anisotropy/data/analyze.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter(action = 'ignore')\n",
    "\n",
    "from anisotropy.database import Database, tables\n",
    "import pathlib\n",
    "import peewee as pw\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "db = Database(pathlib.Path(\"anisotropy.db\").resolve())\n",
    "execution = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data(execution: int, field: str):\n",
    "    if not db.getExecution(execution):\n",
    "        print(\"Execution not found\")\n",
    "\n",
    "    for model in db.tables:\n",
    "        try:\n",
    "            column = getattr(model, field)\n",
    "        \n",
    "        except AttributeError:\n",
    "            pass\n",
    "\n",
    "        else:\n",
    "            break\n",
    "\n",
    "    query = model.select(tables.Shape.alpha, column, tables.Shape.direction, tables.Shape.label)\n",
    "    idn = db.tables.index(model)\n",
    "\n",
    "    for table in reversed(db.tables[ :idn]):\n",
    "        query = query.join(table, pw.JOIN.LEFT_OUTER)\n",
    "        \n",
    "    query = query.switch(tables.Shape)\n",
    "    query = query.where(\n",
    "        tables.Shape.exec_id == execution,\n",
    "    #    tables.Shape.label == structure,\n",
    "    )\n",
    "    query = query.order_by(tables.Shape.label, tables.Shape.direction, tables.Shape.alpha)\n",
    "\n",
    "    with db:\n",
    "        if query.exists():\n",
    "            table = []\n",
    "            for row in query.dicts():\n",
    "                for k in row.keys():\n",
    "                    if type(row[k]) == list:\n",
    "                        row[k] = str(row[k])\n",
    "\n",
    "                table.append(row)\n",
    "        \n",
    "        else:\n",
    "            table = None\n",
    "\n",
    "    if table is None:\n",
    "        print(\"Results not found\")\n",
    "\n",
    "    else:\n",
    "        return pd.DataFrame(table)\n",
    "\n",
    "def permeability(label, direction):\n",
    "    def concrete(execution, field):\n",
    "        df = load_data(execution, field)\n",
    "        return df[df.label == label][df.direction == direction][field].to_numpy()\n",
    "\n",
    "    alpha = concrete(7, \"alpha\")\n",
    "    viscosity = concrete(5, \"viscosity\")\n",
    "    viscosityKinematic = concrete(5, \"viscosityKinematic\")\n",
    "    length = concrete(7, \"length\")\n",
    "    flowRate = concrete(5, \"flowRate\")\n",
    "    areaCellOutlet = concrete(7, \"areaCellOutlet\")\n",
    "    pressureInlet = concrete(5, \"pressureInlet\")\n",
    "    pressureOutlet = concrete(5, \"pressureOutlet\")\n",
    "    density = concrete(5, \"density\")\n",
    "\n",
    "    return viscosity * length * flowRate / (areaCellOutlet * (pressureInlet - pressureOutlet))\n",
    "\n",
    "def nanmean(arr):\n",
    "    temp = arr.copy()\n",
    "\n",
    "    if np.isnan(temp[0]):\n",
    "        temp[0] = temp[1]\n",
    "\n",
    "    for n, item in enumerate(temp):\n",
    "        if np.all(np.isnan(item)):\n",
    "            \n",
    "            vals = temp[n - 1 : n + 2]\n",
    "\n",
    "            if np.sum(~np.isnan(vals)) <= 1:\n",
    "                vals = temp[n - 2 : n + 3]\n",
    "\n",
    "            temp[n] = vals[~np.isnan(vals)].mean()\n",
    "\n",
    "    return temp\n",
    "\n",
    "def filter_group(arr, nan = True, qhigh = True, quantile = 0.97):\n",
    "    temp = arr.copy()\n",
    "    check = True\n",
    "    quan = np.quantile(temp[~np.isnan(temp)], quantile)\n",
    "    limit = 1000\n",
    "\n",
    "    while check:\n",
    "        if nan and np.any(np.isnan(temp)):\n",
    "            temp = nanmean(temp)\n",
    "            check = True\n",
    "        \n",
    "        elif qhigh and np.any(quan < temp):\n",
    "            temp[quan < temp] = np.nan\n",
    "            check = True\n",
    "\n",
    "        else:\n",
    "            check = False \n",
    "        \n",
    "        if limit <= 0:\n",
    "            break\n",
    "\n",
    "        else:\n",
    "            limit -= 1\n",
    "\n",
    "    return temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams.update({\n",
    "    \"font.size\": 18,\n",
    "    \"lines.markersize\": 9.0,\n",
    "    \"lines.linewidth\": 3\n",
    "})\n",
    "savefig = True\n",
    "anisotropy = pd.DataFrame({\"simple\": None, \"bodyCentered\": None, \"faceCentered\": None}, index = [\"A21\", \"A31\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Porosity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = load_data(execution, \"porosity\")\n",
    "alpha = df[\"alpha\"].unique()\n",
    "simple = df[df.label == \"simple\"][df.direction == \"[0.0, 0.0, 1.0]\"][\"porosity\"].to_numpy()\n",
    "bodyCentered = df[df.label == \"bodyCentered\"][df.direction == \"[0.0, 0.0, 1.0]\"][\"porosity\"].to_numpy()\n",
    "faceCentered = df[df.label == \"faceCentered\"][df.direction == \"[0.0, 0.0, 1.0]\"][\"porosity\"].to_numpy()\n",
    "\n",
    "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (12, 6))\n",
    "\n",
    "ax.plot(alpha, np.pad(simple, (0, alpha.size - simple.size), 'constant', constant_values = np.nan), \":\", label = \"КП\")\n",
    "ax.plot(alpha, np.pad(bodyCentered, (0, alpha.size - bodyCentered.size), 'constant', constant_values = np.nan), \"--\", label = \"КОП\")\n",
    "ax.plot(alpha, np.pad(faceCentered, (0, alpha.size - faceCentered.size), 'constant', constant_values = np.nan), \"-.\", label = \"КГЦ\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "plt.ylabel(r\"$m$\")\n",
    "plt.show()\n",
    "\n",
    "if savefig:\n",
    "    fig.tight_layout()\n",
    "    fig.savefig(\"porosity-rounded.tiff\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = load_data(execution, \"flowRate\")\n",
    "simple = df[df.label == \"simple\"].groupby(df.direction)\n",
    "alpha = simple.get_group(\"[0.0, 0.0, 1.0]\")[\"alpha\"].to_numpy()\n",
    "\n",
    "k1 = (permeability(\"simple\", \"[0.0, 0.0, 1.0]\"))\n",
    "k2 = (permeability(\"simple\", \"[1.0, 0.0, 0.0]\"))\n",
    "k3 = (permeability(\"simple\", \"[1.0, 1.0, 1.0]\"))\n",
    "\n",
    "#poly = np.polynomial.Polynomial.fit(alpha, anisotropy_21, 1)\n",
    "\n",
    "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (12, 6))\n",
    "ax.plot(alpha, k2 / k1, \"s\", label = \"$k_2$ / $k_1$\")\n",
    "ax.plot(alpha, k3 / k1, \"^\", label = \"$k_3$ / $k_1$\")\n",
    "#ax.plot(alpha, poly(alpha), \"-\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "#plt.ylabel(\"Анизотропия проницаемости\")\n",
    "#plt.title(\"Простая кубическая\")\n",
    "plt.show()\n",
    "\n",
    "if savefig:\n",
    "    fig.tight_layout()\n",
    "    fig.savefig(\"anisotropy-simple.tiff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "anisotropy[\"simple\"] = [(k2 / k1).mean(), (k3 / k1).mean()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Body-centered structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = load_data(execution, \"flowRate\")\n",
    "bodyCentered = df[df.label == \"bodyCentered\"].groupby(df.direction)\n",
    "alpha = bodyCentered.get_group(\"[0.0, 0.0, 1.0]\")[\"alpha\"].to_numpy()\n",
    "\n",
    "k1 = filter_group(permeability(\"bodyCentered\", \"[0.0, 0.0, 1.0]\"))\n",
    "k2 = filter_group(permeability(\"bodyCentered\", \"[1.0, 0.0, 0.0]\"))\n",
    "k3 = filter_group(permeability(\"bodyCentered\", \"[1.0, 1.0, 1.0]\"))\n",
    "\n",
    "#poly = np.polynomial.Polynomial.fit(alpha, anisotropy_21, 10)\n",
    "\n",
    "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (12, 6))\n",
    "ax.plot(alpha, k2 / k1, \"s\", label = r\"$k_2$ / $k_1$\")\n",
    "ax.plot(alpha, k3 / k1, \"^\", label = r\"$k_3$ / $k_1$\")\n",
    "ax.axvline(0.13, linestyle = \"-.\", color = \"green\")\n",
    "#ax.plot(alpha, poly(alpha), \"-\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "#plt.ylabel(\"Анизотропия проницаемости\")\n",
    "#plt.title(\"Кубическая объемноцентрированная\")\n",
    "\n",
    "if savefig:\n",
    "    fig.tight_layout()\n",
    "    fig.savefig(\"anisotropy-bodycentered.tiff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "anisotropy[\"bodyCentered\"] = [(k2 / k1).mean(), (k3 / k1).mean()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Face-centered structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = load_data(execution, \"flowRate\")\n",
    "faceCentered = df[df.label == \"faceCentered\"].groupby(df.direction)\n",
    "alpha = faceCentered.get_group(\"[0.0, 0.0, 1.0]\")[\"alpha\"].to_numpy()\n",
    "\n",
    "k1 = filter_group(permeability(\"faceCentered\", \"[0.0, 0.0, 1.0]\"))\n",
    "k2 = filter_group(permeability(\"faceCentered\", \"[1.0, 0.0, 0.0]\"))\n",
    "k3 = filter_group(permeability(\"faceCentered\", \"[1.0, 1.0, 1.0]\"))\n",
    "\n",
    "#poly = np.polynomial.Polynomial.fit(alpha, anisotropy_21, 10)\n",
    "\n",
    "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (12, 6))\n",
    "ax.plot(alpha, filter_group(k2 / k1, quantile = 0.97), \"s\", label = r\"$k_2$ / $k_1$\")\n",
    "ax.plot(alpha, filter_group(k3 / k1, quantile = 0.8), \"^\", label = r\"$k_3$ / $k_1$\")\n",
    "#ax.plot(alpha, poly(alpha), \"-\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "#plt.ylabel(\"Анизотропия проницаемости\")\n",
    "#plt.title(\"Кубическая гранецентрированная\")\n",
    "plt.show()\n",
    "\n",
    "if savefig:\n",
    "    fig.tight_layout()\n",
    "    fig.savefig(\"anisotropy-facecentered.tiff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "anisotropy[\"faceCentered\"] = [(k2 / k1).mean(), (k3 / k1).mean()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Anisotropy mean values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>simple</th>\n",
       "      <th>bodyCentered</th>\n",
       "      <th>faceCentered</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A21</th>\n",
       "      <td>2.2591</td>\n",
       "      <td>0.7571</td>\n",
       "      <td>1.1312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A31</th>\n",
       "      <td>1.5660</td>\n",
       "      <td>1.0036</td>\n",
       "      <td>0.9148</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     simple  bodyCentered  faceCentered\n",
       "A21  2.2591        0.7571        1.1312\n",
       "A31  1.5660        1.0036        0.9148"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anisotropy.round(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analytical porosity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def porosity_a(a, label):\n",
    "    if label == \"simple\":\n",
    "        val = (1 - np.pi * (2 - 3 * a ** 2 * (3 - a)) / (12 * (1 - a) ** 3))\n",
    "\n",
    "    elif label == \"bodyCentered\":\n",
    "        a13 = a[a <= 0.134]\n",
    "        a13g = a[a > 0.134]\n",
    "        a = a13\n",
    "        val = (1 - np.pi * np.sqrt(3) * (1 - 2 * a ** 2 * (3 - a)) / (8 * (1 - a) ** 3)\n",
    "        )\n",
    "        a = a13g\n",
    "        val2 = (1 - np.pi * np.sqrt(3) * (1 - 2 * a ** 2 * (3 - a)) / (8 * (1 - a) ** 3) +\n",
    "            np.pi * (np.sqrt(3) - 2 * (1 - a)) ** 2 * \n",
    "            (np.sqrt(3) - (1 - a)) / (8 * (1 - a)**3)\n",
    "        )\n",
    "        val = np.append(val, val2)\n",
    "\n",
    "    elif label == \"faceCentered\":\n",
    "        val = (1 - np.pi * (1 - 3 * a ** 2 * (3 - a)) / (3 * np.sqrt(2) * (1 - a) ** 3))\n",
    "\n",
    "    return val\n",
    "\n",
    "def pad(x, y):\n",
    "    return np.pad(y, (0, x.size - y.size), 'constant', constant_values = np.nan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = np.linspace(0, 0.3, 50)\n",
    "porosity_simple = porosity_a(alpha[alpha <= 0.2929], \"simple\")\n",
    "porosity_bodyCentered = porosity_a(alpha[alpha <= 0.1835], \"bodyCentered\")\n",
    "porosity_faceCentered = porosity_a(alpha[alpha <= 0.134], \"faceCentered\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (8, 6))\n",
    "\n",
    "ax.plot(alpha, pad(alpha, porosity_simple), \":\", label = \"КП\")\n",
    "ax.plot(alpha, pad(alpha, porosity_bodyCentered), \"--\", label = \"КОЦ\")\n",
    "ax.plot(alpha, pad(alpha, porosity_faceCentered), \"-.\", label = \"КГЦ\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "plt.ylabel(r\"$m$\")\n",
    "plt.show()\n",
    "\n",
    "if savefig:\n",
    "    fig.tight_layout()\n",
    "    fig.savefig(\"porosity-analytical.tiff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = load_data(execution, \"porosity\")\n",
    "alpha = df[\"alpha\"].unique()\n",
    "simple = df[df.label == \"simple\"][df.direction == \"[0.0, 0.0, 1.0]\"][\"porosity\"].to_numpy()\n",
    "bodyCentered = df[df.label == \"bodyCentered\"][df.direction == \"[0.0, 0.0, 1.0]\"][\"porosity\"].to_numpy()\n",
    "faceCentered = df[df.label == \"faceCentered\"][df.direction == \"[0.0, 0.0, 1.0]\"][\"porosity\"].to_numpy()\n",
    "\n",
    "part_simple = pad(alpha, simple)[alpha <= 0.29] / porosity_a(alpha[alpha <= 0.29], \"simple\")\n",
    "part_bodyCentered = pad(alpha, bodyCentered)[alpha <= 0.18] / porosity_a(alpha[alpha <= 0.18], \"bodyCentered\")\n",
    "part_faceCentered = pad(alpha, faceCentered)[alpha <= 0.13] / porosity_a(alpha[alpha <= 0.13], \"faceCentered\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 35$"
      ],
      "text/plain": [
       "35"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "porosity_a(alpha[alpha <= 0.18], \"bodyCentered\").size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams.update({\n",
    "    \"lines.markersize\": 6.0\n",
    "})\n",
    "fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (8, 6))\n",
    "\n",
    "ax.plot(alpha, pad(alpha, part_simple), \"o\", label = \"КП\")\n",
    "ax.plot(alpha, pad(alpha, part_bodyCentered), \"s\", label = \"КОП\")\n",
    "ax.plot(alpha, pad(alpha, part_faceCentered), \"^\", label = \"КГЦ\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "#plt.ylabel(r\"\")\n",
    "plt.show()\n",
    "\n",
    "if savefig:\n",
    "    fig.tight_layout()\n",
    "    fig.savefig(\"porosity-proportion.tiff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0.914869058316947$"
      ],
      "text/plain": [
       "0.9148690583169465"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part_simple.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0.866128471396414$"
      ],
      "text/plain": [
       "0.8661284713964136"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part_bodyCentered[~np.isnan(part_bodyCentered)].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAAAQCAYAAABN/ABvAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAABJ0AAASdAHeZh94AAAHyUlEQVR4nO2ae7BXVRXHPxdFNERSUakpXyQGpMFUCKEgqWgBKpnVOOBjRsgxR5SXZmOLr44KliRKD1DGF46OD8RHaCgxkdljJq+TDaQMgoglCgZdA8KE/lj7wLn7nsPvnPO7P/+635k7+/72a33PXvux1tq7adeuXXSgAx1ojX3jDEmfAW4AzgIOBf4JLAJkZv8q2rGkJuDS8NcPaAJWAncD88xsZ72yJa0FjsqhsMHMehbgORZ4IPwcb2Z3R+UzgS8DvYEewDbgzcBrjpltiupfDNxTQ+xOM9snald6vEK7kcBEoC97xuwvwCwz+0O9vELbSnNC0mnAFcBg4GBgE/AqMNvMFtfDrdF6abUwJPUCXgIOB54E/g4MxAf+LElDYoF7wQLgAuBd4CFgK3AG8Avgq8CF7SR7C3B7Rv4HtQhK+iwwJ9Q9MKfa1cDLwPPhW7oCg4DpwARJg8zsrVT9VwDl9HUK8DXg2YyyUuMV+M8EpuETbhGwEfgccA5wnqQLzWxBPbyq6kXSrcBUYD3wVOB2GPAl4FRgcap6FW4N1Ut8YvwcH4ArzezO1EfOCkRuAi7L6Xw3JI3BlbwGGGhmG0P+fsDjwDhJi8xsYTvI3mxm02txyuDYhO8gm4CFwJScqgeZ2faM9jcB1wE/AC5P8s3sFVwJWTKTHXxelF96vCT1DJw3ACea2bupsuHAb/BdfkFVXgGl9SJpPL4o7gMmmNmOqLxz+ndFbg3VS6dUYS9gBLAW+FnU1oD/4ArqmtV5hDEhvS1RciC3A7g+/LyiQbKL4kp8l7gk9J+JrMEPeCSkxxURJukEfEd7G/hVVFxqvAKOwvX3p/SiCO2WAS34Dl2ZVxW9SOqCL5Z1ZCyKwO/DWrxqcWu0Xjql6gwP6ZLYnjWzFuD3wCdCJ7WQ2PZvZJQleaeEHbFe2V0kjZV0naSJkoZLamMnpyGpDzADt3WXF/ieLIwO6V8L1p8Q0vlm9lFUVna8AFYBO4CBknqkG0gaCnQDXqiTVxW9nIEvyIXATkkjJV0TdDO4AJ+i3PLQLnpJm1LHh/T1nA5W4btHb2BpDWHJrndMRtmxKdnH4jZrPbJ7ssd5TrBG0iVm9tu4I0n7hvrr8CO3ECRNwf2Q7rjTdzI++DMKtD0AGAt8hDvTMcqOF2b2vqRrgFnACkmLcLOwF3A2bnt/r05eVfTylZBuB5qBL0QylwPfMrP36uSW1GuIXtInRveQbsnpJ8n/ZC2B7DmSJkk6JEWkM60doIPrlH0PcBq+OLoCJwBzgaOBZyV9MaOvHwEDgIvNbFutD0lhCm4+XIUP/nPAiFoKDvh24P5c5BAmKDteAJjZ7cA38UUzHrgWOB94C7g3NrEq8Kqil8NDOhXYhTu23YATgSXAUODRGryKcEvQEL20Cde2Ex4GxgFn4rvZk/gOcjrwKXy3PhLIDEEWhZnFUYa/AZdJ+gCYjEcoEvsdSSfhp8Rt6VBmQVk9Qx9H4FGiGUCzpFFm9nKN5slxPTenvNJ4SZoG3AzcgUfX3gE+D9wCPCipv5lNq4NXFSSb7f+As81sbfj9aggyvAYMkzS4hg4KcWuUXtInRrL6u8eVovzNNYQRbLXR+A72HnBR+FsVyLeEqsmO1m6yA34Z0qFJRjCh7sfNguuzGhWBmW0wsydwE+LQ0GcuJPXDv3k9rUOU6T7LjheSTgVmAk+Z2SQze8PMtobJMAZ3JidLSkyx0ryoppfk/+bUoki+cyvw6/BzYE6fRbm1QnvrJX1ivBbS3jl9JV5+nr0ZE/0QV9zMiND+oa+NZramEbLxyQVuXiU4MNX/dikzpH2XpLtwp/yqvQkwszclrQD6S+qRjiZFKORAlhwvgFEhXZbR11ZJf8YXyACynfoivKroJWmzOadNciF4QE55UW6ZaC+9pE+MZIBHSErnI6kbMAS/dPpjGaIZ+C6wH36J1SjZSZQkPSH+C8zP+WsOdV4Mv4uaWZ8OaabywqQeF8rnF+wzRtZ4AXQJaV5INslvEy4twauKXpbivkXfuE1A4oyvyShrrzGrWy+7TwwzWy1pCX4UfR+4M1VP+O4718x2x/xDnLszsDqOTUs6yMz+HeX1B36M7xq7owYVZfcB1qXzQv7RuL0N4XIryNiGP7doA0nT8Z31vvSTEEm98aclW6L6nYAbcUfzpb08izgfd5ifqeFAlhqvgN/hdxsTJM01s7dT7b6OT9rt+K11JV5V9BJ27KfxyNhE4KcpXiNwP2oz7iRnoSa3j0MvsfN9OT6Qd8jfuawETsLj2a8DP4zqL8Uvmo7BL4HSeF7SNtwhbgH6ACPxNy2jzewfdcr+Dm5DL8ffyLTgocqRwP643fiTrI8ugW8At0h6Ed/hNgFHAMPw0Ok7eDQoD8lxnXWjHKPseD2G31OcDqyU9ETg0wc3s5qAa3Oe0ZThVVYv4ItoADBL/parGZ8j5+K79KXxpC7JreF6aXXUmdlqPBZ8L/7xk/HJNhsYVOKdFLjiuuFx4kl4uG4e0DfrfqGC7GXAM6HOBUHGMNwcuggYlXXrWhIv4EftYXhYdCpwHvA+vmP2M7MVWQ3DiXYyxR3IsuO1E58gVwMrcH9iMm5GLgbONLPZ9fKqMifMbD3+JmoO7odMxN9HPQ0MMbPHs2SV4NZwvTR1PDvvQAfa4v+O5k7D0lMsqwAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle 0.90543798706737$"
      ],
      "text/plain": [
       "0.90543798706737"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part_faceCentered[~np.isnan(part_faceCentered)].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "19649669bd52b0be75e091dcf60d2128e4a347083ff474cfec5ff9275df3ceed"
  },
  "kernelspec": {
   "display_name": "Python 3.9.9 64-bit ('anisotropy': conda)",
   "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": "3.9.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}