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%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
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from IPython.html.widgets import interact, interactive, fixed
from IPython.display import display
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 $N(0,\sigma^2)$:
Be careful about the sigma=0.0 case.
In [25]:
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)
y = np.zeros(size)
if sigma==0.0:
for i in range(size):
y[i] = m*x[i]+b
return x,y
for i in range(size):
y[i] = m*x[i]+b+np.random.normal(0,sigma)
return x,y
In [26]:
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:
color keyword argument with a default of red.
In [43]:
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', top=False)
ax.get_yaxis().set_tick_params(direction='out', width=1, which='both', right=False)
In [49]:
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)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ticks_out(ax)
plt.scatter(x,y,color=color)
plt.xlim(-1.1,1.1)
plt.ylim(-10.0,10.0)
plt.xlabel("Random Xs")
plt.ylabel("Random Ys")
plt.title("Some Random Points")
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plot_random_line(5.0, -1.0, 2.0, 50)
In [51]:
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 [52]:
interact(plot_random_line, m=(-10.0, 10.0, 0.1), b=(-5.0, 5.0, 0.1), sigma=(0.0, 5.0, .01), size=(10, 10000, 10), color=['red', 'blue', 'green'])
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In [ ]:
#### assert True # use this cell to grade the plot_random_line interact