KuRRe8 · June 6, 2025 17:35 · KuRRe8 · May 8, 2025
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 {
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy - Python 数值计算基石教程\n",
    "\n",
    "欢迎来到 NumPy 教程！NumPy (Numerical Python) 是 Python 科学计算生态系统的核心库。它提供了一个强大的 N 维数组对象 (`ndarray`)，以及用于高效处理这些数组的各种函数。\n",
    "\n",
    "**为什么 NumPy 对 ML/DL/数据科学如此重要？**\n",
    "\n",
    "1.  **高效的数值运算**：NumPy 的核心是用 C 语言编写的，其数组操作（向量化操作）比纯 Python 的列表循环快得多。\n",
    "2.  **`ndarray` 对象**：提供了一个同构（所有元素类型相同）、多维、固定大小的数组，非常适合表示数值数据、向量、矩阵、图像等。\n",
    "3.  **数学函数库**：包含大量的数学、线性代数、傅里叶变换和随机数生成函数。\n",
    "4.  **生态系统基础**：Pandas, Scikit-learn, SciPy, Matplotlib, PyTorch, TensorFlow 等几乎所有科学计算和 ML/DL 库都建立在 NumPy 之上或与之紧密集成。\n",
    "\n",
    "**本教程将涵盖 NumPy 的核心概念和常用操作：**\n",
    "\n",
    "1.  创建 NumPy 数组 (`ndarray`)\n",
    "2.  数组的基本属性\n",
    "3.  数组索引和切片\n",
    "4.  向量化操作和通用函数 (ufuncs)\n",
    "5.  广播 (Broadcasting)\n",
    "6.  基本线性代数\n",
    "7.  随机数生成\n",
    "8.  数组形状操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 准备工作：导入 NumPy\n",
    "\n",
    "按照惯例，我们将 NumPy 导入并简写为 `np`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "print(f\"NumPy version: {np.__version__}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 创建 NumPy 数组 (`ndarray`)\n",
    "\n",
    "有多种方法可以创建 NumPy 数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 从 Python 列表或元组创建\n",
    "list_data = [1, 2, 3, 4, 5]\n",
    "arr_from_list = np.array(list_data)\n",
    "print(f\"Array from list: {arr_from_list}\")\n",
    "print(f\"Type: {type(arr_from_list)}\")\n",
    "\n",
    "tuple_data = (6, 7, 8)\n",
    "arr_from_tuple = np.array(tuple_data)\n",
    "print(f\"Array from tuple: {arr_from_tuple}\")\n",
    "\n",
    "# 创建多维数组 (例如，从嵌套列表)\n",
    "nested_list = [[1, 2, 3], [4, 5, 6]]\n",
    "arr_2d = np.array(nested_list)\n",
    "print(f\"\\n2D Array:\\n{arr_2d}\")\n",
    "\n",
    "# 使用内置函数创建特定数组\n",
    "arr_zeros = np.zeros((2, 3)) # 创建一个 2x3 的全零数组 (默认 float64)\n",
    "print(f\"\\nZeros array (2x3):\\n{arr_zeros}\")\n",
    "\n",
    "arr_ones = np.ones((3, 2), dtype=int) # 创建一个 3x2 的全一数组，指定类型为 int\n",
    "print(f\"\\nOnes array (3x2, int):\\n{arr_ones}\")\n",
    "\n",
    "arr_full = np.full((2, 2), 7.5) # 创建一个 2x2 的数组，所有元素填充为 7.5\n",
    "print(f\"\\nFull array (2x2, fill 7.5):\\n{arr_full}\")\n",
    "\n",
    "arr_eye = np.eye(3) # 创建一个 3x3 的单位矩阵\n",
    "print(f\"\\nIdentity matrix (3x3):\\n{arr_eye}\")\n",
    "\n",
    "# 使用序列生成函数\n",
    "arr_arange = np.arange(0, 10, 2) # 类似 Python 的 range，但不包含结束值，可以有步长\n",
    "print(f\"\\nArray from arange(0, 10, 2): {arr_arange}\")\n",
    "\n",
    "arr_linspace = np.linspace(0, 1, 5) # 在 [0, 1] 之间生成 5 个等间隔的数 (包含结束值)\n",
    "print(f\"\\nArray from linspace(0, 1, 5): {arr_linspace}\")\n",
    "\n",
    "# 使用随机数函数\n",
    "arr_rand = np.random.rand(2, 2) # 生成 [0, 1) 之间的均匀分布随机数 (2x2)\n",
    "print(f\"\\nRandom array (2x2, uniform [0,1)):\\n{arr_rand}\")\n",
    "\n",
    "arr_randn = np.random.randn(3, 1) # 生成符合标准正态分布 (均值0, 方差1) 的随机数 (3x1)\n",
    "print(f\"\\nRandom array (3x1, standard normal):\\n{arr_randn}\")\n",
    "\n",
    "arr_randint = np.random.randint(0, 10, size=(2, 4)) # 生成 [0, 10) 之间的随机整数 (2x4)\n",
    "print(f\"\\nRandom integer array (2x4, [0,10)):\\n{arr_randint}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 数组的基本属性\n",
    "\n",
    "每个 `ndarray` 对象都有一些描述其自身的属性："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "print(f\"Array:\\n{arr}\")\n",
    "\n",
    "# shape: 数组的维度 (一个元组)\n",
    "print(f\"Shape: {arr.shape}\") # (2, 3) -> 2 行 3 列\n",
    "\n",
    "# ndim: 数组的轴（维度）的数量\n",
    "print(f\"Number of dimensions (ndim): {arr.ndim}\") # 2\n",
    "\n",
    "# dtype: 数组中元素的数据类型\n",
    "print(f\"Data type (dtype): {arr.dtype}\") # float64 (默认)\n",
    "\n",
    "# size: 数组中元素的总数\n",
    "print(f\"Total number of elements (size): {arr.size}\") # 6\n",
    "\n",
    "# itemsize: 数组中每个元素的字节大小\n",
    "print(f\"Size of each element in bytes (itemsize): {arr.itemsize}\") # 8 (float64 是 8 字节)\n",
    "\n",
    "# nbytes: 整个数组占用的总字节数 (size * itemsize)\n",
    "print(f\"Total bytes consumed by the elements (nbytes): {arr.nbytes}\") # 48"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 数组索引和切片\n",
    "\n",
    "NumPy 数组的索引和切片非常灵活，对于数据访问和操作至关重要。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 一维数组索引和切片 (类似 Python 列表)\n",
    "arr1d = np.arange(10)\n",
    "print(f\"1D Array: {arr1d}\")\n",
    "print(f\"Element at index 3: {arr1d[3]}\")\n",
    "print(f\"Elements from index 2 to 5 (exclusive): {arr1d[2:5]}\")\n",
    "print(f\"Elements from index 5 onwards: {arr1d[5:]}\")\n",
    "print(f\"Elements up to index 4 (exclusive): {arr1d[:4]}\")\n",
    "print(f\"Every other element: {arr1d[::2]}\")\n",
    "print(f\"Reverse array: {arr1d[::-1]}\")\n",
    "\n",
    "# 多维数组索引和切片\n",
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "print(f\"\\n2D Array:\\n{arr2d}\")\n",
    "\n",
    "# 访问单个元素: arr[row, column]\n",
    "print(f\"Element at row 1, col 2: {arr2d[1, 2]}\") # 6\n",
    "# 或者使用 arr[row][column]，但这通常效率较低，因为它创建了中间数组\n",
    "print(f\"Element using arr[1][2]: {arr2d[1][2]}\") # 6\n",
    "\n",
    "# 切片：使用逗号分隔不同维度的切片\n",
    "print(f\"\\nFirst 2 rows, columns 1 to 3 (exclusive):\\n{arr2d[:2, 1:3]}\")\n",
    "# [[2 3]\n",
    "#  [5 6]]\n",
    "\n",
    "print(f\"\\nRow at index 1: {arr2d[1, :]}\") # 或 arr2d[1]\n",
    "# [4 5 6]\n",
    "\n",
    "print(f\"\\nColumn at index 1:\\n{arr2d[:, 1]}\")\n",
    "# [2 5 8] (注意返回的是一维数组)\n",
    "\n",
    "# *** NumPy 切片是视图 (Views) ***\n",
    "# 对切片的修改会影响原始数组！\n",
    "arr2d_slice = arr2d[:2, :2]\n",
    "print(f\"\\nOriginal slice:\\n{arr2d_slice}\")\n",
    "arr2d_slice[0, 0] = 99\n",
    "print(f\"Slice after modification:\\n{arr2d_slice}\")\n",
    "print(f\"Original arr2d after slice modification:\\n{arr2d}\") # 原始数组也被改变了!\n",
    "\n",
    "# 如果需要副本，使用 .copy()\n",
    "arr2d_copy = arr2d[:2, :2].copy()\n",
    "arr2d_copy[0, 0] = 111\n",
    "print(f\"\\nCopy after modification:\\n{arr2d_copy}\")\n",
    "print(f\"Original arr2d (should be unchanged by copy modification):\\n{arr2d}\")\n",
    "\n",
    "# *** 高级索引 ***\n",
    "print(\"\\n--- Advanced Indexing ---\")\n",
    "arr_adv = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "\n",
    "# 1. 整数数组索引: 使用整数数组指定索引\n",
    "# 获取第0行和第2行的所有列\n",
    "print(f\"Rows 0 and 2:\\n{arr_adv[[0, 2]]}\") \n",
    "# 获取元素 (0, 1), (1, 2), (2, 0)\n",
    "row_indices = np.array([0, 1, 2])\n",
    "col_indices = np.array([1, 2, 0])\n",
    "print(f\"Elements at (0,1), (1,2), (2,0): {arr_adv[row_indices, col_indices]}\") # [2 6 7]\n",
    "\n",
    "# 2. 布尔索引: 使用布尔数组选择元素\n",
    "bool_mask = arr_adv > 5\n",
    "print(f\"\\nBoolean mask (arr_adv > 5):\\n{bool_mask}\")\n",
    "print(f\"Elements greater than 5: {arr_adv[bool_mask]}\") # 返回一个包含满足条件元素的一维数组\n",
    "\n",
    "# 也可以直接使用条件\n",
    "print(f\"Elements where arr_adv % 2 == 0: {arr_adv[arr_adv % 2 == 0]}\")\n",
    "\n",
    "# *** 注意：高级索引总是返回数组的副本，而不是视图！***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 向量化操作和通用函数 (ufuncs)\n",
    "\n",
    "NumPy 的核心优势在于其**向量化 (vectorization)** 能力。这意味着许多操作可以应用于整个数组，而无需编写显式的 Python 循环。这些操作通常是通过**通用函数 (universal functions, ufuncs)** 实现的，它们底层是用 C 编写的，非常高效。\n",
    "\n",
    "**好处：**\n",
    "*   代码更简洁、更易读。\n",
    "*   执行速度快得多。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr_a = np.array([1, 2, 3])\n",
    "arr_b = np.array([4, 5, 6])\n",
    "\n",
    "# 基本算术运算 (element-wise)\n",
    "print(f\"arr_a + arr_b = {arr_a + arr_b}\")\n",
    "print(f\"arr_a - arr_b = {arr_a - arr_b}\")\n",
    "print(f\"arr_a * arr_b = {arr_a * arr_b}\") # 逐元素乘法\n",
    "print(f\"arr_a / arr_b = {arr_a / arr_b}\")\n",
    "print(f\"arr_a ** 2 = {arr_a ** 2}\")\n",
    "\n",
    "# 也可以和标量运算 (利用了广播，见下一节)\n",
    "print(f\"arr_a + 5 = {arr_a + 5}\")\n",
    "print(f\"arr_a * 2 = {arr_a * 2}\")\n",
    "\n",
    "# 比较运算 (element-wise)\n",
    "print(f\"\\narr_a > 1 = {arr_a > 1}\") # 返回布尔数组\n",
    "print(f\"arr_a == arr_b = {arr_a == arr_b}\")\n",
    "\n",
    "# 通用函数 (ufuncs)\n",
    "print(f\"\\nnp.sqrt(arr_a) = {np.sqrt(arr_a)}\")\n",
    "print(f\"np.exp(arr_a) = {np.exp(arr_a)}\") # e^x\n",
    "print(f\"np.sin(arr_a) = {np.sin(arr_a)}\")\n",
    "print(f\"np.log(arr_a) = {np.log(arr_a)}\") # 自然对数\n",
    "print(f\"np.add(arr_a, arr_b) = {np.add(arr_a, arr_b)}\") # 等同于 arr_a + arr_b\n",
    "print(f\"np.maximum(arr_a, np.array([0, 5, 2])) = {np.maximum(arr_a, np.array([0, 5, 2]))}\") # 逐元素取最大值\n",
    "\n",
    "# 聚合函数\n",
    "arr_agg = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "print(f\"\\nArray for aggregation:\\n{arr_agg}\")\n",
    "print(f\"Sum of all elements: {np.sum(arr_agg)} or {arr_agg.sum()}\")\n",
    "print(f\"Sum along columns (axis=0): {np.sum(arr_agg, axis=0)} or {arr_agg.sum(axis=0)}\") # [5 7 9]\n",
    "print(f\"Sum along rows (axis=1): {np.sum(arr_agg, axis=1)} or {arr_agg.sum(axis=1)}\") # [ 6 15]\n",
    "print(f\"Minimum value: {np.min(arr_agg)} or {arr_agg.min()}\")\n",
    "print(f\"Maximum value in each column: {np.max(arr_agg, axis=0)}\") # [4 5 6]\n",
    "print(f\"Mean of all elements: {np.mean(arr_agg)} or {arr_agg.mean()}\")\n",
    "print(f\"Standard deviation: {np.std(arr_agg)} or {arr_agg.std()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. 广播 (Broadcasting)\n",
    "\n",
    "广播是 NumPy 强大的机制，它允许 NumPy 在执行算术运算时处理不同形状的数组，前提是它们的形状满足一定的兼容性规则。\n",
    "\n",
    "**广播规则：**\n",
    "当对两个数组进行操作时，NumPy 逐个比较它们的维度（从末尾维度开始向前比较）：\n",
    "1.  如果两个数组的维度数不同，将维度较少的数组的形状在前面补 1，直到它们的维度数相同。\n",
    "2.  在任何一个维度上，如果两个数组的该维度大小相同，或者其中一个数组的大小为 1，则认为它们在该维度上是兼容的。\n",
    "3.  如果两个数组在所有维度上都兼容，它们就可以一起广播。\n",
    "4.  广播后，每个数组的行为就像其形状沿大小为 1 的维度扩展（复制）以匹配另一个数组的形状一样。\n",
    "5.  如果存在任何一个维度，两个数组的大小都大于 1 且不相同，则无法广播，会引发 `ValueError`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 示例 1: 标量和数组\n",
    "arr = np.array([1, 2, 3])\n",
    "scalar = 5\n",
    "# arr shape: (3,)\n",
    "# scalar conceptually has shape ()\n",
    "# Broadcasting makes scalar act like [5, 5, 5]\n",
    "result = arr + scalar\n",
    "print(f\"Array + Scalar:\\n {arr} + {scalar} = {result}\")\n",
    "\n",
    "# 示例 2: 一维数组和二维数组\n",
    "arr2d = np.array([[10, 20, 30], [40, 50, 60]]) # shape (2, 3)\n",
    "arr1d = np.array([1, 2, 3])               # shape (3,)\n",
    "# Broadcasting rules:\n",
    "# arr2d shape: (2, 3)\n",
    "# arr1d shape: (   3,) -> promoted to (1, 3)\n",
    "# Dimension 2: 3 == 3 (compatible)\n",
    "# Dimension 1: 2 vs 1 (compatible, 1 will be stretched)\n",
    "# arr1d acts like [[1, 2, 3], [1, 2, 3]]\n",
    "result = arr2d + arr1d\n",
    "print(f\"\\n2D Array + 1D Array:\\n{arr2d}\\n + \\n{arr1d}\\n = \\n{result}\")\n",
    "\n",
    "# 示例 3: 列向量和行向量\n",
    "col_vector = np.array([[10], [20], [30]]) # shape (3, 1)\n",
    "row_vector = np.array([1, 2, 3])          # shape (3,) -> treated as (1, 3)\n",
    "# Broadcasting rules:\n",
    "# col_vector shape: (3, 1)\n",
    "# row_vector shape: (1, 3)\n",
    "# Dimension 2: 1 vs 3 (compatible, 1 stretched to 3)\n",
    "# Dimension 1: 3 vs 1 (compatible, 1 stretched to 3)\n",
    "# col acts like [[10, 10, 10], [20, 20, 20], [30, 30, 30]]\n",
    "# row acts like [[ 1,  2,  3], [ 1,  2,  3], [ 1,  2,  3]]\n",
    "result = col_vector + row_vector\n",
    "print(f\"\\nColumn Vector + Row Vector:\\n{col_vector}\\n + \\n{row_vector}\\n = \\n{result}\")\n",
    "\n",
    "# 示例 4: 不兼容的形状\n",
    "arr_a = np.array([[1, 2], [3, 4]]) # shape (2, 2)\n",
    "arr_b = np.array([10, 20, 30])     # shape (3,)\n",
    "try:\n",
    "    result = arr_a + arr_b\n",
    "except ValueError as e:\n",
    "    print(f\"\\nError broadcasting incompatible shapes (2,2) and (3,): {e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. 基本线性代数\n",
    "\n",
    "NumPy 提供了进行线性代数运算的功能，这在 ML/DL 中非常常用。\n",
    "*   **矩阵乘法**: 可以使用 `@` 运算符 (Python 3.5+) 或 `np.dot()` 函数。\n",
    "*   **其他运算**: 位于 `np.linalg` 子模块中，如求逆、行列式、特征值、奇异值分解 (SVD) 等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat_a = np.array([[1, 2], [3, 4]]) # 2x2 matrix\n",
    "mat_b = np.array([[5, 6], [7, 8]]) # 2x2 matrix\n",
    "vec_v = np.array([10, 20])         # 1D vector (shape (2,))\n",
    "\n",
    "print(f\"Matrix A:\\n{mat_a}\")\n",
    "print(f\"Matrix B:\\n{mat_b}\")\n",
    "print(f\"Vector V: {vec_v}\")\n",
    "\n",
    "# 逐元素乘法 (回顾)\n",
    "print(f\"\\nElement-wise product A * B:\\n{mat_a * mat_b}\")\n",
    "\n",
    "# 矩阵乘法 (Dot Product / Matrix Multiplication)\n",
    "# 1. 使用 @ 运算符 (推荐)\n",
    "mat_product = mat_a @ mat_b \n",
    "print(f\"\\nMatrix product A @ B:\\n{mat_product}\")\n",
    "\n",
    "# 2. 使用 np.dot()\n",
    "mat_product_dot = np.dot(mat_a, mat_b)\n",
    "print(f\"Matrix product np.dot(A, B):\\n{mat_product_dot}\")\n",
    "\n",
    "# 矩阵与向量乘法\n",
    "mat_vec_product = mat_a @ vec_v # or np.dot(mat_a, vec_v)\n",
    "print(f\"\\nMatrix-vector product A @ V: {mat_vec_product}\") # Result is 1D array [50, 110]\n",
    "\n",
    "# 转置 (Transpose)\n",
    "print(f\"\\nTranspose of A (A.T):\\n{mat_a.T}\")\n",
    "print(f\"Transpose using np.transpose(A):\\n{np.transpose(mat_a)}\")\n",
    "\n",
    "# 矩阵求逆 (Inverse) - 仅对方阵且可逆矩阵有效\n",
    "try:\n",
    "    mat_a_inv = np.linalg.inv(mat_a)\n",
    "    print(f\"\\nInverse of A:\\n{mat_a_inv}\")\n",
    "    # 验证 A @ A_inv 约等于单位矩阵\n",
    "    print(f\"A @ A_inv (should be close to identity):\\n{mat_a @ mat_a_inv}\")\n",
    "except np.linalg.LinAlgError as e:\n",
    "    print(f\"\\nCould not compute inverse of A: {e}\")\n",
    "\n",
    "# 行列式 (Determinant)\n",
    "det_a = np.linalg.det(mat_a)\n",
    "print(f\"\\nDeterminant of A: {det_a:.2f}\")\n",
    "\n",
    "# 奇异值分解 (Singular Value Decomposition - SVD)\n",
    "U, s, Vh = np.linalg.svd(mat_a)\n",
    "print(\"\\nSVD of A:\")\n",
    "print(f\"  U:\\n{U}\")\n",
    "print(f\"  Singular values (s): {s}\")\n",
    "print(f\"  Vh (V transpose):\\n{Vh}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. 随机数生成\n",
    "\n",
    "`np.random` 模块提供了更丰富、更高效的随机数生成功能，常用于权重初始化、数据增强、模拟等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 设置随机种子以保证结果可复现\n",
    "np.random.seed(42)\n",
    "\n",
    "# 生成均匀分布 [0.0, 1.0)\n",
    "rand_uniform = np.random.rand(3, 2) # 3x2 array\n",
    "print(f\"Uniform random [0,1) (3x2):\\n{rand_uniform}\")\n",
    "\n",
    "# 生成标准正态分布 (mean=0, std=1)\n",
    "rand_normal = np.random.randn(4) # 1D array of size 4\n",
    "print(f\"\\nStandard normal random (size 4): {rand_normal}\")\n",
    "\n",
    "# 生成随机整数 [low, high)\n",
    "rand_int = np.random.randint(1, 100, size=5) # 5 integers from [1, 100)\n",
    "print(f\"\\nRandom integers [1, 100): {rand_int}\")\n",
    "\n",
    "# 从数组中随机选择 (有放回或无放回)\n",
    "population = np.arange(10)\n",
    "choice_replace = np.random.choice(population, size=5, replace=True) # 有放回\n",
    "print(f\"\\nRandom choice (with replacement) from {population}: {choice_replace}\")\n",
    "choice_no_replace = np.random.choice(population, size=5, replace=False) # 无放回\n",
    "print(f\"Random choice (without replacement) from {population}: {choice_no_replace}\")\n",
    "\n",
    "# 打乱数组 (原地操作)\n",
    "arr_to_shuffle = np.arange(9)\n",
    "np.random.shuffle(arr_to_shuffle)\n",
    "print(f\"\\nShuffled array: {arr_to_shuffle}\")\n",
    "\n",
    "# 生成特定分布的随机数 (例如，正态分布)\n",
    "mu, sigma = 10, 2 # 均值和标准差\n",
    "normal_dist = np.random.normal(mu, sigma, size=5)\n",
    "print(f\"\\nNormal distribution (mean=10, std=2): {normal_dist}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. 数组形状操作\n",
    "\n",
    "改变数组的形状而不改变其数据，是常见的操作。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(12) # [ 0  1  2  3  4  5  6  7  8  9 10 11]\n",
    "print(f\"Original array: {arr}, shape: {arr.shape}\")\n",
    "\n",
    "# reshape(): 返回一个具有新形状的数组 (视图或副本，取决于内存布局)\n",
    "reshaped_arr = arr.reshape((3, 4))\n",
    "print(f\"\\nReshaped array (3x4):\\n{reshaped_arr}\")\n",
    "print(f\"Shape after reshape: {reshaped_arr.shape}\")\n",
    "\n",
    "# -1 可以表示推断维度大小\n",
    "reshaped_auto = arr.reshape((2, -1)) # -1 会自动计算为 6\n",
    "print(f\"\\nReshaped array (2x-1):\\n{reshaped_auto}\")\n",
    "print(f\"Shape with -1: {reshaped_auto.shape}\")\n",
    "\n",
    "# ravel() or flatten(): 将多维数组展平成一维数组\n",
    "# ravel() 通常返回视图 (如果可能)\n",
    "raveled_arr = reshaped_arr.ravel()\n",
    "print(f\"\\nRaveled array: {raveled_arr}\")\n",
    "# flatten() 总是返回副本\n",
    "flattened_arr = reshaped_arr.flatten()\n",
    "print(f\"Flattened array: {flattened_arr}\")\n",
    "\n",
    "# 修改 ravel 返回的视图会影响原始数组 (如果它是视图)\n",
    "raveled_arr[0] = 99\n",
    "print(f\"Original reshaped_arr after modifying raveled view:\\n{reshaped_arr}\")\n",
    "\n",
    "# T attribute or transpose(): 转置数组\n",
    "print(f\"\\nOriginal reshaped array (3x4):\\n{reshaped_arr}\")\n",
    "transposed_arr = reshaped_arr.T\n",
    "print(f\"Transposed array (4x3):\\n{transposed_arr}\")\n",
    "print(f\"Shape after transpose: {transposed_arr.shape}\")\n",
    "\n",
    "# 使用 np.newaxis 增加维度\n",
    "arr1d = np.array([1, 2, 3])\n",
    "print(f\"\\nOriginal 1D array: {arr1d}, shape: {arr1d.shape}\")\n",
    "row_vec = arr1d[np.newaxis, :] # 变成行向量\n",
    "print(f\"Row vector: {row_vec}, shape: {row_vec.shape}\")\n",
    "col_vec = arr1d[:, np.newaxis] # 变成列向量\n",
    "print(f\"Column vector:\\n{col_vec}, shape: {col_vec.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 总结\n",
    "\n",
    "NumPy 是 Python 科学计算、机器学习和深度学习的基础。其核心 `ndarray` 对象和相关的函数提供了高效处理数值数据的强大能力。\n",
    "\n",
    "**关键要点：**\n",
    "*   `ndarray` 用于高效存储和操作同构数据。\n",
    "*   利用索引和切片进行灵活的数据访问。\n",
    "*   向量化操作和 ufuncs 显著提高性能，避免 Python 循环。\n",
    "*   广播机制允许不同形状的数组进行运算。\n",
    "*   `np.linalg` 提供了基本的线性代数功能。\n",
    "*   `np.random` 用于生成各种随机数。\n",
    "*   `reshape`, `ravel`, `transpose` 等用于操作数组形状。\n",
    "\n",
    "熟练掌握 NumPy 是进行数据科学和机器学习工作的必备技能。建议多加练习，并查阅 NumPy 官方文档以了解更多高级功能。"
   ]
  }
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diff --git a/opencv_tutorial.ipynb b/opencv_tutorial.ipynb
diff --git a/pandas_tutorial.ipynb b/pandas_tutorial.ipynb
diff --git a/pattern_matching_tutorial.ipynb b/pattern_matching_tutorial.ipynb
diff --git a/python_internals_performance_tutorial.ipynb b/python_internals_performance_tutorial.ipynb
diff --git a/pytorch_tutorial.ipynb b/pytorch_tutorial.ipynb
diff --git a/scikit_learn_tutorial.ipynb b/scikit_learn_tutorial.ipynb
diff --git a/seaborn_tutorial.ipynb b/seaborn_tutorial.ipynb
diff --git a/shap_tutorial.ipynb b/shap_tutorial.ipynb
diff --git a/sigh.md b/sigh.md
diff --git a/stable_baselines3_tutorial.ipynb b/stable_baselines3_tutorial.ipynb
diff --git a/standard_library_tutorial.ipynb b/standard_library_tutorial.ipynb
diff --git a/transformers_tutorial.ipynb b/transformers_tutorial.ipynb