arrayed.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Arrayed SD\n",
    "\n",
    "Arrayed SD allows for arrays to be used in SD models. \n",
    "\n",
    "First let's look at how arrayed SD works. We start with some boilerplate to get a BPTK project up and running:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from BPTK_Py import Model\n",
    "import BPTK_Py\n",
    "\n",
    "model = Model(starttime=0.0, stoptime=20.0, dt=1.0, name=\"Test Model\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we can start creating arrayed components. There are two options for arrayed elements: Vectors (one dimensional arrays) and Matrices (two dimensional arrays). These can be declared as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector = model.converter(\"converter_vector\")\n",
    "\n",
    "# create a vector of length 2 with values 2.0, 3.0\n",
    "vector.setup_vector(2, [2.0, 3.0])\n",
    "\n",
    "matrix = model.converter(\"converter_matrix\")\n",
    "\n",
    "# create a matrix of size 2x3 with values [2.0, 3.0, 4.0], [5.0, 6.0, 7.0]\n",
    "matrix.setup_matrix([2, 3], [[2.0, 3.0, 4.0], [5.0, 6.0, 7.0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variety of operations can be performed on vectors and matrices. Below are some examples, for a more detailed list see the documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# multiply the vector with the matrix\n",
    "multiplied = model.converter(\"multiplied\")\n",
    "multiplied.equation = vector.dot(matrix)\n",
    "\n",
    "# get the second biggest element of the vector\n",
    "rank = model.converter(\"rank\")\n",
    "rank.equation = matrix.arr_rank(2)\n",
    "\n",
    "# Let's get the output of the rank converter\n",
    "data = rank.plot(return_df=True)\n",
    "data[rank.name][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Named Arrays\n",
    "Besides vectors and matrices named arrays are possible. These arrays can make code more readable but do not allow for some functions to be used which require indexed matrices (e.g. the dot operator). Below is an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "named = model.converter(\"named\")\n",
    "named.setup_named_vector({\"germany\": 0.19, \"switzerland\": 0.08, \"austria\": 0.20})\n",
    "\n",
    "named.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then do operations on named vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "named_price = model.converter(\"named_price\")\n",
    "named_price.setup_named_vector({\"germany\": 1.0, \"switzerland\": 1.2, \"austria\": 1.05})\n",
    "\n",
    "total_tax = model.converter(\"total_tax\")\n",
    "total_tax.equation = named * named_price\n",
    "\n",
    "total_tax.plot()\n",
    "\n",
    "\n",
    "net_profit = model.converter(\"net_profit\")\n",
    "net_profit.equation = named_price - total_tax\n",
    "\n",
    "net_profit.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Careful: The location in the vector is used to determine the position in the vector, not vector names!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting\n",
    "Plotting vectors and matrices is straightforward. Let's plot the vector below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "scenario_manager = {\"sm\": {\"model\": model}}\n",
    "\n",
    "bptk = BPTK_Py.bptk()\n",
    "bptk.register_scenario_manager(scenario_manager)\n",
    "bptk.register_scenarios(\n",
    "    scenario_manager=\"sm\",\n",
    "    scenarios=\n",
    "    {\n",
    "        \"testScenario\":{}\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "223a9a7c90a9468a81e01b245122bdb4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from BPTK_Py.visualizations import SimpleDashboard\n",
    "import ipywidgets as widgets\n",
    "\n",
    "dashboard = SimpleDashboard(bptk, scenario_manager=\"sm\", scenario=\"testScenario\")\n",
    "\n",
    "plot = dashboard.add_plot(\n",
    "    equations=[\"converter_vector[0]\", \"converter_vector[1]\"], \n",
    "    names=[\"VectorX\", \"VectorY\"],\n",
    "    title=\"Vector\",\n",
    "    x_label=\"X\",\n",
    "    y_label=\"Y\",\n",
    ")\n",
    "\n",
    "display(plot)\n",
    "dashboard.start()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly matrices can be plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "30affdc89bc347469ae3342dc7fdd284",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from BPTK_Py.visualizations import SimpleDashboard\n",
    "import ipywidgets as widgets\n",
    "\n",
    "dashboard = SimpleDashboard(bptk, scenario_manager=\"sm\", scenario=\"testScenario\")\n",
    "\n",
    "plot = dashboard.add_plot(\n",
    "    equations=[\"converter_matrix[0][0]\", \"converter_matrix[0][1]\", \"converter_matrix[0][2]\", \"converter_matrix[1][0]\", \"converter_matrix[1][1]\", \"converter_matrix[1][2]\"],\n",
    "    names=[\"Matrix00\", \"Matrix01\", \"Matrix02\", \"Matrix10\", \"Matrix11\", \"Matrix12\"],\n",
    "    title=\"Matrix\",\n",
    "    x_label=\"X\",\n",
    "    y_label=\"Y\",\n",
    ")\n",
    "\n",
    "display(plot)\n",
    "dashboard.start()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same works for named arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8167dcecbc794bcfa21e46f96123f131",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from BPTK_Py.visualizations import SimpleDashboard\n",
    "import ipywidgets as widgets\n",
    "\n",
    "dashboard = SimpleDashboard(bptk, scenario_manager=\"sm\", scenario=\"testScenario\")\n",
    "\n",
    "plot = dashboard.add_plot(\n",
    "    equations=[\"net_profit[germany]\", \"net_profit[switzerland]\", \"net_profit[austria]\"],\n",
    "    names=[\"Germany\", \"Switzerland\", \"Austria\"],\n",
    "    title=\"Net Profit\",\n",
    "    x_label=\"X\",\n",
    "    y_label=\"Y\",\n",
    ")\n",
    "\n",
    "display(plot)\n",
    "dashboard.start()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function documentation\n",
    "\n",
    "Below is documentation of all relevant arrayed SD functions. First, let's declare some basic elements to do operations on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "constant = model.converter(\"converter_constant\")\n",
    "constant.equation = 100.0\n",
    "\n",
    "vector3 = model.converter(\"converter_vector3\")\n",
    "vector3.setup_vector(3, [2.0, 3.0, 4.0])\n",
    "\n",
    "matrix33 = model.converter(\"converter_matrix3\")\n",
    "matrix33.setup_matrix([3, 3], [[2.0, 3.0, 4.0], [5.0, 6.0, 7.0], [8.0, 9.0, 10.0]])\n",
    "\n",
    "matrix32 = model.converter(\"converter_matrix32\")\n",
    "matrix32.setup_matrix([3, 2], [[2.0, 3.0], [5.0, 6.0], [8.0, 9.0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Sum\n",
    "Calculates the element-wise sum of an array.\n",
    "\n",
    "Parameter:\n",
    "    - include_all: Boolean -> If true, includes both numbered and named elements.\n",
    "\n",
    "Example (2.0 + 3.0 + 4.0 = 9.0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_sum_converter = model.converter(\"arr_sum_converter\")\n",
    "arr_sum_converter.equation = vector3.arr_sum()\n",
    "\n",
    "data = arr_sum_converter.plot(return_df=True)\n",
    "assert(data[arr_sum_converter.name][0] == 9.0)\n",
    "data[arr_sum_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Product\n",
    "Calculates the element-wise product of an array.\n",
    "\n",
    "Parameter:\n",
    "    - include_all: Boolean -> If true, includes both numbered and named elements.\n",
    "\n",
    "Example (2.0 * 3.0 * 4.0 = 24.0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.0"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_prod_converter = model.converter(\"arr_prod_converter\")\n",
    "arr_prod_converter.equation = vector3.arr_prod()\n",
    "\n",
    "data = arr_prod_converter.plot(return_df=True)\n",
    "assert(data[arr_prod_converter.name][0] == 24.0)\n",
    "data[arr_prod_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array rank\n",
    "Calculates the nth highest element of an array.\n",
    "\n",
    "Parameter: \n",
    "    - rank: int -> The rankth highest element will be returned.\n",
    "\n",
    "Example: (third highest of matrix33 = 8.0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_rank_converter = model.converter(\"arr_rank_converter\")\n",
    "arr_rank_converter.equation = matrix33.arr_rank(3)\n",
    "\n",
    "data = arr_rank_converter.plot(return_df=True)\n",
    "assert(data[arr_rank_converter.name][0] == 8.0)\n",
    "data[arr_rank_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Mean\n",
    "Calculates the element-wise mean of an array.\n",
    "\n",
    "Example (mean of matrix32 = 5.5):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.5"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_mean_converter = model.converter(\"arr_mean_converter\")\n",
    "arr_mean_converter.equation = matrix32.arr_mean()\n",
    "\n",
    "data = arr_mean_converter.plot(return_df=True)\n",
    "assert(data[arr_mean_converter.name][0] == 5.5)\n",
    "data[arr_mean_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Median\n",
    "Calculates the element-wise median of an array.\n",
    "\n",
    "Example (meadian of matrix32 = 5.5):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.5"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_median_converter = model.converter(\"arr_median_converter\")\n",
    "arr_median_converter.equation = matrix32.arr_median()\n",
    "\n",
    "data = arr_median_converter.plot(return_df=True)\n",
    "assert(data[arr_median_converter.name][0] == 5.5)\n",
    "data[arr_median_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Standard Deviation\n",
    "Calculates the element-wise standard deviation of an array.\n",
    "\n",
    "Example (standard deviation of matrix32 = 2.5):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_stddev_converter = model.converter(\"arr_stddev_converter\")\n",
    "arr_stddev_converter.equation = matrix32.arr_stddev()\n",
    "\n",
    "data = arr_stddev_converter.plot(return_df=True)\n",
    "assert(data[arr_stddev_converter.name][0] == 2.5)\n",
    "data[arr_stddev_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Size\n",
    "Calculates the size of an array. The size of the highest level will be returned (for example 3 for a 3 by 2 matrix).\n",
    "\n",
    "Example (size of matrix32 = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_size_converter = model.converter(\"arr_size_converter\")\n",
    "arr_size_converter.equation = matrix32.arr_size()\n",
    "\n",
    "data = arr_size_converter.plot(return_df=True)\n",
    "assert(data[arr_size_converter.name][0] == 3)\n",
    "data[arr_size_converter.name][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array Dot\n",
    "The Dot function uses matrix/vector multiplication logic. It is possible to input illegal arguments. Legal inputs are:\n",
    "- Any vector * constant => vector\n",
    "- Any matrix * constant => matrix\n",
    "- Vector of size m * Vector of size m => constant\n",
    "- Vector of size m * Matrix of size mxn => vector of size m\n",
    "- Matrix of size mxn * Vector of size n => vector of size n\n",
    "- Matrix of size mxn * Matrix of size nxp => matrix of size mxp\n",
    "\n",
    "Below are examples for the described dot operations:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vector x Constant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "vec_dot_constant_converter = model.converter(\"vec_dot_constant_converter\")\n",
    "vec_dot_constant_converter.equation = vector3.dot(constant)\n",
    "\n",
    "vec_dot_constant_converter.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vector x Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_dot_vec_converter = model.converter(\"vec_dot_vec_converter\")\n",
    "vec_dot_vec_converter.equation = vector3.dot(vector3)\n",
    "\n",
    "vec_dot_vec_converter.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vector x Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['vec_dot_mat_converter[0]: 51.0',\n",
       " 'vec_dot_mat_converter[1]: 60.0',\n",
       " 'vec_dot_mat_converter[2]: 69.0']"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_dot_mat_converter = model.converter(\"vec_dot_mat_converter\")\n",
    "vec_dot_mat_converter.equation = vector3.dot(matrix33)\n",
    "\n",
    "vec_dot_mat_converter.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Matrix x Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['mat_dot_vec_converter[0]: 29.0',\n",
       " 'mat_dot_vec_converter[1]: 56.0',\n",
       " 'mat_dot_vec_converter[2]: 83.0']"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat_dot_vec_converter = model.converter(\"mat_dot_vec_converter\")\n",
    "mat_dot_vec_converter.equation = matrix33.dot(vector3)\n",
    "\n",
    "mat_dot_vec_converter.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Matrix x Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Math operations\n",
    "Mathematical operations are executed on a per-element basis. That means that for all basic mathematical operations both arrays have to have equal size, the exception being array constant operations. Below are examples for all basic mathematical operations.\\\n",
    "\n",
    "#### Multiplication\n",
    "Element-wise multiplication works with arrays of the same size or arrays and constants.\n",
    "\n",
    "Example: ([2.0, 3.0, 4.0] * [2.0, 3.0, 4.0] = [4.0, 9.0, 16.0]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['vec_mul_vec_converter[0]: 4.0',\n",
       " 'vec_mul_vec_converter[1]: 9.0',\n",
       " 'vec_mul_vec_converter[2]: 16.0']"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_mul_vec_converter = model.converter(\"vec_mul_vec_converter\")\n",
    "vec_mul_vec_converter.equation = vector3 * vector3\n",
    "\n",
    "vec_mul_vec_converter.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Addition\n",
    "Element-wise multiplication works with arrays of the same size or arrays and constants.\n",
    "\n",
    "Example: ([2.0, 3.0, 4.0] + [2.0, 3.0, 4.0] = [4.0, 6.0, 8.0]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['vec_add_vec_converter[0]: 4.0',\n",
       " 'vec_add_vec_converter[1]: 6.0',\n",
       " 'vec_add_vec_converter[2]: 8.0']"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_add_vec_converter = model.converter(\"vec_add_vec_converter\")\n",
    "vec_add_vec_converter.equation = vector3 + vector3\n",
    "\n",
    "vec_add_vec_converter.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Division\n",
    "Element-wise division works with arrays of the same size or arrays and constants.\n",
    "\n",
    "Example: ([2.0, 3.0, 4.0] / [4.0, 3.0, 2.0] = [4.0, 6.0, 8.0]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['vec_div_vec_converter[0]: 0.5',\n",
       " 'vec_div_vec_converter[1]: 1.0',\n",
       " 'vec_div_vec_converter[2]: 2.0']"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_div_vec_converter = model.converter(\"vec_div_vec_converter\")\n",
    "vector3_alternative = model.converter(\"converter_vector3_alternative\")\n",
    "vector3_alternative.setup_vector(3, [4.0, 3.0, 2.0])\n",
    "vec_div_vec_converter.equation = vector3 / vector3_alternative\n",
    "\n",
    "vec_div_vec_converter.plot()"
   ]
  }
 ],
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