Introduction to NumPy, SciPy, and matplotlib

Introduces some of the most important Python libraries for numerical and scientific computing, as well as the main technical plotting library.

Transcript

1. NumPy, SciPy, and matplotlib Orlando Python User Group May 22, 2014 Craig Finch
2. Background • You need a working knowledge of Python • Basic knowledge of Git to get the code • Code can be found at https://github.com/westover/OrlandoPythonUserGroup • These examples can be found in subdirectory Craig_Finch_NumPy_SciPy_matplotlib • See README.txt for details
3. NumPy, SciPy, and matplotlib • NumPy is the foundation • SciPy is built upon NumPy, with some overlapping functionality • matplotlib complements both NumPy SciPy matplotlib
4. NumPy
5. NumPy Python interpreter NumPy C Extension Python script import numpy a = numpy.array([...]) System linear algebra library
6. NumPy Arrays • Implemented in C for efficiency • Python indexing and slicing • Elements are strongly typed NumPy Type Subtypes (bits) Boolean Unsigned Integer C types, 8, 16, 32, 64 Integer C types, 8, 16, 32, 64 Floating Point C types, 8, 16, 32, 64, 96, 128 Complex Floating Point 2x32, 2x64, 2x96, 2x128 Python object references Much like a Python list
7. Taking advantage of NumPy • Think in parallel! • Replace loops with vector operations • Demo: collision detection Premature optimization is the root of all evil (or at least most of it) in programming. Donald Knuth
8. Start with a collection of spheres, randomly placed in space: Example: finding pairwise distances between spheres
9. Distance between two circles The same principle applies to distance between spheres in three dimensions.
10. Benchmarking • Requires good experimental design ◦ Experiments must be controlled ◦ Results must be repeatable ◦ Results must be statistically significant • Tools ◦ Python cProfile ◦ Robert Kern’s line profiler https://pypi.python. org/pypi/line_profiler/1.0b3 ◦ Linux profilers ▪ oprofile ▪ valgrind (specifically, callgrind)
11. Optimizing numerical code • Module NumPy/distance.py contains six functions that show how to optimize the calculation ◦ Also contains a decorator that times each function • Script NumPy/distance_benchmarking.py compares results ◦ Not a very sophisticated benchmarking tool • Script NumPy/distance_benchmarking.py ensures all functions return the same result
12. Results • Results were presented as a live demo • Results on an Intel Core i5-4460 3.2GHz (using only one core) Benchmarking with 1000 particles. Function=find_distances_2, Time=2.15743207932 sec Function=find_distances_3, Time=0.0198380947113 sec Benchmarking with 3000 particles. Function=find_distances_3, Time=0.0985090732574 sec Function=find_distances_4, Time=0.102454900742 sec Function=find_distances_5, Time=0.0703949928284 sec Function=find_distances_6, Time=0.195425987244 sec
13. Take-Aways: NumPy • Use arrays instead of lists for numerical data • Use vector operations instead of loops whenever possible • If it’s still too slow…. ◦ Write C/C++/Fortran code ◦ Parallelize (multi-core, multi-server) • Understand NumPy, because it’s the foundation for: ◦ SciPy ◦ Pandas ◦ mpi4py
14. SciPy
15. SciPy is 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) Continued on next slide... * or a candy store...
16. SciPy tools, continued • Linear Algebra (scipy.linalg) • Sparse Eigenvalue Problems with ARPACK • Compressed Sparse Graph Routines scipy.sparse. csgraph • Spatial data structures and algorithms (scipy.spatial) • Statistics (scipy.stats) • Multi-dimensional image processing (scipy.ndimage) • File IO (scipy.io) • Weave (scipy.weave) ◦ Write compiled extensions by putting C/C++ code inline with your Python code! ◦ f2py in NumPy for writing extensions in Fortran
17. A few thoughts on 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!
18. SciPy example 1: Filter a signal Signal Filter Filtered Signal Example code: SciPy/linear_filters.py
19. Input signal: a step function
20. Finite impulse response (FIR) filter
21. Filtered signal
22. Code snippets # Filter parameters cutoff = 0.2 numtaps = 100 # Define filter lpf = scipy.signal.firwin(numtaps, cutoff, window= ('hamming')) # Frequency response lpf_freq, lpf_response = scipy.signal.freqz(lpf) # Filter signal, no initial conditions y1 = scipy.signal.lfilter(lpf, [1.0], x)
23. SciPy Example 2: Model a linear system Signal x(t) System h(t) Output y(t) Example code: SciPy/LTI_simulation.py A linear time invariant (LTI) system is a generalization of the digital filter from the previous example:
24. 1st-order LTI system • Model with SciPy class signal.lti ◦ Methods for impulse and step response • Create our own function ◦ Define a discrete-time step function ◦ Apply step function to input of system ◦ Compare results to results from SciPy class ◦ De-convolve to recover original signal
25. Step Response
26. Impulse Response
27. Applying step function at input
28. matplotlib
29. matplotlib • pyplot implements Matlab-style plotting • Object-oriented API for more advanced graphics
30. Basic plotting with matplotlib.pyplot import numpy as np import scipy import matplotlib.pyplot as plt x = np.arange(-2 * np.pi, 2 * np.pi, 0.1) cos_x = np.cos(x) sin_x = np.sin(x) plt.figure() plt.plot(x, cos_x, label='cos(x)', linewidth=2) plt.plot(x, sin_x, label='sin(x)', linewidth=2) plt.xlabel('x') plt.ylabel('y') plt.legend() plt.figure() plt.show()
31. Basic plotting with matplotlib.pyplot
32. How I made this figure with matplotlib
33. Advanced graphics with the API import matplotlib.pyplot as plt from matplotlib.patches import Circle ... fig = plt.figure() ax = fig.add_subplot(111) ... ax.add_patch(Circle(center1, radius, edgecolor='blue', facecolor='lightgray')) ax.add_patch(Circle(center2, radius, edgecolor='red', facecolor='lightgray'))
34. Other matplotlib tricks • Creating math with LaTeX • Axis bounds and aspect ratio plt.text(-1.25, 2.25, "$d=\sqrt{\Delta x^2 + \Delta y^2}$", fontsize=18) plt.axis([-1.5, 3, -1.5, 3]) ax.set_aspect(1.0)
35. Summary • NumPy is the foundation of scientific and numerical computing with Python ◦ Learn it well! • SciPy is a collection of mathematical and scientific tools • matplotlib is a technical plotting package ◦ Primarily 2D plotting ◦ Basic 3D plots available with mplot3d import mpl_toolkits.mplot3d