anisotropy/data/analyze.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter(action = 'ignore')\n",
    "\n",
    "from anisotropy.database import Database, tables\n",
    "import pathlib\n",
    "\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": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "db = Database(pathlib.Path(\"anisotropy.db\").resolve())\n",
    "execution = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "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": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = load_data(execution, \"volume\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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>alpha</th>\n",
       "      <th>volume</th>\n",
       "      <th>direction</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.010</td>\n",
       "      <td>6.299808e-15</td>\n",
       "      <td>[0.0, 0.0, 1.0]</td>\n",
       "      <td>bodyCentered</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.015</td>\n",
       "      <td>6.101743e-15</td>\n",
       "      <td>[0.0, 0.0, 1.0]</td>\n",
       "      <td>bodyCentered</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.020</td>\n",
       "      <td>5.902559e-15</td>\n",
       "      <td>[0.0, 0.0, 1.0]</td>\n",
       "      <td>bodyCentered</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.025</td>\n",
       "      <td>5.702339e-15</td>\n",
       "      <td>[0.0, 0.0, 1.0]</td>\n",
       "      <td>bodyCentered</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.030</td>\n",
       "      <td>5.508176e-15</td>\n",
       "      <td>[0.0, 0.0, 1.0]</td>\n",
       "      <td>bodyCentered</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>316</th>\n",
       "      <td>0.250</td>\n",
       "      <td>1.841166e-15</td>\n",
       "      <td>[1.0, 1.0, 1.0]</td>\n",
       "      <td>simple</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>317</th>\n",
       "      <td>0.255</td>\n",
       "      <td>1.705807e-15</td>\n",
       "      <td>[1.0, 1.0, 1.0]</td>\n",
       "      <td>simple</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>318</th>\n",
       "      <td>0.260</td>\n",
       "      <td>1.574410e-15</td>\n",
       "      <td>[1.0, 1.0, 1.0]</td>\n",
       "      <td>simple</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>319</th>\n",
       "      <td>0.265</td>\n",
       "      <td>1.447357e-15</td>\n",
       "      <td>[1.0, 1.0, 1.0]</td>\n",
       "      <td>simple</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>320</th>\n",
       "      <td>0.270</td>\n",
       "      <td>1.325051e-15</td>\n",
       "      <td>[1.0, 1.0, 1.0]</td>\n",
       "      <td>simple</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>321 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     alpha        volume        direction         label\n",
       "0    0.010  6.299808e-15  [0.0, 0.0, 1.0]  bodyCentered\n",
       "1    0.015  6.101743e-15  [0.0, 0.0, 1.0]  bodyCentered\n",
       "2    0.020  5.902559e-15  [0.0, 0.0, 1.0]  bodyCentered\n",
       "3    0.025  5.702339e-15  [0.0, 0.0, 1.0]  bodyCentered\n",
       "4    0.030  5.508176e-15  [0.0, 0.0, 1.0]  bodyCentered\n",
       "..     ...           ...              ...           ...\n",
       "316  0.250  1.841166e-15  [1.0, 1.0, 1.0]        simple\n",
       "317  0.255  1.705807e-15  [1.0, 1.0, 1.0]        simple\n",
       "318  0.260  1.574410e-15  [1.0, 1.0, 1.0]        simple\n",
       "319  0.265  1.447357e-15  [1.0, 1.0, 1.0]        simple\n",
       "320  0.270  1.325051e-15  [1.0, 1.0, 1.0]        simple\n",
       "\n",
       "[321 rows x 4 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Porosity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "anisotropy[\"simple\"] = [(k2 / k1).mean(), (k3 / k1).mean()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "81.01844712765529"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k1.mean() / (0.9869 * 10**-12) * 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07995710547028301"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k1.mean() * (10**6)**2"
   ]
  },
  {
   "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": "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",
      "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 (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": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}