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Getting Started with Numba

Requirements

Install the following dependencies using pip3 command:

$ pip3 install numba Pillow

Tk comes pre-installed with Python and numpy is installed during the numba installation in case it is not available.

Introduction

To get started with numba, we will compute the Mandelbrot Set, a set of points on the complex plane which always remain bounded by a threshold value while solving the quadratic recurrence equation. It is an iterative problem which is also compute intensive and visual in nature. This makes it a good starting point for new numba users to witness the various ways in which one can achieve code speed-up using numba.

This Mandelbrot Set Generator is built using the Tcl/Tk cross-platform UI framework which comes pre-packaged with the python. UI layer (which includes advanced feature such as Zooming) and computational layer are separated for better understanding.

Project Repository

Brief description of various parts of the code are provided below:

  • Requisite libraries are imported along with the view_mandelbrot() function from canvas.py (UI Layer) which is responsible for rendering the Mandelbrot Set.
  • The domain size is set as a 600x600 grid and the maximum number of iterations for each point on this grid is limited to 1000 (6000 for parallel codes).
  • mandelbrot() function is used to evaluate the Mandelbrot Set. It returns the RBG color of each point on the grid (complex plane) as a nested list of tuples or a NumPy array.

Check out the video demo below:

Video Tutorial

Source Code

To get started with the exercise, simple clone the GitHub Repository

Each implementation has a dedicated file and the recommended learning sequence that should be followed is provided below:

File Name Data Layer Description parallel Execution
01-python-list.py list Pure Python implementation where a list of list of RBG tuples is used to store the computed RBG pixel values. -
02-njit-python-list.py list @numba.njit is applied on the pure Python implementation. -
03-njit-parallel-python-list.py list @numba.njit is applied on the pure Python implementation along with explicit for loop parallelization using numba.prange(). Yes
04-numpy-array.py NumPy array Implementation where a 3-dimensional numpy array is used to store the computed RBG pixel values. -
05-njit-numpy-array.py NumPy array @numba.njit is applied on the NumPy implementation. -
06-njit-parallel-numpy-array.py NumPy array @numba.njit is applied on the NumPy implementation. Numpy is primarily designed to be as fast as possible on a single core, whereas numba automatically compiles a version which can run in parallel utilizing multiple threads if it contains reduction functions, array math functions and many more functions or assignments or operations. Explicit for loop parallelization is also performed using numba.prange() Yes
07-numpy-vectorize.py NumPy array @numpy.vectorize creates a vectorized function which uses broadcasting rules instead of for loops. Although users can write vectorized functions in Python, it is mostly for convenience and is neither optimal nor efficient. -
08-numba-vectorize.py NumPy array @numba.vectorize creates a NumPy ufunc from a Python function as compared to writing C code if using the NumPy API. A ufunc uses broadcasting rules instead of nested for loops. -
09-parallel-numba-vectorize.py NumPy array @numba.vectorize also has the option to create a ufunc which executes in parallel. Yes

To execute the code just run:

$ python3 filename.py

A Tkinter GUI will pop-up. You can use left mouse button to drag and select an area to zoom into. Right click to reset the canvas.