-15, normalizer); + } else { + return - normalizer * Math.log(2 * (1 - q)); + } + } + + @Override + public double q(double k, double compression, double n) { + if (k <= 0) { + return ((k * Z(compression, n) / compression) + 1) / 2; + } else { + return 1 - (Math.exp(-k * Z(compression, n) / compression) / 2); + } + } + + @Override + public double q(double k, double normalizer) { + if (k <= 0) { + return ((k / normalizer) + 1 ) / 2; + } else { + return 1 - (Math.exp(-k / normalizer) / 2); + } + } + + @Override + public double max(double q, double compression, double n) { + if (q <= 0.5) { + return Z(compression, n) / 2d / compression; + } else { + return Z(compression, n) * (1-q) / compression; + } + } + + @Override + public double max(double q, double normalizer) { + if (q <= 0.5) { + return 1d / 2 / normalizer; + } else { + return (1-q) / normalizer; + } + } + + @Override + public double normalizer(double compression, double n) { + return compression / Z(compression, n); + } + + private double Z(double compression, double n) { + return 4 * Math.log(n / compression) + 21; + } + }, + + + /** + * Generates cluster sizes proportional to 1/(1+q). + */ + K_QUADRATIC { + @Override + public double k(double q, double compression, double n) { + return compression * (q * q + 2 * q) / 6; + } + + @Override + public double k(double q, double normalizer) { + return normalizer * (q * q + 2 * q) / 3; + } + + @Override + public double q(double k, double compression, double n) { + return Math.sqrt(compression * (compression + 6 * k)) / compression - 1; + } + + @Override + public double q(double k, double normalizer) { + return Math.sqrt(normalizer * (normalizer + 3 * k)) / normalizer - 1; + } + + @Override + public double max(double q, double compression, double n) { + return 3 / compression / (1 + q); + } + + @Override + public double max(double q, double normalizer) { + return 3 / 2 / normalizer / (1 + q); + } + + @Override + public double normalizer(double compression, double n) { + return compression / 2; + } + + }, + /** * Generates cluster sizes proportional to q*(1-q). This makes the tail error bounds tighter. This version does not * use a normalizer function and thus the number of clusters increases roughly proportional to log(n). That is good diff --git a/core/src/test/java/com/tdunning/math/stats/MergingDigestTest.java b/core/src/test/java/com/tdunning/math/stats/MergingDigestTest.java index e373cf39..21fe6090 100644 --- a/core/src/test/java/com/tdunning/math/stats/MergingDigestTest.java +++ b/core/src/test/java/com/tdunning/math/stats/MergingDigestTest.java @@ -18,17 +18,18 @@ package com.tdunning.math.stats; import com.carrotsearch.randomizedtesting.annotations.Seed; -import com.google.common.collect.Lists; +import org.apache.commons.math3.util.Pair; import org.apache.mahout.common.RandomUtils; +import org.apache.mahout.math.jet.random.AbstractContinousDistribution; +import org.apache.mahout.math.jet.random.Uniform; import org.junit.Before; import org.junit.BeforeClass; import org.junit.Test; +import java.io.FileWriter; import java.io.IOException; import java.nio.ByteBuffer; -import java.util.Iterator; -import java.util.List; -import java.util.Random; +import java.util.*; //to freeze the tests with a particular seed, put the seed on the next line //@Seed("84527677CF03B566:A6FF596BDDB2D59D") @@ -57,4 +58,92 @@ public void testSetUp() { protected TDigest fromBytes(ByteBuffer bytes) { return MergingDigest.fromBytes(bytes); } -} \ No newline at end of file + + + + @Test + public void writeAsymmetricScaleFunctionResults() { + + List scaleFcns = Arrays.asList(ScaleFunction.K_0, ScaleFunction.K_1, + ScaleFunction.K_2, ScaleFunction.K_3, ScaleFunction.K_1_GLUED, + ScaleFunction.K_2_GLUED, ScaleFunction.K_3_GLUED, ScaleFunction.K_QUADRATIC); + + int numTrials = 100; + + Map> digestParams = new HashMap<>(); + + for (ScaleFunction fcn : scaleFcns) { + if (fcn.toString().endsWith("GLUED") || fcn.toString().endsWith("QUADRATIC")) { + digestParams.put(fcn.toString(), new Pair<>(fcn, false)); + } else { + digestParams.put(fcn.toString() + "_USUAL", new Pair<>(fcn, false)); + } + } + writeSeveralDigestUniformResults(digestParams, numTrials, "../docs/asymmetric/data/merging/"); + + } + + public void writeSeveralDigestUniformResults(Map> digestParams, int numTrials, + String writeLocation) { + + int trialSize = 1_000_000; + double compression = 100; + double[] quants = new double[]{0.00001, 0.0001, 0.001, 0.01, 0.1, + 0.5, 0.9, 0.99, 0.999, 0.9999, 0.99999}; + + Map> centroidCounts= new HashMap<>(); + + for (Map.Entry> entry : digestParams.entrySet()) { + centroidCounts.put(entry.getKey(), new ArrayList()); + try { + Map> records = new HashMap<>(); + for (double q : quants) { + records.put(q, new ArrayList()); + } + for (int j = 0; j < numTrials; j++) { + MergingDigest digest = (MergingDigest) factory(compression).create(); + digest.setScaleFunction(entry.getValue().getFirst()); + digest.setUseAlternatingSort(entry.getValue().getSecond()); + Random rand = new Random(); + AbstractContinousDistribution gen = new Uniform(50, 51, rand); + double[] data = new double[trialSize]; + for (int i = 0; i < trialSize; i++) { + data[i] = gen.nextDouble(); + digest.add(data[i]); + } + Arrays.sort(data); + digest.compress(); + for (double q : quants) { + double x1 = Dist.quantile(q, data); + double q1 = Dist.cdf(x1, data); + double q2 = digest.cdf(x1); + records.get(q).add(String.valueOf(Math.abs(q1 - q2)) + "," + + String.valueOf(Math.abs(q1 - q2) / Math.min(q, 1 - q)) + "\n"); + } + centroidCounts.get(entry.getKey()).add(digest.centroids().size()); + } + for (double q : quants) { + FileWriter csvWriter = new FileWriter(writeLocation + entry.getKey() + "_" + String.valueOf(q) + ".csv"); + csvWriter.append("error_q,norm_error_q\n"); + for (String obs : records.get(q)) { + csvWriter.append(obs); + } + csvWriter.flush(); + csvWriter.close(); + } + + FileWriter csvWriter = new FileWriter(writeLocation + entry.getKey() + "_centroid_counts.csv"); + csvWriter.append("centroid_count\n"); + for (Integer ct : centroidCounts.get(entry.getKey())) { + csvWriter.append(ct.toString()).append("\n"); + } + csvWriter.flush(); + csvWriter.close(); + + } catch (IOException e) { + System.out.println(e.toString()); + return; + } + } + } +} diff --git a/core/src/test/java/com/tdunning/math/stats/TDigestTest.java b/core/src/test/java/com/tdunning/math/stats/TDigestTest.java index 41dfd4d7..51066c3b 100644 --- a/core/src/test/java/com/tdunning/math/stats/TDigestTest.java +++ b/core/src/test/java/com/tdunning/math/stats/TDigestTest.java @@ -127,6 +127,82 @@ public void offsetUniform() { } } + @Test + public void writeUniformResultsWithCompression() { + + List scaleFcns = Arrays.asList(ScaleFunction.K_0, ScaleFunction.K_1, + ScaleFunction.K_2, ScaleFunction.K_3, ScaleFunction.K_1_GLUED, + ScaleFunction.K_2_GLUED, ScaleFunction.K_3_GLUED, ScaleFunction.K_QUADRATIC); + + int trialSize = 1_000_000; + + Map> centroidCounts= new HashMap<>(); + + for (ScaleFunction scaleFcn : scaleFcns) { + centroidCounts.put(scaleFcn, new ArrayList()); + try { + Map> records = new HashMap<>(); + double[] quants = new double[]{0.00001, 0.0001, 0.001, 0.01, 0.1, + 0.5, 0.9, 0.99, 0.999, 0.9999, 0.99999}; + for (double q : quants) { + records.put(q, new ArrayList()); + } + for (int j = 0; j < 100; j++) { + for (double compression : new double[]{100}) { + TDigest digest = factory(compression).create(); + digest.setScaleFunction(scaleFcn); + Random rand = new Random(); + AbstractContinousDistribution gen = new Uniform(50, 51, rand); + double[] data = new double[trialSize]; + for (int i = 0; i < trialSize; i++) { + data[i] = gen.nextDouble(); + digest.add(data[i]); + } + Arrays.sort(data); + digest.compress(); + for (double q : quants) { + double x1 = Dist.quantile(q, data); + double q1 = Dist.cdf(x1, data); + double q2 = digest.cdf(x1); + records.get(q).add(String.valueOf(Math.abs(q1 - q2)) + "," + + String.valueOf(Math.abs(q1 - q2) / Math.min(q, 1 - q)) + "\n"); + } + centroidCounts.get(scaleFcn).add(digest.centroids().size()); + } + } + + String fcnName; + + if (scaleFcn.toString().endsWith("GLUED") || scaleFcn.toString().endsWith("QUADRATIC")) { + fcnName = scaleFcn.toString() ; + } else { + fcnName = scaleFcn.toString() + "_USUAL"; + } + + for (double q : quants) { + FileWriter csvWriter = new FileWriter("../docs/asymmetric/data/tree/" + fcnName + "_" + String.valueOf(q) + ".csv"); + csvWriter.append("error_q,norm_error_q\n"); + for (String obs : records.get(q)) { + csvWriter.append(obs); + } + csvWriter.flush(); + csvWriter.close(); + } + + FileWriter csvWriter = new FileWriter("../docs/asymmetric/data/tree/" + fcnName + "_centroid_counts.csv"); + csvWriter.append("centroid_count\n"); + for (Integer ct : centroidCounts.get(scaleFcn)) { + csvWriter.append(ct.toString()).append("\n"); + } + csvWriter.flush(); + csvWriter.close(); + + } catch (IOException e) { + return; + } + } + } + @Test public void bigJump() { TDigest digest = factory(100).create(); diff --git a/docs/asymmetric/README.md b/docs/asymmetric/README.md new file mode 100644 index 00000000..e46b5551 --- /dev/null +++ b/docs/asymmetric/README.md @@ -0,0 +1,34 @@ +This directory contains some empirical results of constructing t-digests with asymmetric scale functions, +which may be of particular interest for distributions with substantial skew. Suitable asymmetric scale functions +can be obtained by gluing the familiar k1, k2, k3 to their tangent lines at some point p in (0, 1). +A theoretical justification for this construction (namely, the proofs that the modified scale functions produce +mergeable data structures that can operate online), together with these results, will be submitted for publication shortly. + +The main goal here is to compare the usual scale functions with their asymmetric counterparts (using the point p=1/2 as a gluing location), +both in terms of accuracy and memory consumption (via number of centroids). A quadratic scale function is considered as well. + +The gist of the results is that for each ki mentioned above, the asymmetric (glued) variant has the +error profile of ki for quantiles greater than 1/2 (i.e., above the median) and that of k0 +(a linear function producing equal-sized bins) for quantiles on the other side. + +The data and summarizing plots can be produced in two steps. + +### Generate data + +In `TDigestTests.java`, run `writeUniformResultsWithCompression` with the `ALVTreeDigest` implementation, i.e., run +`AVLTreeDigestTest.writeUniformResultsWithCompression`. + +In `MergingDigestTest.java`, run `writeAsymmetricScaleFunctionResults`. + +These will write data files to subdirectories of the `data` directory of `asymmetric`. +The data so generated is already present. + + +### Generate plots + +Now run the script `generate_plots.py` located in this directory. + +This script expects to be present the results of running the tests as above. +It will write plots (as PNG files) to subdirectories of the `plots` directory. +The figures so generated are already present. + diff --git a/docs/asymmetric/generate_plots.py b/docs/asymmetric/generate_plots.py new file mode 100644 index 00000000..7fab2657 --- /dev/null +++ b/docs/asymmetric/generate_plots.py @@ -0,0 +1,104 @@ +import os +import pandas as pd +import matplotlib.pyplot as plt + +in_tree = "data/tree/" +out_tree = "plots/tree/" + +in_merging = "data/merging/" +out_merging = "plots/merging/" + + +scale_function_prefixes = ["K_{0}_{1}".format(x, y) for x in ["1", "2", "3"] for y in + ["USUAL", "GLUED"]] + ["K_0_USUAL"] + ["K_QUADRATIC"] + + +def clean_string(s): + return s.replace("K", "k").replace("_USUAL", "").replace("GLUED", "glued"). \ + replace("QUADRATIC", "quadratic") + + +cc_suffix = "_centroid_counts.csv" + +axis_labels = {'.99': 2, '0.99': 2, + '1.0E-5': -5, '0.00001': -5, + '1.0E-4': -4, '0.0001': -4, + '.99999': 5, '0.99999': 5, + '.001': -3, '0.001': -3, + '.9': 1, '0.9': 1, + '.999': 3, '0.999': 3, + '.9999': 4, '0.9999': 4, + '.1': -1, '0.1': -1, + '.01': -2, '0.01': -2, + '.5': 0, '0.5': 0} + + +def generate_figures(prefixes=scale_function_prefixes, save=False, outfilename="t_digest_figs", + location=in_tree, implementation=""): + data = {} + + for prefix in prefixes: + data[prefix] = {} + filenames = filter(lambda x: x.startswith(prefix) and not x.endswith(cc_suffix), + os.listdir(location)) + for filename in filenames: + value = filename.replace(prefix + "_", "").replace(".csv", "") + with open(location + filename, 'r') as f: + data[prefix][value] = pd.read_csv(f) + + centroid_data = {} + centroid_counts = map(lambda x: x + cc_suffix, prefixes) + for cc_name in centroid_counts: + with open(location + cc_name, 'r') as f: + centroid_data[cc_name.replace(cc_suffix, "")] = pd.read_csv(f) + + fig, ax = plt.subplots(len(prefixes), 3, squeeze=False) + fig.set_figheight(4 * len(prefixes)) + fig.set_figwidth(15) + + for prefix in prefixes: + error_q_list, norm_error_q_list = [], [] + pos = [] + for v in data[prefix]: + pos.append(axis_labels[v]) + df = data[prefix][v] + error_q_list.append(df['error_q']) + norm_error_q_list.append(df['norm_error_q']) + ax[prefixes.index(prefix), 0].set_title(clean_string(prefix) + implementation + " error") + ax[prefixes.index(prefix), 0].boxplot(error_q_list, positions=pos, whis=[5, 95], + showfliers=False) + ax[prefixes.index(prefix), 1].set_title( + clean_string(prefix) + implementation + " norm_error") + ax[prefixes.index(prefix), 1].boxplot(norm_error_q_list, positions=pos, whis=[5, 95], + showfliers=False) + ax[prefixes.index(prefix), 2].set_title( + clean_string(prefix) + implementation + " " + cc_suffix.replace(".csv", "").lstrip("_")) + ax[prefixes.index(prefix), 2].hist(centroid_data[prefix]["centroid_count"], range=[5, 95], + bins=30) + + fig.subplots_adjust(left=0.08, right=0.98, bottom=0.05, top=0.9, + hspace=0.4, wspace=0.3) + + if save is True: + plt.savefig(outfilename) + elif save is False: + plt.show() + + +params = [(out_tree, in_tree, " (tree)"), (out_merging, in_merging, " (merging)")] + + +def main(): + for a, b, c in params: + generate_figures(prefixes=["K_0_USUAL", "K_QUADRATIC"], save=True, + outfilename="{}t_digest_figs_K_0q".format(a), location=b, implementation=c) + generate_figures(prefixes=["K_1_{}".format(y) for y in ["USUAL", "GLUED"]], save=True, + outfilename="{}t_digest_figs_K_1".format(a), location=b, implementation=c) + generate_figures(prefixes=["K_2_{}".format(y) for y in ["USUAL", "GLUED"]], save=True, + outfilename="{}t_digest_figs_K_2".format(a), location=b, implementation=c) + generate_figures(prefixes=["K_3_{}".format(y) for y in ["USUAL", "GLUED"]], save=True, + outfilename="{}t_digest_figs_K_3".format(a), location=b, implementation=c) + + +if __name__ == "__main__": + main() diff --git a/docs/asymmetric/plots/merging/t_digest_figs_K_0q.png b/docs/asymmetric/plots/merging/t_digest_figs_K_0q.png new file mode 100644 index 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