Interact Exercise 4

Imports



In [3]:

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



In [4]:

    
from IPython.html.widgets import interact, interactive, fixed
from IPython.display import display









    



:0: FutureWarning: IPython widgets are experimental and may change in the future.

Line with Gaussian noise

Write a function named random_line that creates x and y data for a line with y direction random noise that has a normal distribution $N(0,\sigma^2)$:

$$ y = m x + b + N(0,\sigma^2) $$

Be careful about the sigma=0.0 case.



In [41]:

    
def random_line(m, b, sigma, size=10):
    """Create a line y = m*x + b + N(0,sigma**2) between x=[-1.0,1.0]
    
    Parameters
    ----------
    m : float
        The slope of the line.
    b : float
        The y-intercept of the line.
    sigma : float
        The standard deviation of the y direction normal distribution noise.
    size : int
        The number of points to create for the line.
    
    Returns
    -------
    x : array of floats
        The array of x values for the line with `size` points.
    y : array of floats
        The array of y values for the lines with `size` points.
    """
    # YOUR CODE HERE
    
    #http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.randn.html#numpy.random.randn
    x = np.linspace(-1.0, 1.0, num=size)
    y = (m * x) + b + (sigma * np.random.randn(size))
    return x, y



In [42]:

    
print(random_line(2, 3, 2, 20))









    



(array([-1.        , -0.89473684, -0.78947368, -0.68421053, -0.57894737,
       -0.47368421, -0.36842105, -0.26315789, -0.15789474, -0.05263158,
        0.05263158,  0.15789474,  0.26315789,  0.36842105,  0.47368421,
        0.57894737,  0.68421053,  0.78947368,  0.89473684,  1.        ]), array([ 2.73002584,  0.99870474,  1.79778587,  5.12282987,  2.92003379,
        2.31966011,  9.01716784,  1.34611584,  4.81963413,  3.04496532,
       -1.12553022,  0.97791011,  1.33357251,  3.44947373,  3.6699668 ,
        2.49400079,  6.99536361,  2.84516679,  4.31651931,  6.75180823]))



In [43]:

    
m = 0.0; b = 1.0; sigma=0.0; size=3
x, y = random_line(m, b, sigma, size)
assert len(x)==len(y)==size
assert list(x)==[-1.0,0.0,1.0]
assert list(y)==[1.0,1.0,1.0]
sigma = 1.0
m = 0.0; b = 0.0
size = 500
x, y = random_line(m, b, sigma, size)
assert np.allclose(np.mean(y-m*x-b), 0.0, rtol=0.1, atol=0.1)
assert np.allclose(np.std(y-m*x-b), sigma, rtol=0.1, atol=0.1)

Write a function named plot_random_line that takes the same arguments as random_line and creates a random line using random_line and then plots the x and y points using Matplotlib's scatter function:

Make the marker color settable through a color keyword argument with a default of red.
Display the range $x=[-1.1,1.1]$ and $y=[-10.0,10.0]$.
Customize your plot to make it effective and beautiful.



In [63]:

    
def ticks_out(ax):
    """Move the ticks to the outside of the box."""
    ax.get_xaxis().set_tick_params(direction='out', width=1, which='both')
    ax.get_yaxis().set_tick_params(direction='out', width=1, which='both')



In [77]:

    
def plot_random_line(m, b, sigma, size=10, color='red'):
    """Plot a random line with slope m, intercept b and size points."""
    x, y =  random_line(m, b, sigma, size)
    ax = plt.subplot(111)
    
    plt.scatter(x, y , color=color)
    ticks_out(ax)
    plt.xlim((-1.1, 1.1))
    plt.ylim((-10.0, 10.0))



In [78]:

    
plot_random_line(5.0, -1.0, 2.0, 50)



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assert True # use this cell to grade the plot_random_line function

Use interact to explore the plot_random_line function using:

m: a float valued slider from -10.0 to 10.0 with steps of 0.1.
b: a float valued slider from -5.0 to 5.0 with steps of 0.1.
sigma: a float valued slider from 0.0 to 5.0 with steps of 0.01.
size: an int valued slider from 10 to 100 with steps of 10.
color: a dropdown with options for red, green and blue.



In [79]:

    
# YOUR CODE HERE
interact(plot_random_line, m=(-10.0, 10.0, 0.1), b=(-5.0, 5.0, 0.1), sigma = (0.0, 5.0, 0.01), size = (10, 100, 10), color = ["green", "red", "blue"])



In [ ]:

    
#### assert True # use this cell to grade the plot_random_line interact