Lecture09_Sub_Gradient_01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# &#44221;&#49324;&#54616;&#44053;&#48277;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.  $f(x,y)=(x-2)^2+(y-2)^2+4$ &#51032; &#52572;&#49548;&#44050;&#51012; &#44221;&#49324;&#54616;&#44053;&#48277;&#51012; &#51060;&#50857;&#54616;&#50668; &#44396;&#54616;&#46972;."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1. gradient&#47484; &#44396;&#54620;&#45796;."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial}{\\partial x}f(x, y)=2(x-2)$$ $$\\frac{\\partial}{\\partial y}f(x, y)=2(y-2)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_gradient(v):\n",
    "    \"\"\"&#54200;&#48120;&#48516; &#54632;&#49688;&#47484; &#44396;&#54620;&#45796;. &#51593; &#49884;&#51216;&#50640;&#49436;&#51032; gradient\"\"\"\n",
    "    return [2 * (v_i - 2) for v_i in v]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2. step&#51012; &#44396;&#54620;&#45796;."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_{t+1} = x_{t} -\\rho \\frac{\\partial}{\\partial x}f(x, y)=x_{t}-\\rho \\times 2(x-2)$$\n",
    "$$y_{t+1} = y_{t} -\\rho \\frac{\\partial}{\\partial y}f(x, y)=y_{t}-\\rho \\times 2(y-2)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def step(v, gradient, step_size):\n",
    "    \"\"\"&#54788;&#51116; &#50948;&#52824;&#50640;&#49436; step_size&#50752; gradient &#51060;&#50857;&#54616;&#50668; &#51060;&#46041;&#54620;&#45796;.\"\"\"\n",
    "    return [v_i - step_size * direction_i \n",
    "            for v_i, direction_i in zip(v, gradient)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3. &#49884;&#51089;&#51216;&#51008; &#47004;&#45924;&#54616;&#44172; &#49440;&#53469;&#54644;&#48372;&#51088;."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-4, 9]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "random_generator = np.random.RandomState(42)\n",
    "\n",
    "# &#52395;&#48264;&#51704; &#49884;&#51089;&#51216; x_0, y_0&#47484; &#49440;&#53469;&#54620;&#45796;.\n",
    "v = [random_generator.randint(-10, 10) for _ in range(2)]\n",
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. alpha (&#54617;&#49845;&#47456;)&#47484; &#49444;&#51221;&#54616;&#51088;."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. &#50508;&#44256;&#47532;&#51608;&#51012; &#47688;&#52636; &#51312;&#44148;&#51012; &#49444;&#51221;&#54616;&#51088;.\n",
    "\n",
    "&#51060;&#51204;&#51032; &#50948;&#52824;&#50752; &#54788;&#51116;&#51032; &#50948;&#52824;&#44032; tolerance &#48372;&#45796; &#51089;&#51004;&#47732; &#47688;&#52632;&#45796;. &#51593; $$\\text{dist}(v_t, v_{t+1}) < \\text{tolerance} \\text{  where  } v=(x, y)$$ &#51060;&#47732; &#47688;&#52632;&#45796;."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "def distance(v, w):\n",
    "    return math.sqrt(sum([(v_i - w_i)**2 for v_i, w_i in zip(v, w)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.4314146158724235, 7.169983718517828]\n",
      "[-1.2729059162946232, 5.818390235677062]\n",
      "[-0.41726718564055343, 4.820145049913981]\n",
      "[0.21468114384727552, 4.082871998844846]\n",
      "[0.6814186544753634, 3.538344903112076]\n",
      "[1.0261365588709, 3.136174014650617]\n",
      "[1.2807345521861158, 2.839143022449532]\n",
      "[1.4687727636442554, 2.619765109081703]\n",
      "[1.6076519767439397, 2.4577393604654048]\n",
      "[1.7102238725390735, 2.3380721487044145]\n",
      "[1.7859803055731232, 2.249689643498023]\n",
      "[1.841931666338698, 2.1844130559381862]\n",
      "[1.8832556126511177, 2.136201785240363]\n",
      "[1.9137762025968486, 2.1005944303036768]\n",
      "[1.9363177673252754, 2.0742959381205117]\n",
      "[1.952966270558973, 2.054872684347865]\n",
      "[1.965262340652674, 2.040527269238547]\n",
      "[1.9743438381078438, 2.029932188874182]\n",
      "[1.981051151533985, 2.022106989877018]\n",
      "[1.9860049659922916, 2.0163275396756597]\n",
      "[1.9896637002914348, 2.0120590163266585]\n",
      "[1.9923659283995712, 2.008906416867166]\n",
      "[1.9943617105885405, 2.0065780043133685]\n",
      "[1.9958357336489234, 2.004858310742922]\n",
      "[1.9969244015379088, 2.0035881982057724]\n",
      "[1.9977284580037558, 2.0026501323289514]\n",
      "[1.9983223092662126, 2.001957305856086]\n",
      "[1.9987609094602303, 2.001445605629732]\n",
      "[1.9990848460119461, 2.0010676796527305]\n",
      "[1.9993240955402607, 2.0007885552030302]\n",
      "[1.9995007978496964, 2.0005824025086882]\n",
      "[1.999631304715812, 2.00043014449822]\n"
     ]
    }
   ],
   "source": [
    "cnt = 0  # &#51473;&#44036; &#44208;&#44284;&#44050;&#51012; &#52636;&#47141;&#54624; &#46412; &#49324;&#50857;&#54616;&#44592; &#50948;&#54632;\n",
    "tol = 0.00001\n",
    "gradients = []  # Gradient&#51032; &#48320;&#54868;\n",
    "plot_points = []  # Plotting&#51012; &#50948;&#54620; &#44163;\n",
    "\n",
    "while True:\n",
    "    cnt += 1\n",
    "    gradient = get_gradient(v)  # &#49884;&#51216;&#50640;&#49436;&#51032; gradient\n",
    "    next_v = step(v, gradient, alpha)\n",
    "    if not cnt % 15:\n",
    "        plot_points.append(next_v)\n",
    "        print(next_v)  # Debugging &#50857;\n",
    "    if distance(next_v, v) < tol:\n",
    "        break\n",
    "    gradients.append(next_v)\n",
    "    v = next_v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Numpy array&#47196; &#48320;&#44221;&#54616;&#47732; &#49324;&#50857;&#51060; &#54200;&#54616;&#45796;.\n",
    "gradients = np.array(gradients)\n",
    "\n",
    "x = gradients[:, 0]\n",
    "y = gradients[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# &#46321;&#44256;&#49440;&#51012; &#44536;&#47532;&#44592; &#50948;&#54644;&#49436;&#45716; meshgrid&#44032; &#54596;&#50836;&#54632;\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = (X-2) ** 2 + (Y-2) ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# &#52572;&#49548;&#44050;&#51032; &#48320;&#54868;&#47484; &#54869;&#51064;&#54616;&#44592; &#50948;&#54616;&#50668; plot\n",
    "plot_points = np.array(plot_points)\n",
    "\n",
    "px = plot_points[:, 0]\n",
    "py = plot_points[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d873a20>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "contours = plt.contourf(x, y, Z, 20, cmap='RdGy')\n",
    "plt.plot(px, py, \"b-o\")\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## 2. $f(x, y) = (1-x)^2+100(y-x^2)^2$ &#51032; &#52572;&#49548;&#44050;&#51012; &#44221;&#49324;&#54616;&#44053;&#48277;&#51012; (&#46608;&#45716; &#52572;&#45824;&#44050;&#51012; &#44221;&#49324;&#49345;&#49849;&#48277;&#51012;) &#49324;&#50857;&#54616;&#50668; &#44396;&#54616;&#46972;. &#54644;&#45817; &#54632;&#49688;&#45716; Rosenbrock function&#51060;&#45796;."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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",
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