Explain how pandas.core.groupby.GroupBy.apply decides the return type

puzzle.ipynb

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   "source": [
    "Import pandas:"
   ],
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   "execution_count": 1,
   "source": [
    "import pandas as pd"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define some dummy functions to apply to each group: "
   ],
   "metadata": {}
  },
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   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "def f1(df):\n",
    "    if df[\"ticker\"].iloc[0] == \"A\":\n",
    "        return df[\"price\"] / 2\n",
    "    else:\n",
    "        return df[\"price\"] * 2\n",
    "\n",
    "def f2(df):\n",
    "    if df[\"ticker\"].iloc[0] == \"A\":\n",
    "        return None\n",
    "    else:\n",
    "        return df[\"price\"] * 2"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define a data frame with equal number of groups (ticker column):"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "df1 = pd.DataFrame({\n",
    "    \"ticker\": [\"A\", \"A\", \"B\", \"B\", \"C\", \"C\"],\n",
    "    \"price\": [1, 2, 3, 4, 5, 6], \n",
    "})\n",
    "\n",
    "df1\n"
   ],
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ticker</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>B</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>C</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>C</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "  ticker  price\n",
       "0      A      1\n",
       "1      A      2\n",
       "2      B      3\n",
       "3      B      4\n",
       "4      C      5\n",
       "5      C      6"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
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   "cell_type": "markdown",
   "source": [
    "Define a dataframe with unequal number of groups:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "df2 = pd.DataFrame({\n",
    "    \"ticker\": [\"A\", \"A\", \"B\"],\n",
    "    \"price\": [1, 2, 3],\n",
    "})\n",
    "\n",
    "df2\n"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ticker</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>B</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  ticker  price\n",
       "0      A      1\n",
       "1      A      2\n",
       "2      B      3"
      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Apply `f1` to each data frame:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "df1.groupby(\"ticker\").apply(f1)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "ticker   \n",
       "A       0     0.5\n",
       "        1     1.0\n",
       "B       2     6.0\n",
       "        3     8.0\n",
       "C       4    10.0\n",
       "        5    12.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "df2.groupby(\"ticker\").apply(f1)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "ticker   \n",
       "A       0    0.5\n",
       "        1    1.0\n",
       "B       2    6.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Apply `f2` to each data frame:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "df1.groupby(\"ticker\").apply(f2)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "ticker   \n",
       "A       2    NaN\n",
       "        3    NaN\n",
       "B       2      6\n",
       "        3      8\n",
       "C       4     10\n",
       "        5     12\n",
       "dtype: object"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "metadata": {}
  },
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   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "df2.groupby(\"ticker\").apply(f2)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ticker</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "          2\n",
       "ticker     \n",
       "A       NaN\n",
       "B       6.0"
      ]
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     "execution_count": 8
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   "source": [
    "Applying `f2` on `df1` results in a Series.\n\n",
    "Applying `f2` on `df1` results in a Dataframe.\n\n",
    "Applying `f1` on both `df1` and `df2` results in a Series.\n",
    "\n",
    "Why?"
   ],
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