Interact Exercise 4

Imports



In [13]:

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



In [14]:

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

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 [43]:

    
n=np.random.standard_normal?



In [ ]:

    
n=np.random.standard_normal



In [ ]:

    
n=np.random.randn



In [ ]:

    
n=np.random.randn



In [83]:

    
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.
    """
    N=np.random.normal(0,sigma**2)
    x=np.linspace(-1.0,1.0,size)
    if sigma==0:
        y=m*x +b
    else:
        y=m*x +b+N
    return y



In [84]:

    
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)









    



---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-84-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]

<ipython-input-83-e30e87801516> in random_line(m, b, sigma, size)
     20         The array of y values for the lines with `size` points.
     21     """
---> 22     N=np.random.normal(0,sigma**2)
     23     x=np.linspace(-1.0,1.0,size)
     24     if sigma==0:

mtrand.pyx in mtrand.RandomState.normal (numpy/random/mtrand/mtrand.c:12477)()

ValueError: scale <= 0

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 [85]:

    
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 [109]:

    
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)
    plt.plot(x,random_line(m,b,sigma,size),color)
    plt.ylim(-10.0,10.0)
    plt.vlines(0,-10,10)
    plt.hlines(0,-1,1)
    plt.box(False)



In [110]:

    
plot_random_line(5.0, -1.0, 2.0, 50)



In [ ]:

    
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 [111]:

    
interact(plot_random_line,m=(-10.0,10.0),b=(-5.0,5.0),sigma=(0,5.0,.01),size=(10,100,10),color=('r','g','b'))



In [ ]:

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