Matplotlib exercises

2018-05-27

Matplotlib Exercises

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.

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,500)
y = (np.sin(x-2)**2)*np.exp(-x**2)
plt.plot(x,y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of the function  sin2(x−2)e−x2 \n')
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
ˆ b = argmin ||Xb−y||2
Plot the true parameters b and estimated parameters ˆ b. See Figure 1 for an example plot.

import numpy as np
import matplotlib.pyplot as plt
from numpy import linalg as LA

x = np.random.rand(20,10)
b = np.random.rand(10,1)
z = np.random.standard_normal((20,1))
y = x.dot(b)-z

b1 = LA.lstsq(x,y,rcond=None)[0]

#绘制
x1 = np.array(list(range(10)))
plt.scatter(x1,b,label='Origin-b',color='b',s=25,marker='o')
plt.scatter(x1,b1,label='Estimated-b^',color='y',s=25,marker='^')

plt.xlabel('x')
plt.ylabel('b')
plt.title('Least Square Question\n')
plt.legend()
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)

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde

z = np.random.normal(0,0.5,1000)
z = sorted(z)
kernel = gaussian_kde(z)

plt.hist(z,bins=25,density=True)
plt.plot(z,kernel.pdf(z))

plt.title('kde plot')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()