presentations/pyro_intro.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Introduction to Pyro\n",
    "\n",
    "![logo](pyro_plots.png)\n",
    "\n",
    "Michael Zingale, Alice Harpole\n",
    "\n",
    "Stony Brook University"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Why pyro?\n",
    "\n",
    "  * Python is a good introductory language&mdash;it helps make the way these algorithms work clearer\n",
    "\n",
    "  * High level introduction to core hydro algorithms for students\n",
    "  \n",
    "    * Supplemented with extensive notes deriving the methods ( https://github.com/Open-Astrophysics-Bookshelf/numerical_exercises)\n",
    "    \n",
    "  * Enables easy ability to rapidly prototype code&mdash;core intrastructure is in place\n",
    "  \n",
    "  * Allows for sharing exploration in Jupyter notebooks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Design ideas:\n",
    "\n",
    "  * _Clarity is emphasized over performance_\n",
    "\n",
    "  * Single driver implements core evolution\n",
    "    \n",
    "  * Object-oriented structure: each solver provides a simulation class to manage the different parts of the update\n",
    "  \n",
    "  * All solvers are 2-d: right balance of complexity and usefulness\n",
    "  \n",
    "  * Realtime visualization when run in commandline mode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## History:\n",
    "\n",
    "  - _First version in 2003_: python + Numeric + C extensions\n",
    "  \n",
    "  - _May 2004_: switch to python + numarray + C extensions\n",
    "  \n",
    "    - cvs commit:\n",
    "  \n",
    "      > convert from Numeric to numarray, since numarray seems to be the future.\n",
    "        \n",
    "  - _May 2012_: revived, rewritten in python + NumPy + f2py\n",
    "  \n",
    "  - _Nov 2018_: python + NumPy + Numba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Our usage\n",
    "\n",
    "  * We start new undergraduate researchers out with pyro to learn about simulation workflows\n",
    "    * Typically have UG add a new problem setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Current Solvers\n",
    "\n",
    "  * *linear advection*: 2nd and 4th order FV, WENO; CTU, RK, and SDC time integration\n",
    "  \n",
    "  * *compressible hydrodynamics*: 2nd order CTU PLM, 2nd order MOL RK, 4th order FV solver with RK or SDC integration\n",
    "  \n",
    "  * *shallow water hydrodynamics*\n",
    "  \n",
    "  * *multigrid*: force non-constant coefficient general elliptic equations\n",
    "  \n",
    "  * *implicit thermal diffusion*: using multigrid\n",
    "  \n",
    "  * *incompressible hydrodynamics*: 2nd order accurate approximate projection method\n",
    "  \n",
    "  * *low Mach number atmospheric hydrodynamics*: pseudo-imcompressible method\n",
    "  \n",
    "  * *special relativistic compressible hydrodynamics*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Main driver:\n",
    "\n",
    "* parse runtime parameters\n",
    "\n",
    "* setup the grid\n",
    "\n",
    "  * initialize the data for the desired problem\n",
    "\n",
    "* do any necessary pre-evolution initialization\n",
    "\n",
    "* evolve while t < tmax and n < max_steps\n",
    "\n",
    "  * fill boundary conditions\n",
    "  * get the timestep\n",
    "  * evolve for a single timestep\n",
    "  * t = t + dt\n",
    "  * output\n",
    "  * visualization\n",
    "\n",
    "* clean-up\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "&nbsp;This driver is flexible enough for all of the time-dependent solvers\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Grids\n",
    "\n",
    "* ``patch`` module manages grids and data that lives on them\n",
    "\n",
    "* Fills boundaries, does prolongation/restriction for multigrid\n",
    "\n",
    "* Many convenience functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import pyro.mesh.patch as patch\n",
    "import pyro.mesh.boundary as bnd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2-d grid: nx = 16, ny = 16, ng = 2\n"
     ]
    }
   ],
   "source": [
    "g = patch.Grid2d(16, 16, ng=2)\n",
    "print(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BCs: -x: periodic  +x: periodic  -y: reflect-even  +y: outflow\n"
     ]
    }
   ],
   "source": [
    "bc = bnd.BC(xlb=\"periodic\", xrb=\"periodic\", ylb=\"reflect\", yrb=\"outflow\")\n",
    "print(bc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cc data: nx = 16, ny = 16, ng = 2\n",
      "         nvars = 1\n",
      "         variables:\n",
      "               a: min:    0.0000000000    max:    0.0000000000\n",
      "                  BCs: -x: periodic     +x: periodic     -y: reflect-even +y: outflow     \n",
      "\n"
     ]
    }
   ],
   "source": [
    "d = patch.CellCenterData2d(g)\n",
    "d.register_var(\"a\", bc)\n",
    "d.create()\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Grids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "a = d.get_var(\"a\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data is stored as an ``ArrayIndexer`` object, which makes it easy to implement differencing on the entire array.\n",
    "\n",
    "To implement:\n",
    "$$ b = \\frac{a_{i+1,j} - a_{i-1,j}}{2 \\Delta x}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = g.scratch_array()\n",
    "b.v()[:,:] = (a.ip(1) - a.ip(-1))/(2.0*a.g.dx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Running\n",
    "\n",
    "* Each solver has a collection of problem setups (initial conditions) and inputs files\n",
    "\n",
    "* Commandline:\n",
    "\n",
    "  ```\n",
    "  ./pyro.py solver problem inputs\n",
    "  ```\n",
    "  \n",
    "* Jupyter: all functionality accessible through `Pyro` class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example: advection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [],
   "source": [
    "from pyro import Pyro\n",
    "pyro_sim = Pyro(\"advection\")\n",
    "pyro_sim.initialize_problem(\"tophat\",\n",
    "                            inputs_dict={\"mesh.nx\": 8,\n",
    "                                         \"mesh.ny\": 8})\n",
    "pyro_sim.run_sim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example: advection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31m  0.48\u001b[0m\u001b[31m  0.16\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.48\u001b[0m\u001b[31m  0.48\u001b[0m\u001b[31m  0.16\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.48\u001b[0m \n",
      "\u001b[31m  0.23\u001b[0m\u001b[31m  0.05\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m  0.09\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.05\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m  0.09\u001b[0m\u001b[31m  0.23\u001b[0m \n",
      "\u001b[31m  0.04\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.04\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m  0.02\u001b[0m \n",
      "\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.00\u001b[0m \n",
      "\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m  0.00  0.00 -0.00 -0.00  0.00  0.00 -0.00  0.00\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.00\u001b[0m \n",
      "\u001b[31m  0.02\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m  0.00  0.00  0.00  0.01  0.02  0.02  0.00 -0.00\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.01\u001b[0m \n",
      "\u001b[31m  0.20\u001b[0m\u001b[31m  0.12\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m  0.00  0.01  0.05  0.16  0.20  0.12  0.02  0.00\u001b[31m  0.00\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.05\u001b[0m\u001b[31m  0.16\u001b[0m \n",
      "\u001b[31m  0.49\u001b[0m\u001b[31m  0.20\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m  0.00  0.04  0.23  0.48  0.49  0.20  0.02  0.00\u001b[31m  0.00\u001b[0m\u001b[31m  0.04\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.48\u001b[0m \n",
      "\u001b[31m  0.48\u001b[0m\u001b[31m  0.16\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m -0.00\u001b[0m -0.00  0.02  0.23  0.48  0.48  0.16  0.01 -0.00\u001b[31m -0.00\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.48\u001b[0m \n",
      "\u001b[31m  0.23\u001b[0m\u001b[31m  0.05\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m -0.01 -0.02  0.09  0.23  0.23  0.05  0.00 -0.00\u001b[31m -0.01\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m  0.09\u001b[0m\u001b[31m  0.23\u001b[0m \n",
      "\u001b[31m  0.04\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m -0.01 -0.02 -0.02  0.02  0.04  0.01  0.00  0.00\u001b[31m -0.01\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m -0.02\u001b[0m\u001b[31m  0.02\u001b[0m \n",
      "\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m  0.00 -0.01 -0.01 -0.00  0.00  0.00  0.00  0.00\u001b[31m  0.00\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.01\u001b[0m\u001b[31m -0.00\u001b[0m \n",
      "\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m -0.00\u001b[0m \n",
      "\u001b[31m  0.02\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m -0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.01\u001b[0m \n",
      "\u001b[31m  0.20\u001b[0m\u001b[31m  0.12\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.05\u001b[0m\u001b[31m  0.16\u001b[0m\u001b[31m  0.20\u001b[0m\u001b[31m  0.12\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.01\u001b[0m\u001b[31m  0.05\u001b[0m\u001b[31m  0.16\u001b[0m \n",
      "\u001b[31m  0.49\u001b[0m\u001b[31m  0.20\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.04\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.48\u001b[0m\u001b[31m  0.49\u001b[0m\u001b[31m  0.20\u001b[0m\u001b[31m  0.02\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.00\u001b[0m\u001b[31m  0.04\u001b[0m\u001b[31m  0.23\u001b[0m\u001b[31m  0.48\u001b[0m \n",
      "\n",
      "         ^ y\n",
      "         |\n",
      "         +---> x\n",
      "        \n"
     ]
    }
   ],
   "source": [
    "dens = pyro_sim.get_var(\"density\")\n",
    "dens.pretty_print(show_ghost=True, fmt=\"%6.2f\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example: advection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyro_sim.sim.dovis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other solvers\n",
    "\n",
    "![compressible](quad.png) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other solvers\n",
    "\n",
    "![incompressible](shear.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Multigrid\n",
    "\n",
    "![mg](mg_hg.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![docs](docs.png)"
   ]
  },
  {
   "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": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}