Cell_cycle.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Install packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.decomposition import NMF\n",
    "from numpy import asarray\n",
    "from numpy import savetxt\n",
    "import matplotlib.colors as mcolors\n",
    "import matplotlib.cm\n",
    "import matplotlib.patches as mpatches\n",
    "import umap\n",
    "import matplotlib as mpl\n",
    "import scanpy as sc\n",
    "import scipy\n",
    "import kmapper as km\n",
    "from kmapper import jupyter\n",
    "from kmapper.plotlyviz import plotlyviz\n",
    "from kmapper.plotlyviz import *\n",
    "import plotly.graph_objs as go\n",
    "import sys\n",
    "from sklearn import ensemble\n",
    "from tqdm import tqdm\n",
    "from ripser import Rips\n",
    "from ripser import ripser\n",
    "from persim import plot_diagrams\n",
    "from sklearn.metrics.pairwise import euclidean_distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read in data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pd_data = pd.read_csv(\"cell_cycle.csv\", sep=',', header = 0, index_col = 0) \n",
    "np_data = np.array(pd_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "         ENSG00000000003  ENSG00000000005  ENSG00000000419  ENSG00000000457  \\\n",
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       "A11_355            27.14              0.0            69.77             0.49   \n",
       "A11_356           129.83              0.0            37.72             6.50   \n",
       "...                  ...              ...              ...              ...   \n",
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       "P9_356             60.22              0.0            50.06             0.00   \n",
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       "\n",
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       "...                  ...              ...              ...              ...   \n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "...                  ...  \n",
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       "\n",
       "[1152 rows x 42728 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42728, 2)\n"
     ]
    }
   ],
   "source": [
    "reducer = umap.UMAP()\n",
    "UMAP = reducer.fit_transform(np_data.T)\n",
    "print(UMAP.shape)\n",
    "\n",
    "#savetxt('cellcycle_umap.csv', UMAP, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UMAP shape: (42728, 2)\n"
     ]
    }
   ],
   "source": [
    "UMAP = pd.read_csv(\"cellcycle_umap.csv\", sep=',', header = None)\n",
    "UMAP = UMAP.values \n",
    "\n",
    "print(\"UMAP shape: \"+repr(UMAP.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "frame1 = sns.scatterplot(UMAP[:,0], UMAP[:,1], s=20,  linewidth = 0)\n",
    "plt.title('Cell cycle - UMAP')\n",
    "#plt.xlim(-30000,25000)\n",
    "frame1.axes.get_xaxis().set_ticks([])\n",
    "frame1.axes.get_yaxis().set_ticks([])\n",
    "plt.ylabel('UMAP2')\n",
    "plt.xlabel('UMAP1')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from manifold_utils.mSVD import eigen_plot, eigen_calc_from_dist_mat, eps_projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "np_data = np_data.T\n",
    "N, d = np_data.shape\n",
    " \n",
    "dist_mat = euclidean_distances(np_data, np_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#savetxt('dist_mat_cellcycle.csv', dist_mat, delimiter=',')\n",
    "\n",
    "#dist_mat = pd.read_csv('dist_mat_cellcycle.csv', sep=\",\", header = None)\n",
    "#dist_mat = np.array(dist_mat )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42728, 42728)\n"
     ]
    }
   ],
   "source": [
    "print(dist_mat.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize Landmarks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 42728\n",
      "d = 1152\n",
      "shape of dist_mat: (42728, 42728)\n",
      "Timing computation of density filtrations...\n",
      "\tk = 10, p = 0.01:\n",
      "\t1.7478759288787842 seconds\n",
      "\n",
      "\tk = 10, p = 0.05:\n",
      "\t1.955221176147461 seconds\n",
      "\n",
      "\tk = 10, p = 0.1:\n",
      "\t2.1562209129333496 seconds\n",
      "\n",
      "\tk = 10, p = 0.2:\n",
      "\t3.443699598312378 seconds\n",
      "\n",
      "\tk = 100, p = 0.01:\n",
      "\t1.957956314086914 seconds\n",
      "\n",
      "\tk = 100, p = 0.05:\n",
      "\t1.9637176990509033 seconds\n",
      "\n",
      "\tk = 100, p = 0.1:\n",
      "\t2.1980972290039062 seconds\n",
      "\n",
      "\tk = 100, p = 0.2:\n",
      "\t3.438422918319702 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01:\n",
      "\t1.911062479019165 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05:\n",
      "\t2.080143451690674 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1:\n",
      "\t2.279707431793213 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2:\n",
      "\t3.3215208053588867 seconds\n",
      "\n",
      "Timing computation of landmarks...\n",
      "\tk = 10, p = 0.01, pp = 0.05:\n",
      "\t0.0009999275207519531 seconds\n",
      "\n",
      "\tk = 10, p = 0.01, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.01, pp = 0.2:\n",
      "\t0.0009310245513916016 seconds\n",
      "\n",
      "\tk = 10, p = 0.05, pp = 0.05:\n",
      "\t0.002980947494506836 seconds\n",
      "\n",
      "\tk = 10, p = 0.05, pp = 0.1:\n",
      "\t0.004000425338745117 seconds\n",
      "\n",
      "\tk = 10, p = 0.05, pp = 0.2:\n",
      "\t0.006201505661010742 seconds\n",
      "\n",
      "\tk = 10, p = 0.1, pp = 0.05:\n",
      "\t0.01438283920288086 seconds\n",
      "\n",
      "\tk = 10, p = 0.1, pp = 0.1:\n",
      "\t0.01700305938720703 seconds\n",
      "\n",
      "\tk = 10, p = 0.1, pp = 0.2:\n",
      "\t0.024005889892578125 seconds\n",
      "\n",
      "\tk = 10, p = 0.2, pp = 0.05:\n",
      "\t0.12002754211425781 seconds\n",
      "\n",
      "\tk = 10, p = 0.2, pp = 0.1:\n",
      "\t0.14580368995666504 seconds\n",
      "\n",
      "\tk = 10, p = 0.2, pp = 0.2:\n",
      "\t0.16172337532043457 seconds\n",
      "\n",
      "\tk = 100, p = 0.01, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.01, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.01, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.05, pp = 0.05:\n",
      "\t0.003000497817993164 seconds\n",
      "\n",
      "\tk = 100, p = 0.05, pp = 0.1:\n",
      "\t0.0039010047912597656 seconds\n",
      "\n",
      "\tk = 100, p = 0.05, pp = 0.2:\n",
      "\t0.005994319915771484 seconds\n",
      "\n",
      "\tk = 100, p = 0.1, pp = 0.05:\n",
      "\t0.01393747329711914 seconds\n",
      "\n",
      "\tk = 100, p = 0.1, pp = 0.1:\n",
      "\t0.015995502471923828 seconds\n",
      "\n",
      "\tk = 100, p = 0.1, pp = 0.2:\n",
      "\t0.023005008697509766 seconds\n",
      "\n",
      "\tk = 100, p = 0.2, pp = 0.05:\n",
      "\t0.11381864547729492 seconds\n",
      "\n",
      "\tk = 100, p = 0.2, pp = 0.1:\n",
      "\t0.15752553939819336 seconds\n",
      "\n",
      "\tk = 100, p = 0.2, pp = 0.2:\n",
      "\t0.1992487907409668 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01, pp = 0.1:\n",
      "\t0.0010013580322265625 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01, pp = 0.2:\n",
      "\t0.00099945068359375 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05, pp = 0.05:\n",
      "\t0.0030007362365722656 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05, pp = 0.1:\n",
      "\t0.004003286361694336 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05, pp = 0.2:\n",
      "\t0.00600123405456543 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1, pp = 0.05:\n",
      "\t0.014002084732055664 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1, pp = 0.1:\n",
      "\t0.01600360870361328 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1, pp = 0.2:\n",
      "\t0.023008108139038086 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2, pp = 0.05:\n",
      "\t0.08902788162231445 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2, pp = 0.1:\n",
      "\t0.09985160827636719 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2, pp = 0.2:\n",
      "\t0.17862796783447266 seconds\n",
      "\n",
      "Printing numbers of landmarks...\n",
      "(10, 0.01, 0.05): 21\n",
      "(10, 0.01, 0.1): 42\n",
      "(10, 0.01, 0.2): 85\n",
      "(10, 0.05, 0.05): 106\n",
      "(10, 0.05, 0.1): 213\n",
      "(10, 0.05, 0.2): 427\n",
      "(10, 0.1, 0.05): 213\n",
      "(10, 0.1, 0.1): 427\n",
      "(10, 0.1, 0.2): 854\n",
      "(10, 0.2, 0.05): 427\n",
      "(10, 0.2, 0.1): 854\n",
      "(10, 0.2, 0.2): 1709\n",
      "(100, 0.01, 0.05): 21\n",
      "(100, 0.01, 0.1): 42\n",
      "(100, 0.01, 0.2): 85\n",
      "(100, 0.05, 0.05): 106\n",
      "(100, 0.05, 0.1): 213\n",
      "(100, 0.05, 0.2): 427\n",
      "(100, 0.1, 0.05): 213\n",
      "(100, 0.1, 0.1): 427\n",
      "(100, 0.1, 0.2): 854\n",
      "(100, 0.2, 0.05): 427\n",
      "(100, 0.2, 0.1): 854\n",
      "(100, 0.2, 0.2): 1709\n",
      "(1000, 0.01, 0.05): 21\n",
      "(1000, 0.01, 0.1): 42\n",
      "(1000, 0.01, 0.2): 85\n",
      "(1000, 0.05, 0.05): 106\n",
      "(1000, 0.05, 0.1): 213\n",
      "(1000, 0.05, 0.2): 427\n",
      "(1000, 0.1, 0.05): 213\n",
      "(1000, 0.1, 0.1): 427\n",
      "(1000, 0.1, 0.2): 854\n",
      "(1000, 0.2, 0.05): 427\n",
      "(1000, 0.2, 0.1): 854\n",
      "(1000, 0.2, 0.2): 1709\n",
      "saving\n",
      "[18520, 21011, 29974, 30956, 20911, 24495, 27361, 34971, 18343, 17741, 38921, 18856, 28763, 37373, 33297, 18316, 24792, 28114, 34029, 35395, 23799, 31381, 33336, 31701, 15447, 12910, 24816, 29835, 18585, 28605, 29541, 23533, 18190, 10860, 21027, 20694, 13428, 17942, 27315, 21515, 38818, 30259, 21186, 15051, 27790, 21033, 20175, 27530, 29811, 30214, 21595, 35867, 33859, 38567, 38326, 30713, 37163, 18149, 19682, 24151, 40560, 22737, 22694, 26422, 19195, 18541, 23121, 39831, 38031, 23869, 3663, 34007, 33613, 20465, 26677, 35636, 31500, 30398, 29321, 27202, 32001, 38992, 36979, 39441, 36187, 39868, 18941, 34269, 38089, 18092, 34974, 23859, 28171, 23055, 13156, 21980, 9074, 23207, 24858, 28370, 13718, 18226, 34023, 36898, 37958, 30082, 31903, 18545, 28678, 36919, 26486, 17786, 18659, 27911, 33168, 17940, 18577, 24069, 38367, 28849, 32670, 33095, 24839, 17987, 33177, 31267, 18594, 13246, 29656, 33840, 19568, 23297, 26766, 35692, 35291, 33712, 29875, 26737, 11958, 18643, 5650, 24906, 39817, 36354, 36296, 15955, 32872, 19807, 22930, 20750, 39930, 30998, 29838, 21041, 37036, 36485, 29824, 25231, 28119, 38774, 29295, 20792, 15502, 22979, 40077, 20832, 33514, 32644, 34019, 19486, 23703, 30481, 30239, 24306, 33656, 40028, 20663, 25061, 29783, 38490, 29078, 24736, 5892, 23263, 19777, 28167, 35333, 27700, 18104, 33192, 34883, 18257, 27872, 21216, 30952, 33123, 37927, 35891, 8829, 33876, 26575, 25355, 20016, 33237, 34756, 25448, 34249, 18805, 40287, 31020, 21171, 29816, 18528, 9843, 39055, 24733, 18123, 35782, 23410, 40203, 18376, 20446, 40564, 40067, 21242, 26610, 30420, 26717, 18234, 16346, 24766, 2282, 8990, 34008, 18523, 6924, 34961, 30355, 23653, 17689, 40311, 33211, 26124, 17606, 29071, 35046, 14369, 19080, 29050, 34562, 39457, 33642, 20920, 39159, 19222, 38296, 23905, 28873, 38740, 21227, 40125, 28965, 35009, 22688, 21897, 37469, 24018, 28473, 20499, 25497, 33480, 21201, 25221, 18960, 33427, 15270, 4966, 40295, 17426, 30431, 36611, 16194, 38710, 40541, 32334, 24314, 23358, 37250, 21370, 36817, 17921, 30168, 21419, 34336, 18732, 18992, 37125, 18990, 24172, 26338, 28798, 38598, 39565, 34577, 18783, 25171, 21158, 38890, 37573, 33753, 30172, 33586, 25523, 26848, 20639, 20657, 23119, 37134, 31373, 25270, 26797, 35589, 23576, 37820, 15900, 26349, 30592, 32589, 9739, 25729, 20691, 29368, 29639, 31900, 20104, 40024, 18173, 28411, 26813, 26256, 25658, 38607, 39286, 27333, 37447, 40204, 19159, 15073, 36572, 21364, 35102, 33440, 34321, 26608, 19929, 23939, 18201, 32419, 30583, 33481, 19027, 29247, 20700, 31043, 7283, 34674, 38749, 17988, 33926, 34227, 20337, 37161, 25526, 21540, 23392, 34298, 40321, 26252, 40082, 29570, 35972, 20513, 21159, 36492, 39102, 30634, 17888, 2512, 28244, 16337, 24940, 31918, 37591, 34753, 33622, 35403, 39612, 34561, 37508, 33520, 23846, 18308, 33777, 26688, 32780, 29072, 38218, 38191, 36061, 20710, 33863, 31863, 31684, 21129, 39384, 9245, 23986, 22428, 26305, 38719, 20073, 18373, 17803, 31943, 26056, 34511, 33627, 18170, 25855, 25110, 37170, 40459, 18172, 27340, 17922, 37708, 38452, 22549, 23277, 27120, 20386, 18640, 37058, 16694, 28195, 8045, 33351, 13243, 34660, 30180, 29860, 13439, 19645, 11024, 37657, 36240, 26143, 26974, 30035, 18075, 27750, 28245, 18851, 26858, 22643, 21178, 31873, 34514, 35767, 27802, 39241, 20552, 22860, 37448, 18241, 37073, 21522, 18461, 38689, 33786, 19110, 23412, 36875, 25570, 25504, 25556, 33884, 28049, 36306, 40493, 37941, 17860, 20603, 21411, 17792, 11496, 18826, 33272, 23540, 36960, 20908, 31184, 27632, 29847, 18076, 35584, 10309, 17831, 32737, 10947, 16541, 29790, 23213, 40429, 27189, 37059, 39590, 20817, 34278, 32455, 23097, 37287, 26793, 35364, 17709, 27336, 7352, 38902, 34596, 40639, 26934, 32885, 38247, 25734, 37646, 23022, 15079, 38780, 25060, 31405, 32053, 35617, 28872, 17678, 39074, 23091, 37780, 368, 33919, 20923, 16786, 29942, 32481, 3639, 20318, 26284, 20698, 23492, 22517, 28103, 589, 28565, 17723, 23439, 36742, 39823, 25952, 4277, 34658, 27789, 38166, 18008, 17093, 38733, 29975, 24903, 34770, 30328, 40592, 29911, 39485, 24513, 22716, 19186, 33927, 38012, 15510, 21089, 27411, 25251, 19353, 21017, 23684, 37140, 29305, 23766, 36171, 31311, 33974, 29598, 22721, 33713, 12836, 6009, 21505, 6561, 40586, 18232, 33936, 19248, 34736, 34346, 19190, 40692, 34395, 23889, 20677, 252, 21406, 28362, 29030, 17865, 36890, 31415, 21563, 26617, 38713, 30323, 26110, 5012, 35873, 24863, 28500, 28754, 36029, 2519, 29414, 20632, 30638, 38355, 20273, 14791, 17999, 39705, 34002, 38521, 25224, 37101, 27367, 20900, 30079, 21388, 39826, 18348, 26251, 21217, 18999, 6144, 38309, 17981, 23768, 31936, 26829, 3704, 18593, 39656, 37084, 18218, 20506, 25298, 18002, 27355, 18061, 29209, 20508, 16154, 35918, 23359, 26897, 22016, 39634, 29889, 28858, 27890, 27299, 28320, 39839, 20326, 20765, 37158, 27133, 35206, 39685, 27780, 21407, 31135, 24868, 39032, 37636, 17905, 20523, 37549, 21075, 11009, 38850, 26071, 18772, 22739, 7315, 22744, 21103, 28825, 39945, 33308, 37065, 32074, 10900, 11846, 24481, 39580, 38600, 18085, 21283, 18694, 24606, 29741, 18415, 17781, 24029, 33346, 20613, 40630, 20158, 10690, 15621, 38144, 23948, 23535, 39355, 25991, 27288, 20154, 28440, 18927, 20827, 17712, 18296, 28366, 20061, 15274, 39905, 33103, 12228, 37533, 31365, 38657, 19172, 40367, 23092, 26036, 30810, 31271, 36448, 37260, 37792, 30757, 28548, 37982, 27293, 15707, 19122, 15441, 29418, 24988, 40288, 32650, 10763, 30414, 23131, 21108, 39090, 24672, 34350, 32301, 28961, 30277, 40197, 30288, 2046, 35087, 27445, 25284, 13444, 27033, 38810, 25062, 38472, 19239, 24913, 1440, 27597, 25767, 19875, 39803, 17124, 30061, 23389, 18869, 33413, 39000, 19744, 18638, 37408, 26481, 21424, 34117, 26530, 24332, 27757, 37497, 21219, 40598, 40135, 35744, 38576, 31861, 26000, 17558, 11865, 20762, 24426, 40616, 28892, 23332, 21077, 20812, 17776, 20604, 31291, 33027, 30356, 40413, 37560, 19241, 39546, 37004, 37159, 18177, 36813, 34086, 10589, 18447, 18954, 33873, 35438, 34181, 34550, 33125, 25216, 37499, 20344, 18355, 18795, 22615, 26328, 24443, 21427, 19045, 36792, 33960, 37330, 38048, 30017, 21273, 33906, 31015, 6737, 30723, 18034, 23525, 34634, 32364, 27922, 33195, 24880, 33697, 32523, 29701, 29241, 39446, 25382, 38743, 22834, 26542, 18812, 20330, 35963, 37444, 28542, 33222, 10587, 11888, 17719, 30845, 19235, 25876, 14870, 34758, 36460, 28983, 17757, 38479, 27274, 18356, 38910, 18155, 37242, 34477, 29970, 37611, 37505, 29752, 35412, 35579, 21513, 19751, 26602, 40521, 39136, 39375, 29593, 37364, 30150, 39668, 36262, 18774, 28711, 14083, 30641, 25715, 35652, 24427, 24398, 28839, 29526, 20233, 40022, 39211, 17692, 21169, 21951, 33588, 27137, 32738, 32548, 32048, 30668, 25968, 29347, 29699, 30125, 38877, 18948, 20805, 33046, 35613, 32312, 35668, 23346, 13172, 26875, 18000, 37956, 24524, 36966, 15123, 30202, 36139, 21098, 37500, 24911, 20064, 38625, 24213, 32180, 35231, 19022, 35377, 37451, 28164, 11529, 37088, 17840, 35499, 17933, 34894, 22911, 38043, 35485, 28277, 37665, 20150, 20193, 34563, 33771, 27103, 26353, 15608, 21052, 27979, 39985, 33156, 24012, 24924, 37995, 21220, 38153, 20057, 38509, 33286, 17042, 26423, 33679, 18305, 23354, 37704, 20445, 20153, 21376, 32051, 21010, 37358, 33167, 22161, 23756, 29007, 18718, 35379, 21552, 29212, 31021, 23015, 33871, 19049, 40620, 22719, 39342, 39064, 20070, 20776, 12073, 2585, 34149, 23843, 19076, 11285, 19129, 36913, 32820, 22580, 18493, 8843, 18894, 29457, 29854, 29916, 24492, 29022, 19053, 21311, 32977, 21984, 23837, 17982, 25175, 40122, 25092, 29246, 36433, 17716, 34588, 28745, 14349, 18976, 17688, 20026, 21843, 34754, 29328, 34155, 30134, 36137, 36694, 22845, 30415, 36522, 25624, 33152, 38062, 16195, 19196, 1361, 21333, 29953, 34568, 29196, 20050, 17390, 40681, 21853, 30598, 26810, 23429, 40381, 25352, 23604, 26262, 40693, 29439, 22989, 28241, 33041, 34833, 20287, 22652, 24616, 25491, 28153, 30057, 20846, 19434, 30884, 33615, 40566, 32902, 36016, 20367, 24326, 28375, 20845, 36212, 37799, 13609, 39883, 32863, 19002, 33117, 23443, 28161, 17134, 23607, 22713, 23617, 15466, 17690, 32685, 9284, 34837, 40512, 24325, 18679, 18253, 29886, 39190, 24286, 22695, 39006, 40661, 27977, 38489, 29894, 37624, 30324, 20471, 17825, 30387, 25827, 37563, 21218, 31731, 20270, 34009, 32283, 28672, 33933, 32669, 29632, 1872, 34234, 21361, 27551, 36037, 36738, 26638, 18313, 36381, 29674, 23738, 37738, 34006, 18460, 33021, 13167, 40108, 18364, 35201, 19115, 23217, 21550, 19211, 32135, 36128, 36696, 20198, 17454, 27352, 39921, 19516, 18642, 15741, 36358, 18045, 33475, 34611, 22631, 29822, 40130, 9867, 18863, 18998, 34193, 33478, 39979, 37097, 27647, 31574, 29497, 9095, 33883, 16158, 34586, 19243, 20514, 33061, 19021, 29394, 25766, 35841, 29907, 26248, 18179, 34827, 34496, 20848, 21745, 17735, 34513, 21548, 32177, 37821, 31774, 28806, 14072, 39744, 32641, 14906, 28368, 22321, 20201, 39702, 18317, 11737, 20618, 34313, 5391, 4104, 33581, 28190, 28779, 35304, 25846, 26416, 18974, 38312, 30289, 19054, 20800, 40014, 24110, 33662, 25573, 35414, 20381, 35726, 29131, 26033, 23590, 28783, 37323, 18400, 5609, 40090, 23236, 18868, 29592, 29959, 31508, 32392, 29440, 30218, 20702, 38640, 11715, 39037, 19993, 23608, 7585, 5061, 27296, 18865, 27601, 10486, 32932, 27239, 23962, 28220, 21328, 38206, 25693, 39108, 19120, 34524, 18237, 30107, 37736, 35286, 40405, 23800, 33538, 29934, 33674, 18637, 26526, 30728, 34080, 17765, 21320, 27504, 32273, 22072, 23665, 28166, 33063, 34805, 26011, 20870, 38913, 19059, 26250, 26002, 3632, 24357, 18336, 33493, 16122, 32995, 32773, 18062, 25178, 39807, 32134, 20515, 3339, 18566, 38478, 26062, 38644, 38068, 25641, 18290, 29119, 23851, 6168, 35434, 26589, 25780, 23331, 30156, 18957, 32520, 40267, 37670, 37534, 28127, 35764, 17701, 23274, 33703, 33239, 25993, 33831, 11790, 20261, 21076, 15275, 32905, 35949, 35152, 38302, 32120, 38836, 33249, 39303, 35957, 34970, 23318, 8801, 25981, 14373, 18347, 32631, 20006, 20823, 31704, 40394, 33867, 35667, 12536, 20183, 32921, 32926, 16836, 29940, 37426, 33605, 31765, 24517, 20496, 35111, 8037, 20673, 33349, 33407, 23893, 19894, 33422, 20624, 20222, 23835, 29275, 33252, 33988, 27935, 32149, 27648, 31775, 30930, 19051, 17923, 26237, 39741, 21527, 40053, 22147, 21264, 31403, 40581, 29895, 2041, 20642, 37692, 39788, 18840, 18184, 34607, 31558, 29958, 33266, 28032, 31740, 39316, 26141, 39020, 27200, 40389, 33738, 39183, 32338, 23765, 24317, 34921, 38974, 23337, 38308, 25732, 38240, 13491, 17919, 19247, 24311, 29646, 18923, 38663, 22057, 24547, 11065, 21025, 38683, 38965, 35305, 33003, 20898, 38284, 17852, 17964, 32865, 26066, 7295, 14442, 38027, 25970, 26278, 20567, 37044, 20379, 30525, 39709, 18030, 25595, 35203, 40453, 26177, 40515, 38385, 18797, 11857, 33330, 36206, 14857, 21156, 33281, 21781, 39417, 21004, 31118, 31098, 35173, 33263, 38844, 26179, 38647, 20912, 33571, 26350, 14717, 36859, 28233, 39272, 5339, 34831, 26909, 38127, 39050, 33745, 39894, 16203, 18512, 32583, 6691, 29145, 21323, 27533, 18311, 29190, 38981, 6000, 23072, 35937, 36545, 21653, 38621, 23404, 14040, 28144, 39651, 21868, 29024, 37392, 30381, 23605, 14711, 23571, 20134, 29155, 39420, 17270, 40699, 22752, 15467, 29896, 23189, 31492, 36899, 29834, 29757, 21267, 38742, 14937, 899, 33334, 21524, 29738, 18239, 22258, 8665, 33122, 34981, 18214, 26843, 28416, 25357, 25649, 23569, 19780, 36972, 20606, 38344, 29471, 30424, 4605, 20139, 37962, 31961, 22899, 18366, 36852, 28142, 34397, 32666, 37190, 20240, 28036, 18050, 33408, 32199, 40084, 39506, 17955, 10569, 32346, 25627, 32137, 34987, 36799, 30189, 29455, 18073, 20144, 40237, 35289, 21539, 36790, 30228, 25339, 29949, 34030, 20825, 26089, 18324, 26070, 5780, 20107, 17731, 20810, 34368, 32024, 15709, 37069, 17679, 21430, 21127, 26584, 39170, 33178, 29817, 36873, 11392, 20027, 38904, 35657, 23029, 38060, 40419, 32985, 10869, 21495, 18537, 30909, 18918, 21472, 25362, 37377, 28919, 32414, 32661, 38937, 20370, 27590, 30350]\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "import numpy as np\n",
    "from tda_utils.density_filtration import sort_distances_per_point, indices_for_density_filtration\n",
    "from tda_utils.witness_complex import *\n",
    "\n",
    "dist_per_pt = sort_distances_per_point(dist_mat)\n",
    "\n",
    "# Load in ILC data\n",
    "sct_sparse = np_data\n",
    "dist_mat = dist_mat\n",
    "n, d = sct_sparse.shape\n",
    "print(\"n = \"+str(n))\n",
    "print(\"d = \"+str(d))\n",
    "print(\"shape of dist_mat: \"+str(dist_mat.shape))\n",
    "\n",
    "# Load in distances per point\n",
    "distances_per_point = dist_per_pt\n",
    "\n",
    "# time computation of density filtrations\n",
    "print(\"Timing computation of density filtrations...\")\n",
    "density_indices = dict()\n",
    "density_filtrations = dict()\n",
    "ks = [10, 100, 1000]\n",
    "#      10000]\n",
    "ps = [0.01, 0.05, 0.1, 0.2]\n",
    "for k in ks:\n",
    "    for p in ps:\n",
    "        print(\"\\tk = \"+str(k)+\", p = \"+str(p)+\":\")\n",
    "        start = time()\n",
    "        indices = indices_for_density_filtration(distances_per_point, k, p)\n",
    "        density_indices[(k, p)] = indices\n",
    "        mask = np.zeros(n, dtype=bool)\n",
    "        mask[indices] = True\n",
    "        sqr_mask = np.outer(mask, mask)\n",
    "        density_filtrations[(k, p)] = np.reshape(dist_mat[sqr_mask], (len(indices), len(indices)))\n",
    "        print(\"\\t\"+str(time()-start)+\" seconds\\n\")\n",
    "\n",
    "print(\"Timing computation of landmarks...\")\n",
    "landmark_indices = dict()\n",
    "landmark_mats = dict()\n",
    "pps = [0.05, 0.1, 0.2]\n",
    "for k in ks:\n",
    "    for p in ps:\n",
    "        for pp in pps:\n",
    "            print(\"\\tk = \"+str(k)+\", p = \"+str(p)+\", pp = \"+str(pp)+\":\")\n",
    "            start = time()\n",
    "            landmark_indices[(k, p, pp)], landmark_mats[(k, p, pp)] = choose_landmarks(density_filtrations[(k, p)], pp)\n",
    "            print(\"\\t\"+str(time()-start)+\" seconds\\n\")\n",
    "\n",
    "print(\"Printing numbers of landmarks...\")\n",
    "for k in ks:\n",
    "    for p in ps:\n",
    "        for pp in pps:\n",
    "            toople = (k, p, pp)\n",
    "            print(str(toople)+\": \"+str(len(landmark_indices[toople])))\n",
    "            if toople == (1000, 0.2, 0.2):\n",
    "                print(\"saving\")\n",
    "                landmark_inds = landmark_indices[toople]\n",
    "                dense_inds = density_indices[(k, p)]\n",
    "                true_inds = [dense_inds[ind] for ind in landmark_inds]\n",
    "                print(true_inds)\n",
    "                to_save = np.vstack([sct_sparse[ind, :] for ind in true_inds])\n",
    "                np.save(\"PanSquam_landmarks.npy\", to_save)\n",
    "                np.save(\"PanSquam_Racute_landmark_indices.npy\", true_inds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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23072, 35937, 36545, 21653, 38621, 23404, 14040, 28144, 39651, 21868, 29024, 37392, 30381, 23605, 14711, 23571, 20134, 29155, 39420, 17270, 40699, 22752, 15467, 29896, 23189, 31492, 36899, 29834, 29757, 21267, 38742, 14937, 899, 33334, 21524, 29738, 18239, 22258, 8665, 33122, 34981, 18214, 26843, 28416, 25357, 25649, 23569, 19780, 36972, 20606, 38344, 29471, 30424, 4605, 20139, 37962, 31961, 22899, 18366, 36852, 28142, 34397, 32666, 37190, 20240, 28036, 18050, 33408, 32199, 40084, 39506, 17955, 10569, 32346, 25627, 32137, 34987, 36799, 30189, 29455, 18073, 20144, 40237, 35289, 21539, 36790, 30228, 25339, 29949, 34030, 20825, 26089, 18324, 26070, 5780, 20107, 17731, 20810, 34368, 32024, 15709, 37069, 17679, 21430, 21127, 26584, 39170, 33178, 29817, 36873, 11392, 20027, 38904, 35657, 23029, 38060, 40419, 32985, 10869, 21495, 18537, 30909, 18918, 21472, 25362, 37377, 28919, 32414, 32661, 38937, 20370, 27590, 30350]\n"
     ]
    }
   ],
   "source": [
    "landmarks = np.load(\"PanSquam_landmarks.npy\")\n",
    "\n",
    "landmarks = true_inds\n",
    "print(true_inds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42728, 2)\n",
      "(1709, 1152)\n",
      "(1709, 2)\n"
     ]
    }
   ],
   "source": [
    "N, d = np_data.shape\n",
    "genes = pd_data.columns\n",
    "\n",
    "UMAP = np.array(UMAP)\n",
    "print(UMAP.shape)\n",
    "\n",
    "UMAP_landmark = np.zeros((1,2))\n",
    "data_landmark = np.zeros((1,d))\n",
    "\n",
    "#Going through all of the cells, if index in landmarks we should pull the associated gene expression data\n",
    "for i in landmarks:\n",
    "    next_cell = np_data[i,:]\n",
    "    next_cell = np.reshape(next_cell, (1, d))\n",
    "    data_landmark = np.append(data_landmark, next_cell, axis = 0)\n",
    "        \n",
    "    next_embedding = UMAP[i,:]\n",
    "    next_embedding = np.reshape(next_embedding, (1,2))\n",
    "    UMAP_landmark = np.append(UMAP_landmark, next_embedding, axis = 0)\n",
    "\n",
    "#To get the indices to work out I have a row of zeros at the top that I need to omit\n",
    "data_landmark = data_landmark[1:, :]    \n",
    "UMAP_landmark = UMAP_landmark[1:, :]\n",
    "\n",
    "print(data_landmark.shape)\n",
    "print(UMAP_landmark.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "frame1 = plt.scatter(UMAP[:,0], UMAP[:,1], s=1, c = \"silver\")\n",
    "frame1 = plt.scatter(UMAP_landmark[:,0], UMAP_landmark[:,1], s=1, c = \"red\")\n",
    "plt.title('Racute - UMAP')\n",
    "#plt.xlim(-30000,25000)\n",
    "frame1.axes.get_xaxis().set_ticks([])\n",
    "frame1.axes.get_yaxis().set_ticks([])\n",
    "plt.ylabel('UMAP2')\n",
    "plt.xlabel('UMAP1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Persistence Diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rips = Rips()\n",
    "#diagrams = rips.fit_transform(dist_mat, distance_matrix=True, metric=\"euclidean\")\n",
    "#rips.plot(diagrams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigen plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from manifold_utils.mSVD import eigen_plot, eigen_calc_from_dist_mat, eps_projection, eigen_plot_numPoints, eigen_calc_from_dist_mat_withNumPoints\n",
    "from manifold_utils.iga import chakraborty_express, iga"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "  0%|                                                                                         | 0/1709 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24812\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "  0%|                                                                           | 1/1709 [18:29<526:32:36, 1109.81s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40019\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|                                                                           | 1/1709 [31:00<882:28:47, 1860.03s/it]\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-17-e4be761d6b5f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlandmarks\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[0mcenter\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlandmarks\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m     \u001b[0mradii\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0meigval_list\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0meigvec_list\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0meigen_calc_from_dist_mat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdist_mat\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcenter\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mradint\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m     \u001b[0mrmin\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mradii\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Documents\\GitHub\\manifold_learning\\manifold_utils\\mSVD.py\u001b[0m in \u001b[0;36meigen_calc_from_dist_mat\u001b[1;34m(cloud, dist_mat, center_ind, radint)\u001b[0m\n\u001b[0;32m    177\u001b[0m             \u001b[0mnew_cands\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstack\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mcloud\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mcand\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mcand\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mcands\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    178\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 179\u001b[1;33m                 \u001b[0mpoints\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvstack\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mpoints\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnew_cands\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    180\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mNameError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    181\u001b[0m                 \u001b[0mpoints\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnew_cands\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mvstack\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;32mc:\\users\\hmkri\\desktop\\riesenfeld pearson\\lib\\site-packages\\numpy\\core\\shape_base.py\u001b[0m in \u001b[0;36mvstack\u001b[1;34m(tup)\u001b[0m\n\u001b[0;32m    281\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marrs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    282\u001b[0m         \u001b[0marrs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0marrs\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 283\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_nx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marrs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    284\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    285\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mconcatenate\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "for i in tqdm(range(len(landmarks))):\n",
    "    print(landmarks[i])\n",
    "    center = landmarks[i]\n",
    "    radii, eigval_list, eigvec_list = eigen_calc_from_dist_mat(np_data, dist_mat, center, radint = 10)\n",
    "\n",
    "    rmin = radii[0]\n",
    "    rmax = radii[-1]\n",
    "    \n",
    "    eigen_plot(eigval_list, radii, rmin, rmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dgms = ripser(data_landmark, maxdim=1)['dgms']\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plot_diagrams(dgms, plot_only=[0], ax=plt.subplot(121))\n",
    "plot_diagrams(dgms, plot_only=[1], ax=plt.subplot(122))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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E1AYwPO2PAUpE1AYcP34c69evZ3jaEQcRERG1AT179sTWrVtx5swZxMXFad2OW2CAEhG5KUVRcPbsWdx4440AgJEjR2rckXvhJVwiIjekKApmzpyJgQMH4siRI1q345YYoEREbqYqPBMTE3Hp0iVkZ2dr3ZJbYoASEbmR6uFZNWDokUce0bott8QAJSJyE3WFJ0fbOg4DlIjIDTA8Wx8DlIjIDZSVlSE7O5vh2Yp4GwsRkRvw8/PDl19+iT179uCuu+7Sup02gWegREQuSlEUbN26Vf25ffv2DM9WxAAlInJBVXPbxsTE4LXXXtO6nTaJAUpE5GJqTgxfNdMQtS4GKBGRC+FTVZwHA5SIyEUwPJ0LA5SIyAWICGbNmsXwdCIMUCIiF6DT6dC7d294eHgwPJ2ETkRE6ybcRUlJCYxGI8xmMwICArRuh4jc0A8//IAePXpo3YZbauoxnGegREROSlEUvP766ygqKlKXMTydBwOUiMgJVQ0YWrBgAcaPHw+r1ap1S1QDA5SIyMnUHG07Z84c6PV6rduiGhigREROhLequA4GKBGRk2B4uhYGKBGRk3jppZcYni6EAUpE5CSmTZuGiIgIhqeL0DxA8/Ly8NhjjyEoKAh+fn7o378/0tLS1PUigsWLFyMsLAy+vr4YPXo0jh49avMe5eXlmD17Njp16oR27dph0qRJOHv2rE1NUVER4uPjYTQaYTQaER8fj+LiYpua3Nxc3H333WjXrh06deqEOXPmoKKiwnEfnoiomu7du+PYsWMMTxehaYAWFRXh9ttvh5eXF7788ktkZ2fjzTffRIcOHdSa5cuXY8WKFVi1ahUOHz4Mk8mEO++8E5cvX1Zr5s2bh88++wwbN27Evn37cOXKFcTGxtoM+3700UeRkZGBbdu2Ydu2bcjIyEB8fLy63mq1IiYmBqWlpdi3bx82btyITz/9FM8++2zr7AwianMURcGcOXPw5Zdfqsv8/Pw07IiaRDT0/PPPy4gRI+pdryiKmEwmWbZsmbqsrKxMjEajrFmzRkREiouLxcvLSzZu3KjW5OXliYeHh2zbtk1ERLKzswWAHDx4UK1JSUkRAHLs2DEREdm6dat4eHhIXl6eWrNhwwYxGAxiNpsb9XnMZrMAaHQ9EbVdVqtVpk+fLgDE19dX8vPztW6pzWvqMVzTM9AtW7Zg0KBBePDBBxEcHIwBAwbg3XffVdefOnUKBQUFGDdunLrMYDBg1KhROHDgAAAgLS0NlZWVNjVhYWGIjIxUa1JSUmA0GjFkyBC1ZujQoTAajTY1kZGRCAsLU2vGjx+P8vJym0vK1ZWXl6OkpMTmRUR0PTVH2yYmJsJkMmndFjWRpgF68uRJvP322+jevTu++uorzJgxA3PmzMG6desAAAUFBQCAkJAQm98LCQlR1xUUFMDb2xsdO3ZssCY4OLjW9oODg21qam6nY8eO8Pb2VmtqWrp0qfqdqtFoRERERFN3ARG1MbxVxX1oGqCKomDgwIF47bXXMGDAAEyfPh1PPvkk3n77bZs6nU5n87OI1FpWU82auuqbU1PdwoULYTab1deZM2ca7ImI2jaGp3vRNEBDQ0PRq1cvm2W33norcnNzAUC9pFHzDLCwsFA9WzSZTKioqLCZbLmumvPnz9fa/oULF2xqam6nqKgIlZWVtc5MqxgMBgQEBNi8iIjqs27dOoanG9E0QG+//XZ8//33Nst++OEHdOnSBQDQrVs3mEwmJCUlqesrKiqwe/duDB8+HAAQFRUFLy8vm5r8/HxkZWWpNcOGDYPZbEZqaqpac+jQIZjNZpuarKws5OfnqzXbt2+HwWBAVFSUnT85EbVF8fHxiI+PZ3i6CwcOaLqu1NRU8fT0lCVLlsjx48fl448/Fj8/P1m/fr1as2zZMjEajbJ582bJzMyUKVOmSGhoqJSUlKg1M2bMkPDwcElOTpb09HQZO3as9OvXTywWi1ozYcIE6du3r6SkpEhKSor06dNHYmNj1fUWi0UiIyMlOjpa0tPTJTk5WcLDwyUhIaHRn4ejcImoJqvVanMsIufV1GO4pgEqIvL5559LZGSkGAwGueWWWyQxMdFmvaIosmjRIjGZTGIwGGTkyJGSmZlpU3Pt2jVJSEiQwMBA8fX1ldjYWMnNzbWpuXjxosTFxYm/v7/4+/tLXFycFBUV2dTk5ORITEyM+Pr6SmBgoCQkJEhZWVmjPwsDlIiqs1qt8tRTT8njjz/OEHUBTT2G60REtD0Hdh9NfZo5EbkvRVEwc+ZMJCYmQqfTYc+ePRgxYoTWbVEDmnoM13wqPyIid1MzPNetW8fwdEMMUCIiO6orPDlgyD0xQImI7ITh2bYwQImI7CQzMxMffPABw7ON8NS6ASIid9GvXz98+umnKC4uZni2AQxQIqIWUBQFhYWF6sxpsbGxGndErYWXcImImqlqbtvBgwfjxx9/1LodamUMUCKiZqg+MXxeXl69jz0k98UAJSJqorqeqvLQQw9p3Ra1MgYoEVET8JFkVIUBSkTUSAxPqo4BSkTUSFeuXMGhQ4cYngSAt7EQETVaQEAAkpOTsX//fkyaNEnrdkhjPAMlImqAoijYvXu3+nNQUBDDkwAwQImI6lX1nefo0aPx9ttva90OORkGKBFRHWoOGPL399e6JXIyDFAioho42pYagwFKRFQNw5MaiwFKRPRfIsLwpEZjgBIR/ZdOp4PJZGJ4UqPoRES0bsJdlJSUwGg0wmw2IyAgQOt2iKiZjhw5gr59+2rdBrWyph7DeQZKRG2aoihYuXIlSktL1WUMT2oMBigRtVlVA4aeeeYZ3H333VAUReuWyIUwQImoTao52vaJJ56AhwcPidR4/NNCRG0Ob1Uhe2CAElGbwvAke2GAElGbsmDBAoYn2QUDlIjalClTpuCGG25geFKL8XmgRNSmDBgwACdOnOC92tRiPAMlIremKAqeeeYZ7N+/X13G8CR7YIASkdtSFAUzZ87EypUrERMTg0uXLmndErkRBigRuaWq8ExMTIROp8OqVasQGBiodVvkRhigROR2aoYnBwyRIzBAicitMDyptTBAicitvPPOOwxPahW8jYWI3MoTTzyBbdu24cEHH2R4kkMxQInI5SmKAp1OB51OB4PBgH/+85/Q6XRat0VujpdwicilVc1tO3/+fIgIADA8qVXwDJSIXFbNieEfffRRDB48WOu2qI3gGSgRuaS6nqrC8KTWxAAlIpfDR5KRM2CAEpFLYXiSs2CAEpFLSU1NxbvvvsvwJM1xEBERuZShQ4di3bp1EBGGJ2mKAUpETk9RFBQXF6uTwcfFxWncEREv4RKRk6v6znPYsGHIz8/Xuh0iFQOUiJxW9QFDx48fR0pKitYtEakYoETklOoabXv//fdr3RaRigFKRE6Ht6qQK2CAEpFTYXiSq2CAEpFTKSoqwo4dOxie5PR4GwsROZWgoCB8/fXXOHjwICZPnqx1O0T14hkoEWlOURQcOnRI/blz584MT3J6DFAi0lTVd57Dhw/Hhg0btG6HqNEYoESkmeoDhkQEVqtV65aIGo0BSkSa4GhbcnUMUCJqdQxPcgcMUCJqVQxPchcMUCJqVTqdDl5eXgxPcnk6ERGtm3AXJSUlMBqNMJvNCAgI0LodIqclIjh8+DBuu+02rVshUjX1GM4zUCJyOEVRsGbNGlRUVAD4+SyU4UmurlkBev78ecTHxyMsLAyenp7Q6/U2LyKiKoqiYObMmZg5cyYefvhh8KIXuYtmTeU3bdo05Obm4qWXXkJoaCh0Op29+yIiN1AVnomJidDpdJg8eTKPF+Q2mhWg+/btw969e9G/f39790NEbqJmeHLAELmbZl3CjYiI4GUYIqoXw5PagmYF6MqVK7FgwQKcPn3azu0QkTuYP38+w5PcXqMv4Xbs2NHmu4vS0lL84he/gJ+fH7y8vGxqL126ZL8OicjlTJ48GWvXrsVf/vIXhie5rUYH6MqVKx3ZBxG5kV/+8pc4efIkgoKCtG6FyGEaHaBTp051ZB9E5MIURcHChQsRFxeHvn37AgDDk9xes74D1ev1KCwsrLX84sWLzb4PdOnSpdDpdJg3b566TESwePFihIWFwdfXF6NHj8bRo0dtfq+8vByzZ89Gp06d0K5dO0yaNAlnz561qSkqKkJ8fDyMRiOMRiPi4+NRXFxsU5Obm4u7774b7dq1Q6dOnTBnzhz1pm8iql/V3LbLly/HnXfeicuXL2vdElGraFaA1jcCt7y8HN7e3k1+v8OHDyMxMVH9l2uV5cuXY8WKFVi1ahUOHz4Mk8lU6y/ovHnz8Nlnn2Hjxo3Yt28frly5gtjYWJvnCj766KPIyMjAtm3bsG3bNmRkZCA+Pl5db7VaERMTg9LSUuzbtw8bN27Ep59+imeffbbJn4WoLak5Mfybb74Jf39/rdsiah3SBG+99Za89dZb4uHhIUuWLFF/fuutt2TFihVy7733Sv/+/ZvylnL58mXp3r27JCUlyahRo2Tu3LkiIqIoiphMJlm2bJlaW1ZWJkajUdasWSMiIsXFxeLl5SUbN25Ua/Ly8sTDw0O2bdsmIiLZ2dkCQA4ePKjWpKSkCAA5duyYiIhs3bpVPDw8JC8vT63ZsGGDGAwGMZvNjf4sZrNZADTpd4hcldVqlenTpwsA0el08tFHH2ndElGLNPUY3qSJFP74xz9WhS7WrFljc7nW29sbXbt2xZo1a5oU4LNmzUJMTAzuuOMOvPrqq+ryU6dOoaCgAOPGjVOXGQwGjBo1CgcOHMD06dORlpaGyspKm5qwsDBERkbiwIEDGD9+PFJSUmA0GjFkyBC1ZujQoTAajThw4AB69uyJlJQUREZGIiwsTK0ZP348ysvLkZaWhjFjxtTZe3l5OcrLy9WfS0pKmvTZiVwVH0lG1MSZiE6dOgUAGDNmDDZv3oyOHTu2aOMbN25EWloavvnmm1rrCgoKAAAhISE2y0NCQpCTk6PWeHt71+ojJCRE/f2CggIEBwfXev/g4GCbmprb6dixI7y9vdWauixduhQvv/zy9T4mkdt56623GJ7U5jXrO9Bdu3a1ODzPnDmDuXPn4uOPP4aPj0+9dTXnzRSR686lWbOmrvrm1NS0cOFCmM1m9XXmzJkG+yJyF08++SRGjx7N8KQ2rVlz4QLA2bNnsWXLFuTm5tYarbpixYrr/n5aWhoKCwsRFRWlLrNardizZw9WrVqF77//HsDPZ4ehoaFqTWFhoXq2aDKZUFFRgaKiIptALywsxPDhw9Wa8+fP19r+hQsXbN7n0KFDNuuLiopQWVlZ68y0OoPBAIPBcN3PSuQOqv+Dsn379tixYwc8PPhERGq7mvWnf8eOHejZsydWr16NN998E7t27cLatWvx/vvvIyMjo1HvER0djczMTGRkZKivQYMGIS4uDhkZGbjppptgMpmQlJSk/k5FRQV2796thmNUVBS8vLxsavLz85GVlaXWDBs2DGazGampqWrNoUOHYDabbWqysrKQn5+v1mzfvh0Gg8Em4Inaqqq5bauPU2B4UpvXnJFKgwcPlpdeeklERNq3by8//vijXL58WSZNmiSrV69uzluKiNiMwhURWbZsmRiNRtm8ebNkZmbKlClTJDQ0VEpKStSaGTNmSHh4uCQnJ0t6erqMHTtW+vXrJxaLRa2ZMGGC9O3bV1JSUiQlJUX69OkjsbGx6nqLxSKRkZESHR0t6enpkpycLOHh4ZKQkNCk/jkKl9xR9dG2Hh4ekpmZqXVLRA7R1GN4swK0ffv2cuLECRER6dChg2RlZYmISEZGhnTp0qU5bykitQNUURRZtGiRmEwmMRgMMnLkyFp/ea9duyYJCQkSGBgovr6+EhsbK7m5uTY1Fy9elLi4OPH39xd/f3+Ji4uToqIim5qcnByJiYkRX19fCQwMlISEBCkrK2tS/wxQcje8VYXakqYew3UiTX8umclkws6dO9GrVy/07t0bS5cuxaRJk/Ddd9/h9ttvx5UrV+x7muwiSkpKYDQaYTabERAQoHU7RC3CW1WorWnqMbxZg4iGDh2K/fv3o1evXoiJicGzzz6LzMxMbN68GUOHDm3OWxKRE2F4El1fswJ0xYoV6lnm4sWLceXKFQDREH8AACAASURBVHzyySe4+eab1ckWiMh17d69m+FJdB3NuoRLdeMlXHInq1atQocOHRie1Ga0yiVcACguLsamTZvw448/4re//S0CAwORnp6OkJAQdO7cublvS0QaURQFpaWl6mTwCQkJGndE5NyadSPXkSNH0KNHD7z++ut444031EeDffbZZ1i4cKFdGyQix6v6znPUqFG4dOmS1u0QuYRmBej8+fMxbdo0HD9+3GYavokTJ2LPnj12a46IHK/6gKGMjAzs27dP65aIXEKzAvTw4cOYPn16reWdO3ducPJ1InIudY22nTRpktZtEbmEZgWoj49PnY/u+v7773HDDTe0uCkicjzeqkLUMs0K0HvuuQevvPIKKisrAfz8JJPc3FwsWLAAkydPtmuDRGR/DE+ilmtWgL7xxhu4cOECgoODce3aNYwaNQo333wz/P39sWTJEnv3SER2dv78eXz++ecMT6IWaNF9oLt27UJaWhoURcHAgQNxxx132LM3l8P7QMmVHD9+HN9++y0eeughrVshcgoOvw9UURR88MEH2Lx5M06fPg2dTodu3brBZDI16mHXRKQNRVGQlZWFvn37AgC6d++O7t27a9wVketq0iVcEcGkSZPwm9/8Bnl5eejTpw969+6NnJwcTJs2Dffdd5+j+iSiFqh6nufgwYPx5Zdfat0OkVto0hnoBx98gD179mDHjh0YM2aMzbqdO3fi3nvvxbp16/D444/btUkiar6q8ExMTIROp8PFixe1bonILTTpDHTDhg144YUXaoUnAIwdOxYLFizAxx9/bLfmiKhlaoYnBwwR2U+TAvTIkSOYMGFCvesnTpyI7777rsVNEVHLMTyJHKtJAXrp0iWEhITUuz4kJARFRUUtboqIWobhSeR4TQpQq9UKT8/6vzbV6/WwWCwtboqIWkZEUFpayvAkcqAmDSISEUybNg0Gg6HO9eXl5XZpiohaRq/X48MPP8T06dPxy1/+Uut2iNxSkwJ06tSp163hCFwibSiKgvXr1yMuLg56vR56vZ7hSeRATQrQtWvXOqoPImqB6nPbfv3113j//fe1bonI7TVrLlwich41J4YfO3as1i0RtQkMUCIXxqeqEGmHAUrkohieRNpigBK5qHnz5jE8iTTEACVyUePHj4evry/Dk0gjTX6cGRE5h5iYGJw8eRImk0nrVojaJJ6BErkIRVHw4osv4scff1SXMTyJtMMAJXIBVQOGlixZgujoaFy7dk3rlojaPAYokZOrOdr21Vdfha+vr9ZtEbV5DFAiJ8ZbVYicFwOUyEkxPImcGwOUyEktX76c4UnkxBigRE7qySefRFRUFMOTyEnxPlAiJyIi0Ol0AICgoCAcPHiwwYfYE5F2eAZK5CQURcHMmTOxevVqdRnDk8h58W8nkROoCs/ExETo9Xrceeed6N69u9ZtEVEDeAZKpLHq4anT6fDBBx8wPIlcAAOUSEM1w5MDhohcBwOUSCMMTyLXxgAl0sjWrVsZnkQujIOIiDQSGxuLl19+GTfddBPDk8gF6UREtG7CXZSUlMBoNMJsNiMgIEDrdsgJKYqC8vJyTgZP5ISaegznJVyiVlL1neeECRNQWlqqdTtE1EIMUKJWUH3A0N69e7Fnzx6tWyKiFmKAEjlYXaNtJ06cqHVbRNRCDFAiB+KtKkTuiwFK5CAMTyL3xgAlcpDc3Fxs2rSJ4UnkpngfKJGDdO3aFTt27MB//vMfTJkyRet2iMjOGKBEdqQoCk6cOIEePXoAAPr374/+/ftr3BUROQIv4RLZiaIoePrppxEVFYX9+/dr3Q4RORgDlMgOqsLznXfeQWlpKU6fPq11S0TkYAxQohaqHp5VA4bi4uK0bouIHIwBStQCdYUnR9sStQ0MUKJmYngStW0MUKJmslgsyMvLY3gStVG8jYWomby9vbFp0ybs27cP0dHRWrdDRK2MZ6BETaAoCjZt2oSqx+gaDAaGJ1EbxQB1UearldiQmosP9p/CueJrWrfTJlR95/nggw/iueee07odItIYL+G6oCNni/HYXw+hpMwCAFiy9T9465EBuKtPqMadua+aA4YGDBigdUtEpDGegbqgVz7PVsMTACqtgv/711FUWhUNu3JfHG1LRHVhgLoYRRF8k1NUa/lPV8px6qdSDTpybwxPIqoPA9TFeHjocGOgX63lBk8PhAT4aNCRe5s9ezbDk4jqxAB1QXOju9da9qvbu8Ho66VBN+5t+PDh8PLyYngSUS06qRqPTy1WUlICo9EIs9mMgIAAh25r7/EL+OTwGZRVKri7Xyju6d/Zodtry3JyctClSxet2yAiB2vqMZyjcF3UL7vfgF92v0HrNtyOoij4wx/+gCeffBJhYWEAwPAkojrxEi7RfymKgpkzZ2Lx4sW44447UFFRoXVLROTEGKBE+F94JiYmQqfT4YUXXoC3t7fWbRGRE2OAUptXMzw5YIiIGkPTAF26dCkGDx4Mf39/BAcH495778X3339vUyMiWLx4McLCwuDr64vRo0fj6NGjNjXl5eWYPXs2OnXqhHbt2mHSpEk4e/asTU1RURHi4+NhNBphNBoRHx+P4uJim5rc3FzcfffdaNeuHTp16oQ5c+bwMp6bY3gSUXNpGqC7d+/GrFmzcPDgQSQlJcFisWDcuHEoLf3fhADLly/HihUrsGrVKhw+fBgmkwl33nknLl++rNbMmzcPn332GTZu3Ih9+/bhypUriI2NhdVqVWseffRRZGRkYNu2bdi2bRsyMjIQHx+vrrdarYiJiUFpaSn27duHjRs34tNPP8Wzzz7bOjuDNPHKK68wPImoecSJFBYWCgDZvXu3iIgoiiImk0mWLVum1pSVlYnRaJQ1a9aIiEhxcbF4eXnJxo0b1Zq8vDzx8PCQbdu2iYhIdna2AJCDBw+qNSkpKQJAjh07JiIiW7duFQ8PD8nLy1NrNmzYIAaDQcxmc539lpWVidlsVl9nzpwRAPXWk/M5e/as9OzZUz766COtWyEijZnN5iYdw53qO1Cz2QwACAwMBACcOnUKBQUFGDdunFpjMBgwatQoHDhwAACQlpaGyspKm5qwsDBERkaqNSkpKTAajRgyZIhaM3ToUBiNRpuayMhI9dYFABg/fjzKy8uRlpZWZ79Lly5VLwkbjUZERETYYzdQK+rcuTOOHDnCM08iajKnCVARwfz58zFixAhERkYCAAoKCgAAISEhNrUhISHquoKCAnh7e6Njx44N1gQHB9faZnBwsE1Nze107NgR3t7eak1NCxcuhNlsVl9nzpxp6semVqYoCmbNmoUNGzaoyzjaloiaw2kmUkhISMCRI0ewb9++Wut0Op3NzyJSa1lNNWvqqm9OTXUGgwEGg6HBPsh5VJ8Y/t1338Xtt9+OG2+8Ueu2iMhFOcUZ6OzZs7Flyxbs2rUL4eHh6nKTyQQAtc4ACwsL1bNFk8mEiooKFBUVNVhz/vz5Wtu9cOGCTU3N7RQVFaGysrLWmSm5nppPVXn//fcZnkTUIpoGqIggISEBmzdvxs6dO9GtWzeb9d26dYPJZEJSUpK6rKKiArt378bw4cMBAFFRUfDy8rKpyc/PR1ZWllozbNgwmM1mpKamqjWHDh2C2Wy2qcnKykJ+fr5as337dhgMBkRFRdn/w1Or4SPJiMghHDacqRFmzpwpRqNRvv76a8nPz1dfV69eVWuWLVsmRqNRNm/eLJmZmTJlyhQJDQ2VkpIStWbGjBkSHh4uycnJkp6eLmPHjpV+/fqJxWJRayZMmCB9+/aVlJQUSUlJkT59+khsbKy63mKxSGRkpERHR0t6erokJydLeHi4JCQkNPrzNHUEFzme1WqV6dOnCwDR6XQcbUtE9WrqMVzTAAVQ52vt2rVqjaIosmjRIjGZTGIwGGTkyJGSmZlp8z7Xrl2ThIQECQwMFF9fX4mNjZXc3FybmosXL0pcXJz4+/uLv7+/xMXFSVFRkU1NTk6OxMTEiK+vrwQGBkpCQoKUlZU1+vMwQJ3PJ598wvAkokZp6jGcjzOzo9Z8nBk1jojgmWeewaBBg3jZlogaxMeZUZunKAosFgu8vb2h0+mwcuVKrVsiIjfkFKNwieylasDQAw88wHmMiciheAZKbqPmaNu9e/ciOjpa67aIyE3xDJTcQl23qjA8iciRGKDk8nifJxFpgQHqwiosCsoqrdcvdGMMTyLSCr8DdUFllVa8/Hk2NqefRaVVQfStIXjtvj64wb/tzct74sQJrF+/nuFJRK2OAeqCXtv6H2xIzVV/Tso+jytlFmx4aqiGXWmjR48e2LZtG3JychAXF6d1O0TUhvASrgv6NO1srWUpJy/ibNFVDbppfYqiIDf3f/+AGDFiBMOTiFodA9TFiAgqrEqd65S6F7uVqu88Bw4ciCNHjmjdDhG1YQxQF6PT6eDnXfvKu4cObv8daPUBQ5cuXUJ2drbWLRFRG8YAdTGKIjBfq6y9XIAzbnwJt67Rto888ojWbRFRG8YAdTEeHjrcYvKvtdzf4Inwjr4adOR4vFWFiJwRA9QFPT/xFnjpdTbLnrmzR52Xdl0dw5OInJX7HXHbgDE9g7F1zi+xKf0syisVxPYNxaCugVq35RDl5eXIzs5meBKR0+HzQO2IzwN1jCtXrmDv3r2YOHGi1q0QkRtr6jGcl3DJ6SiKgn//+9/qz+3bt2d4EpHTYYCSU1EUBTNnzkRsbCyWLFmidTtERPVigJLTqArPxMRE6HQ6dOnSReuWiIjqxQAlp1AzPDlgiIicHQPUhf1w/jIyz5rh6uPAGJ5E5Ip4G4sLunC5HNM/+gbpucUAgK5BflgTH4VbTK438ldE8PTTTzM8iVqB1WpFZWXtmczaEm9vb3h42OfckQHqghZtyVLDEwBOX7yKORu+xfZnRmnYVfPodDpERkbCw8MDH374IcOTyAFEBAUFBSguLr5+sZvz8PBAt27d4O3t3eL3YoC6GBFBUvb5Wst/OH8FJy9cwU03tNegq5ZJSEjAuHHj0KNHD61bIXJLVeEZHBwMPz8/6HS66/+SG1IUBefOnUN+fj5uvPHGFu8HBqiLqXoaS80J5XU6oJ3BNf53KoqC5cuX46mnnkJg4M8zKDE8iRzDarWq4RkUFKR1O5q74YYbcO7cOVgsFnh5ebXovTiIyAXFD619e8edt4YgJMBHg26apmpu24ULF2L8+PGwWCxat0Tk1qq+8/Tz89O4E+dQdenWarW2+L1c45SFbDxzZw946XVYl5KDCquCSf3C8MJdt2rd1nXVnBh+7ty58PTkH0Gi1tBWL9vWZM/9wDNQF1RQUoatmQW4WFqBy2UWJP/nPI4XXtG6rQbxqSpE5G4YoC5o0b+O4vvzl9Wfz5eUY97Gb532flCGJxG5IwaoixER7Pq+sNby0xev4scLpRp0dH0vvfQSw5OI3A4D1MXodDp08K09csxDBxjrWO4Mpk2bhoiICIYnEbkVjuBwQb+6vSve2P6DzbLYvmG4wd+gUUcN6969O44dO8ZRgETkVhigLmjWmJvh5+2JjYdzUVapILZvKOZEd9e6LZWiKJg3bx4mTpyoPseT4UnkfEpL6//aR6/Xw8fHp1G1Hh4e8PX1vW5tu3btmtGl8+IlXBek0+nwxIhuWPNYFN6Jj8Jvx/eEj5de67YA/G/A0J///GdMnjwZBQUFWrdERPVo3759va/Jkyfb1AYHB9dbW/OB9127dq2zrrkWLVqEnj17Ij4+HiUlJfjXv/6FgQMHYuzYscjMzGz2+7YUz0Bd0E9XyvH0+nSknr4EAPjFDe3w9mNR6BHir2lfNUfbJiYmwmQyadoTEbm25ORkXLx4Ed988w3+9Kc/YfLkybh48SL+/ve/w2q1YtasWUhOTtakNwaoC1q85agangDw44VSzNnwLbbNG6lZT7xVhcj1XLlS//3jer3tVa3Cwtqj/6vUfLrJ6dOnW9RXdenp6Zg6dSr8/f3x+9//Hp999hmee+453HzzzQCAoKAgVFRU2GVy+KZigLoYEcFXR2tfFj1WcFmzyeQZnkSuqSnfSTqq9np69uyJrVu3YvDgwUhOToaI4PXXX8e4cePg6emJwsJCTcITYIC6HJ1OBx8vPSqttnPI6gD4eWvzv/Ojjz5ieBKRQ0yaNAlffvklIiIiEBoain/+859ISkpCv3794Ofnh7fffluz3higLijU6IPLZbaXXtr7eMJk1GYy+cceewy7du3CHXfcwfAkIrvS6XRYs2aNzbInnngCv/rVrzSf35cB6mJEBKd+qj1E/HKZBad/KkXXTq0zTFxRFIgI9Ho99Ho9Pvjgg1bZLhER4ByT4/M2Fhej0+ng41n3LSvenq3zv7PqO88nnnjCLo8EIiJyRQxQF/Tw4Ihay0b1uAFhHXzrqLav6gOGPvroI6SkpDh8m0REzoiXcF3Q7ybcAgHw98NnUG5RcFcfExZP6u3w7dY12nbEiBEO3y4RkTNigLogb08PvBTbCy/F9oKItMp3AbxVhYjIFi/hujiGJxGRNhigdF2ZmZlYu3Ytw5OIqBpewnVBiiJ4Z89JbDyci/JKBTF9Q/HcuJ7w9XbMhPL9+vXD5s2bUVRUxPAkIvovBqgLemvHcby147j683v7TqHAXIa/xA202zYURUFhYaE6GXxMTIzd3puIyB3wEq4L+uDA6VrLvszKR2FJmV3eX1EUzJw5E4MHD8aJEyfs8p5ERO6GAepiRAQl1yprLVcEdS5vqqrwTExMRF5eHtLT01v8nkRE7ogB6oKkvhUtHJBbPTyrBgw99NBDLXtTIiI3xQB1MQ3dtmJVmv++dYUnBwwRkTMYOXIkfv3rX9davnr1avj5+Wk2pSgD1MX8PHFC3ev0Hs07BWV4EpGzEhFkZGQgKiqq1rq0tDT069ev1sO/WwsD1MXodDqMuLlTreWhAQb84obmPYnlypUrSE1NZXgSUYPKLVYcOnkRP5y/3GrbPH78OC5fvlxvgNa1vLXwNhYXZK5jsNA1i9LsWYkCAgKQnJyM/fv3Y9KkSS1tj4jc0P4TP2HOhm9xsbQCADD8F0FYEx+FAB8vh243LS0Ner0effv2tVleXl6Oo0ePYu7cuQ7dfkN4BupiRARHzpprLS++Wonsc7WX10dRFHz99dfqz0FBQQxPIqpTWaUVCX9LV8MTAA78eBErtv/g8G2np6fDarXCz88POp1Offn4+MBisahnoF988QV69uyJ7t27469//avD+wIYoC5H6h2CCxRfrah/ZTVVc9uOGTMGq1evtlNnROSu0nKKUHS19pWvpOzzjt92Whruu+8+fPvttzavF154AT4+PujVqxcsFgvmz5+PnTt3Ij09Ha+//jouXbrk8N4YoC6moau0ZZbrD8OtOTF8QECAHbsjIndk9K37Mq2/j+O/Bfz2228xevRo9O/f3+Z16dIl9O3bF56enkhNTUXv3r3RuXNn+Pv746677sJXX33l8N4YoG7Eam3g9BR8qgoRNU9kZyMG3tih1vJpw7s6dLsnT55EcXExBg6sPU1penq6evn23Llz6Ny5s7ouPDwceXl5Du0NYIC6nMrK+s8y84qv1buO4UlELfHe1MF4ZHAEOrU3oHtwe7x2Xx88ctuNDt1mWloaPDw80L9/f5vlFosFR44cUQNU6vhuqzUe9chRuC7Gu4EnrvQOrftyrIgwPImoRTq288ayyX2vX2hH6enp6N69O9q3b2+z/OjRoygrK1PPTDt37mxzxnn27FkMGTLE4f3xDNTFWBuYbujgqYt1LtfpdDCZTAxPInIpS5cuxbFjx2ot79evH0QEAwYMAADcdtttyMrKQl5eHi5fvoytW7di/PjxDu+PZ6AuprKy/imrfiio/zaWxYsX4/777691LxURkavz9PTEm2++iTFjxkBRFPzud79DUFCQw7fLM1AX09B1fUWp/t8KVq5cidLSUnUZw5OI3NWkSZPwww8/4MSJE3jqqadaZZs8A3Uxnp51/5vHAwrGXvoEeHseFAGeTtLhnX/ux5YtW5CcnAwPD/5biYjInhigLkZR6v4O9PeeH2Ny0ZdQRPD0v8vwTloldDrgiSeeYHgSETkAj6wupq6nDviiDI/qd9iGJ4B1D3TEY4/weZ5ERI7AAHUxP5mv1FrWHmUwoNw2PO/zwWO9rEDl1dZvkoioDWCAuhirUnsU7gV0wG+SDLbh2dcbCL8N8K09ewgREbUcA7SG1atXo1u3bvDx8UFUVBT27t2rdUs2LleWAwBWeK7GD4bHcdLwKHZ7z8XlW+5DkJ/H/8IzIByY9CeNuyUicl8cRFTNJ598gnnz5mH16tW4/fbb8c4772DixInIzs7GjTc6dsqqxsr48QSWeibifs996rIuugtYF/EZIp9ah8dmhQDQAd1GAnrHPqePiKgt4xloNStWrMCvf/1r/OY3v8Gtt96KlStXIiIiAm+//Xad9eXl5SgpKbF5OdrvPi/GPfoDUEQw/6sy7M+1AAB8dRV4yC8NuPkO4OZohicRkYMxQP+roqICaWlpGDdunM3ycePG4cCBA3X+ztKlS2E0GtVXREREa7QKvVjw9L/L8MeDFYj521VcuvbzRMo3oLhVtk9ERAxQ1U8//QSr1YqQkBCb5SEhISgoKKjzdxYuXAiz2ay+zpw54/A+T742EXH/1qsDhlbd5YNAXx0UAdZZ73T49omI6GcM0BpqTpUnIvVOn2cwGBAQEGDzcqSqR5J9mn7RZrStIjostzyMjGVTHLp9IiItjBw5Er/+9a9rLV+9ejX8/PxgtdY/R7gjcRDRf3Xq1Al6vb7W2WZhYWGts1It1HyeZ2DMfGzrGYj/VBTiM2UEspc9oHWLRER2JyLIyMjAI488UmtdWloa+vXrV+cEM62BAfpf3t7eiIqKQlJSEu677z51eVJSEu655x4NO/tZYmJivc/zXKJhX0REjnT8+HFcvnxZfXh2dWlpaRgxYoQGXf2MAVrN/PnzER8fj0GDBmHYsGFITExEbm4uZsyYoXVr+NWvfoVt27bhgQce4PM8iaj1Xb0E7HgZ+H4b4BcIDJkORE1z+GbT0tKg1+trPU2qvLwcR48exdy5cx3eQ30YoNU8/PDDuHjxIl555RXk5+cjMjISW7duRZcuXTTpR1EU6HQ66HQ6GAwGfPbZZw0+zoyIyGE2PAKcOfTzf18pAD6fC+g8gIGPO3Sz6enpsFqt8PPzq3N91Znpfffdh6+//hrR0dHYtGmTQ3uqwkFENTz99NM4ffo0ysvLkZaWhpEjR2rSh6IomDlzJp555hmI/HybCsOTiDRxLuN/4VndoUSHbzotLQ333Xcfvv32W5vXCy+8AB8fH/Tq1QsAMGfOHKxbt87h/VTHAHVCVeGZmJiIP/3pT/jmm2+0bomI2rKyeu4xv1bk8E1/++23GD16NPr372/zunTpEvr27QtPz58vpI4ZMwb+/v4O76c6BqiTqR6eVQOGBg8erHVbRNSWRQwFfANrL7/lLodu9uTJkyguLsbAgQNrrUtPT69zYFFrYoA6kbrCkwOGiEhzXj7AA+8BfkH/W9b1l8DYFx262bS0NHh4eKB///42yy0WC44cOaJ5gHIQkZNgeBKRU/vFWOCZbODs4Z9H4Yb0dvgm09PT0b17d7Rv395m+dGjR1FWVlbnmWlr4hmok0hNTcVf//pXhicROS8vH6DbL1slPIGf5xs/duxYreX9+vWDiGDAgAGt0kd9eAbqJIYOHYp169ZBRBieRERNNH78eKSnp6O0tBTh4eH47LPPHD5+hAGqIUVRUFxcjMDAn7+cj4uL07gjIiLX9NVXX7X6NnkJVyNVc9sOHToU586d07odIiJqIgaoBqpPDH/ixAkcPHhQ65aIiKiJGKCtrOZTVdatW4f7779f67aIiKiJGKCtqK7w5IAhIiLXxABtJQxPItJS1ZzabZ099wMDtJUUFRVhx44dDE8ialVeXl4AgKtXr2rciXOoqKgAALs8hJu3sbSSoKAgfP311zh48CAmT56sdTtE1Ebo9Xp06NABhYWFAAA/P782+2QnRVFw4cIF+Pn5qZPQtwQD1IEURcHhw4cxZMgQAEDnzp0ZnkTU6kwmEwCoIdqWeXh44MYbb7TLPyIYoA5S9Z3nu+++i/Xr12PKlClat0REbZROp0NoaCiCg4NRWVmpdTua8vb2hoeHfb69ZIA6QM0BQ1arVeuWiIig1+vt8t0f/YwB6gDz58/H2rVrOWCIiMiN6YRjm+2mpKQERqMRABieREQupuoYbjabERAQcN163sbiIAxPIiL3xku4dlR1Mv/WW29h0qRJKCkp0bgjIiJqrKpjdmMvzPISrh2dPXsWERERWrdBREQtcObMGYSHh1+3jgFqR4qi4Ny5c/D392+VG5VLSkoQERGBM2fONOp6Pdni/msZ7r+W4f5rOXvvQxHB5cuXERYW1qhbXXgJ1448PDwa9a8WewsICOBfwBbg/msZ7r+W4f5rOXvuw6qBoI3BQURERETNwAAlIiJqBv3ixYsXa90ENZ9er8fo0aPtMjFyW8T91zLcfy3D/ddyWu5DDiIiIiJqBl7CJSIiagYGKBERUTMwQImIiJqBAUpERNQMDFAXtnr1anTr1g0+Pj6IiorC3r17tW7JoZYuXYrBgwfD398fwcHBuPfee/H999/b1IgIFi9ejLCwMPj6+mL06NE4evSoTU15eTlmz56NTp06oV27dpg0aRLOnj1rU1NUVIT4+HgYjUYYjUbEx8ejuLjYpiY3Nxd333032rVrh06dOmHOnDmoqKhwzId3gKVLl0Kn02HevHnqMu6/huXl5eGxxx5DUFAQ/Pz80L9/f6Slpanruf/qZ7FY8OKLL6Jbt27w9fXFTTfdhFdeeQWKoqg1Lrf/hFzSxo0bxcvLS959913Jzs6WuXPnSrt27SQnJ0fr1hxm/PjxsnbtWsnKypKMjAyJiYmR4K6cuQAACT9JREFUG2+8Ua5cuaLWLFu2TPz9/eXTTz+VzMxMefjhhyU0NFRKSkrUmhkzZkjnzp0lKSlJ0tPTZcyYMdKvXz+xWCxqzYQJEyQyMlIOHDggBw4ckMjISImNjVXXWywWiYyMlDFjxkh6erokJSVJWFiYJCQktM7OaKHU1FTp2rWr9O3bV+bOnasu5/6r36VLl6RLly4ybdo0OXTokJw6dUqSk5PlxIkTag33X/1effVVCQoKki+++EJOnTol//jHP6R9+/aycuVKtcbV9h8D1EXddtttMmPGDJtlt9xyiyxYsECjjlpfYWGhAJDdu3eLiIiiKGIymWTZsmVqTVlZmRiNRlmzZo2IiBQXF4uXl5ds3LhRrcnLyxMPDw/Ztm2biIhkZ2cLADl48KBak5KSIgDk2LFjIiKydetW8fDwkLy8PLVmw4YNYjAYxGw2O+5D28Hly5ele/fukpSUJKNGjVIDlPuvYc8//7yMGDGi3vXcfw2LiYmRJ554wmbZ/fffL4899piIuOb+4yVcF1RRUYG0tDSMGzfOZvm4ceNw4MABjbpqfWazGQAQGBgIADh16hQKCgps9ovBYMCoUaPU/ZKWlobKykqbmrCwMERGRqo1KSkpMBqNGDJkiFozdOhQGI1Gm5rIyEiEhYWpNePHj0d5ebnNJT1nNGvWLMTExOCOO+6wWc7917AtW7Zg0KBBePDBBxEcHIwBAwbg3XffVddz/zVsxIgR2LFjB3744QcAwHfffYd9+/bhrrvuAuCa+4/TX7ign376CVarFSEhITbLQ0JCUFBQoFFXrUtEMH/+fIwYMQKRkZEAoH72uvZLTk6OWuPt7Y2OHTvWqqn6/YKCAgQHB9faZnBwsE1Nze107NgR3t7eTv3/YOPGjUhLS8M333xTax33X8NOnjyJt99+G/Pnz8cLL7yA1NRUzJkzBwaDAY8//jj333U8//zzMJvNuOWWW6DX62G1WrFkyRJMmTIFgGv++WOAurCaj0wTkVZ5jJozSEhIwJEjR7Bv375a65qzX2rW1FXfnBpncubMGcydOxfbt2+Hj49PvXXcf3VTFAWDBg3Ca6+9BgAYMGAAjh49irfffhuPP/64Wsf9V7dPPvkE69evx9/+9jf07t0bGRkZmDdvHsLCwjB16lS1zpX2Hy/huqBOnTpBr9fX+pdSYWFhrX9VuaPZs2djy5Yt2LVrl83j40wmEwA0uF9MJhMqKipQVFTUYM358+drbffChQs2NTW3U1RUhMrKSqf9f5CWlobCwkJERUXB09MTnp6e2L17N/70pz/B09NT7Zv7r26hoaHo1auXzbJbb70Vubm5APjn73p++9vfYsGCBXjkkUfQp08fxMfH45lnnsHSpUsBuOb+Y4C6IG9vb0RFRSEpKclmeVJSEoYPH65RV44nIkhISMDmzZuxc+dOdOvWzWZ9t27dYDKZbPZLRUUFdu/ere6XqKgoeHl52dTk5+cjKytLrRk2bBjMZjNSU1PVmkOHDsFsNtvUZGVlIT8/X63Zvn07DAYDoqKi7P/h7SA6OhqZmZnIyMhQX4MGDUJcXBwyMjJw0003cf814Pbbb69129QPP/yALl26AOCfv+u5evVqrYdU6/V69TYWl9x/jR5uRE6l6jaW9957T7Kzs2XevHnSrl07OX36tNatOczMmTPFaDTK119/Lfn5+err6tWras2yZcvEaDTK5s2bJTMzU6ZMmVLnMPjw8HBJTk6W9PR0GTt2bJ3D4Pv27SspKSmSkpIiffr0qXMYfHR0tKSnp0tycrKEh4c79W0Edak+CleE+68hqamp4unpKUuWLJHjx4/Lxx9/LH5+frJ+/Xq1hvuvflOnTpXOnTurt7Fs3rxZOnXqJL/73e/UGlfbfwxQF/aXv/xFunTpIt7e3jJw4ED1dg53BaDO19q1a9UaRVFk0aJFYjKZxGAwyMiRIyUzM9Pmfa5duyYJCQkSGBgovr6+EhsbK7m5uTY1Fy9elLi4OPH39xd/f3+Ji4uToqIim5qcnByJiYkRX19fCQwMlISEBCkrK3PY53eEmgHK/dewzz//XCIjI8VgMMgtt9wiiYmJ/9/eHbu0soRhHH5XohGTYBGEDaiIxEqQgAFbUxhW0UIERWxS2FsIWtgYC/0DtLMRRCxsRFJoIdiqzZrGUsUioqIgEQmoe4oLyxVPIMw9as7N74FAhswM32zz8m2K+fA7z6+8p6cnb2Zmxmtvb/caGxu9zs5Ob2FhwSuVSv6cv+35cZ0ZAAAG+A8UAAADBCgAAAYIUAAADBCgAAAYIEABADBAgAIAYIAABQDAAAEKAIABAhTAB5eXl7IsS67rGq23LEu7u7t/uCqg+hCgQI3JZDKyLMv/RKNROY6jfD4vSWpra1OhUPDvWS1ncXFRiUTiO0oGqhIBCtQgx3FUKBRUKBR0eHioQCCg4eFhSf/ckGHbtgKB318X7HmeXl9fv7NcoCoRoEANCgaDsm1btm0rkUhofn5e19fXuru7+/QK9+joSJZl6eDgQMlkUsFgUJubm8pmszo7O/M72Y2NDX//+/t7jY6OqqmpSV1dXdrb2/uhkwJfhwAFalyxWNTW1pbi8bii0WjZeXNzc1pZWdH5+bnS6bRmZ2fV3d3td7ITExP+3Gw2q/HxceXzeQ0NDWlqakoPDw/fcRzg2/z+HQ2A/7VcLqdwOCxJen5+ViwWUy6X+3Th8b8tLS1pYGDAH4fDYQUCAdm2/WluJpPR5OSkJGl5eVmrq6s6OTmR4zh/+CTAz6EDBWpQKpWS67pyXVfHx8dKp9MaHBzU1dVV2TXJZLLi/Xt6evzvoVBIkUhEt7e3/6lmoNrQgQI1KBQKKR6P++Pe3l41NzdrfX1d09PTZddUqr6+/sPYsiy9v7+bFQtUKTpQALIsS3V1dXp5eal4TUNDg97e3r6wKqC60YECNahUKunm5kaS9Pj4qLW1NRWLRY2MjFS8R0dHhy4uLuS6rlpbWxWJRBQMBr+qZKDq0IECNWh/f1+xWEyxWEx9fX06PT3Vzs6O+vv7K95jbGxMjuMolUqppaVF29vbX1cwUIUsz/O8ny4CAIC/DR0oAAAGCFAAAAwQoAAAGCBAAQAwQIACAGCAAAUAwAABCgCAAQIUAAADBCgAAAYIUAAADBCgAAAY+AVykq8julD9CgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diagrams(dgms, show=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1709, 1152)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_landmark.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42728, 1152)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dgms = ripser(np_data, maxdim=1)['dgms']\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plot_diagrams(dgms, plot_only=[0], ax=plt.subplot(121))\n",
    "plot_diagrams(dgms, plot_only=[1], ax=plt.subplot(122))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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