fea_manual.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3e595c5e-f144-4580-8027-029be6c99d8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9e589011-d150-4b80-a98f-c6415d5bdefe",
   "metadata": {},
   "outputs": [],
   "source": [
    "figsize = (5, 4.5)\n",
    "labelsize = 12\n",
    "labelpad = 10\n",
    "fontsize = 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4bc98f8f-b86a-4e05-a3f4-3718796e783f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def δ(i: int, j: int) -> int:\n",
    "    if i != j:\n",
    "        return 0\n",
    "    return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e3b316da-d351-4c81-9f0b-399ddef9f3b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def basis_function(i, x, x_arr, h=0.1):\n",
    "    return 1/h * (x - x_arr[i-1]) * (x_arr[i-1] <= x <= x_arr[i]) + 1/h * (x_arr[i+1] - x) * (x_arr[i] < x <= x_arr[i+1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "04d6f13d-f1ec-42fc-9f0a-934e03313082",
   "metadata": {},
   "outputs": [],
   "source": [
    "interval = np.linspace(0, 1, num=11)\n",
    "h = 0.1\n",
    "fun0 = lambda x: basis_function(4, x, x_arr=interval, h=h)\n",
    "fun1 = lambda x: basis_function(5, x, x_arr=interval, h=h)\n",
    "fun2 = lambda x: basis_function(6, x, x_arr=interval, h=h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f6d2a804-6e98-4860-b124-abb6dd6993c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "interval2 = np.linspace(0, 1, num=101)\n",
    "y0 = [fun0(v) for v in interval2]\n",
    "y1 = [fun1(v) for v in interval2]\n",
    "y2 = [fun2(v) for v in interval2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0aafe2e5-97a9-4f41-86d5-9f691e9bde8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=figsize)\n",
    "ax.plot(interval2, y0, label='j-1', color='red');\n",
    "ax.plot(interval2, y1, label='j', color='blue');\n",
    "ax.plot(interval2, y2, label='j+1', color='green');\n",
    "ax.set_box_aspect(1);\n",
    "ax.set_xlabel('x', fontsize=fontsize);\n",
    "ax.minorticks_on();\n",
    "ax.tick_params(axis='both', which='major', labelsize=labelsize);\n",
    "# ax.set_ylim([0, 1]);\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40d63447-6819-42fc-ae9e-488010c10ae0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:fea-env] *",
   "language": "python",
   "name": "conda-env-fea-env-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}