Python is frequently used for high-performance scientific applications. Python is widely used in academia and scientific projects because it is easy to write, and it performs really well.

Due to its high performance nature, scientific computing in Python often refers to external libraries, typically written in faster languages (like C, or FORTRAN for matrix operations). The main libraries used are NumPy, SciPy and Matplotlib. Going into detail about these libraries is beyond the scope of the Python guide. However, a comprehensive introduction to the scientific Python ecosystem can be found in the Python Scientific Lecture Notes

IPython is an enhanced version of Python interpreter. The features it provides are of great interest for the scientists. The inline mode allow graphics and plots to be displayed in the terminal (Qt based version). Moreover the notebook mode supports literate programming and reproducible science generating a web-based Python notebook. This notebook allowing to store chunk of Python code along side to the results and additional comments (HTML, LaTeX, Markdown). The notebook could be shared and exported in various file formats.

NumPy is a low level library written in C (and FORTRAN) for high level mathematical functions. NumPy cleverly overcomes the problem of running slower algorithms on Python by using multidimensional arrays and functions that operate on arrays. Any algorithm can then be expressed as a function on arrays, allowing the algorithms to be run quickly.

NumPy is part of the SciPy project, and is released as a separate library so people who only need the basic requirements can just use NumPy.

NumPy is compatible with Python versions 2.4 through to 2.7.2 and 3.1+.

Numba is an Numpy aware Python compiler (just-in-time (JIT) specializing compiler) which compiles annotated Python (and Numpy) code to LLVM (Low Level Virtual Machine) (through special decorators). Briefly, Numba using system that compiles Python code with LLVM to code which can be natively executed at runtime.

SciPy is a library that uses Numpy for more mathematical functions. SciPy uses NumPy arrays as the basic data structure. SciPy comes with modules for various commonly used tasks in scientific programming, for example: linear algebra, integration (calculus), ordinary differential equation solvers and signal processing.

Matplotlib is a flexible plotting library for creating interactive 2D and 3D plots that can also be saved as manuscript-quality figures. The API in many ways reflects that of MATLAB, easing transition of MATLAB users to Python. Many examples, along with the source code to re-create them, can be browsed at the matplotlib gallery.

Pandas is data manipulation library based on Numpy and which provides many useful functions for accessing, indexing, merging and grouping data easily. The main data structure (DataFrame) is close to what could be found in the R statistical package, that is an heterogeneous data tables with name indexing, time series operations and auto-alignment of data.

Installation of scientific Python packages can be troublesome. Many of these packages are implemented as Python C extensions which need to be compiled. This section lists various so-called scientific Python distributions which provide precompiled and easy-to-install collections of scientific Python packages.

Many people who do scientific computing are on Windows. And yet many of the scientific computing packages are notoriously difficult to build and install. Christoph Gohlke however, has compiled a list of Windows binaries for many useful Python packages. The list of packages has grown from a mainly scientific Python resource to a more general list. It might be a good idea to check it out if you’re on Windows.

Installing NumPy and SciPy can be a daunting task. Which is why the Enthought Python distribution was created. With Enthought, scientific python has never been easier (one click to install about 100 scientific python packages). The Enthought Python Distribution comes in two variants: a free version EPD Free and a paid version with various pricing options.

Continuum Analytics offers the Anaconda Python Distribution which includes all the common scientific python packages and additionally many packages related to data analytics and big data. Anaconda comes in two flavors, a paid for version and a completely free and open source community edition, Anaconda CE, which contains a slightly reduced feature set. Free licenses for the paid-for version are available for academics and researchers.