{
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   "id": "73514e0b-dd70-436e-9ceb-1b7c01e3f27c",
   "metadata": {},
   "source": [
    "This notebook illustrates anonymous functions and functions to store data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1414c718-3e8c-408a-bede-da6980ca6c04",
   "metadata": {},
   "source": [
    "# 1. Anonymous Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3fd9069-e9a7-40c2-9716-f57b3174bc25",
   "metadata": {},
   "source": [
    "Consider the guessing of a secret number.  With `lambda` we can make a function which acts as an *oracle*.  The oracle is a function which returns `True` or `False` depending on whether the input of the oracle matches the secret or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9d3b1a85-c8ca-402a-aa5b-67ce6ba6854a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_oracle():\n",
    "    \"\"\"\n",
    "    Returns an oracle for a single digit number.\n",
    "    \"\"\"\n",
    "    from random import randint\n",
    "    nbr = randint(0, 9)\n",
    "    return lambda x: x == nbr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "185665fd-0256-4597-a6b3-58932dd11e0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "oracle = make_oracle()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a5796990-cda4-4d01-9677-a963d38099d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "function"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(oracle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "96a4cda4-a359-4a06-9e6f-b7131d82c08e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oracle(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "91bed94b-8609-4652-91a6-fda192730966",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oracle(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "246b5e50-7cd1-4b0d-b08c-a4f627d60d8f",
   "metadata": {},
   "source": [
    "Without any feedback on whether our guess was too small or too large, the game gets tedious.  With a list comprehension we can get the answer quickly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "89c45ae4-f229-4e17-abb8-6076eabb75bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[False, False, False, False, False, True, False, False, False, False]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = [oracle(x) for x in range(10)]\n",
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "087c8f5a-d636-4db9-96a6-57a24c4b5197",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = L.index(True)\n",
    "idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "46e62967-2e72-45e1-8f52-d6c6bfd6cc65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oracle(idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "715f939e-3214-4fcb-8e92-211c2173f667",
   "metadata": {},
   "source": [
    "# 2. Monte Carlo with List Comprehensions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bab96fc-0bda-45df-b8da-1f5dcbee6bc0",
   "metadata": {},
   "source": [
    "A Monte Carlo method to estimate $\\pi$ counts the number of points uniformly generated in a square that are in the unit disk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "af45d89a-2d53-40df-a228-03a4e717ea15",
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import uniform as u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19030634-07fd-490c-b503-905cbe1f403b",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10**6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d68f7cc3-8e92-4b82-b25f-27f8e8705c8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [u(0, 1) for _ in range(N)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fc6cdae7-e679-486f-b898-e28e4ced45ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = [u(0, 1) for _ in range(N)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e57db1f7-f968-43a6-a9b2-f0cf684fd295",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = list(zip(X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "076be143-ff5d-4ed9-b1c5-8790c2616ee5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Z do this only for small N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "91a83c32-a1a1-4072-871b-439e43a8c8b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "R = [(x, y) for (x, y) in Z if x**2 + y**2 <= 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3a76100f-25d4-456f-9c15-6f223e46540b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# R only for small N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b3097712-e7d1-49c5-8663-a8f1af178388",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.14318"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4.0*len(R)/N"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0cdecf9-b50a-4b29-b034-34ec96e6a2b6",
   "metadata": {},
   "source": [
    "# 3. Storing Data in Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac32d4ce-c6a4-4220-8609-b90ce1299559",
   "metadata": {},
   "source": [
    "We can add a list or dictionary with a default empty list or dictionary to a function.  This default argument is useful to store data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "515ead4f-855c-409a-b9f0-e6a45f7cd40a",
   "metadata": {},
   "source": [
    "Consider again the guessing of a secret number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d7bc750f-2137-496b-904b-21ccbdc9a275",
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import randint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "728483ee-05ce-4e8a-878d-8e2441c46541",
   "metadata": {},
   "outputs": [],
   "source": [
    "def guess(data={}, **options):\n",
    "    \"\"\"\n",
    "    Prompts to a guess a secret number\n",
    "    stored in the dictionary data.\n",
    "    The dictionary is printed if verbose.\n",
    "    \"\"\"\n",
    "    if len(data) == 0:\n",
    "        data['secret'] = randint(0, 9)\n",
    "    if 'verbose' in options:\n",
    "        if options['verbose']:\n",
    "            print('data =', data)\n",
    "    nbr = int(input('Make a guess : '))\n",
    "    return nbr == data['secret']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c076ff81-18e3-4f39-a5f5-00541c397f8c",
   "metadata": {},
   "source": [
    "The `verbose=True` option shows the dictionary `data`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "090e2f08-6793-444f-9f84-db867dd4b6c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Make a guess :  0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guess()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "46424050-29bc-425d-987d-75394801202e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data = {'secret': 9}\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Make a guess :  9\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guess(verbose=True)"
   ]
  }
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