{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "sys.path.append(\"../..\")  # add the pde package to the python path\n",
    "import pde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize the grid, an initial condition, and the PDE\n",
    "grid = pde.UnitGrid([32, 32])\n",
    "field = pde.ScalarField.random_uniform(grid, -1, 1)\n",
    "eq = pde.DiffusionPDE()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# try our explicit solver\n",
    "solver = pde.EulerSolver(eq)\n",
    "controller = pde.Controller(solver, t_range=1)\n",
    "sol1 = controller.run(field, dt=1e-3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# try the standard scipy solver\n",
    "solver = pde.ScipySolver(eq)\n",
    "controller = pde.Controller(solver, t_range=1)\n",
    "sol2 = controller.run(field);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot both fields and give the deviation as the title\n",
    "title = f\"Mean squared deviation: {((sol1 - sol2) ** 2).average:.2g}\"\n",
    "pde.FieldCollection([sol1, sol2]).plot(title=title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.12.0"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "1ac37180818940768587ba0dd0a18a6a": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "DescriptionStyleModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "StyleView",
       "description_width": ""
      }
     },
     "24f1d41d335348e7a462230118f53105": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "FloatProgressModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "FloatProgressModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "ProgressView",
       "bar_style": "success",
       "description": "100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_8feb988c004d43b0849993651c7987fb",
       "max": 1,
       "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_901c7106a9b74936b494432f6a06d20b",
       "value": 1
      }
     },
     "3059a4b3dbd846f2a4c03b0cd74febef": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "HTMLModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "HTMLModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "HTMLView",
       "description": "",
       "description_tooltip": null,
       "layout": "IPY_MODEL_ff6735ef29ca40d3b20dfa6ca7f89217",
       "placeholder": "​",
       "style": "IPY_MODEL_1ac37180818940768587ba0dd0a18a6a",
       "value": " 1.0/1.0 [00:03<00:00,  3.92s/it]"
      }
     },
     "3fe271e9f7c6496b9f60e8f8783c2058": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "FloatProgressModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "FloatProgressModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "ProgressView",
       "bar_style": "success",
       "description": "100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_e4c925d926c542f7864b2f784930af77",
       "max": 1,
       "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_ae791548724e4f3ea4da4f70fc08d644",
       "value": 1
      }
     },
     "5c4899248cac4a1ca0a6334c19c328f3": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "1.2.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "overflow_x": null,
       "overflow_y": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "7e3b3cd16a7f4c0680f2a168ee051e4b": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "HTMLModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "HTMLModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "HTMLView",
       "description": "",
       "description_tooltip": null,
       "layout": "IPY_MODEL_b3d415cc1fd440d6888f869d1505bc4b",
       "placeholder": "​",
       "style": "IPY_MODEL_97dd8ea15d80487b944fbbfc71239831",
       "value": " 1.0/1.0 [00:00<00:00,  3.86it/s]"
      }
     },
     "8feb988c004d43b0849993651c7987fb": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "1.2.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "overflow_x": null,
       "overflow_y": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "901c7106a9b74936b494432f6a06d20b": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "ProgressStyleModel",
      "state": {
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "ProgressStyleModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "StyleView",
       "bar_color": null,
       "description_width": "initial"
      }
     },
     "97dd8ea15d80487b944fbbfc71239831": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "DescriptionStyleModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "StyleView",
       "description_width": ""
      }
     },
     "ae791548724e4f3ea4da4f70fc08d644": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "ProgressStyleModel",
      "state": {
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "ProgressStyleModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "StyleView",
       "bar_color": null,
       "description_width": "initial"
      }
     },
     "b3d415cc1fd440d6888f869d1505bc4b": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "1.2.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "overflow_x": null,
       "overflow_y": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "d341bc7145f341c5b747d21b8540169d": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "1.2.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "overflow_x": null,
       "overflow_y": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "e4c925d926c542f7864b2f784930af77": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "1.2.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "overflow_x": null,
       "overflow_y": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "e824b7cfd30245f08006c5ec06632d2c": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "HBoxModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "HBoxModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "HBoxView",
       "box_style": "",
       "children": [
        "IPY_MODEL_3fe271e9f7c6496b9f60e8f8783c2058",
        "IPY_MODEL_3059a4b3dbd846f2a4c03b0cd74febef"
       ],
       "layout": "IPY_MODEL_5c4899248cac4a1ca0a6334c19c328f3"
      }
     },
     "f73c4456e7d84980a6cfc690dc3fbfae": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "HBoxModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "HBoxModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "HBoxView",
       "box_style": "",
       "children": [
        "IPY_MODEL_24f1d41d335348e7a462230118f53105",
        "IPY_MODEL_7e3b3cd16a7f4c0680f2a168ee051e4b"
       ],
       "layout": "IPY_MODEL_d341bc7145f341c5b747d21b8540169d"
      }
     },
     "ff6735ef29ca40d3b20dfa6ca7f89217": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "1.2.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "overflow_x": null,
       "overflow_y": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}