Python作业-Matplotlib

Python高级编程技术Matplotib部分

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 matplotlib.pyplot as plt
import numpy as np

def f(x):
    return np.sin(x-2)*np.sin(x-2)*np.exp((-1)*(x*x))
a=np.arange(0.0,2.0,0.001)
plt.plot(a,f(a))
plt.savefig('test',dpi=600)
plt.ylabel("function result")
plt.xlabel("x")
plt.show()

Result:

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 ^b. See Figure 1 for an example plot.

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

X = np.random.randint(1,10,size=(20,10))  
z = np.random.normal(0,1,size=(20,1))
b = np.random.rand(10,1)
y = np.dot(X,b) + z
x = np.linspace(0.0, 1.0, 10) 
bb = np.array(linalg.lstsq(X, y))[0]
plt.scatter(x,b,c='g',marker='o',label='b')
plt.scatter(x,bb,c='r',marker='x',label='b^')

plt.legend()
plt.title('Data plot')
plt.show()

Result:

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

z = np.random.normal(1,100,size=10000)
x = np.linspace(-500,500,1000)
plt.hist(z, 25,density=True)
kernel = stats.gaussian_kde(z)
plt.plot(x,kernel.evaluate(x))
plt.title('Histogram and density estimation')
plt.show()

Result: