Merge pull request #86 from holdenk/master

Add histogram functionality to DoubleRDDFunctions

This pull request add histogram functionality to the DoubleRDDFunctions.

4 files changed, 451 insertions, 0 deletions

diff --git a/core/src/main/scala/org/apache/spark/api/java/JavaDoubleRDD.scala b/core/src/main/scala/org/apache/spark/api/java/JavaDoubleRDD.scala
index 043cb183ba..9f02a9b7d3 100644
--- a/core/src/main/scala/org/apache/spark/api/java/JavaDoubleRDD.scala
+++ b/core/src/main/scala/org/apache/spark/api/java/JavaDoubleRDD.scala
@@ -26,6 +26,8 @@ import org.apache.spark.storage.StorageLevel
 import java.lang.Double
 import org.apache.spark.Partitioner
 
+import scala.collection.JavaConverters._
+
 class JavaDoubleRDD(val srdd: RDD[scala.Double]) extends JavaRDDLike[Double, JavaDoubleRDD] {
 
   override val classManifest: ClassManifest[Double] = implicitly[ClassManifest[Double]]
@@ -182,6 +184,44 @@ class JavaDoubleRDD(val srdd: RDD[scala.Double]) extends JavaRDDLike[Double, Jav
 
   /** (Experimental) Approximate operation to return the sum within a timeout. */
   def sumApprox(timeout: Long): PartialResult[BoundedDouble] = srdd.sumApprox(timeout)
+
+  /**
+   * Compute a histogram of the data using bucketCount number of buckets evenly
+   *  spaced between the minimum and maximum of the RDD. For example if the min
+   *  value is 0 and the max is 100 and there are two buckets the resulting
+   *  buckets will be [0,50) [50,100]. bucketCount must be at least 1
+   * If the RDD contains infinity, NaN throws an exception
+   * If the elements in RDD do not vary (max == min) always returns a single bucket.
+   */
+  def histogram(bucketCount: Int): Pair[Array[scala.Double], Array[Long]] = {
+    val result = srdd.histogram(bucketCount)
+    (result._1, result._2)
+  }
+
+  /**
+   * Compute a histogram using the provided buckets. The buckets are all open
+   * to the left except for the last which is closed
+   *  e.g. for the array
+   *  [1,10,20,50] the buckets are [1,10) [10,20) [20,50]
+   *  e.g 1<=x<10 , 10<=x<20, 20<=x<50
+   *  And on the input of 1 and 50 we would have a histogram of 1,0,0 
+   * 
+   * Note: if your histogram is evenly spaced (e.g. [0, 10, 20, 30]) this can be switched
+   * from an O(log n) inseration to O(1) per element. (where n = # buckets) if you set evenBuckets
+   * to true.
+   * buckets must be sorted and not contain any duplicates.
+   * buckets array must be at least two elements 
+   * All NaN entries are treated the same. If you have a NaN bucket it must be
+   * the maximum value of the last position and all NaN entries will be counted
+   * in that bucket.
+   */
+  def histogram(buckets: Array[scala.Double]): Array[Long] = {
+    srdd.histogram(buckets, false)
+  }
+
+  def histogram(buckets: Array[Double], evenBuckets: Boolean): Array[Long] = {
+    srdd.histogram(buckets.map(_.toDouble), evenBuckets)
+  }
 }
 
 object JavaDoubleRDD {
diff --git a/core/src/main/scala/org/apache/spark/rdd/DoubleRDDFunctions.scala b/core/src/main/scala/org/apache/spark/rdd/DoubleRDDFunctions.scala
index a4bec41752..02d75eccc5 100644
--- a/core/src/main/scala/org/apache/spark/rdd/DoubleRDDFunctions.scala
+++ b/core/src/main/scala/org/apache/spark/rdd/DoubleRDDFunctions.scala
@@ -24,6 +24,8 @@ import org.apache.spark.partial.SumEvaluator
 import org.apache.spark.util.StatCounter
 import org.apache.spark.{TaskContext, Logging}
 
+import scala.collection.immutable.NumericRange
+
 /**
  * Extra functions available on RDDs of Doubles through an implicit conversion.
  * Import `org.apache.spark.SparkContext._` at the top of your program to use these functions.
@@ -76,4 +78,128 @@ class DoubleRDDFunctions(self: RDD[Double]) extends Logging with Serializable {
     val evaluator = new SumEvaluator(self.partitions.size, confidence)
     self.context.runApproximateJob(self, processPartition, evaluator, timeout)
   }
+
+  /**
+   * Compute a histogram of the data using bucketCount number of buckets evenly
+   *  spaced between the minimum and maximum of the RDD. For example if the min
+   *  value is 0 and the max is 100 and there are two buckets the resulting
+   *  buckets will be [0, 50) [50, 100]. bucketCount must be at least 1
+   * If the RDD contains infinity, NaN throws an exception
+   * If the elements in RDD do not vary (max == min) always returns a single bucket.
+   */
+  def histogram(bucketCount: Int): Pair[Array[Double], Array[Long]] = {
+    // Compute the minimum and the maxium
+    val (max: Double, min: Double) = self.mapPartitions { items =>
+      Iterator(items.foldRight(-1/0.0, Double.NaN)((e: Double, x: Pair[Double, Double]) =>
+        (x._1.max(e), x._2.min(e))))
+    }.reduce { (maxmin1, maxmin2) =>
+      (maxmin1._1.max(maxmin2._1), maxmin1._2.min(maxmin2._2))
+    }
+    if (max.isNaN() || max.isInfinity || min.isInfinity ) {
+      throw new UnsupportedOperationException(
+        "Histogram on either an empty RDD or RDD containing +/-infinity or NaN")
+    }
+    val increment = (max-min)/bucketCount.toDouble
+    val range = if (increment != 0) {
+      Range.Double.inclusive(min, max, increment)
+    } else {
+      List(min, min)
+    }
+    val buckets = range.toArray
+    (buckets, histogram(buckets, true))
+  }
+
+  /**
+   * Compute a histogram using the provided buckets. The buckets are all open
+   * to the left except for the last which is closed
+   *  e.g. for the array
+   *  [1, 10, 20, 50] the buckets are [1, 10) [10, 20) [20, 50]
+   *  e.g 1<=x<10 , 10<=x<20, 20<=x<50
+   *  And on the input of 1 and 50 we would have a histogram of 1, 0, 0 
+   * 
+   * Note: if your histogram is evenly spaced (e.g. [0, 10, 20, 30]) this can be switched
+   * from an O(log n) inseration to O(1) per element. (where n = # buckets) if you set evenBuckets
+   * to true.
+   * buckets must be sorted and not contain any duplicates.
+   * buckets array must be at least two elements 
+   * All NaN entries are treated the same. If you have a NaN bucket it must be
+   * the maximum value of the last position and all NaN entries will be counted
+   * in that bucket.
+   */
+  def histogram(buckets: Array[Double], evenBuckets: Boolean = false): Array[Long] = {
+    if (buckets.length < 2) {
+      throw new IllegalArgumentException("buckets array must have at least two elements")
+    }
+    // The histogramPartition function computes the partail histogram for a given
+    // partition. The provided bucketFunction determines which bucket in the array
+    // to increment or returns None if there is no bucket. This is done so we can
+    // specialize for uniformly distributed buckets and save the O(log n) binary
+    // search cost.
+    def histogramPartition(bucketFunction: (Double) => Option[Int])(iter: Iterator[Double]):
+        Iterator[Array[Long]] = {
+      val counters = new Array[Long](buckets.length - 1)
+      while (iter.hasNext) {
+        bucketFunction(iter.next()) match {
+          case Some(x: Int) => {counters(x) += 1}
+          case _ => {}
+        }
+      }
+      Iterator(counters)
+    }
+    // Merge the counters.
+    def mergeCounters(a1: Array[Long], a2: Array[Long]): Array[Long] = {
+      a1.indices.foreach(i => a1(i) += a2(i))
+      a1
+    }
+    // Basic bucket function. This works using Java's built in Array
+    // binary search. Takes log(size(buckets))
+    def basicBucketFunction(e: Double): Option[Int] = {
+      val location = java.util.Arrays.binarySearch(buckets, e)
+      if (location < 0) {
+        // If the location is less than 0 then the insertion point in the array
+        // to keep it sorted is -location-1
+        val insertionPoint = -location-1
+        // If we have to insert before the first element or after the last one
+        // its out of bounds.
+        // We do this rather than buckets.lengthCompare(insertionPoint)
+        // because Array[Double] fails to override it (for now).
+        if (insertionPoint > 0 && insertionPoint < buckets.length) {
+          Some(insertionPoint-1)
+        } else {
+          None
+        }
+      } else if (location < buckets.length - 1) {
+        // Exact match, just insert here
+        Some(location)
+      } else {
+        // Exact match to the last element
+        Some(location - 1)
+      }
+    }
+    // Determine the bucket function in constant time. Requires that buckets are evenly spaced
+    def fastBucketFunction(min: Double, increment: Double, count: Int)(e: Double): Option[Int] = {
+      // If our input is not a number unless the increment is also NaN then we fail fast
+      if (e.isNaN()) {
+        return None
+      }
+      val bucketNumber = (e - min)/(increment)
+      // We do this rather than buckets.lengthCompare(bucketNumber)
+      // because Array[Double] fails to override it (for now).
+      if (bucketNumber > count || bucketNumber < 0) {
+        None
+      } else {
+        Some(bucketNumber.toInt.min(count - 1))
+      }
+    }
+    // Decide which bucket function to pass to histogramPartition. We decide here
+    // rather than having a general function so that the decission need only be made
+    // once rather than once per shard
+    val bucketFunction = if (evenBuckets) {
+      fastBucketFunction(buckets(0), buckets(1)-buckets(0), buckets.length-1) _
+    } else {
+      basicBucketFunction _
+    }
+    self.mapPartitions(histogramPartition(bucketFunction)).reduce(mergeCounters)
+  }
+
 }
diff --git a/core/src/test/scala/org/apache/spark/JavaAPISuite.java b/core/src/test/scala/org/apache/spark/JavaAPISuite.java
index 352036f182..4234f6eac7 100644
--- a/core/src/test/scala/org/apache/spark/JavaAPISuite.java
+++ b/core/src/test/scala/org/apache/spark/JavaAPISuite.java
@@ -365,6 +365,20 @@ public class JavaAPISuite implements Serializable {
   }
 
   @Test
+  public void javaDoubleRDDHistoGram() {
+   JavaDoubleRDD rdd = sc.parallelizeDoubles(Arrays.asList(1.0, 2.0, 3.0, 4.0));
+   // Test using generated buckets
+   Tuple2<double[], long[]> results = rdd.histogram(2);
+   double[] expected_buckets = {1.0, 2.5, 4.0};
+   long[] expected_counts = {2, 2};
+   Assert.assertArrayEquals(expected_buckets, results._1, 0.1);
+   Assert.assertArrayEquals(expected_counts, results._2);
+   // Test with provided buckets
+   long[] histogram = rdd.histogram(expected_buckets);
+   Assert.assertArrayEquals(expected_counts, histogram);
+  }
+
+  @Test
   public void map() {
     JavaRDD<Integer> rdd = sc.parallelize(Arrays.asList(1, 2, 3, 4, 5));
     JavaDoubleRDD doubles = rdd.map(new DoubleFunction<Integer>() {
diff --git a/core/src/test/scala/org/apache/spark/rdd/DoubleRDDSuite.scala b/core/src/test/scala/org/apache/spark/rdd/DoubleRDDSuite.scala
new file mode 100644
index 0000000000..7f50a5a47c
--- /dev/null
+++ b/core/src/test/scala/org/apache/spark/rdd/DoubleRDDSuite.scala
@@ -0,0 +1,271 @@
+/*
+ * 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.spark.rdd
+
+import scala.math.abs
+import scala.collection.mutable.ArrayBuffer
+
+import org.scalatest.FunSuite
+
+import org.apache.spark.SparkContext._
+import org.apache.spark.rdd._
+import org.apache.spark._
+
+class DoubleRDDSuite extends FunSuite with SharedSparkContext {
+  // Verify tests on the histogram functionality. We test with both evenly
+  // and non-evenly spaced buckets as the bucket lookup function changes.
+  test("WorksOnEmpty") {
+    // Make sure that it works on an empty input
+    val rdd: RDD[Double] = sc.parallelize(Seq())
+    val buckets = Array(0.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksWithOutOfRangeWithOneBucket") {
+    // Verify that if all of the elements are out of range the counts are zero
+    val rdd = sc.parallelize(Seq(10.01, -0.01))
+    val buckets = Array(0.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksInRangeWithOneBucket") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1, 2, 3, 4))
+    val buckets = Array(0.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(4)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksInRangeWithOneBucketExactMatch") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1, 2, 3, 4))
+    val buckets = Array(1.0, 4.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(4)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksWithOutOfRangeWithTwoBuckets") {
+    // Verify that out of range works with two buckets
+    val rdd = sc.parallelize(Seq(10.01, -0.01))
+    val buckets = Array(0.0, 5.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(0, 0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksWithOutOfRangeWithTwoUnEvenBuckets") {
+    // Verify that out of range works with two un even buckets
+    val rdd = sc.parallelize(Seq(10.01, -0.01))
+    val buckets = Array(0.0, 4.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(0, 0)
+    assert(histogramResults === expectedHistogramResults)
+  }
+
+  test("WorksInRangeWithTwoBuckets") {
+    // Make sure that it works with two equally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(1, 2, 3, 5, 6))
+    val buckets = Array(0.0, 5.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(3, 2)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksInRangeWithTwoBucketsAndNaN") {
+    // Make sure that it works with two equally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(1, 2, 3, 5, 6, Double.NaN))
+    val buckets = Array(0.0, 5.0, 10.0)
+    val histogramResults = rdd.histogram(buckets)
+    val histogramResults2 = rdd.histogram(buckets, true)
+    val expectedHistogramResults = Array(3, 2)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramResults2 === expectedHistogramResults)
+  }
+
+  test("WorksInRangeWithTwoUnevenBuckets") {
+    // Make sure that it works with two unequally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(1, 2, 3, 5, 6))
+    val buckets = Array(0.0, 5.0, 11.0)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(3, 2)
+    assert(histogramResults === expectedHistogramResults)
+  }
+
+  test("WorksMixedRangeWithTwoUnevenBuckets") {
+    // Make sure that it works with two unequally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(-0.01, 0.0, 1, 2, 3, 5, 6, 11.0, 11.01))
+    val buckets = Array(0.0, 5.0, 11.0)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(4, 3)
+    assert(histogramResults === expectedHistogramResults)
+  }
+
+  test("WorksMixedRangeWithFourUnevenBuckets") {
+    // Make sure that it works with two unequally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(-0.01, 0.0, 1, 2, 3, 5, 6, 11.01, 12.0, 199.0,
+      200.0, 200.1))
+    val buckets = Array(0.0, 5.0, 11.0, 12.0, 200.0)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(4, 2, 1, 3)
+    assert(histogramResults === expectedHistogramResults)
+  }
+
+  test("WorksMixedRangeWithUnevenBucketsAndNaN") {
+    // Make sure that it works with two unequally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(-0.01, 0.0, 1, 2, 3, 5, 6, 11.01, 12.0, 199.0,
+      200.0, 200.1, Double.NaN))
+    val buckets = Array(0.0, 5.0, 11.0, 12.0, 200.0)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(4, 2, 1, 3)
+    assert(histogramResults === expectedHistogramResults)
+  }
+  // Make sure this works with a NaN end bucket
+  test("WorksMixedRangeWithUnevenBucketsAndNaNAndNaNRange") {
+    // Make sure that it works with two unequally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(-0.01, 0.0, 1, 2, 3, 5, 6, 11.01, 12.0, 199.0,
+      200.0, 200.1, Double.NaN))
+    val buckets = Array(0.0, 5.0, 11.0, 12.0, 200.0, Double.NaN)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(4, 2, 1, 2, 3)
+    assert(histogramResults === expectedHistogramResults)
+  }
+  // Make sure this works with a NaN end bucket and an inifity
+  test("WorksMixedRangeWithUnevenBucketsAndNaNAndNaNRangeAndInfity") {
+    // Make sure that it works with two unequally spaced buckets and elements in each
+    val rdd = sc.parallelize(Seq(-0.01, 0.0, 1, 2, 3, 5, 6, 11.01, 12.0, 199.0,
+      200.0, 200.1, 1.0/0.0, -1.0/0.0, Double.NaN))
+    val buckets = Array(0.0, 5.0, 11.0, 12.0, 200.0, Double.NaN)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(4, 2, 1, 2, 4)
+    assert(histogramResults === expectedHistogramResults)
+  }
+
+  test("WorksWithOutOfRangeWithInfiniteBuckets") {
+    // Verify that out of range works with two buckets
+    val rdd = sc.parallelize(Seq(10.01, -0.01, Double.NaN))
+    val buckets = Array(-1.0/0.0 , 0.0, 1.0/0.0)
+    val histogramResults = rdd.histogram(buckets)
+    val expectedHistogramResults = Array(1, 1)
+    assert(histogramResults === expectedHistogramResults)
+  }
+  // Test the failure mode with an invalid bucket array
+  test("ThrowsExceptionOnInvalidBucketArray") {
+    val rdd = sc.parallelize(Seq(1.0))
+    // Empty array
+    intercept[IllegalArgumentException] {
+      val buckets = Array.empty[Double]
+      val result = rdd.histogram(buckets)
+    }
+    // Single element array
+    intercept[IllegalArgumentException] {
+      val buckets = Array(1.0)
+      val result = rdd.histogram(buckets)
+    }
+  }
+
+  // Test automatic histogram function
+  test("WorksWithoutBucketsBasic") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1, 2, 3, 4))
+    val (histogramBuckets, histogramResults) = rdd.histogram(1)
+    val expectedHistogramResults = Array(4)
+    val expectedHistogramBuckets = Array(1.0, 4.0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramBuckets === expectedHistogramBuckets)
+  }
+  // Test automatic histogram function with a single element
+  test("WorksWithoutBucketsBasicSingleElement") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1))
+    val (histogramBuckets, histogramResults) = rdd.histogram(1)
+    val expectedHistogramResults = Array(1)
+    val expectedHistogramBuckets = Array(1.0, 1.0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramBuckets === expectedHistogramBuckets)
+  }
+  // Test automatic histogram function with a single element
+  test("WorksWithoutBucketsBasicNoRange") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1, 1, 1, 1))
+    val (histogramBuckets, histogramResults) = rdd.histogram(1)
+    val expectedHistogramResults = Array(4)
+    val expectedHistogramBuckets = Array(1.0, 1.0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramBuckets === expectedHistogramBuckets)
+  }
+
+  test("WorksWithoutBucketsBasicTwo") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1, 2, 3, 4))
+    val (histogramBuckets, histogramResults) = rdd.histogram(2)
+    val expectedHistogramResults = Array(2, 2)
+    val expectedHistogramBuckets = Array(1.0, 2.5, 4.0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramBuckets === expectedHistogramBuckets)
+  }
+
+  test("WorksWithoutBucketsWithMoreRequestedThanElements") {
+    // Verify the basic case of one bucket and all elements in that bucket works
+    val rdd = sc.parallelize(Seq(1, 2))
+    val (histogramBuckets, histogramResults) = rdd.histogram(10)
+    val expectedHistogramResults =
+      Array(1, 0, 0, 0, 0, 0, 0, 0, 0, 1)
+    val expectedHistogramBuckets =
+      Array(1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0)
+    assert(histogramResults === expectedHistogramResults)
+    assert(histogramBuckets === expectedHistogramBuckets)
+  }
+
+  // Test the failure mode with an invalid RDD
+  test("ThrowsExceptionOnInvalidRDDs") {
+    // infinity
+    intercept[UnsupportedOperationException] {
+      val rdd = sc.parallelize(Seq(1, 1.0/0.0))
+      val result = rdd.histogram(1)
+    }
+    // NaN
+    intercept[UnsupportedOperationException] {
+      val rdd = sc.parallelize(Seq(1, Double.NaN))
+      val result = rdd.histogram(1)
+    }
+    // Empty
+    intercept[UnsupportedOperationException] {
+      val rdd: RDD[Double] = sc.parallelize(Seq())
+      val result = rdd.histogram(1)
+    }
+  }
+
+}