Jake VanderPlas - Losing your Loops: Fast Numerical Computing with NumPy

NumPy, the core array computing library for Python, provides tools for flexible and powerful data analysis, and is the basis for most scientific code written in Python. Getting the most out of NumPy, though, might require slightly changing how you think about writing code: this talk will outline the basic strategies essential to performing fast numerical computations in Python with NumPy.

https://us.pycon.org/2015/schedule/presentation/373/

Transcript

1. Losing Your Loops Fast Numerical Computing with NumPy Jake VanderPlas PyCon 2015
2. Python is Fast . . . for Writing, Testing, and Developing Code
3. Python is Fast . . . for Writing, Testing, and Developing Code
4. Python is Fast . . . for Writing, Testing, and Developing Code
6. Python is Fast . . . because it is interpreted, dynamically typed, and high-level
7. Python is Slow . . . for Repeated Execution of Low-level Tasks
8. Python is Slow (%timeit is a useful magic command available in IPython) A simple function implemented in Python . . .
9. Python is Slow The same function implemented in Fortran . . .
10. Python is Slow Python is ~100x slower than Fortran for this simple task!
11. Python is Slow Why is Python Slow? . . . for Repeated Execution of Low-level Tasks Python is a high-level, interpreted and dynamically-typed language. Each Python operation comes with a small type-checking overhead. With many repeated small operations (e.g. in a loop), this overhead becomes significant!
12. what makes Python fast (for development) is what makes Python slow (for code execution) The paradox . . . * Though JIT compilers like PyPy, Numba, etc. may change this soon . . .
13. NumPy is designed to help us get the best of both worlds . . . - Fast development time of Python - Fast execution time of C/Fortran . . . by pushing repeated operations into a statically-typed compiled layer. import numpy
14. Four Strategies For Speeding-up Code with NumPy 1. Use NumPy’s ufuncs 2. Use NumPy’s aggregations 3. Use NumPy’s broadcasting 4. Use NumPy’s slicing, masking, and fancy indexing Overall goal: push repeated operations into compiled code and Get Rid of Slow Loops!
15. Strategy #1: Use NumPy’s ufuncs
16. Use NumPy’s ufuncs Strategy #1: ufuncs are NumPy’s Universal Functions . . . They operate element-wise on arrays.
17. Use NumPy’s ufuncs Strategy #1: Element-wise operations . . . . . . with Python lists:
18. Use NumPy’s ufuncs Strategy #1: Element-wise operations . . . . . . with Python lists: . . . with NumPy arrays:
19. Use NumPy’s ufuncs Strategy #1: Ufuncs are fast . . .
20. Use NumPy’s ufuncs Strategy #1: Ufuncs are fast . . .
21. Use NumPy’s ufuncs Strategy #1: Ufuncs are fast . . . . . . 100x speedup with NumPy!
22. Use NumPy’s ufuncs Strategy #1: There are many ufuncs available: - Arithmetic Operators: + - * / // % ** - Bitwise Operators: & | ~ ^ >> << - Comparison Oper’s: < > <= >= == != - Trig Family: np.sin, np.cos, np.tan ... - Exponential Family: np.exp, np.log, np.log10 ... - Special Functions: scipy.special.* . . . and many, many more.
23. Strategy #2: Use NumPy’s aggregations
24. Strategy #2: Use NumPy’s aggregations Aggregations are functions which summarize the values in an array (e.g. min, max, sum, mean, etc.)
25. Strategy #2: Use NumPy’s aggregations NumPy aggregations are much faster than Python built-ins . . .
26. Strategy #2: Use NumPy’s aggregations NumPy aggregations are much faster than Python built-ins . . .
27. Strategy #2: Use NumPy’s aggregations NumPy aggregations are much faster than Python built-ins . . . ~70x speedup with NumPy!
28. Strategy #2: Use NumPy’s aggregations NumPy aggregations also work on multi-dimensional arrays . . .
29. Strategy #2: Use NumPy’s aggregations NumPy aggregations also work on multi-dimensional arrays . . .
30. Strategy #2: Use NumPy’s aggregations Lots of aggregations available . . . np.min() np.max() np.sum() np.prod() np.mean() np.std() np.var() np.any() np.all() np.median() np.percentile() np.argmin() np.argmax() . . . np.nanmin() np.nanmax() np.nansum(). . . . . . and all have the same call signature. Use them often!
31. Strategy #3: Use NumPy’s broadcasting
32. Strategy #3: Use NumPy’s broadcasting Broadcasting is a set of rules by which ufuncs operate on arrays of different sizes and/or dimensions.
33. Strategy #3: Use NumPy’s broadcasting Image source: http://astroML.org/ Visualizing Broadcasting...
34. Strategy #3: Use NumPy’s broadcasting Broadcasting rules . . . 1. If array shapes differ, left-pad the smaller shape with 1s 2. If any dimension does not match, broadcast the dimension with size=1 3. If neither non-matching dimension is 1, raise an error.
35. Strategy #3: Use NumPy’s broadcasting 1. If array shapes differ, left-pad the smaller shape with 1s 2. If any dimension does not match, broadcast the dimension with size=1 3. If neither non-matching dimension is 1, raise an error. shape=[3] shape=[] 1. shape=[3] shape=[1] 2. shape=[3] shape=[3] final shape = [3]
36. Strategy #3: Use NumPy’s broadcasting 1. If array shapes differ, left-pad the smaller shape with 1s 2. If any dimension does not match, broadcast the dimension with size=1 3. If neither non-matching dimension is 1, raise an error. shape=[3,3] shape=[3] 1. shape=[3,3] shape=[1,3] 2. shape=[3,3] shape=[3,3] final shape = [3,3]
37. Strategy #3: Use NumPy’s broadcasting 1. If array shapes differ, left-pad the smaller shape with 1s 2. If any dimension does not match, broadcast the dimension with size=1 3. If neither non-matching dimension is 1, raise an error. shape=[3,1] shape=[3] 1. shape=[3,1] shape=[1,3] 2. shape=[3,3] shape=[3,3] final shape = [3,3]
38. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing
39. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing With Python lists, indexing accepts integers or slices . . .
40. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing NumPy arrays are similar . . .
41. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing . . . but NumPy offers other fast and convenient indexing options as well.
42. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing “Masking”: indexing with boolean masks A mask is a boolean array:
43. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing “Masking”: indexing with boolean masks Masks are often constructed using comparison operators and boolean logic, e.g.
44. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing “Fancy Indexing”: passing a list/array of indices . . .
45. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing Multiple dimensions: use commas to separate indices!
46. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing Multiple dimensions: use commas to separate indices!
47. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing Masking in multiple dimensions . . .
48. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing Mixing fancy indexing and slicing . . .
49. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing Mixing masking and slicing . . .
50. Strategy #4: Use NumPy’s slicing, masking, and fancy indexing All of these operations can be composed and combined in nearly limitless ways!
51. Example: Computing Nearest Neighbors Let’s combine all these ideas to compute nearest neighbors of points without a single loop!
52. Example: Computing Nearest Neighbors
53. Example: Computing Nearest Neighbors D i j 2 = (x i - x j )2 + (y i - y j )2 Naive approach requires three nested loops . . . . . . but we can do better.
54. Example: Computing Nearest Neighbors
55. Example: Computing Nearest Neighbors
56. Example: Computing Nearest Neighbors
57. Example: Computing Nearest Neighbors
58. Example: Computing Nearest Neighbors
59. Example: Computing Nearest Neighbors
60. Summary . . . - Writing Python is fast; loops can be slow - NumPy pushes loops into its compiled layer: - fast development time of Python - fast execution time of compiled code Strategies: 1. ufuncs for element-wise operations 2. aggregations for array summarization 3. broadcasting for combining arrays 4. slicing, masking, and fancy indexing for selecting and operating on subsets of arrays
61. ~ Thank You! ~ Email: jakevdp@uw.edu Twitter: @jakevdp Github: jakevdp Web: http://vanderplas.com/ Blog: http://jakevdp.github.io/