Interact Exercise 4

Imports



In [2]:

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



In [3]:

    
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 [4]:

    
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.
    """
    x = np.linspace(-1.0,1.0,size)
    errors = np.random.normal(sigma**2)
    y = np.asarray(m*x + b + errors)
    print(x)
    print(y)



In [5]:

    
#?np.random.normal



In [6]:

    
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)









    



[-1.  0.  1.]
[ 1.86236529  1.86236529  1.86236529]






    



---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-6-dce728037167> in <module>()
      1 m = 0.0; b = 1.0; sigma=0.0; size=3
----> 2 x, y = random_line(m, b, sigma, size)
      3 assert len(x)==len(y)==size
      4 assert list(x)==[-1.0,0.0,1.0]
      5 assert list(y)==[1.0,1.0,1.0]

TypeError: 'NoneType' object is not iterable

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 [7]:

    
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 [8]:

    
def plot_random_line(m, b, sigma, size=10, color='red'):
    """Plot a random line with slope m, intercept b and size points."""
    x = np.linspace(-1.0,1.0,size)
    errors = np.random.normal(loc = 0, scale = sigma**2)
    y = m*x + b + errors
    
    plt.scatter(x, y,size, c = color)
    plt.title('Awesome Random Line')
    plt.xlabel('The x-axis')
    plt.ylabel('The y-axis')
    plt.grid(True)
    plt.xlim(-1.1,1.1)
    plt.ylim(-10.0,10.0)



In [9]:

    
#?plt.xlim



In [10]:

    
plot_random_line(5.0, -1.0, 2.0, 50)



In [126]:

    
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 [133]:

    
interact(plot_random_line, m=[-10.0,1.0,0.1], b = [-5.0,5.0,0.1], sigma = [0.0,5.0,0.01], size=[10,100,10], color = ['red','green','blue'])



In [ ]:

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