{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##断言函数\n",
    "**单元测试通常使用断言函数作为测试的组成部分。**在进行数值计算时，我们经常遇到比较两个近似相等的浮点数这样的基本问题，由于计算机对浮点数的表示本身就不精确，所以浮点数的比较并不是那么简单。\n",
    "\n",
    "numpy.testing包中有很多实用的工具函数考虑了浮点数的比较，可以测试前提是否成立。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[NumPy的testing模块文档](http://docs.scipy.org/doc/numpy/reference/routines.testing.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##1. assert_almost_equal断言近似相等\n",
    "assert_almost_equal函数的作用是，如果两个数字的近似程度没有达到指定精度，就抛出异常。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decimal 6 None\n"
     ]
    }
   ],
   "source": [
    "#使用assert_almost_equal函数来检查它们是否近似相等\n",
    "\n",
    "#指定精度，小数点后7位\n",
    "print \"Decimal 6\", np.testing.assert_almost_equal(0.123456789, 0.123456780, decimal=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decimal 7"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not almost equal to 8 decimals\n ACTUAL: 0.123456789\n DESIRED: 0.12345678",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-4f17955884db>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m#指定精度，小数点后8位\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;31m#抛出异常\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Decimal 7\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.123456789\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.123456780\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m8\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_almost_equal\u001b[1;34m(actual, desired, decimal, err_msg, verbose)\u001b[0m\n\u001b[0;32m    488\u001b[0m         \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    489\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdesired\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mactual\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 490\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_build_err_msg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    491\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    492\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not almost equal to 8 decimals\n ACTUAL: 0.123456789\n DESIRED: 0.12345678"
     ]
    }
   ],
   "source": [
    "#指定精度，小数点后8位\n",
    "#抛出异常\n",
    "print \"Decimal 7\", np.testing.assert_almost_equal(0.123456789, 0.123456780, decimal=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##2. assert_approx_equal断言近似相等\n",
    "如果两个数字的近似程度没有达到指定的有效数字要求，assert_approx_equal函数就抛出异常。\n",
    "\n",
    "触发条件为：abs(actual-expected) >= 10**(significant-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Significance 8 None\n"
     ]
    }
   ],
   "source": [
    "# 指定8位有效数字\n",
    "print \"Significance 8\", np.testing.assert_approx_equal(0.123456789,0.123456780, significant=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Significance 9"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\nItems are not equal to 9 significant digits:\n ACTUAL: 0.123456789\n DESIRED: 0.12345678",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-ad87d6f32eb2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# 指定9位有效数字\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;31m# 抛出异常\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Significance 9\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_approx_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.123456789\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.123456780\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msignificant\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m9\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_approx_equal\u001b[1;34m(actual, desired, significant, err_msg, verbose)\u001b[0m\n\u001b[0;32m    585\u001b[0m         \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    586\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msc_desired\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0msc_actual\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpower\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m10.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msignificant\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 587\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    588\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    589\u001b[0m def assert_array_compare(comparison, x, y, err_msg='', verbose=True,\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nItems are not equal to 9 significant digits:\n ACTUAL: 0.123456789\n DESIRED: 0.12345678"
     ]
    }
   ],
   "source": [
    "# 指定9位有效数字\n",
    "# 抛出异常\n",
    "print \"Significance 9\", np.testing.assert_approx_equal(0.123456789,0.123456780, significant=9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##3. assert_array_almost_equal断言数组近似相等\n",
    "如果两个数组中元素的近似程度没有达到指定的精度要求，assert_array_almost_equal函数将抛出异常。\n",
    "\n",
    "触发条件为： |expected - actual| < 0.5 * 10^(-decimal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Decimal 8 None\n"
     ]
    }
   ],
   "source": [
    "print \"Decimal 8\", np.testing.assert_array_almost_equal([0, 0.123456789], [0, 0.123456780], decimal=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decimal 9"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not almost equal to 9 decimals\n\n(mismatch 50.0%)\n x: array([ 0.         ,  0.123456789])\n y: array([ 0.        ,  0.12345678])",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-a30317f83231>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Decimal 9\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_array_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.123456789\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.123456780\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m9\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_array_almost_equal\u001b[1;34m(x, y, decimal, err_msg, verbose)\u001b[0m\n\u001b[0;32m    840\u001b[0m     assert_array_compare(compare, x, y, err_msg=err_msg, verbose=verbose,\n\u001b[0;32m    841\u001b[0m              \u001b[0mheader\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Arrays are not almost equal to %d decimals'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 842\u001b[1;33m              precision=decimal)\n\u001b[0m\u001b[0;32m    843\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    844\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_array_compare\u001b[1;34m(comparison, x, y, err_msg, verbose, header, precision)\u001b[0m\n\u001b[0;32m    663\u001b[0m                                 names=('x', 'y'), precision=precision)\n\u001b[0;32m    664\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mcond\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 665\u001b[1;33m                 \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    666\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    667\u001b[0m         \u001b[1;32mimport\u001b[0m \u001b[0mtraceback\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not almost equal to 9 decimals\n\n(mismatch 50.0%)\n x: array([ 0.         ,  0.123456789])\n y: array([ 0.        ,  0.12345678])"
     ]
    }
   ],
   "source": [
    "print \"Decimal 9\", np.testing.assert_array_almost_equal([0, 0.123456789], [0, 0.123456780], decimal=9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##4. assert_array_equal断言数组相等\n",
    "如果两个数组对象不相同，assert_array_equal函数将抛出异常。两个数组相等必须形状一致且元素也严格相等，允许数组存在NaN元素。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "比较数组也可以使用assert_allclose函数。该函数有参数atol(absolute tolerance,绝对容差限)和rtol(relative tolerance，相对容差限)。对于两个数组a和b，将测试是否满足以下条件：| a - b | <= (atol+rtol*b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Pass None\n"
     ]
    }
   ],
   "source": [
    "print \"Pass\", np.testing.assert_allclose([0,0.123456789,np.nan],[0,0.123456780,np.nan], rtol=1e-7,atol=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fail"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\nArrays are not equal\n\n(mismatch 50.0%)\n x: array([ 0.      ,  0.123457,       nan])\n y: array([ 0.      ,  0.123457,       nan])",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-9-c3f815d83f4e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Fail\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_array_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.123456789\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.123456780\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_array_equal\u001b[1;34m(x, y, err_msg, verbose)\u001b[0m\n\u001b[0;32m    737\u001b[0m     \"\"\"\n\u001b[0;32m    738\u001b[0m     assert_array_compare(operator.__eq__, x, y, err_msg=err_msg,\n\u001b[1;32m--> 739\u001b[1;33m                          verbose=verbose, header='Arrays are not equal')\n\u001b[0m\u001b[0;32m    740\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    741\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0massert_array_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0merr_msg\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m''\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_array_compare\u001b[1;34m(comparison, x, y, err_msg, verbose, header, precision)\u001b[0m\n\u001b[0;32m    663\u001b[0m                                 names=('x', 'y'), precision=precision)\n\u001b[0;32m    664\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mcond\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 665\u001b[1;33m                 \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    666\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    667\u001b[0m         \u001b[1;32mimport\u001b[0m \u001b[0mtraceback\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not equal\n\n(mismatch 50.0%)\n x: array([ 0.      ,  0.123457,       nan])\n y: array([ 0.      ,  0.123457,       nan])"
     ]
    }
   ],
   "source": [
    "print \"Fail\", np.testing.assert_array_equal([0,0.123456789,np.nan],[0,0.123456780,np.nan])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##5. 数组排序\n",
    "两个数组必须形状一致并且第一个数组元素严格小于第二个数组元素，否则assert_array_less函数将抛出异常。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Pass None\n"
     ]
    }
   ],
   "source": [
    "# assert_array_less函数比较两个有严格顺序的数组\n",
    "print \"Pass\", np.testing.assert_array_less([0,0.1,np.nan], [1,0.2,np.nan])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##6. assert_equal比较对象\n",
    "这里的对象不一定是NumPy数组对象，也可以是Python中的列表、元组或字典。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##7. assert_string_equal字符串比较\n",
    "assert_string_equal函数断言两个字符串变量完全相同。如果测试不通过，将会抛出异常并显示两个字符串之间的差别。该函数区分大小写，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fail"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "Differences in strings:\n- NumPy?    ^\n+ Numpy?    ^",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-11-c4c5684c99d0>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Fail\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_string_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"NumPy\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"Numpy\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_string_equal\u001b[1;34m(actual, desired)\u001b[0m\n\u001b[0;32m    981\u001b[0m     \u001b[0mmsg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m'Differences in strings:\\n%s'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;34m''\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdiff_list\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrstrip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    982\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mactual\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mdesired\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 983\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    984\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    985\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: Differences in strings:\n- NumPy?    ^\n+ Numpy?    ^"
     ]
    }
   ],
   "source": [
    "print \"Fail\", np.testing.assert_string_equal(\"NumPy\", \"Numpy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##8. 浮点数比较\n",
    "浮点数在计算机中是以不精确的方式表示的，这给浮点数的比较带来了问题。NumPy中的assert_array_almost_equal_nulp和assert_array_max_ulp函数可以提供可靠的浮点数比较功能。ULP是Unit of Least Precision的缩写，即浮点数的最小精度单位。根据IEEE 754标准，四则运算的误差必须保持在半个ULP之内。\n",
    "\n",
    "机器精度(machine epsilon)是指浮点运算中的相对舍入误差上界。机器精度等于ULP相对于1的值。NumPy的finfo函数可以获取机器精度。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Eps 2.22044604925e-16\n"
     ]
    }
   ],
   "source": [
    "# 使用finfo函数确定机器精度\n",
    "eps = np.finfo(float).eps\n",
    "print \"Eps\", eps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用assert_array_almost_equal_nulp函数比较两个近似相等的浮点数1.0和1.0+eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one eps None\n"
     ]
    }
   ],
   "source": [
    "print \"one eps\", np.testing.assert_array_almost_equal_nulp(1.0, 1.0+eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "two eps"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "X and Y are not equal to 1 ULP (max is 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-14-c3de8768b01e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"two eps\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_array_almost_equal_nulp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.0\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0meps\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32md:\\Python27_32\\lib\\site-packages\\numpy\\testing\\utils.pyc\u001b[0m in \u001b[0;36massert_array_almost_equal_nulp\u001b[1;34m(x, y, nulp)\u001b[0m\n\u001b[0;32m   1356\u001b[0m             \u001b[0mmax_nulp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnulp_diff\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1357\u001b[0m             \u001b[0mmsg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m\"X and Y are not equal to %d ULP (max is %g)\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnulp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmax_nulp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1358\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1359\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1360\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0massert_array_max_ulp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmaxulp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: X and Y are not equal to 1 ULP (max is 2)"
     ]
    }
   ],
   "source": [
    "print \"two eps\", np.testing.assert_array_almost_equal_nulp(1.0, 1.0+eps*2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**多ULP浮点数的比较**\n",
    "\n",
    "assert_array_max_ulp函数可以指定ULP的数量作为允许的误差上界。参数maxulp接受整数作为ULP数量的上限，默认值为1。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " one eps 1.0\n"
     ]
    }
   ],
   "source": [
    "print \"one eps\", np.testing.assert_array_max_ulp(1.0, 1.0+eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "two eps 2.0\n"
     ]
    }
   ],
   "source": [
    "print \"two eps\", np.testing.assert_array_max_ulp(1.0, 1.0+eps*2,maxulp=2)"
   ]
  }
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