{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##内容索引\n",
    "1. 计算股票收益率----\n",
    "diff做差分、std求标准差、where函数返回满足条件的数组索引\n",
    "\n",
    "2. 日期分析例子----\n",
    "载入文件对日期的处理、where和take函数、argmax和argmin函数\n",
    "\n",
    "3. 周汇总例子----\n",
    "apply_along_axis函数会调用一个自定义函数，作用于每一个数组元素上\n",
    "\n",
    "4. 线性模型预测价格----\n",
    "linalg.lstsq函数\n",
    "\n",
    "5. 绘制趋势线例子----\n",
    "\n",
    "6. ndarray补充----\n",
    "clip函数，修剪；\n",
    "compress函数，压缩；\n",
    "prod函数，相乘；\n",
    "cumprod函数，累积乘积。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上一小节，介绍了numpy中读取数据，计算均值方差，最大最小值等基本操作。这一节中，我将继续学习numpy常用函数，用来做更加深入的股票分析。\n",
    "这里股票分析只是一个例子，不必在意概念细节，只是针对现有的数据来熟悉numpy的操作。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##1. 股票收益率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "简单收益率是指相邻两个价格之间的变化率，而对数收益率是指所有价格取对数后两两之间的差值。由于对数收益率是两两价格相除再去对数，所以其**可以用来衡量价格收益率。**\n",
    "\n",
    "投资者最感兴趣的是收益率的方差或标准差，这代表了投资风险的大小。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###1.1 计算简单收益率\n",
    "diff函数计算离散差分，计算收益率，需要用差值除以前一天的价格。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#cp means closing price\n",
    "cp = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)\n",
    "cp_diff = np.diff(cp)\n",
    "rate_of_returns = cp_diff / cp[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 336.1 ,  339.32,  345.03,  344.32,  343.44,  346.5 ,  351.88,\n",
       "        355.2 ,  358.16,  354.54,  356.85,  359.18,  359.9 ,  363.13,\n",
       "        358.3 ,  350.56,  338.61,  342.62,  342.88,  348.16,  353.21,\n",
       "        349.31,  352.12,  359.56,  360.  ,  355.36,  355.76,  352.47,\n",
       "        346.67,  351.99])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 336.1 ,  339.32,  345.03,  344.32,  343.44,  346.5 ,  351.88,\n",
       "        355.2 ,  358.16,  354.54,  356.85,  359.18,  359.9 ,  363.13,\n",
       "        358.3 ,  350.56,  338.61,  342.62,  342.88,  348.16,  353.21,\n",
       "        349.31,  352.12,  359.56,  360.  ,  355.36,  355.76,  352.47,\n",
       "        346.67])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#去掉最后一个\n",
    "#从开始到倒数第二个\n",
    "cp[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00958048,  0.01682777, -0.00205779, -0.00255576,  0.00890985,\n",
       "        0.0155267 ,  0.00943503,  0.00833333, -0.01010721,  0.00651548,\n",
       "        0.00652935,  0.00200457,  0.00897472, -0.01330102, -0.02160201,\n",
       "       -0.03408832,  0.01184253,  0.00075886,  0.01539897,  0.01450483,\n",
       "       -0.01104159,  0.00804443,  0.02112916,  0.00122372, -0.01288889,\n",
       "        0.00112562, -0.00924781, -0.0164553 ,  0.01534601])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rate_of_returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation =  0.0129221344368\n"
     ]
    }
   ],
   "source": [
    "print \"standard deviation = \", np.std(rate_of_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###1.2 对数收益率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "取对数要注意事先检查数据中不包含0和负值，确保输入满足定义域条件"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "log_rate_of_returns = np.diff(np.log(cp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00953488,  0.01668775, -0.00205991, -0.00255903,  0.00887039,\n",
       "        0.01540739,  0.0093908 ,  0.0082988 , -0.01015864,  0.00649435,\n",
       "        0.00650813,  0.00200256,  0.00893468, -0.01339027, -0.02183875,\n",
       "       -0.03468287,  0.01177296,  0.00075857,  0.01528161,  0.01440064,\n",
       "       -0.011103  ,  0.00801225,  0.02090904,  0.00122297, -0.01297267,\n",
       "        0.00112499, -0.00929083, -0.01659219,  0.01522945])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_rate_of_returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得到收益率为正的情况，where函数可以根据制定条件返回数组的索引值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Indices with positive returns (array([ 0,  1,  4,  5,  6,  7,  9, 10, 11, 12, 16, 17, 18, 19, 21, 22, 23,\n",
      "       25, 28]),)\n"
     ]
    }
   ],
   "source": [
    "pos_return_indices = np.where(log_rate_of_returns > 0)\n",
    "print 'Indices with positive returns', pos_return_indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###1.3 计算波动率\n",
    "波动率volatility是对价格变动的一种度量。**年波动率等于对数收益率的标准差除以其均值，在除以交易日倒数的平方根，通常交易日去252天。**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "129.274789911\n"
     ]
    }
   ],
   "source": [
    "annual_volatility = np.std(log_rate_of_returns) / np.mean(log_rate_of_returns)\n",
    "annual_volatility = annual_volatility / np.sqrt(1. / 252.)\n",
    "print annual_volatility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sqrt函数中的除法运算必须使用浮点数才能得到正确结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monthly volatility 37.3184173773\n"
     ]
    }
   ],
   "source": [
    "print \"Monthly volatility\", annual_volatility * np.sqrt(1. / 12.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##2. 日期分析\n",
    "我们读入收盘价数据，根据星期几来切分数据，计算平均价格，最后找出一周的那一天的平均收盘价最高"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Numpy是面向浮点数运算的，对日期处理需要专门的方法**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "loadtxt函数中有一个特定的参数converters，这是数据列到转换函数之间映射的字典。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#convert funtion\n",
    "import datetime\n",
    "def datestr2num(s):\n",
    "    return datetime.datetime.strptime(s, \"%d-%m-%Y\").date().weekday()\n",
    "\n",
    "#字符串首先会按照指定形式\"%d-%m-%Y\"转换成一个datetime对象，随后datetime对象被转换成date对象，最后调用weekday方法返回一个数字\n",
    "#0代表星期一，6代表星期天"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dates =  [ 4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.  1.  2.\n",
      "  3.  4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.]\n"
     ]
    }
   ],
   "source": [
    "#cp means closing price\n",
    "dates, cp = np.loadtxt('data.csv', delimiter=',', usecols=(1,6), converters={1:datestr2num}, unpack=True)\n",
    "print \"Dates = \", dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#保存各工作日的平均收盘价\n",
    "averages = np.zeros(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**where函数会根据指定的条件返回所有满足条件的数组元素的索引值；take函数根据这些索引值从数组中取出相应的元素。**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Day 0 prices [[ 339.32  351.88  359.18  353.21  355.36]] Average 351.79\n",
      "Day 1 prices [[ 345.03  355.2   359.9   338.61  349.31  355.76]] Average 350.635\n",
      "Day 2 prices [[ 344.32  358.16  363.13  342.62  352.12  352.47]] Average 352.136666667\n",
      "Day 3 prices [[ 343.44  354.54  358.3   342.88  359.56  346.67]] Average 350.898333333\n",
      "Day 4 prices [[ 336.1   346.5   356.85  350.56  348.16  360.    351.99]] Average 350.022857143\n"
     ]
    }
   ],
   "source": [
    "for i in xrange(5):\n",
    "    indices = np.where(dates == i)\n",
    "    prices = np.take(cp, indices)\n",
    "    avg = prices.mean()\n",
    "    print \"Day\", i, \"prices\", prices, \"Average\", avg\n",
    "    averages[i] = avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Highest average 352.136666667\n",
      "Top day of the week 2\n",
      "Lowest average 350.022857143\n",
      "Bottom day of the week 4\n"
     ]
    }
   ],
   "source": [
    "#找出哪个工作日的平均收盘价最高，哪个最低\n",
    "top = averages.max()\n",
    "bottom = averages.min()\n",
    "print \"Highest average\", top\n",
    "print \"Top day of the week\", np.argmax(averages)\n",
    "print \"Lowest average\", bottom\n",
    "print \"Bottom day of the week\", np.argmin(averages)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**argmin函数返回的是averages数组中最小元素的索引值，argmax同理**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##3. 周汇总"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first Monday index is  1\n"
     ]
    }
   ],
   "source": [
    "dates, op, hp, lp, cp = np.loadtxt('data.csv', delimiter=',', usecols=(1,3,4,5,6), converters={1: datestr2num}, unpack=True)\n",
    "cp = cp[:16]\n",
    "dates = dates[:16]\n",
    "#找到第一个星期一\n",
    "first_monday = np.ravel(np.where(dates == 0))[0]\n",
    "print \"The first Monday index is \",first_monday"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The last Friday index is  15\n"
     ]
    }
   ],
   "source": [
    "#找到最后一个周五\n",
    "last_friday = np.ravel(np.where(dates == 4))[-1]\n",
    "print \"The last Friday index is \", last_friday"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weeks indices initial  [ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15]\n"
     ]
    }
   ],
   "source": [
    "#存储三周每一天的索引值\n",
    "weeks_indices = np.arange(first_monday, last_friday+1)\n",
    "print \"Weeks indices initial \",weeks_indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weeks indices after split  [array([1, 2, 3, 4, 5]), array([ 6,  7,  8,  9, 10]), array([11, 12, 13, 14, 15])]\n"
     ]
    }
   ],
   "source": [
    "#切分数组，每5个元素一个子数组\n",
    "weeks_indices = np.split(weeks_indices, 3)\n",
    "print \"Weeks indices after split \", weeks_indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**apply_along_axis函数会调用一个自定义函数，作用于每一个数组元素上。**在调用apply_along_axis时提供我们自定义的函数summarize，并指定要作用的轴或维度的编号以及函数的参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#这里indices是三个array\n",
    "def summarize(indices, open, high, low, close):\n",
    "    monday_open = open[indices[0]]\n",
    "    week_high = np.max(np.take(high, indices))\n",
    "    week_low = np.min(np.take(low, indices))\n",
    "    friday_close = close[indices[-1]]\n",
    "    return (\"APPL\", monday_open, week_high, week_low, friday_close)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Week summary [['APPL' '335.8' '346.7' '334.3' '346.5']\n",
      " ['APPL' '347.8' '360.0' '347.6' '356.8']\n",
      " ['APPL' '356.7' '364.9' '349.5' '350.5']]\n"
     ]
    }
   ],
   "source": [
    "#这里参数1，代表作用于每一行，一共三行，得到三行结果\n",
    "#相当于axis为1的时候进行计算\n",
    "week_summary = np.apply_along_axis(summarize, 1, weeks_indices, op, hp, lp, cp)\n",
    "print \"Week summary\", week_summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##4. 用线性模型预测价格\n",
    "NumPy的linalg包是专门用于线性代数计算的，我们可以根据N个之前的价格利用线性模型进行预测计算。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " 我们假设，一个股价可以用之前股价的线性组合表示出来，即，这个股价等于之前股价的加权和的结果。用线性代数的角度，这是解一个最小二乘法的问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 355.36  355.76  352.47  346.67  351.99]\n",
      "[ 351.99  346.67  352.47  355.76  355.36]\n"
     ]
    }
   ],
   "source": [
    "#1. 获得N个股价的向量b\n",
    "cp = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)\n",
    "N = 5\n",
    "#从倒数第N个数据取到最后\n",
    "b = cp[-N:]\n",
    "print b\n",
    "#翻转数组，越前面数据，日期越新\n",
    "b = b[::-1]\n",
    "print b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zeros N by N\n",
      "[[ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "#2. 初始N*N的二维数组A\n",
    "A = np.zeros((N,N), float)\n",
    "print \"Zeros N by N\\n\", A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      "[[ 360.    355.36  355.76  352.47  346.67]\n",
      " [ 359.56  360.    355.36  355.76  352.47]\n",
      " [ 352.12  359.56  360.    355.36  355.76]\n",
      " [ 349.31  352.12  359.56  360.    355.36]\n",
      " [ 353.21  349.31  352.12  359.56  360.  ]]\n"
     ]
    }
   ],
   "source": [
    "#3. 用b向量的N个股价值填充数组A\n",
    "for i in range(N):\n",
    "    A[i,] = cp[-N-1-i : -1-i]\n",
    "    \n",
    "print \"A:\\n\", A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x:\n",
      "[ 0.78111069 -1.44411737  1.63563225 -0.89905126  0.92009049]\n",
      "residuals:\n",
      "[]\n",
      "rank:\n",
      "5\n",
      "s:\n",
      "[  1.77736601e+03   1.49622969e+01   8.75528492e+00   5.15099261e+00\n",
      "   1.75199608e+00]\n"
     ]
    }
   ],
   "source": [
    "#4. 使用linalg中的lstsq来解决最小平方和的问题\n",
    "(x, residuals, rank, s) = np.linalg.lstsq(A, b)\n",
    "print 'x:\\n', x\n",
    "print 'residuals:\\n', residuals\n",
    "print 'rank:\\n', rank\n",
    "print 's:\\n', s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**返回的元组中包含稍后要用到的系数向量x，一个残差数组，A的秩以及A的奇异值**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "357.939161015\n"
     ]
    }
   ],
   "source": [
    "#5. 使用numpy中的dot函数计算系数向量与最近N个价格构成的向量的点积\n",
    "print np.dot(b, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##5. 绘制趋势线\n",
    "趋势线，是根据股价走势图上很多所谓的枢轴点绘成的曲线，即描绘的是价格变化的趋势。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot\n",
    "from matplotlib.pyplot import show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pivots:\n",
      "[ 338.01        337.88666667  343.88666667  344.37333333  342.07666667\n",
      "  345.57        350.92333333  354.29        357.34333333  354.18\n",
      "  356.06333333  358.45666667  359.14        362.84333333  358.36333333\n",
      "  353.19333333  340.57666667  341.95666667  342.13333333  347.13\n",
      "  353.12666667  350.90333333  351.62333333  358.42333333  359.34666667\n",
      "  356.11333333  355.13666667  352.61        347.11333333  349.77      ]\n"
     ]
    }
   ],
   "source": [
    "#我们假设枢轴点的位置是最高价、最低价、收盘价的均值\n",
    "hp, lp, cp = np.loadtxt('data.csv', delimiter=',', usecols=(4,5,6), unpack=True)\n",
    "pivots = (hp+lp+cp) / 3\n",
    "print \"Pivots:\\n\", pivots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从枢轴点出发，我们可以推导出阻力位和支撑位。\n",
    "> 阻力位是指股价上升时遇到阻力，在转秩前的最高价格\n",
    "\n",
    "> 支撑位是股价下跌时遇到支撑，在反弹前的最低价格\n",
    "\n",
    "他们都是估计量，根据这些估计量，我们可以绘制阻力位和支撑位的趋势线。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#定义直线方程为y = Ax，其中A=[t 1],x=[a b]\n",
    "#展开就是y = at + b\n",
    "def fit_line(t, y):\n",
    "    #vstack垂直组合\n",
    "    A = np.vstack([t, np.ones_like(t)]).T\n",
    "    return np.linalg.lstsq(A, y)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#假设支撑位在枢轴点下方的位置\n",
    "#阻力点在枢轴点上方的一个位置\n",
    "t = np.arange(len(cp))\n",
    "sa, sb = fit_line(t, pivots-(hp-lp))\n",
    "ra, rb = fit_line(t, pivots+(hp-lp))\n",
    "support = sa*t + sb\n",
    "resistance = ra*t + rb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Conditions:\n",
      "[False False  True  True  True  True  True False False  True False False\n",
      " False False False  True False False False  True  True  True  True False\n",
      " False  True  True  True False  True]\n",
      "(array([ 2,  3,  4,  5,  6,  9, 15, 19, 20, 21, 22, 25, 26, 27, 29]),)\n",
      "[ 2  3  4  5  6  9 15 19 20 21 22 25 26 27 29]\n"
     ]
    }
   ],
   "source": [
    "#设置一个判断数据点是否在趋势线之间的条件\n",
    "condition = (cp > support) & (cp < resistance)\n",
    "print \"Conditions:\\n\", condition\n",
    "between_bands = np.where(condition)\n",
    "print between_bands\n",
    "print np.ravel(between_bands)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 341.92421382  342.19081893  342.45742405  342.72402917  342.99063429\n",
      "  343.79044964  345.39008034  346.4565008   346.72310592  346.98971104\n",
      "  347.25631615  348.0561315   348.32273662  348.58934174  349.12255197]\n",
      "[ 345.03  344.32  343.44  346.5   351.88  354.54  350.56  348.16  353.21\n",
      "  349.31  352.12  355.36  355.76  352.47  351.99]\n",
      "[ 352.61688271  352.90732765  353.19777259  353.48821753  353.77866246\n",
      "  354.64999728  356.39266691  357.55444667  357.84489161  358.13533655\n",
      "  358.42578149  359.2971163   359.58756124  359.87800618  360.45889606]\n"
     ]
    }
   ],
   "source": [
    "#复查取值\n",
    "print support[between_bands]\n",
    "print cp[between_bands]\n",
    "print resistance[between_bands]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x50498d0>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dNRTMcRJQ18UNTi1EAnVi7rCH89WSiL2BQCeHQyV621YNMxFbJFakg+WAccAW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\nPdMRqTGgF+LCTY6TM3oBtHo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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4f42f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(t, cp)\n",
    "plot(t, support)\n",
    "plot(t, resistance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number points between bands:  15\n",
      "Ratio between bands:  0.5\n"
     ]
    }
   ],
   "source": [
    "n_betweens_band = len(np.ravel(between_bands))\n",
    "print \"Number points between bands: \", n_betweens_band\n",
    "print \"Ratio between bands: \", float(n_betweens_band)/len(cp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of points between band2 2nd approach:  15\n"
     ]
    }
   ],
   "source": [
    "#提供另外一种计算支撑位和阻力位之间数据点个数的方法\n",
    "# []操作符定义选择条件\n",
    "# intersect1d计算两者相交的结果\n",
    "a1 = cp[cp > support]\n",
    "a2 = cp[cp < resistance]\n",
    "print \"Number of points between band2 2nd approach: \", len(np.intersect1d(a1, a2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##补充： ndarray对象的几种方法\n",
    "> clip，修剪\n",
    "\n",
    "> compress，压缩\n",
    "\n",
    "> prod，相乘\n",
    "\n",
    "> cumprod，累积乘积"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  [0 1 2 3 4]\n",
      "Clipped: [1 1 2 3 3]\n"
     ]
    }
   ],
   "source": [
    "#clip方法\n",
    "#将所有比给定最大值还大的元素全部设为给定最大值\n",
    "#将所有比给定最小值还小的元素全部设为最小值\n",
    "a = np.arange(5)\n",
    "print \"a = \",a\n",
    "print \"Clipped:\", a.clip(1,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4]\n",
      "Compressed:  [3 4]\n"
     ]
    }
   ],
   "source": [
    "#compress方法\n",
    "#返回一个根据给定条件筛选后的数组\n",
    "a = np.arange(5)\n",
    "print a\n",
    "print \"Compressed: \", a.compress(a > 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b =  [1 2 3 4 5]\n",
      "factorial:  120\n"
     ]
    }
   ],
   "source": [
    "# prod方法计算数组中所有元素的乘积\n",
    "# 这种方法可以计算阶乘 factorial\n",
    "b = np.arange(1,6)\n",
    "print  \"b = \", b\n",
    "print \"factorial: \", b.prod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "factorials array:  [  1   2   6  24 120]\n"
     ]
    }
   ],
   "source": [
    "# cumprod方法，计算数组元素的累积乘积\n",
    "print \"factorials array: \", b.cumprod()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.5"
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 },
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