CODE SAMPLES

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These are code fragments for A Student's Guide to Python for Physical Modeling by Jesse M. Kinder and Philip Nelson.

Use of these code fragments is subject to the terms of LICENSE.txt.

This file provides a brief description of each fragment. More details can be found in the comments of the individual scripts and modules.

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CONTENTS

The order of appearance in the text is as follows.

• Chapter 2

  • string_format.py
  • string_percent.py
  • for_loop.py
  • while_loop.py

• Chapter 3

  • vectorize.py
  • projectile.py
  • branching.py
  • nesting.py

• Chapter 4

  • import_text.py
  • save_load.py
  • print_write.py
  • simple_plot.py
  • graph_modifications.py
  • line3d.py
  • subplot.py
  • subplots.py

• Chapter 6

  • measurements.py
  • rotate.py
  • average.py
  • histogram.py
  • contour.py
  • matrix_inversion.py
  • quadrature.py
  • simple_oscillator.py
  • solve_ode.py
  • parametric_oscillator.py
  • ivp_comparison.py
  • vortex.py
  • gradient.py
  • streamlines.py

• Chapter 8

  • data_images.py
  • walker.py
  • html_movie.py
  • waves.py

• Chapter 9

  • convolution.py

• Chapter 10

  • sympy_examples.py
  • first_passage.py
  • data_dictionary.py
  • nd_random_walks.py

• Epilogue

  • surprise.py

• Appendix F

  • scope.py
  • name_collision.py

• Your Turn

  • fancy_plot.py
  • legend.py
  • measurements.py
  • random_walk.py
  • surface.py
  • regression.py

• Additional

  • bar3d.py
  • perrin.py
  • shading.py

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DESCRIPTIONS

string_format.py

Illustrate string formatting using the .format() method.

string_percent.py

Illustrate string formatting using the % method.

for_loop.py

Use a for loop to generate solutions to the quadratic equation.

This script illustrates the funamental form of a for loop. For alternate solutions to the same problem, see while_loop.py and vectorize.py.

while_loop.py

Use a while loop to generate solutions to the quadratic equation.

For alternate solutions to the same problem, see for_loop.py and vectorize.py.

vectorize.py

Use vectorized code to generate solutions to the quadratic equation.

For alternate solutions to the same problem, see for_loop.py and while_loop.py.

projectile.py

Calculate how long an object is in the air when thrown from a spcified height with a range of initial speeds assuming constant acceleration due to gravity:

0.5 * g * t**2 - v0 * t - y0 = 0

This script illustrates good coding practice in the solution of a simple problem: parameters with descriptive names, comments, whitespace, and blocking with '#%%' for debugging in Spyder.

branching.py

This script illustrates branching with the use of multiple conditional statements: if : ... elif : ... else: ...

nesting.py

Use nested for loops to fill a two-dimensional array of values.

This script illustrates "nesting" --- one for loop inside of another.

import_text.py

Load data from a text file by reading the file line by line.

This script reads in data from a text file and stores it in a NumPy array. It can be adapted to load data from files that are difficult or impossible to load with NumPy's np.loadtxt function.

save_load.py

Save array data using NumPy's available methods, then load saved data.

This script demonstrates the various methods of saving and loading data using NumPy arrays.

print_write.py

Write same data to a file and print to display.

This script illustrates the similarites between writing to a text file and printing to the screen.

simple_plot.py

Create and display a basic plot.

graph_modifications.py

This script creates a simple plot with two lines, then modifies several features of the plot, including axis labels, data labels, legend, line style, tick labels, and title.

line3d.py

Create a three-dimensional parametric plot.

This script demonstrates how to create three-dimensional plots using the Axes3D method from the mpl_toolkits.mplot3d module. See also surface.py.

subplot.py

Create four plots in the same figure using plt.subplot().

This script demonstrates PyPlot's subplot method, which can be used to display several plots side-by-side in the same figure. For another approach, see subplots.py. The names are similar, but the behavior of the plt.subplot and plt.subplots is different.

subplots.py

Create four plots in the same figure using plt.subplots().

This script demonstrates PyPlot's subplots method, which can be used to display several plots side-by-side in the same figure. For another approach, see subplots.py. The names are similar, but the behavior of the plt.subplot and plt.subplots is different.

measurements.py

Functions to calculate distance between points using different metrics.

This script illustrates the fundamental form of user-defined functions as well as keyword arguments and default values.

rotate.py

Define function to rotate a vector in two dimensions.

average.py

Compute and return the cummulative average of an array.

This script illustrates some principles of functional programming.

histogram.py

Create histograms of random numbers.

This script illustrates how to use NumPy and PyPlot to create histograms and bar plots.

contour.py

Create a labeled contour plot.

This script illustrates how to generate a grid of coordinates for contour and surface plots. It also demonstrates some options of plt.contour and shows how to label contour lines.

matrix_inversion.py

Invert a simple matrix to solve a system of linear equations.

This script illustrates the use of a special method from the SciPy linear algebra library, scipy.linalg.

quadrature.py

Integrate two functions using quad.

This script demonstrates numerical integration using the quad method of scipy.integrate. The first function is a built-in NumPy funciton whose integral can be computed with pencil and paper for comparison. The second is a user-defined function.

simple_oscillator.py

Define function to use in solution of differential equation for a simple harmonic oscillator.

This script illustrates how to write a function that generates the array required to integrate a second-order ordinary differential equation. It is imported and used in solve_ode.py.

solve_ode.py

Solution of ODE for harmonic oscillator.

This script imports the function F(y,t) in simple_oscillator.py then uses the odeint method of scipy.integrate to solve the ordinary differential equation defined by F(y,t).

See ivp_comparison.py for an example of the solve_ivp method, an alternative to odeint.

parametric_oscillator.py

Define a parametric function that accepts 4 parameters then integrate it using odeint.

This script illustrates two methods for using scipy.integrate's odeint methods to integrate a function that accepts more than two parameters.

ivp_comparison.py

Compare different ODE solvers using solve_ivp.

solve_ivp offers an alternative to odeint for solving ordinary differential equations. See solve_ode.py for an example of odeint.

vortex.py

Create a quiver plot.

This script illustrates the use of PyPlot's quiver method.

gradient.py

Calculate and display the gradient of a two-dimensional Gaussian.

This script illustrates the use of NumPy's gradient function and demonstrates how to display a vector field. It displays the gradient as a quiver plot superimposed on a filled contour plot of the Gaussian.

streamlines.py

Create streamlines from a vector field.

This script demonstrates the use of PyPlot's streamplot method for visualizing solutions to a differential equation defined by a vector field.

data_images.py

Illustrate differences between image and Cartesian coordinates.

The coordinates used in plotting functions and displaying images follow different conventions. This script creates a figure that illustrates the two conventions.

walker.py

Make a movie out of the steps of a two-dimensional random walk.

This script demonstrates the use of the FuncAnimation method of Matplotlib's animation module to create a movie. If ffmpeg or mencoder is installed on this computer, the script will save the movie to an mp4 file.

html_movie.py

Module to generate an HTML document from a collection of images. When viewed in a Web browser, the document will display a movie whose frames are the individual images.

This module is adapted from the scitools library developed by Hans Petter Langtangen.

waves.py

Create an HTML animation of a moving Gaussian waves.

This script illustrates a method for combining a series of plots into an animation using HTML and Javascript. It uses the html_movie.py module, which is adapted from the scitools library developed by Hans Petter Langtangen.

convolution.py

This script creates an eLoG (elongated Laplacian of Gaussian) filter that emphasizes long, vertical lines in a figure. The effect of the filter is demonstrated on a plus sign.

sympy_examples.py

Demonstrate some useful methods available in the SymPy module.

Python may complain about undefined variables if you attempt to run this script. init_session() defines several variables, but Python may not be aware of this. It is better to run the commands one at a time from the command line.

first_passage.py

Define a function to simulate first passage of a random walker.

Simulate a random walker that starts at the origin and takes steps to the right with probability p and to the left with probability 1-p. Return the number of steps for the first passage of location x==L, or give up after N steps.

data_dictionary.py

Store input and data two different simulations in a dictionary.

This script requires first_passage.py to be in the same directory.

nd_random_walks.py

Python class to simulate various random walks in N dimensions.

RandomWalk -- general random walk class
	LatticeWalk     --  random walk on a D-dimensional lattice
					    default is a cubic lattice in D dimensions
		TriangularWalk  -- 2D triangular lattice
		HoneycombWalk   -- 2D honeycomb lattice
	DirectionalWalk --  random walks of variable step size in D dimensions
				        defaults to constant step length in random directions
		UniformWalk     -- step size drawn from uniform distribution
		GaussianWalk    -- step size drawn from normal distribution
		ExponentialWalk -- step size drawn from exponential distribution
		ParetoWalk      -- step size drawn from power law distribution

surprise.py

This script will create a familar but interesting image. It may take about a minute to run.

scope.py

Demonstrate Python's rules of scope --- i.e., how Python looks up variable names.

name_collision.py

Illustrate how Python's rules of scope prevent name collisions.

fancy_plot.py

Add a title and axis labels to a simple plot.

legend.py

Create a plot with a legend to distinguish multiple curves.

random_walk.py

Monte Carlo simulation of a two-dimensional random walk.

This script illustrates the use of a random number generator to create a time series for a random walk.

surface.py

Create a three-dimensional surface plot.

This script demonstrates how to create three-dimensional plots using the Axes3D method from the mpl_toolkits.mplot3d module. See also line3d.py.

regression.py

Example of linear regression on data from the first passage problem.

first_passage.py must be in the working directory. The script could take a while to finish if (samples x nmax) ~ 10**8 or more.

bar3d.py

Create a 3D histogram ("Lego plot").

This script provides a visual example of the Central Limit Theorem.

perrin.py

Generate figure displaying Perrin's experimental data on Brownian motion. This script requires the data set 04brownian/g26perrindata.npy.

The script illustrates loading and plotting a data set and includes LaTeX formatting of axis labels and grid lines.

shading.py

Demonstrate shading of surface plots using Matplotlib's LightSource.

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