[Course] Advanced Computer Programming, Homework, week 12, Matplotlib

在jupyter notebook中书写，%matplotlib inline 可使图片直接显示

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

1.11 Plotting a function

Plot the function f(x)=sin2(x−2)e−x2$f(x)=si{n}^2(x-2)e^{-x^2}$ over the interval [0,2]$[0,2]$. Add proper axis labels, a title, etc.

x = np.linspace(0,2,1000)

def f(x):
    return (np.sin(x-2)**2)*np.exp(-x**2)

y = f(x)

plt.plot(x,y)
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title('$f(x)=sin^2(x−2)e^{−x^2}$')

Text(0.5,1,'$f(x)=sin^2(x−2)e^{−x^2}$')

11.2 Data

使用最小二乘法，画出系数矩阵的对比图像

X = np.random.rand(20,10)  
b = np.random.rand(10)  
z = np.random.normal(size=20)  
y = X.dot(b)+z
b0 = np.linalg.inv((X.T).dot(X)).dot((X.T).dot(y)) 
# print(b0)
x = np.linspace(0,9,10)  
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(x,b,c = 'r',marker = 'o')  
ax.scatter(x,b0,c = 'g',marker = 'x')  
ax.set_title('11.2')  
plt.xlabel('x')  
plt.ylabel('y')  
plt.legend('TE')  

<matplotlib.legend.Legend at 0x2232e112550>

11.3 Histogram and density estimation

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.
画出z的直方图，使用核密度估计法估计密度并且作图

from scipy.stats import gaussian_kde  

x = np.random.normal(size=1000)  
y = np.random.normal(size=1000)  
xx = np.vstack([x,y])  
z = gaussian_kde(xx)(xx)  
f,(ax1,ax2) = plt.subplots(1,2,figsize=(6,3))  
ax1.hist(x, bins=25, normed=True, color='b')  
sc = ax2.scatter(x,y,c=z)
plt.colorbar(sc)

<matplotlib.colorbar.Colorbar at 0x2233238c898>