05_explain_windnum.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sc\n",
    "from scipy import integrate\n",
    "import sympy as sp\n",
    "from src.data_generation import (\n",
    "    calc_dim_tab,\n",
    "    get_tensor_basis,\n",
    "    tag_func,\n",
    "    get_kinetic_H_vw,\n",
    ")\n",
    "import matplotlib.pyplot as plt\n",
    "from numba.typed import List, Dict\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 6\n",
    "N = np.array([1])\n",
    "J = 1\n",
    "component_count = 1\n",
    "# Statistic (bose/fermi)\n",
    "stat_vec = np.array([\"f\"])\n",
    "vv_tab = np.linspace(0.002, 2.002, 200)\n",
    "D = calc_dim_tab(M, N, stat_tab=['f'])\n",
    "\n",
    "vv = 0.5\n",
    "ww = 1\n",
    "vw_tab = np.array([vv, ww])\n",
    "\n",
    "W_disorder_tab = np.array([0.0, 0.0])\n",
    "\n",
    "# Periodic boundary conditions\n",
    "pbc = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generation of Fock basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 0 0 0 0]\n",
      " [0 1 0 0 0 0]\n",
      " [0 0 1 0 0 0]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = get_tensor_basis(\n",
    "                    M, N, statistic=stat_vec, component_count=component_count, verb=0\n",
    "                )\n",
    "print(A[:3])\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 10))\n",
    "sns.heatmap(A, ax=ax, cmap=\"viridis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hashing the basis for more efficient search and indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Getting the basis vectors hashed\n",
    "tab_T = np.array([tag_func(v) for v in A])\n",
    "# Preserving the original order of basis vectors\n",
    "ind = np.argsort(tab_T)\n",
    "# Sorting the new array for more efficient searching (by bisection)\n",
    "t_sorted = tab_T.copy()\n",
    "t_sorted.sort()\n",
    "t_dict = Dict()\n",
    "\n",
    "for key, val in zip(tab_T, np.arange(0, A.shape[0])):\n",
    "    t_dict[key] = val"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constructing Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "H_hop_1 = [List(), List(), List()]\n",
    "H_hop_1 = get_kinetic_H_vw(\n",
    "    A,\n",
    "    M,\n",
    "    J,\n",
    "    t_dict,\n",
    "    vw=vw_tab,\n",
    "    disord_W=W_disorder_tab,\n",
    "    pbc=pbc,\n",
    "    statistic=stat_vec[0],\n",
    "    component_count=component_count,\n",
    "    component_no=0,\n",
    ")\n",
    "H_hop_1 = sc.sparse.coo_matrix(\n",
    "    (H_hop_1[0], (H_hop_1[1], H_hop_1[2])), shape=(D, D)\n",
    ")\n",
    "\n",
    "H_hop_1 = sc.sparse.triu(H_hop_1)\n",
    "\n",
    "H_hop_1 = (\n",
    "    H_hop_1\n",
    "    + H_hop_1.T\n",
    "    - sc.sparse.diags(H_hop_1.diagonal(), format=\"coo\")\n",
    ")\n",
    "\n",
    "H_1 = J * H_hop_1\n",
    "\n",
    "H_tot = H_1\n",
    "\n",
    "H_dense = H_tot.toarray()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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e3Oafc0BVVaxct+1FOUClNKn4njZtWtxyyy1x8sknxxlnnBFvvfVWs560ffv20blz5wYPtzlJ47Yf3hnjJ34yDj/h0Oi/74di0hUToqp/z7jz6rkREXHixV+JM2/49qb9d149L6oG9IxvXT4h+u/7oTj8hEPjUyd+Im69/I5UvwIk4exA0zk30DzrXo9YtnzjIyLi+ZqNf37xpY1fX3FtxPe+/4/9xx218XuX/CTiqWcjbvtdxOw5ESce1+LRISmvO9B01y1aGF864MA4Zv9BsUe37nHOmI9H3507xX8t2fhBsd8dNTp+MPZTm/af8OEhMXb3PWO3Ll1jr+494rujRsf4PfeOnz+6KNWvALBJk2c+hg8fHgsXLozJkyfHsGHD4he/+MU23d6E1um+Xz0YnXvsHF8794vRvU+3ePaxv8bZR1wcK6tXR0REj97doqp/z037Vzy7Ms45YnpMumJCfPaUw6P2xTVx1XdmxQOz/5TqV4AknB1oOucGmmfpExETpvzj79uXXrnxz0d/qojp0yJW1UbUrPzH/n59Iq6+dGPx/cvfRFT1iDjrtIhxH2vh4JCY1x1out8tfyK6degQp35kROzSsWM8WVsbJ94xO158bePtfnbZqWP07dR50/7tt2sX00YfEr133jn+vn59LK+tjRNvnx33PvdMql8BYJNSsbVP9ngXN998c0yZMiVWrVoVS5Ysif3337/ZQcZud0yzrwUAoPLuevGR1BGgzTm870GpI0Cb9NSMEakjQJv09Gn/ljpCmzP68z9IHaHNeWD2GakjbJP3dJe/4447LkaPHh0LFy6MAQMGvPsFAAAAAABQYe/542369esX/fr1ez+yAAAAAAC0mFKz74VBa9ekD7cEAAAAAIDWTvENAAAAAEBWFN8AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZKWcOgAAAAAAQBJFkToBFWLiGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMiK4hsAAAAAgKyUUwcAAAAAAEihVKROQKWY+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACAr5dQBAAAAAACSKFIHoFJMfAMAAAAAkBXFNwAAAAAAWVF8AwAAAACQFcU3AAAAAABZUXwDAAAAAJCVcuoAAAAAAAAplIrUCagUE98AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkpZw6AAAAAABAEvVF6gRUiIlvAAAAAACyovgGAAAAACArim8AAAAAALKi+AYAAAAAICuKbwAAAAAAslJOHQAAAAAAIIkidQAqxcQ3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFlRfAMAAAAAkBXFNwAAAAAAWSmnDgAAAAAAkEKpSJ2ASjHxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWFN8AAAAAAGRF8Q0AAAAAQFbKqQMAAAAAACRRFKkTUCEmvgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMhKOXUAAAAAAIAUSkXqBFSKiW8AAAAAALKi+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyUk4dAAAAAAAgiSJ1ACrFxDcAAAAAAFlRfAMAAAAAkBXFNwAAAAAAWVF8AwAAAACQFcU3AAAAAABZKacOAAAAAACQQqkoUkegQkx8AwAAAABQMVdddVUMHDgwOnToEEOHDo37779/i3tnz54dY8eOjV122SU6d+4cI0eOjLvuuqvJz6n4BgAAAACgIm655ZaYMmVKnH322bFo0aIYM2ZMjB8/PqqrqxvdP3/+/Bg7dmzMmTMnFi5cGIceemgceeSRsWjRoiY9r+IbAAAAAICKuOKKK2LixIlx0kknxX777RczZsyIXXfdNWbOnNno/hkzZsSZZ54Zw4cPj7322isuvvji2GuvveK3v/1tk55X8Q0AAAAAwDapq6uLV199tcGjrq6u0b1vvvlmLFy4MMaNG9dgfdy4cfHggw9u0/PV19fHa6+9Ft27d29STsU3AAAAAADbZPr06dGlS5cGj+nTpze6d/Xq1bFhw4bo1atXg/VevXrFihUrtun5Lr/88li3bl186UtfalLOcpN2AwAAAADkoj51gLZn2rRpMXXq1AZr7du33+o1pVKpwddFUWy21pibbropzj///Lj99tujqqqqSTkV3wAAAAAAbJP27du/a9H9tp49e0a7du02m+5euXLlZlPg73TLLbfExIkT49Zbb43DDjusyTnd6gQAAAAAgPfdDjvsEEOHDo158+Y1WJ83b16MGjVqi9fddNNN8Y1vfCN++ctfxhFHHNGs5zbxDQAAAABARUydOjWOP/74GDZsWIwcOTKuvfbaqK6ujkmTJkXExlunvPDCC3HjjTdGxMbS++tf/3r86Ec/ihEjRmyaFt9xxx2jS5cu2/y8im8AAAAAACri2GOPjdra2rjwwgujpqYmBg0aFHPmzIkBAwZERERNTU1UV1dv2n/NNdfE+vXrY/LkyTF58uRN6xMmTIgbbrhhm59X8Q0AAAAAQMWccsopccoppzT6vXeW2ffee+/78pyKbwAAAADgA6lUFKkjUCE+3BIAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMhKOXUAAAAAAIAkitQBqBQT3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWFN8AAAAAAGSlnDoAAAAAAEASRZE6ARVi4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICslFMHAAAAAABIoVSkTkClmPgGAAAAACArim8AAAAAALKi+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK+XUAQAAAAAAkiiK1AmoEBPfAAAAAABkRfENAAAAAEBWFN8AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZKWcOgAAAAAAQAql+tQJqBQT3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWFN8AAAAAAGSlnDoAAAAAAEASRZE6ARVi4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICslFMHAAAAAABIokgdgEox8Q0AAAAAQFZazcT3XS8+kjoCtDmH9z0odQQAPkC87kDTPTVjROoI0CbtMeWh1BGgbTotdQBoPUx8AwAAAACQFcU3AAAAAABZUXwDAAAAAJCVVnOPbwAAAACAllQqitQRqBAT3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWFN8AAAAAAGSlnDoAAAAAAEASRZE6ARVi4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICslFMHAAAAAABIoj51ACrFxDcAAAAAAFlRfAMAAAAAkBXFNwAAAAAAWVF8AwAAAACQFcU3AAAAAABZKacOAAAAAACQQqkoUkegQkx8AwAAAACQFcU3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFlRfAMAAAAAkJVy6gAAAAAAAEkUReoEVIiJbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACArim8AAAAAALJSTh0AAAAAACCJokidgAox8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWyqkDAAAAAAAkUZ86AJVi4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICslFMHAAAAAABIoVQUqSNQISa+AQAAAADIiuIbAAAAAICsKL4BAAAAAMiK4hsAAAAAgKwovgEAAAAAyEo5dQAAAAAAgCSKInUCKsTENwAAAAAAWVF8AwAAAACQFcU3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFkppw4AAAAAAJBEUaROQIWY+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACAr5dQBAAAAAACSKIrUCagQE98AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkpZw6AAAAAABAEvWpA1ApJr4BAAAAAMiK4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADISjl1AAAAAACAFEpFkToCFWLiGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMiK4hsAAAAAgKyUUwcAAAAAAEiiKFInoEJMfAMAAAAAkBXFNwAAAAAAWVF8AwAAAACQFcU3AAAAAABZUXwDAAAAAJCVcuoAAAAAAABJ1BepE1AhJr4BAAAAAMiK4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADISjl1AAAAAACAJIoidQIqxMQ3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFlRfAMAAAAAkBXFNwAAAAAAWSmnDgAAAAAAkERRpE5AhZj4BgAAAAAgK4pvAAAAAACyovgGAAAAACArim8AAAAAALKi+AYAAAAAICvl1AEAAAAAAJIoitQJqBAT3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWFN8AAAAAAGSlnDoAAAAAAEAS9UXqBFSIiW8AAAAAALKi+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyUk4dAAAAAAAgiaI+dQIqxMQ3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFlxj+8PuIcfiZh1U8TSJyNW1ZbiPy4q4rAxW7/mfxdHXHplxF+ejajqETHxyxHHHdUSaaF1OfLkcXHMGUdFjz5d49mlz8fM06+Pxx54fIv7Bx+yf3zr8gmx2wH9ovbFNfGry26PO6+Z14KJIT3nBprH2YHm+dqBB8U3hwyPqo4d48mXa+Oi+ffEwy++0Ojegz/UL276wrGbrR/28+vj6TUvVzoqtBpec4BcmPj+gHvjjYh99ow4Z8q27X++JmLS9yKGDo6Y/Z8R//q1iIt/HDH3vorGhFbnY18aFSf/8IS46eLb4uQhZ8ZjDyyLi+ecHbvs2rPR/b13q4qLfjctHntgWZw85My4afrsOOVHJ8bozx/cwskhHecGmsfZgeY5Yq994pxDDo0rF/wpPnPTz2PBC8/HrM9+Pvru3Gmr133yxlnxkZ/O3PR49pU1LZQY0vOaA+RE8f0Bd8iIiCknRYw7ZNv233x7RJ+qiLNOjdhjt4hjPhPx+U9HzLq5ojGh1fnC6Z+JP8y6O35/3d1R/fgLMfP0G2LVX1fHkSePa3T/ZyaNjVXVq2Pm6TdE9eMvxO+vuzvuuv7uOObfPtvCySEd5waax9mB5pn4L0Pj1qVL4ldLl8RTa16Of7//3qj522vx1cEHbfW61a+/3uBRXxQtkhdaA685fCAVhUdTH22E4psmWbw04qPDG659dHjE0ici3lqfJhO0tPL25dh76O6xcO4jDdYXzns0Dhi5T6PX7Ddi71g479EGawvueiT2HrZ7tCu3q1hWaC2cG2geZweaZ/vttotBVb3i/urnGqzfX/1cDOnTd6vX3vnl4+Ohid+KX3zuizGi366VjAmtitccIDeKb5pk9csRPbo1XOvZPWL9hlKsWZsmE7S0Lj07Rbtyu1jz0isN1te89Ep069210Wu69+7a6P7y9uXo0nPrb7eFHDg30DzODjRPtx13jPJ228Xq119vsF77+rrYZaeOjV6zct26mPbfc+OUOXfEyb+7I55esyZ+8bljYnjfD7VEZEjOaw6Qm/f04ZZr1qyJn/3sZ7F8+fLo06dPTJgwIXbd9d3/Rbyuri7q6uoarG1fVx/t2+vh24JSqeHXb7/DobT5VsjaO9/dUyqVotjKW37e+b3S/x2mNvQuIXjPnBtoHmcHmqeId/5HX9riOXjmlTXxzD/dz3vRipro06lTfHPI8C1+ICbkyGsOkIsmNc19+/aN2traiIh45plnYv/9949LL700li9fHtdcc00ceOCB8fjjW/6k37dNnz49unTp0uBxyX/4wJC2oGf3jVPf/6x2TUS5XRFdu6TJBC1t7erXYsP6DdH9HVMPXau6xCsvNf7Wh5dXvBLde3fbbP/6t9bHq7WvVSoqtBrODTSPswPNs+aNN2J9ff1m0909dtopVr+xbpt/zqKamtita9f3OR20Tl5zgNw0qfhesWJFbNiwISIizjrrrNh3333jqaeeirlz58Zf/vKXGDNmTJx77rnv+nOmTZsWa9eubfD4f6d2e9frSO/DB0Q8uKDh2v88HHHAPhHbv6f3D0Dbsf6t9fHkwqdjyNjBDdaHHDY4lv7xiUavWfbQkzHksIb7h447KJ5c8HRsWL+hYlmhtXBuoHmcHWiet+rr47GVL8Xo/gMarI/uPyD+XPPiNv+cA6qqYuW6bS/KoS3zmgPkptn3FvnTn/4U5557buy0004REdG+ffs455xz4qGHHnrXa9u3bx+dO3du8HCbkzTWvR6xbPnGR0TE8zUb//ziSxu/vuLaiO99/x/7jztq4/cu+UnEU89G3Pa7iNlzIk48rsWjQ1K3/fDOGD/xk3H4CYdG/30/FJOumBBV/XvGnVfPjYiIEy/+Spx5w7c37b/z6nlRNaBnfOvyCdF/3w/F4SccGp868RNx6+V3pPoVoMU5N9A8zg40z3WLFsaXDjgwjtl/UOzRrXucM+bj0XfnTvFfSzZ+cN93R42OH4z91Kb9J3x4SIzdfc/YrUvX2Kt7j/juqNExfs+94+ePLkr1K0CL85rDB1J94dHURxvR5Bndt+/VVFdXF7169WrwvV69esWqVaven2S0iKVPREyY8o+7c1965cY/H/2pIqZPi1hVG1Gz8h/7+/WJuPrSjcX3L38TUdUj4qzTIsZ9rIWDQ2L3/erB6Nxj5/jauV+M7n26xbOP/TXOPuLiWFm9OiIievTuFlX9e27av+LZlXHOEdNj0hUT4rOnHB61L66Jq74zKx6Y/adUvwK0OOcGmsfZgeb53fInoluHDnHqR0bELh07xpO1tXHiHbPjxdc23n5hl506Rt9OnTft3367djFt9CHRe+ed4+/r18fy2to48fbZce9zz6T6FaDFec0BclIqtvYJBe+w3XbbxaBBg6JcLsfy5cvjxhtvjM997nObvj9//vz4yle+Es8//3yTg9Sv2LvJ18AH3eF9D0odAQCArXhqxojUEaBN2mPKu7+bHNjcvPpbU0doc8b3n5I6Qpvz++oZqSNskyZNfJ933nkNvn77Nidv++1vfxtjxox576kAAAAAAKCZ3lPx/U6XXXbZewoDAAAAAADvlU+UBAAAAAAgK03+cEsAAAAAgCxs+8cf0saY+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACAr5dQBAAAAAACSKIrUCagQE98AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkpZw6AAAAAABAEkWROgEVYuIbAAAAAICsKL4BAAAAAMiK4hsAAAAAgKwovgEAAAAAyIriGwAAAACArJRTBwAAAAAASKK+PnUCKsTENwAAAAAAWVF8AwAAAACQFcU3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFkppw4AAAAAAJBEUaROQIWY+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACAr5dQBAAAAAACSKIrUCagQE98AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkpZw6AAAAAABAEvVF6gRUiIlvAAAAAACyovgGAAAAACArim8AAAAAALKi+AYAAAAAICuKbwAAAAAAslJOHQAAAAAAIIWiqE8dgQox8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVhTfAAAAAABkRfENAAAAAEBWyqkDAAAAAAAkUV+kTkCFmPgGAAAAACArim8AAAAAALKi+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK+XUAQAAAAAAkiiK1AmoEBPfAAAAAABkRfENAAAAAEBWFN8AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZKWcOgAAAAAAQBL19akTUCEmvgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMhKOXUAAAAAAIAkiiJ1AirExDcAAAAAAFlRfAMAAAAAkBXFNwAAAAAAWVF8AwAAAACQFcU3AAAAAABZKacOAAAAAACQQlFfnzoCFWLiGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMiK4hsAAAAAgKyUUwcAAAAAAEiiKFInoEJMfAMAAAAAkBXFNwAAAAAAWVF8AwAAAACQFcU3AAAAAABZUXwDAAAAAJCVcuoAAAAAAABJ1BepE1AhJr4BAAAAAMiK4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADISjl1AAAAAACAJIr61AmoEBPfAAAAAABkRfENAAAAAEBWFN8AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZKWcOgAAAAAAQApFfZE6AhVi4hsAAAAAgKwovgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICslFMHAAAAAABIoqhPnYAKMfENAAAAAEBWFN8AAAAAAGRF8Q0AAAAAQFYU3wAAAAAAZEXxDQAAAABAVsqpAwAAAAAApFDUF6kjUCEmvgEAAAAAyIriGwAAAACArCi+AQAAAADIiuIbAAAAAICsKL4BAAAAAMhKOXUAAAAAAIAkivrUCagQE98AAAAAAGRF8Q0AAAAAQMVcddVVMXDgwOjQoUMMHTo07r///q3uv++++2Lo0KHRoUOH2H333ePqq69u8nMqvgEAAAAAqIhbbrklpkyZEmeffXYsWrQoxowZE+PHj4/q6upG9z/zzDPx6U9/OsaMGROLFi2Ks846K0477bS47bbbmvS8im8AAAAAACriiiuuiIkTJ8ZJJ50U++23X8yYMSN23XXXmDlzZqP7r7766ujfv3/MmDEj9ttvvzjppJPixBNPjB/84AdNel7FNwAAAAAA26Suri5effXVBo+6urpG97755puxcOHCGDduXIP1cePGxYMPPtjoNX/84x8323/44YfHggUL4q233trmnOVt3llh2/V+MnUEGlFXVxfTp0+PadOmRfv27VPH4R3m+eDhVsvZgaZzbqB5nB1oHmenlTstdQAa49yQo3n1t6aO0Oacf/75ccEFFzRYO++88+L888/fbO/q1atjw4YN0atXrwbrvXr1ihUrVjT681esWNHo/vXr18fq1aujT58+25TTxDdbVVdXFxdccMEW/9UGaJyzA03n3EDzODvQPM4ONJ1zA0RETJs2LdauXdvgMW3atK1eUyqVGnxdFMVma++2v7H1rWk1E98AAAAAALRu7du33+Z3ffTs2TPatWu32XT3ypUrN5vqflvv3r0b3V8ul6NHjx7bnNPENwAAAAAA77sddtghhg4dGvPmzWuwPm/evBg1alSj14wcOXKz/XPnzo1hw4bF9ttvv83PrfgGAAAAAKAipk6dGj/96U9j1qxZsWzZsjj99NOjuro6Jk2aFBEbb53y9a9/fdP+SZMmxXPPPRdTp06NZcuWxaxZs+K6666LM844o0nP61YnbFX79u3jvPPO86EV0ETODjSdcwPN4+xA8zg70HTODdAcxx57bNTW1saFF14YNTU1MWjQoJgzZ04MGDAgIiJqamqiurp60/6BAwfGnDlz4vTTT48rr7wy+vbtGz/+8Y/jC1/4QpOet1S8fWdwAAAAAADIgFudAAAAAACQFcU3AAAAAABZUXwDAAAAAJAVxTcAAAAAAFlRfLNFV111VQwcODA6dOgQQ4cOjfvvvz91JGj15s+fH0ceeWT07ds3SqVS/OY3v0kdCVq96dOnx/Dhw6NTp05RVVUVRx99dDzxxBOpY0GrN3PmzBg8eHB07tw5OnfuHCNHjozf//73qWNBmzJ9+vQolUoxZcqU1FGgVTv//POjVCo1ePTu3Tt1LICtUnzTqFtuuSWmTJkSZ599dixatCjGjBkT48ePj+rq6tTRoFVbt25dHHTQQfGTn/wkdRRoM+67776YPHlyPPTQQzFv3rxYv359jBs3LtatW5c6GrRq/fr1i0suuSQWLFgQCxYsiE984hNx1FFHxdKlS1NHgzbh4YcfjmuvvTYGDx6cOgq0CQcccEDU1NRseixZsiR1JICtKhVFUaQOQetz8MEHx5AhQ2LmzJmb1vbbb784+uijY/r06QmTQdtRKpXi17/+dRx99NGpo0CbsmrVqqiqqor77rsvDjnkkNRxoE3p3r17XHbZZTFx4sTUUaBV+9vf/hZDhgyJq666Ki666KL48Ic/HDNmzEgdC1qt888/P37zm9/E4sWLU0cB2GYmvtnMm2++GQsXLoxx48Y1WB83blw8+OCDiVIB8EGxdu3aiNhY4AHbZsOGDXHzzTfHunXrYuTIkanjQKs3efLkOOKII+Kwww5LHQXajOXLl0ffvn1j4MCBcdxxx8XTTz+dOhLAVpVTB6D1Wb16dWzYsCF69erVYL1Xr16xYsWKRKkA+CAoiiKmTp0ao0ePjkGDBqWOA63ekiVLYuTIkfH3v/89dt555/j1r38d+++/f+pY0KrdfPPN8ec//zkefvjh1FGgzTj44IPjxhtvjL333jteeumluOiii2LUqFGxdOnS6NGjR+p4AI1SfLNFpVKpwddFUWy2BgDvp29/+9vx6KOPxgMPPJA6CrQJ++yzTyxevDheeeWVuO2222LChAlx3333Kb9hC/7617/Gd77znZg7d2506NAhdRxoM8aPH7/pzwceeGCMHDky9thjj/jZz34WU6dOTZgMYMsU32ymZ8+e0a5du82mu1euXLnZFDgAvF9OPfXUuOOOO2L+/PnRr1+/1HGgTdhhhx1izz33jIiIYcOGxcMPPxw/+tGP4pprrkmcDFqnhQsXxsqVK2Po0KGb1jZs2BDz58+Pn/zkJ1FXVxft2rVLmBDaho4dO8aBBx4Yy5cvTx0FYIvc45vN7LDDDjF06NCYN29eg/V58+bFqFGjEqUCIFdFUcS3v/3tmD17dtx9990xcODA1JGgzSqKIurq6lLHgFbrk5/8ZCxZsiQWL1686TFs2LD46le/GosXL1Z6wzaqq6uLZcuWRZ8+fVJHAdgiE980aurUqXH88cfHsGHDYuTIkXHttddGdXV1TJo0KXU0aNX+9re/xV/+8pdNXz/zzDOxePHi6N69e/Tv3z9hMmi9Jk+eHL/85S/j9ttvj06dOm16x1GXLl1ixx13TJwOWq+zzjorxo8fH7vuumu89tprcfPNN8e9994bf/jDH1JHg1arU6dOm32GRMeOHaNHjx4+WwK24owzzogjjzwy+vfvHytXroyLLrooXn311ZgwYULqaABbpPimUccee2zU1tbGhRdeGDU1NTFo0KCYM2dODBgwIHU0aNUWLFgQhx566Kav377f3YQJE+KGG25IlApat5kzZ0ZExMc//vEG69dff3184xvfaPlA0Ea89NJLcfzxx0dNTU106dIlBg8eHH/4wx9i7NixqaMBkJnnn38+vvzlL8fq1atjl112iREjRsRDDz2kIwBatVJRFEXqEAAAAAAA8H5xj28AAAAAALKi+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACArim8AAAAAALKi+AYAAAAAICuKbwAAAAAAsqL4BgAAAAAgK4pvAAAAAACyovgGAAAAACAr/x/D9ORu3YiX+QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 2000x2000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20, 20))\n",
    "sns.heatmap(H_dense, ax=ax, cmap=\"viridis\", annot=True, fmt=\".1f\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to construct the chiral symmetry operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1, -1,  1, -1,  1, -1])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dvec = np.array(\n",
    "    [\n",
    "        (lambda snum: 1 if snum % 2 == 0 else -1)(snum)\n",
    "        for snum in range(M)\n",
    "    ]\n",
    ")\n",
    "\n",
    "dvec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "chiral = sc.sparse.coo_matrix(sc.sparse.diags(dvec))\n",
    "\n",
    "ch_evals, ch_evecs = np.linalg.eigh(chiral.toarray())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get the eigenbasis of the chiral operator for further transformation of the Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0 & 0 & 0 & 0 & 0\\\\0 & -1.0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1.0 & 0 & 0 & 0\\\\0 & 0 & 0 & -1.0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1.0 & 0\\\\0 & 0 & 0 & 0 & 0 & -1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0,    0,   0,    0,   0,    0],\n",
       "[  0, -1.0,   0,    0,   0,    0],\n",
       "[  0,    0, 1.0,    0,   0,    0],\n",
       "[  0,    0,   0, -1.0,   0,    0],\n",
       "[  0,    0,   0,    0, 1.0,    0],\n",
       "[  0,    0,   0,    0,   0, -1.0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.Matrix(chiral.toarray())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x151983c70>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "ax.matshow(ch_evecs, cmap=\"viridis\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "sorted_evecs = np.zeros(shape=(D, D))\n",
    "sorted_evals = np.zeros(shape=(D,))\n",
    "\n",
    "for num, i in enumerate(\n",
    "    np.repeat(\n",
    "        np.linspace(0, D // 2, D // 2, endpoint=False, dtype=np.int64),\n",
    "        2,\n",
    "    )\n",
    "):\n",
    "    rownum = np.where(ch_evecs[:, -(num + 1)] == 1)[0][0]\n",
    "    fact = 0 if num % 2 == 0 else int(D / 2)\n",
    "    new_rownum = fact + i\n",
    "    new_row = ch_evecs[rownum].copy()\n",
    "    sorted_evecs[new_rownum] = new_row\n",
    "    sorted_evals[new_rownum] = ch_evals[rownum].copy()\n",
    "\n",
    "ch_evecs = sorted_evecs\n",
    "ch_evals = sorted_evals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x151bedb80>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "ax.matshow(ch_evecs, cmap=\"viridis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we transform the Hamiltonian into the chiral eigenbasis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x2000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H_new_basis = ch_evecs @ H_dense @ (np.linalg.inv(ch_evecs))\n",
    "fig, ax = plt.subplots(figsize=(20, 20))\n",
    "sns.heatmap(H_new_basis, ax=ax, cmap=\"viridis\", annot=True, fmt=\".1f\")\n",
    "ax.vlines(\n",
    "    np.linspace(0, D, N[0] + 1, endpoint=False),\n",
    "    *ax.get_ylim(),\n",
    "    colors=\"r\",\n",
    "    linewidth=5,\n",
    ")\n",
    "ax.hlines(\n",
    "    np.linspace(0, D, N[0] + 1, endpoint=False),\n",
    "    *ax.get_xlim(),\n",
    "    colors=\"r\",\n",
    "    linewidth=5,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the structure of our Hamiltonian is:\n",
    "$$ \\hat{H} = \\left( \\begin{matrix} 0 & h \\\\ h^\\dagger & 0 \\end{matrix}\\right)$$\n",
    "Since for our equation for winding number we only need the off-diagonal block, we will take $h^\\dagger$ and denote is as $u$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x2000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = H_new_basis[D // 2 :, : D // 2]\n",
    "fig, ax = plt.subplots(figsize=(20, 20))\n",
    "sns.heatmap(u, ax=ax, cmap=\"viridis\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then multiply the corner element by phase factor, that we gain once we hop from the end of our system to the beggining.  \n",
    "We have now achieved the momentum space hamiltonian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 1.0 & 0\\\\0 & 0.5 & 1.0\\\\1.0 e^{i k} & 0 & 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[         0.5, 1.0,   0],\n",
       "[           0, 0.5, 1.0],\n",
       "[1.0*exp(I*k),   0, 0.5]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v, w, k = sp.symbols(\"v w k\", real=True)\n",
    "\n",
    "u = sp.Matrix(u)\n",
    "\n",
    "u[-1, 0] = u[-1, 0] * sp.exp(sp.I * k)\n",
    "u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Derivative wrt $k$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\1.0 i e^{i k} & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[             0, 0, 0],\n",
       "[             0, 0, 0],\n",
       "[1.0*I*exp(I*k), 0, 0]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dkh = sp.simplify(sp.Derivative(u, k).doit())\n",
    "dkh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And inverse of $h^\\dagger$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{v^{2}}{v^{3} + w^{3} e^{i k}} & - \\frac{v w}{v^{3} + w^{3} e^{i k}} & \\frac{w^{2}}{v^{3} + w^{3} e^{i k}}\\\\\\frac{w^{2} e^{i k}}{v^{3} + w^{3} e^{i k}} & \\frac{v^{2}}{v^{3} + w^{3} e^{i k}} & - \\frac{v w}{v^{3} + w^{3} e^{i k}}\\\\- \\frac{v w e^{i k}}{v^{3} + w^{3} e^{i k}} & \\frac{w^{2} e^{i k}}{v^{3} + w^{3} e^{i k}} & \\frac{v^{2}}{v^{3} + w^{3} e^{i k}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[         v**2/(v**3 + w**3*exp(I*k)),          -v*w/(v**3 + w**3*exp(I*k)), w**2/(v**3 + w**3*exp(I*k))],\n",
       "[w**2*exp(I*k)/(v**3 + w**3*exp(I*k)),          v**2/(v**3 + w**3*exp(I*k)), -v*w/(v**3 + w**3*exp(I*k))],\n",
       "[-v*w*exp(I*k)/(v**3 + w**3*exp(I*k)), w**2*exp(I*k)/(v**3 + w**3*exp(I*k)), v**2/(v**3 + w**3*exp(I*k))]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_nice = u.subs([(1.0, w), (0.5, v)])\n",
    "hinv_nice = sp.Inverse(u_nice).doit()\n",
    "hinv_nice\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "hinv = sp.Inverse(u).doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we want to utilize the equation for winding number in the form:  \n",
    "$$ \\vartheta= \\frac{1}{2 \\pi i} \\oint \\mathrm{Tr}(h^{-1} \\partial_k h)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1.0 i w^{2} e^{i k}}{v^{3} + w^{3} e^{i k}} & 0 & 0\\\\- \\frac{1.0 i v w e^{i k}}{v^{3} + w^{3} e^{i k}} & 0 & 0\\\\\\frac{1.0 i v^{2} e^{i k}}{v^{3} + w^{3} e^{i k}} & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0*I*w**2*exp(I*k)/(v**3 + w**3*exp(I*k)), 0, 0],\n",
       "[-1.0*I*v*w*exp(I*k)/(v**3 + w**3*exp(I*k)), 0, 0],\n",
       "[1.0*I*v**2*exp(I*k)/(v**3 + w**3*exp(I*k)), 0, 0]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h1_fin_nice = hinv_nice @ dkh\n",
    "h1_fin_nice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{i w e^{i k}}{v + w e^{i k}}$"
      ],
      "text/plain": [
       "I*w*exp(I*k)/(v + w*exp(I*k))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(sp.Derivative(sp.log(v+w*sp.exp(sp.I*k)), k).doit())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "h1_fin = hinv @ dkh\n",
    "expr1 = sp.Trace(h1_fin).doit() / (2 * sp.pi * sp.I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All that is to be done now is to integrate it. For stability reasons, we perform a numeric integration here, up until $\\epsilon$ from the end of the 1st Brillouin zone"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/k4cp3rskiii/miniforge3/envs/ML_Pytorch/lib/python3.8/site-packages/scipy/integrate/quadpack.py:463: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)\n"
     ]
    }
   ],
   "source": [
    "integrand1 = sp.lambdify(k, expr1.doit(), \"scipy\")\n",
    "\n",
    "r1, r1err = integrate.quad(\n",
    "    integrand1, -np.pi, np.pi - np.finfo(float).eps\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et voila, we have obtained the winding number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Winding number is equal 1\n"
     ]
    }
   ],
   "source": [
    "print(f\"Winding number is equal {round(r1)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using this code we could also calculate winding numbers for various disordered datasets, and recreate Fig. 6. Alternatively, you can download generated data from Zenodo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from src.utils import recreate_fig_6\n",
    "from pathlib import Path\n",
    "save_path = Path(\"./00_demonstrations_data/figures/\")\n",
    "data_path = Path(\"./00_demonstrations_data/datasets/\")\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')\n",
    "\n",
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "%aimport src.utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I*log(-v**2/w**2 - 1)/(2*pi) - I*log(-v**2/w**2 + exp(I*(-2.22044604925031e-16 + pi)))/(2*pi)\n",
      "I*log(v/w - 1)/(2*pi) - I*log(v/w + exp(I*(-2.22044604925031e-16 + pi)))/(2*pi)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/k4cp3rskiii/miniforge3/envs/ML_Pytorch/lib/python3.8/site-packages/scipy/integrate/quadpack.py:463: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "recreate_fig_6(save_path, data_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.8.-1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}