byoyo2018-giris-2.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Eniyileme\n",
    "\n",
    "Kısıtsız eniyileme problemlerinin genel yapısı\n",
    "\\begin{align}\n",
    "\\text{minimize} & & E(w) \n",
    "\\end{align}\n",
    "\n",
    "* Algoritma :\n",
    "\\begin{align}\n",
    "w_0 & = \\text{başlangıç değeri} \\\\\n",
    "\\text{for}\\;\\; & \\tau = 1, 2,\\dots \\\\\n",
    "& w_\\tau = w_{\\tau-1} + g_\\tau\n",
    "\\end{align}\n",
    "\n",
    "Burada, $g_\\tau$ bir arama yönüdür. Amaç, döngüler sonucunda başlangıç noktasından daha düşük (idealde en düşük) bir fonksyon değeri bulmaktır.\n",
    "\n",
    "## Bayır inişi\n",
    "* negatif gradyan yönünde arama\n",
    "\\begin{align}\n",
    "g_\\tau & =  - \\eta \\nabla E(w_{\\tau-1})\n",
    "\\end{align}\n",
    "\n",
    "*  $\\nabla E(w) = 0$ olduğunda algoritma çözüm noktasını değiştiremez. Bu tarz noktalara sabit nokta adı verilir.\n",
    "\n",
    "* Bazen algoritma gerçek en küçük noktaya da yakınsar  $w^* = \\arg\\min_{w} E(w)$. Burada bu yakınsamanın hangi şartlarda ve hangi hızda gerçekleştiği önemli kavramsal sorulardır. \n",
    "\n",
    "* Burada, $\\eta$'ya *adım büyüklüğü* veya *öğrenme hızı* gibi isimler verilir. Bu parametrenin düzgün seçilmesi pratikte epey deneme yanılma grektirmektedir. Düzgün seçilmezse algoritma yakınsamaz ve patlar, veya yakınsaması çok uzun sürer. Epey kavramsal çalışma var.\n",
    "\n",
    "* Sadece gradyan hesaplamak gerektiği için kullanılması çok kolay bir algoritmadır. Yapay zeka alanında çok büyük modellerde de uygulanabildiği için çok yaygındır. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "from ipywidgets import interact, interactive, fixed\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import clear_output, display, HTML\n",
    "from matplotlib import rc\n",
    "\n",
    "mpl.rc('font',**{'size': 20, 'family':'sans-serif','sans-serif':['Helvetica']})\n",
    "mpl.rc('text', usetex=True)\n",
    "\n",
    "import time\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.array([7.04, 7.95, 7.58, 7.81, 8.33, 7.96, 8.24, 8.26, 7.84, 6.82, 5.68])\n",
    "x = np.array(np.linspace(-1,1,11))\n",
    "N = len(x)\n",
    "\n",
    "# Design matrix\n",
    "#A = np.vstack((np.ones(N), x, x**2, x**3)).T\n",
    "degree = 9\n",
    "A = np.hstack([np.power(x.reshape(N,1),i) for i in range(degree+1)])\n",
    "\n",
    "# Learning rate\n",
    "eta = 0.001\n",
    "              \n",
    "# initial parameters\n",
    "w = np.array(np.random.randn(degree+1))\n",
    "W = []\n",
    "Err = []\n",
    "for epoch in range(50000):  \n",
    "    # Error\n",
    "    err = y-A.dot(w)\n",
    "    \n",
    "    # Total error\n",
    "    E = np.sum(err**2)/N\n",
    "    \n",
    "    # Gradient\n",
    "    dE = -2.*A.T.dot(err)/N\n",
    "    \n",
    "    if epoch%100 == 0: \n",
    "        #print(epoch,':',E)\n",
    "        # print(w)    \n",
    "        W.append(w)\n",
    "        Err.append(E)\n",
    "\n",
    "    # Perfom one descent step\n",
    "    w = w - eta*dE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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      "text/html": [
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       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
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       "interactive(children=(IntSlider(value=0, description='iteration', max=499), Output()), _dom_classes=('widget-interact',))"
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   "source": [
    "\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "\n",
    "left = -1.5\n",
    "right = 1.5\n",
    "xx = np.linspace(left,right,50)\n",
    "AA = np.hstack((np.power(xx.reshape(len(xx),1),i) for i in range(degree+1)))\n",
    "\n",
    "# Find best\n",
    "A_orth, R = np.linalg.qr(A)\n",
    "w_orth, res, rank, s = np.linalg.lstsq(A_orth, y)\n",
    "w_star = np.linalg.solve(R, w_orth)\n",
    "yy = AA.dot(w_star)\n",
    "\n",
    "#ax.set_xlim((2,15))\n",
    "\n",
    "#dots = plt.Line2D(x,y, linestyle='', markerfacecolor='b',marker='o', alpha=0.5, markersize=5)\n",
    "#ax.add_line(dots)\n",
    "plt.plot(x,y, linestyle='', markerfacecolor='b',marker='o', alpha=0.5, markersize=5)\n",
    "plt.plot(xx, yy, linestyle=':', color='k', alpha=0.3)\n",
    "ln = plt.Line2D(xdata=[], ydata=[], linestyle='-',linewidth=2)\n",
    "\n",
    "\n",
    "ax = fig.gca()\n",
    "ax.add_line(ln)\n",
    "plt.close(fig)\n",
    "\n",
    "ax.set_xlim((left,right))\n",
    "ax.set_ylim((5,9))\n",
    "\n",
    "def plot_gd(iteration=0):\n",
    "    w = W[iteration]\n",
    "    f = AA.dot(w)\n",
    "    #print(w)\n",
    "    ln.set_ydata(f)\n",
    "    ln.set_xdata(xx)\n",
    "    \n",
    "    ax.set_title('$E = '+str(Err[iteration])+'$')\n",
    "    \n",
    "    display(fig)\n",
    "    \n",
    "res = interact(plot_gd, iteration=(0,len(W)-1))"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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Ktqy/iSmdTS7JIq8d7r5ckswsr9KOXn9Tl1YByBx3158+/bJ68t367x+/U4s6F7yMCA2Q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\nADr8PjBiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddcd5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import scipy as sc\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "df_arac = pd.read_csv(u'data/arac.csv',sep=';')\n",
    "#df_arac[['Year','Car']]\n",
    "\n",
    "BaseYear = 1995\n",
    "x = np.matrix(df_arac.Year[0:]).T-BaseYear\n",
    "y = np.matrix(df_arac.Car[0:]).T/1000000.\n",
    "\n",
    "plt.plot(x+BaseYear, y, 'o-')\n",
    "plt.xlabel('Yil')\n",
    "plt.ylabel('Araba (Millions)')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ygycDnU4OzJMHfYpho4Zah5MP/yRjvRJIqCimA5r0aeNH/yvtfZlb5v4kkpxG3iIMYETb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\nECbAAADCBBgAQNh/APsd3elyBjPjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddcd208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from itertools import product\n",
    "\n",
    "def Error_Surface(y, A, left=0, right=1, bottom=0, top=1, step=0.1): \n",
    "    W0 = np.arange(left,right, step)\n",
    "    W1 = np.arange(bottom,top, step)\n",
    "\n",
    "    ErrSurf = np.zeros((len(W1),len(W0)))\n",
    "\n",
    "    for i,j in product(range(len(W1)), range(len(W0))):\n",
    "        e = y - A*np.matrix([W0[j], W1[i]]).T\n",
    "        ErrSurf[i,j] = e.T*e/2\n",
    "    \n",
    "    return ErrSurf\n",
    "\n",
    "BaseYear = 1995\n",
    "x = np.matrix(df_arac.Year[0:]).T-BaseYear\n",
    "y = np.matrix(df_arac.Car[0:]).T/1000000.\n",
    "\n",
    "# Setup the vandermonde matrix\n",
    "N = len(x)\n",
    "A = np.hstack((np.ones((N,1)), x))\n",
    "\n",
    "\n",
    "\n",
    "left = -5\n",
    "right = 15\n",
    "bottom = -4\n",
    "top = 6\n",
    "step = 0.05\n",
    "ErrSurf = Error_Surface(y, A, left=left, right=right, top=top, bottom=bottom)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "#plt.imshow(ErrSurf, interpolation='nearest', \n",
    "#           vmin=0, vmax=10000,origin='lower',\n",
    "#           extent=(left,right,bottom,top), cmap='jet')\n",
    "\n",
    "plt.contour(ErrSurf, \n",
    "            vmin=0, vmax=10000,origin='lower', levels=np.linspace(100,5000,10),\n",
    "            extent=(left,right,bottom,top), cmap='jet')\n",
    "\n",
    "plt.xlabel('$w_0$')\n",
    "plt.ylabel('$w_1$')\n",
    "plt.title('Error Surface')\n",
    "#plt.colorbar(orientation='horizontal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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k4IcyughJcnGV5LSq0WOXepRSFjMJrol86NcXTonfT9piK9XgmqAY3c68Jvka\nNnFeSlsW1X8+Ra+Jv4f6e7qyX9BkBltfjjRyLLGASnLJUqm+wIlJ7MemYw2XOPVrGoKCNNN4kZRw\nMZPEgihpr5FcxCV6rNFj7DWCCWnCxVuC4zPvK3ktIMUD/uUG+Y1DA/r8A2v00a8cUW8hp8V+AO/O\nuVrYVQ/m0aZ4xzHqzkcD+8wJjuoZuzeM0jGmIzL2SzLGbJO0TZLeuXx5k+8GANDuriTIb1jRr6lS\nVX86ckrPv+Llo4WcEyvSvCGRsUdnDuzKRef9T1TF5xw/sEfnim/fjP2cpKC0drGkGTNoWGt3S9ot\nSffcs/4aluUAAK43aUH+S8+NavmSXj36/tt131rv3PDYuJYv6dXB39yk4bFxPbLnBZWrVgu66qGz\nJ+/6S7B6U+F2J5riA9GMXVL4NVJnZOxPSVrvb6+UdLAJ94BLqDeRZtdHCwCtJgjyB0ZO6YmDL2tw\noTdGPVhE5lM/d3u4XvuTD92tX//a87GMPe866i24Oj9Vk+vUazgkqSvSFJ9zTGyER84xKvs1I/Wq\n+DbN2K21R40x640xmyWdoyIeANBsQQb/mWde1OjpCfXkXf3XX3xvmL1L9Xkb+iJ97DnX+IG9LMfE\n+9h7EiOYCjknXOwq7zoqVWsquI5yTjybv1pN6WP3m9oBAGgZ0Sb6Dz15SLcs6o6dHx4b16KevLrz\njnKOUaVmlXMc9Ra8UOo6JjYiI9rfHoxdDwJ7znVUrVlZ18vSjckusDMWAwCAhIc3rdKO/cd1ePSM\nytVauBLc+amyfuGLfxkG8LyfsUte8Vx0npFof7tUX/JXqo/oCGJ5znHatykeAIBWl2yaD6rnt2/+\nsXBypslyVXnXCceuO46JNb93J4YfR7P5XFgJX1PNWuVdE5u462qQsQMAkGLLmmX6xiObNDTYp9/7\nt/fo0Q/cERbSPfHgWvUWvEVfok3x0YK55Cyh0UmMgrkXrJUf2J3MFoEhsAMAMIvR0xOpCyBNlap+\nVbwX2B0Tz9jTiucC0YmWgvXZy5VsmuIJ7AAAzGJosE/DY+OxY8Nj4+opuGFVvORl7NGq+GTGHm2K\nz0eWOrbW+sV4ZOwAAFxzaYV02/cc01Spqn/3B9/VG29PSfKmT+6erY+9QcZes9EJa64exXMAAMzi\nUoV0wWIxl5WxR7Zr1irnmsyq4snYAQC4hNkK6T7/wBr1Flx/gpp6WJ21jz26YFHGGTuBHQCAOZqt\nkC6ZsUcwImRwAAAL30lEQVSDvJRsip+ZsZczWgSGwA4AwBzNVkiXrIrPu05s2eJ4U3xKH3uFjB0A\ngHmVVkj36NMjmvQz9mi/ujEmXLrVyiaa4uMZe97Jbhw7xXMAAMxRspBuaLBPP3/XUv3+X5+ckbFL\nXvP7VLnqbbuzjWM3ms4oYyewAwBwGaKLxUjS8D+9pd//65Nexu5n5UETfFckS883yNitrHKuo0qx\nksn9EdgBALgKz79yVr0FV59/9iV9/YUfSvKa4SWFTfFSfIhbah87i8AAANBcB0ZOad+RV/Xlj6zX\nhhX9Gh4b1yN7XtDZiyVJ8cr4aB97NMjbYBw7M88BANBcuw6d0GfvX62NQwPhuPYnH7o7XLI1ulRr\noz72rGeeI7ADAHCFGo1rnyx6BXPRPvZoxu4m5orPsimewA4AwBVqNK69t8vL1BsF9ujMczUr5R1D\nxg4AQLM1WiCm5A9dK+TTm+KTfez5nJPZXPEUzwEAcIXSxrV7y7B6gXuuGXsuw4ydwA4AwFVIjmv/\nhS/+pSbPTkqqB3Zr4xm74xgZ4x2v+X3sVMUDANCCevJu6jj2QmJ99qA53sqrkqd4DgCAFtSVdxQ0\ntBcaNMVba8MMPqiKr9asahms8EZgBwAgQ17G7m3H+thjBXP1jN3rY/e2s2iOJ7ADAJCRAyOn9A+n\nzmtiuqIPPXlIr45Phueic8Vb1aeVrdWs8jlvO4vmeIrnAADIwIGRU3ri4Mv64q/cHU4v+8mnR8Lz\nyab42NzxfsaeRWU8GTsAABnYdeiEdm6NTy/72x9eo95gelm3XkhnVc/ga5EgX6GPHQCA1tBoetmp\nkr8ee7QqPtbHbsO548sZrMlOYAcAIAONppftCTP2Bn3skSBPUzwAAC0ibXrZR58e0WRKxh7tY/dm\nqvOCfBZN8RTPAQCQgbTpZTf/+C366nfGJCUCuxQZx17vb88iYyewAwCQkeT0st9++Q199TtjsUAu\nJcex20hVPMVzAAC0rEZTylrZMEv3gnwwjp0+dgAAWlZ05rl8ImMvhMVzVrlguBuBHQCA1lWIZOyu\nY+T6RXKx4jlFq+JpigcAoGV1JVZ0K6QE8+g4duaKBwCghc0I7LF+9ZnbbVsVb4zZ5m8OWWt3NOMe\nAAC41rrybmw/nrFH+tid7BaBmfeM3RizWdJBa+1uSSv9fQAAOk4hkbHXK+Ft2P+e9cxzzcjYV/r/\ndks66W8DANBxnnvpDfUWXH35r0b17ZfeiAXuIGOXtWEmX2nHZVv9TD2wTtJTyWv8pvptkvTO5cvn\n6c4AAMjOgZFT+t3nfqAvf2R9uIzr9r3HJCUnqFF9EZh2Hu5mjFkn6ai19mjynLV2t7V2vbV2/eDA\nYBPuDgCAq5O2jOsTD65Vb8H1JqiJzjwXLtvaok3xkeK4qJPW2oOR/c0UzgEAOtVsy7jOzNizG8d+\nTQJ7orl9BmPMNmvt4/725kTABwCg7QXLuG4cGgiPBcu4Rqvivclq/HHs7dgU71fB7zTGjBpjzs73\n6wMAMB/SlnH9xN5jmkxk7NZKOaeNq+L97PzG+X5dAADmU9oyroMLu/TGhWJKH3t249hZthUAgGsk\nuYzrbz51VP/w2tuSjc9CZ4xRzjHtXRUPAMD1Jm3hl5q14blKrQ1nngMA4HpViMw8FxbP+edyLhk7\nAABtJQjsNdsgYyewAwDQPuqLwNhYVbwkv4+dpngAANpGuChMg4ydpngAANpIwfVWdLNWyufqy7ZK\n3uxzZOwAALSRsHhO8SAvSQXXZDJXPIEdAIB5kloVH8vYCewAALSN6BC36CIwUlAVT1M8AABtoxCp\nhC8kiueYeQ4AgDZT72O3yufiIZiqeAAA2kwh5xXMecPdklXxJpOmeBaBAQBgnoz88Kx6C67+/R/9\nrd410Ccp3sfelsu2AgBwPTowckrffPFH+vJH1mvDin4Nj43rkT0v6OxkSZKXwZdZBAYAgPaw69AJ\nfe7+1do4NKC862jj0ICefOhudfvN8/SxAwDQRkZPT2jDiv7YsQ0r+jVZqkpiERgAANrK0GCfhsfG\nY8eGx8bVU/AydhaBAQCgjTy8aZV27D+uw6NnVK7WdHj0jLbvOabJUtWbiS6XTcZO8RwAAPNgy5pl\nkqTPPPOiRk9PaGiwT1PliiSvMj7nUBUPAEBb2bJmWRjgJWnT43+uiWI1nDu+QlU8AADtqz5JDYvA\nAADQ9vJudLU3bz32YLW3K0VgBwCgSYK542tWyjte9n61zfEEdgAAmiQfWeEtWBTmaueLJ7ADANAk\nYVO8vHHskq66n53ADgBAkwTFc0EfuyRVagR2AADaUr0p3quKl3TVs88R2AEAaJJYH7tLUzwAAG0t\nCOyyUt4JMnYCOwAAbYmqeAAAOkh9HLulKh4AgHYXnVK2XhVPxg4AQFuKTimbC4rnKm2csRtjPtXM\n1wcAoJnqgb2+XW7XcezGmM2S7m3W6wMA0GyFSPFcmLFTPAcAQHuqzzwX6WNvx+I5Y8w6a+3BZrw2\nAACtIjrcreBmM47dXO26r1f0osZsttYeNMY8a62d0RxvjNkmaZu/+15J/zCvNzi/BiSdafZNXEO8\nv/bVye9N4v21u05/f7dbaxdeyRdek8DuB+akk34wX2etPepflxrYE891xFq7PvObbBG8v/bWye+v\nk9+bxPtrd7y/xnJZ34wkWWt3z3J6pTFmpaR+Sf3RQA8AAK7OvPexW2v3W2v3+7uL5/v1AQDoZE2r\nirfW7rbWDs0hW58t++8EvL/21snvr5Pfm8T7a3e8vwaaUjwHAACuDcaxA0CbMsasS+xvNcZsbjSr\n56XOt5qU97fN/7ezwfU7g+vm4/6uVsr7m/X+5/r9I7AjE532gZLUaR8oSVl9oLQiY8w6Y4w1xoz6\n/3alXNN23z9/9s59kf11kuTPEXIuJWjMer7VpLy/zZIO+sXZK/39pG3GmFFJJ+fpNq9Y8v35Gt7/\n5Xz/Wjqwd/KHjdQ5waLTPlCSOu0DpYFMPlBaVL+11lhrhyTdLynt963tvn/+9yN6vw9IOudvn5SU\n/Dm91PmWkvL+Vqp+zyf9/aSP+bVbLT8BWsr7k2a//zl//1o6sKuDP2w6LFh01AdKio76QGkgkw+U\nVpR4T+uttWm/T+3+/ZO8UUbjkf0ll3m+pfkF10FB2TpJR1IuW9nOyZ5mv/85f/9aPbB37IeNOitY\n8IHCB0rL8/94frrB6Xb//l03/CTuaNqIKmvt4/7n5ZIGyVJLy+r+Wz2wd+yHzXUSLDoKHyht715r\n7bm0Ex3y/s/Jm/hL8j4f37rM8+1is7V2R/Kg36251d99S+nJUsuaw/3P+fvX0oG9Q37ZZtUhwYIP\nFD5Q2kFqd127f/8inlL93ldKOihJxpjFs51vJ8aYbdbax/3tzf5j8P6OqP6ehpSeLLWy1Pu/ku9f\nUwN7pHgs+m9z5Fxbf9jM9v4iOiFY8IHCB0pLM9401sljbf398z8f1gefE5E1ODZLOhdJFv78Eudb\nUvL9+fe90x/ZcDZyafT9fdi/frTd3t8s93/Z37+WnaDGz2RPWmvP+cNTdllrjxpjFvvH1skrhNnt\nN1UfbPVvZJIfLHb728GKd9H3N+P9N/eOG/Mr909KWhl5T89ba+9pdL5dRIaljMv7Y/J+/3uVfH/j\n8t7f48272yuTdv+d8v2TwsC+w1r7cORYx3z/gKiWDexSZ3/YXA/BAgAw/1o6sAMAgMvT0sVzAADg\n8hDYAQDoIAR2AAA6CIEdAIAOQmAHMCtjzE5jzLPGmOfTxoMDaC0EdgAN+fMprLPW3ivpY5JmLHkK\noLUQ2IHrnJ+JL/b/2SAr91cW3CzpWSmc+Wp9E28VwBzkmn0DAJruKUkfljcZ0lFJW40xR+VNs7pE\n0nAT7w3AZSJjB7Bf0r3+vx2R7X2auU7B4hlfDaClENiB65y19qS84L3eX02wX97iRAflZe33SmF/\ne9stAANcb2iKByB5K5r1J7f9hZeOGmOe9c89nPbFAFoHc8UDANBBaIoHAKCDENgBAOggBHYAADoI\ngR0AgA5CYAcAoIMQ2AEA6CAEdgAAOgiBHQCADvL/AfI6wVvCzNVaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119918710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119835e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# An implementation of Gradient Descent for solving linear a system\n",
    "\n",
    "# Setup the Design matrix\n",
    "N = len(x)\n",
    "A = np.hstack((np.ones((N,1)), x))\n",
    "\n",
    "# Starting point\n",
    "w = np.matrix('[15; -6]')\n",
    "\n",
    "# Number of iterations\n",
    "EPOCH = 5000\n",
    "\n",
    "# Learning rate: The following is the largest possible fixed rate for this problem\n",
    "#eta = 0.00016\n",
    "eta = 0.00015\n",
    "\n",
    "Error = np.zeros((EPOCH))\n",
    "W = np.zeros((2,EPOCH))\n",
    "\n",
    "for tau in range(EPOCH):\n",
    "    # Calculate the error\n",
    "    e = y - A*w    \n",
    "    \n",
    "    # Store the intermediate results\n",
    "    W[0,tau] = w[0]\n",
    "    W[1,tau] = w[1]\n",
    "    Error[tau] = (e.T*e)/2\n",
    "    \n",
    "    # Compute the gradient descent step\n",
    "    g = -A.T*e\n",
    "    w = w - eta*g\n",
    "    #print(w.T)\n",
    "    \n",
    "w_star = w    \n",
    "plt.figure(figsize=(8,8))\n",
    "plt.imshow(ErrSurf, interpolation='nearest', \n",
    "           vmin=0, vmax=1000,origin='lower',\n",
    "           extent=(left,right,bottom,top),cmap='Blues_r')\n",
    "plt.xlabel('w0')\n",
    "plt.ylabel('w1')\n",
    "\n",
    "ln = plt.Line2D(W[0,:300:1], W[1,:300:1], marker='o',markerfacecolor='w')\n",
    "plt.gca().add_line(ln)\n",
    "\n",
    "ln = plt.Line2D(w_star[0], w_star[1], marker='x',markerfacecolor='w')\n",
    "plt.gca().add_line(ln)\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(8,3))\n",
    "plt.semilogy(Error)\n",
    "plt.xlabel('Iteration tau')\n",
    "plt.ylabel('Error')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayır inişini hızlandırmak\n",
    "\n",
    "## Momentum yöntemleri, a.k.a., ağır top\n",
    "\n",
    "\\begin{align}\n",
    "p(\\tau) & =  \\nabla E(w(\\tau-1)) + \\beta p(\\tau-1) \\\\\n",
    "w(\\tau) & =  w(\\tau-1) - \\alpha p(\\tau) \n",
    "\\end{align}\n",
    "\n",
    "$\\beta=0$, bayır inişi\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119d6c0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "from notes_utilities import pnorm_ball_line\n",
    "\n",
    "\n",
    "import time\n",
    "from IPython import display\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "#y = np.array([7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73])\n",
    "y = np.array([8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68])\n",
    "#y = np.array([9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74])\n",
    "x = np.array([10., 8., 13., 9., 11., 14., 6., 4., 12., 7., 5.])\n",
    "N = len(x)\n",
    "\n",
    "# Design matrix\n",
    "A = np.vstack((np.ones(N), x)).T\n",
    "\n",
    "w_best, E, rank, s = np.linalg.lstsq(A, y)\n",
    "err = y-A.dot(w_best)\n",
    "E_min = np.sum(err**2)/N\n",
    "\n",
    "\n",
    "def inspect_momentum(alpha = 0.005, beta = 0.97):\n",
    "    ln = pnorm_ball_line(mu=w_best, A=np.linalg.cholesky(np.linalg.inv(A.T.dot(A))),linewidth=1)\n",
    "    ln2 = pnorm_ball_line(mu=w_best, A=4*np.linalg.cholesky(np.linalg.inv(A.T.dot(A))),linewidth=1)\n",
    "\n",
    "    # initial parameters\n",
    "    w0 = np.array([2., 1.])\n",
    "    w = w0.copy()\n",
    "    p = np.zeros(2)\n",
    "\n",
    "    EPOCHS = 100\n",
    "    W = np.zeros((2,EPOCHS))\n",
    "    for epoch in range(EPOCHS):\n",
    "        # Error\n",
    "        err = y-A.dot(w)\n",
    "        W[:,epoch] = w    \n",
    "        # Mean square error\n",
    "        E = np.sum(err**2)/N\n",
    "\n",
    "        # Gradient\n",
    "        dE = -2.*A.T.dot(err)/N\n",
    "        p = dE + beta*p\n",
    "\n",
    "#        if epoch%10 == 1: \n",
    "#            print(epoch,':',E)\n",
    "            # print(w)    \n",
    "\n",
    "        # Perfom one descent step\n",
    "        w = w - alpha*p\n",
    "\n",
    "\n",
    "#    print(E_min)\n",
    "\n",
    "    plt.plot(W[0,:],W[1,:],'.-b')\n",
    "    plt.plot(w_best[0],w_best[1],'ro')\n",
    "    plt.plot(w0[0],w0[1],'ko')\n",
    "    plt.xlim((1.8,4.3))\n",
    "    plt.ylim((0,1.2))\n",
    "    plt.title('$\\\\alpha = $'+str(alpha)+' $\\\\beta = $'+str(beta))\n",
    "    plt.gca().add_line(ln)\n",
    "    plt.gca().add_line(ln2)\n",
    "    plt.show()\n",
    "    \n",
    "inspect_momentum(alpha=0.0014088, beta=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c85f613f9d80405b88f3d48c9d834e30",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.005, description='alpha', max=0.02, step=0.001), FloatSlider(value=0.97, description='beta', max=0.99, step=0.001), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.inspect_momentum>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from __future__ import print_function\n",
    "from ipywidgets import interact, interactive, fixed\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pylab as plt\n",
    "from IPython.display import clear_output, display, HTML\n",
    "\n",
    "interact(inspect_momentum, alpha=(0, 0.02, 0.001), beta=(0, 0.99, 0.001))"
   ]
  }
 ],
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