Lecture04_Sub_Vectors-and-Matrices.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Our Goal\n",
    "- `v = (2, 0, 3, 9, 0, 1, 0, -5, 8, 7, 1, 7)`\n",
    "- `w = (8, 3, 1, 1, 0, 4, -1, 0, 1, 0, 1, 11)`\n",
    "\n",
    "&#48289;&#53552;&#44036;&#51032; &#50976;&#53364;&#47532;&#46356;&#50504; &#44144;&#47532;&#47484; &#51060;&#50857;&#54616;&#50668; &#50976;&#49324;&#46020;&#47484; &#52769;&#51221;&#54644;&#48372;&#51088;."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## &#54028;&#51060;&#50028;&#51012; &#51060;&#50857;&#54616;&#50668; &#48289;&#53552;&#47484; &#45796;&#47336;&#50612;&#48372;&#51088;."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = (2, 0, 3, 9, 0, 1, 0, -5, 8, 7, 1, 7)\n",
    "w = (8, 3, 1, 1, 0, 4, -1, 0, 1, 0, 1, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#48289;&#53552;&#51032; &#45927;&#49480;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector_add = [v_i + w_i for v_i, w_i in zip(v, w)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 3, 4, 10, 0, 5, -1, -5, 9, 7, 2, 18]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_add"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#48289;&#53552;&#51032; &#48772;&#49480;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector_subtract = [v_i - w_i for v_i, w_i in zip(v, w)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-6, -3, 2, 8, 0, -3, 1, -5, 7, 7, 0, -4]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_subtract"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#48289;&#53552;&#51032; &#49828;&#52860;&#46972; &#44273;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "scala_multiply = [2 * v_i for v_i in v]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 0, 6, 18, 0, 2, 0, -10, 16, 14, 2, 14]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scala_multiply"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#48289;&#53552;&#51032; &#45236;&#51201; &#44396;&#54616;&#44592;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# v_1 * w_1 + ... + v_n * w_n\n",
    "dot = sum(v_i * w_i for v_i, w_i in zip(v, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "118"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#48289;&#53552;&#44036;&#51032; &#44144;&#47532; &#44396;&#54616;&#44592;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "squared_vector : [36, 9, 4, 64, 0, 9, 1, 25, 49, 49, 0, 16]\n",
      "squared_sum : 262\n",
      "distance : 16.186414056238647\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "squared = [elem ** 2 for elem in vector_subtract]\n",
    "print('squared_vector :', squared)\n",
    "\n",
    "squared_sum = sum(squared)\n",
    "print('squared_sum :', squared_sum)\n",
    "\n",
    "distance = math.sqrt(squared_sum)\n",
    "print('distance :', distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# &#54028;&#51060;&#50028;&#51012; &#51060;&#50857;&#54616;&#50668; &#54665;&#47148;&#51012; &#45796;&#47336;&#50612;&#48372;&#51088;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#54665;&#47148;&#51032; &#53356;&#44592; &#44396;&#54616;&#44592;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def shape(A):\n",
    "    num_rows = len(A)\n",
    "    num_cols = len(A[0])\n",
    "    return num_rows, num_cols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#54665;&#47148;&#51032; &#54665;&#44284; &#50676;&#51012; &#50619;&#44592;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# i&#48264;&#51704; &#54665;&#51012; &#50619;&#44592;\n",
    "def get_row(A, i):\n",
    "    return A[i]\n",
    "\n",
    "# j&#48264;&#51704; &#50676;&#51012; &#50619;&#44592;\n",
    "def get_columns(A, j):\n",
    "    return [A_i[i] for A_i in A]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### &#54665;&#47148;&#51012; &#49373;&#49457;&#54616;&#44592;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_matrix(num_rows, num_cols, entry_fn):\n",
    "    \"\"\"(i,j)&#48264;&#51704; &#50896;&#49548;&#44032; entry_fn(i,j)&#51064; num_rows by num_cols list&#47484; &#48152;&#54872;\"\"\"\n",
    "    \n",
    "    return [[entry_fn(i, j) for j in range(num_cols)] for i in range(num_rows)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 5 by 5 &#45800;&#50948; &#54665;&#47148; &#49373;&#49457;&#54616;&#44592;\n",
    "def is_diagonal(i,j):\n",
    "    \"\"\"&#45824;&#44033;&#49440;&#51032; &#50896;&#49548;&#45716; 1, &#45208;&#47672;&#51648; &#50896;&#49548;&#45716; 0\"\"\"\n",
    "    return 1 if i==j else 0\n",
    "\n",
    "identity_matrix = make_matrix(5, 5, is_diagonal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0, 0, 0, 0],\n",
       " [0, 1, 0, 0, 0],\n",
       " [0, 0, 1, 0, 0],\n",
       " [0, 0, 0, 1, 0],\n",
       " [0, 0, 0, 0, 1]]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "identity_matrix"
   ]
  }
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