{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f389f465-1007-443d-873b-d27bfa74cbc7",
   "metadata": {},
   "source": [
    "# Basic model tutorial\n",
    "\n",
    "In this tutorial you will learn the basics of the model interface for a simple inline python model. The API for the model interface is provided here:\n",
    "\n",
    "https://pressio.github.io/rom-tools-and-workflows/romtools/workflows/models.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "358fb709-9c81-45a3-a871-2549de121580",
   "metadata": {},
   "outputs": [],
   "source": [
    "#First, let's import the relavant modules:\n",
    "import romtools\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from romtools.workflows import models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b1ffa4be-246c-44a9-b486-f517b9f7acb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$u$')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pda_path = os.environ[\"pda-src-dir\"]\n",
    "\n",
    "'''\n",
    "Here, we will interface around a very basic model for solving the 1D poisson equation.\n",
    "c u_x - nu * u_xx = 1\n",
    "'''\n",
    "# We will start with defining an advection diffusion problem. This class does NOT meet any interface related to romtools\n",
    "class advectionDiffusionProblem:\n",
    "    def __init__(self , nx):\n",
    "        nx_ = nx\n",
    "        self.x_ = np.linspace(0,1,nx)\n",
    "        dx = 1. / (nx - 1)\n",
    "\n",
    "        ## Assemble diffusion operator and assign boundary conditions\n",
    "        self.Ad_ = np.zeros((nx,nx))\n",
    "        self.Ad_[0,0] = -2./dx**2\n",
    "        self.Ad_[0,1] = 1./dx**2\n",
    "       \n",
    "        self.Ad_[-1,-1] = -2./dx**2\n",
    "        self.Ad_[-1,-2] = 1./dx**2\n",
    "       \n",
    "        for i in range(1,nx_ -1):\n",
    "            self.Ad_[i,i] = -2./dx**2\n",
    "            self.Ad_[i,i-1] = 1./dx**2\n",
    "            self.Ad_[i,i+1] = 1./dx**2\n",
    "        \n",
    "        self.Ac_ = np.zeros((nx,nx))\n",
    "        self.Ac_[0,0] = 1./dx\n",
    "        for i in range(1,nx_ -1 ):\n",
    "            self.Ac_[i,i] = 1/dx\n",
    "            self.Ac_[i,i-1] = -1./dx\n",
    "    \n",
    "        self.f_ = np.ones(nx)\n",
    "\n",
    "    def assemble_system(self,c,nu):\n",
    "        self.A_ = c*self.Ac_ - nu*self.Ad_\n",
    "\n",
    "    def solve(self,c,nu):\n",
    "        self.assemble_system(c,nu)\n",
    "        solution = np.linalg.solve(self.A_,self.f_)\n",
    "        return solution\n",
    "\n",
    "# As an example, we can insatiate this class and solve for a given parameter insance.\n",
    "adr_problem = advectionDiffusionProblem(nx=33)\n",
    "c,nu = 1.,1.e-2\n",
    "u = adr_problem.solve(c,nu)\n",
    "plt.plot(adr_problem.x_,u)\n",
    "plt.xlabel(r'$x$')\n",
    "plt.ylabel(r'$u$')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "217759fb-6ec9-4488-897b-e5b4db9f4b2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Now, let's create a romtools wrapper around this that meets the API of the ModelClass\n",
    "class adrRomToolsModel:\n",
    "    def __init__(self,problem: advectionDiffusionProblem):\n",
    "        self.problem_ = advectionDiffusionProblem\n",
    "\n",
    "    def populate_run_directory(self, run_directory: str, parameter_sample: dict):\n",
    "        # In this example, we don't need any offline data to run our model, so this can be empty\n",
    "        pass\n",
    "        \n",
    "    def run_model(self, run_directory: str, parameter_sample: dict):\n",
    "        #parameter sample will come from a ParameterSpace object, and will be a dictionary of the form:\n",
    "        #[{parameter_name},{value}]\n",
    "        c = parameter_sample['c']\n",
    "        nu = parameter_sample['nu']\n",
    "        u = self.problem_.solve(c,nu)\n",
    "        # return 0 for pass\n",
    "        return 0\n",
    "\n",
    "\n",
    "adr_for_romtools = adrRomToolsModel(adr_problem)\n",
    "\n",
    "#That's it! This type of model can be used for running a sampling workflow. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b1115b8d-0859-4a6a-ae0f-8cf8c888650c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
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 "nbformat": 4,
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}