scipy练习题

最新推荐文章于 2019-05-07 10:47:46 发布

云破林梢添远岫

最新推荐文章于 2019-05-07 10:47:46 发布

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本文链接：https://blog.youkuaiyun.com/qq_38213586/article/details/80758773

这篇博客包含两个练习，分别是利用Scipy求解最小二乘法问题和寻找函数最大值。在练习10.1中，通过生成矩阵A和向量b，找到了使Ax-b²残差最小的x值，并打印了残差范数。在练习10.2中，利用Scipy的优化功能找到给定函数的最大值。

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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))