深度學習代碼實戰——線性代數

1.標量, 向量, 矩陣, 張量

import numpy as np

s = 5

V = np.array([1,2])

m = np.array([[1,2],[2,4]])

t = np.array([
    [[1,2,3],[4,5,6],[7,8,9]],
    [[11,12,13],[14,15,16],[17,18,19]],
    [[21,22,23],[24,25,26],[27,28,29]],
])

print("標量:\n" + str(s))
print("向量:\n" + str(V))
print("矩陣:\n" + str(m))
print("張量:\n" + str(t))

2.矩陣轉置

A = np.array([[1.0,2.0],[1.0,1.0],[2.0,3.0]])
A_t = A.transpose()
print("A:\n",A)
print("A_t:\n",A_t)

3.矩陣加法

a = np.array([[1.0,2.0],[3.0,4.0]])
b = np.array([[6.0,7.0],[8.0,9.0]])
print("矩陣相加:\n",a+b)

4.矩陣乘法

m1 = np.array([[1.0,3.0],[1.0,0.0]])
m2 = np.array([[1.0,2.0],[5.0,0.0]])
print("按矩陣乘法規則:\n",np.dot(m1,m2))
print("按逐元素相乘:\n",np.multiply(m1,m2))
print("按逐元素相乘:\n",m1*m2)
v1 = np.array([1.0,2.0])
v2 = np.array([4.0,5.0])
print("向量內積:\n",np.dot(v1,v2))

5.單位矩陣

print("單位矩陣")
np.identity(3)

6.矩陣的逆

A = [[1.0,2.0],[3.0,4.0]]
A_inv = np.linalg.inv(A)
print("A的逆矩陣:\n",A_inv)

7.範數

a = np.array([[1.0,3.0]])
print("向量 2 範數:\n",np.linalg.norm(a,ord = 2))
print("向量 1 範數:\n",np.linalg.norm(a,ord = 1))
print("向量無窮範數:\n",np.linalg.norm(a,ord = np.inf))

a = np.array([[1.0,3.0],[2.0,1.0]])
print("矩陣 F 範數:\n",np.linalg.norm(a,ord = "fro"))

8.特徵值分解

A = np.array([[1.0,2.0,3.0],
             [4.0,5.0,6.0],
             [7.0,8.0,9.0]])
print("特徵值:\n",np.linalg.eigvals(A))
eigvals, eigvectors = np.linalg.eig(A)
print("特徵值:\n",eigvals)
print("特徵向量:\n",eigvectors)

9.奇異值分解

A = np.array([[1.0,2.0,3.0],
            [4.0,5.0,6.0]])
U, D, V = np.linalg.svd(A)
print("U:\n",U)
print("D:\n",D)
print("V:\n",V)