Python Financial Data Mining Review Questions Chapter 2

Question 1

1. Topic

Generate a 5*5 matrix whose elements are random integers in the interval [1,10].

2. Code

import numpy as np
a = np.random.randint(1,10,25).reshape(5,5)
print(a)

3. Results

[[5 3 7 6 4]
 [3 7 4 3 7]
 [1 7 4 4 3]
 [1 8 5 6 8]
 [8 4 4 2 9]]

Question 2

1. Topic

Generate a 4*4 matrix whose elements conform to a normal distribution.

2. Code

import numpy as np 
b = np.random.randn(16).reshape(4,4)
print(b)

3. Results

[[-0.33990789 -0.53183933  0.12420977 -0.43573047]
 [-1.47714092 -0.22094742 -0.11919983 -0.19049501]
 [-0.54613945  1.30368604 -0.483711   -0.36169592]
 [-1.50361573 -0.06139576 -1.86228913  1.09515015]]

Question 3

1. Topic

Assign all the elements in the second column of the matrix generated in (1) to -1; assign all the elements in the third row to 1000;

2. Code

a[:,1]=-1
a[2,:]=1000   #或者a[2]=1000
print(a)

3. Results

[[   5   -1    7    6    4]
 [   3   -1    4    3    7]
 [1000 1000 1000 1000 1000]
 [   1   -1    5    6    8]
 [   8   -1    4    2    9]]

Question 4

1. Topic

Generate a 4*4 matrix A whose elements are random integers in the interval [-10,10].
Then randomly generate a column vector b consisting of 4 elements, whose elements are random integers in the interval [-5,5].
For the linear equation system Ax=b, find the determinant value corresponding to matrix A, judge whether it has a solution according to whether the determinant value is 0, and if there is a solution, find its solution.

2. Code

import scipy.linalg as sp
A=np.random.randint(-10,10,16).reshape(4,4)
b=np.random.randint(-5,5,4).reshape(-1,1)
print('方程形如Ax=b，其中A=')
print(A)
print('其中b=',b)
print()
dA=np.linalg.det(A)
print("A对应的行列式值为：",dA)
if(abs(dA)>1e-6):
    sv=sp.solve(A,b)
    print("对应的线性方程组解为:",sv)
else:
    print("解不存在。")

3. Results

The equation is of the form Ax=b, where A= 
[[ 3 -1 7 -4] 
 [ 9 0 4 -3] 
 [ 2 -8 6 -4] 
 [ 7 -9 -4 0]] 
where b= [[-5 ] 
 [-1] 
 [ 4] 
 [ 1]] 

The determinant value corresponding to A is: 190.00000000000017 
The corresponding linear equation solution is: [[ 3.6 ] 
 [-3.92631579] 
 [14.88421053] 
 [30.97894737]]