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Interact Exercise 4

Imports





In [1]:



    


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



    











In [2]:



    


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 [3]:



    


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)
    def N(mu, sigma):
        if sigma == 0:
            N = 0
        else:
            N = np.exp(-1*((x-mu)**2)/(2*(sigma**2)))/(sigma*((2*np.pi)**0.5))
        return N
    y = m*x + b + N(0,sigma)
    return x, y



    











In [4]:



    


random_line(0.0,0.0,1.0,500)



    


















    
Out[4]:








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 array([ 0.24197072,  0.24294054,  0.24391033,  0.24488005,  0.24584968,
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         0.27947492,  0.27852923,  0.27758228,  0.27663411,  0.27568475,
         0.27473423,  0.27378259,  0.27282986,  0.27187609,  0.27092129,
         0.26996551,  0.26900878,  0.26805114,  0.26709261,  0.26613324,
         0.26517305,  0.26421209,  0.26325037,  0.26228795,  0.26132484,
         0.26036109,  0.25939672,  0.25843178,  0.25746629,  0.25650028,
         0.2555338 ,  0.25456686,  0.25359952,  0.25263179,  0.25166371,
         0.25069531,  0.24972663,  0.24875769,  0.24778853,  0.24681918,
         0.24584968,  0.24488005,  0.24391033,  0.24294054,  0.24197072]))

















In [5]:



    


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)



    


















    






---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-5-dce728037167> in <module>()
      8 size = 500
      9 x, y = random_line(m, b, sigma, size)
---> 10 assert np.allclose(np.mean(y-m*x-b), 0.0, rtol=0.1, atol=0.1)
     11 assert np.allclose(np.std(y-m*x-b), sigma, rtol=0.1, atol=0.1)

AssertionError:

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 [6]:



    


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 [7]:



    


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)
    plt.scatter(x,y,color=color)
    plt.xlim(min(x),max(x))
    plt.ylim(min(y),max(y))
    plt.tick_params(direction='out', width=1, which='both')



    











In [8]:



    


plot_random_line(5.0, -1.0, 2.0, 50)



    


















    
























In [9]:



    


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 [10]:



    


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=['red','green','blue'])



    


















    
























In [11]:



    


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

Content source: rsterbentz/phys202-2015-work

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