Python 实战 Matplotlib 作业

题目

Exercise 11.1: Plotting a function
Plot the function
f(x) = sin2(x �� 2)e��x2
over the interval [0; 2]. Add proper axis labels, a title, etc.
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), nd an estimator for b, by solving
^b
= arg min
b
kXb �� yk2
Plot the true parameters b and estimated parameters ^b
. See Figure 1 for an example plot.
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.

解答

# -*- coding: utf-8 -*-

""" #1 """
import numpy as np  
import matplotlib.pyplot as plt   
from scipy import stats 

X = np.linspace(0, 2, 1000) 
Y = (np.sin(X-2) ** 2) * (np.exp(-X**2))  

plt.plot(X, Y)  
plt.xlabel('x')  
plt.ylabel('f(x)')  
plt.title(' ###1 ')  
plt.show()

""" #2 """
x = np.random.rand(20, 10)  
b = np.random.rand(10, 1)  
z = np.random.randn(20,1)  
y = np.dot(x,b) + z  

b_estimate = np.linalg.lstsq(x, y)[0]  

est  = plt.scatter(np.linspace(0, 10, 10), b_estimate, color = 'b', marker='o')  
true = plt.scatter(np.linspace(0, 10, 10), b, color = 'r', marker='x')  
plt.legend((true,est), ('True coef', 'Estimated coef'), \
           loc='upper center') 
plt.show()

""" #3 """
bins = 25
size = 10000

z = np.random.normal(size=size)

x_grid = np.linspace(np.min(z), np.max(z), 1000)  

plt.hist(z, bins, normed= True, facecolor='b', alpha=0.75)  

plt.plot(x_grid,  stats.gaussian_kde(z).pdf(x_grid))  
plt.grid(True)  
plt.show()  

结果

回顾

总之就是各种找符合要求的函数。python的易调用性挺强的。