np_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ac93378d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "141a3bb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>population</th>\n",
       "      <th>profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   population   profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"ex_data.txt\",names=[\"population\",\"profit\"])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "442e9061",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>population</th>\n",
       "      <th>profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>5.8707</td>\n",
       "      <td>7.20290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>5.3054</td>\n",
       "      <td>1.98690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>8.2934</td>\n",
       "      <td>0.14454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>13.3940</td>\n",
       "      <td>9.05510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>5.4369</td>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    population   profit\n",
       "92      5.8707  7.20290\n",
       "93      5.3054  1.98690\n",
       "94      8.2934  0.14454\n",
       "95     13.3940  9.05510\n",
       "96      5.4369  0.61705"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "595a8dde",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 97 entries, 0 to 96\n",
      "Data columns (total 2 columns):\n",
      " #   Column      Non-Null Count  Dtype  \n",
      "---  ------      --------------  -----  \n",
      " 0   population  97 non-null     float64\n",
      " 1   profit      97 non-null     float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 1.6 KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4586ae85",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='population', ylabel='profit'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot.scatter(\"population\",\"profit\",c=\"b\",label=\"population\",s=3) # 绘制散点图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "588e78de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ones</th>\n",
       "      <th>population</th>\n",
       "      <th>profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ones  population   profit\n",
       "0     1      6.1101  17.5920\n",
       "1     1      5.5277   9.1302\n",
       "2     1      8.5186  13.6620\n",
       "3     1      7.0032  11.8540\n",
       "4     1      5.8598   6.8233"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.insert(loc=0,column=\"ones\",value=1)# 插入一列 1\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "92829857",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ones</th>\n",
       "      <th>population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ones  population\n",
       "0     1      6.1101\n",
       "1     1      5.5277\n",
       "2     1      8.5186\n",
       "3     1      7.0032\n",
       "4     1      5.8598"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data.iloc[:,0:-1]# 所有行，前两列\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "80b5a613",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    profit\n",
       "0  17.5920\n",
       "1   9.1302\n",
       "2  13.6620\n",
       "3  11.8540\n",
       "4   6.8233"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = data.iloc[:,-1:]# 之前的错误写法是，y = data.iloc[:,-1]，然后reshape一下 todo 查询错误原因\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2302d8cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8f8104c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(97, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4733224b",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = y.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "295637d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(X,y,theta):\n",
    "    \"\"\"\n",
    "    损失函数\n",
    "    \"\"\"\n",
    "    inner = np.power(X @ theta - y, 2)\n",
    "    return np.sum(inner) / (2*len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7a95bfa1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "theta = np.zeros((2,1))\n",
    "theta.shape\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ab797853",
   "metadata": {},
   "outputs": [],
   "source": [
    "cost_init = costFunction(X,y,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9dd7c1f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32.072733877455676\n"
     ]
    }
   ],
   "source": [
    "print(cost_init)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2aaf871d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X,y,theta,alpha,iters):\n",
    "    \"\"\"\n",
    "    梯度下降函数 对代价函数求导 * 步长 alpha    \n",
    "    X @ theta - y 求导得 X.T @ (X @ theta - y )\n",
    "    \"\"\"\n",
    "    costs = []\n",
    "    for i in range(iters):\n",
    "        theta = theta - (X.T @ (X@theta -y )) * alpha / len(X)\n",
    "        cost = costFunction(X,y,theta)\n",
    "        costs.append(cost)\n",
    "#         if i % 100 == 0:\n",
    "#             print(cost)\n",
    "    return theta,costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c5376790",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "candinate_alpha = [0.0003,0.003,0.01]\n",
    "iters = 2000\n",
    "for alpha in candinate_alpha:\n",
    "    _,costs = gradientDescent(X,y,theta,alpha,iters)\n",
    "    ax.plot(np.arange(iters),costs,label=alpha)#绘图 列表\n",
    "    ax.legend()\n",
    "    \n",
    "ax.set(xlabel=\"iters\",ylabel=\"costs\",title=\"cost vs iters\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e9210ce3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(y.min(), y.max(), 100)\n",
    "y_ = theta[0,0] + theta[1,0] * x\n",
    "fig,ax = plt.subplots()\n",
    "ax.scatter(X[:,1], y, label=\"training data\")\n",
    "ax.plot(x,y_,'r',label=\"predict\")\n",
    "ax.legend() # 显示标签\n",
    "ax.set(xlabel=\"population\", ylabel=\"profit\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97c267e5",
   "metadata": {},
   "source": [
    "### 正规方程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "14ba0841",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 特征归一化 使所有特征值归一化到指定区间\n",
    "def normaize_feature(data):\n",
    "    return (data - data.mean()) / data.std()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}