datasets_toy1.ipynb

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    "# Toy1 Dataset - Geometric Solids\n",
    "* **[T81-558: Applications of Deep Learning](https://sites.wustl.edu/jeffheaton/t81-558/)**\n",
    "* Dataset created by [Jeff Heaton](http://sites.wustl.edu/jeffheaton)\n",
    "\n",
    "This is a simple dataset with 10,000 rows, I use it for my [deep learning course](https://sites.wustl.edu/jeffheaton/t81-558/).  There is no noise, no missing values, and it is 100% predictable if you know the rule.  The following fields are present:\n",
    "\n",
    "* **metal** - The metal that the object is made of. Values of gold, silver, bronze, and platinum.\n",
    "* **shape** - The shape of the geometric solid.  Values of box, cylinder, sphere.\n",
    "* **height** - The height (in CM) of the object.  Cylinders always run along the height.\n",
    "* **length** - The length (in CM), or depth, of the object.  For spheres and cylinders the length/width are always the same.\n",
    "* **width** - The width (in CM), or depth, of the object.  For spheres and cylinders the length/width are always the same.\n",
    "* **weight** - The weight (in grams) of the object.\n",
    "\n",
    "The following code shows 10 sample rows."
   ]
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>metal</th>\n",
       "      <th>shape</th>\n",
       "      <th>height</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>silver</td>\n",
       "      <td>cylinder</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>1235.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>bronze</td>\n",
       "      <td>cylinder</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>525.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>bronze</td>\n",
       "      <td>sphere</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>38.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>silver</td>\n",
       "      <td>sphere</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>1186.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>tin</td>\n",
       "      <td>cylinder</td>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2066.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>tin</td>\n",
       "      <td>box</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>292.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>tin</td>\n",
       "      <td>box</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>175.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>platinum</td>\n",
       "      <td>box</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>1349.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>silver</td>\n",
       "      <td>cylinder</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>370.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>platinum</td>\n",
       "      <td>box</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>3796.20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      metal     shape  height  length  width   weight\n",
       "0    silver  cylinder       6       5      5  1235.82\n",
       "1    bronze  cylinder       2       6      6   525.34\n",
       "2    bronze    sphere       2       2      2    38.91\n",
       "3    silver    sphere       6       6      6  1186.39\n",
       "4       tin  cylinder      10       6      6  2066.85\n",
       "5       tin       box      10       2      2   292.40\n",
       "6       tin       box       6       1      4   175.44\n",
       "7  platinum       box       8       2      4  1349.76\n",
       "8    silver  cylinder       5       3      3   370.75\n",
       "9  platinum       box       2       9     10  3796.20"
      ]
     },
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   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "path = \"./data/\"\n",
    "    \n",
    "filename = os.path.join(path,\"toy1.csv\")\n",
    "df = pd.read_csv(filename,na_values=['NA','?'])\n",
    "\n",
    "df[0:10]"
   ]
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   "source": [
    "This dataset deals with the weights of different geometric solids, of different sizes, and of different metals.  Use the columns metal, shape, height, length, and width to determine the weight.\n",
    "\n",
    "The geometric solids are:\n",
    "\n",
    "**Box**\n",
    "\n",
    "$ V = lwh $\n",
    "\n",
    "**Cylinder**\n",
    "\n",
    "$ V = \\pi r^2 h = \\pi {\\frac{w}{2}}^2 h $\n",
    "\n",
    "\n",
    "**Sphere**\n",
    "\n",
    "$ V = \\frac{4}{3} \\pi r^3 = \\frac{4}{3} \\pi {\\frac{h}{2}}^3  $\n",
    "\n",
    "The following code shows how to exactly calculate the weight for any row in the dataset.  Of course, the idea is to create a model, of some sort, that is able to obtain the same value.\n"
   ]
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     "text": [
      "1235.8240101058848\n",
      "525.3371235332852\n",
      "38.913861002465566\n",
      "1186.3910497016493\n",
      "2066.8538067967247\n",
      "292.4\n",
      "175.44\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "def calculate_weight(metal,shape,h,l,w):\n",
    "    metal_name = ['gold','silver','bronze','tin','platinum']\n",
    "    metal_density = [19.32,10.49, 9.29,7.31, 21.09 ]\n",
    "    shape_name = ['sphere','box','cylinder']\n",
    "    \n",
    "    metal = metal_name.index(metal)\n",
    "    shape = shape_name.index(shape)\n",
    "    \n",
    "    if shape==0:\n",
    "        # sphere\n",
    "        vol = (4.0/3.0)  * math.pi * ((l/2.0)**3)\n",
    "    elif shape==1:\n",
    "        # box\n",
    "        vol = l * w * h\n",
    "    elif shape==2:\n",
    "        # cylinder\n",
    "        vol = math.pi * ((w/2.0)**2.0) * h\n",
    "        \n",
    "    weight = vol * metal_density[metal]\n",
    "        \n",
    "    return weight\n",
    "    \n",
    "print(calculate_weight('silver', 'cylinder', 6, 5, 5))\n",
    "print(calculate_weight('bronze', 'cylinder', 2, 6, 6))\n",
    "print(calculate_weight('bronze', 'sphere', 2, 2, 2))\n",
    "print(calculate_weight('silver', 'sphere', 6, 6, 6))\n",
    "print(calculate_weight('tin', 'cylinder', 10, 6, 6))\n",
    "print(calculate_weight('tin', 'box', 10, 2, 2))\n",
    "print(calculate_weight('tin', 'box', 6, 1, 4))"
   ]
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