高级编程技术 numpy课后作业

最新推荐文章于 2020-12-01 23:49:29 发布

Mike_Panda

最新推荐文章于 2020-12-01 23:49:29 发布

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本文通过Python的Numpy库进行多种矩阵操作演示，包括生成随机矩阵与Toeplitz矩阵，执行矩阵加法、乘法等运算，求解线性系统，计算矩阵范数，进行幂迭代求特征值，并实现最近邻搜索算法。

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Exercise 9：Numpy

Generate matrices A, with random Gaussian entries, B, a Toeplitz matrix，where A∈Rn×m and B∈Rm×m, for n = 200, m = 500.

import numpy as np  
from scipy.linalg import toeplitz  
import random  
  
n = 200  
m = 500  
  
A = np.random.normal(size = (n, m))  
  
row = np.random.random(m)  
col = np.random.random(m)  
  
B = toeplitz(row, col)

9-1：Matrix operations

print(A+A)  
print(np.dot(A, A.T))  
print(np.dot(A.T, A))  
print(np.dot(A, B))  
  
def func1(c):  
    return np.dot(A, B-c*np.ones((m, m)))

9-2：Solving a linear system

b = np.random.random(m)  
B_inverse = np.mat(B).I  
print(np.dot(b, B_inverse))

9-3：Norms

print(np.linalg.norm(A))  
print(np.linalg.norm(B, np.inf))  
print(np.linalg.norm(B, -2))   # smallest  
print(np.linalg.norm(B, 2))    # biggest

9-4：Power iteration

import numpy as np  

Z = np.random.normal(size = (200,200))  
print(Z)  
  
def eigenvalue(A, v):  
    Av = A.dot(v)  
    return v.dot(Av)  
  
def power_iteration(A):  
    n, d = A.shape  
    v = np.ones(d)/np.sqrt(d)  
    ev = eigenvalue(A, v)  
    iter_count = 0  
      
    while True:  
        Av = A.dot(v)  
        v_new = Av/np.linalg.norm(Av)  
      
        ev_new = eigenvalue(A, v_new)  
        if np.abs(ev-ev_new) < 0.01:  
            break  
  
        v = v_new  
        ev = ev_new  
  
        iter_count += 1  
  
  
    return ev_new, v_new, iter_count  
  
print(power_iteration(Z))

9-5：Singular values

p = random.random()  
C = np.random.binomial(1, p, size = (n, n))  
print(np.linalg.norm(C, 2))

9-6：Nearest neighbor

import numpy as np  
  
last_smallest = -100  
  
def func2(z, A):  
    global last_smallest  
    n, d = A.shape  
    A_ = np.reshape(A, (1,n*d))  
    A_[0].sort()  
     
    smallest = np.argmin(A_)  
    if A_[0][smallest] >= z:  
        if abs(A_[0][smallest]-z) <= abs(last_smallest-z):  
            return A_[0][smallest]  
        else:  
            return last_smallest  
    elif:
        n*d==1:  
        return A_[0][smallest]  
    else:  
        last_smallest = A_[0][smallest]  
        return func2(z, A_[:, 1:])  
 
A = np.array([[3, 4, 5, 8, 7, 9, 1, 16, 6, 10, 13]])  
print(func2(11.5, A))