Day_073_Gradient_Descent_HW.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 作業重點\n",
    "\n",
    "使用function y=(x+5)² 來練習學習率( leanrning rate ) 調整所造成的影響"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 作業目標:\n",
    "    請嘗試使用不同的組合驗證 learning rate 對所需 iteration 的影響\n",
    "    lr = [0.1, 0.0001]\n",
    "    主要驗證 Lr 對於grandient 收斂的速度\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_x = 3 # The algorithm starts at x=3\n",
    "precision = 0.000001 #This tells us when to stop the algorithm\n",
    "max_iters = 10000 # maximum number of iterations\n",
    "df = lambda x: 2*(x+5) #Gradient of our function "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Rate = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "'''\n",
    "需要執行初始值設定, 下列三個\n",
    "# Learning rate\n",
    "#iteration counter\n",
    "#Step size  \n",
    "'''\n",
    "lr = 0.1\n",
    "iters = 0\n",
    "previous_step_size = 1\n",
    "\n",
    "iters_history = [iters]\n",
    "x_history = [cur_x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1 \n",
      "X value is 1.4\n",
      "Iteration 2 \n",
      "X value is 0.11999999999999966\n",
      "Iteration 3 \n",
      "X value is -0.9040000000000001\n",
      "Iteration 4 \n",
      "X value is -1.7232000000000003\n",
      "Iteration 5 \n",
      "X value is -2.3785600000000002\n",
      "Iteration 6 \n",
      "X value is -2.902848\n",
      "Iteration 7 \n",
      "X value is -3.3222784\n",
      "Iteration 8 \n",
      "X value is -3.65782272\n",
      "Iteration 9 \n",
      "X value is -3.926258176\n",
      "Iteration 10 \n",
      "X value is -4.1410065408\n",
      "Iteration 11 \n",
      "X value is -4.312805232640001\n",
      "Iteration 12 \n",
      "X value is -4.450244186112\n",
      "Iteration 13 \n",
      "X value is -4.5601953488896\n",
      "Iteration 14 \n",
      "X value is -4.64815627911168\n",
      "Iteration 15 \n",
      "X value is -4.718525023289343\n",
      "Iteration 16 \n",
      "X value is -4.774820018631475\n",
      "Iteration 17 \n",
      "X value is -4.81985601490518\n",
      "Iteration 18 \n",
      "X value is -4.855884811924144\n",
      "Iteration 19 \n",
      "X value is -4.884707849539315\n",
      "Iteration 20 \n",
      "X value is -4.907766279631452\n",
      "Iteration 21 \n",
      "X value is -4.926213023705161\n",
      "Iteration 22 \n",
      "X value is -4.940970418964129\n",
      "Iteration 23 \n",
      "X value is -4.952776335171303\n",
      "Iteration 24 \n",
      "X value is -4.962221068137042\n",
      "Iteration 25 \n",
      "X value is -4.969776854509634\n",
      "Iteration 26 \n",
      "X value is -4.9758214836077075\n",
      "Iteration 27 \n",
      "X value is -4.980657186886166\n",
      "Iteration 28 \n",
      "X value is -4.984525749508933\n",
      "Iteration 29 \n",
      "X value is -4.987620599607146\n",
      "Iteration 30 \n",
      "X value is -4.990096479685716\n",
      "Iteration 31 \n",
      "X value is -4.992077183748573\n",
      "Iteration 32 \n",
      "X value is -4.993661746998859\n",
      "Iteration 33 \n",
      "X value is -4.994929397599087\n",
      "Iteration 34 \n",
      "X value is -4.99594351807927\n",
      "Iteration 35 \n",
      "X value is -4.996754814463416\n",
      "Iteration 36 \n",
      "X value is -4.997403851570732\n",
      "Iteration 37 \n",
      "X value is -4.997923081256586\n",
      "Iteration 38 \n",
      "X value is -4.9983384650052685\n",
      "Iteration 39 \n",
      "X value is -4.998670772004215\n",
      "Iteration 40 \n",
      "X value is -4.998936617603372\n",
      "Iteration 41 \n",
      "X value is -4.999149294082697\n",
      "Iteration 42 \n",
      "X value is -4.999319435266157\n",
      "Iteration 43 \n",
      "X value is -4.999455548212926\n",
      "Iteration 44 \n",
      "X value is -4.99956443857034\n",
      "Iteration 45 \n",
      "X value is -4.999651550856273\n",
      "Iteration 46 \n",
      "X value is -4.999721240685018\n",
      "Iteration 47 \n",
      "X value is -4.999776992548014\n",
      "Iteration 48 \n",
      "X value is -4.999821594038411\n",
      "Iteration 49 \n",
      "X value is -4.999857275230729\n",
      "Iteration 50 \n",
      "X value is -4.999885820184583\n",
      "Iteration 51 \n",
      "X value is -4.999908656147666\n",
      "Iteration 52 \n",
      "X value is -4.9999269249181335\n",
      "Iteration 53 \n",
      "X value is -4.999941539934507\n",
      "Iteration 54 \n",
      "X value is -4.999953231947606\n",
      "Iteration 55 \n",
      "X value is -4.999962585558085\n",
      "Iteration 56 \n",
      "X value is -4.999970068446467\n",
      "Iteration 57 \n",
      "X value is -4.999976054757174\n",
      "Iteration 58 \n",
      "X value is -4.999980843805739\n",
      "Iteration 59 \n",
      "X value is -4.999984675044591\n",
      "Iteration 60 \n",
      "X value is -4.999987740035673\n",
      "Iteration 61 \n",
      "X value is -4.999990192028538\n",
      "Iteration 62 \n",
      "X value is -4.999992153622831\n",
      "Iteration 63 \n",
      "X value is -4.999993722898265\n",
      "Iteration 64 \n",
      "X value is -4.999994978318612\n",
      "Iteration 65 \n",
      "X value is -4.999995982654889\n",
      "Iteration 66 \n",
      "X value is -4.999996786123911\n"
     ]
    }
   ],
   "source": [
    "while previous_step_size > precision and iters < max_iters:\n",
    "    prev_x = cur_x #Store current x value in prev_x\n",
    "    cur_x = cur_x - lr * df(prev_x) #Gradient descent\n",
    "    previous_step_size = abs(cur_x - prev_x) # 取較大的值, Change in x\n",
    "    iters = iters+1 #iteration count\n",
    "    print(\"Iteration\",iters,\"\\nX value is\",cur_x) #Print iterations\n",
    "     # Store parameters for plotting\n",
    "    iters_history.append(iters)\n",
    "    x_history.append(cur_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Totally iteations:  66\n",
      "The local minimum occurs at -4.999996786123911\n"
     ]
    },
    {
     "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": [
    "print(\"Totally iteations: \", iters)\n",
    "print(\"The local minimum occurs at\", cur_x)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "#適用於 Jupyter Notebook, 宣告直接在cell 內印出執行結果\n",
    "\n",
    "plt.plot(iters_history, x_history, 'o-', ms=3, lw=1.5, color='black')\n",
    "plt.xlabel(r'$iters$', fontsize=16)\n",
    "plt.ylabel(r'$x$', fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Rate = 0.0001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1 \n",
      "X value is 2.9984\n",
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      "Iteration 9904 \n",
      "X value is -3.8965480138398876\n",
      "Iteration 9905 \n",
      "X value is -3.8967687042371195\n",
      "Iteration 9906 \n",
      "X value is -3.896989350496272\n",
      "Iteration 9907 \n",
      "X value is -3.8972099526261728\n",
      "Iteration 9908 \n",
      "X value is -3.8974305106356475\n",
      "Iteration 9909 \n",
      "X value is -3.8976510245335203\n",
      "Iteration 9910 \n",
      "X value is -3.8978714943286135\n",
      "Iteration 9911 \n",
      "X value is -3.898091920029748\n",
      "Iteration 9912 \n",
      "X value is -3.898312301645742\n",
      "Iteration 9913 \n",
      "X value is -3.898532639185413\n",
      "Iteration 9914 \n",
      "X value is -3.898752932657576\n",
      "Iteration 9915 \n",
      "X value is -3.8989731820710447\n",
      "Iteration 9916 \n",
      "X value is -3.8991933874346305\n",
      "Iteration 9917 \n",
      "X value is -3.8994135487571437\n",
      "Iteration 9918 \n",
      "X value is -3.8996336660473925\n",
      "Iteration 9919 \n",
      "X value is -3.899853739314183\n",
      "Iteration 9920 \n",
      "X value is -3.9000737685663203\n",
      "Iteration 9921 \n",
      "X value is -3.900293753812607\n",
      "Iteration 9922 \n",
      "X value is -3.9005136950618446\n",
      "Iteration 9923 \n",
      "X value is -3.9007335923228323\n",
      "Iteration 9924 \n",
      "X value is -3.900953445604368\n",
      "Iteration 9925 \n",
      "X value is -3.901173254915247\n",
      "Iteration 9926 \n",
      "X value is -3.901393020264264\n",
      "Iteration 9927 \n",
      "X value is -3.901612741660211\n",
      "Iteration 9928 \n",
      "X value is -3.901832419111879\n",
      "Iteration 9929 \n",
      "X value is -3.902052052628057\n",
      "Iteration 9930 \n",
      "X value is -3.9022716422175314\n",
      "Iteration 9931 \n",
      "X value is -3.9024911878890878\n",
      "Iteration 9932 \n",
      "X value is -3.90271068965151\n",
      "Iteration 9933 \n",
      "X value is -3.9029301475135796\n",
      "Iteration 9934 \n",
      "X value is -3.903149561484077\n",
      "Iteration 9935 \n",
      "X value is -3.90336893157178\n",
      "Iteration 9936 \n",
      "X value is -3.903588257785466\n",
      "Iteration 9937 \n",
      "X value is -3.9038075401339087\n",
      "Iteration 9938 \n",
      "X value is -3.904026778625882\n",
      "Iteration 9939 \n",
      "X value is -3.904245973270157\n",
      "Iteration 9940 \n",
      "X value is -3.904465124075503\n",
      "Iteration 9941 \n",
      "X value is -3.9046842310506875\n",
      "Iteration 9942 \n",
      "X value is -3.9049032942044772\n",
      "Iteration 9943 \n",
      "X value is -3.9051223135456365\n",
      "Iteration 9944 \n",
      "X value is -3.9053412890829273\n",
      "Iteration 9945 \n",
      "X value is -3.9055602208251106\n",
      "Iteration 9946 \n",
      "X value is -3.9057791087809455\n",
      "Iteration 9947 \n",
      "X value is -3.9059979529591895\n",
      "Iteration 9948 \n",
      "X value is -3.906216753368598\n",
      "Iteration 9949 \n",
      "X value is -3.906435510017924\n",
      "Iteration 9950 \n",
      "X value is -3.9066542229159205\n",
      "Iteration 9951 \n",
      "X value is -3.906872892071337\n",
      "Iteration 9952 \n",
      "X value is -3.907091517492923\n",
      "Iteration 9953 \n",
      "X value is -3.9073100991894245\n",
      "Iteration 9954 \n",
      "X value is -3.9075286371695865\n",
      "Iteration 9955 \n",
      "X value is -3.907747131442153\n",
      "Iteration 9956 \n",
      "X value is -3.9079655820158643\n",
      "Iteration 9957 \n",
      "X value is -3.908183988899461\n",
      "Iteration 9958 \n",
      "X value is -3.9084023521016813\n",
      "Iteration 9959 \n",
      "X value is -3.908620671631261\n",
      "Iteration 9960 \n",
      "X value is -3.9088389474969345\n",
      "Iteration 9961 \n",
      "X value is -3.909057179707435\n",
      "Iteration 9962 \n",
      "X value is -3.9092753682714934\n",
      "Iteration 9963 \n",
      "X value is -3.909493513197839\n",
      "Iteration 9964 \n",
      "X value is -3.9097116144951998\n",
      "Iteration 9965 \n",
      "X value is -3.909929672172301\n",
      "Iteration 9966 \n",
      "X value is -3.9101476862378663\n",
      "Iteration 9967 \n",
      "X value is -3.910365656700619\n",
      "Iteration 9968 \n",
      "X value is -3.9105835835692786\n",
      "Iteration 9969 \n",
      "X value is -3.910801466852565\n",
      "Iteration 9970 \n",
      "X value is -3.9110193065591945\n",
      "Iteration 9971 \n",
      "X value is -3.9112371026978825\n",
      "Iteration 9972 \n",
      "X value is -3.9114548552773427\n",
      "Iteration 9973 \n",
      "X value is -3.9116725643062873\n",
      "Iteration 9974 \n",
      "X value is -3.911890229793426\n",
      "Iteration 9975 \n",
      "X value is -3.9121078517474674\n",
      "Iteration 9976 \n",
      "X value is -3.912325430177118\n",
      "Iteration 9977 \n",
      "X value is -3.9125429650910823\n",
      "Iteration 9978 \n",
      "X value is -3.9127604564980643\n",
      "Iteration 9979 \n",
      "X value is -3.9129779044067647\n",
      "Iteration 9980 \n",
      "X value is -3.9131953088258835\n",
      "Iteration 9981 \n",
      "X value is -3.9134126697641185\n",
      "Iteration 9982 \n",
      "X value is -3.913629987230166\n",
      "Iteration 9983 \n",
      "X value is -3.91384726123272\n",
      "Iteration 9984 \n",
      "X value is -3.9140644917804734\n",
      "Iteration 9985 \n",
      "X value is -3.9142816788821175\n",
      "Iteration 9986 \n",
      "X value is -3.9144988225463413\n",
      "Iteration 9987 \n",
      "X value is -3.914715922781832\n",
      "Iteration 9988 \n",
      "X value is -3.9149329795972756\n",
      "Iteration 9989 \n",
      "X value is -3.9151499930013562\n",
      "Iteration 9990 \n",
      "X value is -3.915366963002756\n",
      "Iteration 9991 \n",
      "X value is -3.915583889610155\n",
      "Iteration 9992 \n",
      "X value is -3.9158007728322333\n",
      "Iteration 9993 \n",
      "X value is -3.916017612677667\n",
      "Iteration 9994 \n",
      "X value is -3.9162344091551313\n",
      "Iteration 9995 \n",
      "X value is -3.9164511622733005\n",
      "Iteration 9996 \n",
      "X value is -3.9166678720408457\n",
      "Iteration 9997 \n",
      "X value is -3.9168845384664377\n",
      "Iteration 9998 \n",
      "X value is -3.9171011615587443\n",
      "Iteration 9999 \n",
      "X value is -3.9173177413264324\n",
      "Iteration 10000 \n",
      "X value is -3.917534277778167\n",
      "Totally iteations:  10000\n",
      "The local minimum occurs at -3.917534277778167\n"
     ]
    },
    {
     "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": [
    "cur_x = 3 # The algorithm starts at x=3\n",
    "precision = 0.000001 #This tells us when to stop the algorithm\n",
    "max_iters = 10000 # maximum number of iterations\n",
    "df = lambda x: 2*(x+5) #Gradient of our function \n",
    "'''\n",
    "需要執行初始值設定, 下列三個\n",
    "# Learning rate\n",
    "#iteration counter\n",
    "#Step size  \n",
    "'''\n",
    "lr = 0.0001\n",
    "iters = 0\n",
    "previous_step_size = 1\n",
    "\n",
    "iters_history = [iters]\n",
    "x_history = [cur_x]\n",
    "\n",
    "while previous_step_size > precision and iters < max_iters:\n",
    "    prev_x = cur_x #Store current x value in prev_x\n",
    "    cur_x = cur_x - lr * df(prev_x) #Gradient descent\n",
    "    previous_step_size = abs(cur_x - prev_x) # 取較大的值, Change in x\n",
    "    iters = iters+1 #iteration count\n",
    "    print(\"Iteration\",iters,\"\\nX value is\",cur_x) #Print iterations\n",
    "     # Store parameters for plotting\n",
    "    iters_history.append(iters)\n",
    "    x_history.append(cur_x)\n",
    "    \n",
    "print(\"Totally iteations: \", iters)\n",
    "print(\"The local minimum occurs at\", cur_x)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "#適用於 Jupyter Notebook, 宣告直接在cell 內印出執行結果\n",
    "\n",
    "plt.plot(iters_history, x_history, 'o-', ms=3, lw=1.5, color='black')\n",
    "plt.xlabel(r'$iters$', fontsize=16)\n",
    "plt.ylabel(r'$x$', fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由於學習速度較慢，收斂速度因此減慢很多"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}