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Example 71 with Max

use of org.apache.commons.math3.stat.descriptive.rank.Max in project metron by apache.

the class StatisticalBinningPerformanceDriver method main.

public static void main(String... argv) {
    DescriptiveStatistics perfStats = new DescriptiveStatistics();
    OnlineStatisticsProvider statsProvider = new OnlineStatisticsProvider();
    List<Double> values = new ArrayList<>();
    GaussianRandomGenerator gaussian = new GaussianRandomGenerator(new MersenneTwister(0L));
    for (int i = 0; i < NUM_DATA_POINTS; ++i) {
        // get the data point out of the [0,1] range
        double d = 1000 * gaussian.nextNormalizedDouble();
        values.add(d);
        statsProvider.addValue(d);
    }
    for (int perfRun = 0; perfRun < NUM_RUNS; ++perfRun) {
        StellarStatisticsFunctions.StatsBin bin = new StellarStatisticsFunctions.StatsBin();
        long start = System.currentTimeMillis();
        Random r = new Random(0);
        for (int i = 0; i < TRIALS_PER_RUN; ++i) {
            // grab a random value and fuzz it a bit so we make sure there's no cheating via caching in t-digest.
            bin.apply(ImmutableList.of(statsProvider, values.get(r.nextInt(values.size())) - 3.5, PERCENTILES));
        }
        perfStats.addValue(System.currentTimeMillis() - start);
    }
    System.out.println("Min/25th/50th/75th/Max Milliseconds: " + perfStats.getMin() + " / " + perfStats.getPercentile(25) + " / " + perfStats.getPercentile(50) + " / " + perfStats.getPercentile(75) + " / " + perfStats.getMax());
}
Also used : DescriptiveStatistics(org.apache.commons.math3.stat.descriptive.DescriptiveStatistics) GaussianRandomGenerator(org.apache.commons.math3.random.GaussianRandomGenerator) ArrayList(java.util.ArrayList) Random(java.util.Random) MersenneTwister(org.apache.commons.math3.random.MersenneTwister)

Example 72 with Max

use of org.apache.commons.math3.stat.descriptive.rank.Max in project metron by apache.

the class StellarStatisticsFunctionsTest method run.

/**
 * Runs a Stellar expression.
 * @param expr The expression to run.
 * @param variables The variables available to the expression.
 */
private static Object run(String expr, Map<String, Object> variables) {
    StellarProcessor processor = new StellarProcessor();
    Object ret = processor.parse(expr, new DefaultVariableResolver(x -> variables.get(x), x -> variables.containsKey(x)), StellarFunctions.FUNCTION_RESOLVER(), Context.EMPTY_CONTEXT());
    byte[] raw = SerDeUtils.toBytes(ret);
    Object actual = SerDeUtils.fromBytes(raw, Object.class);
    if (ret instanceof StatisticsProvider) {
        StatisticsProvider left = (StatisticsProvider) ret;
        StatisticsProvider right = (StatisticsProvider) actual;
        // N
        tolerantAssertEquals(prov -> prov.getCount(), left, right);
        // sum
        tolerantAssertEquals(prov -> prov.getSum(), left, right, 1e-3);
        // sum of squares
        tolerantAssertEquals(prov -> prov.getSumSquares(), left, right, 1e-3);
        // sum of squares
        tolerantAssertEquals(prov -> prov.getSumLogs(), left, right, 1e-3);
        // Mean
        tolerantAssertEquals(prov -> prov.getMean(), left, right, 1e-3);
        // Quadratic Mean
        tolerantAssertEquals(prov -> prov.getQuadraticMean(), left, right, 1e-3);
        // SD
        tolerantAssertEquals(prov -> prov.getStandardDeviation(), left, right, 1e-3);
        // Variance
        tolerantAssertEquals(prov -> prov.getVariance(), left, right, 1e-3);
        // Min
        tolerantAssertEquals(prov -> prov.getMin(), left, right, 1e-3);
        // Max
        tolerantAssertEquals(prov -> prov.getMax(), left, right, 1e-3);
        // Kurtosis
        tolerantAssertEquals(prov -> prov.getKurtosis(), left, right, 1e-3);
        // Skewness
        tolerantAssertEquals(prov -> prov.getSkewness(), left, right, 1e-3);
        for (double d = 10.0; d < 100.0; d += 10) {
            final double pctile = d;
            // This is a sketch, so we're a bit more forgiving here in our choice of \epsilon.
            tolerantAssertEquals(prov -> prov.getPercentile(pctile), left, right, 1e-2);
        }
    }
    return ret;
}
Also used : StellarProcessor(org.apache.metron.stellar.common.StellarProcessor) java.util(java.util) Assert.assertNotNull(org.junit.Assert.assertNotNull) SerDeUtils(org.apache.metron.common.utils.SerDeUtils) StellarProcessor(org.apache.metron.stellar.common.StellarProcessor) RunWith(org.junit.runner.RunWith) Assert.assertTrue(org.junit.Assert.assertTrue) Test(org.junit.Test) GaussianRandomGenerator(org.apache.commons.math3.random.GaussianRandomGenerator) DefaultVariableResolver(org.apache.metron.stellar.dsl.DefaultVariableResolver) Function(java.util.function.Function) String.format(java.lang.String.format) SummaryStatistics(org.apache.commons.math3.stat.descriptive.SummaryStatistics) ImmutableList(com.google.common.collect.ImmutableList) MersenneTwister(org.apache.commons.math3.random.MersenneTwister) DescriptiveStatistics(org.apache.commons.math3.stat.descriptive.DescriptiveStatistics) StellarFunctions(org.apache.metron.stellar.dsl.StellarFunctions) Assert(org.junit.Assert) Parameterized(org.junit.runners.Parameterized) Assert.assertEquals(org.junit.Assert.assertEquals) Joiner(com.google.common.base.Joiner) Context(org.apache.metron.stellar.dsl.Context) Before(org.junit.Before) DefaultVariableResolver(org.apache.metron.stellar.dsl.DefaultVariableResolver)

Example 73 with Max

use of org.apache.commons.math3.stat.descriptive.rank.Max in project incubator-systemml by apache.

the class DataGenMR method runJob.

/**
 * <p>Starts a Rand MapReduce job which will produce one or more random objects.</p>
 *
 * @param inst MR job instruction
 * @param dataGenInstructions array of data gen instructions
 * @param instructionsInMapper instructions in mapper
 * @param aggInstructionsInReducer aggregate instructions in reducer
 * @param otherInstructionsInReducer other instructions in reducer
 * @param numReducers number of reducers
 * @param replication file replication
 * @param resultIndexes result indexes for each random object
 * @param dimsUnknownFilePrefix file path prefix when dimensions unknown
 * @param outputs output file for each random object
 * @param outputInfos output information for each random object
 * @return matrix characteristics for each random object
 * @throws Exception if Exception occurs
 */
public static JobReturn runJob(MRJobInstruction inst, String[] dataGenInstructions, String instructionsInMapper, String aggInstructionsInReducer, String otherInstructionsInReducer, int numReducers, int replication, byte[] resultIndexes, String dimsUnknownFilePrefix, String[] outputs, OutputInfo[] outputInfos) throws Exception {
    JobConf job = new JobConf(DataGenMR.class);
    job.setJobName("DataGen-MR");
    // whether use block representation or cell representation
    MRJobConfiguration.setMatrixValueClass(job, true);
    byte[] realIndexes = new byte[dataGenInstructions.length];
    for (byte b = 0; b < realIndexes.length; b++) realIndexes[b] = b;
    String[] inputs = new String[dataGenInstructions.length];
    InputInfo[] inputInfos = new InputInfo[dataGenInstructions.length];
    long[] rlens = new long[dataGenInstructions.length];
    long[] clens = new long[dataGenInstructions.length];
    int[] brlens = new int[dataGenInstructions.length];
    int[] bclens = new int[dataGenInstructions.length];
    FileSystem fs = FileSystem.get(job);
    String dataGenInsStr = "";
    int numblocks = 0;
    int maxbrlen = -1, maxbclen = -1;
    double maxsparsity = -1;
    for (int i = 0; i < dataGenInstructions.length; i++) {
        dataGenInsStr = dataGenInsStr + Lop.INSTRUCTION_DELIMITOR + dataGenInstructions[i];
        MRInstruction mrins = MRInstructionParser.parseSingleInstruction(dataGenInstructions[i]);
        MRType mrtype = mrins.getMRInstructionType();
        DataGenMRInstruction genInst = (DataGenMRInstruction) mrins;
        rlens[i] = genInst.getRows();
        clens[i] = genInst.getCols();
        brlens[i] = genInst.getRowsInBlock();
        bclens[i] = genInst.getColsInBlock();
        maxbrlen = Math.max(maxbrlen, brlens[i]);
        maxbclen = Math.max(maxbclen, bclens[i]);
        if (mrtype == MRType.Rand) {
            RandInstruction randInst = (RandInstruction) mrins;
            inputs[i] = LibMatrixDatagen.generateUniqueSeedPath(genInst.getBaseDir());
            maxsparsity = Math.max(maxsparsity, randInst.getSparsity());
            PrintWriter pw = null;
            try {
                pw = new PrintWriter(fs.create(new Path(inputs[i])));
                // for obj reuse and preventing repeated buffer re-allocations
                StringBuilder sb = new StringBuilder();
                // seed generation
                Well1024a bigrand = LibMatrixDatagen.setupSeedsForRand(randInst.getSeed());
                for (long r = 0; r < Math.max(rlens[i], 1); r += brlens[i]) {
                    long curBlockRowSize = Math.min(brlens[i], (rlens[i] - r));
                    for (long c = 0; c < Math.max(clens[i], 1); c += bclens[i]) {
                        long curBlockColSize = Math.min(bclens[i], (clens[i] - c));
                        sb.append((r / brlens[i]) + 1);
                        sb.append(',');
                        sb.append((c / bclens[i]) + 1);
                        sb.append(',');
                        sb.append(curBlockRowSize);
                        sb.append(',');
                        sb.append(curBlockColSize);
                        sb.append(',');
                        sb.append(bigrand.nextLong());
                        pw.println(sb.toString());
                        sb.setLength(0);
                        numblocks++;
                    }
                }
            } finally {
                IOUtilFunctions.closeSilently(pw);
            }
            inputInfos[i] = InputInfo.TextCellInputInfo;
        } else if (mrtype == MRType.Seq) {
            SeqInstruction seqInst = (SeqInstruction) mrins;
            inputs[i] = genInst.getBaseDir() + System.currentTimeMillis() + ".seqinput";
            // always dense
            maxsparsity = 1.0;
            double from = seqInst.fromValue;
            double to = seqInst.toValue;
            double incr = seqInst.incrValue;
            // handle default 1 to -1 for special case of from>to
            incr = LibMatrixDatagen.updateSeqIncr(from, to, incr);
            // Correctness checks on (from, to, incr)
            boolean neg = (from > to);
            if (incr == 0)
                throw new DMLRuntimeException("Invalid value for \"increment\" in seq().");
            if (neg != (incr < 0))
                throw new DMLRuntimeException("Wrong sign for the increment in a call to seq()");
            // Compute the number of rows in the sequence
            long numrows = UtilFunctions.getSeqLength(from, to, incr);
            if (rlens[i] > 0) {
                if (numrows != rlens[i])
                    throw new DMLRuntimeException("Unexpected error while processing sequence instruction. Expected number of rows does not match given number: " + rlens[i] + " != " + numrows);
            } else {
                rlens[i] = numrows;
            }
            if (clens[i] > 0 && clens[i] != 1)
                throw new DMLRuntimeException("Unexpected error while processing sequence instruction. Number of columns (" + clens[i] + ") must be equal to 1.");
            else
                clens[i] = 1;
            PrintWriter pw = null;
            try {
                pw = new PrintWriter(fs.create(new Path(inputs[i])));
                StringBuilder sb = new StringBuilder();
                double temp = from;
                double block_from, block_to;
                for (long r = 0; r < rlens[i]; r += brlens[i]) {
                    long curBlockRowSize = Math.min(brlens[i], (rlens[i] - r));
                    // block (bid_i,bid_j) generates a sequence from the interval [block_from, block_to] (inclusive of both end points of the interval)
                    long bid_i = ((r / brlens[i]) + 1);
                    long bid_j = 1;
                    block_from = temp;
                    block_to = temp + (curBlockRowSize - 1) * incr;
                    // next block starts from here
                    temp = block_to + incr;
                    sb.append(bid_i);
                    sb.append(',');
                    sb.append(bid_j);
                    sb.append(',');
                    sb.append(block_from);
                    sb.append(',');
                    sb.append(block_to);
                    sb.append(',');
                    sb.append(incr);
                    pw.println(sb.toString());
                    sb.setLength(0);
                    numblocks++;
                }
            } finally {
                IOUtilFunctions.closeSilently(pw);
            }
            inputInfos[i] = InputInfo.TextCellInputInfo;
        } else {
            throw new DMLRuntimeException("Unexpected Data Generation Instruction Type: " + mrtype);
        }
    }
    // remove the first ","
    dataGenInsStr = dataGenInsStr.substring(1);
    RunningJob runjob;
    MatrixCharacteristics[] stats;
    try {
        // set up the block size
        MRJobConfiguration.setBlocksSizes(job, realIndexes, brlens, bclens);
        // set up the input files and their format information
        MRJobConfiguration.setUpMultipleInputs(job, realIndexes, inputs, inputInfos, brlens, bclens, false, ConvertTarget.BLOCK);
        // set up the dimensions of input matrices
        MRJobConfiguration.setMatricesDimensions(job, realIndexes, rlens, clens);
        MRJobConfiguration.setDimsUnknownFilePrefix(job, dimsUnknownFilePrefix);
        // set up the block size
        MRJobConfiguration.setBlocksSizes(job, realIndexes, brlens, bclens);
        // set up the rand Instructions
        MRJobConfiguration.setRandInstructions(job, dataGenInsStr);
        // set up unary instructions that will perform in the mapper
        MRJobConfiguration.setInstructionsInMapper(job, instructionsInMapper);
        // set up the aggregate instructions that will happen in the combiner and reducer
        MRJobConfiguration.setAggregateInstructions(job, aggInstructionsInReducer);
        // set up the instructions that will happen in the reducer, after the aggregation instrucions
        MRJobConfiguration.setInstructionsInReducer(job, otherInstructionsInReducer);
        // set up the replication factor for the results
        job.setInt(MRConfigurationNames.DFS_REPLICATION, replication);
        // set up map/reduce memory configurations (if in AM context)
        DMLConfig config = ConfigurationManager.getDMLConfig();
        DMLAppMasterUtils.setupMRJobRemoteMaxMemory(job, config);
        // set up custom map/reduce configurations
        MRJobConfiguration.setupCustomMRConfigurations(job, config);
        // determine degree of parallelism (nmappers: 1<=n<=capacity)
        // TODO use maxsparsity whenever we have a way of generating sparse rand data
        int capacity = InfrastructureAnalyzer.getRemoteParallelMapTasks();
        long dfsblocksize = InfrastructureAnalyzer.getHDFSBlockSize();
        // correction max number of mappers on yarn clusters
        if (InfrastructureAnalyzer.isYarnEnabled())
            capacity = (int) Math.max(capacity, YarnClusterAnalyzer.getNumCores());
        int nmapers = Math.max(Math.min((int) (8 * maxbrlen * maxbclen * (long) numblocks / dfsblocksize), capacity), 1);
        job.setNumMapTasks(nmapers);
        // set up what matrices are needed to pass from the mapper to reducer
        HashSet<Byte> mapoutputIndexes = MRJobConfiguration.setUpOutputIndexesForMapper(job, realIndexes, dataGenInsStr, instructionsInMapper, null, aggInstructionsInReducer, otherInstructionsInReducer, resultIndexes);
        MatrixChar_N_ReducerGroups ret = MRJobConfiguration.computeMatrixCharacteristics(job, realIndexes, dataGenInsStr, instructionsInMapper, null, aggInstructionsInReducer, null, otherInstructionsInReducer, resultIndexes, mapoutputIndexes, false);
        stats = ret.stats;
        // set up the number of reducers
        MRJobConfiguration.setNumReducers(job, ret.numReducerGroups, numReducers);
        // print the complete MRJob instruction
        if (LOG.isTraceEnabled())
            inst.printCompleteMRJobInstruction(stats);
        // Update resultDimsUnknown based on computed "stats"
        byte[] resultDimsUnknown = new byte[resultIndexes.length];
        for (int i = 0; i < resultIndexes.length; i++) {
            if (stats[i].getRows() == -1 || stats[i].getCols() == -1) {
                resultDimsUnknown[i] = (byte) 1;
            } else {
                resultDimsUnknown[i] = (byte) 0;
            }
        }
        boolean mayContainCtable = instructionsInMapper.contains("ctabletransform") || instructionsInMapper.contains("groupedagg");
        // set up the multiple output files, and their format information
        MRJobConfiguration.setUpMultipleOutputs(job, resultIndexes, resultDimsUnknown, outputs, outputInfos, true, mayContainCtable);
        // configure mapper and the mapper output key value pairs
        job.setMapperClass(DataGenMapper.class);
        if (numReducers == 0) {
            job.setMapOutputKeyClass(Writable.class);
            job.setMapOutputValueClass(Writable.class);
        } else {
            job.setMapOutputKeyClass(MatrixIndexes.class);
            job.setMapOutputValueClass(TaggedMatrixBlock.class);
        }
        // set up combiner
        if (numReducers != 0 && aggInstructionsInReducer != null && !aggInstructionsInReducer.isEmpty())
            job.setCombinerClass(GMRCombiner.class);
        // configure reducer
        job.setReducerClass(GMRReducer.class);
        // job.setReducerClass(PassThroughReducer.class);
        // By default, the job executes in "cluster" mode.
        // Determine if we can optimize and run it in "local" mode.
        MatrixCharacteristics[] inputStats = new MatrixCharacteristics[inputs.length];
        for (int i = 0; i < inputs.length; i++) {
            inputStats[i] = new MatrixCharacteristics(rlens[i], clens[i], brlens[i], bclens[i]);
        }
        // set unique working dir
        MRJobConfiguration.setUniqueWorkingDir(job);
        runjob = JobClient.runJob(job);
        /* Process different counters */
        Group group = runjob.getCounters().getGroup(MRJobConfiguration.NUM_NONZERO_CELLS);
        for (int i = 0; i < resultIndexes.length; i++) {
            // number of non-zeros
            stats[i].setNonZeros(group.getCounter(Integer.toString(i)));
        }
        String dir = dimsUnknownFilePrefix + "/" + runjob.getID().toString() + "_dimsFile";
        stats = MapReduceTool.processDimsFiles(dir, stats);
        MapReduceTool.deleteFileIfExistOnHDFS(dir);
    } finally {
        for (String input : inputs) MapReduceTool.deleteFileIfExistOnHDFS(new Path(input), job);
    }
    return new JobReturn(stats, outputInfos, runjob.isSuccessful());
}
Also used : Group(org.apache.hadoop.mapred.Counters.Group) DataGenMRInstruction(org.apache.sysml.runtime.instructions.mr.DataGenMRInstruction) InputInfo(org.apache.sysml.runtime.matrix.data.InputInfo) GMRCombiner(org.apache.sysml.runtime.matrix.mapred.GMRCombiner) FileSystem(org.apache.hadoop.fs.FileSystem) DataGenMRInstruction(org.apache.sysml.runtime.instructions.mr.DataGenMRInstruction) MRInstruction(org.apache.sysml.runtime.instructions.mr.MRInstruction) JobConf(org.apache.hadoop.mapred.JobConf) PrintWriter(java.io.PrintWriter) Path(org.apache.hadoop.fs.Path) DMLConfig(org.apache.sysml.conf.DMLConfig) SeqInstruction(org.apache.sysml.runtime.instructions.mr.SeqInstruction) RandInstruction(org.apache.sysml.runtime.instructions.mr.RandInstruction) MRType(org.apache.sysml.runtime.instructions.mr.MRInstruction.MRType) DMLRuntimeException(org.apache.sysml.runtime.DMLRuntimeException) MatrixChar_N_ReducerGroups(org.apache.sysml.runtime.matrix.mapred.MRJobConfiguration.MatrixChar_N_ReducerGroups) RunningJob(org.apache.hadoop.mapred.RunningJob) Well1024a(org.apache.commons.math3.random.Well1024a)

Example 74 with Max

use of org.apache.commons.math3.stat.descriptive.rank.Max in project vcell by virtualcell.

the class TimeSeriesMultitrialData method chiSquaredTest.

public static double chiSquaredTest(double[] rawData1, double[] rawData2) {
    try {
        int numBins = 1 + (int) Math.ceil(Math.sqrt(rawData1.length));
        // rawData2 = ramp(0,10,rawData2.length);
        Max max = new Max();
        max.incrementAll(rawData1);
        max.incrementAll(rawData2);
        Min min = new Min();
        min.incrementAll(rawData1);
        min.incrementAll(rawData2);
        long[] histogram1 = calcHistogram(rawData1, min.getResult(), max.getResult(), numBins);
        long[] histogram2 = calcHistogram(rawData2, min.getResult(), max.getResult(), numBins);
        // 
        // remove histogram indices where both bins are zero
        // 
        ArrayList<Long> histogram1List = new ArrayList<Long>();
        ArrayList<Long> histogram2List = new ArrayList<Long>();
        for (int i = 0; i < histogram1.length; i++) {
            if (histogram1[i] != 0 || histogram2[i] != 0) {
                histogram1List.add(histogram1[i]);
                histogram2List.add(histogram2[i]);
            // }else{
            // histogram1List.add(new Long(1));
            // histogram2List.add(new Long(1));
            }
        }
        histogram1 = new long[histogram1List.size()];
        histogram2 = new long[histogram2List.size()];
        for (int i = 0; i < histogram1List.size(); i++) {
            histogram1[i] = histogram1List.get(i);
            histogram2[i] = histogram2List.get(i);
        }
        if (histogram1.length == 1) {
            return 0.0;
        }
        ChiSquareTest chiSquareTest = new ChiSquareTest();
        return chiSquareTest.chiSquareTestDataSetsComparison(histogram1, histogram2);
    } catch (Exception e) {
        e.printStackTrace(System.out);
        return -1;
    }
}
Also used : Min(org.apache.commons.math3.stat.descriptive.rank.Min) Max(org.apache.commons.math3.stat.descriptive.rank.Max) ArrayList(java.util.ArrayList) ChiSquareTest(org.apache.commons.math3.stat.inference.ChiSquareTest) ExpressionException(cbit.vcell.parser.ExpressionException)

Example 75 with Max

use of org.apache.commons.math3.stat.descriptive.rank.Max in project vcell by virtualcell.

the class TimeSeriesMultitrialData method kolmogorovSmirnovTest.

public static double kolmogorovSmirnovTest(double[] rawData1, double[] rawData2) {
    try {
        int numBins = 1 + (int) Math.ceil(Math.sqrt(rawData1.length));
        // rawData2 = ramp(0,10,rawData2.length);
        TimeSeriesMultitrialData.MinMaxHelp minMaxHelp1 = new TimeSeriesMultitrialData.MinMaxHelp(rawData1);
        TimeSeriesMultitrialData.MinMaxHelp minMaxHelp2 = new TimeSeriesMultitrialData.MinMaxHelp(rawData2);
        double min = Math.min(minMaxHelp1.min, minMaxHelp2.min);
        double max = Math.max(minMaxHelp1.max, minMaxHelp2.max);
        double[] cdf1 = calculateCDF(rawData1, min, max, numBins);
        double[] cdf2 = calculateCDF(rawData2, min, max, numBins);
        KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
        return test.kolmogorovSmirnovStatistic(cdf1, cdf2);
    } catch (Exception e) {
        e.printStackTrace(System.out);
        return -1;
    }
}
Also used : KolmogorovSmirnovTest(org.apache.commons.math3.stat.inference.KolmogorovSmirnovTest) ExpressionException(cbit.vcell.parser.ExpressionException)

Aggregations

ArrayList (java.util.ArrayList)26 List (java.util.List)19 Collectors (java.util.stream.Collectors)13 DescriptiveStatistics (org.apache.commons.math3.stat.descriptive.DescriptiveStatistics)13 Arrays (java.util.Arrays)11 Map (java.util.Map)11 IntStream (java.util.stream.IntStream)10 RandomGenerator (org.apache.commons.math3.random.RandomGenerator)10 Array2DRowRealMatrix (org.apache.commons.math3.linear.Array2DRowRealMatrix)9 RealMatrix (org.apache.commons.math3.linear.RealMatrix)9 Plot2 (ij.gui.Plot2)8 File (java.io.File)8 IOException (java.io.IOException)8 TooManyEvaluationsException (org.apache.commons.math3.exception.TooManyEvaluationsException)7 Test (org.testng.annotations.Test)7 StoredDataStatistics (gdsc.core.utils.StoredDataStatistics)6 Collections (java.util.Collections)6 HashMap (java.util.HashMap)6 Random (java.util.Random)6 UnivariateFunction (org.apache.commons.math3.analysis.UnivariateFunction)6