如何在python中從其上下三角形的2個向量創建相關矩陣？

Question

我有兩個向量，每個向量對應一個相關矩陣的一半。 說，

a = [0.1 0.2 0.3 0.4 0.5 0.6]
b = [0.11 0.22 0.33 0.44 0.55 0.66]

我想做的是將它們組裝成這樣的矩陣：

correlation_matrix = [1     0.1  0.2  0.3
                      0.11  1    0.4  0.5   <-- a
             b -->    0.22  0.44 1    0.6
                      0.33  0.55 0.66 1]

是否有一個函數在python中執行它？

Answer 1

這是使用numpy做到這一點的一種方法。

import numpy as np

a = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6])
b = np.array([0.11, 0.22, 0.33, 0.44, 0.55, 0.66])

首先設置您期望的最終相關矩陣的大小，並創建一個單位矩陣：

n = 4
results = np.identity(n)

獲得上三角指數和分配的值a 。 切換行和列索引並指定b值：

rows, cols = np.triu_indices(n, 1)  # The 1 denotes offset from diagonal
results[rows, cols] = a
results[cols, rows] = b

結果：

array([[1.  , 0.1 , 0.2 , 0.3 ],
       [0.11, 1.  , 0.4 , 0.5 ],
       [0.22, 0.44, 1.  , 0.6 ],
       [0.33, 0.55, 0.66, 1.  ]])

Answer 2

您可以使用基本的for循環和if語句：

a = [0.1, 0.2 ,0.3,0.4 ,0.5 ,0.6]
b = [0.11, 0.22, 0.33 ,0.44, 0.55 ,0.66]

count_a = 0
count_b = 0
for i in range(4):
    for j in range(4):
        if j == i :
            print ("{:<5}".format(1), end = " ")
        elif (i>j):
            print ("{:<5}".format(b[count_b]), end = " ")
            count_b += 1
        elif (i<j):
            print ("{:<5}".format(a[count_a]), end = " ")
            count_a += 1
    print()

輸出：

1     0.1   0.2   0.3   
0.11  1     0.4   0.5   
0.22  0.33  1     0.6   
0.44  0.55  0.66  1     

編輯：

a = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]
b = [0.11, 0.22, 0.33, 0.44, 0.55, 0.66]

Matrix = []
count_a = 0
count_b = 0
for i in range(4):
    row = []
    for j in range(4):
        if j == i:
            row.append(1)
        elif (i > j):
            row.append(b[count_b])
            count_b += 1
        elif (i < j):
            row.append(a[count_a])
            count_a += 1
    Matrix.append(row)

print (Matrix)

輸出：

[[1, 0.1, 0.2, 0.3], 
[0.11, 1, 0.4, 0.5], 
[0.22, 0.33, 1, 0.6], 
[0.44, 0.55, 0.66, 1]]

要么：

import numpy as np
print(np.matrix(Matrix))

輸出：

[[1.   0.1  0.2  0.3 ]
 [0.11 1.   0.4  0.5 ]
 [0.22 0.33 1.   0.6 ]
 [0.44 0.55 0.66 1.  ]]