{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mesh Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sigmaepsilon.mesh provides some useful classes and algorithms for mesh management and operations related to the geometry or the topology of polygonal meshes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyvista as pv\n",
    "import numpy as np\n",
    "from sigmaepsilon.mesh import PolyData\n",
    "\n",
    "d, h, a = 6.0, 15.0, 15.0\n",
    "cyl = pv.CylinderStructured(\n",
    "    center=(0.0, 0.0, 0.0),\n",
    "    direction=(0.0, 0.0, 1.0),\n",
    "    radius=np.linspace(d / 2, a / 2, 15),\n",
    "    height=h,\n",
    "    theta_resolution=100,\n",
    "    z_resolution=40,\n",
    ")\n",
    "mesh: PolyData = PolyData.from_pv(cyl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nodal Distribution Factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.47580645, 0.23790323, ..., 0.23790323, 0.11895161,\n",
       "        0.25      ],\n",
       "       [0.52419355, 0.47794118, 0.23897059, ..., 0.23897059, 0.11948529,\n",
       "        0.13104839],\n",
       "       [0.52205882, 0.47972973, 0.23986486, ..., 0.23986486, 0.11993243,\n",
       "        0.13051471],\n",
       "       ...,\n",
       "       [0.12807377, 0.12207031, 0.24414062, ..., 0.24414062, 0.48828125,\n",
       "        0.51229508],\n",
       "       [0.12792969, 0.12220149, 0.24440299, ..., 0.24440299, 0.48880597,\n",
       "        0.51171875],\n",
       "       [0.12779851, 0.25      , 0.5       , ..., 0.5       , 1.        ,\n",
       "        0.51119403]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mesh.nodal_distribution_factors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nodal Adjacency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To access the nodal adjacency matrix as a scipy sparse matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<60600x60600 sparse array of type '<class 'numpy.intc'>'\n",
       "\twith 1527274 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mesh.nodal_adjacency(frmt=\"scipy-csr\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<networkx.classes.graph.Graph at 0x20a5d6d3820>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mesh.nodal_adjacency(frmt=\"nx\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as an `Awkward` array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre>[[0, 1, 15, 16, 1515, 1516, 1530, 1531],\n",
       " [0, 1, 2, 15, 16, 17, 1515, 1516, 1517, 1530, 1531, 1532],\n",
       " [1, 2, 3, 16, 17, 18, 1516, 1517, 1518, 1531, 1532, 1533],\n",
       " [2, 3, 4, 17, 18, 19, 1517, 1518, 1519, 1532, 1533, 1534],\n",
       " [3, 4, 5, 18, 19, 20, 1518, 1519, 1520, 1533, 1534, 1535],\n",
       " [4, 5, 6, 19, 20, 21, 1519, 1520, 1521, 1534, 1535, 1536],\n",
       " [5, 6, 7, 20, 21, 22, 1520, 1521, 1522, 1535, 1536, 1537],\n",
       " [6, 7, 8, 21, 22, 23, 1521, 1522, 1523, 1536, 1537, 1538],\n",
       " [7, 8, 9, 22, 23, 24, 1522, 1523, 1524, 1537, 1538, 1539],\n",
       " [8, 9, 10, 23, 24, 25, 1523, 1524, 1525, 1538, 1539, 1540],\n",
       " ...,\n",
       " [59060, 59061, 59062, 59075, 59076, ..., 60576, 60577, 60590, 60591, 60592],\n",
       " [59061, 59062, 59063, 59076, 59077, ..., 60577, 60578, 60591, 60592, 60593],\n",
       " [59062, 59063, 59064, 59077, 59078, ..., 60578, 60579, 60592, 60593, 60594],\n",
       " [59063, 59064, 59065, 59078, 59079, ..., 60579, 60580, 60593, 60594, 60595],\n",
       " [59064, 59065, 59066, 59079, 59080, ..., 60580, 60581, 60594, 60595, 60596],\n",
       " [59065, 59066, 59067, 59080, 59081, ..., 60581, 60582, 60595, 60596, 60597],\n",
       " [59066, 59067, 59068, 59081, 59082, ..., 60582, 60583, 60596, 60597, 60598],\n",
       " [59067, 59068, 59069, 59082, 59083, ..., 60583, 60584, 60597, 60598, 60599],\n",
       " [59068, 59069, 59083, 59084, 60583, 60584, 60598, 60599]]\n",
       "-----------------------------------------------------------------------------\n",
       "type: 60600 * var * int64</pre>"
      ],
      "text/plain": [
       "<Array [[0, 1, 15, 16, ..., 1516, 1530, 1531], ...] type='60600 * var * int64'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mesh.nodal_adjacency(frmt=\"jagged\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or as a Numba-jittable CSR matrix from `sigmaepsilon.math`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60600x60600 CSR matrix of 1527274 values."
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mesh.nodal_adjacency(frmt=\"csr\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pseudo Peripheral Nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sigmaepsilon.math.topology.graph import pseudo_peripheral_nodes\n",
    "\n",
    "csr = mesh.nodal_adjacency(frmt=\"csr\")\n",
    "ppn = pseudo_peripheral_nodes(csr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rooted Level Structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sigmaepsilon.math.topology.graph import rooted_level_structure\n",
    "\n",
    "rls = rooted_level_structure(csr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Nearest-Neighbours with ``Scipy`` or ``SkLearn``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 4],\n",
       "       [1, 2, 0],\n",
       "       [2, 1, 3],\n",
       "       [3, 2, 7],\n",
       "       [4, 5, 0]], dtype=int64)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sigmaepsilon.mesh import grid, PolyData, PointData\n",
    "from sigmaepsilon.mesh.cells import H8\n",
    "\n",
    "size = 80, 60, 20\n",
    "shape = 10, 8, 4\n",
    "coords, topo = grid(size=size, shape=shape, eshape=\"H8\")\n",
    "pd = PointData(coords=coords)\n",
    "cd = H8(topo=topo)\n",
    "mesh = PolyData(pd, cd)\n",
    "mesh.k_nearest_cell_neighbours(k=3, knn_options=dict(max_distance=10.0))[:5]"
   ]
  }
 ],
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