Objective

Develop a toolbox in C++ covering various data science and scientific computing areas.
Implement module A) and one module among B), C), D), of your choice.

Components

A) Statistics module (mandatory)

B) Interpolation module

C) Numerical integration module

D) ODE module

Requirements and descriptions for each module are provided in the sections below.

A) Statistics module (mandatory)

Implement a module to perform statistical analyses on data imported from a CSV or a JSON file and output relevant information to a text file. Parse input and output filenames as command line arguments.

• Implement utilities for statistical operations like mean, median, standard deviation, variance, frequency count, classification, and correlation analyses.
• Implement iterators for seamless data traversal.
• Consider using std::variant for storing numerical or categorical data and std::optional for possibly missing/NA values.
• Select a dataset from Kaggle, and use it to test your implementation by performing statistical analysis on a real application.

B) Interpolation module

Implement a module to support composite linear and polynomial interpolation, and (bonus) cardinal cubic B-spline interpolation of a given set of data .

• Implement a common interface that stores a list of nodes over an interval and the corresponding observed values for all kinds of interpolation.
• The implemented class(es) should expose a call operator (operator()) returning the interpolated value at a given point.
• Test your implementation through practical examples. Showcase the accuracy, efficiency, and order of convergence of each method implemented.

C) Numerical integration module

Implement a module for approximating integrals using composite numerical integration formulas of the form

where and are the weights and nodes of the quadrature formula, respectively.

• Consider methods such as the midpoint rule, the trapezoidal rule, Simpson's rule, and (bonus) Gaussian quadrature formulas.
• Test your implementation through practical examples. Showcase the accuracy, efficiency, and order of convergence of each method implemented.

D) ODE module

Implement a module for solving Ordinary Differential Equations (ODEs) of the form

where , using explicit Runge-Kutta methods, such as Forward Euler, RK4, and (bonus) the explicit midpoint method.

• The module should handle both scalar () and vector ODE problems.
• Output the solution to a CSV file with header columns t, y1, y2, ..., yN.
• Test your implementation through practical examples. Showcase the accuracy, stability, efficiency, and order of convergence of each method implemented.

General guidelines

1. Emphasize the use of modern C++ features, including STL containers, algorithms, iterators, smart pointers, and other utilities.
2. Utilize either run-time (class abstraction and inheritance) or compile-time (templates and policies) polymorphism, providing motivation for your choice.
3. Write error-safe code and handle exceptions properly.
4. Provide clear documentation of code design, algorithms, and decisions made.
5. Promote code readability, modular design, and adherence to coding standards.
6. Provide sample applications demonstrating the functionality of each module.

Integration of third-party libraries

• The integration of third-party libraries is highly encouraged, such as:

  • Boost (e.g., the modules Histogram, JSON, Math, Odeint).
  • Eigen, for linear algebra classes (vectors, matrices, linear solvers).
  • GetPot, for parsing comand line arguments and configuration files.
  • GNU GSL, for a wide range of mathematical routines.
  • muParserX, to parse string expressions such as "sin(pi * x) * exp(x)" as mathematical functions.

  or any other library of your choice, and showcase their synergy with your code.

• Discuss considerations and challenges in using third-party libraries.

Code organization

• Organize your implementation into subfolders and files with meaningful names.

• Ensure a clear separation between function declarations and definitions by placing them in different files whenever possible.

• The 2 modules implemented should be part of the same framework, e.g., by sharing namespaces, styling, and common utilities. However, each of them should be compilable as a standalone shared library, allowing independent use.

• Before submission, ensure your code's compatibility with various compilers by testing it, e.g. on GodBolt, and enabling the following compilation flags:

  -std=c++17 -Wall -Wextra -Wpendantic -Werror
  

Submission

1. Include a README file that:
   • Clearly states which module(s) you implemented.
   • Lists all group members with their name, email address, and highlights their individual contribution to the project.
   • Provides a concise discussion of the obtained results, such as insights from statistical analyses, observations on the convergence order of implemented methods, and any other pertinent information.
2. Provide a working compilation script as the preferred method for building the libraries and testing your implementation. Clearly specify the commands needed to compile the code successfully. Bonus: use Makefile or CMake as build tools.
3. Submit a single compressed file (named Homework_02_Surname1_Surname2.ext) containing all source code, the README, and any other relevant files or third-party libraries (please comply to their licences).

Evaluation grid

1. Module A) + Module B), C), or D) (up to 1 point each):
   • Successful compilation, implementation correctness, results correctness.
2. Effective utilization of modern C++ features (up to 1 point):
   • STL, smart pointers, exceptions, const correctness, ...
3. Documentation, build instructions, and discussion of results (up to 1 point)
4. Code organization (up to 0.5 points):
   • Clear separation between function declarations and definitions, consistent use of namespaces and styling, organized file structure with meaningful names, compilability as standalone shared libraries.
5. Integration of third-party libraries (up to 0.5 points)
6. Bonus points (up to 1 point).