qntlb / numerical-methods-summation-exercise

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 have 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 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.