An algorithm to compute the coefficients of a function development in a spherical harmonics convergent series

Table of contents

• Introduction
• Repository structure
• Documentation
• How to use

Introduction

This program computes the coefficients of a function development in a spherical harmonics convergent series, by using a standard mathematical algorithm.

When running the program, you have simply to input the generic shape of the equation and the values of m and l and the coefficients will be calculated.

Some program features:

• Can calculate coefficients for any generic function, entered by the user during the program running.
• coefficients are expressed as complex numbers.
• It works well for each negative or positive value of m, with very good accuracy until m < 5. For higher m values, the accuracy gradually decrease.

NOTE: equations are displayed in green color in order to be correctly visualized in both normal and dark mode.

Output example:

The software is and will stay free, but if you want to support me with a donation it would be really appreciated!

Repository structure

Here the diagram structure of the repository:

SAFD-agorithm/
├── include/
│   ├── aliases.hpp
│   ├── utils.hpp
│   ├── functions.hpp
├── src/
│   ├── utils.cpp
│   ├── functions.cpp
│   ├── main.cpp
├── scripts/
│   ├── debug.sh
├── test/
│   ├── test_utils.cpp
│   ├── test_functions.cpp
├── doc/
│   ├── algorithm_explanation.md
│   ├── download_and_run.md
│   ├── CREDITS.md
│   ├── CONTRIBUTING.md
├── img/
│── README.md
│── LICENSE
│── CITATION.cff
│── .gitignore
│── .valgrindrc
│── .all-contributorsrc
│── makefile

Documentation

Extra documentation is available in the doc folder:

• Download, compile and run: contains documentation about how to download, compile and run the program as well as a complete list of prerequisites.
• Algorithm explanation and physical background: contains information about the mathematical and physical explanation related to the coefficients computation and a detailed description of the used algorithm.
• Credits: contains a list of all the people who contributed to this project.
• Contributing: contains information about how to contribute to this project.

How to use

When running the program, some options are displayed:

Available options:
   1. Display the single value of a f(m,l) coefficient.
   2. Display all the values of f(m,l) coefficients from m to 0 and from l to 0.
   3. Quit the program. 

Option choice: 

The first one is used to compute a single value of the coefficient for a certain m and l.

The second one is used, instead, to compute all the values of from m to 0 and from l to 0.

Third option explanation is trivial.

When one of the options has been chosen, an output like this will be displayed:

Option choice: 1

Enter the f(th,phi) equation shape (avoid backspaces): 

You can enter the function shape and the values of m and l. For example:

Enter the f(th,phi) equation shape (avoid backspaces): 3*cos(th)+pow(sin(phi),5)
Enter the value of m: 2
Enter the value of l: 3

and the final result is displayed with both real and imaginary parts:

f(2,3) = 0.0546019 + -0.00160564i