numpy作业

最新推荐文章于 2021-09-02 12:49:15 发布

qq_21577653

最新推荐文章于 2021-09-02 12:49:15 发布

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本文链接：https://blog.youkuaiyun.com/qq_21577653/article/details/80406160

本文通过一系列的Python代码示例展示了不同类型的矩阵运算，包括矩阵加法、乘法、求解线性方程组、范数计算及奇异值分解等，并对比了随机矩阵与Toeplitz矩阵的特性。

9.1

import numpy as np
import scipy.linalg as lp

n = 200
m = 500

A = np.random.normal(size=(n,m))
B = lp.toeplitz(list(range(0,m)))

print('A + A')
print(A + A)
print()
print('AAT')
print(np.dot(A,A.T))
print('ATA')
print(np.dot(A.T,A))
print()
print("AB")
print(np.dot(A,B))
print()

def n1(A,B,k):
t = np.eye(m)
print(np.dot(A , B - k * t))

n1(A,B,5)

9.2

import numpy as np
import scipy.linalg as lp

n = 200
m = 500

A = np.random.normal(size=(n,m))
B = lp.toeplitz(list(range(0,m)))

b = np.random.normal(size=m)

print(np.linalg.solve(B,b))

9.3

import numpy as np

import scipy.linalg as lp

n = 200
m = 500

A = np.random.normal(size=(n,m))
B = lp.toeplitz(list(range(0,m)))

print(lp.norm(A, 'fro'))
print(lp.norm(B, np.inf))
temp = lp.svdvals(B)
print('Max:')
print(max(temp))
print('Min:')

print(min(temp))

9.4

import numpy as np
import time
np.random.seed()
n=20
def solve(Z,esp):
u = np.ones(n)
u = u.reshape(n,1)
max_u = np.max(u)
sub = np.inf
iteration = 0
startTime=time.clock()
while sub > esp:
u = np.dot(Z,u)
temp = np.max(u)
sub = np.fabs(temp - max_u)
max_u = temp
u = u / max_u
iteration += 1
endTime = time.clock()
return [max_u,iteration, endTime-startTime]
esp = 1e-6
Z = np.random.normal(0,1,size = (n,n))
print(solve(Z,esp))

9.5

import numpy as np
import scipy.linalg as lp
import math

n = 200
m = 500

p = 0.5
C = np.random.binomial(1, p, (n, n))
U, svd, Vh = lp.svd(C)
print("Max SVD:\n\t", end = '')
print(max(svd))
print("n * p:\n\t", end = '')
print(n * p)

print("They are almost equal.")

9.6

import numpy as np
import scipy.linalg as lp

n = 200
m = 500

A = np.random.normal(size=(n,m))
B = lp.toeplitz(list(range(0,m)))

def n6(A, z):
return A[np.argmin([abs(A[i] - z) for i in range(len(A))])]

print(n6([np.random.normal(0, 10) for i in range(1000)], 1))