examples.py

import matplotlib.pyplot as plt
import numpy as np

import customplot

# Apply the style parameters globally.
plt.style.use('styles/light.mplstyle')

###############################################################################

def cartesian_2d_minimal():
    '''
Example of a minimal two-dimensional Cartesian plot.
    '''

    fig, ax = plt.subplots()

    x = np.linspace(0, 20, 10000)
    y = np.sqrt(x)
    ax.plot(x, y, label=r'$y=\sqrt{x}$')

    customplot.polish(ax, title='This is a bare minimum example!')

    customplot.show()

###############################################################################

def cartesian_2d():
    '''
Example of a two-dimensional Cartesian plot.
    '''

    # Create Matplotlib figure and axes instances.
    fig, ax = plt.subplots()

    # Set the locations of the grid lines on the x-axis. Grid lines will be
    # drawn at the following x-coordinates.
    # [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    customplot.limit(ax, 'x', first=-2, last=10, step=1)

    # Set the locations of the grid lines on the y-axis. Grid lines will be
    # drawn at the following y-coordinates.
    # [-2, -1, 0, 1, 2, 3, 4]
    customplot.limit(ax, 'y', first=-2, last=4, step=1)

    x = np.linspace(0, 20, 10000)
    y = np.sqrt(x)
    ax.plot(x, y, color='red', label=r'$y=\sqrt{x}$')

    customplot.polish(ax, title='This is the square root function!')

    # Set the ratio of the scales on the x-axis and y-axis (aspect ratio). As
    # far as possible, this should be set to 1 (so that shapes are not
    # distorted).
    customplot.aspect(ax, 1)

    # Use either `plt.show` or `customplot.show`.
    customplot.show()

###############################################################################

def cartesian_2d_discontinuous():
    '''
Example of a two-dimensional Cartesian plot of a discontinuous function.
    '''

    # Create Matplotlib figure and axes instances.
    fig, ax = plt.subplots()

    # Set the locations of the grid lines on the x-axis. Grid lines will be
    # drawn at the following x-coordinates.
    # [-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8]
    customplot.limit(ax, 'x', first=-4, last=4, step=0.5)

    # Set the locations of the grid lines on the y-axis. Grid lines will be
    # drawn at the following y-coordinates.
    # [-4, -3, -2, -1, 0, 1, 2, 3, 4]
    customplot.limit(ax, 'y', first=-1.5, last=2.5, step=0.5)

    x = np.linspace(-4, 4, 10000)
    y = np.heaviside(x, 0.5)

    # Remove the vertical line at the point of discontinuity.
    y = customplot.sanitise(y, maximum_diff=0.1)

    ax.plot(x, y, color='red', label=r'$y=u(x)$')

    # Show the values of the function near the point of discontinuity.
    ax.plot(0, 0, color='red', linestyle='none', marker='o')
    ax.plot(0, 1, color='red', linestyle='none', marker='o')
    ax.plot(0, 0.5, color='red', linestyle='none', marker='o', mfc='red')

    customplot.polish(ax, title='This is the unit step function!')

    # Set the ratio of the scales on the x-axis and y-axis (aspect ratio). As
    # far as possible, this should be set to 1 (so that shapes are not
    # distorted).
    customplot.aspect(ax, 1)

    # Use either `plt.show` or `customplot.show`.
    customplot.show()

###############################################################################

def cartesian_2d_symbolic_1():
    '''
Example of a two-dimensional Cartesian plot with symbolic labels on the x-axis.
Said labels contain the symbol for pi (π).
    '''

    fig, ax = plt.subplots()

    # Set the locations of the grid lines on the x-axis. Note that `symbolic`
    # has been set to True. As a result, grid lines will be drawn at the
    # following x-coordinates.
    # [-2π, -1.75π, -1.5π, -1.25π, -π, -0.75π, -0.5π, -0.25π, 0, 0.25π, 0.5π, 0.75π, π, 1.25π, 1.5π, 1.75π, 2π]
    customplot.limit(ax, 'x', symbolic=True, first=-2, last=2, step=0.25)

    # Set the locations of the grid lines on the y-axis. Grid lines will be
    # drawn at the following y-coordinates.
    # [-3, -2, -1, 0, 1, 2, 3]
    customplot.limit(ax, 'y', first=-3, last=3, step=1)

    x = np.linspace(-2 * np.pi, 2 * np.pi, 10000)
    y = np.cos(x)
    ax.plot(x, y, color='green', label=r'$y=\cos x$')

    customplot.polish(ax, title='This is a trigonometric function!')
    customplot.aspect(ax, 1)

    customplot.show()

###############################################################################

def cartesian_2d_symbolic_2():
    '''
Example of a two-dimensional Cartesian plot with symbolic labels on the x-axis
and y-axis. Said labels contain the symbols for pi (π), the Euler–Mascheroni
constant (γ) and the reciprocal Fibonacci constant (ψ).
    '''

    fig, ax = plt.subplots()

    # Set the locations of the grid lines on the x-axis. Note that `symbolic`
    # has been set to True, and a value has been provided for `s` and `v`. As a
    # result, grid lines will be drawn at the following x-coordinates.
    # [-2π/γ, -1.75π/γ, -1.5π/γ, -1.25π/γ, -π/γ, -0.75π/γ, -0.5π/γ, -0.25π/γ, 0, 0.25π/γ, 0.5π/γ, 0.75π/γ, π/γ, 1.25π/γ, 1.5π/γ, 1.75π/γ, 2π/γ]
    customplot.limit(ax, 'x', symbolic=True, s=r'\pi/\gamma', v=np.pi / np.euler_gamma, first=-2, last=2, step=0.25)

    # Set the locations of the grid lines on the y-axis. Note that `symbolic`
    # has been set to True, and a value has been provided for `s` and `v`. As a
    # result, grid lines will be drawn at the following y-coordinates.
    # [-1.33ψ, -ψ, -0.67ψ, -0.33ψ, 0, 0.33ψ, 0.67ψ, ψ, 1.33ψ]
    customplot.limit(ax, 'y', symbolic=True, s=r'\psi', v=3.359886, first=-4 / 3, last=4 / 3, step=1 / 3)

    x = np.linspace(-12, 12, 10000)
    y = 3.359886 * np.cos(np.euler_gamma * x)
    ax.plot(x, y, color='green', label=r'$y=\psi\,\cos\gamma x$')

    customplot.polish(ax, title='This is a scaled trigonometric function!')
    customplot.aspect(ax, 1)

    customplot.show()

###############################################################################

def interactive():
    '''
Example of an interactive plot.
    '''

    fig, ax = plt.subplots()
    customplot.limit(ax, 'x', first=-6, last=6, step=1)
    customplot.limit(ax, 'y', first=-3, last=3, step=1)

    x = np.linspace(-8, 8, 10000)
    y = np.sin(x)
    ax.plot(x, y, label=r'$y=\sin x$')
    # ax.text(0, 0, r'$(0,0)$', size='large')
    # ax.text(np.pi, 0, r'$(\pi,0)$', size='large')

    customplot.polish(ax, title='This is an interactive plot!')
    customplot.aspect(ax, 1)

    # Call `customplot.show` with the figure instance as an argument.
    customplot.show(fig)

    # After doing this, the plot window will open, and a GUI will be emulated
    # in the terminal. This GUI has several parts.

    # The upper part displays information about the figure and the current
    # Matplotlib axes selected. Pressing Page Up and Page Down will switch
    # between axes.

    # The main part contains some entries which can be typed into. These map to
    # the arguments of `customplot.limit`.
    # 'Symbolic': `symbolic` argument of `customplot.limit`. Leaving it blank
    # causes `symbolic=False` to be passed to the function, while typing
    # anything causes `symbolic=True` to be passed.
    # 'Symbol': `s` argument of `customplot.limit`.
    # 'Value': `v` argument of `customplot.limit`.
    # 'Limits': `first`, `last` and `step` arguments of `customplot.limit`.
    # Type in three space-separated numbers, which will be used as the
    # aforementioned arguments.
    # 'Label': the label of an axis of coordinates.
    # After you're done typing, press Enter. The plot will get updated. To
    # quit, press Escape.

###############################################################################

def cartesian_2d_ellipse():
    '''
Example of a two-dimensional Cartesian plot of an ellipse.
    '''

    fig, ax = plt.subplots()
    customplot.limit(ax, 'x', first=-3, last=5, step=1)
    customplot.limit(ax, 'y', first=-9, last=4, step=1)

    t = np.linspace(0, 2 * np.pi, 10000)
    x = 3 * np.cos(t) + 1
    y = 5 * np.sin(t) - 2
    ax.plot(x, y, label=r'$\dfrac{(x-1)^2}{9}+\dfrac{(y+2)^2}{25}=1$')

    customplot.polish(ax, title='This is an ellipse!')
    customplot.aspect(ax, 1)

    customplot.show()

###############################################################################

def polar():
    '''
Example of a polar plot.
    '''

    fig = plt.figure()
    ax = fig.add_subplot(projection='polar')

    # In a polar plot, the y-axis is actually the radial axis. In most cases,
    # this axis should start from zero. Grid lines will be drawn at the
    # following r-coordinates.
    # [0, 1, 2, 3, 4]
    # However, the first and last grid lines will not be labelled (otherwise,
    # the figure gets cluttered).
    customplot.limit(ax, 'y', first=0, last=4, step=1)

    t = np.linspace(0, 2 * np.pi, 10000)
    r = 1 - np.cos(t)
    ax.plot(t, r, label=r'$r=1-\cos t$')

    # The polar coordinate axes should be labelled 't' and 'r', not 'x' and
    # 'y'. These labels are surrounded by dollar signs so that they are
    # rendered the way mathematical expressions would be rendered.
    customplot.polish(ax, labels=('$t$', '$r$'), title='This is a cardioid!')

    # An aspect ratio is meaningless in polar plots. Hence, `customplot.aspect`
    # is not called.

    customplot.show()

###############################################################################

def polar_symbolic():
    '''
Example of a polar plot with symbolic labels on the angular axis. Said labels
contain the symbol for pi (π).
    '''

    fig = plt.figure()
    ax = fig.add_subplot(projection='polar')

    # In a polar plot, the x-axis is actually the angular axis. Note that
    # `symbolic` has been set to True. As a result, grid lines will be drawn at
    # the following t-coordinates.
    # [0, 0.25π, 0.5π, 0.75π, π, 1.25π, 1.5π, 1.75π]
    # No grid line is drawn at 2π because a t-coordinate of 2π is the same as a
    # t-coordinate of 0.
    customplot.limit(ax, 'x', symbolic=True, first=0, last=2, step=0.25)

    # In a polar plot, the y-axis is actually the radial axis. In most cases,
    # this axis should start from zero. Grid lines will be drawn at the
    # following r-coordinates.
    # [0.0, 0.5, 1.0, 1.5, 2.0]
    # However, the first and last grid lines will not be labelled (otherwise,
    # the figure gets cluttered).
    customplot.limit(ax, 'y', first=0, last=2, step=0.5)

    # This is not a trigonometric function, so the range of values the
    # independent variable `t` may take is not restricted. Here, the upper
    # limit on `t` has been chosen in such a way that the visible portion of
    # the graph does not end abruptly.
    t = np.linspace(0, 25, 10000)
    r = np.sqrt(t / np.pi / 2)
    ax.plot(t, r, label=r'$r=\sqrt{\dfrac{t}{2\pi}}$')

    # The polar coordinate axes should be labelled 't' and 'r', not 'x' and
    # 'y'. These labels are surrounded by dollar signs so that they are
    # rendered the way mathematical expressions would be rendered.
    customplot.polish(ax, labels=('$t$', '$r$'), title='This is a spiral!')

    # An aspect ratio is meaningless in polar plots. Hence, `customplot.aspect`
    # is not called.

    customplot.show()

###############################################################################

def subplots():
    '''
Example of subplots.
    '''

    fig = plt.figure()
    axs = [None] * 3
    axs[0] = fig.add_subplot(2, 2, 1)
    axs[1] = fig.add_subplot(2, 2, 3)
    axs[2] = fig.add_subplot(1, 2, 2, projection='polar')

    customplot.limit(axs[0], 'x', first=0, last=8, step=1)
    customplot.limit(axs[0], 'y', first=0, last=4, step=1)
    x = np.linspace(0, 8, 10000)
    y = x / 2
    axs[0].plot(x, y, color='green', label=r'$x-2y=0$')
    customplot.polish(axs[0], title='This is a line!')
    customplot.aspect(axs[0], 1)

    customplot.limit(axs[1], 'x', first=0, last=10, step=1)
    customplot.limit(axs[1], 'y', first=-2, last=2, step=1)
    x = np.linspace(0, 10, 4000)
    y = np.random.normal(scale=0.2, size=4000)
    axs[1].plot(x, y, label=r'$\nu=\psi(\tau)$')
    customplot.polish(axs[1], labels=(r'$\tau$', r'$\nu$'), title='This is Gaussian noise!')
    customplot.aspect(axs[1], 1)

    customplot.limit(axs[2], 'x', first=0, last=2 * np.pi, step=np.pi / 6)
    customplot.limit(axs[2], 'y', first=0, last=5, step=1)
    phi = np.linspace(0, 2 * np.pi, 10000)
    rho = 4 * np.sin(3 * phi)
    axs[2].plot(phi, rho, color='red', label=r'$\rho=4\,\sin 3\varphi$')
    customplot.polish(axs[2], labels=(r'$\varphi$', r'$\rho$'), title='This is a flower!')

    customplot.show()

###############################################################################

def cartesian_3d_curve():
    '''
Example of a three-dimensional Cartesian plot of a curve.
    '''

    fig = plt.figure()
    ax = fig.add_subplot(projection='3d')
    customplot.limit(ax, 'x', first=0, last=12, step=1)
    customplot.limit(ax, 'y', first=-2, last=2, step=1)
    customplot.limit(ax, 'z', first=-2, last=2, step=1)

    x = np.linspace(0, 12, 10000)
    y = (3 / 4) ** x * np.cos(np.pi * x)
    z = (3 / 4) ** x * np.sin(np.pi * x)
    ax.plot(x, y, z, color='gray', label=r'$y+iz=(-0.75)^x$')

    customplot.polish(ax, title='This is a helix!')

    # An aspect ratio is meaningless in three-dimensional plots, because there
    # are three axes of coordinates. Hence, if the second argument of
    # `customplot.aspect` is any non-zero number, the scales on the x-axis,
    # y-axis and z-axis will be made equal.
    customplot.aspect(ax, 1)

    customplot.show()

###############################################################################

def cartesian_3d_curve_symbolic():
    '''
Example of a three-dimensional Cartesian plot of a curve with symbolic labels
on the x-axis. Said labels contain the symbol for pi (π).
    '''

    fig = plt.figure()
    ax = fig.add_subplot(projection='3d')
    customplot.limit(ax, 'x', symbolic=True, first=-4, last=4, step=0.5)
    customplot.limit(ax, 'y', first=-3, last=3, step=1)
    customplot.limit(ax, 'z', first=-3, last=3, step=1)

    x = np.linspace(-4 * np.pi, 4 * np.pi, 10000)
    y = np.cos(x)
    z = np.sin(x)
    ax.plot(x, y, z, label=r'$y+iz=e^{ix}$')

    customplot.polish(ax, title='This is a spring!')

    # An aspect ratio is meaningless in three-dimensional plots, because there
    # are three axes of coordinates. Hence, if the second argument of
    # `customplot.aspect` is any non-zero number, the scales on the x-axis,
    # y-axis and z-axis will be made equal.
    customplot.aspect(ax, 1)

    customplot.show()

###############################################################################

def cartesian_3d_surface_symbolic():
    '''
Example of a three-dimensional Cartesian plot of a surface with symbolic labels
on the x-axis and the y-axis. Said labels contain the symbol for pi (π).
    '''

    fig = plt.figure()
    ax = fig.add_subplot(projection='3d')
    customplot.limit(ax, 'x', symbolic=True, first=-6, last=6, step=1)
    customplot.limit(ax, 'y', symbolic=True, first=-6, last=6, step=1)
    customplot.limit(ax, 'z', first=-4, last=4, step=2)

    x = np.linspace(-6 * np.pi, 6 * np.pi, 1000)
    y = np.linspace(-6 * np.pi, 6 * np.pi, 1000)
    X, Y = np.meshgrid(x, y)
    Z = 1.5 * np.cos(X / 2) * np.sin(Y / 5)
    surf = ax.plot_surface(X, Y, Z, color='skyblue', label=r'$z=1.5\cdot\cos\,0.5x\cdot\sin\,0.2y$')

    # https://github.com/matplotlib/matplotlib/issues/4067
    # The following two lines prevent the program from encountering the error
    # described in the above issue.
    surf._facecolors2d = surf._facecolor3d
    surf._edgecolors2d = surf._edgecolor3d

    customplot.polish(ax, title='This is an interference pattern!')
    customplot.aspect(ax, 1)

    customplot.show()

###############################################################################

if __name__ == '__main__':
    cartesian_2d_minimal()
    cartesian_2d()
    cartesian_2d_discontinuous()
    cartesian_2d_symbolic_1()
    cartesian_2d_symbolic_2()
    interactive()
    cartesian_2d_ellipse()
    polar()
    polar_symbolic()
    subplots()
    cartesian_3d_curve()
    cartesian_3d_curve_symbolic()
    cartesian_3d_surface_symbolic()