NumPy, SciPy, and matplotlib Orlando Python User Group May 22, 2014 Craig Finch 

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 

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

NumPy 

NumPy Python interpreter NumPy C Extension Python script import numpy a = numpy.array([...]) System linear algebra library 

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 

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 

Start with a collection of spheres, randomly placed in space: Example: finding pairwise distances between spheres 

Distance between two circles The same principle applies to distance between spheres in three dimensions. 

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) 

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 

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 

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 

SciPy 

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... 

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 

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! 

SciPy example 1: Filter a signal Signal Filter Filtered Signal Example code: SciPy/linear_filters.py 

Input signal: a step function 

Finite impulse response (FIR) filter 

Filtered signal 

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) 

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: 

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 

Step Response 

Impulse Response 

Applying step function at input 

matplotlib 

matplotlib ● pyplot implements Matlab-style plotting ● Object-oriented API for more advanced graphics 

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() 

Basic plotting with matplotlib.pyplot 

How I made this figure with matplotlib 

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')) 

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) 

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