Computational Physics Programming Style and Practices & Visualizing Data via Plotting

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1 Computational Physics Programming Style and Practices & Visualizing Data via Plotting Prof. Paul Eugenio Department of Physics Florida State University Jan 30,

2 Announcements Read Chapter 2 section 2.7 Good Programming style Chapter 3 sections Graphics and Visualization Chapter 4: pages Accuracy and Speed

3 Programming Conventions to follow in this class

4 Documentation via docstring Include documenting comments in your programs Each program should include a prolog comment block or docstring Each function should start with a docstring def def g(m,n): """ triple-double-quotes""" g(m,n): """ """ Greatest Greatest Common Common Divisor Divisor Euclid's Euclid's prescription: g(m,n) g(m,n) m if if n 0 0 else else g(m,n) g(m,n) g(n, g(n, m mod mod n) n) both both m & n must must both both be be nonnegative integers integers """ """ # Now Now for for the the code code The use of docstring will have helpful advantages later on

5 Program Prolog via docstring #! #! /usr/bin/env /usr/bin/env python python """ """ gcd.py gcd.py calculates calculates the the greatest greatest common common divisor divisor g(m,n) g(m,n) of of two two nonnegative nonnegative integers integers m m and and n n using using Euclid Euclid prescription. prescription. Paul Paul Eugenio Eugenio PHZ4151C PHZ4151C Exercise Exercise 2, 2, Problem Problem 4 4 Jan Jan 28, 28, """ """ from from future future import import division, division, print_function print_function

6 Functions, variables, and constants Use meaningful variable names Function names: lower_case_with_underscores Examples: catalan(), generate_data() Names to AVOID l (lowercase el), O (uppercase oh), or I (uppercase eye)

7 Functions, variables, and constants Use meaningful variable names Function names: lower_case_with_underscores Examples: catalan(), generate_data() Names to AVOID l (lowercase el), O (uppercase oh), or I (uppercase eye) Variables: b, B, lower, mixedcase Examples: N, i, j, maxangularmomentum

8 Functions, variables, and constants Use meaningful variable names Function names: lower_case_with_underscores Examples: catalan(), generate_data() Names to AVOID l (lowercase el), O (uppercase oh), or I (uppercase eye) Variables: b, B, lower, mixedcase Examples: N, i, j, maxangularmomentum Constants: CAPITAL_WITH_UNDERSCORES Examples: RADIUS_EARTH, exceptions for common use single constants i.e., g 9.81, c 3e8

9 Coding conventions Use the right type of variables int for integer quantities: indices, quantum numbers,.. float and complex for quantities that are real or complex bool for truly boolean types

10 Coding conventions Use the right type of variables int for integer quantities: indices, quantum numbers,.. float and complex for quantities that are real or complex bool for truly boolean types Import functions at the beginning of the program easy to find, check, and add to them ensures that functions are imported before use

11 Coding conventions Use the right type of variables int for integer quantities: indices, quantum numbers,.. float and complex for quantities that are real or complex bool for truly boolean types Import functions at the beginning of the program easy to find, check, and add to them ensures that functions are imported before use Give your constants names constants in your program should be given names and defined at the beginning for your program G e-11, Z 28, BOHR_RADIUS e-11

12 Coding conventions Use the right type of variables int for integer quantities: indices, quantum numbers,.. float and complex for quantities that are real or complex bool for truly boolean types Import functions at the beginning of the program easy to find, check, and add to them ensures that functions are imported before use Give your constants names constants in your program should be given names and defined at the beginning for your program G e-11 # Newtonian constant of gravitation [ m**2 /(kg * s**2) ] Z 28 # Atomic Number for Nickel BOHR_RADIUS e-11 # units [m]

13 Divide and Conquer Employ user-defined function, use for repeated and complicated operations greatly increases the legibility of your programs avoid overuse a single line or two of code is often better left in the main part of the program

14 Good Programming Practices Print out partial results & update throughout your program define a function and test it

15 Good Programming Practices Print out partial results & update throughout your program define a function and test it Lay out your programs clearly most of the work should NOT be in the main part of the program i.e. Divide and Conquer!

16 Good Programming Practices Print out partial results & update throughout your program define a function and test it Lay out your programs clearly most of the work should NOT be in the main part of the program i.e. Divide and Conquer! Don't make your programs unnecessarily complicated

17 Visualizing Data via Plotting

18 Plotting with Matplotlib Matplotlib Matplotlib is is the the standard standard package package for for plotting plotting in in Python Python import import matplotlib.pyplot as as plt plt import import numpy numpy as as np np def def sigma(t): return return t*np.exp(-t) x np.linspace(0, 10, 10, 101) 101) y np.zeros(len(x)) for for i in in range(len(x)): y[i] y[i] sigma(x[i]) plt.plot(x, y) y) plt.savefig( sigma.png ) plt.show() pyplot is a module in matplotlib package Create an array of linearly spaced values

19 Plotting with Matplotlib Matplotlib Matplotlib is is the the standard standard package package for for plotting plotting in in Python Python import import matplotlib.pyplot as as plt plt import import numpy numpy as as np np def def sigma(t): return return t*np.exp(-t) x np.linspace(0, 10, 10, 101) 101) y np.zeros(len(x)) for for i in in range(len(x)): y[i] y[i] sigma(x[i]) plt.plot(x, y) y) plt.savefig( sigma.png ) plt.show() create an array of linearly spaced values hpc-login % display sigma.png

20 Decorating the Plot See See for for more more examples examples import import matplotlib.pyplot matplotlib.pyplot as as plt plt plt.rc('text', plt.rc('text', usetextrue) usetextrue) plt.plot(x,y) plt.plot(x,y) plt.legend([r"$d\sigma/dt plt.legend([r"$d\sigma/dt t^2 t^2 e^{-t}$"]) e^{-t}$"]) plt.title("scattering plt.title("scattering Probability") Probability") plt.xlabel("t") plt.xlabel("t") plt.ylabel(r"$d\sigma/dt$") plt.ylabel(r"$d\sigma/dt$") plt.savefig("sigma-t.png") plt.savefig("sigma-t.png") plt.show() plt.show() Equation rendering with LaTex set up with: matplotlib.pyplot.rc('text', usetextrue) then use: r"<latex-equation>" Use this when you want to render Latex equations

21 b 0 for for i in in range(len(x)): range(len(x)): y[i] y[i] sigma_b(x[i], sigma_b(x[i], b) b) plt.plot(x,y) plt.plot(x,y) plt.hold(true) plt.hold(true) b 1 for for i in in range(len(x)): range(len(x)): y[i] y[i] sigma_b(x[i], sigma_b(x[i], b) b) plt.plot(x,y) plt.plot(x,y) Multiple Curves See See for for more more examples examples Using hold(false) makes plot() create a new figure

22 Multiple SubPlots rows plt.figure(1) plt.figure(1) plt.subplot(211) plt.subplot(211) x x np.linspace(0,10,101) np.linspace(0,10,101) b b 0 0 y y sigma_b(x, sigma_b(x, b) b) plt.plot(x,y) plt.plot(x,y) plt.legend([r"$d\sigma/dt plt.legend([r"$d\sigma/dt (t)^2 (t)^2 e^{-t}$"]) e^{-t}$"]) sets up b b 1 1 second plot y y sigma_b(x, sigma_b(x, b) b) plt.subplot(212) plt.subplot(212) plt.plot(x,y) plt.plot(x,y) plt.xlabel("t") plt.xlabel("t") plt.legend([r"$d\sigma/dt plt.legend([r"$d\sigma/dt (t-1)^2 (t-1)^2 e^{-t}$"]) e^{-t}$"]) plt.show() plt.show() columns plot #

23 Multiple SubPlots rows plt.figure(1) plt.figure(1) plt.subplot(211) plt.subplot(211) x x np.linspace(0,10,101) np.linspace(0,10,101) b b 0 0 y y sigma_b(x, sigma_b(x, b) b) plt.plot(x,y) plt.plot(x,y) plt.legend([r"$d\sigma/dt plt.legend([r"$d\sigma/dt (t)^2 (t)^2 e^{-t}$"]) e^{-t}$"]) sets up b b 1 1 second plot y y sigma_b(x, sigma_b(x, b) b) with 2x2 plt.subplot(223) spacing plt.subplot(223) plt.plot(x,y) plt.plot(x,y) plt.xlabel("t") plt.xlabel("t") plt.legend([r"$d\sigma/dt plt.legend([r"$d\sigma/dt (t-1)^2 (t-1)^2 e^{-t}$"]) e^{-t}$"]) plt.show() plt.show() columns plot #

24 See Plotting Examples plot1.py plot2.py plot3.py plot4.py

25 matplotlib, pylab, and pyplot matplotlib is the whole package pylab is a module in matplotlib that gets installed alongside matplotlib matplotlib.pyplot is a module in matplotlib pylab combines the pyplot functionality (for plotting) with the numpy functionality in a single namespace, making that namespace more MATLAB-like The pyplot interface is generally preferred for programs The pylab interface is convenient for interactive calculations and plotting, as it minimizes typing

26 matplotlib, pylab, and pyplot Python preferred programming import matplotlib.pyplot as plt import numpy as np plt.rc( text, usetextrue) x np.linspace(0,3,31) y x*np.exp(-x) plt.plot(x,y) plt.title("scattering") plt.xlabel("t") plt.ylabel(r"$d\sigma/dt$") plt.savefig( sigma.png ) plt.show() Convenient for interactive plotting from pylab import * rc( text, usetextrue) x linspace(0,10,101) y x*exp(-x) plot(x,y) title("scattering") xlabel("t") ylabel(r"$d\sigma/dt$") savefig( sigma.png ) show() Notice the use of vectorization!

27 display sigma.png

28 Scatter Plots import import numpy numpy as as np np import import matplotlib.pyplot matplotlib.pyplot as as plt plt # # Generate Generate data... data... x x np.random.random(25) np.random.random(25) y y np.random.random(25) np.random.random(25) # # Plot... Plot... plt.scatter(x, plt.scatter(x, y, y, c"b", c"b", s10) s10) point size plt.show() plt.show() b: blue g: green r: red c: cyan color m: magenta y: yellow k: black w:white

29 hpc-login 590% wavedrops.py Enter a number of wave sources: 1 Density Plots hpc-login 590% wavedrops.py Enter a number of wave sources: 2 hpc-login 590% wavedrops.py Enter a number of wave sources: 100

30 #! /usr/bin/env python Density Plots from future import division, print_function import numpy as np import matplotlib.pyplot as plt wavelength 5.0 k 2*np.pi/waveLength waveamp 1.0 size points 500 spacing size/points numberofsources int(input("enter a number of wave sources: ")) xsource [] ysource [] wavedrops.py For brevity, all comments are left out See Textbook example ripples.py for details continued next slide

31 Density Plots for i in range(numberofsources): xsource + [(i+1)*size/(numberofsources+1)] ysource + [size/2] waveimage np.zeros([points,points], float) for i in range(points): y spacing*i for j in range(points): x spacing*j for n in range(numberofsources): r np.sqrt( (x-xsource[n])**2 + \ (y-ysource[n])**2 ) waveimage[i,j] + waveamp*np.sin(k*r) plt.imshow(waveimage, origin"lower", extent[0,size,0,size]) plt.gray() plt.savefig("density.png") plt.show()

32 Let's get working

Computational Physics

Computational Physics Intro to Python Prof. Paul Eugenio Department of Physics Florida State University Jan 16, 2018 http://comphy.fsu.edu/~eugenio/comphy/ Announcements Read Chapter 2 Python programming