Iterative Averaging

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Motivation

Iterative Averaging is the process of updating an array to so that each index becomes the average of the indices one before and one after it. After repeating this for many iterations, the array may converge to one set of numbers. For example, when given the following array, we can perform iterations of this algorithm until the array eventually converges:

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 1.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.25 0.5 1.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.125 0.25 0.625 1.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0625 0.125 0.375 0.625 1.0
0.0 0.0 0.0 0.0 0.0 0.03125 0.0625 0.21875 0.375 0.6875 1.0
0.0 0.0 0.0 0.0 0.015625 0.03125 0.125 0.21875 0.453125 0.6875 1.0
0.0 0.0 0.0 0.0078125 0.015625 0.0703125 0.125 0.2890625 0.453125 0.7265625 1.0
0.0 0.0 0.00390625 0.0078125 0.0390625 0.0703125 0.1796875 0.2890625 0.5078125 0.7265625 1.0
0.0 0.001953125 0.00390625 0.021484375 0.0390625 0.109375 0.1796875 0.34375 0.5078125 0.75390625 1.0
0.0 0.001953125 0.01171875 0.021484375 0.0654296875 0.109375 0.2265625 0.34375 0.548828125 0.75390625 1.0
0.0 \vdots 1.0
0.0 \vdots 1.0
0.0 \vdots 1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


X10-like Phasers have been added to Java since JDK7. We will gain some experience with using Phasers in a parallel for-loop context. Phasers allow us to change the structure of our loops and reduce overhead in the algorithm.

For more information on the algorithm and how we can use Phasers to make it better, review Topic 3.5 from the RiceX course.

Background

Java Phaser

Check out the reference page on phasers

Guide to the Java Phaser

Attention niels epting.svg Warning: Our use of the forall loop with Phasers does not accurately convey their finicky nature. More than other features, Phasers seem to require more care to get performance improvements.

PhasableDoubleArrays

Slices

Lecture

Code to Implement

Warmup

SequentialIterativeAverager

class: SequentialIterativeAverager.java Java.png
methods: iterativelyAverage
package: iterativeaveraging.warmup
source folder: src/main/java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) Sequential.svg (sequential implementation only)

PhaserWarmup

class: PhaserWarmup.java Java.png
methods: warmup
warmupPhased
package: phaser.warmup
source folder: src/main/java

method: public static void warmup(List<Character> letters, List<Integer> digits) Sequential.svg (sequential implementation only)

method: public static void warmupPhased(List<Character> letters, List<Integer> digits) Sequential.svg (sequential implementation only)

Studio

IterativeAveragingUtils

class: IterativeAveragingUtils.java Java.png
methods: sliceDoubleArrayIntoRangesForIterativeAveraging
createPhasableDoubleArraysForIterativeAveraging
package: iterativeaveraging.util.studio
source folder: src/main/java

sliceDoubleArrayIntoRangesForIterativeAveraging

Each IterativeAverager should slice the data into ranges. The constructor for each IterativeAverager is passed the number of slices to create.

Circle-information.svg Tip: Use Slices.createNSlices(min, maxExclusive, numSlices)

If you are to create 3 slices an array of length 11:

IterativeAveraging.png

the IndexedRanges should have these properties:

sliceIndexID minInclusive maxExclusive
sliceA 0 1 4
sliceB 1 4 7
sliceC 2 7 10

createPhasableDoubleArraysForIterativeAveraging

Parallel

class: ParallelIterativeAverager.java Java.png
methods: iterativelyAverage
package: iterativeaveraging.studio
source folder: src/main/java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) Parallel.svg (parallel implementation required)

For this method, you should not be using Phasers. Instead, implement a parallel version of the Iterative Averaging algorithm shown above sequentially. Make use of the PhasableDoubleArrays class. The return value should be the current version of the array after it has gone through the number of iterations passed in the method.

sequential loop
    parallel loop
        work

PhasedParallel

class: PhasedParallelIterativeAverager.java Java.png
methods: iterativelyAverage
package: iterativeaveraging.studio
source folder: src/main/java

method: public double[] iterativelyAverage(double[] originalArray, int iterationCount) Parallel.svg (parallel implementation required)

Before you get started on this, make sure you review the Background section in order to understand how to utilize Phasers (it will look different than the RiceX implementation!). This time, we will use Phasers to create a parallel version of the algorithm that has less overhead. Here are a few notes to keep in mind when working on this assignment:

  • Think carefully as to how the loops in this version will be structured. Drawing out the computation graph may help
  • Bulk registering a Phaser indicates how many times phaser.arriveAndAwaitAdvance() needs to be called before any of the threads are able to move on. Make sure to register the right number!
create phaser
register phaser for each task
parallel loop
    sequential loop
        work
        arrive and await advance on phaser

Optional Challenge

PointToPointPhasedParallel

class: PointToPointPhasedParallelIterativeAverager.java Java.png
methods: iterativelyAverage
package: iterativeaveraging.challenge
source folder: src/main/java

Testing Your Solution

Correctness

class: RigidIterativeAveragingTestSuite.java Junit.png
package: iterativeaveraging.rigid.studio
source folder: src/test/java
class: IterativeAveragingUtilsTestSuite.java Junit.png
package: iterativeaveraging.util.studio
source folder: src/test/java
class: ParallelIterativeAveragerTestSuite.java Junit.png
package: iterativeaveraging.rigid.studio
source folder: src/test/java
class: PhasedIterativeAveragerTestSuite.java Junit.png
package: iterativeaveraging.rigid.studio
source folder: src/test/java