{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "468002e0",
   "metadata": {},
   "source": [
    "# Transformation of phase space data\n",
    "\n",
    "For some research purposes you may wish to manipulate the data in the phase space - for instance, rotate the data around an axis because different simulation codes are using different coordinate systems. This example shows how you can use this code to translate, rotate, and re-grid the phase space data. All these operations occur using the `transform` module.\n",
    "\n",
    "First, we will start by reading in our example data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0394c267",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-04-13T05:31:57.152711Z",
     "iopub.status.busy": "2023-04-13T05:31:57.152275Z",
     "iopub.status.idle": "2023-04-13T05:31:58.500168Z",
     "shell.execute_reply": "2023-04-13T05:31:58.499246Z"
    }
   },
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "import sys\n",
    "sys.path.append('../')  # not necessary when the library is installed\n",
    "from ParticlePhaseSpace import DataLoaders\n",
    "from ParticlePhaseSpace import PhaseSpace\n",
    "\n",
    "test_data_loc = Path(r'../tests/test_data/coll_PhaseSpace_xAng_0.00_yAng_0.00_angular_error_0.0.phsp').absolute()\n",
    "ps_data = DataLoaders.Load_TopasData(test_data_loc)\n",
    "PS = PhaseSpace(ps_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85db836b",
   "metadata": {},
   "source": [
    "let's get a list of the available transform methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0d3c7eff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-04-13T05:31:58.503938Z",
     "iopub.status.busy": "2023-04-13T05:31:58.503588Z",
     "iopub.status.idle": "2023-04-13T05:31:58.508638Z",
     "shell.execute_reply": "2023-04-13T05:31:58.507814Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "project\n",
      "regrid\n",
      "rotate\n",
      "translate\n"
     ]
    }
   ],
   "source": [
    "PS.transform.get_methods()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93ca9a39",
   "metadata": {},
   "source": [
    "## Translations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c6ebe7ee",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-04-13T05:31:58.512351Z",
     "iopub.status.busy": "2023-04-13T05:31:58.512010Z",
     "iopub.status.idle": "2023-04-13T05:32:02.933148Z",
     "shell.execute_reply": "2023-04-13T05:32:02.932218Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS_translated = PS.transform.translate(direction='z', distance=100.0, in_place=False)\n",
    "PS.plot.position_hist_1D()\n",
    "PS_translated.plot.position_hist_1D()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e50a26a",
   "metadata": {},
   "source": [
    "you can see that the data has been translated 100 mm forward in the z direction; you can also translate in x or y."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c110989",
   "metadata": {},
   "source": [
    "## Rotations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eed584ab",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-04-13T05:32:02.937381Z",
     "iopub.status.busy": "2023-04-13T05:32:02.937070Z",
     "iopub.status.idle": "2023-04-13T05:32:04.940880Z",
     "shell.execute_reply": "2023-04-13T05:32:04.939792Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS_rotated = PS.transform.rotate(rotation_axis='z', angle=45, in_place=False)\n",
    "PS.plot.particle_positions_hist_2D(xlim=[-5,5], ylim=[-5,5])\n",
    "PS_rotated.plot.particle_positions_hist_2D(xlim=[-5,5], ylim=[-5,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f69ec008",
   "metadata": {},
   "source": [
    "Looking at the gamma plot in particular, it is clear that the requested transformation was succesful; the particle positions are rotated around the z-axis by 45 degrees.\n",
    "\n",
    "## Rotation of momentum\n",
    "\n",
    "When rotating the data, you may also wish to rotate the momentum vector as well. In this case, you only have to pass an additional keyword:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6cebaa08",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-04-13T05:32:04.945277Z",
     "iopub.status.busy": "2023-04-13T05:32:04.944990Z",
     "iopub.status.idle": "2023-04-13T05:32:09.471977Z",
     "shell.execute_reply": "2023-04-13T05:32:09.471147Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS_rotated = PS.transform.rotate(rotation_axis='x', angle=45, in_place=False, rotate_momentum_vector=True)\n",
    "PS.plot.momentum_hist_1D()\n",
    "PS_rotated.plot.momentum_hist_1D()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76fc3163",
   "metadata": {},
   "source": [
    "note in this case, the momentum which was nearly entirely z directed is now split evenly into y and z, as you would expect after a rotation around the x axis!\n",
    "\n",
    "## Projection\n",
    "\n",
    "Another transformation one can carry out it to project the particles in some direction. This operation will update all particle positions accordingly. This is a valid approach under the assumption that the particles do not experience any forces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c003dfab",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-04-13T05:32:09.476693Z",
     "iopub.status.busy": "2023-04-13T05:32:09.475821Z",
     "iopub.status.idle": "2023-04-13T05:32:14.070082Z",
     "shell.execute_reply": "2023-04-13T05:32:14.068953Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PS_project = PS.transform.project(direction='z', distance=100, in_place=False)\n",
    "PS.plot.position_hist_1D()\n",
    "PS_project.plot.position_hist_1D()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ed17d2b",
   "metadata": {},
   "source": [
    "Note that the z coordinate has been updated exactly the same way as in the translate case. However, the x and y values are significantly different; whereas they aren't changed by a translation operation, for the projection operation they exhibit substantial broadening as the beam diverges travelling forward (note the x and y limits on the axes!). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "037e4bb0",
   "metadata": {},
   "source": [
    "## Regridding\n",
    "\n",
    "It is also possible to transform the phase space data by regridding it; however, this is somewhat complex and is therefore covered in a [dedicated tutorial](https://bwheelz36.github.io/ParticlePhaseSpace/grid_merge.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "340de382",
   "metadata": {},
   "source": [
    "## Other (less supported!) transformations\n",
    "\n",
    "Finally, it may be the case that you wish to transform your data in some way we have not listed here. This is very possible with this code; you can directly change all data fields by directly interacting with the pandas data stored at `PhaseSpace.ps_data`. \n",
    "\n",
    "**HOWEVER!**\n",
    "- you do this at your own risk, since there is no way for us to check the validity of any operations you make\n",
    "- following any edits to the underling data, you should manually `reset_phase_space`, because you have quite likely invalidated any previously calculated quantities. [reset_phase_space](https://bwheelz36.github.io/ParticlePhaseSpace/code_docs.html#ParticlePhaseSpace._ParticlePhaseSpace.PhaseSpace.reset_phase_space) removes any calculated data from the phase space, reducing it to just the [required columns](https://bwheelz36.github.io/ParticlePhaseSpace/phase_space_format.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9672b769",
   "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}