{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 一般函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 三角函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    sin(x)\n",
    "    cos(x)\n",
    "    tan(x)\n",
    "    sinh(x)\n",
    "    conh(x)\n",
    "    tanh(x)\n",
    "    arccos(x)\n",
    "    arctan(x)\n",
    "    arcsin(x)\n",
    "    arccosh(x)\n",
    "    arctanh(x)\n",
    "    arcsinh(x)\n",
    "    arctan2(x,y)\n",
    "\n",
    "`arctan2(x,y)` 返回 `arctan(x/y)` 。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 向量操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    dot(x,y)\n",
    "    inner(x,y)\n",
    "    cross(x,y)\n",
    "    vdot(x,y)\n",
    "    outer(x,y)\n",
    "    kron(x,y)\n",
    "    tensordot(x,y[,axis])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 其他操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    exp(x)\n",
    "    log(x)\n",
    "    log10(x)\n",
    "    sqrt(x)\n",
    "    absolute(x)\n",
    "    conjugate(x)\n",
    "    negative(x)\n",
    "    ceil(x)\n",
    "    floor(x)\n",
    "    fabs(x)\n",
    "    hypot(x)\n",
    "    fmod(x)\n",
    "    maximum(x,y)\n",
    "    minimum(x,y)\n",
    "\n",
    "`hypot` 返回对应点 `(x,y)` 到原点的距离。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.12310563,  5.38516481,  6.70820393])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1,2,3])\n",
    "y = np.array([4,5,6])\n",
    "np.hypot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 类型处理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    iscomplexobj\n",
    "    iscomplex\n",
    "    isrealobj\n",
    "    isreal\n",
    "    imag\n",
    "    real\n",
    "    real_if_close\n",
    "    isscalar\n",
    "    isneginf\n",
    "    isposinf\n",
    "    isinf\n",
    "    isfinite\n",
    "    isnan\n",
    "    nan_to_num\n",
    "    common_type\n",
    "    typename\n",
    "\n",
    "正无穷："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.inf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "负无穷："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-inf"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-np.inf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "非法值（Not a number）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.nan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "检查是否为无穷："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isinf(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isinf(np.inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isinf(-np.inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "非法值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Miniconda\\lib\\site-packages\\IPython\\kernel\\__main__.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ nan])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([0]) / 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这并不会报错，而是返回一个非法值。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "只有 `0/0` 会得到 `nan`，非0值除以0会得到无穷："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Miniconda\\lib\\site-packages\\IPython\\kernel\\__main__.py:2: RuntimeWarning: divide by zero encountered in divide\n",
      "  from IPython.kernel.zmq import kernelapp as app\n",
      "c:\\Miniconda\\lib\\site-packages\\IPython\\kernel\\__main__.py:2: RuntimeWarning: invalid value encountered in divide\n",
      "  from IPython.kernel.zmq import kernelapp as app\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ nan,  inf,  inf,  inf,  inf])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(5.0)\n",
    "b = a / 0.0\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`nan` 与任何数进行比较都是 `False`："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b == np.nan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "想要找出 `nan` 值需要使用 `isnan`："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isnan(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 修改形状"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    atleast_1d\n",
    "    atleast_2d\n",
    "    atleast_3d\n",
    "    expand_dims\n",
    "    apply_over_axes\n",
    "    apply_along_axis\n",
    "    hstack\n",
    "    vstack\n",
    "    dstack\n",
    "    column_stack\n",
    "    hsplit\n",
    "    vsplit\n",
    "    dsplit\n",
    "    split\n",
    "    squeeze"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 其他有用函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    fix\n",
    "    mod\n",
    "    amax\n",
    "    amin\n",
    "    ptp\n",
    "    sum\n",
    "    cumsum\n",
    "    prod\n",
    "    cumprod\n",
    "    diff\n",
    "    angle\n",
    "\n",
    "    unwrap\n",
    "    sort_complex\n",
    "    trim_zeros\n",
    "    fliplr\n",
    "    flipud\n",
    "    rot90\n",
    "    diag\n",
    "    eye\n",
    "    select\n",
    "    extract\n",
    "    insert\n",
    "\n",
    "    roots\n",
    "    poly\n",
    "    any\n",
    "    all\n",
    "    disp\n",
    "    unique\n",
    "    nansum\n",
    "    nanmax\n",
    "    nanargmax\n",
    "    nanargmin\n",
    "    nanmin\n",
    "\n",
    "`nan` 开头的函数会进行相应的操作，但是忽略 `nan` 值。"
   ]
  }
 ],
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