{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numpy 基础" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "\n", "在这节课中，我们将会学习到 Numpy 的相关内容。\n", "\n", "`NumPy（Numerical Python）`是一个开源的 **Python** 科学计算库，用于快速处理任意维度的数组。\n", "\n", "对于同样的数值计算任务，使用 `NumPy` 比直接使用 **Python** 要简洁的多。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `ndarray` 介绍" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`NumPy` 提供了一个`N` 维数组类型 `ndarray`，它描述了**相同类型**的 `items` 的集合。\n", " \n", "|语文|数学|英语|政治|体育|\n", "|--|--|--|--|--|\n", "|80|89|86|67|79|\n", "|78|97|89|76|81|\n", "\n", "用 `ndarray` 进行存储：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 创建ndarray\n", "score = np.array([[80, 89, 86, 67, 79],[78, 97, 89, 67, 81]])\n", "\n", "# 打印结果\n", "score\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `ndarray` 的属性 \n", "数组属性反映了数组本身固有的信息。\n", "\n", "|属性名字|\t属性解释|\n", "|--|--|\n", "|ndarray.shape|\t数组维度的元组|\n", "|ndarray.ndim|\t数组维数|\n", "|ndarray.size|\t数组中的元素数量|\n", "|ndarray.dtype|\t数组元素的类型|\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ `shape`：数组形状" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 创建不同形状的数组\n", "a = np.array([[1, 2, 3],[4, 5, 6]])\n", "b = np.array([1, 2, 3, 4])\n", "c = np.array([[[1, 2, 3],[4, 5, 6]],[[1, 2, 3],[4, 5, 6.0]]])\n", "\n", "# 分别打印出形状\n", "print(a.shape)\n", "print(b.shape)\n", "print(c.shape)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ `ndim`:数组维数" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 创建不同形状的数组\n", "a = np.array([[1, 2, 3],[4, 5, 6]])\n", "b = np.array([1, 2, 3, 4])\n", "c = np.array([[[1, 2, 3],[4, 5, 6]],[[1, 2, 3],[4, 5, 6.0]]])\n", "\n", "# 分别打印出维数\n", "print(a.ndim)\n", "print(b.ndim)\n", "print(c.ndim)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ `size`：数组元素数量" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 创建不同形状的数组\n", "a = np.array([[1, 2, 3],[4, 5, 6]])\n", "b = np.array([1, 2, 3, 4])\n", "c = np.array([[[1, 2, 3],[4, 5, 6]],[[1, 2, 3],[4, 5, 6.0]]])\n", "\n", "# 分别打印出数组元素数量\n", "print(a.size)\n", "print(b.size)\n", "print(c.size)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ `dtype`：数组元素的类型" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 创建不同形状的数组\n", "a = np.array([[1, 2, 3],[4, 5, 6]])\n", "b = np.array([1, 2, 3, 4])\n", "c = np.array([[[1, 2, 3],[4, 5, 6]],[[1, 2, 3],[4, 5, 6.0]]])\n", "\n", "# 分别打印出数组元素数量\n", "print(a.dtype)\n", "print(b.dtype)\n", "print(c.dtype)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **编程练习**\n", "\n", "要求：把二维数组 [[1, 2, 3],[4, 5, 6],[7,8,9]] 转为 ndarray 格式。并查看其形状、维数和元素数量。" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 请编写你的答案\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.array([[1, 2, 3],[4, 5, 6],[7, 8, 9]])\n", "print(a)\n", "print(a.shape)\n", "print(a.ndim)\n", "print(a.size)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `ndarray` 的类型\n", "\n", "|名称|描述|\n", "|--|--|\n", "|np.bool|用一个字节存储的布尔类型（True或False）|\n", "|np.int8|一个字节大小，-128 至 127|\n", "|np.int16|整数，-32768 至 32767|\n", "|np.int32|整数，$-2^{31}$ 至 $2^{32} -1$|\n", "|np.int64|整数，$-2^{63}$ 至 $2^{63} - 1$|\n", "|np.uint8|无符号整数，0 至 255|\n", "|np.uint16|无符号整数，0 至 65535|\n", "|np.uint32|\t无符号整数，0 至 $2^{32} - 1$|\n", "|np.uint64|\t无符号整数，0 至 $2^{64} - 1$ |\n", "|np.float16\t|半精度浮点数：16位，正负号1位，指数5位，精度10位|\n", "|np.float32\t|单精度浮点数：32位，正负号1位，指数8位，精度23位|\n", "|np.float64\t|双精度浮点数：64位，正负号1位，指数11位，精度52位|\n", "|np.complex64|复数，分别用两个32位浮点数表示实部和虚部|\n", "|np.complex128|复数，分别用两个64位浮点数表示实部和虚部|\n", "|np.object_|python对象|\n", "|np.string_|字符串|\n", "|np.unicode_|unicode类型| \n", "\n", "\n", "**注意：创建数组的时候指定类型**" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# 创建数组时指定类型为 np.float32\n", "a = np.array([[1, 2, 3],[4, 5, 6]], dtype=np.float32)\n", "\n", "# 创建数组时未指定类型\n", "b = np.array([[1, 2, 3],[4, 5, 6]])\n", "\n", "# 打印结果\n", "print(\"数组a：\\n%s,\\n数据类型：%s\"%(a,a.dtype))\n", "print(\"数组b：\\n%s,\\n数据类型：%s\"%(b,b.dtype))\n" ] }, { "cell_type": "markdown", "metadata": { "toc-hr-collapsed": true }, "source": [ "### 基本操作" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 生成元素值为 `0 ` 和 `1` 的数组的方法 \n", "\n", "+ 生成全部元素值为 `0` 的数组" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "zero = np.zeros([3, 4])\n", "zero\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ 生成全部元素值为 `1` 的数组" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "one = np.ones([3, 4])\n", "one\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ 生成对角数组(对角线的地方是 `1`，其余地方是 `0`)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eyes = np.eye(10, 5)\n", "eyes\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ 创建方阵对角矩阵" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# np.eye(5, 5) 可简写为 (5)\n", "eyes1 = np.eye(5)\n", "eyes1\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 从现有数组生成" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a = [[1, 2, 3], [4, 5, 6]]\n", "\n", "# 从现有的数组中创建\n", "a1 = np.array(a)\n", "a\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a1\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 生成固定范围的数组" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 生成等间隔的数组\n", "a = np.linspace(0, 90, 10)\n", "a\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 生成等间隔的数组\n", "b = np.arange(0, 90, 10)\n", "b\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 形状修改" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from numpy import array\n", "a = array([[ 0, 1, 2, 3, 4, 5],\n", " [10,11,12,13,14,15],\n", " [20,21,22,23,24,25],\n", " [30,31,32,33,34,35]])\n", "a.shape\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 在转换形状的时候，一定要注意数组的元素匹配\n", "# 只是将形状进行了修改，但并没有将行列进行转换\n", "b = a.reshape([3, 8])\n", "b\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 数组的形状被修改为: (2, 12), -1: 表示同过自动计算得到此处的值\n", "c = a.reshape([-1, 12])\n", "c\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "d = a.T\n", "d.shape\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 类型修改" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arr = np.array([[[1, 2, 3], [4, 5, 6]], [[12, 3, 34], [5, 6, 7]]])\n", "arr.dtype\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arr.astype(np.float32)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **编程练习**\n", "\n", "要求：创建一个 3x3 并且值从0到8的矩阵\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 请编写你的答案\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "Z = np.arange(9).reshape(3,3)\n", "print(Z)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 数组去重" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arr = np.array([[1, 2, 3, 4],[3, 4, 5, 6]])\n", "np.unique(arr)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 数组运算\n", "\n", "数组的算术运算是元素级别的操作，新的数组被创建并且被结果填充。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "运算|函数\n", "--- | --- \n", "`a + b` | `add(a,b)`\n", "`a - b` | `subtract(a,b)`\n", "`a * b` | `multiply(a,b)`\n", "`a / b` | `divide(a,b)`\n", "`a ** b` | `power(a,b)`\n", "`a % b` | `remainder(a,b)`\n", "\n", "以乘法为例，数组与标量相乘，相当于数组的每个元素乘以这个标量：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.array([1, 2, 3, 4])\n", "a * 3\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "数组按元素相乘：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a = np.array([1, 2])\n", "b = np.array([3, 4])\n", "a * b\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "使用函数" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.multiply(a, b)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "函数还可以接受第三个参数，表示将结果存入第三个参数中：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.multiply(a, b, a)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **编程练习**\n", "\n", "要求：把二维数组 [[1, 2, 3],[4, 5, 6],[7,8,9]] 转为 ndarray 格式。并对每个元素 +1。" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 请编写你的答案\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.array([[1, 2, 3],[4, 5, 6],[7, 8, 9]])\n", "print(a+1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 矩阵 \n", "使用 `mat` 方法将 `2` 维数组转化为矩阵：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.array([[1, 2, 4],\n", " [2, 5, 3],\n", " [7, 8, 9]])\n", "A = np.mat(a)\n", "A\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 也可以使用 **Matlab** 的语法传入一个字符串来生成矩阵：\n", "A = np.mat('1,2,4;2,5,3;7,8,9')\n", "A\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "矩阵与向量的乘法：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x = np.array([[1], [2], [3]])\n", "x\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "A*x\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "b = np.array([[1, 2],\n", " [3, 4],\n", " [5, 6]])\n", "B = np.mat(b)\n", "A*B\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`A.I` 表示 `A` 矩阵的逆矩阵：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "A.I\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "矩阵指数表示矩阵连乘：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "A ** 4\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **编程练习**\n", "\n", "要求：分别把二维数组 [[1, 2] ,[3, 4]] 和 [5, 6] ,[7, 8]]转为 matrix 格式。并计算矩阵的乘积。" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 请编写你的答案\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.mat([[1, 2],[4, 5]])\n", "b = np.mat([[5, 6],[7, 8]])\n", "print(a*b)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 统计函数" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "|方法|作用|\n", "|--|--|\n", "|`a.sum(axis=None)`|求和|\n", "|`a.prod(axis=None)`|求积|\n", "|`a.min(axis=None)`|最小值|\n", "|`a.max(axis=None)`|最大值|\n", "|`a.argmin(axis=None)`|最小值索引|\n", "|`a.argmax(axis=None)`|最大值索引|\n", "|`a.ptp(axis=None)`|最大值减最小值|\n", "|`a.mean(axis=None)`|平均值|\n", "|`a.std(axis=None)`|标准差|\n", "|`a.var(axis=None)`|方差|" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "from numpy import array\n", "a = array([[1, 2, 3],\n", " [4, 5, 6]])\n", "a\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "求所有元素的和：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sum(a)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a.sum()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**指定求和的维度**：\n", "沿着第一维求和" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.sum(a, axis=0)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a.sum(axis=0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "沿着第二维求和：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.sum(a, axis=1)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a.sum(axis=1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "沿着最后一维求和：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.sum(a, axis=-1)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a.sum(axis=-1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **编程练习**\n", "\n", "要求：创建一个长度为30的随机向量并找到它的平均值\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 请编写你的答案\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "Z = np.random.random(30)\n", "m = Z.mean()\n", "print(m)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 比较和逻辑函数" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "运算符|函数|\n", ":---: | :---: \n", "`==` | `equal`\n", "`!=` | `not_equal`\n", "`>` | `greater`\n", "`>=` | `greater_equal`\n", "`<` | `less`\n", "`<=` | `less_equal`\n", "\n", "数组元素的比对，我们可以直接使用运算符进行比较，比如判断数组中元素是否大于某个数：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from numpy import array\n", "a = array([[ 0, 1, 2, 3, 4, 5],\n", " [10,11,12,13,14,15],\n", " [20,21,22,23,24,25],\n", " [30,31,32,33,34,35]])\n", "\n", "a > 10\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 判断数组中元素大于10的元素赋值为 -10 \n", "a[a > 10] = -10\n", "a\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "但是当数组元素较多时，查看输出结果便变得很麻烦，这时我们可以使用`all()`方法，直接比对矩阵的所有对应的元素是否满足条件。假如判断某个区间的值是否全是大于 `20`:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from numpy import array\n", "a = array([[ 0, 1, 2, 3, 4, 5],\n", " [10,11,12,13,14,15],\n", " [20,21,22,23,24,25],\n", " [30,31,32,33,34,35]])\n", "\n", "a[1:3,1:3]\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.all(a[1:3,1:3] > 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "使用 `any()` 来判断数组某个区间的元素是否存在大于 `20`的元素:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.any(a[1:3,1:3] > 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **编程练习**\n", "\n", "要求：把二维数组 [[1, 2, 3],[4, 5, 6],[7,8,9]] 转为 ndarray 格式。判断是否全部大于 0。" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 请编写你的答案\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "a = np.array([[1, 2, 3],[4, 5, 6],[7, 8, 9]])\n", "print(np.all(a > 0))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `IO` 操作" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`savetxt` 可以将数组写入文件，默认使用科学计数法的形式保存：" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "data = np.array([[1, 2],\n", " [3, 4]])\n", "\n", "# 保存文件\n", "np.savetxt('out.txt', data)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 读取文件\n", "with open('out.txt') as f:\n", " for line in f:\n", " print(line)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 读取文件\n", "np.loadtxt('out.txt')\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 }