openPMD.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This file is part of postpic.\n",
    "\n",
    "postpic is free software: you can redistribute it and/or modify\n",
    "it under the terms of the GNU General Public License as published by\n",
    "the Free Software Foundation, either version 3 of the License, or\n",
    "(at your option) any later version.\n",
    "\n",
    "postpic is distributed in the hope that it will be useful,\n",
    "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
    "GNU General Public License for more details.\n",
    "\n",
    "You should have received a copy of the GNU General Public License\n",
    "along with postpic. If not, see <http://www.gnu.org/licenses/>.\n",
    "\n",
    "Copyright Stephan Kuschel 2016-2018\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, download the example data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "downloading _openPMDdata/example-2d.tar.gz ...\n",
      "done.\n"
     ]
    }
   ],
   "source": [
    "def download(url, file):\n",
    "    import urllib3\n",
    "    import shutil\n",
    "    import os\n",
    "    if os.path.isfile(file):\n",
    "        return\n",
    "    urllib3.disable_warnings()\n",
    "    http = urllib3.PoolManager()\n",
    "    print('downloading {:} ...'.format(file))\n",
    "    with http.request('GET', url, preload_content=False) as r, open(file, 'wb') as out_file:\n",
    "        shutil.copyfileobj(r, out_file)\n",
    "\n",
    "# download the example data\n",
    "import os\n",
    "if not os.path.exists('_openPMDdata'):\n",
    "    os.mkdir('_openPMDdata')\n",
    "    download('https://github.com/openPMD/openPMD-example-datasets/'\n",
    "        + 'raw/776ae3a96c02b20cfae56efafcbda6ca76d4c78d/example-2d.tar.gz',\n",
    "            '_openPMDdata/example-2d.tar.gz')\n",
    "\n",
    "import tarfile\n",
    "tar = tarfile.open('_openPMDdata/example-2d.tar.gz')\n",
    "tar.extractall('_openPMDdata')\n",
    "print('done.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'v0.3.1+318.ga7cb0c4'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import postpic as pp\n",
    "pp.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<OpenPMDh5reader at \"_openPMDdata/example-2d/hdf5/data00000300.h5\">\n",
      "The simulations was running on 2 spatial dimensions.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "pp.chooseCode('openpmd')\n",
    "# open a specific dump\n",
    "dr = pp.readDump('_openPMDdata/example-2d/hdf5/data00000300.h5')\n",
    "print(dr)\n",
    "# the dumpreader knwos all the information of the simulation\n",
    "print('The simulations was running on {} spatial dimensions.'.format(dr.simdimensions()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['fields', 'particles']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<HDF5 group \"/data/300/fields\" (4 members)>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# if needed, postpic can be bypassed and the underlying datastructer (h5 in this case)\n",
    "# can be accessed directly via keys\n",
    "print(dr.keys())\n",
    "dr['fields']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Field data\n",
    "\n",
    "Field data is data, which is already on a grid, examples are Electric Field, Magnetic Field, Number Density, A velocity field of the streaming particles... Such data can be accessed by the datareader directly. It is represented in postpic by a postpic.Field object, which is a numpy array holding the data plus information about the axis.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<Field \"Ez\" (51, 201)>\n"
     ]
    },
    {
     "data": {
      "image/png": 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aLCYSDDFTpKOkggYu612vtKpDRZmHsalV3WD/ksUN+UqQwN6QLAn7UFBPZlt0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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa594036eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ez = dr.Ez()\n",
    "print(ez)\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(ez.T, origin='lower', extent=ez.extent*1e6)\n",
    "ax.set_xlabel('y [$\\mu m$]');\n",
    "ax.set_ylabel('z [$\\mu m$]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Particle data\n",
    "\n",
    "Particle data is represented in postpic by a postpic.MultiSpecies object. It contains a number of particles and it offers a very easy to use interface to access the properties or derived quantities or even use derived quantities to create a postpic.Field object, which can finally be plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['electrons', 'ions']\n",
      "<MultiSpecies including all \"electrons\" (37728)>\n"
     ]
    }
   ],
   "source": [
    "# the multispecies Object is used to access particle data\n",
    "print(dr.listSpecies())\n",
    "ms = pp.MultiSpecies(dr, 'electrons')\n",
    "# now, ms is representing the species \"electrons\"\n",
    "print(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37728\n"
     ]
    }
   ],
   "source": [
    "# we can access the properties for each individual particle, like the x coordinate\n",
    "x = ms('x')\n",
    "print(len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ekin = gamma_m1 * mass * c**2\n",
       "Ekin_MeV = Ekin / elementary_charge / 1e6\n",
       "Ekin_MeV_amu = Ekin / elementary_charge / 1e6 / mass_u\n",
       "Ekin_MeV_qm = Ekin / elementary_charge / 1e6 / mass_u * charge_e\n",
       "Ekin_keV = Ekin / elementary_charge / 1e3\n",
       "Ekin_keV_amu = Ekin / elementary_charge / 1e3 / mass_u\n",
       "Ekin_keV_qm = Ekin / elementary_charge / 1e3 / mass_u * charge_e\n",
       "Eruhe = mass * c**2\n",
       "_np2 = (px**2 + py**2 + pz**2)/(mass * c)**2\n",
       "angle_xaxis = arctan2(sqrt(py**2 + pz**2), px)\n",
       "angle_xy = arctan2(py, px)\n",
       "angle_xz = arctan2(pz, px)\n",
       "angle_yaxis = arctan2(sqrt(pz**2 + px**2), py)\n",
       "angle_yx = arctan2(px, py)\n",
       "angle_yz = arctan2(pz, py)\n",
       "angle_zaxis = arctan2(sqrt(px**2 + py**2), pz)\n",
       "angle_zx = arctan2(px, pz)\n",
       "angle_zy = arctan2(py, pz)\n",
       "beta = sqrt(gamma**2 - 1) / gamma\n",
       "betax = vx / c\n",
       "betay = vy / c\n",
       "betaz = vz / c\n",
       "charge = charge\n",
       "charge_e = charge / elementary_charge\n",
       "gamma = _np2 / (sqrt(1 + _np2) + 1) + 1\n",
       "gamma_m = gamma * mass\n",
       "gamma_m1 = _np2 / (sqrt(1 + _np2) + 1)\n",
       "id = id\n",
       "m = mass\n",
       "m_u = mass / atomic_mass\n",
       "mass = mass\n",
       "mass_u = mass / atomic_mass\n",
       "p = sqrt(px**2 + py**2 + pz**2)\n",
       "px = px\n",
       "py = pz\n",
       "pz = py\n",
       "q = charge\n",
       "q_e = charge / elementary_charge\n",
       "r_xy = sqrt(x**2 + y**2)\n",
       "r_xyz = sqrt(x**2 + y**2 + z**2)\n",
       "r_yz = sqrt(y**2 + z**2)\n",
       "r_zx = sqrt(z**2 + x**2)\n",
       "t = time\n",
       "time = time\n",
       "v = beta * c\n",
       "vx = px / (gamma * mass)\n",
       "vy = py / (gamma * mass)\n",
       "vz = pz / (gamma * mass)\n",
       "w = weight\n",
       "weight = weight\n",
       "x = x\n",
       "x_um = x * 1e6\n",
       "y = y\n",
       "y_um = y * 1e6\n",
       "z = z\n",
       "z_um = y * 1e6\n",
       "--> 56 known particle scalars."
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# or do something more complicated such as:\n",
    "pr = ms('sqrt(px**2 + py**2)')\n",
    "# actually ridiculous things will work:\n",
    "pr = ms('x + x**2 + (gamma**2 - 2) - sin(px/pz)')\n",
    "# you can look at  for a list of predefined values\n",
    "pp.particle_scalars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Tbl6hqrfldDyTQlk0InK/qt6z6Di6WEw3h716GUYGJhTDyMCEcjzct+gA9sBi\nugnMoxhGBvaNYhgZmFBuEhH5kIg8JSIPdtreLSKPishn0/aDJxjPy0Tk0yLykIh8QUR+IrXfIiKf\nFJEvpv3lJYhpYT+nw2KvXjeJiPwF4DrwS6r6rant3cB1Vf3ZBcRzJ3Cnqn5GRNaBPwJ+CPgR4DlV\nfa+I/DRwWVV/asEx/TAL+jkdFvtGuUlU9feA5xYdR4OqPq6qn0nHG8BDwEuAe4EPp24fJv5DXXRM\npwYTyvHxLhF5IL2andhrThcR+SbgDcD/Bu5Q1cch/sMFbl+CmGAJfk45mFCOh18AXgXcDTwO/NxJ\nByAia8B/BP6Bqj5/0s/fiz1iWvjPKRcTyjGgqk+qaq2qAfgA8MaTfL6IlMR/kP9OVf9Tan4yeYXG\nMzy16JgW/XM6DCaUY6D5B5l4M/Dgfn2P4dkCfBB4SFV/vnPp48A70vE7gI8tOqZF/pwOi/3W6yYR\nkV8Fvpc4EvZJ4GfS+d2AAl8DfqzxBycQz5uA/w58Hgip+R8RPcFHgJcDDwNvVdUT+SXEATG9nQX9\nnA6LCcUwMrBXL8PIwIRiGBmYUAwjAxOKYWRgQjGMDEwohpGBCcUwMjChnCFE5JtEZFtEPntE91tJ\n80TGIvKio7jnacWEcvb4sqrefRQ3UtXtdK/HjuJ+pxkTyilCRH68MxvwqyLy6YzP/I6IfHM6vrWZ\niSkivy4i/1JE/oeIfF1E3iQivyQi/09EPnjcf5bThgnlFKGq/zr9D/8dwCPAz9/gIwB/GvhiOn4d\ncbwVwLcBX1HVNxEncn0Q+CngW4G3iEj/KGM/7ZzJZR/OAe8H/puq/ueDOonIK4BH0zB2iEJ5QEQG\nwCXgn6f2beCDzYBEEdkCxscS+SnFvlFOGSLyI8ArgH+a0f1u4IHO+ben89cCn+kI6PWkGYci8lLg\nMbXRsjOYUE4RIvLtwE8Cf6vzj/wgXg8M0mdfTZw3/3nia9fnOv1ex1RQr2dWXAb26nXaeBdwC/Dp\nOBeK+1X17xzQ/25gW0Q+R/zH/xBx0tYl4A8A0mvYiqpeSZ/pisZI2HyUM0Qq3PCJTtmkLwFvSJVP\nbua+XwPuUdVlWzbixLBXr7NFDVxMvz5eB8LNiKRJOAIl05mJ5xL7RjGMDOwbxTAyMKEYRgYmFMPI\nwIRiGBmYUAwjAxOKYWRgQjGMDEwohpHB/wdQMlwcme1JAgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa58cdc82b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we can use the particle properties to create a Field for plotting.\n",
    "# Particle Shapes as in the Simulation will be included\n",
    "# calculate the number density\n",
    "nd = ms.createField('z', 'x', bins=[200, 50])\n",
    "# note, that particle weights are included automatically\n",
    "# and plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(nd.T, origin='lower', extent=nd.extent*1e6)\n",
    "ax.set_xlabel('z [$\\mu m$]');\n",
    "ax.set_ylabel('x [$\\mu m$]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa58cdfd080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a Field object nd holding the charge density\n",
    "# note, that particle weights are included automatically\n",
    "qd = ms.createField('z', 'x', weights='charge', bins=[200, 50])\n",
    "# and plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(qd.T, origin='lower', extent=qd.extent*1e6)\n",
    "ax.set_xlabel('z [$\\mu m$]');\n",
    "ax.set_ylabel('x [$\\mu m$]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NffKWptvnFTdgx7NEQt6nTBxQNH5GmMlCJ+tN0/zSa8VtorZBsvlzkIxqZ/j+iveTP+Hw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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa58cda5898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# average kinetic energy on grid\n",
    "ekin = ms.createField('z', 'x', weights='Ekin_MeV', bins=[200, 50])\n",
    "ekinavg = ekin/nd\n",
    "# and plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(ekinavg.T, origin='lower', extent=ekinavg.extent*1e6)\n",
    "ax.set_xlabel('z [$\\mu m$]');\n",
    "ax.set_ylabel('x [$\\mu m$]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pEI2CZDa3jcVYbDgkcdk8fbsN7fq5dV/wTkRicltd083kv7XNqSdF8jL/t2CID5Txb0NL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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa58cdda128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = ms.createField('z', 'p', bins=[200,50])\n",
    "# and plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(f.T, origin='lower', extent=f.extent, aspect='auto')\n",
    "ax.set_xlabel('z [m]');\n",
    "ax.set_ylabel('p');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa594036e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = ms.createField('z', 'gamma', bins=[200,50])\n",
    "# and plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(f.T, origin='lower', extent=f.extent, aspect='auto')\n",
    "ax.set_xlabel('z [$\\mu m$]');\n",
    "ax.set_ylabel('$\\gamma$');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S8E1VIRI5xcUkSQgkNypmjzNvIqc6f2zkwFV6yEHzGqe2PAqIFwnY/qGASGAv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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa58ce81c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = ms.createField('z', 'beta', bins=[200,50])\n",
    "# and plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(f.T, origin='lower', extent=f.extent, aspect='auto')\n",
    "ax.set_xlabel('z [$\\mu m$]');\n",
    "ax.set_ylabel(r'$\\beta$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Simulationreader\n",
    "\n",
    "The Simulationreader represents an entire simulation, i.e. a series of dumps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 5 dumps in this simulationreader object.\n",
      "<FileSeries at \"_openPMDdata/example-2d/hdf5/*.h5\">\n"
     ]
    }
   ],
   "source": [
    "sr = pp.readSim('_openPMDdata/example-2d/hdf5/*.h5')\n",
    "print('There are {:} dumps in this simulationreader object.'.format(len(sr)))\n",
    "print(sr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulation time of current dump t = 3.29e-14 s\n",
      "Simulation time of current dump t = 6.58e-14 s\n",
      "Simulation time of current dump t = 9.87e-14 s\n",
      "Simulation time of current dump t = 1.32e-13 s\n",
      "Simulation time of current dump t = 1.65e-13 s\n"
     ]
    }
   ],
   "source": [
    "for dr in sr:\n",
    "    print('Simulation time of current dump t = {:.2e} s'.format(dr.time()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3qsLMabK85/NQ8L0T22lZYiJjVsR7mhejW9qkq6QmWQa0/1s3kZ1/08W10gAV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\nMAzDMAzDMAxjLvz/ZADhz8mhbu0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa58ccee898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,5)\n",
    "for dr, ax in zip(sr, axs):\n",
    "    f = dr.Ez()\n",
    "    ax.imshow(f.T, origin='lower', extent=f.extent*1e6)\n",
    "    ax.set_xlabel('y [$\\mu m$]');\n",
    "    ax.set_ylabel('z [$\\mu m$]');\n",
    "    ax.set_title('{:.2f} fs'.format(dr.time()*1e15))\n",
    "fig.set_size_inches(13,3)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}