scipy练习题

Exercise 10.1: Least squares Generate matrix A ∈ Rm×n with m > n. Also generate some vector b ∈ Rm. Now find x = argminxkAx−bk2. Print the norm of the residual.

import numpy as np  
import scipy.linalg as li  
  
m = 10  
n = 20 
A = np.random.rand(m, n)  
b = np.random.rand(m, 1)  
A = np.mat(A)  
b = np.mat(b)  
x = li.inv(A.T * A) * A.T * b  
print(x)  

Exercise 10.2: Optimization Find the maximum of the function

import numpy as np  
import scipy.optimize as op  
import math  
  
def func(x):  
    return (-(math.sin(x-2)**2)*math.exp(-(x ** 2)))  
  
a = op.fminbound(func, -10, 10)  
print(-func(a)) 

Exercise 10.3: Pairwise  distances Let X be a matrix with n rows and m columns. How can you compute the pairwise distances between every two rows?
As an example application, consider n cities, and we are given their coordinates in two columns. Now we want a nice table that tells us for each two cities, how far they are apart.

Again, make sure you make use of Scipy's functionality instead of writing your own routine.

import numpy as np  
import scipy.spatial.distance as dis  
import math  
  
X = np.random.rand(m, n)
print(X)  
Y = dis.pdist(X)  
print('Distance is :')
print(dis.squareform(Y))