{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "decd332f-f209-4d5d-b197-500aff0a9c58",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This is a demonstration of data visualization for random matrices.\n",
    "Author: Makoto Yamashita\n",
    "Created: 2024-01-25\n",
    "Last modified: 2024-01-29\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as anm\n",
    "from ipywidgets import interact\n",
    "\n",
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39b6fe08-77d7-4e34-a25e-c4e0ae61653e",
   "metadata": {},
   "source": [
    "generate random symmetric matrices of size N, compute their eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cd198986-dbc6-4b48-a51c-69f858c8a9c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 30\n",
    "SAMPLE_SIZE = 100\n",
    "rand_mats = []\n",
    "eigvals = []\n",
    "for i in range(SAMPLE_SIZE):\n",
    "    this_mat = np.empty([N,N])\n",
    "    for j in range(N):\n",
    "        this_mat[j,j] = 2 * np.random.rand() - 1\n",
    "        for k in range(0,j):\n",
    "            this_mat[j,k] = this_mat[k,j]\n",
    "        for k in range(j+1,N):\n",
    "            this_mat[j,k] = 2 * np.random.rand() - 1\n",
    "    rand_mats.append(this_mat)\n",
    "    eigvals.append(np.linalg.eigvals(this_mat))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be1a972d-cfc4-4ae9-88a6-3668ff621631",
   "metadata": {},
   "source": [
    "represent matrices as grayscale images, animate them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f8de0212-c323-4294-9a88-1d0ca275a461",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x10af29ba0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eb8a7d00693c441ca24a9ee750ee94f7",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1, ax1 = plt.subplots()\n",
    "im = plt.imshow(rand_mats[0], cmap='gray', vmin=-1.0, vmax=1.0)\n",
    "\n",
    "def updatefig(frame_number):\n",
    "    \"\"\"Update the image with new data.\"\"\"\n",
    "    im.set_data(rand_mats[frame_number])\n",
    "\n",
    "anm.FuncAnimation(fig1, updatefig, SAMPLE_SIZE, repeat=True, blit=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28359647-5421-4b93-96ab-b34fa172f5b1",
   "metadata": {},
   "source": [
    "histogram plot of eigenvalues, interactive control to choose sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "858f52a0-49c4-42e3-bfa1-0de181deb4cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d093f02ae7284106b43740a109cae7c2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=49, description='mat_ind', max=99), Output()), _dom_classes=('widget-int…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.show_hist(mat_ind)>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HIST_BINS = np.linspace(-8, 8, 16)\n",
    "fig2, ax2 = plt.subplots()\n",
    "\n",
    "def show_hist(mat_ind):\n",
    "    \"\"\"Draw histogram of the eigenvalues for the mat_ind-th matrix.\"\"\"\n",
    "    plt.figure(fig2)\n",
    "    plt.clf()\n",
    "    plt.hist(eigvals[mat_ind], bins=HIST_BINS)\n",
    "    plt.ylim((0,6))\n",
    "    plt.show()\n",
    "\n",
    "interact(show_hist, mat_ind=(0,SAMPLE_SIZE-1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f647945-82ae-4c9b-85b0-3edb4e660aab",
   "metadata": {},
   "source": [
    "increase matrix and sample sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c2a00732-f7df-40a4-8e69-63d574cd08e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "N2 = 100\n",
    "SAMPLE_SIZE2 = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "17fb5591-7540-40b2-b57c-acf6f9d045a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "rand_mats2 = []\n",
    "eigvals2 = []\n",
    "for i in range(SAMPLE_SIZE2):\n",
    "    this_mat = np.empty([N2,N2])\n",
    "    for j in range(N2):\n",
    "        this_mat[j,j] = np.random.rand()\n",
    "        for k in range(0,j):\n",
    "            this_mat[j,k] = this_mat[k,j]\n",
    "        for k in range(j+1,N2):\n",
    "            this_mat[j,k] = np.random.rand()\n",
    "    rand_mats2.append(this_mat)\n",
    "    eigvals2.append(np.linalg.eigvals(this_mat))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17dfee06-18c9-40d3-9737-89658fc2f7e0",
   "metadata": {},
   "source": [
    "get histogram of eigenvalues for each matrix, animate it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d686b5a8-811d-4dab-b5c8-aba287b97179",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.animation.ArtistAnimation at 0x10b0f2830>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c156fd6b1f184089a2ef837cd6ee6ed0",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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A6HmVoiiKskeUYdWqVXHhhRfGwIEDu44dOHAgKpVKDBgwIGq1WrePRRz5CmB7e3t0dnZGU1NTr20nYtTch8qeANAjtn5xetkT0qlWq9Hc3Jz6+TvtS8Af+tCH4nvf+163Y1deeWWMGTMm5syZc1j8RUQ0NDREQ0NDb00EAKiLtAHY2NgYY8eO7XbsuOOOi+HDhx92HACgP0n7HkAAgKzSXgE8kkcffbTsCQAAdecKIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGTSBmBHR0eceeaZ0djYGC0tLXHBBRfEpk2byp4FAFB3aQNwzZo1MWPGjHj66adj9erVsX///pg6dWrs3r277GkAAHV1TNkDyvLNb36z2/1ly5ZFS0tLrF+/Pn7913+9pFUAAPWX9grg/9bZ2RkREcOGDSt5CQBAfaW9AviziqKI2bNnx+TJk2Ps2LFv+Hm1Wi1qtVrX/Wq12hvzAAB6lACMiE9/+tPx3e9+N5544ok3/byOjo5YuHBhL63q20bNfajsCQB9Qr3/vNz6xel1/fr0TelfAr7uuuviwQcfjEceeSTe9a53vennzps3Lzo7O7tu27Zt66WVAAA9J+0VwKIo4rrrrosHHnggHn300Rg9evT/+ZiGhoZoaGjohXUAAPWTNgBnzJgRK1asiH/4h3+IxsbG2LlzZ0RENDc3x5AhQ0peBwBQP2lfAl6yZEl0dnbG2WefHSeeeGLXbeXKlWVPAwCoq7RXAIuiKHsCAEAp0l4BBADISgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkIwABABIRgACACQjAAEAkhGAAADJCEAAgGQEIABAMgIQACAZAQgAkEz6ALzzzjtj9OjRMXjw4Bg/fnw8/vjjZU8CAKir1AG4cuXKmDVrVsyfPz+effbZ+MAHPhDTpk2Ll156qexpAAB1kzoAb7vttrjqqqvik5/8ZJx22mmxePHiaG9vjyVLlpQ9DQCgbo4pe0BZ9u7dG+vXr4+5c+d2Oz516tR48sknj/iYWq0WtVqt635nZ2dERFSr1foN7aMO1vaUPQGA8Bx1JIf+mxRFUfKS8qQNwFdffTUOHDgQra2t3Y63trbGzp07j/iYjo6OWLhw4WHH29vb67IRAN6u5sVlL3jn2rVrVzQ3N5c9oxRpA/CQSqXS7X5RFIcdO2TevHkxe/bsrvsHDx6Mn/70pzF8+PA3fMxbVa1Wo729PbZt2xZNTU09+rXfCZxf39ffz9H59X39/Ryd31tXFEXs2rUr2traevTr9iVpA3DEiBExcODAw672vfLKK4ddFTykoaEhGhoauh07/vjj6zUxIiKampr65f/Yhzi/vq+/n6Pz6/v6+zk6v7cm65W/Q9J+E8igQYNi/PjxsXr16m7HV69eHe9///tLWgUAUH9prwBGRMyePTs+/vGPx4QJE+LXfu3XYunSpfHSSy/FNddcU/Y0AIC6SR2Av/d7vxf/8R//ETfccEO8/PLLMXbs2Hj44Ydj5MiRZU+LhoaG+MIXvnDYS879hfPr+/r7OTq/vq+/n6Pz4+2oFJm/BxoAIKG07wEEAMhKAAIAJCMAAQCSEYAAAMkIwD5g8+bNcf7558eIESOiqakpJk2aFI888kjZs3rUQw89FBMnTowhQ4bEiBEj4qKLLip7Ul3UarUYN25cVCqV2LhxY9lzesTWrVvjqquuitGjR8eQIUPiF3/xF+MLX/hC7N27t+xpb9mdd94Zo0ePjsGDB8f48ePj8ccfL3tSj+no6IgzzzwzGhsbo6WlJS644ILYtGlT2bPqpqOjIyqVSsyaNavsKT1q+/btcdlll8Xw4cNj6NChMW7cuFi/fn3Zs3rE/v3743Of+1zXnymnnHJK3HDDDXHw4MGyp/UrArAPmD59euzfvz++/e1vx/r162PcuHFx7rnnvuG/WdzX/P3f/318/OMfjyuvvDKee+65+M53vhOXXHJJ2bPq4vrrr+93//TQCy+8EAcPHoy77747nn/++fiLv/iLuOuuu+Kzn/1s2dPekpUrV8asWbNi/vz58eyzz8YHPvCBmDZtWrz00ktlT+sRa9asiRkzZsTTTz8dq1evjv3798fUqVNj9+7dZU/rcWvXro2lS5fGu9/97rKn9KjXXnstJk2aFMcee2x84xvfiO9///tx66231v1fpuotN998c9x1111xxx13xL/+67/GLbfcEn/2Z38Wt99+e9nT+peCd7Sf/OQnRUQUjz32WNexarVaRETxz//8zyUu6xn79u0rTjrppOJLX/pS2VPq7uGHHy7GjBlTPP/880VEFM8++2zZk+rmlltuKUaPHl32jLfkfe97X3HNNdd0OzZmzJhi7ty5JS2qr1deeaWIiGLNmjVlT+lRu3btKk499dRi9erVxVlnnVXMnDmz7Ek9Zs6cOcXkyZPLnlE306dPLz7xiU90O3bRRRcVl112WUmL+idXAN/hhg8fHqeddlr8zd/8TezevTv2798fd999d7S2tsb48ePLnve2bdiwIbZv3x4DBgyIM844I0488cSYNm1aPP/882VP61H//u//Hp/61Kfib//2b2Po0KFlz6m7zs7OGDZsWNkzfm579+6N9evXx9SpU7sdnzp1ajz55JMlraqvzs7OiIg++ev1ZmbMmBHTp0+Pc845p+wpPe7BBx+MCRMmxMUXXxwtLS1xxhlnxD333FP2rB4zefLk+Na3vhWbN2+OiIjnnnsunnjiifjIRz5S8rL+JfW/BNIXVCqVWL16dZx//vnR2NgYAwYMiNbW1vjmN7/ZLy73/+hHP4qIiAULFsRtt90Wo0aNiltvvTXOOuus2Lx5c794UiqKIn7/938/rrnmmpgwYUJs3bq17El19cMf/jBuv/32uPXWW8ue8nN79dVX48CBA9Ha2trteGtra795y8XPKooiZs+eHZMnT46xY8eWPafH3H///bFhw4ZYu3Zt2VPq4kc/+lEsWbIkZs+eHZ/97GfjmWeeic985jPR0NAQl19+ednz3rY5c+ZEZ2dnjBkzJgYOHBgHDhyIRYsWxcc+9rGyp/UrrgCWZMGCBVGpVN70tm7duiiKIq699tpoaWmJxx9/PJ555pk4//zz49xzz42XX3657NN4Q0d7fofe1Dt//vz47d/+7Rg/fnwsW7YsKpVKfOUrXyn5LN7c0Z7j7bffHtVqNebNm1f25J/L0Z7fz9qxY0f85m/+Zlx88cXxyU9+sqTlb1+lUul2vyiKw471B5/+9Kfju9/9btx3331lT+kx27Zti5kzZ8by5ctj8ODBZc+pi4MHD8Z73/veuOmmm+KMM86Iq6++Oj71qU/FkiVLyp7WI1auXBnLly+PFStWxIYNG+Lee++NP//zP49777237Gn9in8KriSvvvpqvPrqq2/6OaNGjYrvfOc7MXXq1Hjttdeiqamp62OnnnpqXHXVVTF37tx6T31Ljvb8nnrqqfjgBz8Yjz/+eEyePLnrYxMnToxzzjknFi1aVO+pb9nRnuNHP/rR+NrXvtYtIA4cOBADBw6MSy+99B37h9rRnt+hJ9kdO3bElClTYuLEifHlL385Bgzoe3+/3Lt3bwwdOjS+8pWvxIUXXth1fObMmbFx48ZYs2ZNiet61nXXXRerVq2Kxx57LEaPHl32nB6zatWquPDCC2PgwIFdxw4cOBCVSiUGDBgQtVqt28f6opEjR8aHP/zh+NKXvtR1bMmSJXHjjTfG9u3bS1zWM9rb22Pu3LkxY8aMrmM33nhjLF++PF544YUSl/UvXgIuyYgRI2LEiBH/5+ft2bMnIuKwJ9MBAwa8o78l/mjPb/z48dHQ0BCbNm3qCsB9+/bF1q1bY+TIkfWe+bYc7Tn+5V/+Zdx4441d93fs2BG/8Ru/EStXroyJEyfWc+LbcrTnF/HfP5JiypQpXVdw+2L8RUQMGjQoxo8fH6tXr+4WgIfehtEfFEUR1113XTzwwAPx6KOP9qv4i4j40Ic+FN/73ve6HbvyyitjzJgxMWfOnD4ffxERkyZNOuxH92zevPkd/2fm0dqzZ89hf4YMHDjwHf2c1yeV+A0oHIWf/OQnxfDhw4uLLrqo2LhxY7Fp06bij//4j4tjjz222LhxY9nzesTMmTOLk046qfjHf/zH4oUXXiiuuuqqoqWlpfjpT39a9rS62LJlS7/6LuDt27cXv/RLv1R88IMfLP7t3/6tePnll7tufdH9999fHHvsscVf//VfF9///veLWbNmFccdd1yxdevWsqf1iD/4gz8ompubi0cffbTbr9WePXvKnlY3/e27gJ955pnimGOOKRYtWlT84Ac/KP7u7/6uGDp0aLF8+fKyp/WIK664ojjppJOKr3/968WWLVuKr371q8WIESOK66+/vuxp/YoA7APWrl1bTJ06tRg2bFjR2NhY/Oqv/mrx8MMPlz2rx+zdu7f4oz/6o6KlpaVobGwszjnnnOJf/uVfyp5VN/0tAJctW1ZExBFvfdVf/dVfFSNHjiwGDRp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      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "HIST_BINS2 = np.linspace(-8, 8, 20)\n",
    "fig3, ax3 = plt.subplots()\n",
    "# return value of hist function is a triple whose last entry is a\n",
    "# container of Artist objects\n",
    "bc_list = [ax3.hist(mat_evs, bins=HIST_BINS2, color='C0')[2] for mat_evs in eigvals2]\n",
    "\n",
    "anm.ArtistAnimation(fig3, bc_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "908a19f1-3590-4dfa-9dd1-2c66b5fe0400",
   "metadata": {},
   "source": [
    "histogram of collated eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "739f2bec-05f1-4585-b59b-df6f8c15a22c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f1196be20de142acbaffc153b3c9a705",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "HIST_BINS3 = np.linspace(-8, 8, 60)\n",
    "coll_eigs2 = np.concatenate(eigvals2)\n",
    "fig4, ax4 = plt.subplots()\n",
    "\n",
    "# dummy assignment to supress printing of the return value\n",
    "# (this is only needed at the end of a cell)\n",
    "_ = ax4.hist(coll_eigs2, HIST_BINS3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0a1fda23-5c13-4426-a62a-b3caa0e036af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10c233ca0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9de261449600477faa1c22c8e8351943",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig42, ax42 = plt.subplots()\n",
    "xvar = np.linspace(-6, 6, 100)\n",
    "# semicircle distribution with radius R = 6, normazized by\n",
    "# SAMPLE_SIZE2 * N2 (number of eigenvalues) and\n",
    "# 16 / 60 (area of each sample from HIST_BINS3)\n",
    "ax42.plot(xvar, np.sqrt(36 - xvar**2)*(2*SAMPLE_SIZE2*N2*16)/(np.pi * 36 * 60))\n",
    "ax42.hist(coll_eigs2, HIST_BINS3)\n",
    "ax42.legend([\"semicircle distribution\", \"sampled eigenvalues\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b815476-ba18-453f-a21f-d16e1e0a3e40",
   "metadata": {},
   "source": [
    "compute trace of quadratic polynomials in random matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "64b6fbfc-1df9-44c5-8547-129a0133bfa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10c3332e0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "36ab755d426b4b5e907af932ed58e724",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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mzBnFxsbq4sWLuu222/TSSy/xfxQAAN/y0Tdz+NL48eOVnZ2tSZMmSZJWrlypnJwc5efne+7vJ0kvvviiNm3apNTUVC1fvvyq5t69e7fKyso0fPjweqndFAF3I2ibzab169frgQceqPb4q6++qldeeUXff/99rZdzP/30Ux09elTdunVTeXm55s+fry1btujLL79UfHx8tWPcbrfcbrdnv7y8XG3btjX6RpIAgKtT242Jg8358+fVqVMnrVmzRgkJCXU690MPPaQePXpc8SvmuBF07QLiPYDXYvny5fqnf/qnK764+vbtq5EjR6p79+7q16+f3n//fXXs2FELFiyocUxmZqYcDodna9u2bV2XDwBAwAsLC9PKlSt14sSJOp3X7XZ77g+IGxNUl4B37Nihw4cPa+3atdc8tlGjRrrjjjt05MiRGvukp6d7fY/hpRVAAADgbcCAAXU+p91u18yZM+t8XhMFVQBctmyZevbsqe7du1/zWMuylJ+fr27dutXYx263y26330iJAAAAfhcQAfDMmTM6evSoZ7+goED5+flq0aKF2rVrJ+mX1bgPPvhAf/rTn6qdY/To0WrTpo0yMzMlSbNnz1bfvn0VHx+v8vJyvfHGG8rPz9ebb75Z/ycEAADgRwERAPfu3auBAwd69i9dhh0zZoyys7MlSWvWrJFlWXr00UernaOwsNDrk0enTp3S+PHjVVJSIofDoR49emj79u3q3bt3/Z0IAMB4AfbZy4DF41y7gPsUcEPCp4gAAFfr4sWL+vbbbxUVFaWWLVv6u5ygd/LkSZWWlqpjx44KCQnxOsbv7wBZAQQAINCFhIQoMjJSpaWlkqSmTZvW+H25uH6WZencuXMqLS1VZGRklfCHXxAAAQDwkUvfPnUpBKL+REZG8m1ftSAAAgDgIzabTTExMYqKitKFCxf8XU7Qaty4MSt/V0AABADAx0JCQggo8Kug+yYQAAAA1I4ACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGCYUH8XAADAjWg/ffMV+xx75R4fVAIEDlYAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADBMQAXD79u0aOnSoXC6XbDabNmzY4HV87NixstlsXlvfvn2vOO+6devUpUsX2e12denSRevXr6+nMwAAAGg4AiIAnj17Vt27d9fChQtr7DNkyBAVFxd7ti1bttQ65+7duzVixAiNGjVKX375pUaNGqWHH35Yn332WV2XDwAA0KCE+ruAq5GSkqKUlJRa+9jtdjmdzqueMysrS4MGDVJ6erokKT09XXl5ecrKytLq1atvqF4AAICGLCBWAK9Gbm6uoqKi1LFjRz311FMqLS2ttf/u3buVnJzs1TZ48GDt2rWrxjFut1vl5eVeGwAAQKAJiBXAK0lJSdFDDz2k2NhYFRQUaNasWbrzzju1b98+2e32aseUlJQoOjraqy06OlolJSU1/pzMzEzNnj27TmsHADQM7advvmKfY6/c4/O5gPoQFAFwxIgRnj/feuut6tWrl2JjY7V582YNGzasxnE2m81r37KsKm2/lp6errS0NM9+eXm52rZtewOVAwAA+F5QBMDLxcTEKDY2VkeOHKmxj9PprLLaV1paWmVV8NfsdnuNK4oAAACBImjeA/hrJ0+eVFFRkWJiYmrsk5CQoJycHK+2rVu3KjExsb7LAwAA8KuAWAE8c+aMjh496tkvKChQfn6+WrRooRYtWigjI0MPPvigYmJidOzYMc2YMUOtWrXS73//e8+Y0aNHq02bNsrMzJQkPfvss+rfv7/mzp2r+++/Xxs3btS2bdu0c+dOn58fAACALwVEANy7d68GDhzo2b/0PrwxY8Zo0aJFOnjwoFauXKlTp04pJiZGAwcO1Nq1a9W8eXPPmMLCQjVq9P8LnomJiVqzZo1mzpypWbNmqUOHDlq7dq369OnjuxMDAADwg4AIgElJSbIsq8bjH3300RXnyM3NrdI2fPhwDR8+/EZKAwAACDhB+R5AAAAA1IwACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQLiu4AB3KAMx1X0Kav/OgAADQIrgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYJiACIDbt2/X0KFD5XK5ZLPZtGHDBs+xCxcu6Pnnn1e3bt3UrFkzuVwujR49Wt9//32tc2ZnZ8tms1XZzp8/X89nAwAA4F8BEQDPnj2r7t27a+HChVWOnTt3Tl988YVmzZqlL774Qv/xH/+hb7/9Vvfdd98V542IiFBxcbHXFhYWVh+nAAAA0GCE+ruAq5GSkqKUlJRqjzkcDuXk5Hi1LViwQL1791ZhYaHatWtX47w2m01Op7NOawUAAGjoAmIF8FqVlZXJZrMpMjKy1n5nzpxRbGysbr75Zt17773av39/rf3dbrfKy8u9NgAAgEATdAHw/Pnzmj59uh577DFFRETU2O8f/uEflJ2drU2bNmn16tUKCwvTb3/7Wx05cqTGMZmZmXI4HJ6tbdu29XEKAAAA9SqoAuCFCxf0yCOPqLKyUm+99Vatffv27auRI0eqe/fu6tevn95//3117NhRCxYsqHFMenq6ysrKPFtRUVFdnwIAAEC9C4j3AF6NCxcu6OGHH1ZBQYE+/vjjWlf/qtOoUSPdcccdta4A2u122e32Gy0VAADAr4JiBfBS+Dty5Ii2bdumli1bXvMclmUpPz9fMTEx9VAhAABAwxEQK4BnzpzR0aNHPfsFBQXKz89XixYt5HK5NHz4cH3xxRf6z//8T128eFElJSWSpBYtWqhJkyaSpNGjR6tNmzbKzMyUJM2ePVt9+/ZVfHy8ysvL9cYbbyg/P19vvvmm708QAADAhwIiAO7du1cDBw707KelpUmSxowZo4yMDG3atEmSdNttt3mN++STT5SUlCRJKiwsVKNG/7/geerUKY0fP14lJSVyOBzq0aOHtm/frt69e9fvyQAAAPhZQATApKQkWZZV4/Hajl2Sm5vrtf/666/r9ddfv9HSAAAAAk5QvAcQAAAAV48ACAAAYJiAuAQMwAcyHFfRp6z+6wDqQfvpm/1dAtCgsAIIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABgmIALg9u3bNXToULlcLtlsNm3YsMHruGVZysjIkMvlUnh4uJKSkvT1119fcd5169apS5custvt6tKli9avX19PZwAAANBwBEQAPHv2rLp3766FCxdWe/zVV1/VvHnztHDhQu3Zs0dOp1ODBg3S6dOna5xz9+7dGjFihEaNGqUvv/xSo0aN0sMPP6zPPvusvk4DAACgQQj1dwFXIyUlRSkpKdUesyxLWVlZeuGFFzRs2DBJ0jvvvKPo6Gi99957mjBhQrXjsrKyNGjQIKWnp0uS0tPTlZeXp6ysLK1evbp+TgQAAKABCIgVwNoUFBSopKREycnJnja73a4BAwZo165dNY7bvXu31xhJGjx4cK1j3G63ysvLvTYAAIBAExArgLUpKSmRJEVHR3u1R0dH6/jx47WOq27Mpfmqk5mZqdmzZ99AtQCuSYbjKvqU1X8dABBkAn4F8BKbzea1b1lWlbYbHZOenq6ysjLPVlRUdP0FAwAA+EnArwA6nU5Jv6zoxcTEeNpLS0urrPBdPu7y1b4rjbHb7bLb7TdYMQAAgH8F/ApgXFycnE6ncnJyPG0VFRXKy8tTYmJijeMSEhK8xkjS1q1bax0DAAAQDAJiBfDMmTM6evSoZ7+goED5+flq0aKF2rVrpylTpmjOnDmKj49XfHy85syZo6ZNm+qxxx7zjBk9erTatGmjzMxMSdKzzz6r/v37a+7cubr//vu1ceNGbdu2TTt37vT5+QEAAPhSQATAvXv3auDAgZ79tLQ0SdKYMWOUnZ2tadOm6aefftIzzzyjv//97+rTp4+2bt2q5s2be8YUFhaqUaP/X/BMTEzUmjVrNHPmTM2aNUsdOnTQ2rVr1adPH9+dGAAAgB8ERABMSkqSZVk1HrfZbMrIyFBGRkaNfXJzc6u0DR8+XMOHD6+DCgEAAAJHwL8HEAAAANeGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYJ9XcBAG5QhqNh/ayMsvqvAwBwQ1gBBAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMEERANu3by+bzVZlmzhxYrX9c3Nzq+3/zTff+LhyAAAA3wv1dwF1Yc+ePbp48aJn/6uvvtKgQYP00EMP1Tru8OHDioiI8Oy3bt263moEAABoKIIiAF4e3F555RV16NBBAwYMqHVcVFSUIiMj67EyAACAhicoLgH/WkVFhVatWqXHH39cNput1r49evRQTEyM7rrrLn3yySc+qhAAAMC/gmIF8Nc2bNigU6dOaezYsTX2iYmJ0ZIlS9SzZ0+53W69++67uuuuu5Sbm6v+/fvXOM7tdsvtdnv2y8vL67J0AAAAnwi6ALhs2TKlpKTI5XLV2KdTp07q1KmTZz8hIUFFRUV67bXXag2AmZmZmj17dp3WCwAA4GtBdQn4+PHj2rZtm5588slrHtu3b18dOXKk1j7p6ekqKyvzbEVFRddbKgAAgN8E1QrgihUrFBUVpXvuueeax+7fv18xMTG19rHb7bLb7ddbHgAAQIMQNAGwsrJSK1as0JgxYxQa6n1a6enp+u6777Ry5UpJUlZWltq3b6+uXbt6PjSybt06rVu3zh+lAwAA+FTQBMBt27apsLBQjz/+eJVjxcXFKiws9OxXVFRo6tSp+u677xQeHq6uXbtq8+bNuvvuu31ZMgAAgF8ETQBMTk6WZVnVHsvOzvbanzZtmqZNm+aDqgAAABqeoPoQCAAAAK6MAAgAAGAYAiAAAIBhguY9gEBAyXBcRZ+y+q/Dn67mMYDx2k/f7O8SvDS0eoDrxQogAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGFC/V0AgBpkOPxdAQAgSLECCAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYJigCIAZGRmy2Wxem9PprHVMXl6eevbsqbCwMN1yyy1avHixj6oFAADwr1B/F1BXunbtqm3btnn2Q0JCauxbUFCgu+++W0899ZRWrVql//mf/9Ezzzyj1q1b68EHH/RFuQAAAH4TNAEwNDT0iqt+lyxevFjt2rVTVlaWJKlz587au3evXnvtNQIgAAAIekFxCViSjhw5IpfLpbi4OD3yyCP661//WmPf3bt3Kzk52att8ODB2rt3ry5cuFDfpQIAAPhVUATAPn36aOXKlfroo4/07//+7yopKVFiYqJOnjxZbf+SkhJFR0d7tUVHR+vnn3/WiRMnavw5brdb5eXlXhsAAECgCYpLwCkpKZ4/d+vWTQkJCerQoYPeeecdpaWlVTvGZrN57VuWVW37r2VmZmr27Nl1UDECVobD3xXgelzN85ZRVv91wKP99M3+LsHvruYxOPbKPT6oBCYKihXAyzVr1kzdunXTkSNHqj3udDpVUlLi1VZaWqrQ0FC1bNmyxnnT09NVVlbm2YqKiuq0bgAAAF8IihXAy7ndbh06dEj9+vWr9nhCQoL+/Oc/e7Vt3bpVvXr1UuPGjWuc1263y26312mtAAAAvhYUK4BTp05VXl6eCgoK9Nlnn2n48OEqLy/XmDFjJP2ycjd69GhP/6efflrHjx9XWlqaDh06pOXLl2vZsmWaOnWqv04BAADAZ4JiBfB///d/9eijj+rEiRNq3bq1+vbtq08//VSxsbGSpOLiYhUWFnr6x8XFacuWLUpNTdWbb74pl8ulN954g1vAAAAAIwRFAFyzZk2tx7Ozs6u0DRgwQF988UU9VQQAANBwBcUlYAAAAFw9AiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABgm1N8FAAgyGQ5/VwA/az99s79LCBpX81gee+UeH1SCYMMKIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhgmKAJiZmak77rhDzZs3V1RUlB544AEdPny41jG5ubmy2WxVtm+++cZHVQMAAPhHUATAvLw8TZw4UZ9++qlycnL0888/Kzk5WWfPnr3i2MOHD6u4uNizxcfH+6BiAAAA/wn1dwF14b/+67+89lesWKGoqCjt27dP/fv3r3VsVFSUIiMj67E6AACAhiUoVgAvV1ZWJklq0aLFFfv26NFDMTExuuuuu/TJJ5/Ud2kAAAB+FxQrgL9mWZbS0tL0u9/9TrfeemuN/WJiYrRkyRL17NlTbrdb7777ru666y7l5ubWuGrodrvldrs9++Xl5XVePwAAQH0LugA4adIkHThwQDt37qy1X6dOndSpUyfPfkJCgoqKivTaa6/VGAAzMzM1e/bsOq0XAADA14LqEvDkyZO1adMmffLJJ7r55puveXzfvn115MiRGo+np6errKzMsxUVFd1IuQAAAH4RFCuAlmVp8uTJWr9+vXJzcxUXF3dd8+zfv18xMTE1Hrfb7bLb7ddbJgAAQIMQFAFw4sSJeu+997Rx40Y1b95cJSUlkiSHw6Hw8HBJv6zefffdd1q5cqUkKSsrS+3bt1fXrl1VUVGhVatWad26dVq3bp3fzgMAAMAXgiIALlq0SJKUlJTk1b5ixQqNHTtWklRcXKzCwkLPsYqKCk2dOlXfffedwsPD1bVrV23evFl33323r8oGAADwi6AIgJZlXbFPdna21/60adM0bdq0eqoIAACg4QqqD4EAAADgygiAAAAAhiEAAgAAGCYo3gMIwGAZDt/Ok1FWNz8PqCPtp2++Yp9jr9zj87nQsLECCAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhQv1dAFDvMhz+rgDwu/bTN/u7BPhRQ3z+r6amY6/c44NKzMQKIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGGCKgC+9dZbiouLU1hYmHr27KkdO3bU2j8vL089e/ZUWFiYbrnlFi1evNhHlQIAAPhP0ATAtWvXasqUKXrhhRe0f/9+9evXTykpKSosLKy2f0FBge6++27169dP+/fv14wZM/SHP/xB69at83HlAAAAvhU0AXDevHl64okn9OSTT6pz587KyspS27ZttWjRomr7L168WO3atVNWVpY6d+6sJ598Uo8//rhee+01H1cOAADgW6H+LqAuVFRUaN++fZo+fbpXe3Jysnbt2lXtmN27dys5OdmrbfDgwVq2bJkuXLigxo0bVxnjdrvldrs9+2VlZZKk8vLyGz0F1Ce35e8KEEwC9PVe6T7n7xIQJOrqd97V/J2sr9+vl+a1LHN/PwRFADxx4oQuXryo6Ohor/bo6GiVlJRUO6akpKTa/j///LNOnDihmJiYKmMyMzM1e/bsKu1t27a9geoBBJRXHP6uAPArR1bw/KzTp0/L4TDzNR0UAfASm83mtW9ZVpW2K/Wvrv2S9PR0paWlefYrKyv1448/qmXLlrX+HNSsvLxcbdu2VVFRkSIiIvxdjrF4HhoGnoeGgeehYajP58GyLJ0+fVoul6tO5w0kQREAW7VqpZCQkCqrfaWlpVVW+S5xOp3V9g8NDVXLli2rHWO322W3273aIiMjr79weERERPAPbQPA89Aw8Dw0DDwPDUN9PQ+mrvxdEhQfAmnSpIl69uypnJwcr/acnBwlJiZWOyYhIaFK/61bt6pXr17Vvv8PAAAgWARFAJSktLQ0LV26VMuXL9ehQ4eUmpqqwsJCPf3005J+uXw7evRoT/+nn35ax48fV1pamg4dOqTly5dr2bJlmjp1qr9OAQAAwCeC4hKwJI0YMUInT57UH//4RxUXF+vWW2/Vli1bFBsbK0kqLi72uidgXFyctmzZotTUVL355ptyuVx644039OCDD/rrFIxkt9v14osvVrm0Dt/ieWgYeB4aBp6HhoHnoX7ZLJM/Aw0AAGCgoLkEDAAAgKtDAAQAADAMARAAAMAwBEAAAADDEADRoLRv3142m81ru/w7nlH33nrrLcXFxSksLEw9e/bUjh07/F2SUTIyMqr8vXc6nf4uK+ht375dQ4cOlcvlks1m04YNG7yOW5aljIwMuVwuhYeHKykpSV9//bV/ig1iV3oexo4dW+X10bdvX/8UG0QIgGhwLt3K59I2c+ZMf5cU1NauXaspU6bohRde0P79+9WvXz+lpKR43TYJ9a9r165ef+8PHjzo75KC3tmzZ9W9e3ctXLiw2uOvvvqq5s2bp4ULF2rPnj1yOp0aNGiQTp8+7eNKg9uVngdJGjJkiNfrY8uWLT6sMDgFzX0AETyaN2/O6ocPzZs3T0888YSefPJJSVJWVpY++ugjLVq0SJmZmX6uzhyhoaH8vfexlJQUpaSkVHvMsixlZWXphRde0LBhwyRJ77zzjqKjo/Xee+9pwoQJviw1qNX2PFxit9t5fdQxVgDR4MydO1ctW7bUbbfdpn/9139VRUWFv0sKWhUVFdq3b5+Sk5O92pOTk7Vr1y4/VWWmI0eOyOVyKS4uTo888oj++te/+rskoxUUFKikpMTrtWG32zVgwABeG36Qm5urqKgodezYUU899ZRKS0v9XVLAYwUQDcqzzz6r22+/XTfddJM+//xzpaenq6CgQEuXLvV3aUHpxIkTunjxoqKjo73ao6OjVVJS4qeqzNOnTx+tXLlSHTt21A8//KCXX35ZiYmJ+vrrr9WyZUt/l2ekS3//q3ttHD9+3B8lGSslJUUPPfSQYmNjVVBQoFmzZunOO+/Uvn37+JaQG0AARL3LyMjQ7Nmza+2zZ88e9erVS6mpqZ62f/zHf9RNN92k4cOHe1YFUT9sNpvXvmVZVdpQf359+atbt25KSEhQhw4d9M477ygtLc2PlYHXhv+NGDHC8+dbb71VvXr1UmxsrDZv3uy5PI9rRwBEvZs0aZIeeeSRWvu0b9++2vZLn/Q6evQoAbAetGrVSiEhIVVW+0pLS6usfMB3mjVrpm7duunIkSP+LsVYl95vVlJSopiYGE87rw3/i4mJUWxsLK+PG0QARL1r1aqVWrVqdV1j9+/fL0le/wCj7jRp0kQ9e/ZUTk6Ofv/733vac3JydP/99/uxMrO53W4dOnRI/fr183cpxoqLi5PT6VROTo569Ogh6Zf3zObl5Wnu3Ll+rs5sJ0+eVFFREb8XbhABEA3G7t279emnn2rgwIFyOBzas2ePUlNTdd9996ldu3b+Li9opaWladSoUerVq5cSEhK0ZMkSFRYW6umnn/Z3acaYOnWqhg4dqnbt2qm0tFQvv/yyysvLNWbMGH+XFtTOnDmjo0ePevYLCgqUn5+vFi1aqF27dpoyZYrmzJmj+Ph4xcfHa86cOWratKkee+wxP1YdfGp7Hlq0aKGMjAw9+OCDiomJ0bFjxzRjxgy1atXK639acR0soIHYt2+f1adPH8vhcFhhYWFWp06drBdffNE6e/asv0sLem+++aYVGxtrNWnSxLr99tutvLw8f5dklBEjRlgxMTFW48aNLZfLZQ0bNsz6+uuv/V1W0Pvkk08sSVW2MWPGWJZlWZWVldaLL75oOZ1Oy263W/3797cOHjzo36KDUG3Pw7lz56zk5GSrdevWVuPGja127dpZY8aMsQoLC/1ddsCzWZZl+St8AgAAwPe4DyAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGOb/APEaFvIJSxSkAAAAAElFTkSuQmCC",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "HIST_BINS3 = np.linspace(-8, 15, 50)\n",
    "# sample Tr(XX) by moving X by moving X in rand_mats\n",
    "# drop the first term to be consistent with Tr(XY)\n",
    "tr_list1 = [np.trace(x * x) for x in rand_mats][1:]\n",
    "# sample Tr(XY) by fixing Y = rand_mats[0] and moving X in rand_mats\n",
    "# drop the self-product of the first matrix\n",
    "tr_list2 = [np.trace(x * rand_mats[0]) for x in rand_mats][1:]\n",
    "fig5, ax5 = plt.subplots()\n",
    "\n",
    "ax5.hist(tr_list1, bins=HIST_BINS3, histtype='barstacked')\n",
    "ax5.hist(tr_list2, bins=HIST_BINS3, histtype='barstacked')\n",
    "ax5.set_ylim((0,20))\n",
    "ax5.legend([\"Tr(XX)\", \"Tr(XY)\"])"
   ]
  },
  {
   "cell_type": "code",
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