{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "81c543e7",
   "metadata": {},
   "source": [
    "# Basics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bef1d38",
   "metadata": {},
   "source": [
    "This notebook (available on [Github](https://github.com/wolearyc/ramannoodle/blob/main/docs/source/notebooks/basic-tutorial.ipynb)) contains a short tutorial showcasing ramannoodle's workflow and basic capabilities.\n",
    "\n",
    "We'll begin with some imports, plus some customizations to matplotlib. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3956373a-63a1-4128-b0f2-e2711b5a5213",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib_inline\n",
    "\n",
    "matplotlib_inline.backend_inline.set_matplotlib_formats('png')\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "plt.rcParams['font.family'] = 'sans-serif'\n",
    "plt.rcParams[\"mathtext.default\"] = 'regular'\n",
    "plt.rcParams['axes.linewidth'] = 0.5\n",
    "plt.rcParams['xtick.major.width'] = 0.5\n",
    "plt.rcParams['xtick.minor.width'] = 0.5\n",
    "plt.rcParams['lines.linewidth'] = 1.5\n",
    "\n",
    "import ramannoodle as rn"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7da690f-f4db-4509-8c89-014e7a49c83b",
   "metadata": {},
   "source": [
    "We will be computing TiO2's Raman spectrum using data available in `tests/data/TiO2` (see [Github repo](https://github.com/wolearyc/ramannoodle)). We will be basing this spectrum on frozen phonon calculations and use [InterpolationModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.interpolation.InterpolationModel) to estimate polarizabilities.\n",
    "\n",
    "### Setup\n",
    "\n",
    "First, we will read in phonons. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6102769c-0416-497a-b6a9-e451b66ca71d",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dir = \"../../../test/data/TiO2\"\n",
    "phonon_outcar = f\"{data_dir}/phonons_OUTCAR\"\n",
    "\n",
    "# Read the phonons\n",
    "phonons = rn.io.vasp.outcar.read_phonons(phonon_outcar)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6831e95",
   "metadata": {},
   "source": [
    "Then we'll read in a reference structure and start building our polarizability model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f14761e9-96a8-4317-94cb-47153683eb88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InterpolationModel with \u001b[1;31;49m0/324\u001b[0m degrees of freedom specified."
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# Read a reference (minimum) structure.\n",
    "ref_structure = rn.io.vasp.outcar.read_ref_structure(f\"{data_dir}/ref_eps_OUTCAR\")\n",
    "\n",
    "# We'll need the polarizability of the minimum structure. \n",
    "_, ref_polarizability = rn.io.vasp.outcar.read_positions_and_polarizability(\n",
    "   f\"{data_dir}/ref_eps_OUTCAR\"\n",
    ")\n",
    "model = rn.pmodel.InterpolationModel(ref_structure, ref_polarizability)\n",
    "\n",
    "# Using __repr__, we can check out model.\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58d82797",
   "metadata": {},
   "source": [
    "We've set up `model`, but we are not yet ready to use it to predict polarizabilities. The `__repr__` string of the model indicates that we haven't specified any of the 324 degrees of freedom in this system. To specify these, we'll need to add data! Specifically, we will walk through the system's symmetrically distinct degrees of freedom and add relevant polarizabilities for displacements along those degrees of freedom.\n",
    "\n",
    "### Building up our model\n",
    "\n",
    "You can find the TiO2 supercell we're using for these calculations at `tests/data/TiO2/POSCAR`. Note that there are only **two** symmetrically distinct atoms - one Ti and one O. If we understand how movement of an atom influences the polarizability, we can use symmetry to derive the behavior of those that are symmetrically equivalent. \n",
    "\n",
    "Let's focus on a single Ti atom: atom 5 in our structure. Visualize the POSCAR mentioned above, for example using [VESTA](https://jp-minerals.org/vesta/en/). Think about displacing atom 5 along the x-axis. Convince yourself that displacements in the `+x` direction can be related by symmetry to displacements in the `-x` direction. These displacements **symmetrically equivalent**. \n",
    "\n",
    "Atom 5's displacement along the x-axis is a degree of freedom (DOF) of the system. Convince yourself that TiO2 structure contains many DOFs that are **symmetrically equivalent** to this DOF.\n",
    "\n",
    " [InterpolationModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.interpolation.InterpolationModel)'s key assumption is that every DOF modulates the polarizability independently. The module estimates this modulation using an interpolation around each DOF. We need to \"add\" each DOF to `model`, specifying specific displacements as well as polarizabilities for these displacements (which we calculate using VASP). Internally, the model will handle all symmetry considerations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "147f6a26-a22a-4cff-9659-336d6316e0b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InterpolationModel with \u001b[1;33;49m72/324\u001b[0m degrees of freedom specified."
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# OUTCARS are polarizability calculation where atom 5 (Ti) \n",
    "# was displaced +0.1 and +0.2 angstrom in the x direction\n",
    "model.add_dof_from_files(\n",
    "    [f\"{data_dir}/Ti5_0.1x_eps_OUTCAR\", f\"{data_dir}/Ti5_0.2x_eps_OUTCAR\"],\n",
    "    file_format = 'outcar', interpolation_order=2\n",
    ")\n",
    "\n",
    "# (36 equivalent Ti atoms) * (2 equivalent directions) --> 72 dofs should be added\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6c70688",
   "metadata": {},
   "source": [
    "We've added a total of 72 interpolations (i.e. 72 DOFs). Convince yourself that this makes sense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "370ffc55-8cdb-4101-84b1-4f3a5940525e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InterpolationModel with \u001b[1;33;49m108/324\u001b[0m degrees of freedom specified."
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# atom 5 moving +0.1 and +0.2 angstroms in the z direction\n",
    "model.add_dof_from_files([f\"{data_dir}/Ti5_0.1z_eps_OUTCAR\",\n",
    "                          f\"{data_dir}/Ti5_0.2z_eps_OUTCAR\"],\n",
    "                         file_format = 'outcar', interpolation_order=2)\n",
    "\n",
    "# (36 equivalent Ti atoms) * (1 equivalent direction) --> another 36 DOFs\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8613d742",
   "metadata": {},
   "source": [
    "Now, let's move on to the oxygen motions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "25e7947c-b9f5-4d9d-bb33-3fc447217c0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InterpolationModel with \u001b[1;33;49m180/324\u001b[0m degrees of freedom specified."
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# atom 43 moving in the z direction\n",
    "# Convince yourself that we need all of these displacements. \n",
    "model.add_dof_from_files([f\"{data_dir}/O43_0.2z_eps_OUTCAR\",\n",
    "                          f\"{data_dir}/O43_0.1z_eps_OUTCAR\", \n",
    "                          f\"{data_dir}/O43_m0.1z_eps_OUTCAR\", \n",
    "                          f\"{data_dir}/O43_m0.2z_eps_OUTCAR\"], file_format= 'outcar', interpolation_order=2)\n",
    "\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c4603def-3dcf-469e-b78c-0ab4c239a18d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InterpolationModel with \u001b[1;33;49m252/324\u001b[0m degrees of freedom specified."
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.add_dof_from_files([f\"{data_dir}/O43_0.1x_eps_OUTCAR\",\n",
    "                         f\"{data_dir}/O43_0.2x_eps_OUTCAR\"], \n",
    "                         file_format = 'outcar', interpolation_order=2)\n",
    "\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7189ea1e-3f41-4347-a3a1-2d6adb5b62e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InterpolationModel with \u001b[1;32;49m324/324\u001b[0m degrees of freedom specified."
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.add_dof_from_files([f\"{data_dir}/O43_0.1y_eps_OUTCAR\",\n",
    "                          f\"{data_dir}/O43_0.2y_eps_OUTCAR\"],\n",
    "                            file_format = 'outcar', interpolation_order=2)\n",
    "\n",
    "# We should now have specified all 324 DOFs\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d46db59c",
   "metadata": {},
   "source": [
    "The model should contain 324 interpolations, indicating that all 324 DOFs of the system are accounted for. \n",
    "\n",
    "### Visualizing model parameters\n",
    "\n",
    "Just for fun, let's visualize the interpolations for a specific atom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fcb23aaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2400x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "atom_number = 5 # Feel free to change this!\n",
    "\n",
    "fig = plt.figure(constrained_layout = True, figsize = (8, 2))\n",
    "gs = fig.add_gridspec(1,6, wspace=0)\n",
    "axes = gs.subplots(sharex=True, sharey=True)\n",
    "interp_displacements = np.linspace(-0.21,0.21,50)\n",
    "\n",
    "target_interps = []\n",
    "signs = []\n",
    "for direction_i in [0,1,2]:\n",
    "    basis_vector = model.cart_basis_vectors[0] * 0\n",
    "    basis_vector[atom_number-1][direction_i] = 1\n",
    "    for basis, interp in zip(model.cart_basis_vectors,model._interpolations):\n",
    "        if np.dot(basis.flatten(), basis_vector.flatten()) < -0.9:\n",
    "            target_interps.append(interp)\n",
    "            signs.append(-1)\n",
    "        elif np.dot(basis.flatten(), basis_vector.flatten()) > 0.9:\n",
    "            target_interps.append(interp)\n",
    "            signs.append(1)\n",
    "\n",
    "\n",
    "for axis_i, (i,j) in enumerate([(0,0),(1,1),(2,2),(0,1),(0,2),(1,2)]):\n",
    "    axis = axes[axis_i] # type: ignore\n",
    "    colors = ['purple', 'red', 'orange']\n",
    "    labels = ['x','y','z']\n",
    "\n",
    "    for interp,sign,color,label in zip(target_interps,signs,colors,labels):\n",
    "        axis.plot(interp_displacements, \n",
    "                  interp(sign*interp_displacements)[:,i,j], color = color, label = label)\n",
    "    axis.set_xlabel(r\"$\\delta$ (Å)\")\n",
    "    subscripts = ['x','y','z']\n",
    "    alpha_string = r\"$\\alpha_{\" + subscripts[i] + subscripts[j] + \"}$\"\n",
    "    axis.set_title(alpha_string)\n",
    "    if axis_i == 0:\n",
    "        l = axis.legend(fontsize = \"small\", frameon = False)\n",
    "        \n",
    "l = axes[0].set_ylabel(r\"$\\Delta\\alpha$\")\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b34a5dc5",
   "metadata": {},
   "source": [
    "### Calculating a Raman spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f4a9b56",
   "metadata": {},
   "source": [
    "With the model specified, we're ready to calculate a Raman spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b1f2cb2c-8444-4b6a-ae8e-f1ac6c6a6e98",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2400x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute and plot spectrum\n",
    "spectrum = phonons.get_raman_spectrum(model)\n",
    "wavenumbers, intensities = spectrum.measure(laser_correction = True, \n",
    "                                           laser_wavelength = 532, \n",
    "                                           bose_einstein_correction = True, \n",
    "                                           temperature = 300)\n",
    "fig = plt.figure(constrained_layout = True, figsize = (8, 3))\n",
    "axis = fig.add_subplot(111)\n",
    "axis.plot(wavenumbers, intensities)\n",
    "axis.set_ylabel(\"Intensity (a.u.)\")\n",
    "l = axis.set_xlabel(r\"Raman shift ($\\mathregular{cm^{-1}}$)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "049753d4",
   "metadata": {},
   "source": [
    "`spectrum.calculate` returns a fairly unprocessed spectrum - literally a list of phonon frequencies and intensities. To make a nicer, more realistic visualization, we can broaden the spectra through convolutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e0806350-ac5d-4f09-826d-b9dc85ec471b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's make it prettier. \n",
    "wavenumbers, intensities = spectrum.measure(laser_correction = True, \n",
    "                                laser_wavelength = 532, \n",
    "                                           bose_einstein_correction = True, \n",
    "                                           temperature = 300)\n",
    "wavenumbers, intensities = rn.spectrum.utils.convolve_spectrum(wavenumbers, intensities)\n",
    "\n",
    "fig = plt.figure(constrained_layout = True, figsize = (8, 3))\n",
    "axis = fig.add_subplot(111)\n",
    "axis.plot(wavenumbers, intensities)\n",
    "axis.set_ylabel(\"Intensity (a.u.)\")\n",
    "l = axis.set_xlabel(r\"Raman shift ($\\mathregular{cm^{-1}}$)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14cbffbc",
   "metadata": {},
   "source": [
    "And there you have it! Using ramannoodle's [InterpolationModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.interpolation.InterpolationModel), we calculated a full Raman spectrum for TiO2 using data from just a handful of polarizability calculations.\n",
    "\n",
    "Next, we will introduce [ARTModel](../generated/ramannoodle.pmodel.html#ramannoodle.pmodel.art.ARTModel) and give a more complete overview of ramannoodle's workflow: [Full workflow](../notebooks/full-workflow.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ea8798d",
   "metadata": {},
   "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}