1. 导入 NumPy

import numpy as np

2. 创建数组

2.1 一维数组

a = np.array([1, 2, 3, 4, 5])
print(a)

2.2 多维数组

b = np.array([[1, 2, 3], [4, 5, 6]])
print(b)

2.3 特殊数组

• 全零数组：

  zeros = np.zeros((3, 3))
  print(zeros)
  

• 全一数组：

  ones = np.ones((3, 3))
  print(ones)
  

• 单位矩阵：

  identity = np.eye(3)
  print(identity)
  

• 随机数组：

  random_array = np.random.rand(3, 3)
  print(random_array)
  

3. 数组属性

a = np.array([[1, 2, 3], [4, 5, 6]])

print(a.shape)      # (2, 3)
print(a.dtype)      # 数据类型
print(a.size)       # 元素总数
print(a.ndim)       # 维度数

4. 数组索引和切片

4.1 一维数组

a = np.array([1, 2, 3, 4, 5])
print(a[0])         # 1
print(a[1:4])       # [2, 3, 4]

4.2 多维数组

b = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(b[0, 0])      # 1
print(b[0, :])      # [1, 2, 3]
print(b[:, 1])      # [2, 5, 8]
print(b[1:3, 1:3])  # [[5, 6], [8, 9]]

5. 数组操作

5.1 数学运算

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

print(a + b)        # [5, 7, 9]
print(a - b)        # [-3, -3, -3]
print(a * b)        # [4, 10, 18]
print(a / b)        # [0.25, 0.4, 0.5]
print(np.sqrt(a))   # [1., 1.41421356, 1.73205081]

5.2 广播

a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([1, 0, 1])

print(a + b)        # [[2, 2, 4], [5, 5, 7]]

6. 数组重塑

a = np.arange(12)
print(a)            # [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]

b = a.reshape((3, 4))
print(b)            # [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]

c = a.reshape((2, 2, 3))
print(c)            # [[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]]]

7. 数组连接和拆分

7.1 连接

a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6]])

# 水平连接
c = np.hstack((a, b))
print(c)            # [[1, 2, 5, 6], [3, 4, 5, 6]]

# 垂直连接
d = np.vstack((a, b))
print(d)            # [[1, 2], [3, 4], [5, 6]]

7.2 拆分

a = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])

# 水平拆分
b, c = np.hsplit(a, 2)
print(b)            # [[1, 2], [5, 6]]
print(c)            # [[3, 4], [7, 8]]

# 垂直拆分
d, e = np.vsplit(a, 2)
print(d)            # [[1, 2, 3, 4]]
print(e)            # [[5, 6, 7, 8]]

8. 数组排序

a = np.array([3, 1, 2])
print(np.sort(a))           # [1, 2, 3]

b = np.array([[3, 1, 2], [6, 4, 5]])
print(np.sort(b, axis=0))   # [[3, 1, 2], [6, 4, 5]]
print(np.sort(b, axis=1))   # [[1, 2, 3], [4, 5, 6]]

9. 数组统计

a = np.array([[1, 2, 3], [4, 5, 6]])

print(np.sum(a))            # 21
print(np.mean(a))           # 3.5
print(np.median(a))         # 3.5
print(np.min(a))            # 1
print(np.max(a))            # 6
print(np.std(a))            # 标准差
print(np.var(a))            # 方差

10. 数组布尔操作

a = np.array([1, 2, 3, 4, 5])
b = np.array([0, 1, 2, 3, 4])

print(a > 3)                # [False, False, False, True, True]
print(np.any(a > 3))        # True
print(np.all(a > 3))        # False

11. 数组搜索和选择

a = np.array([1, 2, 3, 4, 5])

# 查找非零元素的索引
print(np.nonzero(a))        # (array([0, 1, 2, 3, 4]),)

# 条件选择
b = np.where(a > 3, a, 0)
print(b)                    # [0, 0, 0, 4, 5]

12. 文件读写

# 保存数组
np.save('array.npy', a)

# 读取数组
b = np.load('array.npy')
print(b)                    # [1, 2, 3, 4, 5]

13. 高级功能

13.1 广播机制

a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([1, 0, 1])

print(a + b)                # [[2, 2, 4], [5, 5, 7]]

13.2 线性代数

a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6], [7, 8]])

# 矩阵乘法
print(np.dot(a, b))         # [[19, 22], [43, 50]]

# 求逆矩阵
print(np.linalg.inv(a))     # [[-2. ,  1. ], [ 1.5, -0.5]]

14. 常用函数

• 生成等差数列：

  a = np.arange(0, 10, 2)
  print(a)                  # [0, 2, 4, 6, 8]
  

• 生成等比数列：

  a = np.linspace(0, 1, 5)
  print(a)                  # [0.  , 0.25, 0.5 , 0.75, 1.  ]
  

• 生成对数等比数列：

  a = np.logspace(0, 1, 5)
  print(a)                  # [1.        , 1.77827941, 3.16227766, 5.62341325, 10.       ]