{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "23f1215b",
   "metadata": {},
   "source": [
    "# How to use the VoxelFields class"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1916200",
   "metadata": {},
   "source": [
    "## What are VoxelFields?\n",
    "From a high-level perspective, evoxels is organized around two core abstractions: VoxelFields and VoxelGrid. VoxelFields provides a uniform, NumPy-based container for any number of 3D fields on the same regular grid, maximizing interoperability with image I/O libraries (e.g. tifffile, h5py, napari, scikit-image) and visualization tools (PyVista, VTK). VoxelGrid couples these fields to either a PyTorch or JAX backend, offering pre-defined boundary conditions, finite difference stencils and FFT libraries.\n",
    "\n",
    "It is meant to organize, plot and export multiple fields on the same underlying grid (i.e. same shape, origin, spacing and grid convention).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edb30356",
   "metadata": {},
   "source": [
    "## Getting started\n",
    "Import the evoxels library together with numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8c4b8ded",
   "metadata": {},
   "outputs": [],
   "source": [
    "import evoxels as evo\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e3b9646",
   "metadata": {},
   "source": [
    "Create a voxel fields object and explore some of its properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "92f802c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VoxelFields object is now defined as\n",
      " - grid with 20 x 10 x 5 points,\n",
      " - defined with cell_center grid convention.\n",
      " - Physical domain size (20, 10, 5)\n",
      " - and the resulting grid spacing (1.0, 1.0, 1.0)\n",
      " - First grid point (origin) is located at (0.5, 0.5, 0.5)\n",
      " - Float precision of data is set to float32\n"
     ]
    }
   ],
   "source": [
    "Nx, Ny, Nz = [20, 10, 5]\n",
    "vf = evo.VoxelFields((Nx, Ny, Nz), domain_size=(Nx, Ny, Nz))\n",
    "print(\"VoxelFields object is now defined as\")\n",
    "print(f\" - grid with {vf.Nx} x {vf.Ny} x {vf.Nz} points,\")\n",
    "print(f\" - defined with {vf.convention} grid convention.\")\n",
    "print(f\" - Physical domain size {vf.domain_size}\")\n",
    "print(f\" - and the resulting grid spacing {vf.spacing}\")\n",
    "print(f\" - First grid point (origin) is located at {vf.origin}\")\n",
    "print(f\" - Float precision of data is set to {vf.precision}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4af60d98",
   "metadata": {},
   "source": [
    "The ``cell_center`` grid convention assumes that field values 'live' at the center of each voxel (denoted by red dots in the figure below). Fluxes between two voxels are computed at so-called staggered field positions, i.e.\n",
    "- x fluxes live on sides staggered to the right (blue)\n",
    "- y fluxes live staggered to the top (green)\n",
    "\n",
    "<img src=\"../voxelsss-grid.png\" width=\"300px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e06d071",
   "metadata": {},
   "source": [
    "Initialize field with random noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "709ed67d",
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = 0.5 + 0.1*np.random.rand(Nx, Ny, Nz)\n",
    "noise[0,:,:] = 0.1\n",
    "vf.add_field(\"c\", noise)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8155ef06",
   "metadata": {},
   "source": [
    "Explore plotting utilities of voxelFields class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1a690734",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "vf.plot_slice('c', 2, direction='z', time='0')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d168815",
   "metadata": {},
   "source": [
    "Interactive plotting to scroll through slices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b4b53fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# %matplotlib widget\n",
    "# vf.plot_field_interactive(\"c\", direction='x', colormap='turbo')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6c2df95",
   "metadata": {},
   "source": [
    "We can now plug the initial concentration field into the Periodic Cahn-Hilliard solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e853dab3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 18.3363 s after 100 iterations (0.1834 s/iter)\n",
      "GPU-RAM (nvidia-smi)  current: 135 MB (135.0 MB max)\n",
      "GPU-RAM (torch)       current: 8.14 MB (24.19 MB max, 38.00 MB reserved)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "vf.add_field(\"c\", noise)\n",
    "\n",
    "end_time = 100\n",
    "dt = 1\n",
    "evo.run_cahn_hilliard_solver(\n",
    "        vf, 'c', 'torch', jit='False', device='cuda',\n",
    "        time_increment=dt, frames=10, max_iters=int(end_time/dt),\n",
    "        verbose='plot', vtk_out=False, plot_bounds=(0,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85d7d173",
   "metadata": {},
   "source": [
    "Export the final concentration field after solve to vtk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3549b716",
   "metadata": {},
   "outputs": [],
   "source": [
    "vf.export_to_vtk(filename='test.vtk')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57d30d94",
   "metadata": {},
   "source": [
    "## Staggered grid positions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b227729d",
   "metadata": {},
   "source": [
    "For some FFT solvers with mixed boundary conditions it is preferable to work with a staggered grid i.e. the node positions are shifted in a specific direction. To compute tortuosity, we utilize Dirichlet BCs in x-direction while the y- and z-direction are governed by zero-flux or periodic boundary conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ef26826",
   "metadata": {},
   "source": [
    "The VoxelFields object has the grid convention as an attribute which can be set to ``staggered_x``. Note that there are now nodes located at the left and right boundary i.e. the grid spacing equals ``dx = Lx/(Nx-1)`` as exemplified below.\n",
    "\n",
    "The field values are now stored at the blue positions.\n",
    "\n",
    "<img src=\"../voxelsss-grid.png\" width=\"300px\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c99d906e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VoxelFields object is now defined as\n",
      " - grid with 21 x 10 x 5 points,\n",
      " - defined with staggered_x grid convention.\n",
      " - Physical domain size (20, 10, 5)\n",
      " - and the resulting grid spacing (1.0, 1.0, 1.0)\n",
      " - First grid point (origin) is located at (0, 0.5, 0.5)\n",
      " - Float precision of data is set to float32\n"
     ]
    }
   ],
   "source": [
    "Nx, Ny, Nz = [21, 10, 5]\n",
    "vf = evo.VoxelFields((Nx, Ny, Nz), domain_size=(Nx-1, Ny, Nz), convention='staggered_x')\n",
    "print(\"VoxelFields object is now defined as\")\n",
    "print(f\" - grid with {vf.Nx} x {vf.Ny} x {vf.Nz} points,\")\n",
    "print(f\" - defined with {vf.convention} grid convention.\")\n",
    "print(f\" - Physical domain size {vf.domain_size}\")\n",
    "print(f\" - and the resulting grid spacing {vf.spacing}\")\n",
    "print(f\" - First grid point (origin) is located at {vf.origin}\")\n",
    "print(f\" - Float precision of data is set to {vf.precision}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0d17d98",
   "metadata": {},
   "source": [
    "As this staggered grid positions are rather unusual, there is no 100% consistent way to visualize these fields. In a general sense, our data is still zonal data and will therefore be visualized with ``imshow`` in python and be exported using ``cell_data`` for the ``.vtk`` format. However, to highlight the difference, the origin is now shifted such that the first datapoints correlate with x=0 and the last with x=Lx."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "21896ed8",
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = 0.5 + 0.1*np.random.rand(Nx, Ny, Nz)\n",
    "noise[0,:,:] = 0.1\n",
    "vf.add_field(\"c\", noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3f190f8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "vf.plot_slice('c', 2, direction='z', time='0')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "voxenv",
   "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": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}