gradient_decent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient Decent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Task\n",
    "Function J($\\theta$1, $\\theta$2)\n",
    "\n",
    "Goal: Min of J w.r.t. $\\theta$1, $\\theta$2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Update rule:\n",
    "\n",
    "$\\theta$j = $\\theta$j - $\\alpha$$\\frac{\\partial v}{\\partial t}$J($\\theta$1, $\\theta$2)\n",
    "\n",
    "$\\alpha$ = learning rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gradient Decent Animation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"https://miro.medium.com/max/795/1*OG1d4edy5BFYeQ0yHjBOJA.gif\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Let's impliment our own gradient decent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Declare Some Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Staring point\n",
    "cur_x = 3\n",
    "# Learning rate\n",
    "rate = 0.01\n",
    "# This tells us when to stop the algorithm\n",
    "precision = 0.000001\n",
    "previous_step_size = 1\n",
    "# maximum number of iterations\n",
    "max_iters = 10000\n",
    "#iteration counter\n",
    "iters = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Define our function and it's gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Our function\n",
    "f = lambda x: (x+5)**2\n",
    "# Gradient of our function\n",
    "df = lambda x: 2*(x+5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# f = lambda x: x**4  - 20*x**2 + 10*x\n",
    "# df = lambda x: 4*x**3 - 40*x + 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Gradient Decent Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1 \n",
      "X value is 2.84\n",
      "Iteration 2 \n",
      "X value is 2.6832\n",
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      "Iteration 507 \n",
      "X value is -4.999715088248159\n",
      "Iteration 508 \n",
      "X value is -4.999720786483196\n",
      "Iteration 509 \n",
      "X value is -4.999726370753532\n",
      "Iteration 510 \n",
      "X value is -4.999731843338461\n",
      "Iteration 511 \n",
      "X value is -4.999737206471692\n",
      "Iteration 512 \n",
      "X value is -4.999742462342258\n",
      "Iteration 513 \n",
      "X value is -4.999747613095413\n",
      "Iteration 514 \n",
      "X value is -4.999752660833504\n",
      "Iteration 515 \n",
      "X value is -4.999757607616834\n",
      "Iteration 516 \n",
      "X value is -4.999762455464498\n",
      "Iteration 517 \n",
      "X value is -4.999767206355208\n",
      "Iteration 518 \n",
      "X value is -4.999771862228104\n",
      "Iteration 519 \n",
      "X value is -4.999776424983542\n",
      "Iteration 520 \n",
      "X value is -4.9997808964838715\n",
      "Iteration 521 \n",
      "X value is -4.999785278554194\n",
      "Iteration 522 \n",
      "X value is -4.9997895729831106\n",
      "Iteration 523 \n",
      "X value is -4.999793781523448\n",
      "Iteration 524 \n",
      "X value is -4.999797905892979\n",
      "Iteration 525 \n",
      "X value is -4.999801947775119\n",
      "Iteration 526 \n",
      "X value is -4.999805908819617\n",
      "Iteration 527 \n",
      "X value is -4.999809790643225\n",
      "Iteration 528 \n",
      "X value is -4.99981359483036\n",
      "Iteration 529 \n",
      "X value is -4.999817322933753\n",
      "Iteration 530 \n",
      "X value is -4.999820976475077\n",
      "Iteration 531 \n",
      "X value is -4.999824556945576\n",
      "Iteration 532 \n",
      "X value is -4.999828065806665\n",
      "Iteration 533 \n",
      "X value is -4.9998315044905315\n",
      "Iteration 534 \n",
      "X value is -4.999834874400721\n",
      "Iteration 535 \n",
      "X value is -4.999838176912706\n",
      "Iteration 536 \n",
      "X value is -4.999841413374452\n",
      "Iteration 537 \n",
      "X value is -4.999844585106963\n",
      "Iteration 538 \n",
      "X value is -4.999847693404824\n",
      "Iteration 539 \n",
      "X value is -4.999850739536727\n",
      "Iteration 540 \n",
      "X value is -4.999853724745993\n",
      "Iteration 541 \n",
      "X value is -4.999856650251073\n",
      "Iteration 542 \n",
      "X value is -4.999859517246051\n",
      "Iteration 543 \n",
      "X value is -4.99986232690113\n",
      "Iteration 544 \n",
      "X value is -4.999865080363108\n",
      "Iteration 545 \n",
      "X value is -4.999867778755846\n",
      "Iteration 546 \n",
      "X value is -4.999870423180729\n",
      "Iteration 547 \n",
      "X value is -4.999873014717115\n",
      "Iteration 548 \n",
      "X value is -4.999875554422772\n",
      "Iteration 549 \n",
      "X value is -4.999878043334316\n",
      "Iteration 550 \n",
      "X value is -4.99988048246763\n",
      "Iteration 551 \n",
      "X value is -4.999882872818278\n",
      "Iteration 552 \n",
      "X value is -4.999885215361912\n",
      "Iteration 553 \n",
      "X value is -4.999887511054674\n",
      "Iteration 554 \n",
      "X value is -4.999889760833581\n",
      "Iteration 555 \n",
      "X value is -4.999891965616909\n",
      "Iteration 556 \n",
      "X value is -4.999894126304571\n",
      "Iteration 557 \n",
      "X value is -4.999896243778479\n",
      "Iteration 558 \n",
      "X value is -4.999898318902909\n",
      "Iteration 559 \n",
      "X value is -4.999900352524851\n",
      "Iteration 560 \n",
      "X value is -4.9999023454743545\n",
      "Iteration 561 \n",
      "X value is -4.999904298564868\n",
      "Iteration 562 \n",
      "X value is -4.9999062125935705\n",
      "Iteration 563 \n",
      "X value is -4.999908088341699\n",
      "Iteration 564 \n",
      "X value is -4.9999099265748645\n",
      "Iteration 565 \n",
      "X value is -4.999911728043367\n",
      "Iteration 566 \n",
      "X value is -4.9999134934825\n",
      "Iteration 567 \n",
      "X value is -4.99991522361285\n",
      "Iteration 568 \n",
      "X value is -4.999916919140593\n",
      "Iteration 569 \n",
      "X value is -4.999918580757781\n",
      "Iteration 570 \n",
      "X value is -4.999920209142625\n",
      "Iteration 571 \n",
      "X value is -4.999921804959773\n",
      "Iteration 572 \n",
      "X value is -4.9999233688605775\n",
      "Iteration 573 \n",
      "X value is -4.999924901483366\n",
      "Iteration 574 \n",
      "X value is -4.999926403453699\n",
      "Iteration 575 \n",
      "X value is -4.999927875384625\n",
      "Iteration 576 \n",
      "X value is -4.999929317876933\n",
      "Iteration 577 \n",
      "X value is -4.999930731519394\n",
      "Iteration 578 \n",
      "X value is -4.999932116889006\n",
      "Iteration 579 \n",
      "X value is -4.999933474551226\n",
      "Iteration 580 \n",
      "X value is -4.999934805060202\n",
      "Iteration 581 \n",
      "X value is -4.999936108958998\n",
      "Iteration 582 \n",
      "X value is -4.999937386779818\n",
      "Iteration 583 \n",
      "X value is -4.999938639044221\n",
      "Iteration 584 \n",
      "X value is -4.999939866263337\n",
      "Iteration 585 \n",
      "X value is -4.99994106893807\n",
      "Iteration 586 \n",
      "X value is -4.999942247559309\n",
      "Iteration 587 \n",
      "X value is -4.999943402608123\n",
      "Iteration 588 \n",
      "X value is -4.9999445345559606\n",
      "Iteration 589 \n",
      "X value is -4.999945643864842\n",
      "Iteration 590 \n",
      "X value is -4.999946730987545\n",
      "Iteration 591 \n",
      "X value is -4.999947796367794\n",
      "Iteration 592 \n",
      "X value is -4.999948840440438\n",
      "Iteration 593 \n",
      "X value is -4.999949863631629\n",
      "Iteration 594 \n",
      "X value is -4.999950866358997\n",
      "Iteration 595 \n",
      "X value is -4.9999518490318176\n",
      "The local minimum occurs at -4.9999518490318176\n"
     ]
    }
   ],
   "source": [
    "while previous_step_size > precision and iters < max_iters:\n",
    "    # Store current x value in prev_x\n",
    "    prev_x = cur_x\n",
    "    # Grad descent step\n",
    "    cur_x = cur_x - rate * df(prev_x)\n",
    "    # Change in x\n",
    "    previous_step_size = abs(cur_x - prev_x)\n",
    "    #iteration count\n",
    "    iters += 1\n",
    "    print(\"Iteration\",iters,\"\\nX value is\",cur_x) #Print iterations\n",
    "    \n",
    "print(\"The local minimum occurs at\", cur_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7f36f40e80>]"
      ]
     },
     "execution_count": 186,
     "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": [
    "x = np.arange(-10,0,0.2)\n",
    "y = np.array([f(each) for each in x])\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.plot(cur_x, f(cur_x), 'ro', markersize=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "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": [
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "def f(x, y):\n",
    "    return np.sin(np.sqrt(x ** 2 + y ** 2))\n",
    "\n",
    "x = np.linspace(-6, 6, 30)\n",
    "y = np.linspace(-6, 6, 30)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = f(X, Y)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "# ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
    "ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='viridis', edgecolor='none')\n",
    "ax.plot([0],[4],[2.5], 'ro', markersize=20)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z')\n",
    "ax.view_init(60, 35)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}