Exercise 10.1:

#最小二乘法
import numpy as np  
import scipy.linalg as sl  
  
m = int(input("Plz enter m: "))  
n = int(input("Plz enter n: "))  
if n>m:
    temp = m
    m = n
    n = m
A = np.random.rand(m, n)  
b = np.random.rand(m, 1)  
A = np.mat(A)  
b = np.mat(b)  
x = sl.inv(A.T * A) * A.T * b  
print(x)

Exercise 10.2: Optimization

Find the maximum of the function

f(x) = sin2(x−2)e−x2

import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as so  
import math 
''' 根据图像大约获得最大值的区间
x = np.linspace(-10, 10, 50)
y = (np.sin(x-2)**2) * (np.e**(-x**2))
plt.plot(x, y)
plt.show()
''' 
def func(x):  
    return (-(math.sin(x-2)**2)*math.exp(-(x ** 2)))  
  
a = so.fminbound(func, -10, 10)  
print(-func(a))

Exercise 10.3:

Pairwise distances Let X be a matrix with nrows and m columns. How can you compute the pairwise distances between everytwo rows?

As an example application, consider ncities, and we are given their coordinates in two columns. Now we want a nicetable that tells us for each two cities, how far they are apart.

Again, make sure you make use of Scipy’sfunctionality instead of writing your own routine.

import numpy as np  
import scipy.spatial.distance as ssd  
import math  
  
m = int(input("Plz enter m: "))  
n = int(input("Plz enter n: "))  
X = np.random.rand(m, n)  
Y = ssd.pdist(X)  
z = ssd.squareform(Y)  
print(z)