5-构建非线性回归模型.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 使用numpy生成200个随机的数据点"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "生成从-0.5到0.5均匀分布的200个数据点，包含首尾数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data = np.linspace(-0.5, 0.5, 200) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        0.25376884,  0.25879397,  0.2638191 ,  0.26884422,  0.27386935,\n",
       "        0.27889447,  0.2839196 ,  0.28894472,  0.29396985,  0.29899497,\n",
       "        0.3040201 ,  0.30904523,  0.31407035,  0.31909548,  0.3241206 ,\n",
       "        0.32914573,  0.33417085,  0.33919598,  0.34422111,  0.34924623,\n",
       "        0.35427136,  0.35929648,  0.36432161,  0.36934673,  0.37437186,\n",
       "        0.37939698,  0.38442211,  0.38944724,  0.39447236,  0.39949749,\n",
       "        0.40452261,  0.40954774,  0.41457286,  0.41959799,  0.42462312,\n",
       "        0.42964824,  0.43467337,  0.43969849,  0.44472362,  0.44974874,\n",
       "        0.45477387,  0.45979899,  0.46482412,  0.46984925,  0.47487437,\n",
       "        0.4798995 ,  0.48492462,  0.48994975,  0.49497487,  0.5       ])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将1维数据升成2维数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data = x_data[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "生成噪声数据与`x_data`的shape一致"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = np.random.normal(0, 0.02,  x_data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "noise为均值为0，方差为0.02的高斯分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "       [ 1.88918332e-02],\n",
       "       [-2.05192540e-02],\n",
       "       [ 1.31610920e-03],\n",
       "       [ 5.13536111e-03],\n",
       "       [-6.70461366e-03],\n",
       "       [ 4.01668620e-03],\n",
       "       [ 1.00774261e-02],\n",
       "       [-1.72600444e-02],\n",
       "       [-3.25460837e-02],\n",
       "       [ 1.98581294e-02],\n",
       "       [ 4.04288751e-03],\n",
       "       [ 1.18008057e-02],\n",
       "       [ 1.11155351e-02],\n",
       "       [-2.32165126e-02],\n",
       "       [-1.71263971e-02],\n",
       "       [-3.41766443e-02],\n",
       "       [ 2.21120390e-02],\n",
       "       [-1.84588148e-04],\n",
       "       [-3.72386019e-03],\n",
       "       [-4.32389632e-03],\n",
       "       [-2.13103499e-02],\n",
       "       [-1.72848888e-02],\n",
       "       [ 1.48784552e-02],\n",
       "       [-2.36931867e-02],\n",
       "       [ 8.84999571e-03],\n",
       "       [ 8.28411251e-03],\n",
       "       [ 3.32487888e-02],\n",
       "       [ 2.53298705e-02],\n",
       "       [-1.16342662e-02],\n",
       "       [-1.19096175e-02],\n",
       "       [ 2.00142503e-03],\n",
       "       [-3.50181655e-02],\n",
       "       [ 2.25669341e-02],\n",
       "       [-1.77459685e-02],\n",
       "       [ 8.55880298e-04],\n",
       "       [-1.43449406e-03],\n",
       "       [ 3.69661385e-03],\n",
       "       [ 3.30054068e-02],\n",
       "       [-1.58685048e-02],\n",
       "       [-2.70982362e-02],\n",
       "       [-1.91836836e-02],\n",
       "       [ 6.21600170e-03],\n",
       "       [ 2.84387660e-02],\n",
       "       [-3.12532209e-02],\n",
       "       [-1.16846894e-02],\n",
       "       [ 2.21410991e-02],\n",
       "       [-1.09839352e-02],\n",
       "       [-6.19793848e-04],\n",
       "       [-2.33704854e-02],\n",
       "       [ 1.65666947e-02],\n",
       "       [ 2.39120058e-02],\n",
       "       [-3.33620295e-03],\n",
       "       [-1.33585015e-03],\n",
       "       [ 1.28368542e-02],\n",
       "       [ 3.80231761e-02],\n",
       "       [ 7.69449595e-03],\n",
       "       [-6.59717689e-03]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "构建数据y_data\n",
    "\n",
    "$y\\_data = x\\_data^2 + noise$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_data = np.square(x_data) + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2265081 ],\n",
       "       [ 0.21483734],\n",
       "       [ 0.24736461],\n",
       "       [ 0.22616856],\n",
       "       [ 0.24174798],\n",
       "       [ 0.23659293],\n",
       "       [ 0.22926659],\n",
       "       [ 0.21840314],\n",
       "       [ 0.22753151],\n",
       "       [ 0.20459139],\n",
       "       [ 0.22316266],\n",
       "       [ 0.20236621],\n",
       "       [ 0.18438452],\n",
       "       [ 0.17810799],\n",
       "       [ 0.15594597],\n",
       "       [ 0.15431757],\n",
       "       [ 0.19156092],\n",
       "       [ 0.1666612 ],\n",
       "       [ 0.14756404],\n",
       "       [ 0.16514514],\n",
       "       [ 0.19293691],\n",
       "       [ 0.15827142],\n",
       "       [ 0.15133263],\n",
       "       [ 0.17290005],\n",
       "       [ 0.16632887],\n",
       "       [ 0.14399978],\n",
       "       [ 0.12173182],\n",
       "       [ 0.14130323],\n",
       "       [ 0.10081262],\n",
       "       [ 0.11440011],\n",
       "       [ 0.10721051],\n",
       "       [ 0.12728202],\n",
       "       [ 0.13366772],\n",
       "       [ 0.12448584],\n",
       "       [ 0.11105888],\n",
       "       [ 0.07960471],\n",
       "       [ 0.09266004],\n",
       "       [ 0.10878699],\n",
       "       [ 0.11219907],\n",
       "       [ 0.10373325],\n",
       "       [ 0.07876585],\n",
       "       [ 0.10244395],\n",
       "       [ 0.10066073],\n",
       "       [ 0.06630474],\n",
       "       [ 0.08098576],\n",
       "       [ 0.09017536],\n",
       "       [ 0.04096704],\n",
       "       [ 0.0666451 ],\n",
       "       [ 0.04422439],\n",
       "       [ 0.07867178],\n",
       "       [ 0.03788684],\n",
       "       [ 0.0796297 ],\n",
       "       [ 0.04886694],\n",
       "       [ 0.03798049],\n",
       "       [ 0.03231702],\n",
       "       [ 0.04146118],\n",
       "       [ 0.03689472],\n",
       "       [ 0.06789637],\n",
       "       [ 0.04727773],\n",
       "       [ 0.05976595],\n",
       "       [ 0.02652792],\n",
       "       [ 0.00377031],\n",
       "       [ 0.00144523],\n",
       "       [ 0.04676879],\n",
       "       [ 0.01804072],\n",
       "       [ 0.02996472],\n",
       "       [ 0.00864707],\n",
       "       [ 0.04368118],\n",
       "       [ 0.00474848],\n",
       "       [ 0.02293862],\n",
       "       [-0.00129203],\n",
       "       [ 0.00606756],\n",
       "       [ 0.0117718 ],\n",
       "       [ 0.04322111],\n",
       "       [-0.00655922],\n",
       "       [ 0.02697352],\n",
       "       [ 0.00973215],\n",
       "       [ 0.00048826],\n",
       "       [-0.02961067],\n",
       "       [ 0.01673574],\n",
       "       [ 0.00826897],\n",
       "       [-0.01732122],\n",
       "       [-0.01530234],\n",
       "       [-0.010303  ],\n",
       "       [ 0.00622487],\n",
       "       [-0.01011067],\n",
       "       [ 0.03225698],\n",
       "       [ 0.0140282 ],\n",
       "       [-0.02146315],\n",
       "       [ 0.01781903],\n",
       "       [ 0.00532087],\n",
       "       [ 0.02454139],\n",
       "       [-0.02710614],\n",
       "       [ 0.00205836],\n",
       "       [ 0.02480807],\n",
       "       [ 0.03499191],\n",
       "       [-0.00244034],\n",
       "       [ 0.00198833],\n",
       "       [ 0.00531013],\n",
       "       [ 0.03003617],\n",
       "       [ 0.0159297 ],\n",
       "       [-0.0157121 ],\n",
       "       [-0.00718128],\n",
       "       [-0.00987596],\n",
       "       [-0.00332695],\n",
       "       [ 0.03041473],\n",
       "       [ 0.03026877],\n",
       "       [ 0.00463452],\n",
       "       [-0.02201854],\n",
       "       [ 0.01327925],\n",
       "       [-0.00261779],\n",
       "       [ 0.01189483],\n",
       "       [-0.00570958],\n",
       "       [ 0.01055159],\n",
       "       [-0.01187765],\n",
       "       [-0.00679223],\n",
       "       [-0.01935511],\n",
       "       [-0.02151399],\n",
       "       [ 0.02987965],\n",
       "       [ 0.00390498],\n",
       "       [-0.01396241],\n",
       "       [ 0.01433757],\n",
       "       [ 0.0428222 ],\n",
       "       [-0.01609301],\n",
       "       [ 0.05224668],\n",
       "       [ 0.01266591],\n",
       "       [ 0.05471644],\n",
       "       [ 0.01973944],\n",
       "       [ 0.0295913 ],\n",
       "       [ 0.01424093],\n",
       "       [ 0.04249495],\n",
       "       [ 0.01534368],\n",
       "       [ 0.00048638],\n",
       "       [ 0.02216145],\n",
       "       [ 0.0295694 ],\n",
       "       [ 0.04400744],\n",
       "       [ 0.02294523],\n",
       "       [ 0.08656449],\n",
       "       [ 0.03720644],\n",
       "       [ 0.04746143],\n",
       "       [ 0.03036883],\n",
       "       [ 0.04721128],\n",
       "       [ 0.0422631 ],\n",
       "       [ 0.06667472],\n",
       "       [ 0.0294858 ],\n",
       "       [ 0.05359383],\n",
       "       [ 0.05973626],\n",
       "       [ 0.05026996],\n",
       "       [ 0.06341544],\n",
       "       [ 0.07195086],\n",
       "       [ 0.04713858],\n",
       "       [ 0.03442824],\n",
       "       [ 0.08945864],\n",
       "       [ 0.0763201 ],\n",
       "       [ 0.08680522],\n",
       "       [ 0.08889766],\n",
       "       [ 0.05739383],\n",
       "       [ 0.06636266],\n",
       "       [ 0.05224163],\n",
       "       [ 0.11151003],\n",
       "       [ 0.09224363],\n",
       "       [ 0.09178509],\n",
       "       [ 0.09431629],\n",
       "       [ 0.08051157],\n",
       "       [ 0.08776928],\n",
       "       [ 0.12321537],\n",
       "       [ 0.08797697],\n",
       "       [ 0.12390391],\n",
       "       [ 0.12677228],\n",
       "       [ 0.15522172],\n",
       "       [ 0.15083806],\n",
       "       [ 0.1174597 ],\n",
       "       [ 0.12082062],\n",
       "       [ 0.13841843],\n",
       "       [ 0.10513612],\n",
       "       [ 0.16650901],\n",
       "       [ 0.13003439],\n",
       "       [ 0.15252503],\n",
       "       [ 0.15417395],\n",
       "       [ 0.16329486],\n",
       "       [ 0.19664395],\n",
       "       [ 0.15186085],\n",
       "       [ 0.14477242],\n",
       "       [ 0.15687879],\n",
       "       [ 0.18652079],\n",
       "       [ 0.21303638],\n",
       "       [ 0.15768771],\n",
       "       [ 0.18165007],\n",
       "       [ 0.2199202 ],\n",
       "       [ 0.19129   ],\n",
       "       [ 0.20619948],\n",
       "       [ 0.18804463],\n",
       "       [ 0.23262816],\n",
       "       [ 0.24467032],\n",
       "       [ 0.22216947],\n",
       "       [ 0.22896768],\n",
       "       [ 0.24798874],\n",
       "       [ 0.27807393],\n",
       "       [ 0.25269462],\n",
       "       [ 0.24340282]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义placeholder用于接收训练的数据\n",
    "\n",
    "可以认为是输入层"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = tf.placeholder(tf.float32, [None, 1], name=\"x_input\")\n",
    "y = tf.placeholder(tf.float32, [None, 1], name=\"y_input\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'x_input:0' shape=(?, 1) dtype=float32>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'y_input:0' shape=(?, 1) dtype=float32>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义隐藏层\n",
    "\n",
    "即：\n",
    "\n",
    "$$a_1 = w_1 \\times x + b_1$$\n",
    "$$out_1 = activation(a_1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "W_1 = tf.Variable(tf.random_normal([1, 10]))\n",
    "b_1 = tf.Variable(tf.zeros([1, 10]))\n",
    "a_1 = tf.matmul(x, W_1) + b_1\n",
    "out_1 = tf.nn.tanh(a_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Variable 'Variable:0' shape=(1, 10) dtype=float32_ref>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Variable 'Variable_1:0' shape=(1, 10) dtype=float32_ref>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'add:0' shape=(?, 10) dtype=float32>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'Tanh:0' shape=(?, 10) dtype=float32>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义输出层\n",
    "\n",
    "即输出变为维度为1的数据\n",
    "\n",
    "$$a_2=out_1 \\times w_2 + b_2$$\n",
    "$$out_2 = activation(a_2)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "W_2 = tf.Variable(tf.random_normal([10, 1]))\n",
    "b_2 = tf.Variable(tf.zeros([1, 1]))\n",
    "a_2 = tf.matmul(out_1, W_2) + b_2\n",
    "out_2 = tf.nn.tanh(a_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Variable 'Variable_2:0' shape=(10, 1) dtype=float32_ref>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Variable 'Variable_3:0' shape=(1, 1) dtype=float32_ref>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'add_1:0' shape=(?, 1) dtype=float32>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'Tanh_1:0' shape=(?, 1) dtype=float32>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss = tf.reduce_mean(tf.square(out_2- y_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'Mean:0' shape=() dtype=float32>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Operation 'GradientDescent' type=NoOp>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 初始化变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Operation 'init' type=NoOp>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 [0.5895318]\n",
      "10 [0.20922647]\n",
      "20 [0.0060149524]\n",
      "30 [0.1843556]\n",
      "40 [0.1003089]\n",
      "50 [0.13533525]\n",
      "60 [0.12173258]\n",
      "70 [0.11502971]\n",
      "80 [0.10597257]\n",
      "90 [0.09566488]\n",
      "100 [0.08471802]\n",
      "110 [0.073716804]\n",
      "120 [0.0631451]\n",
      "130 [0.053354483]\n",
      "140 [0.044561643]\n",
      "150 [0.036864456]\n",
      "160 [0.030268965]\n",
      "170 [0.02471658]\n",
      "180 [0.020110523]\n",
      "190 [0.016335653]\n",
      "200 [0.013272908]\n",
      "210 [0.010808831]\n",
      "220 [0.008840564]\n",
      "230 [0.0072781206]\n",
      "240 [0.0060446877]\n",
      "250 [0.0050758338]\n",
      "260 [0.004318233]\n",
      "270 [0.0037280833]\n",
      "280 [0.0032696333]\n",
      "290 [0.002913902]\n",
      "300 [0.0026375009]\n",
      "310 [0.0024217074]\n",
      "320 [0.0022516712]\n",
      "330 [0.0021157593]\n",
      "340 [0.0020050034]\n",
      "350 [0.0019125998]\n",
      "360 [0.0018335049]\n",
      "370 [0.0017640385]\n",
      "380 [0.0017015848]\n",
      "390 [0.0016443208]\n",
      "400 [0.0015909949]\n",
      "410 [0.0015407717]\n",
      "420 [0.0014930917]\n",
      "430 [0.0014475897]\n",
      "440 [0.0014040194]\n",
      "450 [0.0013622175]\n",
      "460 [0.0013220676]\n",
      "470 [0.0012834821]\n",
      "480 [0.001246395]\n",
      "490 [0.001210748]\n",
      "500 [0.00117649]\n",
      "510 [0.0011435741]\n",
      "520 [0.0011119553]\n",
      "530 [0.001081591]\n",
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      "550 [0.0010244558]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "9980 [0.0003649567]\n",
      "9990 [0.0003649482]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "    for epc in range(10000):\n",
    "        sess.run([loss, train_step], {x:x_data,y:y_data})\n",
    "        if epc % 10 == 0:\n",
    " #           loss_value = sess.run([loss])\n",
    "            loss_value = sess.run([loss], {x:x_data,y:y_data})\n",
    "\n",
    "            print(epc, loss_value)\n",
    "    prediction_value = sess.run(out_2, feed_dict={x:x_data})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 画图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.32277691e-01],\n",
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       "       [ 2.18243316e-01],\n",
       "       [ 2.14714557e-01],\n",
       "       [ 2.11179495e-01],\n",
       "       [ 2.07639098e-01],\n",
       "       [ 2.04094201e-01],\n",
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       "       [ 1.92786649e-01],\n",
       "       [ 1.96514860e-01],\n",
       "       [ 2.00252637e-01],\n",
       "       [ 2.03999147e-01],\n",
       "       [ 2.07753509e-01],\n",
       "       [ 2.11515188e-01],\n",
       "       [ 2.15283185e-01],\n",
       "       [ 2.19056919e-01],\n",
       "       [ 2.22835600e-01],\n",
       "       [ 2.26618424e-01],\n",
       "       [ 2.30404809e-01],\n",
       "       [ 2.34193787e-01],\n",
       "       [ 2.37985104e-01]], dtype=float32)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.scatter(x_data, y_data)\n",
    "plt.plot(x_data, prediction_value, \"r-\", lw=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}