justhomework/AIandML/e1_python_basics/e1.1_numpy.ipynb

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    "# 人工智能与机器学习-实验1\n",
    "\n",
    "## Part.II Numpy练习\n",
    "\n",
    "|学号       |姓名    |\n",
    "|----------|--------|\n",
    "|2020114490|江一和|\n",
    "|2020113874|何一涛|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 数组\n",
    "\n",
    "创建一个长度为10全为0的一维数组，然后让第5个元素等于1。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.zeros(10)\n",
    "a[4] = 1\n",
    "print(a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 向量内积\n",
    "\n",
    "随机生成2个长度为$10^6$的向量，分别用numpy函数和for循环计算其内积。并比较耗时情况。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "250200.07698508396\n",
      "numpy:0.9696483612060547ms\n",
      "250200.07698508215\n",
      "for:509.42516326904297ms\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "a = np.random.rand(1000000)\n",
    "b = np.random.rand(1000000)\n",
    "tic = time.time()\n",
    "c = np.dot(a,b)\n",
    "toc = time.time()\n",
    "print(c)\n",
    "print(\"numpy:\" + str(1000*(toc-tic)) + \"ms\")\n",
    "c = 0\n",
    "tic = time.time()\n",
    "for i in range(1000000):\n",
    "    c += a[i]*b[i]\n",
    "toc = time.time()\n",
    "print(c)\n",
    "print(\"for:\" + str(1000*(toc-tic)) + \"ms\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 矩阵乘法\n",
    "\n",
    "生成一个$4\\times5$和一个$5\\times4$的矩阵，并计算它们的乘积。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.23931254 0.18071967 0.37310061 0.12620676 0.13512026]\n",
      " [0.30783951 0.91376617 0.67098953 0.32039883 0.01034717]\n",
      " [0.96111339 0.50345747 0.44325113 0.69203477 0.68494092]\n",
      " [0.72068532 0.70385745 0.863872   0.04211034 0.64406034]]\n",
      "[[0.77360967 0.69983706 0.6007846  0.86168637]\n",
      " [0.81774926 0.45233242 0.25631712 0.78721015]\n",
      " [0.70753124 0.97739082 0.85224573 0.38800176]\n",
      " [0.99206956 0.76979289 0.32823954 0.65932597]\n",
      " [0.28726144 0.0885248  0.9055978  0.25378116]]\n",
      "[[0.76091893 0.72300482 0.67186089 0.61074278]\n",
      " [1.78095556 1.5321393  1.10554506 1.45880543]\n",
      " [2.35214635 1.9269402  1.93165995 2.02658896]\n",
      " [1.97111455 1.75651195 1.94670048 1.70148712]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.random.rand(4,5)\n",
    "b = np.random.rand(5,4)\n",
    "c = np.dot(a,b)\n",
    "print(a)\n",
    "print(b)\n",
    "print(c)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 函数\n",
    "\n",
    "函数$f$定义如下，其中$x$是任意实数:\n",
    "$$\n",
    "f(x)=\\frac{\\sin⁡(x+1)(x+1)}{2e^x}\n",
    "$$，\n",
    "\n",
    "生成一个数组$a\\in \\mathbb{R}^5$，计算$b = f(a)$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.11783325 0.48074153 0.73572425 0.20476283 0.88648351]\n",
      "[0.44669072 0.45593449 0.41020043 0.45832847 0.36950327]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "def f(x):\n",
    "    return np.sin(x+1)*(x+1)/(2*np.exp(x))\n",
    "a = np.random.rand(5)\n",
    "b = f(a)\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. 平均值\n",
    "\n",
    "随机生成一个5行10列的矩阵，然后每行元素减去该行的平均值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.24236313 0.55447699 0.95304607 0.79666384 0.92822022 0.27138421\n",
      "  0.47722097 0.74169242 0.21323861 0.83588465]\n",
      " [0.81246374 0.77727719 0.45686829 0.08864242 0.00963438 0.50045921\n",
      "  0.51131599 0.1215012  0.16156761 0.9299535 ]\n",
      " [0.53098614 0.39056825 0.4658711  0.26826016 0.42102393 0.11597775\n",
      "  0.8880885  0.96429013 0.79650161 0.42915054]\n",
      " [0.71644738 0.84851284 0.03352013 0.89332467 0.3272176  0.67425642\n",
      "  0.58702405 0.39927189 0.56726108 0.92623776]\n",
      " [0.30084031 0.32070728 0.05854519 0.83081661 0.70783952 0.20550454\n",
      "  0.08244311 0.93941383 0.13424483 0.71656674]]\n",
      "[[-0.35905598 -0.04694212  0.35162696  0.19524473  0.32680111 -0.3300349\n",
      "  -0.12419814  0.14027331 -0.3881805   0.23446554]\n",
      " [ 0.37549539  0.34030884  0.01989994 -0.34832593 -0.42733397  0.06349086\n",
      "   0.07434764 -0.31546716 -0.27540075  0.49298515]\n",
      " [ 0.00391433 -0.13650356 -0.06120071 -0.25881165 -0.10604788 -0.41109406\n",
      "   0.36101669  0.43721832  0.2694298  -0.09792127]\n",
      " [ 0.11913999  0.25120546 -0.56378725  0.29601729 -0.27008979  0.07694904\n",
      "  -0.01028333 -0.19803549 -0.0300463   0.32893038]\n",
      " [-0.12885189 -0.10898492 -0.37114701  0.40112441  0.27814732 -0.22418765\n",
      "  -0.34724909  0.50972163 -0.29544737  0.28687455]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.random.rand(5,10)\n",
    "b = a - np.mean(a,axis=1,keepdims=True)\n",
    "print(a)\n",
    "print(b)"
   ]
  }
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