Math 480: Open Source Mathematical Software

2016-05-20

William Stein

Lectures 24: Matplotlib Pyplot vs Sage vs MATLAB

Notes:

Homework and peer grading due at 6pm tonight.
I wrote a lot more about numpy on Wednesday; read it yourself.
(Start screencast!) Today -- matplotlib for a while
Then work on homework

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 0x7f1713324fd0>]

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], 'ro-')
plt.show()

[<matplotlib.lines.Line2D object at 0x7f17133627d0>]

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]), color='red', marker='o'), frame=True)

# Another example with two curves:

x = np.linspace(-2*np.pi, 2*np.pi)    # 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 0x7f17131778d0>, <matplotlib.lines.Line2D object at 0x7f1713122d90>]

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()

What will this do?

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

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


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%md
### 2. Figures and Axes

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(221)    # 2=numrows, 1=numcols, 1=fignum (which is from 1 to numrows*numcols)
    plt.plot(t1, f(t1), 'bo', t2, f(t2), 'k')

    plt.subplot(222)    # 2=numrows, 1=numcols, 2=fignum... (yes, MATLAB is horrible.)
    plt.plot(t2, np.cos(2*np.pi*t2), 'r--')

    plt.subplot(223)    # 2=numrows, 1=numcols, 2=fignum... (yes, MATLAB is horrible.)
    plt.plot(t2, np.cos(2*np.pi*t2), 'r--')

    plt.subplot(224)    # 2=numrows, 1=numcols, 2=fignum... (yes, MATLAB is horrible.)
    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 2x1 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 (which is from 1 to numrows*numcols)
    plt.plot(t1, f(t1), 'bo', t2, f(t2), 'k')

    plt.subplot(212)    # 2=numrows, 1=numcols, 2=fignum... (yes, MATLAB is horrible.)
    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)
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