The Joy of SciPy, Part I
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The summary runs the spigot algorithm for calculating digits of pi in CPython, Cython, PyPy and Numba and compares their performance. The algorithm implements a spigot algorithm by A. Sale, D. Saada, S. Rabinowitz to generate n digits of pi by iterating through the calculations.
![Exercise
Run the algorithm below using CPython, Cython, PyPy and Numba and
compare their performance. This is implementing a spigot algorithm
by A. Sale, D. Saada, S. Rabinowitz, as mentioned on
http://mail.python.org/pipermail/edu-sig/2012-December/010721.html.
Code: https://gist.github.com/deeplook/4947835.
def pi_digits(n):
"Generate n digits of Pi."
k, a, b, a1, b1 = 2, 4, 1, 12, 4
while n > 0:
p, q, k = k * k, 2 * k + 1, k + 1
a, b, a1, b1 = a1, b1, p * a + q * a1, p * b + q * b1
d, d1 = a / b, a1 / b1
while d == d1 and n > 0:
yield int(d)
n -= 1
a, a1 = 10 * (a % b), 10 * (a1 % b1)
d, d1 = a / b, a1 / b1
>>> list(pi_digits(20))
[3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4]](https://image.slidesharecdn.com/joy-of-scipy-part1-130215031604-phpapp01/85/The-Joy-of-SciPy-Part-I-16-320.jpg)
The Joy of SciPy, Part I
- 1. The Joy of SciPy Part I, Dinu Gherman Part II, Dave Kammeyer (not included here) Python Users Berlin Meet-up, 2013-02-14
- 2. About… Science… Visualisation Analytics Numbers Data Math Big Data Algorithms Machine Learning … and Python
- 3. Science, a Reminder Domains Math Education Visualisation Data Models Publication Theory Experiments
- 4. From Scientific Python “Components”… Nat. Language Toolkit Matplotlib Mol. Modelling Toolkit SymPy Chaco PIL BioPython.org NumPy Veusz OpenCV PsychoPy.org Blaze … Scikit-image AstroPython.org Scikit-learn Stackless Pandas … PyPy PyTables Cython Disco Sphinx Numba ReST (sample) Theano ………
- 5. … to Integrated Scientific Environments Legacy: Py-Distributions: Py-Environments: Mathematica ScientificPython IPython.org Matlab Enthought, EPD SciPy.org Maple Anaconda Sagemath.org Magma Python(x, y) Wakari.io Mathics.org Orange
- 6. IPython Shell • Extended Inter- active Python shell • Extensions • Help • Tab completion • History • Multi-line editing • Debugger • Shell access • Bookmarks • Magic functions • DEMO…
- 7. IPython Notebook • IPython shell in the browser • Markdown text + executable Python code • JSON container, including output • Literate Programming – finally • Great tutorial experience • Easy to share running code – w/o hassle
- 8. IPython Notebook Demo • Tour of the IPython notebook (built-in) • Installing a custom extension • Combined later with Matplotlib demo
- 9. IPython Extension Demo • Show object graphs • Reuse a previously written package • Run interactively in the notebook • Notebook: http://nbviewer.ipython.org/4770302/ • Code: https://gist.github.com/deeplook/4731035
- 10. Matplotlib • Scientific plots • 2D, 3D, interactive • Smart axes, grids • Beautiful math (TeX) • Widgets, annotations, … • http://matplotlib.org/gallery.html
- 11. Matplotlib Demo • Simple plots • Bézier path editor • Magic cube
- 12. Conferences • http://conference.scipy.org • https://www.euroscipy.org • http://pydata.org † Videos (e.g. by John Hunter , Fernando Pérez et al.): http://pyvideo.org/category/17/pycon-us-2012
- 13. Selected Books
- 14. What to take away • Use available Python tools for your scientific domain (trivia)! • Use IPython shell & notebook, Matplotlib – far too powerful to leave to scientists! ;-) • Have fun with science – seriously! http://io9.com/5973726/15+year-old-whiz-kid-has- research-on-dwarf-galaxies-published-in-nature
- 16. Exercise Run the algorithm below using CPython, Cython, PyPy and Numba and compare their performance. This is implementing a spigot algorithm by A. Sale, D. Saada, S. Rabinowitz, as mentioned on http://mail.python.org/pipermail/edu-sig/2012-December/010721.html. Code: https://gist.github.com/deeplook/4947835. def pi_digits(n): "Generate n digits of Pi." k, a, b, a1, b1 = 2, 4, 1, 12, 4 while n > 0: p, q, k = k * k, 2 * k + 1, k + 1 a, b, a1, b1 = a1, b1, p * a + q * a1, p * b + q * b1 d, d1 = a / b, a1 / b1 while d == d1 and n > 0: yield int(d) n -= 1 a, a1 = 10 * (a % b), 10 * (a1 % b1) d, d1 = a / b, a1 / b1 >>> list(pi_digits(20)) [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4]