Math 152: Intro to Mathematical Software

2017-03-03

Kiran Kedlaya; University of California, San Diego

adapted from lectures by William Stein, University of Washington

Lecture 22: Plotting: Matplotlib Pyplot vs Sage vs MATLAB

We follow http://matplotlib.org/users/pyplot_tutorial.html, and shows how to use the MATLAB-stype interface to matplotlib. We will cover topics:

plot: plotting a list of values
array of plots: axes and figures

%auto
import numpy as np
import matplotlib.pyplot as plt

1. Plot

plt.plot([1,2,3,10])
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991f0b1450>]

MPL's plt.plot is VERY different than Sage's plot!

plt.plot(x values, y yalues, options, [repeat])

plt.plot([1,2,3,10], [0,2,4,6],[0,1,2,3],[2,5,5,7], 'ro-')
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991e1704d0>, <matplotlib.lines.Line2D object at 0x7f991e1706d0>]

zip([2,3,4],[1,2,3],[0,0,1])

[(2, 1, 0), (3, 2, 0), (4, 3, 1)]

In Sage, you use the line command instead, and have to put the points together (using zip).

Also, in Sage, use frame=True to draw a frame instead of $x,y$ -axes.

show( line(zip([1,2,3,10], [0,2,4,6],[0,1,2,3]), color='red', marker='o'), frame=True)

3D rendering not yet implemented

# Another example with two curves:

x = np.linspace(-2*np.pi, 2*np.pi, 200)    # remember from wednesday
y1 = np.sin(x)                        # apply function to array is entry wise.
y2 = np.cos(x)

plt.plot(x,y1, x,y2)                  # give x and corresponding y's
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991e625a10>, <matplotlib.lines.Line2D object at 0x7f991e625ad0>]

This is similar to MATLAB! -- see http://www.mathworks.com/help/matlab/ref/plot.html

Guess what this will do?

t = np.arange(0, 5, 0.2)
plt.plot(t, t, 'r--', t, t**2, 'bs', t, t**3, 'g^')
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991ea14fd0>, <matplotlib.lines.Line2D object at 0x7f991ea14990>, <matplotlib.lines.Line2D object at 0x7f991ea39890>]

What will this do?

plt.plot(t, t**3 + t, 'g', linewidth=5)
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991e10d250>]

Exercise: Plot the polynomial $x^4 + 2x - 1$ using both matplotlib and Sage's plot commands, for $-3\leq x \leq 3$ .

2. Figures and Axes

def f(t):
    return np.exp(-t) * np.cos(2*np.pi*t)

def makefigure():
    t1 = np.arange(0, 5, 0.1)
    t2 = np.arange(0, 5, 0.02)

    plt.subplot(231)    # 2=numrows, 2=numcols, 1=fignum (which is from 1 to numrows*numcols)
    plt.plot(t1, f(t1), 'bo', t2, f(t2), 'k')

    plt.subplot(232)    # 2=numrows, 2=numcols, 2=fignum... (yes, MATLAB is horrible.)
    plt.plot(t2, np.cos(2*np.pi*t2), 'r--')

    plt.subplot(234)    # 2=numrows, 2=numcols, 3=fignum
    plt.plot(t2, np.cos(2*np.pi*t2), 'r--')

    plt.subplot(236)    # 2=numrows, 2=numcols, 4=fignum
    plt.plot(t2, np.cos(2*np.pi*t2), 'r--')

    plt.show()

makefigure()

Exercise: Copy the above code and instead make a 2x4 grid of plots (instead of a 2x2 grid). Just put whatever plots you want in.

def f(t):
    return np.exp(-t) * np.cos(2*np.pi*t)

def makefigure():
    t1 = np.arange(0, 5, 0.1)
    t2 = np.arange(0, 5, 0.02)

    # MODIFY THIS CODE:

    plt.subplot(211)    # 2=numrows, 1=numcols, 1=fignum
    plt.plot(t1, f(t1), 'bo', t2, f(t2), 'k')

    plt.subplot(212)    # 2=numrows, 1=numcols, 2=fignum
    plt.plot(t2, np.cos(2*np.pi*t2), 'r--')

    plt.show()

makefigure()

In Sage, there is graphics_array (inspired by Mathematica...) to do the above grid layout.

%var t
g1 = plot(exp(-t)*cos(2*pi*t), 0, 5)
g2 = plot(cos(2*pi*t), 0, 5)
show(graphics_array([[g1,g2,g1], [g2,g1,g1]]), frame=True)

Exercise: modify the above code to make a 2x2 array of plots using Sage plotting.

# EDIT ME!
%var t
g1 = plot(exp(-t)*cos(2*pi*t), 0, 5)
g2 = plot(cos(2*pi*t), 0, 5)
show(graphics_array([[g1], [g2]]), frame=True)

%md
Adding text...

t = np.arange(0, 5, 0.2)
plt.plot(t, t, 'r--', t, t**2, 'bs', t, t**3, 'g^')
plt.text(2, 40, 'this is some text')
plt.xlabel("This is the x axis", fontsize=10, color="blue")
plt.ylabel("And the y axis")
plt.title("This is an example: $x^3+e^x$")
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991e6a5fd0>, <matplotlib.lines.Line2D object at 0x7f991e69f210>, <matplotlib.lines.Line2D object at 0x7f991e69f850>]
<matplotlib.text.Text object at 0x7f991e4c1290>
<matplotlib.text.Text object at 0x7f991e9e1350>
<matplotlib.text.Text object at 0x7f991e3ea510>
<matplotlib.text.Text object at 0x7f991eab7fd0>


t = range(1,500,20)
u = [random() for i in t]
plt.plot(t, u)
plt.xscale('log')
plt.show()

[<matplotlib.lines.Line2D object at 0x7f991e616d10>]