[Matplotlib课后练习]

Exercise 11.1: Plotting a function

Plot the functionf(x) = sin2(x−2)e−x2 over the interval [0,2].

Add proper axis labels, a title, etc.

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace (0 , 2, 100)
y = np.power(np.sin(x - 2), 2) * np.exp(-x*x)
plt.plot(x, y)
plt.ylabel('y')
plt.xlabel('x')
plt.title('exercise 1')
plt.show()

Exercise 11.2: Data

Create a data matrix X with 20 observations of 10 variables. Generate a vector b with parameters Then generate the response vector y = Xb+z where z is a vector with standard normally distributed variables.

Now (by only using y and X), find an estimator for b, by solving

Plot the true parameters b and estimated parameters ˆ b. See Figure 1 for an example plot.

import matplotlib.pyplot as plt
import numpy as np
import numpy.matlib as npm
import numpy.linalg
def find_B(X, y):
    return numpy.linalg.solve(X.T*X, X.T*y)

X = npm.randn((20, 10))
b = npm.randn((10, 1)) 
z = npm.randn((20, 1)) 
y = X * b + z

x = np.linspace(0, 9, 10)
paramb, = plt.plot(x, b, 'rx', label = 'True coefficients')
B = find_B(X, y)
paramB, = plt.plot(x, B, 'bo', label = 'Estimated coefficients')
plt.ylabel('index')
plt.xlabel('value')
plt.title('Parameter plot')
plt.legend(handles=[paramb, paramB])
plt.show()

Exercise 11.3: Histogram and density estimation

Generate a vector z of 10000 observations from your favorite exotic distribution. Then make a plot that shows a histogram of z (with 25 bins), along with an estimate for the density, using a Gaussian kernel density estimator (see scipy.stats). See Figure 2 for an example plot.

import matplotlib.pyplot as plt
import numpy.matlib as npm
from scipy import stats
import numpy as np
z = np.random.normal(size=10000)
bins = 25
n, bins, p = plt.hist(z, bins, normed=True) 
y = stats.gaussian_kde(z)
plt.plot(bins, y(bins), 'g--') 
plt.title('Histogram')
plt.show()