课件/16_numpy.ipynb

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   "source": [
    "# NumPy基础"
   ]
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    "**NumPy** (https://www.numpy.org/, pronounced **[nᴧmpᴧɪ]**，\n",
    "是 **Numerical Python** 的简称）是高性能科学计算和数据分析的基础包。\n",
    "\n",
    "其部分功能如下：\n",
    "\n",
    "* **ndarray** ，一个具有矢量算术运算和复杂广播能力的快速且节省空间的多维数组。\n",
    "* 用于对数组数据进行快速运算的标准数学函数。\n",
    "* 用于读写磁盘数据的工具以及用于操作内存映射文件的工具。\n",
    "* 线性代数、随机数生成以及傅里叶变换功能。\n",
    "* 用于集成由C、C++、Fortran等语言编写的代码的工具。\n",
    "\n",
    "除了为Python提供快速的数组处理能力，Numpy在数据分析方面还有另外一个主要作用，\n",
    "即作为算法之间传递数据的容器。对于数值型数据，Numpy数组在存储和处理数据时要比\n",
    "内置的Python数据结构高效得多。此外，由低级语言（比如C和Fortran）编写的库可以\n",
    "直接操作Numpy数组中的数据，无需进行任何数据复制工作。 \n",
    "\n",
    "## Import numpy library as np\n",
    "\n",
    "这种导入方式对于编写代码有帮助，在科学计算领域几乎成为一种标准写法。"
   ]
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   "source": [
    "import numpy as np"
   ]
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   "source": [
    "## **ndarray** ：一种多维数组对象\n",
    "\n",
    "NumPy最重要的一个特点就是N维数组对象—— **ndarray** （整个库的核心对象），\n",
    "该对象是一个快速而灵活的大数据集容器，可以用它高效地存储大量的数值元素，\n",
    "提高数组计算的运算速度，还能用它与各种扩展库进行数据交换。\n",
    "\n",
    "可以利用ndarray对整块数据执行一些数学运算，其语法跟标量元素之间的运算一样。 "
   ]
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   "source": [
    "data_set = np.random.random((2, 4))\n",
    "data_set"
   ]
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   "outputs": [],
   "source": [
    "data_set * 10"
   ]
  },
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   "outputs": [],
   "source": [
    "data_set + data_set"
   ]
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   "source": [
    "ndarray是一个通用的同构数据多维容器，**其中的所有元素必须是相同类型的**。\n",
    "\n",
    "每个数组都有一个**shape**（一个表示各维度大小的元组）和\n",
    "一个**dtype**（一个用于说明数组数据类型的对象）属性。"
   ]
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   "source": [
    "print(data_set.shape)  # (2, 4)\n",
    "print(data_set.dtype)  # float64"
   ]
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   "source": [
    "可以通过修改数组的shape属性，在保持数组元素个数不变的情况下，改变数组每个维度的大小。 "
   ]
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   "source": [
    "data_set.shape = (4, 2)\n",
    "data_set"
   ]
  },
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   "source": [
    "⚠️️ 只是改变每个轴的大小，数组元素在内存中的位置没有改变。\n",
    "\n",
    "当设置某个轴的元素个数为 **-1** 时，将自动计算次此此轴的长度。 "
   ]
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   "source": [
    "data_set.shape = (3, -1)\n",
    "data_set"
   ]
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   "source": [
    "如果改变shape失败，会报`ValueError`错误。 "
   ]
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   "source": [
    "## ndarray的数据类型\n",
    "\n",
    "**dtype** 是一个特殊的对象，它含有ndarray将一块内存解释为特定数据类型所需的信息。\n",
    "多数情况下，它们直接映射到相应的机器表示，使得“读写磁盘上的二进制数据流”以及\n",
    "“集成低级语言代码（如C、Fortran）”等工作变得更加简单。\n",
    "\n",
    "**数值型dtype的命名方式：一个类型名（如float），后面跟一个用于表示各元素位长的数字。**\n",
    "标准的双精度浮点值（即Python中的float对象）需要占用8字节（即64位）。\n",
    "因此，该类型在NumPy中就计作float64。\n",
    "\n",
    "通常只需知道所处理的数据的大致类型是浮点数、复数、整数、布尔值、字符串还是普通\n",
    "的Python对象即可。当你需要控制数据在内存和磁盘中的存储方式时（尤其是大数据集），\n",
    "就得了解如何控制存储类型。\n",
    "\n",
    "可以通过ndarray的`astype`方法显式地转换其dtype： "
   ]
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   "source": [
    "arr = np.array([1, 2, 3])\n",
    "arr.dtype"
   ]
  },
  {
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   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "print(float_arr)\n",
    "float_arr.dtype"
   ]
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   "source": [
    "如果将浮点数转换成整数，则小数部分将会被截断。\n",
    "\n",
    "如果某字符串数组表示的全是数字，可以用`astype`将其转换为数值形式："
   ]
  },
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   "source": [
    "numeric_strings = np.array(['1.25', '-1.5', '40'], dtype=np.string_)\n",
    "numeric_strings.astype(float)"
   ]
  },
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   "source": [
    "传递给`dtype`参数的都是类型（type）对象，如果转换失败，就会引发一个`ValueError`。\n",
    "\n",
    "需要指定dtype参数时，也可以传递一个字符串来表示元素的数值类型。\n",
    "NumPy中每个数值类型都有几种字符串表示方式，字符串和类型之间的对应关系\n",
    "都存在`typeDict`字典中。\n",
    "\n",
    "获得与float64类型（与Python内置的float类型相同）对应的所有键值： "
   ]
  },
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   "outputs": [],
   "source": [
    "[key for key, value in np.typeDict.items() if value is np.float64]"
   ]
  },
  {
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   },
   "source": [
    "用简洁的类型代码来表示dtype："
   ]
  },
  {
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   "outputs": [],
   "source": [
    "empty_uint32 = np.empty(8, dtype='u4')\n",
    "empty_uint32.dtype"
   ]
  },
  {
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   },
   "source": [
    "完整的类型列表可以通过下面的语句得到，将`np.typeDict`字典中所有的值转换为一个集合："
   ]
  },
  {
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   "outputs": [],
   "source": [
    "set(np.typeDict.values())"
   ]
  },
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   },
   "source": [
    "上面显示的数值类型与数组的dtype属性是不同的对象。\n",
    "通过dtype对象的`type`属性可以获得与其对应的数值类型："
   ]
  },
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   "outputs": [],
   "source": [
    "data_set.dtype.type"
   ]
  },
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   "source": [
    "通过NumPy的数值类型也可创建数值对象："
   ]
  },
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   "outputs": [],
   "source": [
    "a = np.int16(200)\n",
    "a * a"
   ]
  },
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   "source": [
    "⚠️️ NumPy的数值对象的运算速度比Python的内置类型的运算速度慢很多，\n",
    "如果程序中需要大量地对单个数值运算，应当尽量避免使用NumPy的数值对象。"
   ]
  },
  {
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   "source": [
    "v1 = 3.14\n",
    "v2 = np.float64(v1)\n",
    "\n",
    "%timeit v1*v1\n",
    "%timeit v2*v2"
   ]
  },
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   "source": [
    "⚠️️ 浮点数只能表示近似的分数值。在复杂计算中，由于可能会积累一些浮点错误，\n",
    "因此比较操作只能在一定小数位以内有效。 "
   ]
  },
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   "source": [
    "## 检查ndarray"
   ]
  },
  {
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   },
   "outputs": [],
   "source": [
    "ds = np.arange(1, 10, 2)\n",
    "ds"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "ds.ndim"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "ds.shape"
   ]
  },
  {
   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "ds.dtype"
   ]
  },
  {
   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "ds.itemsize"
   ]
  },
  {
   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "x = ds.data\n",
    "list(x)"
   ]
  },
  {
   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "ds"
   ]
  },
  {
   "cell_type": "code",
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   "outputs": [],
   "source": [
    "# Memory Usage\n",
    "ds.size * ds.itemsize"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## 创建ndarray"
   ]
  },
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   },
   "source": [
    "**array(object, dtype=None, copy=True, order='K', subok=False, ndmin=0)**"
   ]
  },
  {
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   "source": [
    "np.array?"
   ]
  },
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   "outputs": [],
   "source": [
    "data_1 = [6, 7.5, 8, 0, 1]\n",
    "array_1 = np.array(data_1)\n",
    "array_1"
   ]
  },
  {
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   },
   "source": [
    "嵌套序列（比如由一组等长列表组成的列表）将会被转换为一个多维数组："
   ]
  },
  {
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   "outputs": [],
   "source": [
    "data_2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "array_2 = np.array(data_2)\n",
    "array_2"
   ]
  },
  {
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   },
   "source": [
    "除非显式说明，`np.array` 会尝试为新建的这个数组推断出一个较为合适的数据类型。\n",
    "数据类型保存在一个特殊的**dtype**对象中。"
   ]
  },
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     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "array_1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "array_2.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### 新建数组的函数\n",
    "\n",
    "创建指定形状和类型的数组：\n",
    "\n",
    "**zeros(shape, dtype=float, order='C')**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.zeros((2, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**np.ones(shape, dtype=None, order='C')**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.ones((2, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**empty(shape, dtype=float, order='C')**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.empty((2, 3, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "`np.empty`创建的数组中都是一些未初始化的垃圾值。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Python内置函数range的数组版：\n",
    "\n",
    "**arange([start,] stop[, step,], dtype=None)**\n",
    "\n",
    "Python内置函数**range**的数组版："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "list(range(1, 10, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.arange(1, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.arange(1, 10, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.arange(1, 10, 2, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "如果没有特别制定，创建的数组其数据类型都是**float64**(浮点数)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Most Common Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Multi dimensional array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**np.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.linspace(1, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.linspace(0, 2, num=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.linspace(0, 2, num=4, endpoint=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**np.random.random_sample(size=None)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.random.random((2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.random.random_sample((2, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### 统计分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set = np.random.random((2, 3))\n",
    "data_set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**np.max(a, axis=None, out=None, keepdims=<class 'numpy._globals._NoValue'>)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.max(data_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.max(data_set, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.max(data_set, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**np.min(a, axis=None, out=None, keepdims=<class 'numpy._globals._NoValue'>)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.min(data_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**mean(a, axis=None, dtype=None, out=None, keepdims=<class 'numpy._globals._NoValue'>)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.mean(data_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.sum(data_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.reshape(data_set, (3, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.reshape(data_set, (6, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.reshape(data_set, (6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.ravel?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "np.ravel(data_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## 基本的索引和切片"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "一维数组表面上看和Python列表的功能差不多："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[2:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[2:5] = 11\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "将一个标量值赋值给一个切片时，该值会自动传播到整个选区。\n",
    "\n",
    "**跟列表最重要的区别在于，数组切片是原始数组的视图。**\n",
    "这意味着数据不会被复制，视图上的任何修改都会直接反映到源数组上。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice[1] = 12345\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr_slice[:]=64\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**如果你想要得到的是ndarray切片的一份副本而非视图，需要显式地进行复制操作，例如：arr[5:8].copy()。**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[5:8].copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "对于高维数组，能做的事情更多。在一个二维数组中，各索引位置上的元素不再是标量而是一维数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "因此，可以对各个元素进行递归访问。另外，你可以传入一个以逗号隔开的索引列表来选取单个元素。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d[1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d[1, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "在多维数组中，如果省略了后面的索引，则返回对象会是一个维度低一点的ndarray\n",
    "（即返回的低维数组含有原始高维数组某条轴上的所有数据。\n",
    "括号外面的“维度”是一维、二维、三维、四维之类的意思，而括号里面的应该理解为“轴”。）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "data_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[1, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### 高维数组的切片索引\n",
    "\n",
    "可以在一个或多个轴上进行切片，也可以跟整数索引混合使用。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "可以看出，其是沿着第0轴（第一个轴）切片的，即切片是沿着一个轴向选取元素的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set = np.random.random((5, 10))\n",
    "data_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[2:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "可以一次传入多个切片，就像传入多个索引那样："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[2:4, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[2:4, 0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "“只有冒号”表示选取整个轴，因此可以这样对高维轴进行切片："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[:, :2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### Stepping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[2:4:1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[::]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_set[2:4, ::2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### 花式索引（Fancy indexing）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "指的是利用整数数组进行索引。假设有一个 8 * 4 数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr = np.empty((8, 4))\n",
    "for i in range(8):\n",
    "    arr[i] = i\n",
    "\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "为了以特定顺序选取行子集，只需传入一个用于指定顺序的整数列表或ndarray即可："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[[4, 3, 0, 6]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "使用负数索引将会从末尾开始选取行："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[[-3, -5, -7]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "一次传入多个索引数组会有一点特别。它返回的是一个一维数组，其中的元素对应各个索引元组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[[1, 5, 7, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "最终选出的是元素(1, 0)、(5, 3)、(7, 1)和(2, 2)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "花式索引跟切片不一样，它总是将数据复制到新数组中。"
   ]
  }
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