numerical-methods-summation-exercise

This exercise is related to computer arithmetic:

Computer Arithmetic / Machine Precision (2): Summation

1. Implement a class that implements the interface DoubleVector of the package info.quantlab.numericalmethods.lecture.computerarithmetics.summation.

Important: The interface you have to implement is not part of this project. It is imported from another project that is referenced by this project. To take a look at this interface, you can select "Open Declaration" in your IDE (right-click on the interface name) or look here: https://github.com/qntlb/numerical-methods-lecture/blob/master/src/main/java/info/quantlab/numericalmethods/lecture/computerarithmetics/summation/DoubleVector.java

The class implementing DoubleVector should allow to calculate the sum of the elements of the vector in a numerically stable way.

Note: As your task is to implement the interface, read the JavaDoc of that interface for a specification of what to do.

2. When done with 1) implement the method createDoubleVector of the class SummationAssignmentSolution, such that it allows to create an object of the class you have implemented in 1).

A class like SummationAssignmentSolution is called a Factory, because it allows to create objects. It basically allows us to create an object of your class, without knowing the name of your class. We will use this method to test your implementation.

Hint: This is a trivial task. If your class in 1) is named DoubleVectorFromArray and if it has a constructor DoubleVectorFromArray(double[] values), then the body of the implementation of the factory class is just

  public DoubleVector createDoubleVector(double[] values) {
    return new DoubleVectorFromArray(values);
  }

You can test your implementation by running the unit test in src/test/java.

Main Task

The main task of this exercise is to provide a more accurate ("numerically stable") summation to the method sum.

For large vectors or values with different sizes, naive summation may result in the accumulation of rounding errors. Your code should avoid this.

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Importing in Eclipse from GitHub

Import this git repository into Eclipse and start working.

• Click on the link to your repository (the link starts with qntlb/computational-finance… )
• Click on “Clone or download” and copy the URL to your clipboard.
• Go to Eclipse and select File -> Import -> Git -> Projects from Git (with smart import).
• Select “Clone URI” and paste the GitHub URL from step 2.
• Select “master” or "main", then Next -> Next -> Finish.

Note: If you choose "Projects from Git" without the option "(with smart import)" you may experience that the project is not imported into Eclipse, but it was successfully checked out (downloaded) via git, i.e. you find the project files in your local git folder. In that case, you can import the project "as maven project" (see below).

Importing in Eclipse (as Maven Project)

If you checked out the git repository manually (git clone), then import the local git folder as Maven Project;

• File -> Import -> Maven -> Existing Maven Projects
• Select the project folder in your local git folder.

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Notes

The project is configured to run automated Unit Test, JavaDoc, and Checkstyle upon a git push (via GitHub Actions).

Code Style

We are checking your codestyle via Checkstyle. A failing checkstyle run is not impacting your grade, but you could try to improve. If desired, you can run the check locally on a command line via the maven command

mvn checkstyle:check 

(run from the project directory).

Checkstyle will report style issues of your code. If you like to clean up the formatting, you may use Source -> Clean up... in Eclipse.

JavaDoc

We are generating documentation from the code via JavaDoc. A failing JavaDoc run is not impacting your grade, but you could try to improve your documentation. If desired, you can generate the documentation locally on a command line via the maven command

mvn javadoc:javadoc 

If successful, the javadoc will then reside in target/apidocs. The project is configured to support LaTeX in JavaDocs (use \( and \) to open and close a math environment).

Note that JavaDoc is HTML. This implies that an < needs to be written as < and > needs to be written as >.

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