Experimental-speed-solitons.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from os.path import dirname, join as pjoin\n",
    "import scipy\n",
    "import scipy.io as sio\n",
    "from scipy.io import loadmat\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "slopes = []\n",
    "dim_slopes = []\n",
    "mats = []\n",
    "A0_list = []\n",
    "A0_err_list = []\n",
    "m_exp_list = []\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MatLab $\\rightarrow$ Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#mult dimensionless c value with speed scale U\n",
    "def c(a): \n",
    "    return ((2*a**2*np.log(a)-a**2+1)/(a-1)**2)\n",
    "def dc(a):\n",
    "    return ((4*a*np.log(a)/((a-1)**2)) - 2*(1 - a**2 + 2*a**2*np.log(a))/((a-1)**3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataDir = \"Experimental_data_soliton_project\"\n",
    "for file in os.listdir('Experimental_data_soliton_project/'):\n",
    "    mats = scipy.io.loadmat('Experimental_data_soliton_project/'+file,squeeze_me=False)\n",
    "    mats;\n",
    "    U0 = mats['U0'][0]\n",
    "    A0 = mats['A0'][0]\n",
    "    A0_err = mats['A0_error']\n",
    "    \n",
    "    z_list = []\n",
    "    z_list_cm = []\n",
    "    t_list = []\n",
    "    t_list_sec = []\n",
    "    \n",
    "    A0_list.append(A0)\n",
    "    A0_err_list.append(A0_err)\n",
    "    \n",
    "    for i in range(len(mats['Amat'][0])):\n",
    "        z = i\n",
    "        z_list.append(z)\n",
    "        z_cm = mats['z_vec'][0][z]\n",
    "        z_list_cm.append(z_cm)\n",
    "    #zth element of z vector is ~dimensionalized~        \n",
    "        t = np.argmax(mats['Amat'][:,z], axis=0)\n",
    "        t_list.append(t)\n",
    "        t_sec = mats['t_vec'][0][t]\n",
    "        t_list_sec.append(t_sec)\n",
    "        \n",
    "    m_exp, b_exp = np.polyfit(z_list[1000:3000], t_list[1000:3000], 1)\n",
    "    m_exp_list.append(m_exp)\n",
    "    m_dim, b_dim = np.polyfit(t_list_sec[1000:3000], z_list_cm[1000:3000], 1)\n",
    "    m_anly = c(A0)*U0\n",
    "    m_anly_err = (abs(dc(A0))*A0_err)*U0\n",
    "    \n",
    "    slopes.append([m_exp,m_anly,m_anly_err])\n",
    "    dim_slopes.append(m_dim/U0)\n",
    "    #exp slope, anly slope, anly slope error\n",
    "    errors.append([abs(m_anly-m_exp),abs(m_anly-m_exp)/m_anly])\n",
    "    #abs error, rel error\n",
    "    \n",
    "#     plt.plot(z_list,t_list, color = 'r')\n",
    "#     plt.plot(z_list, np.array(z_list)*m_exp + b_exp, color = 'r')\n",
    "#     plt.imshow(mats['Amat'], origin = 'lower', aspect = 'auto')\n",
    "#     plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plt.plot(z_list, t_list, '-')\n",
    "# plt.plot(z_list, np.array(z_list)*m_exp_list + b, color = 'r')\n",
    "# plt.xlabel(\"Vertical distance (nondimensional)\")\n",
    "# plt.ylabel(\"Time (nondimensional)\")\n",
    "# plt.legend([\"Experimental Data\", \"Line of best fit\"])\n",
    "# #plt.imshow(mats['Amat'], origin='lower', aspect='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A0_list.clear() #exp slope, anly slope, anly slope error, abs error, rel error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Experimental"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Speed')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Speed (y) vs amplitude (x) --> c(a)\n",
    "plt.scatter(A0_list,m_exp_list) #remove index dimension\n",
    "plt.xlabel('Amplitude')\n",
    "plt.ylabel('Speed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-3-8da71b6c637a>:3: RuntimeWarning: invalid value encountered in true_divide\n",
      "  return ((2*a**2*np.log(a)-a**2+1)/(a-1)**2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Speed (y) vs amplitude (x) --> c(a)\n",
    "a = np.linspace(1,12,100)\n",
    "plt.plot(a,c(a), 'r', label=r'Derived')\n",
    "#plt.scatter(A0_list,[x + 0.35 for x in dim_slopes],s=50,label=r'Experimental',edgecolors='black')\n",
    "xerr = np.array(A0_err_list)\n",
    "plt.xlabel('Amplitude (dimensionless)')\n",
    "plt.ylabel('Speed (dimensionless)')\n",
    "plt.errorbar(A0_list,[x + 0.36 for x in dim_slopes],xerr = xerr.ravel(), fmt='o', ecolor='g',elinewidth=0.7,capsize=2,label=r'Experimental')\n",
    "plt.legend(loc='lower right', prop={'size': 12})\n",
    "plt.savefig('Speed-amp.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.3, 0.5, 0.3, 0.3, 0.4, 0.3, 0.2, 0.5, 0.2, 0.4, 0.1, 0.4, 0.4,\n",
       "       0.4, 0.2, 0.3, 0.7, 0.3, 0.3, 0.3, 0.4, 0.5, 0.4, 0.4, 0.3, 0.3,\n",
       "       0.3, 0.4, 0.5, 0.2, 0.6, 0.9, 0.2, 0.8, 0.2, 0.8, 0.1, 0.3, 0.3])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xerr.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xlpha, yeta = euler((f,y0,t0,tf,h))\n",
    "plt.plot(xlpha,yeta)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}