{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numpy 简介" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 导入numpy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Numpy**是**Python**的一个很重要的第三方库，很多其他科学计算的第三方库都是以**Numpy**为基础建立的。\n", "\n", "**Numpy**的一个重要特性是它的数组计算。\n", "\n", "在使用**Numpy**之前，我们需要导入`numpy`包：" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from numpy import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "使用前一定要先导入 Numpy 包，导入的方法有以下几种：\n", "\n", "```python \n", " import numpy\n", " import numpy as np\n", " from numpy import *\n", " from numpy import array, sin\n", "```\n", "\n", "事实上，在**ipython**中可以使用magic命令来快速导入**Numpy**的内容。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using matplotlib backend: Qt4Agg\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 数组上的数学操作" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "假如我们想将列表中的每个元素增加`1`，但列表不支持这样的操作（报错）：" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "ename": "TypeError", "evalue": "can only concatenate list (not \"int\") to list", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0ma\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;31mTypeError\u001b[0m: can only concatenate list (not \"int\") to list" ] } ], "source": [ "a = [1, 2, 3, 4]\n", "a + 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "转成 `array` ：" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([1, 2, 3, 4])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = array(a)\n", "a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`array` 数组支持每个元素加 `1` 这样的操作：" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([2, 3, 4, 5])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a + 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "与另一个 `array` 相加，得到对应元素相加的结果：" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([3, 5, 7, 9])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = array([2, 3, 4, 5])\n", "a + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "对应元素相乘：" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 2, 6, 12, 20])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a * b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "对应元素乘方：" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1, 8, 81, 1024])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a ** b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 提取数组中的元素" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "提取第一个元素：" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "提取前两个元素：" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([1, 2])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "最后两个元素：" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([3, 4])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[-2:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "将它们相加：" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([4, 6])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:2] + a[-2:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 修改数组形状" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "查看 `array` 的形状：" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(4L,)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "修改 `array` 的形状：" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[1, 2],\n", " [3, 4]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.shape = 2,2\n", "a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 多维数组" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`a` 现在变成了一个二维的数组，可以进行加法：" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[2, 4],\n", " [6, 8]])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a + a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "乘法仍然是对应元素的乘积，并不是按照矩阵乘法来计算：" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 1, 4],\n", " [ 9, 16]])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a * a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "linspace 用来生成一组等间隔的数据：" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.314, 0.628, 0.942, 1.257, 1.571, 1.885, 2.199,\n", " 2.513, 2.827, 3.142, 3.456, 3.77 , 4.084, 4.398, 4.712,\n", " 5.027, 5.341, 5.655, 5.969, 6.283])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = linspace(0, 2*pi, 21)\n", "%precision 3\n", "a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "三角函数：" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.000e+00, 3.090e-01, 5.878e-01, 8.090e-01, 9.511e-01,\n", " 1.000e+00, 9.511e-01, 8.090e-01, 5.878e-01, 3.090e-01,\n", " 1.225e-16, -3.090e-01, -5.878e-01, -8.090e-01, -9.511e-01,\n", " -1.000e+00, -9.511e-01, -8.090e-01, -5.878e-01, -3.090e-01,\n", " -2.449e-16])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = sin(a)\n", "b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "画出图像：" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VtDNnhk7zU6tW+Vcdffv6HSklPBV6kRhq3hyeesp3y++/HzrNj/75T1/kr7oK\nrrwydBrZQYVeJKbatPHbGrdv73e+DO2bb/xwTefO0KdP6DSyM12MFYmxc86BjRt9gZ06FQ4/PEyO\njRv9E05REdx5Z5gMUjoVepGY69bNF9rWrX2xz/XWAt9+C2ee6RdCPfQQWJn7KEoIGroRyQM9esA1\n1/hZOeec47f//f777D3e9u3wj3/41a61a8Ohh/pplCry0VTuQm9mvzOzhWa2zcyOL+N2bc1siZl9\nYmY3lffxRKRsvXvDZ5/5uesDB8JBB/kngLffztymaB995GfTHHEEXH21n9s/bx48/jhUrJiZx5DM\nS6ejnw+cDfyjtBuYWUXgEaAtUB84z8yOTuMxI6u4uDh0hHKLc3ZQ/p1Vrw6XXeYP85g92xf7Sy6B\nI4/0Y+fLlqV+n199BYMHQ+PGfgz+u+/8K4Z58/zOmkuXZi5/CHH//UlGuQu9c26Jc+7j3dysMbDU\nOfepc24LMBo4s7yPGWVx/mWJc3ZQ/tIceijcdpufkfPMM7B2Lfz619C0KTz6KPzrX6X/7ObN/oSr\njh191z5rlt9eeOVKf2jIccf9OEyjv//oy/YY/UHAyp0+X5X4mojkiJlfZDVoEHzxBdxyC0yZAocd\n9t/j+TuPu9eq5cfcO3Xyxf2pp6BtW38ClsRPmf9sZjYJqFnCt251zr2SxP3nyXEJIvmhcmXo0MG/\nrV/vV9gOHOiLe7Vqfg/8Cy/0wzK1a4dOK5mS9uHgZjYF+INzbm4J32sC9HPOtU18fguw3Tk3oITb\n6klBRKQcdnc4eKZeiJX2ILOBemZ2KPD/gS5AiRus7i6oiIiUTzrTK882s5VAE+BVM3s98fVaZvYq\ngHNuK3AN8AawCHjOOReBxdoiIoUj7aEbERGJtuArY+O8oMrMRpjZGjObHzpLeZhZHTObklj4tsDM\nrg2dKRVmVsXMZpnZB2a2yMz6h86UKjOraGbvm1kykxsix8w+NbN5iT/Du6HzpMLMqpvZi2a2OPH7\n0yR0pmSZ2VGJv/Mdb+vL+v8btKNPLKj6CGgNfAG8B5wXl+EdM2sGbARGOeeODZ0nVWZWE6jpnPvA\nzH4OzAHOisvfP4CZVXXOfWtmlYDpwA3OuemhcyXLzHoDjYC9nHMRPzPqp8xsBdDIOVfGrPxoMrOR\nwFTn3IjE708159z60LlSZWYV8PWzsXNuZUm3Cd3Rx3pBlXNuGvBN6Bzl5Zxb7Zz7IPHxRmAxUCts\nqtQ4576NdJGzAAACLklEQVRNfLgHUBGITcExs9pAe+AxSp/QEAexy25m+wDNnHMjwF9PjGORT2gN\nLCutyEP4Qq8FVRGRmBnVEJgVNklqzKyCmX0ArAGmOOcWhc6UgoeAPsD20EHS4IDJZjbbzK4IHSYF\nhwFfmdnfzGyumf3VzKqGDlVO5wLPlHWD0IVeV4IjIDFs8yLQK9HZx4Zzbrtz7jigNtDczIoCR0qK\nmXUA/umce58YdsQ7aeqcawi0A65ODGfGQSXgeGCIc+54YBNwc9hIqTOzPYAzgBfKul3oQv8FsPPu\n2XXwXb3kiJlVBsYATznnXg6dp7wSL7tfBU4InSVJJwMdE2PczwItzWxU4Ewpc859mXj/FfASfjg2\nDlYBq5xz7yU+fxFf+OOmHTAn8fdfqtCF/j8LqhLPTF2A8YEzFQwzM+BxYJFz7uHQeVJlZv/PzKon\nPt4TOBWI0AmqpXPO3eqcq+OcOwz/0vst51y30LlSYWZVzWyvxMfVgNPwu9pGnnNuNbDSzI5MfKk1\nsDBgpPI6D98olCnoFkXOua1mtmNBVUXg8ZjN+HgWaAHsn1g8drtz7m+BY6WiKdAVmGdmOwrkLc65\nvwfMlIoDgZGJWQcVgCedc28GzlRecRzGrAG85PsFKgFPO+cmho2Ukp7A04kmcxlwSeA8KUk8ubYG\ndnttRAumRETyXOihGxERyTIVehGRPKdCLyKS51ToRUTynAq9iEieU6EXEclzKvQiInlOhV5EJM/9\nHzC+mVy4trE1AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "plot(a, b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 从数组中选择元素" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "假设我们想选取数组b中所有非负的部分，首先可以利用 `b` 产生一组布尔值：" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ True, True, True, True, True, True, True, True, True,\n", " True, True, False, False, False, False, False, False, False,\n", " False, False, False], dtype=bool)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b >= 0" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mask = b >= 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "画出所有对应的非负值对应的点：" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(a[mask], b[mask], 'ro')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }