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Scientific Python

Introduction to the scientific python stack: Jupyter / IPython, NumPy, SciPy, matplotlib, pandas, SymPy, scikit-learn


IPython

  • Powerful interactive shell
  • Supports tab completion of just about everything
  • Inline help system for modules, classes etc. with ?, source code with ??
  • Browser based notebook (Jupyter) with support for (runnable) code, text, mathematical expressions using LATEX, inline plots etc.
  • Could be used as a computational lab notes/worksheets
  • Magic functions to access the shell, run R code etc.
  • Parallel computing

Jupyter - Computational Narratives

The Jupyter Notebook is a tool for creating and sharing computational narratives. The Jupyter Notebook works with over 40 languages. Jupyter Notebooks render on GitHub.

  • Computers are optimized for producing, consuming and processing data.
  • Humans are optimized for producing, consuming and processing narratives/stories.
  • For code and data to be useful to humans, we need tools for creating and sharing narratives that involve code and data.

Jupyter & Data Science

The Jupyter Notebook is a tool that allows us to explore the fundamental questions of Data Science

  • with a particular dataset
  • with code and data
  • in a manner that produces a computational narrative
  • that can be shared, reproduced, modified, and extended.

At the end of it all, those computational narratives encapsulate the goal or end point of Data Science. The character of the narrative (prediction, inference, data generation, insight, etc.) will vary from case to case.

NumPy

NumPy is the fundamental package for scientific computing with Python. It contains among other things:

  • A powerful N-dimensional array object
  • Sophisticated (broadcasting) functions
  • Tools for integrating C/C++ and Fortran code
  • Useful linear algebra, Fourier transform, and random number capabilities
  • Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data.

Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

NumPy provides a powerful N-dimensions array object

  • Methods on these arrays are fast because they relies on well-optimised librairies for linear algebra (BLAS, ATLAS, MKL)
  • NumPy is tolerant to python’s lists

NumPy inherits from years of computer based numerical analysis problem solving.

Numpy is the core library for scientific computing in Python. It provides a high-performance multidimensional array object (MATLAB style), and tools for working with these arrays.

Arrays

  • A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers.
  • The number of dimensions is the rank of the array; the shape of an array is a tuple of integers giving the size of the array along each dimension.
  • We can initialize numpy arrays from nested Python lists, and access elements using square brackets.
  • Numpy also provides many functions to create arrays.

SciPy

SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering. SciPy core packages: IPython, NumPy, SciPy Library, SimPy, matplotlib, pandas.

SciPy Library

SciPy is a collection of mathematical algorithms and convenience functions built on top of NumPy includes modules for: statistics, integration & ODE solvers, linear algebra, optimization, FFT, etc.

We use the terms SciPy and SciPy Library interchangeably. Meaning depends on context.

SciPy is a toolbox for researchers/scientists, it contains many hidden treasures for them.

SciPy & NumPy

Numpy provides a high-performance multidimensional array and basic tools to compute with and manipulate these arrays.

SciPy builds on this, and provides a large number of functions that operate on numpy arrays and are useful for different types of scientific and engineering applications.

SciPy provides numerous numerical routines, that run efficiently on top of NumPy arrays for: optimization, signal processing, linear algebra and many more. It also provides some convenient data structures as compressed sparse matrix and spatial data structures. If you had already use some scikits (scikit-learn, scikit-image) you already used scipy extensively.

SciPy:

  • Contains linear algebra routines that overlap with NumPy; SciPy’s linear algebra routines always run on the optimized system libraries (LAPACK, ATLAS, Intel Math Kernel Library, etc.)
  • Sparse matrix support
  • Extends NumPy’s statistical capabilities
  • Under active development, new toys added constantly!

SciPy - A big box of tools: Special functions (scipy.special),Integration (scipy.integrate),Optimization (scipy.optimize),Interpolation (scipy.interpolate),Fourier Transforms (scipy.fftpack),Signal Processing (scipy.signal),Statistics (scipy.stats),Linear Algebra (scipy.linalg),File IO (scipy.io),Sparse Eigenvalue Problems with ARPACK,Compressed Sparse Graph Routines (scipy.sparse.csgraph),Spatial data structures and algorithms (scipy.spatial),Multi-dimensional image processing (scipy.ndimage),Weave (scipy.weave)

matplotlib

The ultimate plotting library that renders 2D and 3D high-quality plots for python.

  • pyplot implements Matlab-style plotting
  • Object-oriented API for more advanced graphics
  • The API mimics, in many ways the MATLAB one, easing the transition from MATLAB users to python
  • Once again, no surprises, matplotlib is a very stable and mature project (expect one major release per year)

matplotlib tries to make easy things easy and hard things possible. You can generate plots, histograms, power spectra, bar charts, errorcharts, scatterplots, etc, with just a few lines of code.

For simple plotting the pyplot interface provides a MATLAB-like interface, particularly when combined with IPython. For the power user, you have full control of line styles, font properties, axes properties, etc, via an object oriented interface or via a set of functions familiar to MATLAB users.

With just a little bit of extra work we can easily plot a more complex chart e.g. multiple lines at once, and add a title, legend, and axis labels.

Notes

TL;DR

  • NumPy is the foundation
  • SciPy is built upon NumPy, with some overlapping functionality
  • matplotlib complements both

NumPy, SciPy, matplotlib

  • NumPy is the foundation of scientific and numerical computing with Python
  • SciPy is a collection of mathematical and scientific tools
  • matplotlib is a technical plotting package

NumPy Arrays

  • Implemented in C for efficiency
  • Python indexing and slicing
  • Elements are strongly typed

Taking advantage of NumPy

  • Think in parallel!
  • Replace loops with vector operations

matplotlib

  • Primarily 2D plotting
  • Basic 3D plots available with mplot3d (import mpl_toolkits.mplot3d)

Other Notes

NumPy/SciPy/scikit-learn rely on many low-level Fortran/C library such as BLAS, ATLAS, the Intel MKL…

  • most of these libraries are shipped by your favorite OS unoptimized (well, maybe not the case for Mac)
  • you may want to re-compile these libraries or to use a packaged python distribution (anaconda, canopy)
  • libraries for performance: numba, cython, …

Pandas

pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language.

  • “R for Python”
  • Provides easy to use data structures & a ton of useful helper functions for data cleanup and transformations
  • Fast! (backed by NumPy arrays)
  • Integrates well with other libs e.g. scikit-learn
  • pandas provides the DataFrame class, which is very similar to a data.frame in R
  • Built on top of NumPy arrays, and allows mixed column types
  • Copes well with missing values (unlike NumPy)
  • Intelligently matches on columns/indices (supports SQL-like joins etc.)
  • Read and write .csv, .xls, HTML tables etc.
  • Lots of useful data analysis tools built in

SymPy

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible.

SymPy is written entirely in Python and does not require any external libraries.

scikit-learn

  • Machine Learning algorithms implemented in Python on top of NumPy & SciPy
  • Conveniently maintains the same interface to a wide range of algorithms
  • Includes algorithms for: Classification, Regression, Clustering, Dimensionality reduction
  • As well as lots of useful utilities (cross-validation, preprocessing etc.)

Many More Tools ..

  • Performance: Numba, Weave, Numexpr, Theano …
  • Visualization: Bokeh, Seaborn, Plotly, Chaco, mpld3, ggplot, MayaVi, vincent, toyplot, HoloViews …
  • Data Structures & Computation: Blaze, Dask, DistArray, XRay, Graphlab, SciDBpy, pySpark …
  • Packaging & distribution: pip/wheels, conda, EPD, Canopy, Anaconda …
Author

Eueung Mulyana

Engineer. Lecturer. Programmer. Open Source Enthusiast.