loads.ipynb

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   "outputs": [],
   "source": [
    "from rich import print"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6118391-3fd3-4ea8-a0fc-8ffd6c7cb87c",
   "metadata": {
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    "tags": []
   },
   "source": [
    "# Load Cases 🐃 🚚"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bdbda39-e409-4d8e-8f09-947a6f7791cf",
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   "source": [
    "## 1. Like working with different currencies 💱\n",
    "\n",
    "Totals (or sub-totals) need to be collected for each load category separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">50</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">90</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">15</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span>\n",
       "</pre>\n"
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       "\u001b[33mD\u001b[0m=\u001b[1;36m50\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m90\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m15\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;36m10\u001b[0m\n"
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   "source": [
    "D_2 = 25\n",
    "L_2 = 30\n",
    "S_2 = 15\n",
    "W_2 = 10\n",
    "\n",
    "D_1 = 25\n",
    "L_1 = 60\n",
    "\n",
    "D = D_1 + D_2\n",
    "L = L_1 + L_2\n",
    "S = S_2\n",
    "W = W_2\n",
    "print(f\"{D=}, {L=}, {S=}, {W=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f986aa9-4f85-4892-9b64-c9e3bd1725e7",
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    "tags": []
   },
   "source": [
    "## 2. Factoring allows for conversion to \"a common currency\" 💶"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "84f432cc-5373-4f19-9aeb-5638d718a144",
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">fact</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">212.5</span>\n",
       "</pre>\n"
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       "\u001b[33mfact\u001b[0m=\u001b[1;36m212\u001b[0m\u001b[1;36m.5\u001b[0m\n"
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   ],
   "source": [
    "fact = 1.25*D + 1.5*L + 1.0*S\n",
    "print(f\"{fact=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4456fe3-036e-41c2-8565-2b9645e7ad13",
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   "source": [
    "## 3. Managing the many possible combinations of factored loads  🏋️‍♀‍💃🌨"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### A. Separate functions 🙅\n",
    "\n",
    "**Pros:**\n",
    "* One function, one name\n",
    "* Conceptually simple\n",
    "\n",
    "**Cons:**\n",
    "* Repetitive code\n",
    "    * Difficult to maintain, buggy\n",
    "* Inconsistent function signatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
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   "source": [
    "def LC1(D: float) -> float:\n",
    "    return 1.4 * D\n",
    "\n",
    "def LC2(D: float, L: float) -> float:\n",
    "    return 1.25 * D + 1.5 * L\n",
    "\n",
    "def LC2a(D: float, L: float, S: float) -> float:\n",
    "    return 1.25 * D + 1.5 * L + 1.0 * S\n",
    "\n",
    "def LC2b(D: float, L: float, W: float) -> float:\n",
    "    return 0.9 * D + 1.5 * L + 0.4 * W\n",
    "\n",
    "def LC2c(D: float, L: float, W: float) -> float:\n",
    "    return 1.25 * D + 1.5 * L + 0.4 * W\n",
    "    "
   ]
  },
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">50</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">90</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">15</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span>\n",
       "</pre>\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">fact_lc2b</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">184.0</span>\n",
       "</pre>\n"
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       "\u001b[33mfact_lc2b\u001b[0m=\u001b[1;36m184\u001b[0m\u001b[1;36m.0\u001b[0m\n"
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   "source": [
    "print(f\"{D=}, {L=}, {S=}, {W=}\")\n",
    "\n",
    "fact_lc2b = LC2b(D=D, L=L, W=W)\n",
    "\n",
    "print(f\"{fact_lc2b=}\")"
   ]
  },
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   "cell_type": "markdown",
   "id": "fcdd58f3-8d1d-4dd7-989f-cbb71c662c91",
   "metadata": {
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     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## B. A generic function (with `dict`s) 👩‍💻"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b535756-2d42-4cd3-9fb2-b49cb043d039",
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   "source": [
    "Pros: \n",
    "* One function to rule them all\n",
    "* Factors can be stored in separate file\n",
    "* Extensible\n",
    "    * As long as you don't have any new load types\n",
    "\n",
    "Cons: \n",
    "* Using the function \"manually\" can get tedious\n",
    "* Tediousness can lead to data entry errors in use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "b0716522-1c65-45f7-8699-669cdb6e03f8",
   "metadata": {
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   "outputs": [],
   "source": [
    "def factor_loads(\n",
    "    D_factor: float = 0,\n",
    "    D: float = 0,\n",
    "    L_factor: float = 0,\n",
    "    L: float = 0,\n",
    "    S_factor: float = 0,\n",
    "    S: float = 0,\n",
    "    W_factor: float = 0,\n",
    "    W: float = 0,\n",
    "    E_factor: float = 0,\n",
    "    E: float = 0,\n",
    ") -> float:\n",
    "    \"\"\"\n",
    "    Returns the factored load for the given load factors\n",
    "    and loads.\n",
    "    \"\"\"\n",
    "    factored_load = (\n",
    "        D_factor * D\n",
    "        + L_factor * L\n",
    "        + S_factor * S\n",
    "        + W_factor * W\n",
    "        + E_factor * E\n",
    "    )\n",
    "    return factored_load"
   ]
  },
  {
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   "execution_count": 50,
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">50</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">90</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">15</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span>\n",
       "</pre>\n"
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       "\u001b[33mD\u001b[0m=\u001b[1;36m50\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m90\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m15\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;36m10\u001b[0m\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">fact_lc2a</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">197.5</span>\n",
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   "source": [
    "fact_lc2a = factor_loads(\n",
    "    D_factor=1.25, \n",
    "    D=D, \n",
    "    L_factor=1.5, \n",
    "    L=L\n",
    ")\n",
    "\n",
    "print(f\"{D=}, {L=}, {S=}, {W=}\")\n",
    "print(f\"{fact_lc2a=}\")"
   ]
  },
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   "cell_type": "code",
   "execution_count": 54,
   "id": "677f6dd5-a7f1-4cad-bd9e-a28ff896e3ec",
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">fact</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.26</span>\n",
       "</pre>\n"
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       "\u001b[33mfact\u001b[0m=\u001b[1;36m1\u001b[0m\u001b[1;36m.26\u001b[0m\n"
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   ],
   "source": [
    "combos = {\n",
    "    \"LC1\": {\n",
    "     \"D_factor\": 1.4\n",
    "    },\n",
    "     \"LC2a\": {\n",
    "         \"D_factor\": 1.25,\n",
    "         \"L_factor\": 1.5,\n",
    "     },\n",
    "      \"LC2b\": {\n",
    "          \"D_factor\": 1.25,\n",
    "          \"L_factor\": 1.5,\n",
    "          \"S_factor\": 1.0,\n",
    "      }\n",
    "}\n",
    "\n",
    "loads = {\"D\": 0.9, \"L\": 2.4, \"S\": 1.3}\n",
    "combo = \"LC1\"\n",
    "\n",
    "fact = factor_loads(**loads, **combos[combo])\n",
    "print(f\"{fact=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aacc339c-c13f-4103-8797-af2bb72a6031",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## C. A Generic Function (with arrays)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d15e7d20-2989-409f-9d9f-e4d53b30c419",
   "metadata": {
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   },
   "source": [
    "Pros: \n",
    "* Fast, simple code\n",
    "* Flexible for variable number of load types\n",
    "    * As long as both vectors are the same length\n",
    "* Extensible\n",
    "\n",
    "Cons: \n",
    "* No \"position labels\"\n",
    "* Can be brittle\n",
    "    * If you update the number of load types, all inputs need to change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "84393b8a-0c11-4b0c-8687-4daab16f48b7",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "LC1 = [1.4, 0, 0, 0, 0]\n",
    "LC2 = [1.25, 1.5, 0, 0, 0]\n",
    "LC2a = [1.25, 1.5, 1.0, 0, 0]\n",
    "LC2b = [0.9, 1.5, 0, 0.4, 0]\n",
    "\n",
    "load = [D, L, S, W, 0]\n",
    "\n",
    "def factor_vec_load(load_vector: np.ndarray, factor_vector: np.ndarray) -> float:\n",
    "    \"\"\"\n",
    "    Returns the loads in 'load_vector' factored by 'factor_vector'.\n",
    "    Both arrays must be the same length.\n",
    "    \"\"\"\n",
    "    # return sum(load_vector * factor_vector)\n",
    "    return load_vector @ factor_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "a16001b7-f418-47be-9d4b-0073b483dd3b",
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">load</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">50</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">90</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">15</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span>,  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">])</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mload\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m50\u001b[0m, \u001b[1;36m90\u001b[0m, \u001b[1;36m15\u001b[0m, \u001b[1;36m10\u001b[0m,  \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">fact_lc2</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">197.5</span>\n",
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       "\u001b[33mfact_lc2\u001b[0m=\u001b[1;36m197\u001b[0m\u001b[1;36m.5\u001b[0m\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">fact_lc2a</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">212.5</span>\n",
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       "\u001b[33mfact_lc2a\u001b[0m=\u001b[1;36m212\u001b[0m\u001b[1;36m.5\u001b[0m\n"
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   ],
   "source": [
    "load = np.array(load)\n",
    "\n",
    "fact_lc2 = factor_vec_load(\n",
    "    np.array(load), \n",
    "    np.array(LC2)\n",
    ")\n",
    "fact_lc2a = factor_vec_load(\n",
    "    np.array(load), \n",
    "    np.array(LC2a)\n",
    ")\n",
    "\n",
    "print(f\"{load=}\")\n",
    "print(f\"{fact_lc2=}\")\n",
    "print(f\"{fact_lc2a=}\")"
   ]
  },
  {
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   "id": "d0d858e7-4225-450a-ab6c-872ad27241f9",
   "metadata": {
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     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 4. Storing Load Combinations 📚"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a549bd23-6437-4875-87f6-fe7298a29a7c",
   "metadata": {
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    "tags": []
   },
   "source": [
    "Choose one of two datatypes:\n",
    "\n",
    "1. `dict`\n",
    "2. `list` and `np.array`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b9056d6-1209-494a-8ce9-a8668344aeef",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### `dict`\n",
    "\n",
    "**Pros:**\n",
    "* Key, value pairs make it easy to understand the data, e.g. `{\"D\": 12.3, \"L\": 4.8}`\n",
    "* Do not have to fill in loads that are `0.0`\n",
    "\n",
    "**Cons:**\n",
    "* No vector math available\n",
    "    * Must loop to add/sub values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d033704-a92c-4e09-82b1-1c3b81219a44",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### `np.array`\n",
    "\n",
    "**Pros:**\n",
    "* Fast and simple vector math\n",
    "\n",
    "**Cons:**\n",
    "* No labels on data, e.g. `[12.3, 4.8, 0., 0., 0.]`\n",
    "* Fixed length vectors require empty values, i.e. `0.0`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02c4899c-b8bd-4507-8a5e-9b01b7691fa5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Factor Dictionaries 📔\n",
    "\n",
    "```json\n",
    "{\n",
    "    \"LC1\": {\n",
    "        \"DL_factor\": 1.4\n",
    "    },\n",
    "    \"LC2a\": {\n",
    "        \"DL_factor\": 1.25,\n",
    "        \"LL_factor\": 1.5\n",
    "    },\n",
    "    \"LC2b\": {\n",
    "        \"DL_factor\": 1.25,\n",
    "        \"LL_factor\": 1.5,\n",
    "        \"SL_factor\": 1.0\n",
    "    },\n",
    "    ...\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "9fe3d80e-ede5-4ab7-9937-334b34efc489",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">{</span>\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC1'</span>: <span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'D_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.4</span><span style=\"font-weight: bold\">}</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2'</span>: <span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'D_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'L_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span><span style=\"font-weight: bold\">}</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2a'</span>: <span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'D_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'L_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span><span style=\"font-weight: bold\">}</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2b'</span>: <span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'D_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'L_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'S_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.0</span><span style=\"font-weight: bold\">}</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2c'</span>: <span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'D_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'L_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'W_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.0</span><span style=\"font-weight: bold\">}</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2d'</span>: <span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'D_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'L_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'W_factor'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4</span><span style=\"font-weight: bold\">}</span>\n",
       "<span style=\"font-weight: bold\">}</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m{\u001b[0m\n",
       "    \u001b[32m'LC1'\u001b[0m: \u001b[1m{\u001b[0m\u001b[32m'D_factor'\u001b[0m: \u001b[1;36m1.4\u001b[0m\u001b[1m}\u001b[0m,\n",
       "    \u001b[32m'LC2'\u001b[0m: \u001b[1m{\u001b[0m\u001b[32m'D_factor'\u001b[0m: \u001b[1;36m1.25\u001b[0m, \u001b[32m'L_factor'\u001b[0m: \u001b[1;36m1.5\u001b[0m\u001b[1m}\u001b[0m,\n",
       "    \u001b[32m'LC2a'\u001b[0m: \u001b[1m{\u001b[0m\u001b[32m'D_factor'\u001b[0m: \u001b[1;36m0.9\u001b[0m, \u001b[32m'L_factor'\u001b[0m: \u001b[1;36m1.5\u001b[0m\u001b[1m}\u001b[0m,\n",
       "    \u001b[32m'LC2b'\u001b[0m: \u001b[1m{\u001b[0m\u001b[32m'D_factor'\u001b[0m: \u001b[1;36m1.25\u001b[0m, \u001b[32m'L_factor'\u001b[0m: \u001b[1;36m1.5\u001b[0m, \u001b[32m'S_factor'\u001b[0m: \u001b[1;36m1.0\u001b[0m\u001b[1m}\u001b[0m,\n",
       "    \u001b[32m'LC2c'\u001b[0m: \u001b[1m{\u001b[0m\u001b[32m'D_factor'\u001b[0m: \u001b[1;36m1.25\u001b[0m, \u001b[32m'L_factor'\u001b[0m: \u001b[1;36m1.5\u001b[0m, \u001b[32m'W_factor'\u001b[0m: \u001b[1;36m1.0\u001b[0m\u001b[1m}\u001b[0m,\n",
       "    \u001b[32m'LC2d'\u001b[0m: \u001b[1m{\u001b[0m\u001b[32m'D_factor'\u001b[0m: \u001b[1;36m0.9\u001b[0m, \u001b[32m'L_factor'\u001b[0m: \u001b[1;36m1.5\u001b[0m, \u001b[32m'W_factor'\u001b[0m: \u001b[1;36m0.4\u001b[0m\u001b[1m}\u001b[0m\n",
       "\u001b[1m}\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import json\n",
    "\n",
    "with open(\"NBCC_dict.json\", 'r') as file:\n",
    "    nbcc_dict = json.load(file)\n",
    "\n",
    "print(nbcc_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5ce50026-0877-407f-8776-bd387bc48255",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">factor_loads</span><span style=\"font-weight: bold\">(</span><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2.4</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.6</span>,**nbcc_dict<span style=\"font-weight: bold\">[</span><span style=\"color: #008000; text-decoration-color: #008000\">\"LC2a\"</span><span style=\"font-weight: bold\">])</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.5100000000000002</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;35mfactor_loads\u001b[0m\u001b[1m(\u001b[0m\u001b[33mD\u001b[0m=\u001b[1;36m2\u001b[0m\u001b[1;36m.4\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.9\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m3\u001b[0m\u001b[1;36m.6\u001b[0m,**nbcc_dict\u001b[1m[\u001b[0m\u001b[32m\"LC2a\"\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m=\u001b[1;36m3.5100000000000002\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f'{factor_loads(D=2.4, L=0.9, S=3.6,**nbcc_dict[\"LC2a\"])=}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81d33dec-a446-4930-baac-338b4aa0fad4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Vector dictionaries ➡➡➡➡➡\n",
    "\n",
    "```json\n",
    "{\n",
    "    \"LC1\": [1.4, 0, 0, 0, 0],\n",
    "    \"LC2\": [1.25, 1.5, 0, 0, 0],\n",
    "    \"LC2a\": [0.9, 1.5, 0, 0, 0],\n",
    "    \"LC2b\": [1.25, 1.5, 1.0, 0, 0],\n",
    "    \"LC2c\": [1.25, 1.5, 0, 0.4, 0],\n",
    "    \"LC2d\": [0.9, 1.5, 0.4, 0, 0],\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "1114a577-9e4c-4064-a79b-c27c60e601e1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">{</span>\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC1'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.4</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2a'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2b'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2c'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC2d'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>,\n",
       "    <span style=\"color: #008000; text-decoration-color: #008000\">'LC3'</span>: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.25</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>\n",
       "<span style=\"font-weight: bold\">}</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m{\u001b[0m\n",
       "    \u001b[32m'LC1'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m1.4\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m,\n",
       "    \u001b[32m'LC2'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m1.25\u001b[0m, \u001b[1;36m1.5\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m,\n",
       "    \u001b[32m'LC2a'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m0.9\u001b[0m, \u001b[1;36m1.5\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m,\n",
       "    \u001b[32m'LC2b'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m1.25\u001b[0m, \u001b[1;36m1.5\u001b[0m, \u001b[1;36m1.0\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m,\n",
       "    \u001b[32m'LC2c'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m1.25\u001b[0m, \u001b[1;36m1.5\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0.4\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m,\n",
       "    \u001b[32m'LC2d'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m0.9\u001b[0m, \u001b[1;36m1.5\u001b[0m, \u001b[1;36m0.4\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m,\n",
       "    \u001b[32m'LC3'\u001b[0m: \u001b[1m[\u001b[0m\u001b[1;36m1.25\u001b[0m, \u001b[1;36m0.0\u001b[0m, \u001b[1;36m1.5\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m\n",
       "\u001b[1m}\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open('NBCC_vec.json', 'r') as json_file:\n",
    "    nbcc_vec = json.load(json_file)\n",
    "print(nbcc_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "724c8eee-fdd5-454e-abfb-3436ec75e436",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">factor_vec_load</span><span style=\"font-weight: bold\">(</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">np.array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2.4</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.6</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">])</span>, <span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">np.array</span><span style=\"font-weight: bold\">(</span>nbcc_vec<span style=\"font-weight: bold\">[</span><span style=\"color: #008000; text-decoration-color: #008000\">\"LC2a\"</span><span style=\"font-weight: bold\">]))</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.5100000000000002</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;35mfactor_vec_load\u001b[0m\u001b[1m(\u001b[0m\u001b[1;35mnp.array\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m2.4\u001b[0m, \u001b[1;36m0.9\u001b[0m, \u001b[1;36m3.6\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m, \u001b[1;35mnp.array\u001b[0m\u001b[1m(\u001b[0mnbcc_vec\u001b[1m[\u001b[0m\u001b[32m\"LC2a\"\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m\u001b[1m)\u001b[0m=\u001b[1;36m3.5100000000000002\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f'{factor_vec_load(np.array([2.4, 0.9, 3.6, 0, 0]), np.array(nbcc_vec[\"LC2a\"]))=}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d63a1d-92e5-49df-bdc2-b7ffb0e06d44",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## A third way! `typing.NamedTuple`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c36c21b4-170f-458f-b580-46207ad7e82e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Using `typing.NamedTuple` we can define a datatype that is both `dict`-ish and `array`-ish.\n",
    "\n",
    "* The NamedTuple has named fields (`dict`-like)\n",
    "* The named fields accept default values(`dict`-like)\n",
    "    * We can skip empty `0.0` values\n",
    "* The NamedTuple is `tuple`-like and can be converted directly to a `np.array`\n",
    "* The NamedTuple can also import values from a JSON file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "f7952f1b-e276-4a04-a826-ff93a049a7d8",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from typing import NamedTuple, Any\n",
    "\n",
    "class Load(NamedTuple):\n",
    "    \"\"\"\n",
    "    A class to describe loads according to the Canadian National\n",
    "    Building Code (NBCC).\n",
    "    \n",
    "    The loads themselves can be of any type as long as they play\n",
    "    well with either scalar arithmetic operators or numpy array\n",
    "    operators.\n",
    "    \n",
    "    If array values are used, all arrays should be the same length.\n",
    "    \"\"\"\n",
    "    D: Any = 0.0\n",
    "    L: Any = 0.0\n",
    "    S: Any = 0.0\n",
    "    W: Any = 0.0\n",
    "    E: Any = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "1553bc4d-5f65-494b-9e6b-c0acf06ddbf8",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "## Examples\n",
    "\n",
    "L0 = Load() # An empty load\n",
    "L1 = Load(D=2.3, L=2.4, S=0.9) # Not all fields need be entered\n",
    "L2 = Load( # A load with array values\n",
    "    D=np.array([0.6, 1.1, 0.4]), \n",
    "    L=np.array([2.4, 3.6, 0.8]),\n",
    "    S=np.array([0.5, 1.2, 3.6]),\n",
    "    W=np.zeros(3),\n",
    "    E=np.zeros(3),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "57aba69f-bd26-48e5-8df4-e97dd27bb74d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">L0</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">Load</span><span style=\"font-weight: bold\">(</span><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">E</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span><span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mL0\u001b[0m=\u001b[1;35mLoad\u001b[0m\u001b[1m(\u001b[0m\u001b[33mD\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mE\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">L1</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">Load</span><span style=\"font-weight: bold\">(</span><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2.3</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2.4</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.9</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">E</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span><span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mL1\u001b[0m=\u001b[1;35mLoad\u001b[0m\u001b[1m(\u001b[0m\u001b[33mD\u001b[0m=\u001b[1;36m2\u001b[0m\u001b[1;36m.3\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m2\u001b[0m\u001b[1;36m.4\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.9\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mE\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">L2</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">Load</span><span style=\"font-weight: bold\">(</span><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.6</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.1</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4</span><span style=\"font-weight: bold\">])</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2.4</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.6</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.8</span><span style=\"font-weight: bold\">])</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.2</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.6</span><span style=\"font-weight: bold\">])</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>.<span style=\"font-weight: bold\">])</span>, \n",
       "<span style=\"color: #808000; text-decoration-color: #808000\">E</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>.<span style=\"font-weight: bold\">]))</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mL2\u001b[0m=\u001b[1;35mLoad\u001b[0m\u001b[1m(\u001b[0m\u001b[33mD\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0.6\u001b[0m, \u001b[1;36m1.1\u001b[0m, \u001b[1;36m0.4\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m2.4\u001b[0m, \u001b[1;36m3.6\u001b[0m, \u001b[1;36m0.8\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0.5\u001b[0m, \u001b[1;36m1.2\u001b[0m, \u001b[1;36m3.6\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m.\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m, \n",
       "\u001b[33mE\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m.\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"{L0=}\")\n",
    "print(f\"{L1=}\")\n",
    "print(f\"{L2=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "544a4a02-b0fa-4e4a-bbdd-1f72ec63ce4b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## NamedTuple as `dict` and as vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "c6b542be-c333-4157-b4ae-411e24768a74",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.35 , 6.775, 1.7  ])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_loads(**L2._asdict(), **nbcc_dict[\"LC2\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "c4c26895-fb8a-4939-9b96-50fb7a0de064",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.35 , 6.775, 1.7  ])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_vec_load(np.array(L2).T, np.array(nbcc_vec[\"LC2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dd7f282-5111-45a8-8584-91c23e819624",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 5. Load Aliases 🕵️‍♀️"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a729b31e-eea1-47a2-bc1f-8dac51a911ae",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "> Sometimes it can be nice to describe what the load is called instead of just \"dead load\". To use in calculations, we need to have an alias look-up., e.g. \"Asphalt topping\" `->` \"DL\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de8c337f-d88c-42b7-ac3e-af0b450d0fc1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Example\n",
    "\n",
    "Loads on a building might include:\n",
    "\n",
    "* Member self-weight (\"SW\")\n",
    "* Super-imposed dead load (\"SDL\")\n",
    "* We may want to use specific names for specific loads\n",
    "    * e.g. \"Planter soil\" instead of just \"live load\" even though it is a live load.\n",
    "\n",
    "```python\n",
    "load_categories_lookup = {\n",
    "    \"SW\": \"DL\",\n",
    "    \"SDL\": \"DL\",\n",
    "    \"Planter Soil\": \"LL\",\n",
    "    \"Snow\": \"SL\", \n",
    "    \"Rain\": \"SL\"\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "14332850-d3f4-4e76-9260-2c49d789bf77",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def alias_to_service_loads(alias_loads: dict, alias_lookup: dict) -> Load:\n",
    "    \"\"\"\n",
    "    Returns a dictionary of service loads (i.e. loads conforming to the\n",
    "    code categories of DL, LL, SL, etc.) obtained from the given loads\n",
    "    in 'alias_loads' correlated against the load types in 'alias_lookup'.\n",
    "    \n",
    "    If the load type in 'alias_loads' is not listed in 'alias_lookup', no \n",
    "    transformation takes place.\n",
    "    \"\"\"\n",
    "    service_loads = {}\n",
    "    for load_name, load_mag in alias_loads.items():\n",
    "        load_type = alias_lookup.get(load_name, load_name)\n",
    "        \n",
    "        if load_type in service_loads:\n",
    "            service_loads[load_type] = service_loads[load_type] + load_mag\n",
    "        else:\n",
    "            service_loads.update({load_type: load_mag})\n",
    "            \n",
    "    return Load(**service_loads)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "58fa1b0d-7a2c-4d50-91d0-33dceae828e4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "alias_lookup = {\n",
    "    \"SW\": \"D\",\n",
    "    \"SDL\": \"D\",\n",
    "    \"Planter Soil\": \"L\",\n",
    "    \"Snow\": \"S\", \n",
    "    \"Rain\": \"S\"\n",
    "}\n",
    "\n",
    "loads = {\"SW\": 14, \"SDL\": 30, \"Planter Soil\": 180, \"Snow\": 30, \"Rain\": 2}\n",
    "\n",
    "service_loads = alias_to_service_loads(\n",
    "    alias_loads=loads, \n",
    "    alias_lookup=alias_lookup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "a18a390e-04f3-47e4-b312-4a55121e67d0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">loads</span>=<span style=\"font-weight: bold\">{</span><span style=\"color: #008000; text-decoration-color: #008000\">'SW'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">14</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'SDL'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">30</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'Planter Soil'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">180</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'Snow'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">30</span>, <span style=\"color: #008000; text-decoration-color: #008000\">'Rain'</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"font-weight: bold\">}</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mloads\u001b[0m=\u001b[1m{\u001b[0m\u001b[32m'SW'\u001b[0m: \u001b[1;36m14\u001b[0m, \u001b[32m'SDL'\u001b[0m: \u001b[1;36m30\u001b[0m, \u001b[32m'Planter Soil'\u001b[0m: \u001b[1;36m180\u001b[0m, \u001b[32m'Snow'\u001b[0m: \u001b[1;36m30\u001b[0m, \u001b[32m'Rain'\u001b[0m: \u001b[1;36m2\u001b[0m\u001b[1m}\u001b[0m\n"
      ]
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">service_loads</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">Load</span><span style=\"font-weight: bold\">(</span><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">44</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">180</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">32</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">E</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span><span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mservice_loads\u001b[0m=\u001b[1;35mLoad\u001b[0m\u001b[1m(\u001b[0m\u001b[33mD\u001b[0m=\u001b[1;36m44\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m180\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m32\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mE\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"{loads=}\")\n",
    "print(f\"{service_loads=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd8ea0a5-76f8-499e-8d4c-a6084903ca1c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 6. Find maximum and minimum factored loads"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a83f73b1-543b-4115-9a49-e9f9b0762f64",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**Two approaches:**\n",
    "1. Return just the max/min load\n",
    "2. Return the max/min load AND which load case produced it (traceability)\n",
    "\n",
    "**Additionally!**\n",
    "\n",
    "It would be good if our \"max\" and \"min\" functions could take either _scalar_ or _array_ input.\n",
    "\n",
    "**We need a Numpy function for this.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dae0a5b-090e-4595-8471-adbb961c4e38",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Why Numpy?\n",
    "\n",
    "* If we want element-wise maximum between arrays, we cannot use (`<`, `>`, etc.)\n",
    "* Need to use `np.maximum`\n",
    "* `np.maximum` works on both scalar and array inputs!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b88c1c7-0c18-49fc-9c0d-17f33ba68550",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 1. Return Max/Min Loads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "cb67a40c-590f-4a63-af41-b57b5c1cbcec",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def factored_max(load: Load, load_combinations: dict) -> Any:\n",
    "    \"\"\"\n",
    "    Returns a value representing the maximum factored load of 'load' calculated\n",
    "    from all of the load combinations in 'load_combinations'.\n",
    "    \n",
    "    If 'load' contains scalar values, the maximum factored load is a scalar maximum.\n",
    "    If 'load' contains array values, the maximum factored load is the envelope of\n",
    "    maximum values across the input arrays in 'load'.\n",
    "    \"\"\"\n",
    "    fl = float('-inf') # acc\n",
    "    for load_combination, load_factors in load_combinations.items():\n",
    "        current_fl = factor_vec_load(\n",
    "            np.array(load).T, \n",
    "            np.array(load_factors)\n",
    "        )\n",
    "        fl = np.maximum(current_fl, fl)\n",
    "    return fl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "5fdf1dfa-272b-49b9-95a8-2a1dcdfb308c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def factored_min(load: Load, load_combinations: dict) -> Any:\n",
    "    \"\"\"\n",
    "    Returns a value representing the minimum factored load of 'load' calculated\n",
    "    from all of the load combinations in 'load_combinations'.\n",
    "    \n",
    "    If 'load' contains scalar values, the minimum factored load is a scalar minimum.\n",
    "    If 'load' contains array values, the minimum factored load is the envelope of\n",
    "    minimum values across the input arrays in 'load'.\n",
    "    \"\"\"\n",
    "    fl = float('inf') # acc\n",
    "    for load_combination, load_factors in load_combinations.items():\n",
    "        current_fl = factor_vec_load(\n",
    "            np.array(load).T, \n",
    "            np.array(load_factors)\n",
    "        )\n",
    "        fl = np.minimum(current_fl, fl)\n",
    "    return fl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "abdd0d03-49b1-49c1-aee9-84a292fa1269",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">Load</span><span style=\"font-weight: bold\">(</span>\n",
       "    <span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.6</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.1</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4</span><span style=\"font-weight: bold\">])</span>,\n",
       "    <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2.4</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.6</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.8</span><span style=\"font-weight: bold\">])</span>,\n",
       "    <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.5</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.2</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.6</span><span style=\"font-weight: bold\">])</span>,\n",
       "    <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>.<span style=\"font-weight: bold\">])</span>,\n",
       "    <span style=\"color: #808000; text-decoration-color: #808000\">E</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>., <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>.<span style=\"font-weight: bold\">])</span>\n",
       "<span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;35mLoad\u001b[0m\u001b[1m(\u001b[0m\n",
       "    \u001b[33mD\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0.6\u001b[0m, \u001b[1;36m1.1\u001b[0m, \u001b[1;36m0.4\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m,\n",
       "    \u001b[33mL\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m2.4\u001b[0m, \u001b[1;36m3.6\u001b[0m, \u001b[1;36m0.8\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m,\n",
       "    \u001b[33mS\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0.5\u001b[0m, \u001b[1;36m1.2\u001b[0m, \u001b[1;36m3.6\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m,\n",
       "    \u001b[33mW\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m.\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m,\n",
       "    \u001b[33mE\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m., \u001b[1;36m0\u001b[0m.\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m\n",
       "\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "c9178d9d-feca-450a-8878-6e62780de26c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'LC1': [1.4, 0, 0, 0, 0],\n",
       " 'LC2': [1.25, 1.5, 0, 0, 0],\n",
       " 'LC2a': [0.9, 1.5, 0, 0, 0],\n",
       " 'LC2b': [1.25, 1.5, 1.0, 0, 0],\n",
       " 'LC2c': [1.25, 1.5, 0, 0.4, 0],\n",
       " 'LC2d': [0.9, 1.5, 0.4, 0, 0],\n",
       " 'LC3': [1.25, 0.0, 1.5, 0, 0]}"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbcc_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "14a24a16-6b55-4d52-8d6b-2dc89db9cd29",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">max_factored</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.85</span> , <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">7.975</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">5.9</span>  <span style=\"font-weight: bold\">])</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mmax_factored\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m4.85\u001b[0m , \u001b[1;36m7.975\u001b[0m, \u001b[1;36m5.9\u001b[0m  \u001b[1m]\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">min_factored</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.84</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.54</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.56</span><span style=\"font-weight: bold\">])</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mmin_factored\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0.84\u001b[0m, \u001b[1;36m1.54\u001b[0m, \u001b[1;36m0.56\u001b[0m\u001b[1m]\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_factored = factored_max(L2, nbcc_vec)\n",
    "print(f\"{max_factored=}\")\n",
    "\n",
    "min_factored = factored_min(L2, nbcc_vec)\n",
    "print(f\"{min_factored=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b7137c1-e55c-4b8e-93ce-c5a75d4db5e9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 2. Return Max/Min governing combination"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27704fa6-bc2c-462b-8a7d-1075b9710e75",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**Two steps:**\n",
    "\n",
    "1. Build a vector/matrix of the load combinations\n",
    "2. Get the index of each extrema"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "e10c7249-fa9a-4932-8289-4aa749d2ed4c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def get_factored_matrix(load: Load, load_combinations: dict) -> np.ndarray:\n",
    "    \"\"\"\n",
    "    Returns either a 1D or 2D array representing the loads in 'load' being\n",
    "    factored by 'load_combinations'. Each factored load combination is a\n",
    "    row in the resulting matrix.\n",
    "    \n",
    "    If the values in 'load' are scalars, then a 1D matrix is returned\n",
    "    If the values in 'load' are 1D arrays, then a 2D matrix is returned\n",
    "    \"\"\"\n",
    "    acc = None\n",
    "    for idx, (load_combination, load_factors) in enumerate(\n",
    "        load_combinations.items()\n",
    "    ):\n",
    "        current_fact = factor_vec_load(\n",
    "            np.array(load).T, np.array(load_factors)\n",
    "        )\n",
    "        if idx == 0: acc = np.array([current_fact])\n",
    "        else: acc = np.concatenate([acc, [current_fact]])\n",
    "    return acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "9331b72c-d4f0-49fe-9c3b-f272cbb98f5c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def factored_max_trace(load: Load, load_combinations: dict) -> Any:\n",
    "    \"\"\"\n",
    "    Returns a value representing the maximum factored load of 'load' calculated\n",
    "    from all of the load combinations in 'load_combinations'.\n",
    "    \n",
    "    If 'load' contains scalar values, the maximum factored load is a scalar maximum.\n",
    "    If 'load' contains array values, the maximum factored load is the envelope of\n",
    "    maximum values across the input arrays in 'load'.\n",
    "    \"\"\"\n",
    "    factored_matrix = get_factored_matrix(load, load_combinations)\n",
    "    max_trace = np.argmax(factored_matrix, axis=0)\n",
    "    return max_trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "cac35370-6c38-4f84-a6ea-dbdb9b2560bc",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def factored_min_trace(load: Load, load_combinations: dict) -> Any:\n",
    "    \"\"\"\n",
    "    Returns a value representing the minimum factored load of 'load' calculated\n",
    "    from all of the load combinations in 'load_combinations'.\n",
    "    \n",
    "    If 'load' contains scalar values, the minimum factored load is a scalar minimum.\n",
    "    If 'load' contains array values, the minimum factored load is the envelope of\n",
    "    minimum values across the input arrays in 'load'.\n",
    "    \"\"\"\n",
    "    factored_matrix = get_factored_matrix(load, load_combinations)\n",
    "    min_trace = np.argmin(factored_matrix, axis=0)\n",
    "    return min_trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "16acd642-f58d-4842-a567-6ee92a1ee529",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'LC1': [1.4, 0, 0, 0, 0],\n",
       " 'LC2': [1.25, 1.5, 0, 0, 0],\n",
       " 'LC2a': [0.9, 1.5, 0, 0, 0],\n",
       " 'LC2b': [1.25, 1.5, 1.0, 0, 0],\n",
       " 'LC2c': [1.25, 1.5, 0, 0.4, 0],\n",
       " 'LC2d': [0.9, 1.5, 0.4, 0, 0],\n",
       " 'LC3': [1.25, 0.0, 1.5, 0, 0]}"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbcc_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "d2ad627c-1806-476a-b03c-77fd8a412676",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">[[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.84</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.54</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.56</span> <span style=\"font-weight: bold\">]</span>\n",
       " <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.35</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6.775</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.7</span>  <span style=\"font-weight: bold\">]</span>\n",
       " <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.14</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6.39</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.56</span> <span style=\"font-weight: bold\">]</span>\n",
       " <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.85</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">7.975</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">5.3</span>  <span style=\"font-weight: bold\">]</span>\n",
       " <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.35</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6.775</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.7</span>  <span style=\"font-weight: bold\">]</span>\n",
       " <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.34</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6.87</span>  <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3</span>.   <span style=\"font-weight: bold\">]</span>\n",
       " <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.5</span>   <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.175</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">5.9</span>  <span style=\"font-weight: bold\">]]</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m[\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0.84\u001b[0m  \u001b[1;36m1.54\u001b[0m  \u001b[1;36m0.56\u001b[0m \u001b[1m]\u001b[0m\n",
       " \u001b[1m[\u001b[0m\u001b[1;36m4.35\u001b[0m  \u001b[1;36m6.775\u001b[0m \u001b[1;36m1.7\u001b[0m  \u001b[1m]\u001b[0m\n",
       " \u001b[1m[\u001b[0m\u001b[1;36m4.14\u001b[0m  \u001b[1;36m6.39\u001b[0m  \u001b[1;36m1.56\u001b[0m \u001b[1m]\u001b[0m\n",
       " \u001b[1m[\u001b[0m\u001b[1;36m4.85\u001b[0m  \u001b[1;36m7.975\u001b[0m \u001b[1;36m5.3\u001b[0m  \u001b[1m]\u001b[0m\n",
       " \u001b[1m[\u001b[0m\u001b[1;36m4.35\u001b[0m  \u001b[1;36m6.775\u001b[0m \u001b[1;36m1.7\u001b[0m  \u001b[1m]\u001b[0m\n",
       " \u001b[1m[\u001b[0m\u001b[1;36m4.34\u001b[0m  \u001b[1;36m6.87\u001b[0m  \u001b[1;36m3\u001b[0m.   \u001b[1m]\u001b[0m\n",
       " \u001b[1m[\u001b[0m\u001b[1;36m1.5\u001b[0m   \u001b[1;36m3.175\u001b[0m \u001b[1;36m5.9\u001b[0m  \u001b[1m]\u001b[0m\u001b[1m]\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "factored_matrix = get_factored_matrix(L2, nbcc_vec)\n",
    "print(factored_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "1c4d5fdf-36e9-4c23-af82-a9a414095e1a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">factored_max_trace</span><span style=\"font-weight: bold\">(</span>L2, nbcc_vec<span style=\"font-weight: bold\">)</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span><span style=\"font-weight: bold\">]</span>, <span style=\"color: #808000; text-decoration-color: #808000\">dtype</span>=<span style=\"color: #800080; text-decoration-color: #800080\">int64</span><span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;35mfactored_max_trace\u001b[0m\u001b[1m(\u001b[0mL2, nbcc_vec\u001b[1m)\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m3\u001b[0m, \u001b[1;36m3\u001b[0m, \u001b[1;36m6\u001b[0m\u001b[1m]\u001b[0m, \u001b[33mdtype\u001b[0m=\u001b[35mint64\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">factored_min_trace</span><span style=\"font-weight: bold\">(</span>L2, nbcc_vec<span style=\"font-weight: bold\">)</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">array</span><span style=\"font-weight: bold\">([</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span><span style=\"font-weight: bold\">]</span>, <span style=\"color: #808000; text-decoration-color: #808000\">dtype</span>=<span style=\"color: #800080; text-decoration-color: #800080\">int64</span><span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;35mfactored_min_trace\u001b[0m\u001b[1m(\u001b[0mL2, nbcc_vec\u001b[1m)\u001b[0m=\u001b[1;35marray\u001b[0m\u001b[1m(\u001b[0m\u001b[1m[\u001b[0m\u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m, \u001b[1;36m0\u001b[0m\u001b[1m]\u001b[0m, \u001b[33mdtype\u001b[0m=\u001b[35mint64\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"{factored_max_trace(L2, nbcc_vec)=}\")\n",
    "print(f\"{factored_min_trace(L2, nbcc_vec)=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe1d2f28-4f31-4032-a1c5-680c384326af",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 7. Occupancies 🏠 🏢 🏥\n",
    "\n",
    "> In buildings, loads can often be grouped together in different occupancies.\n",
    ">\n",
    "> `dict`s can be useful for organizing these."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "214c645a-9793-4294-a9e7-a51efc58b1c3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### A. Occupancy dictionaries 📔"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "0ba2c2d0-d914-4389-8c52-d7a4580ca744",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "occupancies_dict = {\n",
    "    \"Residential\": {\n",
    "        \"SW\": 1.3,\n",
    "        \"SDL\": 1.1,\n",
    "        \"L\": 2.4,\n",
    "    },\n",
    "    \"Residential Roof\": {\n",
    "        \"SW\": 0.6,\n",
    "        \"SDL\": 0.3,\n",
    "        \"Snow\": 1.1,\n",
    "        \"Rain\": 0.2,\n",
    "    },\n",
    "    \"Residential Amenity Roof\": {\n",
    "        \"SW\": 1.4,\n",
    "        \"SDL\": 1.0,\n",
    "        \"Planter Soil\": 3.6,\n",
    "        \"L\": 4.8,\n",
    "    },\n",
    "    \"Rooftop Mech\": {\n",
    "         \"D\": 1.83,\n",
    "     },\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "7bd78f1a-959a-463f-8e47-8a485aed3429",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">occupancy</span>=<span style=\"color: #008000; text-decoration-color: #008000\">'Residential Roof'</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33moccupancy\u001b[0m=\u001b[32m'Residential Roof'\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">service_loads</span>=<span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">Load</span><span style=\"font-weight: bold\">(</span><span style=\"color: #808000; text-decoration-color: #808000\">D</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.8999999999999999</span>, <span style=\"color: #808000; text-decoration-color: #808000\">L</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">S</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.3</span>, <span style=\"color: #808000; text-decoration-color: #808000\">W</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span>, <span style=\"color: #808000; text-decoration-color: #808000\">E</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.0</span><span style=\"font-weight: bold\">)</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mservice_loads\u001b[0m=\u001b[1;35mLoad\u001b[0m\u001b[1m(\u001b[0m\u001b[33mD\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.8999999999999999\u001b[0m, \u001b[33mL\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mS\u001b[0m=\u001b[1;36m1\u001b[0m\u001b[1;36m.3\u001b[0m, \u001b[33mW\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m, \u001b[33mE\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.0\u001b[0m\u001b[1m)\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">max_trace</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mmax_trace\u001b[0m=\u001b[1;36m6\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #808000; text-decoration-color: #808000\">factored</span>=<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3.075</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[33mfactored\u001b[0m=\u001b[1;36m3\u001b[0m\u001b[1;36m.075\u001b[0m\n"
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "occupancy = \"Residential Roof\"\n",
    "\n",
    "service_loads = alias_to_service_loads(\n",
    "    occupancies_dict[occupancy],\n",
    "    alias_lookup\n",
    ")\n",
    "print(f\"{occupancy=}\")\n",
    "print(f\"{service_loads=}\")\n",
    "factored = factored_max(\n",
    "    service_loads,\n",
    "    nbcc_vec\n",
    ")\n",
    "max_trace = factored_max_trace(\n",
    "    service_loads,\n",
    "    nbcc_vec\n",
    ")\n",
    "\n",
    "print(f\"{max_trace=}\")\n",
    "print(f\"{factored=}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ad2c514-6deb-46ec-9b3c-4aff0bda7f75",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### B. Occupancy vectors ➡➡➡➡➡\n",
    "\n",
    "> If you are wanting to use vectors for occupancies, it is easiest to use have your vectors already as _service loads_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "f062189b-966e-457d-b755-1162e52d432e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# \n",
    "occupancies_vec = {\n",
    "    \"Residential\": np.array([2.4, 2.4, 0, 0, 0]),\n",
    "    \"Residential Roof\": np.array([0.9, 0, 1.3, 0, 0]),\n",
    "    \"Residential Amenity Roof\": np.array([2.6, 4.8, 0, 0, 0]),\n",
    "    \"Rooftop Mech\": np.array([1.83, 0, 0, 0, 0]),\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6323c872-c36a-46e3-89e2-e9d48b4e9db3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Practical Example 🔨\n",
    "\n",
    "Simply supported beam with one UDL and one point load.\n",
    "\n",
    "Analysis engine: `pycba`, by Colin Caprani (https://ccaprani.github.io/pycba/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "60c66719-a7ca-4b9f-82a1-64ce162a877f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import pycba as cba\n",
    "\n",
    "with open('NBCC_vec_full.json', 'r') as file:\n",
    "    nbcc_full = json.load(file)\n",
    "\n",
    "# For a simply supported beam with a UDL and point load\n",
    "# point load is at a distance 'a' from the left of the beam\n",
    "\n",
    "r = [-1, 0, -1, 0] # Two nodes, vertical restraints\n",
    "L = 6.9 # m\n",
    "w = Load(90., 240., 0., -100., 0.) # kN/m\n",
    "p = Load(220, 0., 130., 0., 0.) # kN/m\n",
    "a = 4.7 # m\n",
    "EI = 1 # Not required for moments and shear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "eee4df8a-0487-46ca-af9a-baa2f81138a6",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "    <span style=\"color: #008000; text-decoration-color: #008000\">'D'</span>: <span style=\"font-weight: bold\">&lt;</span><span style=\"color: #ff00ff; text-decoration-color: #ff00ff; font-weight: bold\">pycba.results.BeamResults</span><span style=\"color: #000000; text-decoration-color: #000000\"> object at </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0x00000222B87B07F0</span><span style=\"color: #000000; text-decoration-color: #000000\">&gt;,</span>\n",
       "<span style=\"color: #000000; text-decoration-color: #000000\">    </span><span style=\"color: #008000; text-decoration-color: #008000\">'L'</span><span style=\"color: #000000; text-decoration-color: #000000\">: &lt;pycba.results.BeamResults object at </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0x00000222B86E79A0</span><span style=\"color: #000000; text-decoration-color: #000000\">&gt;,</span>\n",
       "<span style=\"color: #000000; text-decoration-color: #000000\">    </span><span style=\"color: #008000; text-decoration-color: #008000\">'S'</span><span style=\"color: #000000; text-decoration-color: #000000\">: &lt;pycba.results.BeamResults object at </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0x00000222B86FB0A0</span><span style=\"color: #000000; text-decoration-color: #000000\">&gt;,</span>\n",
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       "<span style=\"color: #000000; text-decoration-color: #000000\">    </span><span style=\"color: #008000; text-decoration-color: #008000\">'E'</span><span style=\"color: #000000; text-decoration-color: #000000\">: &lt;pycba.results.BeamResults object at </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0x00000222B87B2FB0</span><span style=\"font-weight: bold\">&gt;</span>\n",
       "<span style=\"font-weight: bold\">}</span>\n",
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       "\u001b[39m    \u001b[0m\u001b[32m'L'\u001b[0m\u001b[39m: <pycba.results.BeamResults object at \u001b[0m\u001b[1;36m0x00000222B86E79A0\u001b[0m\u001b[39m>,\u001b[0m\n",
       "\u001b[39m    \u001b[0m\u001b[32m'S'\u001b[0m\u001b[39m: <pycba.results.BeamResults object at \u001b[0m\u001b[1;36m0x00000222B86FB0A0\u001b[0m\u001b[39m>,\u001b[0m\n",
       "\u001b[39m    \u001b[0m\u001b[32m'W'\u001b[0m\u001b[39m: <pycba.results.BeamResults object at \u001b[0m\u001b[1;36m0x00000222B87B3580\u001b[0m\u001b[39m>,\u001b[0m\n",
       "\u001b[39m    \u001b[0m\u001b[32m'E'\u001b[0m\u001b[39m: <pycba.results.BeamResults object at \u001b[0m\u001b[1;36m0x00000222B87B2FB0\u001b[0m\u001b[1m>\u001b[0m\n",
       "\u001b[1m}\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beam_results = {}\n",
    "\n",
    "for load_type in w._fields: # load_type = D, L, S, etc.\n",
    "    w_span = [1, 1, getattr(w, load_type), 0, 0]\n",
    "    pl_span = [1, 2, getattr(p, load_type), a, 0]\n",
    "    load_matrix = [w_span, pl_span]\n",
    "    \n",
    "    beam = cba.BeamAnalysis([L], [EI], r, load_matrix)\n",
    "    beam.analyze()\n",
    "    beam_results.update({load_type: beam.beam_results})\n",
    "    \n",
    "print(beam_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aac87ce5-4f7c-48e2-9ab1-d01dcd1c21f7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Post-process results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "80fc715b-51e0-4917-a9db-89cc38fb19b5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "r0_results = Load(*[\n",
    "    [beam_results[\"D\"].R[0]],\n",
    "    [beam_results['L'].R[0]],\n",
    "    [beam_results['S'].R[0]],\n",
    "    [beam_results['W'].R[0]],\n",
    "    [beam_results['E'].R[0]],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "aece1579-75ae-448e-b64c-77a7aa0c5c2c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "r1_results = Load(*[\n",
    "    [beam_results[\"D\"].R[1]],\n",
    "    [beam_results['L'].R[1]],\n",
    "    [beam_results['S'].R[1]],\n",
    "    [beam_results['W'].R[1]],\n",
    "    [beam_results['E'].R[1]],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "36beeba2-7abf-45f5-8633-edf9bcb4c695",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "moment_results = Load(*[\n",
    "    [beam_results[\"D\"].results.M],\n",
    "    [beam_results['L'].results.M],\n",
    "    [beam_results['S'].results.M],\n",
    "    [beam_results['W'].results.M],\n",
    "    [beam_results['E'].results.M],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "065bcb3c-a000-44bb-8dc4-61a4778f3cd7",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "shear_results = Load(*[\n",
    "    [beam_results[\"D\"].results.V],\n",
    "    [beam_results['L'].results.V],\n",
    "    [beam_results['S'].results.V],\n",
    "    [beam_results['W'].results.V],\n",
    "    [beam_results['E'].results.V],\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb1b64a6-3952-484a-aad1-2e9e3b95be42",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Calculate factored loads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "9f44ee33-7641-407e-b2b4-29c39c2788df",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "m_max = factored_max(np.array(moment_results), nbcc_full)\n",
    "m_min = factored_min(np.array(moment_results), nbcc_full)\n",
    "\n",
    "v_max = factored_max(np.array(shear_results), nbcc_full)\n",
    "v_min = factored_min(np.array(shear_results), nbcc_full)\n",
    "\n",
    "r0_max = factored_max(np.array(r0_results), nbcc_full)\n",
    "r0_min = factored_min(np.array(r0_results), nbcc_full)\n",
    "\n",
    "r1_max = factored_max(np.array(r1_results), nbcc_full)\n",
    "r1_min = factored_min(np.array(r1_results), nbcc_full)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d5d472d-6581-43d7-bc6e-49cce6008f61",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Plot Force Diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "dfd1deb4-05b6-451f-bdb0-ff4dda63394e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x222b86756f0>]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EU+dRVF5z2TFatRKdAtzROcADEf7uCPF2NbeSuMDPrWku+9Rfjsq+UImzF6qQXVyJ9PxypOWX4fT5ChRXGPDHyfP44+R5y2Mi/N0R08EXQzu3QUxHX7hr+aeWqKkphBBN2NBqO/R6PTw9PVFaWgqdTid3OUR0HUaTwIGsC1h/JA9b0wpwqtC6tcNJpUBUsCd6h3ihT5g3ugfrEObrBpWMfVOqDEacLCjHoZwSHDhTggNZF5D5p1YatVKBPmHeGNalDUZ2C0SHNu4yVUtkHxr6+c0AQ0SyqTOakJhxHuuO5OH3o/lWrSxKBdCznReGdvLDkAg/RId4wdlJJWO1DXO+vAb7Tl/AzpOF2JFehDPnK63u7xLggZHdA3FXjyB0CfSQqUoi28UAwwBDZLNS8/T4OeksViXnorDsYmjxcFbjzq4BiI0KwJCOfg7Rl+TM+QpsP1GI34/lI/HUedRd0ru4a5AO9/dthzG9guHnrpWxSiLbwQDDAENkU8qqa7HyYA6W7cvG0Vy9Zb+3qxNG9QjCyG6BGNTBFxq1405PVVJpwMbjBVh/5By2nyiCwSh1QlYrFbg90h8P9gvB7ZH+sl4WI5IbAwwDDJFNSM8vw/8Sz2DFgbOoMBgBSP1Z7oj0x7g+7TCsi79Dh5arKak0YE1KLn5KOouUs6WW/SE+LpgyKAzj+4XAy1UjY4VE8mCAYYAhko0QAtvTi/DptlPYderi6JwObdwwZVAYxvRqCx83fjjXO5FfhuX7s/Hj/rMoraoFADg7KTG2V1vMHNoBHdnxl1oRBhgGGKIWZzQJrDtyDp9sPWW5TKRUALFdAzA1pj2GRPhy0rdrqDIYsTolB0t2ncHxc9L5UyiAkd0C8cSwCPRo5ylzhUTNjwGGAYaoxdQZTVhxMAcfbzmJ0+ZRNy5OKkwcEIpHbmmPdt6uMldoX4QQ2H/mAj7bnoGEY/mW/bd28sNfh3dC//Y+MlZH1LwYYBhgiJqdySTw6+FzeG/jCWSY523xcnXCw4PbY1pMe3jzMtFNS8srw+Jtp7A6JRdG8wimYV3a4G8juqB7W7bIkONhgGGAIWo2QghsSSvAWxtOWC51eLs6YdZtHTF5UBjcOPNsk8sursTHW09h+f5sy1Ds+B5BmDeiM/vIkENhgGGAIWoWx8/p8c9fj1mmzvfQqvHorR3wyC3t4eFs//O22LrTRRV4f+MJ/JKSCyEAlVKByQNDMTe2M1u8yCEwwDDAEDWpovIavPP7CSzblwWTkFZonj6kPR6/rSOH+8ogNU+PtzecwMbjUh8ZTxcnzI3thMmDwuCkan3D0slxMMAwwBA1iTqjCV8nnsH7CSdQVlMHQLp08dyoSIT4sHOu3HadLMIra48hNa8MANCxjRv+cU933NLJT+bKiG4MAwwDDNFNS84uwfMrD1uGRHdvq8PC0d0wIJyjYGyJ0STww74svPP7CRRXGAAAY3oF44X4KLTx4BIFZF8YYBhgiG5YaVUt3t6Qhm/3nIEQgM5ZjedGdcWE/iFQcpp7m1VaVYt3f0/D/3bz343sFwMMAwzRDdl0PB8LVhxGgXmRxft6t8Xf47tysUE7kpJdgr9f0nLWL8wbbz0QjXA/N5krI7o+BhgGGKJGKa2qxStrjuHnA2cBAOF+bvjX2O4YHMG+FPaozmjCkl2n8W7CCVQajHB2UmL+yEhMi2nP1hiyaQwwDDBEDbYltQDPrTiEfH0NFArg0VvC8fSILnB2UsldGt2ksxcqMf/nQ5Zh7wPCffD2/dEI9WUHbLJNDDAMMETXVWUw4p+/HsN3e7IASK0ub93fE/04Vb1DEULg2z1ZWPTbcVQajHDVqPD51H4YwtY1skEN/fzmZAFErdSxXD3u/nCnJbw8MiQcv/31VoYXB6RQKDBlUBjWPzkUA8J9UGkwYvbSA8gurpS7NKIb1qgA88knn6Bnz57Q6XTQ6XSIiYnBunXrLPdXV1dj9uzZ8PX1hbu7O8aNG4f8/Hyr58jKykJ8fDxcXV3h7++PZ555BnV1dVbHbN26FX369IFWq0VERASWLFly4++QiKyYTAL/3ZmJsR/9gZMF5fD30OKbGQOw8O4ouGh4yciRhfq64n+PDEB0O0+UVNZi1rdJqK41yl0W0Q1pVIBp164dXn/9dSQlJWH//v244447MGbMGBw9ehQA8NRTT2HNmjVYvnw5tm3bhtzcXNx3332WxxuNRsTHx8NgMGDXrl34+uuvsWTJEixcuNByTGZmJuLj43H77bcjOTkZc+fOxaOPPooNGzY00Vsmar1KKg2Y8fU+vLr2GAxGE2K7+mPdk7fi1k5t5C6NWoizkwqfTO4LHzcNjubq8feVh+GgPQnIwd10HxgfHx+89dZbuP/++9GmTRssXboU999/PwAgNTUVXbt2RWJiIgYNGoR169Zh9OjRyM3NRUBAAABg8eLFmD9/PgoLC6HRaDB//nz8+uuvOHLkiOU1JkyYgJKSEqxfv77BdbEPDJG1lOwSPPHdAeSUVEGrVuKF0VGYPDAUCgVHpLRGu04WYfJ/98AkgFfHdMOUmPZyl0QEoAX6wBiNRvzwww+oqKhATEwMkpKSUFtbi9jYWMsxkZGRCA0NRWJiIgAgMTERPXr0sIQXAIiLi4Ner7e04iQmJlo9R/0x9c9xNTU1NdDr9VYbEUkdOL/ZfQYPLE5ETkkV2vu6YuUTQzBlUBjDSys2OMIPz42KBAD8Y80xJJ0plrkiosZpdIA5fPgw3N3dodVqMWvWLKxcuRJRUVHIy8uDRqOBl5eX1fEBAQHIy8sDAOTl5VmFl/r76++71jF6vR5VVVVXrWvRokXw9PS0bCEhIY19a0QOp8pgxFPLkvHiqiMwGE2I6xaA1f93C6KC2SpJwMxbOyC+RxDqTAJPfHcAF8zLEBDZg0YHmC5duiA5ORl79uzB448/jmnTpuHYsWPNUVujLFiwAKWlpZYtOztb7pKIZJVTUoX7F+/CquRcqJQKPH9XVyye3Bc6Zye5SyMboVAo8Ob9PdGhjRvy9TWY//Mh9ochu9HoAKPRaBAREYG+ffti0aJFiI6OxgcffIDAwEAYDAaUlJRYHZ+fn4/AwEAAQGBg4GWjkup/v94xOp0OLi4uV61Lq9VaRkfVb0St1f7TxRjz4U4czdXDx02DpY8OxMyhHXjJiC7jplXj3xN6w0mlwO/H8rF0b5bcJRE1yE3PA2MymVBTU4O+ffvCyckJmzZtstyXlpaGrKwsxMTEAABiYmJw+PBhFBQUWI5JSEiATqdDVFSU5ZhLn6P+mPrnIKJrW7YvCxM/342icgO6Bumwes4QDOzgK3dZZMO6t/XE/JFSf5hX1x5Den6ZzBURXV+jAsyCBQuwfft2nD59GocPH8aCBQuwdetWTJo0CZ6enpgxYwbmzZuHLVu2ICkpCdOnT0dMTAwGDRoEABgxYgSioqIwZcoUpKSkYMOGDXjhhRcwe/ZsaLXSQnGzZs1CRkYGnn32WaSmpuLjjz/Gjz/+iKeeeqrp3z2RAzGaBF5dewzzfz6MWqPAXT0C8fPjMWjnzSnj6foeGRKOWzv5obrWhL/+kMz5YcjmNSrAFBQUYOrUqejSpQuGDx+Offv2YcOGDbjzzjsBAO+99x5Gjx6NcePGYejQoQgMDMSKFSssj1epVFi7di1UKhViYmIwefJkTJ06Fa+88orlmPDwcPz6669ISEhAdHQ03nnnHXzxxReIi4trordM5HiqDEY8/m0S/rszEwDwVGxnfPRQH7hq1DJXRvZCqVTgnfHR8HXT4Pg5Pd5cnyZ3SUTXxLWQiOxcYVkNHv3ffqRkl0CjUuKd8dG4OzpY7rLITm1JLcD0JfsAAEum98ewLv4yV0StDddCImoFThaU4d6P/0BKdgm8XJ3w3cyBDC90U26P9MfDg9sDAJ796RCHVpPNYoAhslNJZ4ox7pNEnL1QhTDz5HT9uRAjNYHnRkWiYxs3FJTV4PlVXGqAbBMDDJEd2pJagElf7EFpVS16h3phxeODEe7nJndZ5CCcnVR4/8HeUCsV+O1wHlYl58hdEtFlGGCI7MyqgzmY+b/9qK41YViXNlj66CD4umvlLoscTI92npgb2wkAsHDVUZy9UClzRUTWGGCI7MiXOzMxd1ky6kwC9/Zui8+n9oOLRiV3WeSgZt3WEX1CvVBWU4enf0yBycRLSWQ7GGCI7IAQAu8lnMAra6VlOx4ZEo53HoiGk4r/C1PzUauUeHd8L7hqVNiTWWwZpk9kC/jXj8jGCSHw+vpUfLApHQDwtxGd8eLorlAquSwANb/2fm54IV6aKf2t39NwsoCz9JJtYIAhsmFCCPxjzTF8ui0DALBwdBTm3NGJaxpRi5o4IAS3dW4DQ50JTy8/hDqjSe6SiBhgiGyVySTw/KojWLLrNADgX/d2xyO3hMtbFLVKCoUCr4/rAQ9nNVKyS/DZjgy5SyJigCGyRUaTwLM/H8LSPVlQKoC37u+JSQPD5C6LWrEgTxe8dHc3AMD7CelIy+OlJJIXAwyRjTGZBBasOISfks5CpVTgvQd74YF+IXKXRYRxfdpieKQ/DEYT/rY8BbW8lEQyYoAhsiHSZaPD+HH/WSgVwAcTemFMr7Zyl0UEQLqU9Np9PeDp4oTDOaVYvPWU3CVRK8YAQ2QjhBBYuPoIvt+bDaUCeO/BXhjdk+sakW0J0DnjH/dIl5L+vTkdqXl6mSui1ooBhsgG1I82+nZ3FhQK4O0HotnyQjZrTK9g3BkVgFqjwPyfDsHICe5IBgwwRDKrn+dlya7TUCiAN8f1xH192sldFtFVKRQK/HNsd2lU0tlSfMkJ7kgGDDBEMvt46ynLPC+v3duDHXbJLgTonPFCfFcAwDsJaThdVCFzRdTaMMAQyeibxNN4a0MaAOCF+K6YOCBU5oqIGm58vxAMifBFda0Jz604BCF4KYlaDgMMkUxWHjyLF385CgD46x0RePTWDjJXRNQ4CoUCi+7tCRcnFXZnFOP7vdlyl0StCAMMkQwSjuXjb8sPAQAeHtweT93ZWeaKiG5MqK8r/hbXBQCw6LfjOFdaJXNF1FowwBC1sP2nizFn6QEYTQL39WmLhaOjuLYR2bWHB7dH71AvlNXUYaG5VZGouTHAELWg9PwyzPh6P2rqTBge6Y83x/XkqtJk91RKBd4Y1xNOKgUSjuVj/ZE8uUuiVoABhqiF5JVWY9qXe1FaVYveoV748KE+UKv4vyA5hs4BHvjL0I4AgJdWH4G+ulbmisjR8a8nUQsorarFtC/3Ire0Gh3auOG/0/rDRaOSuyyiJjXnjgi093VFvr4Gb5tH1xE1FwYYomZWU2fEY//bj7T8MrTx0OLr6QPg46aRuyyiJufspMJr9/YAAHyz+wwOZF2QuSJyZAwwRM1ICIFnfzqEPZnF8NCq8fX0AQjxcZW7LKJmMzjCD+P6tIMQwIKfD3PFamo2DDBEzej9jen4JTkXaqUCH0/ug6hgndwlETW75+O7wtvVCWn5Zfh8R4bc5ZCDYoAhaiYrDpzFB5vSAQD/HNsdt3ZqI3NFRC3Dx02DF+KjAAAfbExHdnGlzBWRI2KAIWoGezLOY/7P0kR1s27riAlcIoBamfv6tMXgjr6oqTPhpdVHucwANTkGGKImllFYjse+SUKtUeCuHoF41jxLKVFrolAo8MqY7nBSKbA5tQC/H8uXuyRyMAwwRE2otLIWj369H6VVtegV4oV3x/fiRHXUakX4u+OxodIaX/9YfRSVhjqZKyJHwgBD1ETqjCb83w8HkVFUgWBPZ3w+tR+cnTjXC7Vuc27vhHbeLsgtrbb0CSNqCgwwRE1k0bpUbD9RCBcnFT6b2g9tPLRyl0QkOxeNCv+4pxsA4L87MnEiv0zmishRMMAQNYEf92fjvzszAQDvjI9G97aeMldEZDuGdw3AnVEBqDMJvLDqCDv0UpNggCG6SUlnivHCyiMAgCeHd8JdPYJkrojI9rx0dxRcnFTYm1mMlQdz5C6HHAADDNFNyCutxl++OQCD0YRR3QPx5PBOcpdEZJPaebvi/4ZHAABe+y0VZVzskW4SAwzRDaqpM2LWt0koKq9BZKAH3n4gmiOOiK5hxi3hCPdzQ1F5Df7NDr10kxhgiG7QP9YcQ3J2CXTOanw2pR/ctGq5SyKyaVq1Ci/dLc3Q+9Ufp5HODr10ExhgiG7Asn1ZWLonCwoF8O+JvRHqywUaiRpiWBd/S4fel9dwhl66cY0KMIsWLUL//v3h4eEBf39/jB07FmlpaVbHDBs2DAqFwmqbNWuW1TFZWVmIj4+Hq6sr/P398cwzz6CuznqCo61bt6JPnz7QarWIiIjAkiVLbuwdEjWx5OwSvLjqKADg6Ts7Y1gXf5krIrIvL8ZHQaNW4o+T57H+SJ7c5ZCdalSA2bZtG2bPno3du3cjISEBtbW1GDFiBCoqKqyOmzlzJs6dO2fZ3nzzTct9RqMR8fHxMBgM2LVrF77++mssWbIECxcutByTmZmJ+Ph43H777UhOTsbcuXPx6KOPYsOGDTf5doluzvnyGjz+bRIMRhPujArAE8Mi5C6JyO6E+rpi1m0dAQCvrj2GKoNR5orIHinETbTfFRYWwt/fH9u2bcPQoUMBSC0wvXr1wvvvv3/Fx6xbtw6jR49Gbm4uAgICAACLFy/G/PnzUVhYCI1Gg/nz5+PXX3/FkSNHLI+bMGECSkpKsH79+gbVptfr4enpidLSUuh0uht9i0QWRpPAtC/3YufJInRo44ZfZg+Bh7OT3GUR2aUqgxGx725DTkkV/u+OCDw9gmuGkaShn9831QemtLQUAODj42O1/7vvvoOfnx+6d++OBQsWoLLy4lLqiYmJ6NGjhyW8AEBcXBz0ej2OHj1qOSY2NtbqOePi4pCYmHjVWmpqaqDX6602oqb0703p2HmyCC5OKiye3JfhhegmuGhUeHG01KH30+0ZyC6uvM4jiKzdcIAxmUyYO3cuhgwZgu7du1v2P/TQQ/j222+xZcsWLFiwAN988w0mT55suT8vL88qvACw/J6Xl3fNY/R6Paqqqq5Yz6JFi+Dp6WnZQkJCbvStEV1m+4lC/HuzNOzztfu6o3OAh8wVEdm/uG4BGBLhC0OdCYvWHZe7HLIzNzzuc/bs2Thy5Ah27txptf+xxx6z/NyjRw8EBQVh+PDhOHXqFDp27HjjlV7HggULMG/ePMvver2eIYaaxLnSKsxdlgwhgIkDQnFv73Zyl0TkEBQKBV4cHYW7PtiB3w7nYXfGeQzq4Ct3WWQnbqgFZs6cOVi7di22bNmCdu2u/cd84MCBAICTJ08CAAIDA5Gfn291TP3vgYGB1zxGp9PBxcXliq+j1Wqh0+msNqKbVWs0Yc7SgyiuMCAqSGeZw4KImkZkoA4PDQwFIM2tZDRxWDU1TKMCjBACc+bMwcqVK7F582aEh4df9zHJyckAgKAgaX2YmJgYHD58GAUFBZZjEhISoNPpEBUVZTlm06ZNVs+TkJCAmJiYxpRLdNPe2pCGpDMX4KFV45PJfeDspJK7JCKHM+/OLtA5q3H8nB7L9mXLXQ7ZiUYFmNmzZ+Pbb7/F0qVL4eHhgby8POTl5Vn6pZw6dQqvvvoqkpKScPr0aaxevRpTp07F0KFD0bNnTwDAiBEjEBUVhSlTpiAlJQUbNmzACy+8gNmzZ0Or1QIAZs2ahYyMDDz77LNITU3Fxx9/jB9//BFPPfVUE799oqvbklqAz7ZnAADeeqAnwnzdZK6IyDH5uGkwN7YzAOCd39NQWsV1kuj6GhVgPvnkE5SWlmLYsGEICgqybMuWLQMAaDQabNy4ESNGjEBkZCSefvppjBs3DmvWrLE8h0qlwtq1a6FSqRATE4PJkydj6tSpeOWVVyzHhIeH49dff0VCQgKio6Pxzjvv4IsvvkBcXFwTvW2ia8vXV+Pp5SkAgIcHt8fI7lxhmqg5TYkJQ8c2bjhfYcB/uE4SNcBNzQNjyzgPDN0oo0lgyn/3YNep8+gapMPKJwbz0hFRC9iaVoCHv9oHtVKB358aig5t3OUuiWTQIvPAEDmiT7aexK5T5+GqUeHDh3ozvBC1kGFd/HF7lzaoMwksWpcqdzlk4xhgiC6x/3Qx3tsoNV+/MqY7OvIbIFGLej6+K1RKBRKO5WN3xnm5yyEbxgBDZFZaWYsnf0iG0SQwtlcwxvVpK3dJRK1OhL8HJg6Q5vD656/HYOKwaroKBhgiSFME/H3VYeSUVCHM1xX/vLcHFAqF3GURtUpzYzvDXavGkRw9ViXnyF0O2SgGGCIAKw7k4NdD56BWKvDvCb3hrr3hSaqJ6Cb5uWsx+3Zppfc316dxtWq6IgYYavWyiyvx0mppIdG5sZ0QHeIlb0FEhOlD2qOtlwvy9NX4YkeG3OWQDWKAoVatzmjC3GXJKK+pQ//23nh8WITcJRERAGcnFZ4d2QUA8Mm2Uygoq5a5IrI1DDDUqn289ZRlqYB3x/eCSsl+L0S24p7oYPQK8UKlwYh3fz8hdzlkYxhgqNU6mHUBH5hn/HxlbDeE+LjKXBERXUqhUOCF+K4AgB/3ZyM9v0zmisiWMMBQq1RpqMO8H1NgNAncHR2Msb04ZJrIFvVr74MRUQEwCeCN9Wlyl0M2hAGGWqU31qUis6gCgTpn/HNMdw6ZJrJhz46MhEqpwMbj+dibWSx3OWQjGGCo1fnjZBG+TjwDAHjz/p7wdHWSuSIiupYIf3c82F+a3G7RuuNw0CX8qJEYYKhV0VfX4hnzKtOTB4ViaOc2MldERA0xd3gnuDipcDCrBOuP5MldDtkABhhqVV5Zcwy5pdUI83XF3+/qKnc5RNRA/jpnzBzaAQDw5oY01BpNMldEcmOAoVYj4Vg+fko6C4UCeOeBaLhqONsukT15bGgH+LlrkFlUgR/2ZsldDsmMAYZaheIKAxasOARA+iPYr72PzBURUWO5a9X46/BOAIAPNqWjvKZO5opITgww1Cq8vPooisoN6Bzgjnl3dpa7HCK6QRMHhKK9ryuKyg34cmem3OWQjBhgyOFtOJqH1Sm5UCkVePuBaGjVKrlLIqIb5KRS4ukR0hIDn23PQHGFQeaKSC4MMOTQSioNeH7lEQDSpaOe7bzkLYiIblp8jyBEBelQXlOHT7aelLsckgkDDDm0V9YcQ1F5DSL83fGk+do5Edk3pVJhWejx68QzyC2pkrkikgMDDDmszan5WHEwB0qFNGGdsxMvHRE5its6t8HAcB8Y6kz4YGO63OWQDBhgyCGVVtViwYrDAIAZt4SjT6i3zBURUVNSKBR4dmQkAGB5UjZOFpTLXBG1NAYYckiv/Xoc+foadPBzs3T4IyLH0jfMG7FdpYUe3/mdCz22Ngww5HB2nSrCsv3ZAIA3eOmIyKE9E9cFCgWw7kgeUrJL5C6HWhADDDmU6loj/m6+dDR5UCj6c8I6IofWJdAD9/ZqCwB4m60wrQoDDDmUDzal4/T5SgTqnC3Xx4nIsc2N7Qy1UoEd6UXYk3Fe7nKohTDAkMM4mluKz7ZnAABeGdMNOmcnmSsiopYQ6uuK8f1DAADv/H4CQgiZK6KWwABDDqHOaMJzPx+G0SRwV49AjOgWKHdJRNSC/u+OCGjUSuw9XYwd6UVyl0MtgAGGHMJXf5zG4ZxS6JzVePmebnKXQ0QtLMjTBZMHhgGQRiSxFcbxMcCQ3csursS7CScAAM/Hd4W/h7PMFRGRHB4f1hEuTiqknC3FxuMFcpdDzYwBhuyaEAIvrT6KqlojBoT7YHy/ELlLIiKZtPHQYvqQ9gCkVhiTia0wjowBhuzahqN52JxaACeVAq/d2x0KhULukohIRo8N7QAPrRqpeWX49fA5ucuhZsQAQ3arvKYOL68+BgD4y9COiPD3kLkiIpKbl6sGj97aAQDw3sYTMLIVxmExwJDdeuf3NOTpqxHm64o5d0TIXQ4R2YhHbmkPL1cnZBRWYHVKjtzlUDNhgCG7dCSnFF/vOg0AeHVMdy4XQEQWHs5OmGluhfn3ppOoM5pkroiaAwMM2R2jSeDvKw/DJIC7o4MxtHMbuUsiIhszbXB7eLs6IbOoAr8k58pdDjUDBhiyO0v3nMGhs6XwcFbjxdFd5S6HiGyQu1aNx4Z2BAD8Z3M6W2EcEAMM2ZWi8hq8tUFasO2ZuC6c84WIrmpqTBh83DQ4fb4SKw+yL4yjaVSAWbRoEfr37w8PDw/4+/tj7NixSEuzXv2zuroas2fPhq+vL9zd3TFu3Djk5+dbHZOVlYX4+Hi4urrC398fzzzzDOrq6qyO2bp1K/r06QOtVouIiAgsWbLkxt4hOZQ31qVCX12HbsE6TDLPuklEdCVuWjX+MlTqC/OfzSdRy1YYh9KoALNt2zbMnj0bu3fvRkJCAmprazFixAhUVFRYjnnqqaewZs0aLF++HNu2bUNubi7uu+8+y/1GoxHx8fEwGAzYtWsXvv76ayxZsgQLFy60HJOZmYn4+HjcfvvtSE5Oxty5c/Hoo49iw4YNTfCWyV4lnSnG8qSzAIBXx3aHSsk5X4jo2qbEhMHPXYOs4kqsPMBWGEeiEDexYERhYSH8/f2xbds2DB06FKWlpWjTpg2WLl2K+++/HwCQmpqKrl27IjExEYMGDcK6deswevRo5ObmIiAgAACwePFizJ8/H4WFhdBoNJg/fz5+/fVXHDlyxPJaEyZMQElJCdavX9+g2vR6PTw9PVFaWgqdTnejb5FsRJ3RhHs+/APHzunxYL8QvHF/T7lLIiI78fn2DPzrt+MI8XHB5qeHwUnF3hO2rKGf3zf1r1haWgoA8PHxAQAkJSWhtrYWsbGxlmMiIyMRGhqKxMREAEBiYiJ69OhhCS8AEBcXB71ej6NHj1qOufQ56o+pf44rqampgV6vt9rIcXy3JwvHzunh6eKEZ0d2kbscIrIjkwaFws9dg+ziKqw4cFbucqiJ3HCAMZlMmDt3LoYMGYLu3bsDAPLy8qDRaODl5WV1bEBAAPLy8izHXBpe6u+vv+9ax+j1elRVVV2xnkWLFsHT09OyhYRwTRxHUVhWg7d/v9hx19ddK3NFRGRPXDVqzLpNGpH00ZZTHJHkIG44wMyePRtHjhzBDz/80JT13LAFCxagtLTUsmVnZ8tdEjWR19eloqy6Dj3aemLigFC5yyEiO/TQwFD4uEl9YTgvjGO4oQAzZ84crF27Flu2bEG7du0s+wMDA2EwGFBSUmJ1fH5+PgIDAy3H/HlUUv3v1ztGp9PBxcXlijVptVrodDqrjezfgawL+Nnc5PvKmG7suEtEN8RVo7bMzvvhlpNcI8kBNCrACCEwZ84crFy5Eps3b0Z4eLjV/X379oWTkxM2bdpk2ZeWloasrCzExMQAAGJiYnD48GEUFBRYjklISIBOp0NUVJTlmEufo/6Y+ueg1sFkEvjHaqlf1AN926F3qLfMFRGRPZsSEwYv8+y8aw+xFcbeNSrAzJ49G99++y2WLl0KDw8P5OXlIS8vz9IvxdPTEzNmzMC8efOwZcsWJCUlYfr06YiJicGgQYMAACNGjEBUVBSmTJmClJQUbNiwAS+88AJmz54NrVbq2zBr1ixkZGTg2WefRWpqKj7++GP8+OOPeOqpp5r47ZMt++nAWaScLYWHVo1nR0bKXQ4R2Tl3rRqP3iJ98f7P5pMwsRXGrjUqwHzyyScoLS3FsGHDEBQUZNmWLVtmOea9997D6NGjMW7cOAwdOhSBgYFYsWKF5X6VSoW1a9dCpVIhJiYGkydPxtSpU/HKK69YjgkPD8evv/6KhIQEREdH45133sEXX3yBuLi4JnjLZA/01bV4c30qAODJ2E5o48GOu0R086YObg+dsxonC8qx7kie3OXQTbipeWBsGeeBsW//XHsMX+zMRIc2blj/5FBo1Jy3gYiaxvsbT+D9jemIDPTAb3+9FUr2rbMpLTIPDFFzOFlQjiW7TgMAFo6OYnghoiY1fXA43LVqpOaV4fdj+dd/ANkkfjKQTRFC4B9rjqLOJBDb1R/DuvjLXRIRORhPVyc8PLg9AGmlage9EOHwGGDIpmxOLcCO9CJoVEq8EB8ldzlE5KBm3BIOV40KR3P12HqiUO5y6AYwwJDNMNSZ8K9fjwMAHrklHO393GSuiIgclbebBpMGShNjfrT5JFth7BADDNmMb3efQUZRBfzcNZh9e0e5yyEiB/forR2gUSmx/8wF7MkslrscaiQGGLIJFyoM+GBTOgDg6RFd4OHsJHNFROToAnTOeKCfNJv8R1tOylwNNRYDDNmEDzalo7SqFpGBHhjfjwtxElHLmHVbR6iUCuxIL0JKdonc5VAjMMCQ7E4WlOOb3WcAAC+OjuJ6R0TUYkJ8XDGmVzAAtsLYGwYYkt1rvx2H0TxsekiEn9zlEFEr88SwCCgUwO/H8pGWVyZ3OdRADDAkq+0nCrE5tQBqpQJ/v6ur3OUQUSsU4e+OUd0DAQCfbGUrjL1ggCHZGE3CMmx6akx7dGjjLnNFRNRaPTEsAgCwOiUXZ85XyFwNNQQDDMnm56SzSMsvg85Zjb8Oj5C7HCJqxbq39cSwLm1gEsDnOzLkLocagAGGZFFpqMM7CWkAgL8O7wQvV43MFRFRa/f4bdL8Uz/uP4vCshqZq6HrYYAhWXyxIxP5+hqE+LhgSkyY3OUQEWFAuA/6hHrBUGfCV39kyl0OXQcDDLW4wrIafLrtFADgmbhIaNUqmSsiIgIUCgUeN/eF+SbxDPTVtTJXRNfCAEMt7v2NJ1BhMCI6xAt39wySuxwiIovhkf7o5O+Ospo6LN2TJXc5dA0MMNSiThaU4Yd92QCA5+/qCoWCk9YRke1QKhWYZe4L89+dmaiuNcpcEV0NAwy1qNfXpcJoErgzKgADwn3kLoeI6DL39ApGsKczCstqsOJAjtzl0FUwwFCL2ZtZjI3HC6BSKvDcqEi5yyEiuiInlRIzh3YAAHy6/RSMJiFzRXQlDDDUIoQQeH2dNGndhP4h6MhJ64jIhj3YPwTerk44c74Svx0+J3c5dAUMMNQifj+WjwNZJXBxUuHJ4Z3kLoeI6JpcNWpMG9wegNQKIwRbYWwNAww1uzqjCW+uTwUAzLglHP46Z5krIiK6vqkx7eHspMSRHD0ST52Xuxz6EwYYanY/HziLU4UV8HZ1wmO3dZC7HCKiBvFx02B8vxAAwOLtXF7A1jDAULOqrjXivYR0AMDs2yOgc3aSuSIiooZ79JYOUCqA7ScKcfycXu5y6BIMMNSsluw6jTx9Ndp6cckAIrI/ob6uGNVDmnDzc7bC2BQGGGo2JZUGfLzlJABg3p2duWQAEdmlv5iHVK9OyUVuSZXM1VA9BhhqNou3ZUBfXYfIQA+M7d1W7nKIiG5Iz3ZeGNTBB3UmgS93cpFHW8EAQ82iQF+NJbuk/9H/NqILVEouGUBE9usv5uUFvt+bhdIqLvJoCxhgqFl8uOUkqmtN6BPqheFd/eUuh4jopgzr3AZdAjxQYTBykUcbwQBDTS67uBLf75X+B38mLpILNhKR3VMoFJblBb78IxM1dVzkUW4MMNTk3t+YjlqjwK2d/BDT0VfucoiImsQ90cEI1EmLPK5J4fICcmOAoSaVnl+GlQfPApD6vhAROQqNWmlZXuCLHRlcXkBmDDDUpN5NOAGTAOK6BSA6xEvucoiImtRDA0LhqlEhNa8Mf5zk8gJyYoChJnPobAnWHcmDQgE8zdYXInJAnq5OluUFPt/Bie3kxABDTebt308AAO7t1RadAzxkroaIqHk8MiQcCgWw7UQhTuSXyV1Oq8UAQ01i3+libD9RCLVSgbmxneUuh4io2YT6uiIuKhAA8N8dnNhOLgww1CTeNbe+PNAvBKG+rjJXQ0TUvGYODQcArDyYg8KyGpmraZ0YYOim7TpVhMSM89ColJhzR4Tc5RARNbu+YT7oHeoFg9GEb3afkbucVqnRAWb79u24++67ERwcDIVCgVWrVlnd//DDD0OhUFhtI0eOtDqmuLgYkyZNgk6ng5eXF2bMmIHy8nKrYw4dOoRbb70Vzs7OCAkJwZtvvtn4d0fNTghhaX2ZMCAEbb1cZK6IiKhlPHqLNLHdt7vPoLqWE9u1tEYHmIqKCkRHR+Ojjz666jEjR47EuXPnLNv3339vdf+kSZNw9OhRJCQkYO3atdi+fTsee+wxy/16vR4jRoxAWFgYkpKS8NZbb+Hll1/GZ5991thyqZntSC/C/jMXoFErMft2tr4QUesR1y0A7bxdUFxhwIoDOXKX0+qoG/uAUaNGYdSoUdc8RqvVIjAw8Ir3HT9+HOvXr8e+ffvQr18/AMB//vMf3HXXXXj77bcRHByM7777DgaDAV9++SU0Gg26deuG5ORkvPvuu1ZBh+QlhMA7CVLry+SBYQjQOctcERFRy1GrlJg+JByvrj2GL//IxMQBIVw6pQU1Sx+YrVu3wt/fH126dMHjjz+O8+cvTvaTmJgILy8vS3gBgNjYWCiVSuzZs8dyzNChQ6HRaCzHxMXFIS0tDRcuXLjia9bU1ECv11tt1Ly2pBUgJbsELk4qPD6so9zlEBG1uPH92sFdq8bJgnLsSC+Su5xWpckDzMiRI/G///0PmzZtwhtvvIFt27Zh1KhRMBql64N5eXnw97denVitVsPHxwd5eXmWYwICAqyOqf+9/pg/W7RoETw9PS1bSEhIU781uoQQAu+aW1+mDg5DGw+tzBUREbU8D2cnPNCvHQBpkUdqOU0eYCZMmIB77rkHPXr0wNixY7F27Vrs27cPW7dubeqXsrJgwQKUlpZatuzs7GZ9vdbu92P5OJKjh5tGhb8MZesLEbVe0wdLE9ttTSvEyQJObNdSmn0YdYcOHeDn54eTJ08CAAIDA1FQUGB1TF1dHYqLiy39ZgIDA5Gfn291TP3vV+tbo9VqodPprDZqHkIIfLAxHQDw8JD28HHTXOcRRESOK9TXFXd2la4SfPXHaXmLaUWaPcCcPXsW58+fR1BQEAAgJiYGJSUlSEpKshyzefNmmEwmDBw40HLM9u3bUVtbazkmISEBXbp0gbe3d3OXTNeRcCwfx85JrS/1wwiJiFqzR26RJrb7+cBZlFQaZK6mdWh0gCkvL0dycjKSk5MBAJmZmUhOTkZWVhbKy8vxzDPPYPfu3Th9+jQ2bdqEMWPGICIiAnFxcQCArl27YuTIkZg5cyb27t2LP/74A3PmzMGECRMQHBwMAHjooYeg0WgwY8YMHD16FMuWLcMHH3yAefPmNd07pxsihMAHm6TWl2mD28ObrS9ERBgY7oOoIB2qa034fi+7MLSERgeY/fv3o3fv3ujduzcAYN68eejduzcWLlwIlUqFQ4cO4Z577kHnzp0xY8YM9O3bFzt27IBWe7GT53fffYfIyEgMHz4cd911F2655RarOV48PT3x+++/IzMzE3379sXTTz+NhQsXcgi1Ddh4vABHc/Vw1ajw6K1sfSEiAgCFQmFphflf4mnUGk0yV+T4FEIIIXcRzUGv18PT0xOlpaXsD9NEhBC4+8OdOJKjx+PDOmL+yEi5SyIishk1dUYMeX0zisoN+PfE3rgnOljukuxSQz+/uRYSNdjm1AIcyZFaX2ay9YWIyIpWrcLkQWEAgC93ckh1c2OAoQYRQuB988ijKTFhHHlERHQFkweFQaNSIjm7BMnZJXKX49AYYKhBtqQV4HBOKVycVHiMrS9ERFfk567F6Ghp1O3Xu07LW4yDY4Ch67p03pepMWHwdeesu0REV/Pw4PYAgLWHclFQVi1vMQ6MAYaua0d6EVLOlsLZScmRR0RE19GznRf6hHqh1iiwdE+W3OU4LAYYuq4PN0uzKE8cEMo1j4iIGuDhIdKQ6u/2ZMFQxyHVzYEBhq5pd8Z57D1dDI1KyTWPiIgaaFT3QPh7aFFYVoN1R87JXY5DYoCha6pvfXmgXzsEejrLXA0RkX1wUiktQ6q5PlLzYIChqzqQdQE7TxZBrVRg1m1sfSEiaoyJA0I5pLoZMcDQVdW3vtzbuy1CfFxlroaIyL608dBidE8OqW4uDDB0RUdySrE5tQBKBfDE7RFyl0NEZJemcUh1s2GAoSv6aIvU+nJ3dDDC/dxkroaIyD5Fh3iht3lI9Q9cpbpJMcDQZdLzy7DuSB4AYDZbX4iIbsq0mPYAgO/2nOEq1U2IAYYu88nWUwCAuG4B6BzgIXM1RET2bVSPQPi5a5Cvr0HCsXy5y3EYDDBkJbu4Er+k5AIAnhjG1hciopulVaswoX8oAHbmbUoMMGTl8x0ZMJoEbonwQ3SIl9zlEBE5hIcGhkKlVGBPZjHS8srkLschMMCQRWFZDZbtkzqZPXE7530hImoqwV4uuLNrAADgf4mn5S3GQTDAkMWXf2Sips6EXiFeiOngK3c5REQOZepgaWbelQdzoK+ulbka+8cAQwCA0qpafJN4BgDwxLCOUCgUMldERORYYjr4opO/OyoNRvycdFbucuweAwwBAL7dfQblNXXoHOCOWHMzJxERNR2FQoGpMVIrzDeJZ2AyCZkrsm8MMIQqgxH/3ZkJAHh8WEcolWx9ISJqDvf2aQd3rRoZRRX441SR3OXYNQYYwrJ9WSiuMKCdtwvu7hksdzlERA7LXavGuD5tAQD/M1+2pxvDANPK1RpN+HyH1Pryl6EdoFbxPwkiouY0xXwZadPxfOSWVMlcjf3ip1Ur99vhc8gpqYKvmwYP9AuRuxwiIocX4e+BQR18YBLAD3uz5C7HbjHAtGJCCCzelgEAeHhwezg7qWSuiIiodZg8SGqF+X5fNtdHukEMMK3Y9vQiHD+nh6tGZWnSJCKi5jciKhB+7loUltXg96NcH+lGMMC0YovNizZO6B8KL1eNzNUQEbUeGrUSE/pLl+2/3c3OvDeCAaaVSskuQWLGeaiVCsy4NVzucoiIWp2JA0OhVACJGedxsoDrIzUWA0wr9el2qfXlnuhgtPVykbkaIqLWp62XC+6IlCYO/XY3O/M2FgNMK3S6qALrjuQBAB67rYPM1RARtV6TB4UCAH4+cBaVhjqZq7EvDDCt0Gc7MiAEcHuXNogM1MldDhFRqzW0UxuE+riirLoOa1Jy5S7HrjDAtDJF5TX4ybyI2KzbOspcDRFR66ZUKjBpoNQK883uMxCC6yM1FANMK/O/xDMw1JkQHeKFAeE+cpdDRNTqPdAvBBq1Ekdy9Dh0tlTucuwGA0wrUmUw4pvE0wCkZQMUCi7aSEQkNx83De7qHggAWLqHnXkbigGmFfnpwFlcqKxFiI8L4roFyl0OERGZPTRQmkx0dUou9NW1MldjHxhgWgmjSeC/O6RlA2YMCYdKydYXIiJb0b+9NyL83VFVa8QvB3PkLscuMMC0EgnH8nH6fCU8XZy4aCMRkY1RKC525v1uTxY78zYAA0wr8bm59WXyoFC4adUyV0NERH92X+920KqVSM0rw4GsErnLsXmNDjDbt2/H3XffjeDgYCgUCqxatcrqfiEEFi5ciKCgILi4uCA2Nhbp6elWxxQXF2PSpEnQ6XTw8vLCjBkzUF5ebnXMoUOHcOutt8LZ2RkhISF48803G//uCACQdKYYSWcuQKNSYlpMe7nLISKiK/B0dcLonsEA2Jm3IRodYCoqKhAdHY2PPvroive/+eab+Pe//43Fixdjz549cHNzQ1xcHKqrqy3HTJo0CUePHkVCQgLWrl2L7du347HHHrPcr9frMWLECISFhSEpKQlvvfUWXn75ZXz22Wc38Bbp8+2ZAICxvYPhr3OWuRoiIrqah8yXkdYeykVpJTvzXpO4CQDEypUrLb+bTCYRGBgo3nrrLcu+kpISodVqxffffy+EEOLYsWMCgNi3b5/lmHXr1gmFQiFycnKEEEJ8/PHHwtvbW9TU1FiOmT9/vujSpUuDaystLRUARGlp6Y2+PYeQWVgu2j+3VoTNXyvS8vRyl0NERNdgMplE3HvbRNj8teLLnRlylyOLhn5+N2kfmMzMTOTl5SE2Ntayz9PTEwMHDkRiYiIAIDExEV5eXujXr5/lmNjYWCiVSuzZs8dyzNChQ6HRaCzHxMXFIS0tDRcuXLjia9fU1ECv11ttBHz5RyaEAIZ1aYPOAR5yl0NERNegUCgsrTBL2Zn3mpo0wOTlSQsEBgQEWO0PCAiw3JeXlwd/f3+r+9VqNXx8fKyOudJzXPoaf7Zo0SJ4enpatpAQjrQprazF8v3SsgEzb+WijURE9mBs77ZwcVIhvaAc+05f+Us7OdAopAULFqC0tNSyZWdny12S7JbuzUJVrRGRgR4Y3NFX7nKIiKgBdM5OuCda6sz7/V525r2aJg0wgYHS7K75+flW+/Pz8y33BQYGoqCgwOr+uro6FBcXWx1zpee49DX+TKvVQqfTWW2tWa3RhK93nQYAzLglnMsGEBHZkQkDpKsIvx0+x868V9GkASY8PByBgYHYtGmTZZ9er8eePXsQExMDAIiJiUFJSQmSkpIsx2zevBkmkwkDBw60HLN9+3bU1l78R0tISECXLl3g7e3dlCU7rN8On0Oevhp+7lrc0ytY7nKIiKgReoV4ITLQAzV1Jqw8eFbucmxSowNMeXk5kpOTkZycDEDquJucnIysrCwoFArMnTsX//znP7F69WocPnwYU6dORXBwMMaOHQsA6Nq1K0aOHImZM2di7969+OOPPzBnzhxMmDABwcHSB+1DDz0EjUaDGTNm4OjRo1i2bBk++OADzJs3r8neuCMTQuC/O6Wh01NjwqBVq2SuiIiIGkOhUGDiAKkz7w/7stmZ90oaO7xpy5YtAsBl27Rp04QQ0hCwF198UQQEBAitViuGDx8u0tLSrJ7j/PnzYuLEicLd3V3odDoxffp0UVZWZnVMSkqKuOWWW4RWqxVt27YVr7/+eqPqbM3DqPdmnhdh89eKTs//JorKquUuh4iIbkBJhUF0fv43ETZ/rUg6Uyx3OS2moZ/fCiEcM9bp9Xp4enqitLS01fWHmfVNEtYfzcOE/iF4fVxPucshIqIbNG9ZMlYczMH4fu3w5v3RcpfTIhr6+e0wo5BIknW+Er8fk4aaP3JLuMzVEBHRzZhgvoy0JuUcyqrZmfdSDDAO5qtdmTAJYGhnTlxHRGTv+rf3Rsc2bqiqNWJ1Sq7c5dgUBhgHUlZ9ceK6GWx9ISKyewqFAhP6mzvz7uX8ZpdigHEgy/efRXlNHSL83TG0k5/c5RARURMY17cdNColDueU4khOqdzl2AwGGAdhNAl8nXgaAPDw4PacuI6IyEH4uGkwopu0nM4P+zgzbz0GGAexJbUAZ85XQuesxn192spdDhERNaH6OWF+OZiLKoNR5mpsAwOMg/hqlzRx3cQBoXDVqGWuhoiImlJMB1+E+riirKYOvx0+J3c5NoEBxgGk5ZXhj5PnoVQAU2LC5C6HiIiamFKpwAN92wEAlu1nZ16AAcYhLDG3vsR1C0Q7b1eZqyEiouZwf792UCqAvZnFyCyqkLsc2THA2LkLFQasOJADAJg+hEOniYgcVZCnC27r3AYA8CNbYRhg7N33+7JQU2dCt2Ad+rfnSt1ERI7swf4hAICfks6izmiSuRp5McDYsVqjCd8kngEgtb5w6DQRkWO7IzIAvm4aFJbVYEtaodzlyIoBxo79fjQf50qr4eeuwd3RQXKXQ0REzUyjVlqmyli2r3VfRmKAsWNf7zoNQBo6rVWr5C2GiIhaRP1lpC1pBSjQV8tcjXwYYOzUsVw99p4uhlqpwKSBHDpNRNRaRPh7oE+oF4wmgZ/NgzhaIwYYO/U/87IBcd0DEejpLG8xRETUoupbYZbvz4YQQuZq5MEAY4dKKg1YlSyl7ocHt5e3GCIianGjewbDTaNCRlEF9mYWy12OLBhg7NCP+7NRXWtC1yAd+oVx6DQRUWvjplVjdM9gAMDypLMyVyMPBhg7YzQJ/M88dPrhwWEcOk1E1Eo90E9aWuDXQ+dQXlMnczUtjwHGzmxJLcDZC1XwdHHCPdFcdZqIqLXqG+aNDn5uqKo14rdDrW+BRwYYO/O1ufPuhP4hcNFw6DQRUWulUChwv7kVZnlS65sThgHGjpwsKMeO9CIoFMDkQRw6TUTU2o3rIy3wuO/0BWQUlstdTotigLEj35hbX4ZHBiDEh6tOExG1dgE6Z8sCjz+1ss68DDB2orymzjJh0bTBbH0hIiLJA/2kOWF+PnAWRlPrmROGAcZOrDqYg/KaOnTwc8OQjn5yl0NERDZieFd/eLs6IV9fg+3prWeBRwYYOyCEwLe7paHTkwaFQank0GkiIpJo1SqM6SWNSv1pf+u5jMQAYwf2nb6A1LwyODspcX/fdnKXQ0RENma8+TJSwrF8XKgwyFxNy2CAsQPfmFtfxvZqC08XJ5mrISIiWxMVrEO3YB0MRhN+SW4dCzwywNi4grJqrD8iTVDEodNERHQ1D5hb6H9sJZeRGGBs3LK92ag1CvQJ9UL3tp5yl0NERDZqTK+2cFIpcOycHsfP6eUup9kxwNiwOqMJS/dmAQCmxLD1hYiIrs7bTYPYrgEAgJ9bwZwwDDA2bFNqAc6VVsPHTYNR3YPkLoeIiGzcuD7SZaRVyTmoNZpkrqZ5McDYsPqh0w/2D4GzE9c9IiKia7utSxv4uWtQVG7A9hOOPScMA4yNyii8uO7RQwNC5S6HiIjsgJNKeXFOGAe/jMQAY6O+N/d9ub2LP9c9IiKiBqufL2zT8QKHnhOGAcYGVdcasdycnCcPYusLERE1XNcgHaKCpDlh1hzKlbucZsMAY4N+O3wOJZW1aOvlgts6+8tdDhER2Zlx5lYYRx6NxABjg77bI10+mjggBCque0RERI00plcw1EoFUs6WIj2/TO5ymkWTB5iXX34ZCoXCaouMjLTcX11djdmzZ8PX1xfu7u4YN24c8vPzrZ4jKysL8fHxcHV1hb+/P5555hnU1dU1dak26fg5PZLOXIBaqcD4/iFyl0NERHbIz12LYV2kFvyfDjhmK0yztMB069YN586ds2w7d+603PfUU09hzZo1WL58ObZt24bc3Fzcd999lvuNRiPi4+NhMBiwa9cufP3111iyZAkWLlzYHKXanKXm1pe4boHw93CWuRoiIrJX9Z15Vx7IQZ0DzgmjbpYnVasRGBh42f7S0lL897//xdKlS3HHHXcAAL766it07doVu3fvxqBBg/D777/j2LFj2LhxIwICAtCrVy+8+uqrmD9/Pl5++WVoNJorvmZNTQ1qamosv+v19jeNckVNHVYelBbhmjSQnXeJiOjG3RHpD29XJxSU1WDnySJLi4yjaJYWmPT0dAQHB6NDhw6YNGkSsrKkVoWkpCTU1tYiNjbWcmxkZCRCQ0ORmJgIAEhMTESPHj0QEBBgOSYuLg56vR5Hjx696msuWrQInp6eli0kxP4uv/ySnIvymjp08HNDTEdfucshIiI7plErcU90MABYvhw7kiYPMAMHDsSSJUuwfv16fPLJJ8jMzMStt96KsrIy5OXlQaPRwMvLy+oxAQEByMvLAwDk5eVZhZf6++vvu5oFCxagtLTUsmVnZzftG2tmQgh8t0eaefehgaFQKNh5l4iIbs595qUFNhzNQ1l1rczVNK0mv4Q0atQoy889e/bEwIEDERYWhh9//BEuLi5N/XIWWq0WWq222Z6/uaWcLcXRXD00aqXluiUREdHN6NnOEx3buOFUYQXWHcnD+H72d3Xiapp9GLWXlxc6d+6MkydPIjAwEAaDASUlJVbH5OfnW/rMBAYGXjYqqf73K/WrcRRLza0vo3sEwcv1yv18iIiIGkOhUFhaYVYecKzLSM0eYMrLy3Hq1CkEBQWhb9++cHJywqZNmyz3p6WlISsrCzExMQCAmJgYHD58GAUFBZZjEhISoNPpEBUV1dzlykJfXYs1KecAAJM48y4RETWhsb2ltZESM87j7IVKmatpOk0eYP72t79h27ZtOH36NHbt2oV7770XKpUKEydOhKenJ2bMmIF58+Zhy5YtSEpKwvTp0xETE4NBgwYBAEaMGIGoqChMmTIFKSkp2LBhA1544QXMnj3bri8RXcsvB3NQVWtE5wB39An1lrscIiJyIG29XBDTQRoY8kuy4ywt0OQB5uzZs5g4cSK6dOmC8ePHw9fXF7t370abNm0AAO+99x5Gjx6NcePGYejQoQgMDMSKFSssj1epVFi7di1UKhViYmIwefJkTJ06Fa+88kpTl2oTpM679TPvsvMuERE1vfv6SK0wPx84CyGEzNU0DYVwlHfyJ3q9Hp6enigtLYVOp5O7nKtKzi7B2I/+gFatxJ6/D2f/FyIianLlNXXo988EVNea8MvsIYgO8ZK7pKtq6Oc310KS2ffm1pd4dt4lIqJm4q5VI66bNBBmhYMsLcAAIyN9dS1Wp0jXIx/izLtERNSM6kcjrU7JhaHO/pcWYICR0S/JuaiqNaKTvzv6hrHzLhERNZ8hHX3h76HFhcpabE0ruP4DbBwDjEyEEJaFG9l5l4iImptapbQMqV7hAHPCMMDI5NDZUhw/J828W987nIiIqDndaw4wm1MLUFpl30sLMMDI5Pu97LxLREQtq2uQDpGBHjAYTVh3+Jzc5dwUBhgZlNfUWTrvTujvOOtSEBGR7au/jGTvK1QzwMhgTUouKg1GdGjjhgHhPnKXQ0RErcg90cFQKIA9mcXIKamSu5wbxgAjgx/2ZQOQWl/YeZeIiFpSsJcLBoXXLy1gv60wDDAt7Pg5PVKyS+CkurhCKBERUUuq78y78kCO3S4twADTwpaZW1/ujAqAn7tjLk5JRES2bWSPQGjUSqQXlOPYOb3c5dwQBpgWVF1rtHSaerA/Z94lIiJ56JydcGfXAADAKjvtzMsA04I2HM1DaVUt2nq54JYIP7nLISKiVqx+NNIvybkwmuzvMhIDTAv6Ya90+eiBfu2gUrLzLhERyee2zm3g5eqEgrIa7DpVJHc5jcYA00JOF1UgMeM8FArggX6c+4WIiOSlUSsxumcQAPucE4YBpoX8uF9qfRnaqQ3aernIXA0REdHF0UgbjuShymCUuZrGYYBpAXVGE5YnnQXAmXeJiMh29An1RoiPCyoMRiQcz5e7nEZhgGkBW9IKUVhWA183DYabe30TERHJTaFQYEy01Aqz2s4mtWOAaQH1l4/u69MWGjVPORER2Y6xvYMBAFvTCnGhwiBzNQ3HT9NmVlBWjc2pBQCAB3n5iIiIbEyEvweignSoMwn8dsR+VqhmgGlmKw/kwGgS6BPqhQh/D7nLISIiukx9K8wvB3NlrqThGGCakRDCcvloPIdOExGRjbrbvEL13tP2s0I1A0wzOpBVglOFFXBxUiHePNaeiIjI1gR5umBguA8AYHWyfbTCMMA0o+Xm1pe7egTBw9lJ5mqIiIiubkyv+qUF7GM0EgNMM6moqcOaFCnFsvMuERHZuru6B8FJpUBqXhnS8srkLue6GGCayW+Hz6HCYER7X1f0b+8tdzlERETX5OnqhGFd/AEAq+ygFYYBppks3y/NvPtAvxAoFFy4kYiIbN+YXtJopNXJuTDZ+ArVDDDNIKOwHHtPF0OpAMb1aSd3OURERA0S2zUAbhoVckqqkJR1Qe5yrokBphn8ZF73aFgXfwR6OstcDRERUcM4O6kQ1z0QgO135mWAaWJGk8DPB8yXj/qy9YWIiOxL/Wik3w7nodZokrmaq2OAaWI70guRr6+Bt6sTF24kIiK7M6SjL3zdNCiuMGDXqfNyl3NVDDBNbLn58tGYXly4kYiI7I9apcRdPaTJV215Ujt+wjah0spaJBzNBwDcz8tHRERkp+6OlkYj/X40D9W1RpmruTIGmCa0OiUHBqMJXYN06N7WU+5yiIiIbki/MG8EeTqjrKYOW9MK5C7nihhgmlD96CO2vhARkT1TKhWWVpjVKbZ5GYkBpomcyC9DytlSqJUKjDVPBERERGSv7jEHmE3HC1BWXStzNZdjgGki9a0vd0T6w9ddK3M1REREN6dbsA4d/NxQU2fCxuP5cpdzGZsOMB999BHat28PZ2dnDBw4EHv37pW7pCuqM5qw4oA04Q8vHxERkSNQKC65jGSDo5FsNsAsW7YM8+bNw0svvYQDBw4gOjoacXFxKCiwvc5E204Uoqi8Br5uGtwe6S93OURERE3iHnOXiB3pRbhQYZC5Gms2G2DeffddzJw5E9OnT0dUVBQWL14MV1dXfPnll3KXdpn6y0dje7eFk8pmTykREVGjdGzjjm7BOtSZBH47ck7ucqyo5S7gSgwGA5KSkrBgwQLLPqVSidjYWCQmJl7xMTU1NaipqbH8rtfrm6W23R89itCibVb7/m4SmKbxQ6fa24CjMUDbvoBnO4CrUBMRka0TAjCUA2X5QHk+UJ5n/jkPKMvDZ6YMVGly4PxbLXLXW3+uFQx5Bb1iJ8pStk0GmKKiIhiNRgQEWE/FHxAQgNTU1Cs+ZtGiRfjHP/7R7LWpq4sRLP50GUsBhCgKgZTjQMpiaZ9bGyC4DxDcW9ra9gHceXmJiFqYsQ4oSgNyDwI5B6Tb86cAJxdA6wE466RbFx/p75abn7S5mm9dfABXX8DFG1DZ5EcGXYmhEqg8D1QVAxVF0s8VRUBlkXRbUQiUFwAVBUB5IVBXddWnagtcvF4jrO/LrSlvrndwXQ7zX+OCBQswb948y+96vR4hISFN/jqBY17BCf1frfYpTEaEiRxo8s1/IPKPSP9xpG+QtnoewUBwLyCo18VbD66XRERNxFgLFKYB55KB3GTgXAqQd/jKH041pdI37MZw9pQCjYs34Gq+dfYEnL0AFy/p1lkn7dNecqv1ANRatko3hskktYrU6IFqPVBTZv65FKguAapKLvn5gvR71QVpqyy+ZiC5Ko2H9EXbPUC61QUDHoGARxAuKL1RaHC67CERoZE3+UZvnE0GGD8/P6hUKuTnWw/bys/PR2Bg4BUfo9VqodU2//DldhHdr3HvVOmmtgrIOyJ908k1f+MpTAPKcoG0XCDtt4sPcfMHgnoCQdFAYE8gsAfgHQ4o2ZeGiK7BUAHkHwPyDpmDyiHpd2PN5cdq3KUvTG3NLcL+UYDRIH0oVuulD8bKYvO380Kg4rx0W1Vs/hZ/QXqe6lJpu5DZ+HqVainIaDwArTugcTNv7oCTK6BxlW6dXAEnZ0DtIt06uQJqZykAqbTSrVoLqDSAyunirdLJfKsGlCrpd6UKUCgBhUoKT40JUEKYNyNgMgKmOvNmBEy1Ulg0GqR9RoO01Rmk819nAOqqgboaKUjUVptvq4DaSunWUAnUVki3hgrp55pyc2gpk25vltJJaj1z9QXcfC+2qrn6Ae5tpM8fd39zy1sb6d/lKrzNmy2xyQCj0WjQt29fbNq0CWPHjgUAmEwmbNq0CXPmzJG3uIZwcgFC+ktbvZoyKdRYvhklA0UnpOa7kxulrZ7GHQjoBgR0lwJNQHfAv+s1/+MiIgclBKDPAfKPSq0p+Uek2/OncFl7PiAFhKBocytvtBRcfCNu7kuRse7it/uq4ovf8qsuXNIaYL61tBiYbw1l0nOYLnkO2ZhDjEJ58WdAOsf151IIQJhwxXMrB6Xa3Jqlu9iqZdXq5Sm1hFk2r4uhRePu0K1eNhlgAGDevHmYNm0a+vXrhwEDBuD9999HRUUFpk+fLndpN0brAYTFSFs9Q6X5j1IKcM78LarguJS8s/dI26W8w6Vg4x8FBERJtz4deV2ayFFUlQCFqdLfhYJjUotKwVGp1eNK3AOkLzhB0VJLbmDP5mnBVamlb+zubRr/WMulkDLrW0OFeSs3t0aYt/qf66qlloq6aqkFw1hjbtW4pJXDZG4FubQ15JrEJQHlZijMLT8a6dwonS62Cqm1UkuQ2kX62cl8q3a5pJXJRdosrU/mliiNm7l1yt3cWuUuHefAIeRm2Own34MPPojCwkIsXLgQeXl56NWrF9avX39Zx167pnG9vKXGWAecPyl9w8o7JP0hyz8qXau+kCltqWsvHq/SAn6dgDaRgH8k0Kar9LN3ewYbIltVrZdaYAuOS4Gl/lafc+XjlWrAr7P0pSWwx8XNHgYGKJXmfjG65n+t+nBiqpNCjTCafzdd/Lm+tcXS6mIOBwrFxZ8tl56U0n6l+uKmUPESv41QCCFspJ2saen1enh6eqK0tBQ6XQv8j9PcKoouhpmCY9IfvILj0nXTK1FppGZjv85Amy7SrV8naZ/GrWVrJ2qNhJCGpBadkLbCE9JooMI0oOwa82no2kmXjP27mgNLd+n/XzWXKKHWoaGf3www9sxkAkqzgIJUoPD4xdvCE9fuge4ZIgUZq62jtJ+tNkSNU1MGFGdILafnT0m3RenSbc015qNyD7zYamppPe0i9WEgasUYYFpDgLkakwkozZa+6RWlSU3TRSeB8+nSiIKrUToB3mGATwepb41PuPSzdzjgFQqoNS33HohsSWWxdPm2OPPibXGGFFgqrrG8iUIpXc6tbwH16yJd4vXrxKBCdBUN/fzm121HpFRKQcQ7DOg8wvq+ymKpOfv8yUu2U9JmrLm4788USqlp2zsM8AqT/ih7h0nBxitU+jbJ68Jkr2qrgJJsqUXzwmngwhnptsR8e7VOtPVcfQHfThdbM+sv3/qE89IPUTNhgGltXH2A0EHSdimTSepAWHzq4jfLC6cvfuOsrZT+uJdmAdhx+fOqNNLyCZ4h5q2d9aYLZt8bkofJJLU86s8CpTlA6VmphbL+tiT72q0o9dwDpUDibW6Z9AmXwop3OFtTiGTAAEMSpRLwCpG2DsOs7xNCmtSqOPPiN9L6b6ilWdKHgtEgBZ/ijKu/hrOXFGY8ggBdkDQzcf2tR6C0ufqxJYcarrb64rotZeekTZ8D6C/9OVf67/N6NB4XWxTrWxi9219scdS4NvObIaLGYICh61MozNNL+wOhAy+/31gnfViUZJm/2Zq/3ZaYb/U50lwP1SXSln/k6q+lVEuzQ3oEXJwlsn5a6/rZIus3F2+GHUdUV2OeDbbwT2u2FJoXmsuXfi/Lk/57ahDzf8O6tlJIv7SVsD60OHtxvg0iO8IAQzdPpb7YenM11aXSN+HSHCnQlJ2Tfi87J31bLs+TPqxMddKSC2W5139dhdK8AJ15amxXH/P6LJfc1s9M6ex18We1Mz+oWoLJZJ6NteSSWVxLzNPTm2d0rSy+OF19/YJzjZ1CXaW92ILnEWRev8V8qwuWQotHEDuhEzkYBhhqGfXTX/t3vfoxxlrpW3bZOekbtmUzf+uu/zZeUSh9KAqTtHZLZVHjalFprKfk1nqYV+X1vDj7Zf1smPWzY2pcASfzbf3smOr6dVocZJE6Y93FdVvq12v581othkvWa6mfVbV+u3T6+OpS8xDiGxzkqFRfsjKyufXN/ZIWObc2F0MLW06IWiUGGLIdKqeL35qvp85gvUx8ZZF5Mbrii9/sK89fvk6LMEr9IW4k+FyV4uJic5Zb88JzKqeLU4tbLTanln5WqC7O+qlUXbLo3KVrtVz64Sys12oRJmlxOWGUWjwsC87VXZyN1FQrhRNjzcVp1+tqzFv1xVtTbROdjz9Ru1iv01L/86WtZa7mhebqF53TevLyIBFdEwMM2Se15uI38IYSwtwXx7yirqWlwLxMfU39kvXlV1iz5ZKVY+vXbLGsuyKklosbWb7eVllWAnazboGyrCLsfrHlSushtWhZWrK8LllwTsdhxETULBhgqPVQKC5+yHq2u/nnM9aaL7NUXWzJMJpbNmqrrBeZq//ZVGu+NUo/W1pP6tdpMV1cr+VqK+JaWmfM67TUr81iac1RXWzpsdxqrBeaU2kvbzGqX2ROpWXrBxHZPAYYohulMl8SaolF6oiIyAq/ZhEREZHdYYAhIiIiu8MAQ0RERHaHAYaIiIjsDgMMERER2R0GGCIiIrI7DDBERERkdxhgiIiIyO4wwBAREZHdYYAhIiIiu8MAQ0RERHaHAYaIiIjsDgMMERER2R2HXY1aCAEA0Ov1MldCREREDVX/uV3/OX41DhtgysrKAAAhISEyV0JERESNVVZWBk9Pz6verxDXizh2ymQyITc3Fx4eHlAoFE32vHq9HiEhIcjOzoZOp2uy56WLeI6bF89v8+M5bl48v81L7vMrhEBZWRmCg4OhVF69p4vDtsAolUq0a9eu2Z5fp9Pxf5xmxnPcvHh+mx/PcfPi+W1ecp7fa7W81GMnXiIiIrI7DDBERERkdxhgGkmr1eKll16CVquVuxSHxXPcvHh+mx/PcfPi+W1e9nJ+HbYTLxERETkutsAQERGR3WGAISIiIrvDAENERER2hwGGiIiI7A4DDBEREdkdBphG+uijj9C+fXs4Oztj4MCB2Lt3r9wl2aVFixahf//+8PDwgL+/P8aOHYu0tDSrY6qrqzF79mz4+vrC3d0d48aNQ35+vkwV27fXX38dCoUCc+fOtezj+b15OTk5mDx5Mnx9feHi4oIePXpg//79lvuFEFi4cCGCgoLg4uKC2NhYpKeny1ix/TAajXjxxRcRHh4OFxcXdOzYEa+++qrVAn88v42zfft23H333QgODoZCocCqVaus7m/I+SwuLsakSZOg0+ng5eWFGTNmoLy8vAXfhXXB1EA//PCD0Gg04ssvvxRHjx4VM2fOFF5eXiI/P1/u0uxOXFyc+Oqrr8SRI0dEcnKyuOuuu0RoaKgoLy+3HDNr1iwREhIiNm3aJPbv3y8GDRokBg8eLGPV9mnv3r2iffv2omfPnuLJJ5+07Of5vTnFxcUiLCxMPPzww2LPnj0iIyNDbNiwQZw8edJyzOuvvy48PT3FqlWrREpKirjnnntEeHi4qKqqkrFy+/Cvf/1L+Pr6irVr14rMzEyxfPly4e7uLj744APLMTy/jfPbb7+J559/XqxYsUIAECtXrrS6vyHnc+TIkSI6Olrs3r1b7NixQ0RERIiJEye28DuRMMA0woABA8Ts2bMtvxuNRhEcHCwWLVokY1WOoaCgQAAQ27ZtE0IIUVJSIpycnMTy5cstxxw/flwAEImJiXKVaXfKyspEp06dREJCgrjtttssAYbn9+bNnz9f3HLLLVe932QyicDAQPHWW29Z9pWUlAitViu+//77lijRrsXHx4tHHnnEat99990nJk2aJITg+b1Zfw4wDTmfx44dEwDEvn37LMesW7dOKBQKkZOT02K11+MlpAYyGAxISkpCbGysZZ9SqURsbCwSExNlrMwxlJaWAgB8fHwAAElJSaitrbU635GRkQgNDeX5boTZs2cjPj7e6jwCPL9NYfXq1ejXrx8eeOAB+Pv7o3fv3vj8888t92dmZiIvL8/qHHt6emLgwIE8xw0wePBgbNq0CSdOnAAApKSkYOfOnRg1ahQAnt+m1pDzmZiYCC8vL/Tr189yTGxsLJRKJfbs2dPiNTvsatRNraioCEajEQEBAVb7AwICkJqaKlNVjsFkMmHu3LkYMmQIunfvDgDIy8uDRqOBl5eX1bEBAQHIy8uToUr788MPP+DAgQPYt2/fZffx/N68jIwMfPLJJ5g3bx7+/ve/Y9++ffjrX/8KjUaDadOmWc7jlf5m8Bxf33PPPQe9Xo/IyEioVCoYjUb861//wqRJkwCA57eJNeR85uXlwd/f3+p+tVoNHx8fWc45AwzJbvbs2Thy5Ah27twpdykOIzs7G08++SQSEhLg7OwsdzkOyWQyoV+/fnjttdcAAL1798aRI0ewePFiTJs2Tebq7N+PP/6I7777DkuXLkW3bt2QnJyMuXPnIjg4mOeXAHAUUoP5+flBpVJdNkojPz8fgYGBMlVl/+bMmYO1a9diy5YtaNeunWV/YGAgDAYDSkpKrI7n+W6YpKQkFBQUoE+fPlCr1VCr1di2bRv+/e9/Q61WIyAggOf3JgUFBSEqKspqX9euXZGVlQUAlvPIvxk35plnnsFzzz2HCRMmoEePHpgyZQqeeuopLFq0CADPb1NryPkMDAxEQUGB1f11dXUoLi6W5ZwzwDSQRqNB3759sWnTJss+k8mETZs2ISYmRsbK7JMQAnPmzMHKlSuxefNmhIeHW93ft29fODk5WZ3vtLQ0ZGVl8Xw3wPDhw3H48GEkJydbtn79+mHSpEmWn3l+b86QIUMuG/p/4sQJhIWFAQDCw8MRGBhodY71ej327NnDc9wAlZWVUCqtP6JUKhVMJhMAnt+m1pDzGRMTg5KSEiQlJVmO2bx5M0wmEwYOHNjiNXMUUiP88MMPQqvViiVLlohjx46Jxx57THh5eYm8vDy5S7M7jz/+uPD09BRbt24V586ds2yVlZWWY2bNmiVCQ0PF5s2bxf79+0VMTIyIiYmRsWr7dukoJCF4fm/W3r17hVqtFv/6179Eenq6+O6774Srq6v49ttvLce8/vrrwsvLS/zyyy/i0KFDYsyYMRzm20DTpk0Tbdu2tQyjXrFihfDz8xPPPvus5Rie38YpKysTBw8eFAcPHhQAxLvvvisOHjwozpw5I4Ro2PkcOXKk6N27t9izZ4/YuXOn6NSpE4dR24v//Oc/IjQ0VGg0GjFgwACxe/duuUuySwCuuH311VeWY6qqqsQTTzwhvL29haurq7j33nvFuXPn5Cvazv05wPD83rw1a9aI7t27C61WKyIjI8Vnn31mdb/JZBIvvviiCAgIEFqtVgwfPlykpaXJVK190ev14sknnxShoaHC2dlZdOjQQTz//POipqbGcgzPb+Ns2bLlin93p02bJoRo2Pk8f/68mDhxonB3dxc6nU5Mnz5dlJWVyfBuhFAIccm0hkRERER2gH1giIiIyO4wwBAREZHdYYAhIiIiu8MAQ0RERHaHAYaIiIjsDgMMERER2R0GGCIiIrI7DDBERERkdxhgiIiIyO4wwBAREZHdYYAhIiIiu/P/XLrsS0bO8xYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Moment envelope\")\n",
    "ax.plot(m_max)\n",
    "ax.plot(m_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "c5323291-1a32-4d3b-b204-934846cb98c4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x222b8a0f220>]"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Shear Envelope\")\n",
    "ax.plot(v_max)\n",
    "ax.plot(v_min)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "youtube",
   "language": "python",
   "name": "youtube"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}