Python For Quantum Mechanics

Cheatsheet: Week 5

Making a Plot

• Making a plot:

  • Plotting a line between points with \(x\)-coordinates array_of_x_coords_1 and \(y\)-coordinates array_of_y_coords_1, and another line between points with \(x\)-coordinates array_of_x_coords_2 and \(y\)-coordinates array_of_y_coords_2, and another…

  • plt.plot(array_of_x_coords_1, array_of_y_coords_1, array_of_x_coords_2, array_of_y_coords_2, ...)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html

• Displaying a plot:

  • plt.show()

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html

Formatting

• Formatting a Line:

  • Making a plot with

    • line coloured my_colour (string),

    • line width as my_linewidth (float),

    • line style my_linestyle (string), and

    • marker as my_marker (string).

  • plt.plot(array_of_x_coords, array_of_y_coords, c=my_colour, lw=my_linewidth, ls=my_linestyle, marker=my_marker)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html

  • Adding errorbars with

    • \(x\) error bar of size x_error,

    • \(y\) error bar of size y_error, and

    • error bar cap of size my_capsize:

  • plt.errorbar(array_of_x_coords, array_of_y_coords, c=my_colour, lw=my_linewidth, ls=my_linestyle, marker=my_marker, xerr=x_error, yerr=y_error)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.errorbar.html

• Formatting Axes:

  • Setting \(x\)-limits left and right and \(y\)-limits bottom and top:

    • plt.xlim((left,right))

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlim.html

    • plt.ylim((bottom,top))

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylim.html

  • Changing ticks to my_xticks and my_yticks with labels my_xlabels and my_ylabels:

    • plt.xticks(ticks=my_xticks, labels=my_xlabels)

    • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html

    • plt.yticks(ticks=my_yticks, labels=my_ylabels)

    • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html

  • Adding grid lines

    • plt.grid()

    • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.grid.html

• Labels:

  • Adding a title

    • plt.title('This is the Title')

  • Labeling axes

    • plt.xlabel('This is the x axis')

    • plt.ylabel('This is the y axis')

  • Introducing legends

    • Give line a name using the label keyword when plotting and set equal to a string

    • plt.legend()

    • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html

  • Annotations and adding lines

    • Adding vertical line at x_coord from bottom_lim and top_lim

      • plt.vlines(x_coord, bottom_lim, top_lim, c=my_colour, lw=my_linewidth, ls=my_linestyle)

      • Documnetation: https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.vlines.html

    • Adding horizontal line at y_coord from left_lim and right_lim

      • plt.hlines(y_coord, left_lim, right_lim, c=my_colour, lw=my_linewidth, ls=my_linestyle)

      • Documnetation: https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.hlines.html

    • Annotating a point (x_pos,y_pos) with text at position (x_text,y_text) with an arrow between with style my_arrowstyle

      • plt.annotate('annotating text here', (x_pos,y_pos), c=my_colour, xytext=(x_text,y_text), arrowprops={'arrowstyle':my_arrowstyle, 'lw':my_linewidth, 'ls':my_linestyle})

      • https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.annotate.html

• Log Plots:

  • Making log-log plots

    • plt.loglog(array_of_x_coords, array_of_y_coords, c=my_colour, lw=my_linewidth, ls=my_linestyle, marker=my_marker)

    • Documnetation: https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.loglog.html

  • Making semi-log plots

    • plt.semilogy(array_of_x_coords, array_of_y_coords, c=my_colour, lw=my_linewidth, ls=my_linestyle, marker=my_marker)

    • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.semilogy.html

    • plt.semilogx(array_of_x_coords, array_of_y_coords, c=my_colour, lw=my_linewidth, ls=my_linestyle, marker=my_marker)

    • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.semilogx.html

Figure Object

• Creating a figure fig with width and height

  • fig = plt.figure(figsize=(width,height))

  • Adding axes ax to figure with proportio of figure, position and size as left, bottom, width, and height

    • ax = fig.add_axes([left, bottom, width, height])

  • Documnetation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html

• Adjusted functions

plt.	ax.
xlim	set_xlim
ylim	set_ylim
xticks	set_xticks
yticks	set_yticks
title	set_title
xlabel	set_xlabel
ylabel	set_ylabel

• Saving an image

  • Save fig as first_image.png

  • fig.savefig('first_image.png')

Multiple Plots

• Making sub-plots using plt.subplot()

  • Quickly create subplots in a rows\(\times\)columns shape and enable the axis number instance_num

  • plt.subplot(rows, columns, instance_num)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html

  • plt.suptitle('This is the Overall Title')

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.suptitle.html

• Plots in Plots

  • Can call fig.add_axes() to add multiple sets of axes.

• Making sub-plots using fig.add_subplot()

  • fig. version of plt.subplot

  • fig.add_subplot(rows, columns, instance_num)

  • To give hgap and vgap of horizontal and verticle space between plots use

  • fig.subplots_adjust(hspace=hgap, wspace=vgap)

  • Documentation: https://matplotlib.org/3.3.4/api/_as_gen/matplotlib.figure.Figure.html

• Making sub-plots using plt.subplots()

  • Can create a figure and set axes that share/don’t share axes according to bool_x and bool_y using

  • fig,ax = plt.subplots(2,2,sharex=bool_x,sharey=bool_y)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html

Other Plots

• Histogram

  • A histogram of my_data, my_bins number of bins (or an array giving the bin edges), and with count number or density deternmined by den_bool is created using

    • ax.hist(my_data, density=den_bool, bins=my_bins, color=my_colour, orientation=my_orientation)

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.hist.html

• Scatter Plot

  • A scatter plot of points with coordinates (my_data_x, my_data_y)

    • ax.scatter(my_data_x, my_data_y, c=my_colour, marker=my_marker)

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.scatter.html

• Bar Chart

  • A bar chart with bar labels my_labels, heights my_data, widths my_width, and colours my_colours.

    • ax.bar(my_labels, my_data, width=my_width, color=my_colours)

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.bar.html

  • A horizontal bar chart with bar labels my_labels, widths my_data, heights my_height, and colours my_colours.

    • ax.barh(my_labels, my_data, height=my_height, color=my_colours)

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.barh.html

• Pie Chart

  • A pie chart of data, labeled as my_labels with colours my_colours, exploded by explode_array with shadow determined by shadow_bool.

    • ax.pie(data, labels=my_labels, colors=my_colours, explode=explode_array, shadow = shadow_bool)

    • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pie.html

3D Plots

• Line the 3D space

  • Adding the projection='3d' as a keyword designation in fig.add_axes() creates an Axes3D object.

  • Plotting points 3D line through points (x_array, y_array, z_array) ax.plot3D(x_array, y_array, z_array)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/mpl_toolkits.mplot3d.axes3d.Axes3D.html

• Heat maps

  • Create an image im of a heatmap of Z_mesh on axis my_ax accoding to the colourmap my_map with

  • im = my_ax.imshow(Z_mesh, cmap=my_map).

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html

  • Add a colourbar shrunk by my_shrink to the figure with

  • fig.colorbar(im, ax=my_ax, shrink=my_shrink).

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html

  • Set a limit of my_vmin to my_vmaxon the colour values using

  • im.set_clim(vmin=my_vmin, vmax=my_vmax).

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html

• Surface plots

  • Three different types of surfaceplots of (X_mesh, Y_mesh, Z_mesh) in 3D:

    • ax.plot_surface(X_mesh, Y_mesh, Z_mesh),

    • ax.plot_wireframe(X_mesh, Y_mesh, Z_mesh), and

    • ax.contour3D(X_mesh, Y_mesh, Z_mesh)

  • Change angle of view to angles my_azim and my_elev

  • ax.view_init(azim=my_azim, elev=my_elev)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/mpl_toolkits.mplot3d.axes3d.Axes3D.html

5.7 Animations

• Changing to an interactive backend

  • %matplotlib notebook makes interactive plots

  • %matplotlib inline is default and makes noninteractive plots

• Making an initialisation function

  • An empty plot is first performend using line, = ax.plot([], [])

  • An function init() function which will change the data plotted to x and y using line.set_data(x,y) and will return line,.

• Making an animation function

  • The animate function animate(i) will be called for each frame of the animation and will take in frame number i. This will update the plotted values using line.set_data() again, once again returning line,.

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.lines.Line2D.html

• Animating a plot

  • Animation requires us to import a function.

    • from matplotlib.animation import FuncAnimation

  • To animate fig with my_frame_num number of frames, a interval of my_inter milliseconds between frames, and a repeat delay of my_delay milliseconds.

  • anim = FuncAnimation(fig, animate, init_func=init, frames=my_frame_num, interval=my_inter, repeat_delay=my_delay, blit=True)

  • Documentation: https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html

• Saving an animation

Tutorial 5

1. Noise in qubits

2. Particle in a Box

3. Normal Distribution

4. Monte Carlo \(\pi\) Estimation

5. Ball Animation

Exercises 5

1. Settlers of Histogram

2. Normal Distribution

3. Particle in a Box

4. Plotting a Sphere

5. Snake Animation