persistance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Scikit-tda\n",
    "\n",
    "######  Persistence images from geographical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install scikit-tda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/pandas/core/arrays/masked.py:60: UserWarning: Pandas requires version '1.3.6' or newer of 'bottleneck' (version '1.3.5' currently installed).\n",
      "  from pandas.core import (\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "import geopandas as gpd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ripser\n",
    "import persim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Importing geodata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "WySviRaw = gpd.read_file('./wyoming/data/processed data/SVI2018 WY counties with death rate HepVu/SVI2018_WY_counties_with_death_rate_HepVu.shp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "geometry_df = WySviRaw[['FIPS','geometry']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>FIPS</th>\n",
       "      <th>geometry</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>56003</td>\n",
       "      <td>POLYGON ((-108.62184 44.99613, -108.62182 44.9...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>56007</td>\n",
       "      <td>POLYGON ((-107.92977 41.65419, -107.92974 41.6...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>56009</td>\n",
       "      <td>POLYGON ((-106.07807 43.49447, -106.01737 43.4...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    FIPS                                           geometry\n",
       "0  56003  POLYGON ((-108.62184 44.99613, -108.62182 44.9...\n",
       "1  56007  POLYGON ((-107.92977 41.65419, -107.92974 41.6...\n",
       "2  56009  POLYGON ((-106.07807 43.49447, -106.01737 43.4..."
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geometry_df.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/geopandas/geodataframe.py:1543: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  super().__setitem__(key, value)\n"
     ]
    }
   ],
   "source": [
    "# create a new column in df that contains the x and y coordinates of the centroid of each polygon\n",
    "geometry_df['coords'] = geometry_df['geometry'].apply(lambda x: x.representative_point().coords[:])\n",
    "geometry_df['coords'] = [coords[0] for coords in geometry_df['coords']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the centroids\n",
    "plt.scatter(*zip(*geometry_df['coords']), s=10, c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# put each coordinates into array and then stack them together\n",
    "data_coordinates = np.array([np.array(coord) for coord in geometry_df['coords']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(23, 2)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_coordinates.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Ploting persistence diagrams for point cloud data(geodata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def diagram_sizes(dgms):\n",
    "    return \", \".join([f\"|$H_{i}$|={len(d)}\" for i, d in enumerate(dgms)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Method 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dgm_clean = ripser.ripser(data_coordinates)['dgms']\n",
    "persim.plot_diagrams(\n",
    "    dgm_clean,\n",
    "    show=True,\n",
    "    title=f\"Clean\\n{diagram_sizes(dgm_clean)}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Method 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ripser import Rips\n",
    "rips = Rips()\n",
    "dgm_wyoming = rips.transform(data_coordinates)\n",
    "rips.plot(show=True, title=f\"Noisy\\n{diagram_sizes(dgm_wyoming)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(\n",
    "    dgm_wyoming,\n",
    "    title=\"Noisy Data\",\n",
    "    lifetime=True,\n",
    "    show=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from persim import PersistenceImager\n",
    "\n",
    "pimager = PersistenceImager(pixel_size=0.2)\n",
    "\n",
    "# The `fit()` method can be called on one or more (*,2) numpy arrays\n",
    "# to automatically determine the miniumum birth and persistence ranges needed to capture all persistence pairs.\n",
    "# The ranges and resolution are automatically adjusted to accomodate the specified pixel size.\n",
    "pimager.fit(dgm_wyoming[1:3])\n",
    "\n",
    "# The `transform()` method can then be called on one or more (*,2) numpy arrays\n",
    "# to generate persistence images from diagrams.\n",
    "imgs = pimager.transform(dgm_wyoming[1:3])\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(10,5))\n",
    "axs[0].set_title(\"Original Diagram\")\n",
    "persim.plot_diagrams(dgm_wyoming[1:3],  lifetime=True, ax=axs[0], labels=[\"$H_1$\", \"$H_2$\"])\n",
    "\n",
    "axs[1].set_title(\"Persistence Image\")\n",
    "pimager.plot_image(imgs[0], ax=axs[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Persistence Landscapes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "dgms_wy = ripser.ripser(data_coordinates, maxdim=2)['dgms']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from persim import PersLandscapeApprox, PersLandscapeExact\n",
    "from persim.landscapes import plot_landscape_simple\n",
    "\n",
    "pla = PersLandscapeApprox(dgms=dgm_wyoming,hom_deg=0)\n",
    "ax = plot_landscape_simple(pla, depth_range=range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Storage of diagrams\n",
    "dgms - diagram informations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = ripser.ripser(data_coordinates, maxdim=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['dgms', 'cocycles', 'num_edges', 'dperm2all', 'idx_perm', 'r_cover'])\n"
     ]
    }
   ],
   "source": [
    "print(data.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[0.        , 0.61818582],\n",
       "        [0.        , 0.63626379],\n",
       "        [0.        , 0.75611877],\n",
       "        [0.        , 0.76975465],\n",
       "        [0.        , 0.81474233],\n",
       "        [0.        , 0.82400411],\n",
       "        [0.        , 0.83168441],\n",
       "        [0.        , 0.83470851],\n",
       "        [0.        , 0.89327586],\n",
       "        [0.        , 0.94367933],\n",
       "        [0.        , 0.94796997],\n",
       "        [0.        , 0.99185222],\n",
       "        [0.        , 1.02945971],\n",
       "        [0.        , 1.04245818],\n",
       "        [0.        , 1.04312027],\n",
       "        [0.        , 1.06845665],\n",
       "        [0.        , 1.09901524],\n",
       "        [0.        , 1.1155889 ],\n",
       "        [0.        , 1.12855875],\n",
       "        [0.        , 1.22580111],\n",
       "        [0.        , 1.22833312],\n",
       "        [0.        , 1.57510161],\n",
       "        [0.        ,        inf]]),\n",
       " array([[2.19983959, 2.27290154],\n",
       "        [1.586285  , 1.652542  ],\n",
       "        [1.41161966, 1.62912273],\n",
       "        [1.30482137, 1.56469655],\n",
       "        [1.24739003, 1.67056787],\n",
       "        [1.10546327, 1.20986855],\n",
       "        [1.02705455, 1.03896987]]),\n",
       " array([], shape=(0, 2), dtype=float64)]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['dgms']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Ripser options\n",
    "ripser class method returns diagram  data directly, better to use the below method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "persiatance_data = ripser.ripser(data_coordinates, maxdim=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['dgms', 'cocycles', 'num_edges', 'dperm2all', 'idx_perm', 'r_cover'])\n"
     ]
    }
   ],
   "source": [
    "print(persiatance_data.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dgm = persiatance_data['dgms']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Plotting all the dimentions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(data_dgm, show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Plotting H_1 persistance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(data_dgm[1], show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Plotting H_0 persistance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(data_dgm[0], show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  Persistence Images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Persistanace for H_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(data_dgm[1], show=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PI Resolution = (12, 5)\n"
     ]
    }
   ],
   "source": [
    "pimgr = PersistenceImager(pixel_size=0.1)\n",
    "pimgr.fit(data_dgm[1])\n",
    "imgs = pimgr.transform(data_dgm[1])\n",
    "print(f\"PI Resolution = {pimgr.resolution}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 7))\n",
    "ax = plt.subplot(121)\n",
    "pimgr.plot_image(imgs, ax)\n",
    "plt.title(\"PI of $H_1$ for Wyoming\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Persistanace for H_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(data_dgm[0], show=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.61818582],\n",
       "       [0.        , 0.63626379],\n",
       "       [0.        , 0.75611877],\n",
       "       [0.        , 0.76975465],\n",
       "       [0.        , 0.81474233],\n",
       "       [0.        , 0.82400411],\n",
       "       [0.        , 0.83168441],\n",
       "       [0.        , 0.83470851],\n",
       "       [0.        , 0.89327586],\n",
       "       [0.        , 0.94367933],\n",
       "       [0.        , 0.94796997],\n",
       "       [0.        , 0.99185222],\n",
       "       [0.        , 1.02945971],\n",
       "       [0.        , 1.04245818],\n",
       "       [0.        , 1.04312027],\n",
       "       [0.        , 1.06845665],\n",
       "       [0.        , 1.09901524],\n",
       "       [0.        , 1.1155889 ],\n",
       "       [0.        , 1.12855875],\n",
       "       [0.        , 1.22580111],\n",
       "       [0.        , 1.22833312],\n",
       "       [0.        , 1.57510161],\n",
       "       [0.        ,        inf]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_dgm[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the data_dgm without the infinite values raw\n",
    "data_dgm_no_inf = data_dgm[0][:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.61818582],\n",
       "       [0.        , 0.63626379],\n",
       "       [0.        , 0.75611877],\n",
       "       [0.        , 0.76975465],\n",
       "       [0.        , 0.81474233],\n",
       "       [0.        , 0.82400411],\n",
       "       [0.        , 0.83168441],\n",
       "       [0.        , 0.83470851],\n",
       "       [0.        , 0.89327586],\n",
       "       [0.        , 0.94367933],\n",
       "       [0.        , 0.94796997],\n",
       "       [0.        , 0.99185222],\n",
       "       [0.        , 1.02945971],\n",
       "       [0.        , 1.04245818],\n",
       "       [0.        , 1.04312027],\n",
       "       [0.        , 1.06845665],\n",
       "       [0.        , 1.09901524],\n",
       "       [0.        , 1.1155889 ],\n",
       "       [0.        , 1.12855875],\n",
       "       [0.        , 1.22580111],\n",
       "       [0.        , 1.22833312],\n",
       "       [0.        , 1.57510161]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_dgm_no_inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PI Resolution = (0, 10)\n"
     ]
    }
   ],
   "source": [
    "pimgr = PersistenceImager(pixel_size=0.1)\n",
    "pimgr.fit(data_dgm_no_inf)\n",
    "imgs = pimgr.transform(data_dgm_no_inf)\n",
    "print(f\"PI Resolution = {pimgr.resolution}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 7))\n",
    "ax = plt.subplot(121)\n",
    "pimgr.plot_image(imgs, ax)\n",
    "plt.title(\"PI of $H_1$ for Wyoming\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Persistanace for H_1 with Lifetime plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persim.plot_diagrams(data_dgm[1], show=True, lifetime=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# using the class module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n"
     ]
    }
   ],
   "source": [
    "rips = ripser.Rips(maxdim=1, coeff=2)\n",
    "diagrams_h1 = rips.fit_transform(data_coordinates)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Lly+HVqvF+PHjkZ6ejsrKSrv9Dx8+jFmzZmHu3Ln4/vvvsX37dnzzzTeYN2+eM2+DiEjSnJrimDFjBoqLi/Gf//mfUKvVkMlkNj9fsWKFQ68zZswYJCQkYN26dda22NhYTJs2DRqNpk3/1atXY926dTh79qy17e2338Zrr72Gqqoqh/bJKQ4icjdX5YxTJwk//vhjFBUV4Z577nF6x9euXUNpaSmWLVtm056WloYjR47Y3SYlJQXLly9HUVER0tPTodfr8dFHH+GBBx5odz8mk8n6TUfgxoEjIvIETk1x9OvXD8HBwZ3acV1dHcxmM9RqtU27Wq1GbW2t3W1SUlKwdetWZGVlwc/PD2FhYejZsyfefvvtdvej0WigUqmsj6ioqE7VTUTUVZwK6Ndffx1Lly5FRUVFpwu4eXpEEIQ2ba1OnjyJZ599Fi+99BJKS0vxySef4Pz581iwYEG7r5+bmwuDwWB9ODoVQkQkNqemOJKSktDc3IyBAwciMDDQ5nocAHDx4sXbvkafPn0gl8vbjJb1en2bUXUrjUaDe+65B3/4wx8AACNHjkRQUBDGjx+PVatWITw8vM02SqUSSqXS0bdGRCQZTgX0Y489hurqarzyyit2TxI6ws/PD4mJiSguLsbDDz9sbS8uLsZ//Md/2N2mqakJCoVtyXK5HMCNkTcRUXfiVEAfOXIER48eRXx8fKd2npOTg5kzZyIpKQnJycl49913UVlZaZ2yyM3NRXV1NbZs2QIAyMzMxJNPPol169ZhypQp0Ol0WLRoEe6++25ERER0qhYiIqlxKqCHDh2Kq1evdnrnWVlZqK+vx8qVK6HT6RAXF4eioiLExMQAAHQ6nc2a6OzsbBiNRqxduxbPP/88evbsifvuuw+vvvpqp2shIpIap9ZB79+/H3l5efjLX/6CESNGtJmDlvL6Yq6DJiJ3c1XOOBXQPj43Fn+0twLDbDY7XZC7MaCJyN1E/aLKgQMHnN4hERE5xqmAnjhxoqvrICKimzgc0MePH0dcXBx8fHxw/PjxW/YdOXJkpwsjIvJ2Dgf0qFGjUFtbi9DQUIwaNQoymczu2mOpz0ETEXkKhwP6/Pnz6Nu3r/XfRETkXg4HdOvaZACoqKhASkpKm2/1tbS04MiRIzZ9iYjIOU5dLCk1NdXu9TZa71NIRESd51RAt3fFufr6egQFBXW6KCIi6uAyu0ceeQTAjROB2dnZNleJM5vNOH78OFJSUlxbIRGRl+pQQKtUKgA3RtDBwcEICAiw/szPzw9jx47Fk08+6doKiYi8VIcCuqCgAADQv39/LFmyhNMZRERu5NQc9IoVK6BUKvGvf/0LGzZsgNFoBADU1NTgypUrLi2QiMhbOfVV74qKCkydOhWVlZUwmUyYPHkygoOD8dprr6G5uRnr1693dZ1ERF7HqRH0c889h6SkJFy6dMlmHvrhhx/Gp59+6rLiiIi8mVMj6MOHD+OLL76An5+fTXtMTAyqq6tdUhgRkbdzagRtsVjsXm/j559/RnBwcKeLIiIiJwN68uTJWLNmjfW5TCbDlStXsGLFCmRkZLiqNiIir+bUHVVqamqQmpoKuVyOM2fOICkpCWfOnEGfPn1QUlKC0NBQd9TqEryjChG5m6h3VImIiEB5eTn+67/+C6WlpbBYLJg7dy4ef/xxm5OGRETkPIdH0AkJCfj0009xxx13YOXKlViyZAkCAwPdXZ/LcQRNRO7mqpxxeA761KlTaGxsBADk5eXxCylERG7WoTuqzJkzB+PGjYMgCFi9ejV69Ohht+9LL73ksgKJiLyVw1Mcp0+fxooVK3D27FmUlZVh2LBhbS7YD9xY0VFWVubyQl2FUxxE5G4uyxnBCTKZTPjll1+c2bSNd955R+jfv7+gVCqFhIQEoaSk5Jb9m5ubhRdffFGIjo4W/Pz8hIEDBwobN250eH8Gg0EAIBgMhs6WTkRkl6tyxqlVHBaLxfnfCP+msLAQixYtQn5+Pu655x5s2LAB6enpOHnyJKKjo+1uM336dPzyyy/YuHEj7rrrLuj1erS0tLikHiIiKXF4imPPnj1IT0+Hr68v9uzZc8u+Dz30kEM7HzNmDBISErBu3TprW2xsLKZNmwaNRtOm/yeffILf/va3OHfuHHr16uXQPm7GKQ4icrcuXwc9bdo01NbWIjQ0FNOmTWu3n0wms/s18Jtdu3YNpaWlWLZsmU17Wloajhw5YnebPXv2ICkpCa+99ho++OADBAUF4aGHHsKf//zndtdfm0wmmEwm6/OGhobb1kZEJAUOB/S/T2u0N8VRWVmJFStWOPR6dXV1MJvNUKvVNu1qtRq1tbV2tzl37hwOHz4Mf39/7Nq1C3V1dXj66adx8eJFbNq0ye42Go0GeXl5DtVERCQlTl2Loz2XLl3Cli1bOrTNzTefFdq5IS1w4xeDTCbD1q1bcffddyMjIwNvvPEGNm/ejKtXr9rdJjc3FwaDwfqoqqrqUH1ERGJx6iShK/Tp0wdyubzNaFmv17cZVbcKDw9Hv379rPdGBG7MWQuCgJ9//hmDBg1qs41SqbS5uS0Rkadw6Qi6I/z8/JCYmIji4mKb9uLi4nbvDH7PPfe0ua3Wjz/+CB8fH0RGRrq1XiKiriZaQANATk4O3nvvPWzatAmnTp3C4sWLUVlZiQULFgC4MT0xa9Ysa/8ZM2agd+/emDNnDk6ePImSkhL84Q9/wO9+9ztepImIup0OTXE88sgjt/z55cuXO7TzrKws1NfXY+XKldDpdIiLi0NRURFiYmIAADqdDpWVldb+PXr0QHFxMX7/+98jKSkJvXv3xvTp07Fq1aoO7ZeIyBN06HrQc+bMcahfQUGB0wW5G9dBE5G7iXI9aCkHLxFRdyPqHDQREbWPAU1EJFEMaCIiiWJAExFJFAOaiEiiGNBERBLFgCYikigGNBGRRDGgiYgkigFNRCRRDGgiIoliQBMRSRQDmohIohjQREQSxYAmIpIoBjQRkUQxoImIJIoBTUQkUQxoIiKJYkB3c9fNFuiNzbBYHL43MBFJRIduGkue5YOjF7DmX2dQ33gNUb0CsOLB4bh/mFrssojIQRxBd1Nf/FSHP/3ze9Q3XgMAVF28iqe3lqHqYpPIlRGRoxjQ3dTOsuo2bdfMFuw9rhOhGiJyhugBnZ+fjwEDBsDf3x+JiYk4dOiQQ9t98cUXUCgUGDVqlHsL7GZkMrErICJHiRrQhYWFWLRoEZYvXw6tVovx48cjPT0dlZWVt9zOYDBg1qxZmDRpUhdV6nkeTejXps1P7oMHR4aLUA0ROUPUgH7jjTcwd+5czJs3D7GxsVizZg2ioqKwbt26W243f/58zJgxA8nJyV1UqedJuasPVk2LQ58efgCAmN6BWD8zAZF3BIpcGRE5SrRVHNeuXUNpaSmWLVtm056WloYjR460u11BQQHOnj2Lf/zjH1i1atVt92MymWAymazPGxoanC/awzwxNga//U0UDFevo1eQH2Sc3yDyKKKNoOvq6mA2m6FW2y77UqvVqK2ttbvNmTNnsGzZMmzduhUKhWO/WzQaDVQqlfURFRXV6do9iULug949lAxnIg8k+knCm4NDEAS7YWI2mzFjxgzk5eVh8ODBDr9+bm4uDAaD9VFVVdXpmomIuoJoUxx9+vSBXC5vM1rW6/VtRtUAYDQacezYMWi1WixcuBAAYLFYIAgCFAoF9u/fj/vuu6/NdkqlEkql0j1vgojIjUQbQfv5+SExMRHFxcU27cXFxUhJSWnTPyQkBN999x3Ky8utjwULFmDIkCEoLy/HmDFjuqp0IqIuIepXvXNycjBz5kwkJSUhOTkZ7777LiorK7FgwQIAN6YnqqursWXLFvj4+CAuLs5m+9DQUPj7+7dpJyLqDkQN6KysLNTX12PlypXQ6XSIi4tDUVERYmJiAAA6ne62a6KJiLormSAIXnWZs4aGBqhUKhgMBoSEhIhdDhF1Q67KGdFXcRARkX0MaCIiiWJAExFJFAOaiEiiGNBERBLFgCYikigGNBGRRDGgiYgkigFNRCRRDGgiIoliQBMRSRQDmohIohjQREQSxYAmIpIoUa8HTdKgb2jG+0cv4Ky+EQkxPTFjTAx6KPnRIBIb/xd6uV8ampH59mHojSYAwCff12LPtzXY+dQ98FPwDywiMfF/oJfbcvSCNZxbnahuwP87oROpIiJqxYD2cmf1jXbbz/1qv52Iug4D2sslxPS02z462n47EXUdBrSXmzEmBiP6qWza0uPCMHFwX5EqIqJWPEno5XooFdjxVAo++b4W5369gtHRd2DCoD6QyWRil0bk9RjQBD+FDx6Kj3DJa7WYLfjq/EUAwJgBvaCQ8480ImcxoMllTtca8bvN36D68lUAQL+eASiY8xsMVgeLXBmRZ+LwhlzmhY++tYYzAFRfvooXPjouYkVEnk30gM7Pz8eAAQPg7++PxMREHDp0qN2+O3fuxOTJk9G3b1+EhIQgOTkZ+/bt68JqqT0XG6/h258NbdrLqy7jUuM1ESoi8nyiBnRhYSEWLVqE5cuXQ6vVYvz48UhPT0dlZaXd/iUlJZg8eTKKiopQWlqK1NRUZGZmQqvVdnHldLNAPzkCfOVt2gN85Qjwa9tORLcnEwRBEGvnY8aMQUJCAtatW2dti42NxbRp06DRaBx6jeHDhyMrKwsvvfSSQ/0bGhqgUqlgMBgQEhLiVN1k38r/exKbvjhv0zZv3AD88cFhIlVEJA5X5YxoJwmvXbuG0tJSLFu2zKY9LS0NR44cceg1LBYLjEYjevXq1W4fk8kEk+l/v8rc0NDgXMF0W8sfiEXfYCV2aX+GDDI8nNAPT44fKHZZRB5LtICuq6uD2WyGWq22aVer1aitrXXoNV5//XU0NjZi+vTp7fbRaDTIy8vrVK3kGLmPDE/deyeeuvdOsUsh6hZEP0l48xciBEFw6EsS27Ztw8svv4zCwkKEhoa22y83NxcGg8H6qKqq6nTNRERdQbQRdJ8+fSCXy9uMlvV6fZtR9c0KCwsxd+5cbN++Hffff/8t+yqVSiiVyk7XS0TU1UQbQfv5+SExMRHFxcU27cXFxUhJSWl3u23btiE7OxsffvghHnjgAXeXSUQkGlG/SZiTk4OZM2ciKSkJycnJePfdd1FZWYkFCxYAuDE9UV1djS1btgC4Ec6zZs3Cm2++ibFjx1pH3wEBAVCpVO3uh4jIE4ka0FlZWaivr8fKlSuh0+kQFxeHoqIixMTEAAB0Op3NmugNGzagpaUFzzzzDJ555hlr++zZs7F58+auLp+IyK1EXQctBq6DJiJ3c1XOiL6Kg4iI7GNAExFJFAOaiEiiGNBERBLFgCYikigGNBGRRPGWVyIxWwTsPV6Dw2fqEKbyx2N3RyOiZ4DYZRE5xGw24/r162KXIRpfX1/I5e6/zjkDWiQ5/12Of5bXWJ+/f+QCdj6dgrtCef8+ki5BEFBbW4vLly+LXYroevbsibCwMIcu7uYsBrQIvq8x2IQzADQ0t+CdA2fxt6xR4hRF5IDWcA4NDUVgYKBbw0mqBEFAU1MT9Ho9ACA8PNxt+2JAi+B0rdFu+w/ttBNJgdlstoZz7969xS5HVAEBN6Yj9Xo9QkND3TbdwZOEIhjRz/6FnUa2004kBa1zzoGBgSJXIg2tx8Gdc/EMaBEMUgfjibHRNm19g5V4JvUukSoicpwrpjWumy1ovm52QTXi6YrpHU5xiGTVtBFIGxaGQ2d+RZgqAI+M7oc7gvzELovIrcwWAT9faoLh6o1Rp1IhR3SvQN75vR0MaBFNGNwXEwb3FbuMbmHv8Rr8rfhHXKhvQmL0Hfjjg7EYGdlT7LLoJr80NFvDGQBMLWZUXGzEEHWwV55wvB1OcZDH++pcPX6/TYuzvzbCbBHw9YWLePy9r3Cp8ZrYpdFNLje1na+91mLBVQ+f7nAXBjR5vMJvqnDzVc2NzS3Y+51OnIKoXT7tDJK7avQ8YcIEzJ07t017fn4+AgMDYTZL6xcFA5o8Xnujr+Zr0vrPRrB7niXQT4EAX/fPQQuCgPLyciQmJrb5WWlpKeLj47vk24EdwYAmj5c+ou0XBeQ+MkwZHiZCNXQrocFKhAb7Q+4jgwwyqAJ8EdO7a5btnTlzBkajsd2AttcuNgY0ebyH4iOwYOKd8FPc+Dj3DPTF6v8zEtFd9B+fHCeTyeArl+H9Ixfwu/e/wfwPStt8q9ZdSktLIZfLMXLkSJt2k8mE77//XpIBzVUc1C0sSx+KBRMHovryVdzZtwf8u+BPZuo4QRCQXfANvqs2AAB+NZqwZPu3UPjIMG10P7fuu6ysDGazud0v2rQG9N69e/H888/DYrFg6dKlmDdvnlvruhWOoKnb6Bnoh+ERKoazhJVWXLKG87/bfOSC+/ddWoqHH34YWq3W5vHiiy/C398fw4YNQ0tLC3JycvDZZ5+hrKwMr776Ki5evOj22trDgCaiLvPva6AdaXclrVaLe++9F6NGjbJ5XLx4ESNHjoRCocDXX3+N4cOHo1+/fggODkZGRgb27dvn9trawykOF6i+fBX/LK+G6boFGSPCMSSMlwwlsmfswN4IVipgNLXYtE8epnbrfs+dO4fLly8jISGhzc/Kysqs0xs1NTXo1+9/p1oiIyNRXV3t1tpuhSPoTvryXD0mvf45XvvkNN789AzS3yzBfx+rErssIkkKUirw1mOjoQrwtbaNH9QHz00a5Nb9lpaWwsfHB6NGjbJpb2lpwfHjx60BLdy8oB5dt0bbHtEDOj8/HwMGDIC/vz8SExNx6NChW/Y/ePAgEhMT4e/vj4EDB2L9+vVdVKl9f/n4FJqvW6zPLQLwStEpj78QDJG7pA4NxVcvTsKHT47B/sUT8MHcMQhSuveP+bKyMgwaNAg9evSwaf/+++/R3NxsHVn369fPZsT8888/u/V6z7cjakAXFhZi0aJFWL58ObRaLcaPH4/09HRUVlba7X/+/HlkZGRg/Pjx1sn9Z599Fjt27Ojiym+wWAS7JzwuN11H5cUmESoi8gz+vnKk3NkHg9VdMx2o0Wjwww8/tGmPj4+HIAgYPXo0AODuu+/GiRMnUF1dDaPRiKKiIkyZMqVLarRH1DnoN954A3PnzrUuY1mzZg327duHdevWQaPRtOm/fv16REdHY82aNQCA2NhYHDt2DKtXr8ajjz7aoX03Nja65FtDMSE+OF9nG8ZBfnKofC1obGzs9OsTSYXJZILFYoHZbJbcV6JdRSaT4a9//StSU1NhsViwZMkS9OzZ0+77NZvNsFgsaGpqavNzV/3fFy2gr127htLSUixbtsymPS0tDUeOHLG7zdGjR5GWlmbTNmXKFGzcuBHXr1+Hr69vm21MJhNMJpP1eUNDAwAgIiKis2/hlsJedevLE3W5mJgYrF+/HlevXhW7FLeKjIzEhx9+aH2u1Wrb7VtXV4cHHngAFRUVbqlFtCmOuro6mM1mqNW2Z2/VajVqa2vtblNbW2u3f0tLC+rq6uxuo9FooFKprI+oqCjXvAEiIjcTfZndzWdIBUG45VlTe/3ttbfKzc1FTk6O9XlDQwOioqJQU1ODkJAQZ8sm8jomkwk6nQ79+/eHv7+/2OWIrrm5GRcuXEBZWRmUSqXNzxoaGlzyV7poAd2nTx/I5fI2o2W9Xt9mlNwqLCzMbn+FQtHuTSyVSmWbgwcAQUFBCAoKcrJ6Iu8jl8vh4+MDuVwuuau+iaH1eAQGBrb5heWqOXrRpjj8/PyQmJiI4uJim/bi4mKkpKTY3SY5OblN//379yMpKcnu/DMRkScTdZldTk4O3nvvPWzatAmnTp3C4sWLUVlZiQULFgC4MT0xa9Ysa/8FCxagoqICOTk5OHXqFDZt2oSNGzdiyZIlYr0FIq9j78sc3qgrjoOoc9BZWVmor6/HypUrodPpEBcXh6KiIsTExAAAdDqdzZroAQMGoKioCIsXL8Y777yDiIgIvPXWWx1eYkdEHdf6V2pTUxMCAgJErkZ8TU03lte68693meBlvw4bGhqgUqlgMBh4kpCog3Q6HS5fvozQ0FAEBgZ65Y1eBUFAU1MT9Ho9evbsafebhq7KGdFXcRCR5wgLu3GXGr1eL3Il4uvZs6f1eLgLA5qIHCaTyRAeHo7Q0FBcv+7+S4RKla+vb5esZGFAE1GHcald1xD9anZERGQfA5qISKIY0EREEuV1c9Ctqwpbr2pHRORqrfnS2VXMXhfQRqMRAHhVOyJyO6PRCJVK5fT2XvdFFYvFgpqaGgQHBzu9yL71inhVVVX8souL8di6D4+t+9x8bAVBgNFoREREBHx8nJ9J9roRtI+PDyIjI13yWiEhIfyguwmPrfvw2LrPvx/bzoycW/EkIRGRRDGgiYgkigHtBKVSiRUrVti9EQB1Do+t+/DYuo+7jq3XnSQkIvIUHEETEUkUA5qISKIY0EREEsWAJiKSKAa0HSUlJcjMzERERARkMhl27959220OHjyIxMRE+Pv7Y+DAgVi/fr37C/VAHT22n3/+OWQyWZvHDz/80DUFewiNRoPf/OY3CA4ORmhoKKZNm4bTp0/fdjt+bm/PmWPrqs8tA9qOxsZGxMfHY+3atQ71P3/+PDIyMjB+/HhotVq8+OKLePbZZ7Fjxw43V+p5OnpsW50+fRo6nc76GDRokJsq9EwHDx7EM888gy+//BLFxcVoaWlBWloaGhsb292Gn1vHOHNsW3X6cyvQLQEQdu3adcs+L7zwgjB06FCbtvnz5wtjx451Y2Wez5Fje+DAAQGAcOnSpS6pqbvQ6/UCAOHgwYPt9uHn1jmOHFtXfW45gnaBo0ePIi0tzaZtypQpOHbsmFfft82VRo8ejfDwcEyaNAkHDhwQuxzJMxgMAIBevXq124efW+c4cmxbdfZzy4B2gdraWqjVaps2tVqNlpYW1NXViVRV9xAeHo53330XO3bswM6dOzFkyBBMmjQJJSUlYpcmWYIgICcnB+PGjUNcXFy7/fi57ThHj62rPrdedzU7d7n50qXC/3xB09lLmtINQ4YMwZAhQ6zPk5OTUVVVhdWrV2PChAkiViZdCxcuxPHjx3H48OHb9uXntmMcPbau+txyBO0CYWFhqK2ttWnT6/VQKBTo3bu3SFV1X2PHjsWZM2fELkOSfv/732PPnj04cODAbS+ry89tx3Tk2NrjzOeWAe0CycnJKC4utmnbv38/kpKS4OvrK1JV3ZdWq0V4eLjYZUiKIAhYuHAhdu7cic8++wwDBgy47Tb83DrGmWNrj1Of206dYuymjEajoNVqBa1WKwAQ3njjDUGr1QoVFRWCIAjCsmXLhJkzZ1r7nzt3TggMDBQWL14snDx5Uti4caPg6+srfPTRR2K9Bcnq6LH929/+JuzatUv48ccfhRMnTgjLli0TAAg7duwQ6y1I0lNPPSWoVCrh888/F3Q6nfXR1NRk7cPPrXOcObau+twyoO1oXSJz82P27NmCIAjC7NmzhYkTJ9ps8/nnnwujR48W/Pz8hP79+wvr1q3r+sI9QEeP7auvvirceeedgr+/v3DHHXcI48aNEz7++GNxipcwe8cUgFBQUGDtw8+tc5w5tq763PJyo0REEsU5aCIiiWJAExFJFAOaiEiiGNBERBLFgCYikigGNBGRRDGgiYgkigFN9D8uXLgAmUyG8vJyp7Z39O47RI5iQJPXyM7Otrn9UO/evTF16lQcP34cABAVFQWdTnfLy0gCwMsvv4xRo0Z1QcXk7RjQ5FWmTp1qvf3Qp59+CoVCgQcffBAAIJfLERYWBoXC/lV4BUFAS0tLV5ZLXo4BTV5FqVQiLCwMYWFhGDVqFJYuXYqqqir8+uuvbaY4Wm/8uW/fPiQlJUGpVOKDDz5AXl4evv32W+tIfPPmzdbXr6urw8MPP4zAwEAMGjQIe/bsEeeNUrfAgCavdeXKFWzduhV33XXXLa9//MILL0Cj0eDUqVNIS0vD888/j+HDh1tH4llZWda+eXl5mD59Oo4fP46MjAw8/vjjuHjxYle8HeqGeEcV8ip79+5Fjx49ANy4w3h4eDj27t0LH5/2xyorV67E5MmTrc979OgBhUKBsLCwNn2zs7Px2GOPAQBeeeUVvP322/j6668xdepUF78T8gYcQZNXSU1NRXl5OcrLy/HVV18hLS0N6enpqKioaHebpKQkh19/5MiR1n8HBQUhODgYer2+UzWT9+IImrxKUFAQ7rrrLuvzxMREqFQq/P3vf8e8efPa3cZRN9+JRCaTwWKxOFcseT2OoMmryWQy+Pj44OrVqw5v4+fnB7PZ7MaqiG7gCJq8islkst4o9dKlS1i7di2uXLmCzMxMh1+jf//+OH/+PMrLyxEZGYng4GAolUp3lUxejCNo8iqffPIJwsPDER4ejjFjxuCbb77B9u3bce+99zr8Go8++iimTp2K1NRU9O3bF9u2bXNfweTVeMsrIiKJ4giaiEiiGNBERBLFgCYikigGNBGRRDGgiYgkigFNRCRRDGgiIoliQBMRSRQDmohIohjQREQSxYAmIpIoBjQRkUT9f82t8UP1rNamAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "\n",
    "plt.subplot(121)\n",
    "rips.plot(diagrams_h1, show=False, lifetime=True)\n",
    "plt.title(\"PD of $H_1$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PI Resolution = (12, 5)\n"
     ]
    }
   ],
   "source": [
    "pimgr = PersistenceImager(pixel_size=0.1)\n",
    "pimgr.fit(diagrams_h1)\n",
    "imgs = pimgr.transform(diagrams_h1)\n",
    "print(f\"PI Resolution = {pimgr.resolution}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 7))\n",
    "ax = plt.subplot(121)\n",
    "pimgr.plot_image(imgs, ax)\n",
    "plt.title(\"PI of $H_1$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Persistanace for H_0 with Lifetime plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "diagrams_h0 = rips.fit_transform(data_coordinates)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "\n",
    "plt.subplot(121)\n",
    "rips.plot(diagrams_h0, show=False, lifetime=True)\n",
    "plt.title(\"PD of $H_1$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.61818582],\n",
       "       [0.        , 0.63626379],\n",
       "       [0.        , 0.75611877],\n",
       "       [0.        , 0.76975465],\n",
       "       [0.        , 0.81474233],\n",
       "       [0.        , 0.82400411],\n",
       "       [0.        , 0.83168441],\n",
       "       [0.        , 0.83470851],\n",
       "       [0.        , 0.89327586],\n",
       "       [0.        , 0.94367933],\n",
       "       [0.        , 0.94796997],\n",
       "       [0.        , 0.99185222],\n",
       "       [0.        , 1.02945971],\n",
       "       [0.        , 1.04245818],\n",
       "       [0.        , 1.04312027],\n",
       "       [0.        , 1.06845665],\n",
       "       [0.        , 1.09901524],\n",
       "       [0.        , 1.1155889 ],\n",
       "       [0.        , 1.12855875],\n",
       "       [0.        , 1.22580111],\n",
       "       [0.        , 1.22833312],\n",
       "       [0.        , 1.57510161],\n",
       "       [0.        ,        inf]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diagrams_h0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the data_dgm without the infinite values raw\n",
    "dgm_h0_no_inf_ = diagrams_h0[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PI Resolution = (0, 1)\n"
     ]
    }
   ],
   "source": [
    "pimgr = PersistenceImager(pixel_size=1)\n",
    "pimgr.fit(dgm_h0_no_inf_)\n",
    "imgs = pimgr.transform(dgm_h0_no_inf_)\n",
    "print(f\"PI Resolution = {pimgr.resolution}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 7))\n",
    "ax = plt.subplot(121)\n",
    "pimgr.plot_image(imgs, ax)\n",
    "plt.title(\"PI of $H_1$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  Test 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "import time\n",
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "from scipy.stats import multivariate_normal as mvn\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from ripser import Rips\n",
    "from persim import PersistenceImager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PersistenceImager(birth_range=(0.0, 1.0), pers_range=(0.0, 1.0), pixel_size=0.2, weight=persistence, weight_params={'n': 1.0}, kernel=gaussian, kernel_params={'sigma': [[1.0, 0.0], [0.0, 1.0]]})\n"
     ]
    }
   ],
   "source": [
    "# Printing a PersistenceImager() object will print its defining attributes\n",
    "pimgr = PersistenceImager(pixel_size=0.2, birth_range=(0,1))\n",
    "print(pimgr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PersistenceImager(birth_range=(0.0, 2.0), pers_range=(0.0, 1.0), pixel_size=0.1, weight=persistence, weight_params={'n': 1.0}, kernel=gaussian, kernel_params={'sigma': [[1.0, 0.0], [0.0, 1.0]]})\n",
      "(20, 10)\n"
     ]
    }
   ],
   "source": [
    "# PersistenceImager() attributes can be adjusted at or after instantiation.\n",
    "# Updating attributes of a PersistenceImager() object will automatically update all other dependent attributes.\n",
    "pimgr.pixel_size = 0.1\n",
    "pimgr.birth_range = (0, 2)\n",
    "print(pimgr)\n",
    "print(pimgr.resolution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n"
     ]
    }
   ],
   "source": [
    "rips = Rips()\n",
    "dgms = rips.fit_transform(data_coordinates)\n",
    "H0_dgm = dgms[0]\n",
    "H1_dgm = dgms[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.subplot(121)\n",
    "plt.scatter(data_coordinates[:,0], data_coordinates[:,1], s=4)\n",
    "plt.title(\"Wyoming County Centroids\")\n",
    "\n",
    "plt.subplot(122)\n",
    "rips.plot(dgms, legend=False, show=False)\n",
    "plt.title(\"Persistence diagram of $H_0$ and $H_1$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The resolution of the persistence image is adjusted by choosing the pixel size, given in the same units as the diagram\n",
    "pimgr = PersistenceImager(pixel_size=1)\n",
    "pimgr.fit(H1_dgm)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(20,5))\n",
    "pimgr.plot_diagram(H1_dgm, skew=True, ax=axs[0])\n",
    "axs[0].set_title('Diagram', fontsize=16)\n",
    "\n",
    "pimgr.plot_image(pimgr.transform(H1_dgm), ax=axs[1])\n",
    "axs[1].set_title('Pixel Size: 1', fontsize=16)\n",
    "\n",
    "pimgr.pixel_size = 0.1 \n",
    "pimgr.plot_image(pimgr.transform(H1_dgm), ax=axs[2])\n",
    "axs[2].set_title('Pixel Size: 0.1', fontsize=16)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "H0_dgm = H0_dgm[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/persim/images.py:800: UserWarning: Attempting to set identical low and high xlims makes transformation singular; automatically expanding.\n",
      "  ax.set_xlim(bmin, bmax)\n",
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/persim/images.py:805: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  (1 / 50 * self.pixel_size)\n",
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/matplotlib/lines.py:66: RuntimeWarning: invalid value encountered in scalar multiply\n",
      "  scaled_offset = offset * lw\n",
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/persim/images.py:866: UserWarning: Attempting to set identical low and high xlims makes transformation singular; automatically expanding.\n",
      "  ax.matshow(pers_img.T, **{\"origin\": \"lower\"})\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The resolution of the persistence image is adjusted by choosing the pixel size, given in the same units as the diagram\n",
    "pimgr = PersistenceImager(pixel_size=1)\n",
    "pimgr.fit(H0_dgm)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(20,5))\n",
    "pimgr.plot_diagram(H0_dgm, skew=True, ax=axs[0])\n",
    "axs[0].set_title('Diagram', fontsize=16)\n",
    "\n",
    "pimgr.plot_image(pimgr.transform(H0_dgm), ax=axs[1])\n",
    "axs[1].set_title('Pixel Size: 1', fontsize=16)\n",
    "\n",
    "pimgr.pixel_size = 0.1 \n",
    "pimgr.plot_image(pimgr.transform(H0_dgm), ax=axs[2])\n",
    "axs[2].set_title('Pixel Size: 0.1', fontsize=16)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "TDA",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}