docs/Demo.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <img style=\"float: left; padding-right: 10px; width: 45px\" src=\"https://raw.githubusercontent.com/Harvard-IACS/2018-CS109A/master/content/styles/iacs.png\"> CS207 Systems Development for Computational Science: \n",
    "## autodiff Demo\n",
    "\n",
    "\n",
    "\n",
    "**Harvard University**<br/>\n",
    "**Fall 2018**<br/>\n",
    "**Team Members**: Will Claybaugh, Erin Williams, and Bruce Xiong\n",
    "\n",
    "<hr style=\"height:2pt\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "#NOTE: You must replace 'C:/Users/erina/cs207-FinalProject/' below with the local path to autodiff on your machine\n",
    "sys.path.insert(0, \"C:/Users/erina/cs207-FinalProject/\")\n",
    "\n",
    "import autodiff.autodiff as ad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Return the value and derivatives of the dual number: Basic Example**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(a,b):\n",
    "    return a/b*ad.sin(a*b)\n",
    "\n",
    "out = f(ad.DualNumber('x',2),ad.DualNumber('y',3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1862769987992839"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.value\n",
    "# Should return -0.186276998"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(float, {'y': 1.3423193818002492, 'x': 1.82720207390109})"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.82720207390109"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.derivatives['x']\n",
    "# Should return 1.8272020739"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3423193818002492"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.derivatives['y']\n",
    "# Should return 1.34231938"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.derivatives['z']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Handling Edge Cases**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(a):\n",
    "    return a**(1/3)\n",
    "\n",
    "new = g(ad.DualNumber('x',0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(float, {'x': inf})"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new.derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Handling pre-existing code: the Riemann Zeta Function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reimann_zeta(x, stop = 10000):\n",
    "    output = 0\n",
    "    i = 1\n",
    "    while i < stop:\n",
    "        output +=1/(i**x)\n",
    "        i += 1\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0083492773819207"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reimann_zeta(7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "demo = reimann_zeta(ad.DualNumber('y', 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0083492773819207"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demo.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.00603351696087561"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demo.derivatives['y']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Provides warning when results are unstable**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:/Users/erina/cs207-FinalProject\\autodiff.py:308: UserWarning: Computation is close to a branch. Derivatives may not be accurate.\n",
      "  warnings.warn(\"Computation is close to a branch. Derivatives may not be accurate.\")\n"
     ]
    }
   ],
   "source": [
    "demo = reimann_zeta(ad.DualNumber('y',7), ad.DualNumber('x', 100.00))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0083492773817515"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demo.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.006033516960057043, 0.0)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demo.derivatives['y'], demo.derivatives['x']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Handling Numpy arrays**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "a = ad.DualNumber('x',np.array([2,3]))\n",
    "b = ad.DualNumber('y',np.array([[4,5,6,7],[8,9,10,11]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = ad.dot(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([32, 37, 42, 47])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(<function autodiff.DualNumber.np_closure.<locals>.inner_func()>,\n",
       "            {'x[0]': array([4., 5., 6., 7.]),\n",
       "             'x[1]': array([ 8.,  9., 10., 11.]),\n",
       "             'y[0,0]': array([2., 0., 0., 0.]),\n",
       "             'y[0,1]': array([0., 2., 0., 0.]),\n",
       "             'y[0,2]': array([0., 0., 2., 0.]),\n",
       "             'y[0,3]': array([0., 0., 0., 2.]),\n",
       "             'y[1,0]': array([3., 0., 0., 0.]),\n",
       "             'y[1,1]': array([0., 3., 0., 0.]),\n",
       "             'y[1,2]': array([0., 0., 3., 0.]),\n",
       "             'y[1,3]': array([0., 0., 0., 3.])})"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4., 5., 6., 7.])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.derivatives[\"x[0]\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 0., 0., 0.])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.derivatives['y[0,0]']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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