Example-gradient-less-optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import examples as eg\n",
    "import numpy as np\n",
    "from numpy import *\n",
    "import dionysus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The circular coordinates pipeline for examining different smoothness cost-functions:\n",
    "\n",
    "    Step 1. Getting the point cloud\n",
    "    Step 2. Computing the Vietoris-Rips filtration and its cohomology\n",
    "    Step 3. Selecting the Cocycle\n",
    "    Step 4. First smoothing using Least Squares (Optional)\n",
    "    Step 5. Second smoothing using a new cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1 - Getting the point cloud"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "annulus = eg.pinched_torus_example(n=200)\n",
    "#The examples.py generates data points in form of point clouds that can be analyzed using the imported dionysus module."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2 - Computing Vietoris-Rips Complexes and Cohomology"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EHgOu7XvqjWMeEWcA3w283Gx1a1ur7rb1lVIb+NALKvfNMG+gNz8swUHgF6uVEVcAr2TmsWkXNUxEfN/KDDMiLqf3b2vqP5BVTXcDz2TmR9bYrZXHvE7tbTzuEXFuRGyr7r8duAb4at9uB4E91f0bgb/P6l3CaalTd9v6ykjXxJyWXOOCyhHxQaCbmQeB34iIG4BT9N58u3VqBa8SEZ+it3Jge0QcAT5A780SMvNj9K4xeh3wLPDfwC9Np9I3q1H3jcCvRMQp4H+Am6f9A1m5ErgF+FI12wR4P/D90O5jTr3a23jcdwIHImILvf9Q7s/MR/p+Pu8G/jwinqX383nz9Mp9Q526W9VX/Ci9JBWq1BGKJM09G7gkFcoGLkmFsoFLUqFs4JJUKBu4JBXKBi5Jhfp/5D5TOa5DojEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAXI0lEQVR4nO3df4zkdX3H8dfrloVbepQl3Fpg744lkZwRUdZu8My1idIY8EfhqrZiqlWLvbSVVht6DZhGhZh4zaXatLSaq6hoCWqVbA5/5EICqbXpIXvsAR54yeWswkLKeeeCyPa43Xv3j505Z2e/353vzH5nvjPfeT6SCTPf+d7MewP32g+f7+f7/jgiBADofWuKLgAAkA8CHQBKgkAHgJIg0AGgJAh0ACiJM4r64vXr18fY2FhRXw8APWn//v0/i4iRpPcKC/SxsTFNTU0V9fUA0JNs/yTtPaZcAKAkCHQAKAkCHQBKgkAHgJIg0AGgJAh0ACiJwpYtortNTs9o195Denp2ThcND2nH1Zu1bXy06LIArIBAxzKT0zO65Z7HNHdyQZI0MzunW+55TJIIdaCLMeWCZXbtPXQ6zKvmTi5o195DBVWEfrTvyDH98Zce0osvzRddSs8g0LHM07NzTR0H8rbvyDF94IsP6afHX9SLLy00/gOQRKAjwUXDQ00dB/JUDfPR84Z0959s0fp1ZxVdUs8g0LHMjqs3a2hwYMmxocEB7bh6c0EVoV/Uh/nIOYR5M7goimWqFz5Z5YJOIsxXj0BHom3jowQ4OoYwzwdTLgAKRZjnh0AHUBjCPF8NA932Wts/sP2I7YO2b0045/22j9o+UHl8sD3lAigLwjx/WebQT0i6KiJesD0o6fu2vxsR++rO+1pE3Jh/iQDKhjBvj4aBHhEh6YXKy8HKI9pZFIDyIszbJ9Mcuu0B2wckPSvpvoh4MOG0d9h+1PY3bG9M+ZzttqdsTx09enQVZQPoRYR5e2UK9IhYiIgrJG2QdKXtV9Wdcq+ksYh4taT7JN2Z8jm7I2IiIiZGRhI3rQZQUoR5+zW1yiUiZiU9IOmauuPHIuJE5eXnJf1mPuUBKAPCvDOyrHIZsT1ceT4k6U2SflR3zoU1L6+V9ESeRQLoXYR552RZ5XKhpDttD2jxF8DXI+Jbtm+TNBUReyT9pe1rJc1LOi7p/e0qGEDvIMw7y4uLWDpvYmIipqamCvluAO1HmLeH7f0RMZH0HneKAsgdYV4MAh1Argjz4hDoAHJDmBeLQAeQC8K8eAQ6gFUjzLsDgQ5gVQjz7kGgA2gZYd5dCHQALSHMuw+BDqBphHl3ItABNIUw714EOoDMCPPuRqADyIQw734EOoCGCPPeQKADWBFh3jsIdACpCPPeQqADSESY9x4CHcAyhHlvItABLEGY9y4CHcBphHlvI9ABSCLMy4BAB0CYl0TDQLe91vYPbD9i+6DtWxPOOcv212wftv2g7bF2FAsgf4R5eWQZoZ+QdFVEvEbSFZKusb2l7pwbJP08Il4u6TOS/i7fMgG0A2FeLg0DPRa9UHk5WHlE3WnXSbqz8vwbkn7HtnOrEkDuCPPyyTSHbnvA9gFJz0q6LyIerDtlVNKTkhQR85Kek3R+wudstz1le+ro0aOrqxxAywjzcsoU6BGxEBFXSNog6Urbr2rlyyJid0RMRMTEyMhIKx8BYJUI8/JqapVLRMxKekDSNXVvzUjaKEm2z5B0rqRjeRQIID+EebllWeUyYnu48nxI0psk/ajutD2S3ld5/k5J90dE/Tw7gAIR5uV3RoZzLpR0p+0BLf4C+HpEfMv2bZKmImKPpDskfcX2YUnHJV3ftooBNI0w7w8NAz0iHpU0nnD8YzXP/0/S7+dbGoA8EOb9gztFgRIjzPsLgQ6UFGHefwh0oIQI8/5EoAMlQ5j3LwIdKBHCvL8R6EBJEOYg0IESIMwhEehAzyPMUUWgAz2MMEctAh3oUYQ56hHoQA8izJGEQAd6DGGONAQ60EMIc6yEQAd6BGGORgh0oAcQ5siCQAe6HGGOrAh0oIsR5mgGgQ50KcIczSLQgS5EmKMVBDrQZQhztIpAB7oIYY7VaBjotjfafsD247YP2v5wwjlvsP2c7QOVx8faUy5QXoQ5VuuMDOfMS7opIh62fY6k/bbvi4jH6877z4h4W/4lAuVHmCMPDUfoEfFMRDxcef4LSU9IGm13YUC/IMyRl6bm0G2PSRqX9GDC26+3/Yjt79q+LOXPb7c9ZXvq6NGjTRcLlA1hjjxlDnTb6yR9U9JHIuL5urcflnRxRLxG0j9Jmkz6jIjYHRETETExMjLSas1AKRDmyFumQLc9qMUwvysi7ql/PyKej4gXKs+/I2nQ9vpcKwVKhDBHO2RZ5WJJd0h6IiI+nXLOBZXzZPvKyucey7NQoCwIc7RLllUuWyW9V9Jjtg9Ujn1U0iZJiojPSXqnpD+zPS9pTtL1ERFtqBfoaYQ52qlhoEfE9yW5wTm3S7o9r6KAMiLM0W7cKQp0AGGOTiDQgTYjzNEpBDrQRoQ5OolAB9qEMEenEehAGxDmKAKBDuSMMEdRCHQgR4Q5ikSgAzkhzFE0Ah3IAWGObkCgA6tEmKNbEOjAKhDm6CYEOtAiwhzdJku3RaCnTE7PaNfeQ3p6dk4XDQ9px9WbtW08310TCXN0IwIdpTI5PaNb7nlMcycXJEkzs3O65Z7HJCm3UCfM0a2YckGp7Np76HSYV82dXNCuvYdy+XzCHN2MQEepPD0719TxZhDm6HYEOkrlouGhxONrbE1Oz7T8uYQ5egGBjlLZcfVmDQ0OLDu+EKFb7nmspVAnzNErCHSUyrbxUX3q7ZdrwMt3TWxlLp0wRy8h0FE628ZHdSplj/Jm5tIJc/QaAh2llDaXnna8HmGOXtQw0G1vtP2A7cdtH7T94YRzbPsfbR+2/ajt17anXCCbpLn0ocEB7bh6c8M/S5ijV2W5sWhe0k0R8bDtcyTtt31fRDxec86bJV1aebxO0mcr/wQKUb2JqP6OUUnauvP+1LtICXP0soaBHhHPSHqm8vwXtp+QNCqpNtCvk/TliAhJ+2wP276w8meBQmwbH10S1o3uIiXM0euauvXf9pikcUkP1r01KunJmtdPVY4tCXTb2yVtl6RNmzY1VymwSivdRXrBuWsJc/S8zIFue52kb0r6SEQ838qXRcRuSbslaWJiInkZArpWJ5petbOmtBUuM7NzhDlKIVOg2x7UYpjfFRH3JJwyI2ljzesNlWMoiU40vWp3TRcND2kmIdQtEeYohSyrXCzpDklPRMSnU07bI+mPKqtdtkh6jvnzcml306tWNFtT2l2kL/v1swhzlEKWEfpWSe+V9JjtA5VjH5W0SZIi4nOSviPpLZIOS3pR0gfyLxVFamfTq1Y1W1PtypeZ2TlZi2H+rb/4bcIcpZBllcv3tfh/pSudE5I+lFdR6LxGc9Fp0xVZb9Rph1Zq2jY+ygVQlBZ3iuL0XPTM7JxCv5qLrm1ktZobddqllZpYmogyI9CRaS662vRqdHho8SLi8JA+9fbLC13l0mxNhDnKji3okHkuuv5GnW6QtSbCHP2AETpW3ciq2xHm6BcEOrpyfjwvhDn6CVMuSG1k1W3TK80izNFvCHRI6p758bzaCxDm6EcEOjoiS1Dn1V6AMEe/Yg4dbZdlnbuUT3sBwhz9jEBH22UN6tW2FyDM0e+YckFL8mhbW398Ne0FCHOAETpakHUKpSotkNfYubQXIMyBRQQ6mpZX29qFiCW/CFppL0CYA7/ClAua1mrb2pu+/ogWYulGVbW/CGqncD7zrisarmwhzIGlGKGjaa20Ctg2PqpTkbzrYHXKpnYK56++dkBjN39bW3fenziVQ5gDyxHoaFqrc91pgT9gL5vCqUZ/0vw8YQ4kI9DRtFZb6ab9IqifhqlXOy1DmAPpmENHS1ppFZDWM6a6JdxKnp6dI8yBBgh0dFTaL4LaW/6TnL/uTMIcaIBAR+GSNm+unYQ5c2CNnp+b16bzzybMgRUQ6OgKtSP32rtQz193JmEOZNTwoqjtL9h+1vYPU95/g+3nbB+oPD6Wf5noJ9vGR/VfN1+lu7dv0S9PLBDmQEZZRuhfknS7pC+vcM5/RsTbcqkIEKtZgFY0DPSI+J7tsfaXgn6yUnMvwhxoTV5z6K+3/YikpyX9dUQcTDrJ9nZJ2yVp06ZNOX01es1KG1lccO5awhxoUR6B/rCkiyPiBdtvkTQp6dKkEyNit6TdkjQxMbHy3SQorbTmXp/89uP65YkFwhxo0aoDPSKer3n+Hdv/Ynt9RPxstZ+N7tfKHqBpNxH97IWX9PKXrSPMgRatOtBtXyDpfyMibF+pxZUzx1ZdGbpeoz1Ak8Je0rJ15lVnrDFhDqxCw0C3fbekN0hab/spSR+XNChJEfE5Se+U9Ge25yXNSbo+okFzDvScpHBu1Bc9KezXDq5JDHNJ+vjvvpIwB1bBRWXvxMRETE1NFfLdaE79SFxabKq10q365509qJ+/eLKp7/mfnW9tuUagX9jeHxETSe/RbRENpY3EB+zUP9NsmI9m2DcUwMoIdDSUdhFzISJxa7mVDA8N6syBpf/ZZemlDqAxAh2SFqdVtu68X5fU7RI0OT2jtHF4tQ96VkODA3rPloslLV4Arf2MZlvxAliO5lxYcbXKrr2HUi9ivvjSvKTFHYeSNqmwFncpql5I/b3xUd3x/R/TmwVoEy6KQlt33p84rTJaCeOV/gtJW4JYVb3Qye38QD5WuijKCL3PJC0/fDpljrx6zkq7Ca0U5tULnYQ50BnMofeR6tTKTGXUXZ1aGT57MPH8auBnufBZP89evdBJmAOdQ6D3kbTlhxFK3Ly5eht/dUPolYS0bNNoGm0BnUWg95G0qZXn5k6eDu3aQK6uPKluOPEP77oidcXL8NDSUf7hZ18gzIEOYw69j6TNh180PJS6eXOtbeOjmvrJcd2176dL5s4H11i/fGles3OLNxPNzM7p9gcO6zd+/SzCHOggRuh9JGk+vNmbej657XJ95l1XLBmRL0To5ELSskUT5kAHMULvI9UReLPtbpOcmD91+vmplKUu//v8/7VUJ4DWEOh9JsvUSiNJF1eTXER/FqCjmHJB09IurtaiPwvQeQQ6mpY28l4jJa6SAdAZTLmgKZPTM/rlifllx9eesUY73/FqQhwoEIGOVPVtAt74ihF9c//Msvnzc4fO0K3XvoowBwpGoPeZrJs6J3VgrF9/XrXurEHCHOgCBHqfmJye0Sf2HDx984+0fFPnWkkrWdIacWW5SAqg/bgo2geqo+3aMK+q3dS5VjMhzfJEoDswQi+BRtMojdaNJ4V3o7a5VSxPBLpHwxG67S/Yftb2D1Pet+1/tH3Y9qO2X5t/mUiT1hK3uoWc1Hi0XT/CTlvJYknveO1oahMvAMXKMkL/kqTbJX055f03S7q08nidpM9W/okOSGuJu2vvodNBu9Jou36E/beTjyVe/Fxj6dZrL9N7Xz+WZ/kActRwhB4R35N0fIVTrpP05Vi0T9Kw7QvzKhArW2m3oaq0TSrOO3twyQh7cnomdSXLy85ZS5gDXS6POfRRSU/WvH6qcuyZ+hNtb5e0XZI2bdqUw1fj3KHBxIud59Z0Q8zalOvWew+mrmSh0RbQ/Tp6UTQidkvaLS1uEt3J7y4rp+w4UX+8UVOuyekZ/fzF5b8YqljJAnS/PJYtzkjaWPN6Q+UYOmA2JYTTjqdJWrpYZYmVLEAPyGOEvkfSjba/qsWLoc9FxLLpFrTHSrsQNVK73HGl/136wy2bWMkC9IAsyxbvlvTfkjbbfsr2Dbb/1PafVk75jqQjkg5L+ldJf962arFMq7sQTU7PaMc3Hjm93DHN8NCgPrnt8hwqBdBuDUfoEfHuBu+HpA/lVhGa0uouRLfeezBx27haQ4MD+sS1l+VWK4D24k7REsi6C1HWKRZLq9qeDkAxCPQelrVzYvXc2u6JK/nxzrfmXSqADiDQe1RSe9u0zolS9n1Ah2vWrwPoLXRb7FEr3fKfJEujrcE1Zs4c6GGM0HtUllv+qyanZ2Ql9zMfsHUqgjlzoAQI9B7VzPrzXXsPJYa5Jf39H7yGEAdKgimXHrXj6s0aHFh6f//ggBPXn6eN5kPJ8+0AehOB3svqh90paxHPX3dm4vFR+rMApUKg96hdew/p5KmlCX7yVCy7KLrvyDE9Pzev+h5e7DQElA+B3qOyXBTdd+SYPvDFh7Tp/LN123WXsdMQUHJcFO1RaRdF19ianJ7RBeeu1Qe++JBGzxvS3X+yRSPnnMUGFUDJEeg9KG3PT0laiNBN/35AA16jTeeffTrMAZQfgd5jstzCv3BKCp8izIE+wxx6j8l6C/+pEGEO9BkCvcekXQwFAKZcekC1q2KWfixVNNkC+g+B3uWaaXtbRZMtoD8R6F3u1nsPZgrzNVq8UZQmW0D/ItC72OT0jH7+4slM54bYmALod1wU7WJpvc2TJHVZBNBfCPQulnVFC31ZAEgZA932NbYP2T5s++aE999v+6jtA5XHB/Mvtbwmp2e0def9uuTmb2vrzvs1OT0jaeVRd/VfHH1ZAFQ1nEO3PSDpnyW9SdJTkh6yvSciHq879WsRcWMbaiy1lfYGfeMrRnTXvp8u6YprSbdddxl9WQAsk+Wi6JWSDkfEEUmy/VVJ10mqD3S0IG1v0E/sOagT86eWtTh/+2tHCXMAibJMuYxKerLm9VOVY/XeYftR29+wvTHpg2xvtz1le+ro0aMtlFs+afPks3MnE5cr7jtyvN0lAehReV0UvVfSWES8WtJ9ku5MOikidkfERERMjIyM5PTVva3Z1Snc+g8gTZZAn5FUO+LeUDl2WkQci4gTlZefl/Sb+ZRXfjuu3qyhwYElx4YGB7TurIHE81meCCBNlkB/SNKlti+xfaak6yXtqT3B9oU1L6+V9ER+JZbbtvFRfertly/ZTeiG37pEL80H28YBaErDi6IRMW/7Rkl7JQ1I+kJEHLR9m6SpiNgj6S9tXytpXtJxSe9vY82ls2189PSyw9pt4973+ov1uf84oqdn57ilH0BDjkjZKr7NJiYmYmpqqpDv7lbVMK/dNg4AatneHxETSe9xp2iX+MGPjxPmAFaFQO8SI+ecpYmx8whzAC2j22KXuGT9r+krN7yu6DIA9DBG6ABQEgQ6AJQEgQ4AJUGgA0BJEOgAUBIEOgCUBIEOACVBoANASRTWy8X2UUk/KeTLV2e9pJ8VXUQH8fOWGz9v77k4IhI3lCgs0HuV7am0xjhlxM9bbvy85cKUCwCUBIEOACVBoDdvd9EFdBg/b7nx85YIc+gAUBKM0AGgJAh0ACgJAr0Jtq+xfcj2Yds3F11PO9n+gu1nbf+w6Fo6wfZG2w/Yftz2QdsfLrqmdrK91vYPbD9S+XlvLbqmdrM9YHva9reKrqVdCPSMbA9I+mdJb5b0Sknvtv3KYqtqqy9JuqboIjpoXtJNEfFKSVskfajk/35PSLoqIl4j6QpJ19jeUnBN7fZhSU8UXUQ7EejZXSnpcEQciYiXJH1V0nUF19Q2EfE9SceLrqNTIuKZiHi48vwXWvyLP1psVe0Ti16ovBysPEq7QsL2BklvlfT5omtpJwI9u1FJT9a8fkol/gvfz2yPSRqX9GCxlbRXZQrigKRnJd0XEWX+ef9B0t9IOlV0Ie1EoAM1bK+T9E1JH4mI54uup50iYiEirpC0QdKVtl9VdE3tYPttkp6NiP1F19JuBHp2M5I21rzeUDmGkrA9qMUwvysi7im6nk6JiFlJD6i810y2SrrW9v9ocar0Ktv/VmxJ7UGgZ/eQpEttX2L7TEnXS9pTcE3IiW1LukPSExHx6aLraTfbI7aHK8+HJL1J0o+Krao9IuKWiNgQEWNa/Ht7f0S8p+Cy2oJAzygi5iXdKGmvFi+YfT0iDhZbVfvYvlvSf0vabPsp2zcUXVObbZX0Xi2O3g5UHm8puqg2ulDSA7Yf1eJg5b6IKO1yvn7Brf8AUBKM0AGgJAh0ACgJAh0ASoJAB4CSINABoCQIdAAoCQIdAEri/wFCweh2/tM0UwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prime = 23 #choose the prime base for the coefficient field that we use to construct the persistence cohomology.\n",
    "\n",
    "vr = dionysus.fill_rips(annulus, 2, 4.) #Vietoris-Rips complex\n",
    "cp = dionysus.cohomology_persistence(vr, prime, True) #Create the persistent cohomology based on the chosen parameters.\n",
    "dgms = dionysus.init_diagrams(cp, vr) #Calculate the persistent diagram using the designated coefficient field and complex.\n",
    "dionysus.plot.plot_bars(dgms[1], show=True) \n",
    "dionysus.plot.plot_diagram(dgms[1], show=True) \n",
    "#dionysus.plot.plot_diagram(dgms[0], show=True) \n",
    "#Plot the barcode and diagrams using matplotlib incarnation within Dionysus2. This mechanism is different in Dionysus."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3 - Selecting the cocycle and visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "module"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "threshold = 1\n",
    "bars = [bar for bar in dgms[1] if bar.death-bar.birth > threshold] #choosing cocycle that persist at least threshold=1.\n",
    "cocycles = [cp.cocycle(bar.data) for bar in bars]\n",
    "#plt is the matplotlib incarnation.\n",
    "\n",
    "#Red highlight cocyles that persist more than threshold value on barcode, when more than one cocyles have persisted over threshold values, this plots the first one.\n",
    "dionysus.plot.plot_bars(dgms[1], show=False)\n",
    "plt.plot([[bar.birth,bar.death] for bar in dgms[1] if bar.death-bar.birth > threshold][0],[[x,x] for x,bar in enumerate(dgms[1]) if bar.death-bar.birth > threshold][0],'r')\n",
    "plt.title('Showing the selected cycles on bar codes (red bars)')\n",
    "plt.show()\n",
    "\n",
    "#Red highlight ***ALL*** cocyles that persist more than threshold value on diagram.\n",
    "dionysus.plot.plot_diagram(dgms[1], show=False)\n",
    "Lt1 = [[point.birth,point.death] for point in dgms[1] if point.death-point.birth > threshold] \n",
    "for Lt3 in Lt1:\n",
    "    #print(Lt3)\n",
    "    plt.plot(Lt3[0],Lt3[1],'ro')\n",
    "plt.title('Showing the selected cycles on diagram (red points)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "chosen_cocycle= cocycles[0]\n",
    "chosen_bar= bars[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4 - First smoothing using Least Squares (Optional)\n",
    "\n",
    "If it is computed the smoothed coefficients can be used as initial condition for the optimization code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "vr_8 = dionysus.Filtration([s for s in vr if s.data <= max([bar.birth for bar in bars])])\n",
    "coords = dionysus.smooth(vr_8, chosen_cocycle, prime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.67312146, -1.37451098, -3.05826372,  0.48873713,  2.35892311,\n",
       "       -2.17771542,  1.36940685,  1.80185836,  0.70409856, -1.96707472,\n",
       "       -2.23585118, -0.95008248,  3.29371294, -0.34403295, -3.84761921,\n",
       "        1.42051272, -2.77180455,  1.55974964,  1.93420009, -1.04703595,\n",
       "        1.54535866, -3.60881534, -2.88547645,  1.43178865, -1.48169108,\n",
       "        3.30632454, -2.19826852,  0.62478487, -1.34096396,  1.64387073,\n",
       "        1.79028863,  1.67195216,  2.86586025,  2.37386202, -1.57085332,\n",
       "       -1.13563069,  2.82515809,  2.00831069, -1.31832037, -2.07797586,\n",
       "        0.81300261, -0.52920814, -3.72967777, -1.89591003,  3.69583043,\n",
       "        2.39202283,  0.53616103,  2.41538442,  2.09390966, -0.12945963,\n",
       "        2.28337064, -1.9543261 ,  0.17813405,  1.60263529, -2.87567906,\n",
       "       -1.99303913, -1.9908043 ,  1.91325815,  2.20271798,  0.08494396,\n",
       "       -3.8989019 ,  3.79472091,  1.95324127,  3.48392092, -0.93486881,\n",
       "        1.84718667, -3.18722767,  0.0979552 , -0.10991299,  3.47673091,\n",
       "        2.92970299, -2.62855229, -0.58653684,  2.0835857 ,  2.30302452,\n",
       "        2.14324228,  2.68178081,  0.1207898 , -1.53747561,  1.62640164,\n",
       "       -1.61375186, -3.05480747, -1.99495316, -4.08246558,  1.23276904,\n",
       "        2.41590384,  0.14832218, -1.91967149, -1.26579285,  3.23776769,\n",
       "        1.49945189, -1.42121388, -1.61599527,  1.87580584, -1.27329723,\n",
       "       -0.84364545,  3.87731179, -0.99314095,  2.23206464,  4.0434151 ,\n",
       "       -2.15255459, -1.61513101,  1.45718914, -1.78516476, -1.14662079,\n",
       "        1.89036192, -1.91944996,  2.00778251,  2.07062331, -2.0980154 ,\n",
       "        2.8569305 ,  0.84964217, -2.02750617,  1.56204202,  0.70821849,\n",
       "       -1.94250163, -2.78871326,  4.00862484, -2.08081134, -1.69823613,\n",
       "        1.38581091, -1.9361833 , -1.06948149,  0.11564845,  3.77549312,\n",
       "        2.13917767,  0.52641979,  1.29676559, -3.5512567 ,  1.67227352,\n",
       "       -3.04660802, -0.95150882,  1.55003989,  1.3197688 ,  0.44638179,\n",
       "       -4.07910724,  2.12999241, -1.81371986, -2.41829769,  1.82835122,\n",
       "        0.54249917,  2.12182478, -0.81045815, -0.66131238,  1.86685739,\n",
       "       -1.79788482,  2.00166423, -0.55544895, -3.05988969, -4.01904175,\n",
       "       -3.42182197, -1.11106552,  0.20893559, -3.05189363,  0.6498935 ,\n",
       "       -1.71374042,  0.54458605, -2.19114579,  1.35117608, -3.29027184,\n",
       "       -1.22984668, -0.34355142,  0.41437418,  2.48354618,  2.82875148,\n",
       "       -1.38612794, -1.8830852 , -2.55983763,  2.00350634, -2.03174739,\n",
       "        3.32778678,  1.76159588, -0.51149015, -3.24631071,  1.41349114,\n",
       "       -0.87669378,  2.55541468,  1.75032016,  1.28683639, -0.02208781,\n",
       "        3.89440126,  3.25631988,  2.46818658, -1.23913782,  1.12257595,\n",
       "       -2.0716679 , -1.55034065,  1.37369549, -1.77394069, -4.04192848,\n",
       "        1.12062254,  1.94190363,  3.90678083,  1.85050149,  3.51922798,\n",
       "       -3.8411657 , -0.98990794, -2.22781262,  0.8353626 ,  2.89155059])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(annulus.T)\n",
    "annulus.T[1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.rcParams['lines.markersize'] = 150\n",
    "scatter(annulus.T[0,:],annulus.T[1,:],s=20, c=coords, cmap=\"hsv\")\n",
    "plt.axis('equal')\n",
    "plt.title('Smoothing of coordinates using least squares')\n",
    "plt.show()\n",
    "\n",
    "toll = 1e-5\n",
    "p,val = (chosen_bar,coords)\n",
    "edges_costant = []\n",
    "thr = p.birth # i want to check all edges that were there when the cycle was created\n",
    "for s in vr:\n",
    "    if s.dimension() != 1:\n",
    "        continue\n",
    "    elif s.data > thr:\n",
    "        break\n",
    "    if abs(val[s[0]]-val[s[1]]) <= toll:\n",
    "        edges_costant.append([annulus[s[0],:],annulus[s[1],:]])\n",
    "edges_costant = np.array(edges_costant)\n",
    "scatter(annulus.T[0,:],annulus.T[1,:],s=20, c=coords, cmap=\"hsv\")\n",
    "plot(edges_costant.T[0,:],edges_costant.T[1,:], c='k')\n",
    "plt.axis('equal')\n",
    "plt.title('Visualizing constant edges')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5 - Second smoothing using a new cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import utils\n",
    "l2_cocycle,f,bdry = utils.optimizer_inputs(vr, bars, chosen_cocycle, coords, prime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00],\n",
       "       [ 0.00000000e+00],\n",
       "       [ 4.62728814e-12],\n",
       "       ...,\n",
       "       [ 5.82303357e-02],\n",
       "       [-2.97533516e-02],\n",
       "       [-8.04065267e-01]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#l2_cocycle.reshape(-1, 1)\n",
    "l2_cocycle = l2_cocycle.reshape(-1, 1)\n",
    "l2_cocycle.shape\n",
    "f-bdry*l2_cocycle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " final_simplex: (array([[ 0.71495163, -0.21490076,  0.26219679, ...,  0.14836786,\n",
       "         0.00444708,  0.11313936],\n",
       "       [ 0.70755065, -0.21520511,  0.25167291, ...,  0.16326735,\n",
       "         0.00448208,  0.11123789],\n",
       "       [ 0.71582606, -0.21317336,  0.26311858, ...,  0.15682781,\n",
       "         0.00439735,  0.11104843],\n",
       "       ...,\n",
       "       [ 0.7046633 , -0.21439864,  0.25672088, ...,  0.15435457,\n",
       "         0.00441328,  0.11169819],\n",
       "       [ 0.71638148, -0.21925313,  0.25318754, ...,  0.15623423,\n",
       "         0.00451634,  0.11240168],\n",
       "       [ 0.70490182, -0.20981963,  0.26204754, ...,  0.15619847,\n",
       "         0.00428757,  0.11087957]]), array([1.37706373, 1.37708225, 1.3771205 , 1.37715332, 1.37716463,\n",
       "       1.37728239, 1.37728661, 1.37730112, 1.37734214, 1.37734587,\n",
       "       1.37741803, 1.37744251, 1.37745204, 1.37748647, 1.37748739,\n",
       "       1.37749222, 1.37750051, 1.37754715, 1.37759263, 1.37761073,\n",
       "       1.37761733, 1.37767347, 1.37770231, 1.37777692, 1.37783978,\n",
       "       1.37785145, 1.37787009, 1.37787473, 1.37787598, 1.37788813,\n",
       "       1.37791506, 1.37795276, 1.37796397, 1.37800558, 1.3780088 ,\n",
       "       1.3780251 , 1.3780515 , 1.3780752 , 1.3780923 , 1.3781049 ,\n",
       "       1.37812646, 1.37812927, 1.37816999, 1.37817499, 1.37818443,\n",
       "       1.37818689, 1.3782044 , 1.37821215, 1.37821924, 1.37823474,\n",
       "       1.378235  , 1.37824455, 1.37824953, 1.37829562, 1.37831058,\n",
       "       1.37832285, 1.3784416 , 1.3784737 , 1.37849004, 1.37850782,\n",
       "       1.3785497 , 1.37856758, 1.37857845, 1.37861192, 1.37861228,\n",
       "       1.37862708, 1.3786444 , 1.3786625 , 1.37866804, 1.37868019,\n",
       "       1.37868488, 1.37868955, 1.37869356, 1.37869506, 1.37869537,\n",
       "       1.3786957 , 1.37873219, 1.37876196, 1.37880227, 1.37882716,\n",
       "       1.37884498, 1.37886421, 1.37886546, 1.3788722 , 1.37889428,\n",
       "       1.37890602, 1.37890916, 1.37897814, 1.37900221, 1.37901142,\n",
       "       1.37902787, 1.37905548, 1.37907294, 1.37907978, 1.37910954,\n",
       "       1.37913125, 1.37913203, 1.37913522, 1.37913555, 1.37915344,\n",
       "       1.37916562, 1.37918161, 1.37922226, 1.37922686, 1.37923999,\n",
       "       1.37925573, 1.37925749, 1.37926562, 1.37927488, 1.37930469,\n",
       "       1.37934731, 1.37937311, 1.37939579, 1.37940303, 1.37941242,\n",
       "       1.37942307, 1.37943187, 1.37944842, 1.37945049, 1.37945086,\n",
       "       1.37951057, 1.37951428, 1.3795378 , 1.37954858, 1.37967162,\n",
       "       1.37969534, 1.37969668, 1.37969737, 1.37972189, 1.37972942,\n",
       "       1.3797667 , 1.37977719, 1.37982695, 1.37983515, 1.37983784,\n",
       "       1.37984819, 1.37987421, 1.37987631, 1.3798808 , 1.37988753,\n",
       "       1.37989029, 1.37989063, 1.37990515, 1.3799298 , 1.37995358,\n",
       "       1.37997923, 1.3799837 , 1.37999548, 1.38001299, 1.38001757,\n",
       "       1.38001826, 1.38003319, 1.38007538, 1.3800756 , 1.38010713,\n",
       "       1.38011162, 1.38011374, 1.38011479, 1.38013802, 1.38016469,\n",
       "       1.38019961, 1.38021632, 1.38022624, 1.38024331, 1.38024592,\n",
       "       1.38024659, 1.38025096, 1.38025485, 1.38026689, 1.38029705,\n",
       "       1.38030925, 1.38032249, 1.3803308 , 1.38036886, 1.38039873,\n",
       "       1.380441  , 1.38045847, 1.38046074, 1.3804688 , 1.38046993,\n",
       "       1.38048421, 1.38049098, 1.38051   , 1.38052679, 1.3805396 ,\n",
       "       1.38055756, 1.38056921, 1.38057183, 1.38057291, 1.38057491,\n",
       "       1.38058207, 1.38058785, 1.3805999 , 1.38063044, 1.38064219,\n",
       "       1.3806533 , 1.38066905, 1.38067101, 1.3806743 , 1.38069756,\n",
       "       1.38070646]))\n",
       "           fun: 1.377063725640201\n",
       "       message: 'Maximum number of function evaluations has been exceeded.'\n",
       "          nfev: 40000\n",
       "           nit: 39406\n",
       "        status: 1\n",
       "       success: False\n",
       "             x: array([ 7.14951626e-01, -2.14900765e-01,  2.62196787e-01, -5.69971072e-02,\n",
       "       -1.42609375e-01,  2.69089139e-01,  7.54076710e-02, -3.14901425e-02,\n",
       "        5.60097670e-02,  3.82596594e-01,  3.20371910e-01, -1.12569508e-01,\n",
       "       -3.17043387e-02,  6.68293525e-03, -4.20195876e-02, -4.10791816e-02,\n",
       "        1.02416970e-01,  4.32354990e-03, -1.14177532e-01, -1.71630481e-01,\n",
       "        8.38643527e-02,  9.81511167e-02,  1.22067711e-01,  8.08512233e-02,\n",
       "        3.93714653e-02, -1.46533057e-01, -2.47117050e-03, -1.36382264e-03,\n",
       "       -2.94029208e-03,  7.74640363e-02,  4.53157909e-02,  1.31184489e-01,\n",
       "        3.09119220e-03, -8.52613142e-03, -4.90840504e-02, -2.01146866e-01,\n",
       "       -4.41957200e-02, -6.92669418e-02,  1.17283905e-02,  1.36153779e-01,\n",
       "        1.29290255e-01,  7.40513655e-01, -3.95581446e-01, -1.20664321e-01,\n",
       "       -5.21014623e-03, -7.06444521e-02, -5.04447881e-04, -7.69616575e-03,\n",
       "       -2.99512025e-02,  7.01695910e-01, -4.47050590e-02,  6.74594039e-03,\n",
       "        3.01289418e-01, -1.51336668e-01,  2.36481306e-01, -1.84911779e-02,\n",
       "        4.02398748e-02, -6.13747442e-02, -6.76749876e-02, -1.55941441e-02,\n",
       "        1.89526808e-01, -4.50698043e-02, -1.98237023e-01,  4.34003611e-02,\n",
       "        3.67997605e-02, -2.32950643e-02,  2.04387680e-01,  3.10125757e-03,\n",
       "        3.08929209e-01,  9.86096093e-03, -1.23786657e-03, -4.85819176e-02,\n",
       "        1.33072034e-02, -1.63444486e-01, -1.69614079e-01, -2.51950191e-01,\n",
       "       -2.52732994e-02,  3.96265479e-03,  5.59544991e-02, -5.99870476e-03,\n",
       "        2.14535638e-02,  1.29279136e-01,  3.44469754e-02, -2.19747669e-01,\n",
       "       -2.20298539e-02,  9.89732384e-04,  1.68352834e-03,  4.07058928e-02,\n",
       "        6.03178095e-01, -9.13113605e-03, -1.09601036e-01,  3.90880834e-02,\n",
       "        1.01944109e-02, -1.28860405e-02,  3.62243121e-02,  2.14129734e-02,\n",
       "       -7.09735205e-03,  5.30232121e-03, -6.74485600e-02, -2.41210748e-01,\n",
       "        7.73394214e-02, -3.29058853e-02,  6.18331601e-03, -7.01295996e-02,\n",
       "        8.40408048e-01, -4.43019607e-03,  4.18439041e-02,  1.39333852e-02,\n",
       "       -3.12162004e-02, -2.00019479e-01, -7.36492961e-02, -4.14506753e-03,\n",
       "        1.17107731e-02,  1.94207100e-02,  3.63013075e-01,  3.34834625e-02,\n",
       "        8.14959810e-03, -8.40634424e-02,  2.59051264e-01, -2.45032766e-02,\n",
       "       -5.83395902e-02,  7.97327704e-02,  5.99476259e-03,  1.32246678e-03,\n",
       "       -7.56098258e-02, -1.19327645e-01, -1.38812171e-04, -5.23751832e-02,\n",
       "        1.69860414e-01, -1.00081692e-01,  4.01630867e-01, -1.51033497e-01,\n",
       "       -2.60379111e-02,  8.28321496e-02,  4.40174162e-01,  5.74231018e-01,\n",
       "       -2.21554383e-01, -3.79800850e-02,  2.49476578e-01, -4.13115250e-02,\n",
       "       -9.92155798e-05, -1.01342151e-01,  5.47000296e-01, -1.47403693e-02,\n",
       "        4.81799974e-02,  3.30829914e-02, -1.27967261e-01,  2.33555641e-02,\n",
       "       -9.48829075e-03, -1.32887230e-01,  2.69657141e-01,  3.06345656e-02,\n",
       "        7.30057789e-03,  1.58179545e-01,  1.78610191e-01,  2.32245976e-02,\n",
       "       -2.59326526e-05,  2.24466526e-01,  1.00467699e-01,  3.33651038e-01,\n",
       "       -1.76842780e-02, -3.73571447e-03,  2.31833940e-02, -3.37607078e-01,\n",
       "        1.65577719e-02,  2.77404584e-02, -3.53162637e-02, -1.01721204e-02,\n",
       "       -2.20972061e-02,  1.84870359e-01, -2.59128884e-02,  5.65755160e-02,\n",
       "        8.60430012e-01, -3.81193270e-02, -8.51540915e-02, -1.27769848e-01,\n",
       "       -6.58772660e-02,  5.01167680e-02, -2.33205028e-02, -1.28755227e-02,\n",
       "       -2.55155338e-02,  4.09342840e-02, -3.70341179e-02, -5.01473718e-02,\n",
       "       -1.78912606e-01,  1.67575288e-01, -1.11770258e-01, -2.45378585e-04,\n",
       "        1.71048757e-01,  1.81471170e-01,  1.10314689e-02,  1.99776158e-02,\n",
       "       -5.52319431e-02,  2.65674813e-02,  2.77749450e-02,  4.78323918e-02,\n",
       "       -2.11352187e-01,  1.48367862e-01,  4.44707626e-03,  1.13139360e-01])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "##It does not seem to work to have double invokes here...\n",
    "import scipy as scp\n",
    "from scipy.optimize import minimize\n",
    "#cost = lambda z: cost_functions.cost_Lpnorm_mvj(z, F= f, B= bdry, p= 20)\n",
    "#grad = lambda z: cost_functions.grad_Lpnorm_mvj(z, F= f, B= bdry, p= 20)\n",
    "def cost(z):\n",
    "    import cost_functions\n",
    "    return cost_functions.cost_Lpnorm_mvj(z, F= f, B= bdry, p= 20)\n",
    "\n",
    "def grad(z):\n",
    "    import cost_functions\n",
    "    return cost_functions.grad_Lpnorm_mvj(z, F= f, B= bdry, p= 20)\n",
    "\n",
    "#res = minimize(cost, l2_cocycle, method='L-BFGS-B', jac = grad)\n",
    "res=scp.optimize.minimize(cost, l2_cocycle, method=\"Nelder-Mead\") \n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7888, 1)\n",
      "(7888, 1)\n",
      "[array([[ 0.11583309],\n",
      "       [ 0.12876784],\n",
      "       [ 0.13742165],\n",
      "       [-0.05721079],\n",
      "       [-0.01727273],\n",
      "       [ 0.0786415 ],\n",
      "       [-0.05709237],\n",
      "       [-0.00692939],\n",
      "       [-0.05713997],\n",
      "       [ 0.07865411],\n",
      "       [ 0.07864679],\n",
      "       [ 0.32294084],\n",
      "       [-0.01727163],\n",
      "       [-0.00689554],\n",
      "       [ 0.078652  ],\n",
      "       [-0.05710637],\n",
      "       [ 0.14310418],\n",
      "       [-0.00690504],\n",
      "       [-0.01048052],\n",
      "       [ 0.32243803],\n",
      "       [-0.04987355],\n",
      "       [ 0.07866034],\n",
      "       [ 0.07865529],\n",
      "       [-0.05692918],\n",
      "       [-0.00687819],\n",
      "       [-0.00692194],\n",
      "       [ 0.15725742],\n",
      "       [-0.00689204],\n",
      "       [-0.00687162],\n",
      "       [-0.05710125],\n",
      "       [-0.05709784],\n",
      "       [-0.05710709],\n",
      "       [-0.05710052],\n",
      "       [-0.00692131],\n",
      "       [ 0.1121909 ],\n",
      "       [ 0.32242834],\n",
      "       [-0.00691983],\n",
      "       [-0.00690888],\n",
      "       [-0.00687895],\n",
      "       [ 0.07865915],\n",
      "       [-0.05710851],\n",
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      "       [ 0.07863872],\n",
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      "       [ 0.07865664],\n",
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      "       [ 0.1279519 ],\n",
      "       [-0.00690098],\n",
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      "       [ 0.12874449],\n",
      "       [ 0.13635161],\n",
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      "       [ 0.07866404],\n",
      "       [-0.00691008],\n",
      "       [-0.05709652],\n",
      "       [-0.00688781],\n",
      "       [-0.00681668],\n",
      "       [-0.61258713],\n",
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      "       [-0.65324363],\n",
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      "       [ 0.07864663],\n",
      "       [ 0.08843447],\n",
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      "       [-0.05711934],\n",
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      "       [-0.00688207],\n",
      "       [-0.00689692],\n",
      "       [-0.00693135],\n",
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      "       [-0.0068843 ],\n",
      "       [-0.00692186],\n",
      "       [ 0.07865891],\n",
      "       [-0.04987975],\n",
      "       [ 0.07864862],\n",
      "       [ 0.3115681 ],\n",
      "       [-0.00690464],\n",
      "       [-0.05711282],\n",
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      "       [ 0.0786546 ],\n",
      "       [-0.00692327],\n",
      "       [ 0.07867267],\n",
      "       [ 0.07846984],\n",
      "       [-0.05710368],\n",
      "       [-0.00688874],\n",
      "       [-0.00691904],\n",
      "       [-0.61258539],\n",
      "       [-0.00688709],\n",
      "       [-0.00691328],\n",
      "       [-0.00682891],\n",
      "       [-0.05710331],\n",
      "       [-0.00689113],\n",
      "       [ 0.04924474],\n",
      "       [ 0.07867219],\n",
      "       [ 0.07866153],\n",
      "       [-0.0068779 ],\n",
      "       [-0.00690917],\n",
      "       [ 0.07865748],\n",
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      "       [-0.00688029],\n",
      "       [-0.00690143],\n",
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      "       [-0.05708675],\n",
      "       [ 0.12350657],\n",
      "       [-0.00687303],\n",
      "       [-0.00689065],\n",
      "       [-0.05715958],\n",
      "       [-0.04988417],\n",
      "       [-0.02776184],\n",
      "       [-0.00688112],\n",
      "       [ 0.16344936],\n",
      "       [ 0.14617596],\n",
      "       [-0.00691383],\n",
      "       [ 0.07865236],\n",
      "       [-0.00691478],\n",
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      "       [-0.56861397],\n",
      "       [ 0.07866848],\n",
      "       [-0.05710474],\n",
      "       [ 0.15994358],\n",
      "       [-0.00692745],\n",
      "       [-0.0568712 ],\n",
      "       [-0.00690977],\n",
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      "       [-0.00692545],\n",
      "       [-0.00867938],\n",
      "       [ 0.31825761],\n",
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      "       [ 0.07863751],\n",
      "       [ 0.14490289],\n",
      "       [-0.00690547],\n",
      "       [-0.00683904],\n",
      "       [ 0.0786658 ],\n",
      "       [-0.00689618],\n",
      "       [-0.05710183],\n",
      "       [-0.00692906],\n",
      "       [-0.00691058],\n",
      "       [-0.04988438],\n",
      "       [ 0.07866217],\n",
      "       [ 0.32242458],\n",
      "       [ 0.07866221],\n",
      "       [-0.00690168],\n",
      "       [-0.00692598]]), 385.14357139608904]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.11583309],\n",
       "       [ 0.12876784],\n",
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       "       [-0.00691008],\n",
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       "       [ 0.07867219],\n",
       "       [ 0.07866153],\n",
       "       [-0.0068779 ],\n",
       "       [-0.00690917],\n",
       "       [ 0.07865748],\n",
       "       [-0.05712099],\n",
       "       [-0.00688029],\n",
       "       [-0.00690143],\n",
       "       [ 0.07865698],\n",
       "       [-0.05708675],\n",
       "       [ 0.12350657],\n",
       "       [-0.00687303],\n",
       "       [-0.00689065],\n",
       "       [-0.05715958],\n",
       "       [-0.04988417],\n",
       "       [-0.02776184],\n",
       "       [-0.00688112],\n",
       "       [ 0.16344936],\n",
       "       [ 0.14617596],\n",
       "       [-0.00691383],\n",
       "       [ 0.07865236],\n",
       "       [-0.00691478],\n",
       "       [-0.02775898],\n",
       "       [-0.56861397],\n",
       "       [ 0.07866848],\n",
       "       [-0.05710474],\n",
       "       [ 0.15994358],\n",
       "       [-0.00692745],\n",
       "       [-0.0568712 ],\n",
       "       [-0.00690977],\n",
       "       [-0.06446709],\n",
       "       [-0.00887723],\n",
       "       [-0.00692545],\n",
       "       [-0.00867938],\n",
       "       [ 0.31825761],\n",
       "       [-0.05711793],\n",
       "       [ 0.07863751],\n",
       "       [ 0.14490289],\n",
       "       [-0.00690547],\n",
       "       [-0.00683904],\n",
       "       [ 0.0786658 ],\n",
       "       [-0.00689618],\n",
       "       [-0.05710183],\n",
       "       [-0.00692906],\n",
       "       [-0.00691058],\n",
       "       [-0.04988438],\n",
       "       [ 0.07866217],\n",
       "       [ 0.32242458],\n",
       "       [ 0.07866221],\n",
       "       [-0.00690168],\n",
       "       [-0.00692598]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "#import tensorflow_probability as tfp\n",
    "'''Following seems deprecated in newer version of tfp\n",
    "#pip install --upgrade tensorflow-probability==0.70\n",
    "#alternatively, we can use tensorflow to minimize the cost function without gradient information, here we can use multiple black-box functions like Adams\n",
    "#For more: Check at https://www.tensorflow.org/probability/api_docs/python/tfp/math/minimize\n",
    "x = tf.Variable(0.)\n",
    "cost_fun = lambda: cost_functions.cost_Lpnorm_mvj(x, F= f, B= bdry, p= 20)\n",
    "res_tfp=tfp.math.minimize(\n",
    "        cost_fun,\n",
    "        num_steps=1000,\n",
    "        optimizer=tfp.optimizers.Adam(learning_rate=0.1)\n",
    "        )\n",
    "'''\n",
    "#Following seems working, c.f. \n",
    "#https://stackoverflow.com/questions/55552715/tensorflow-2-0-minimize-a-simple-function\n",
    "def cost(z):\n",
    "    import cost_functions\n",
    "    return cost_functions.cost_Lpnorm_mvj(z, F= f, B= bdry, p= 20)\n",
    "#type(bdry)\n",
    "#scipy.sparse.csr.csr_matrix\n",
    "B_mat = bdry.todense()\n",
    "import tensorflow as tf\n",
    "print(f.shape)\n",
    "print((B_mat*l2_cocycle).shape)\n",
    "z = tf.Variable(l2_cocycle, trainable=True)\n",
    "\n",
    "#L1 in tensorflow language\n",
    "cost_z = tf.reduce_sum( tf.abs(f - B_mat @ z) )\n",
    "#L2 in tensorflow language\n",
    "cost_z = tf.reduce_sum( tf.pow( tf.abs(f - B_mat @ z),2 ) )\n",
    "#Lp+alpha*Lq norm in tensorflow language\n",
    "lp=1\n",
    "lq=2\n",
    "alpha=.5\n",
    "cost_z = (1-alpha)*tf.pow( tf.reduce_sum( tf.pow( tf.abs(f - B_mat @ z),lp ) ), 1/lp) + alpha* tf.pow( tf.reduce_sum( tf.pow( tf.abs(f - B_mat @ z),lq ) ), 1/lq)\n",
    "\n",
    "#Gradient Descedent Optimizer\n",
    "opt_gd = tf.train.GradientDescentOptimizer(0.1).minimize(cost_z)\n",
    "#Adams Optimizer\n",
    "opt_adams = tf.train.AdamOptimizer(1e-4).minimize(cost_z)\n",
    "#The latter is much better in terms of result\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    for i in range(1000):#How many iterations you want to run?\n",
    "        #print(sess.run([x,loss]))\n",
    "        sess.run(opt_adams)\n",
    "    res_tf=sess.run([z,cost_z])\n",
    "type(res_tf)\n",
    "print(res_tf)\n",
    "res_tf=res_tf[0]\n",
    "res_tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "color = np.mod(res_tf.T[0,:],1)\n",
    "scatter(annulus.T[0,:],annulus.T[1,:],s=20, c=color, cmap=\"hsv\")\n",
    "#scatter(*annulus.T, c= color, cmap=\"hsv\")\n",
    "plt.colorbar()\n",
    "plt.axis('equal')\n",
    "plt.title('Smoothed values mod 1 - {}*L{} + {}*L{} elastic norm with TensorFlow'.format(1-alpha,lp,alpha,lq))\n",
    "plt.show()\n",
    "toll = 1e-5\n",
    "edges_constant = []\n",
    "thr = chosen_bar.birth # i want to check constant edges in all edges that were there when the cycle was created\n",
    "for s in vr:\n",
    "    if s.dimension() != 1:\n",
    "        continue\n",
    "    elif s.data > thr:\n",
    "        break\n",
    "    if abs(color[s[0]]-color[s[1]]) <= toll:\n",
    "        edges_constant.append([annulus[s[0],:],annulus[s[1],:]])\n",
    "edges_constant = np.array(edges_constant)        \n",
    "#scatter(*annulus.T, c=color, cmap=\"hsv\", alpha=.5)\n",
    "scatter(annulus.T[0,:],annulus.T[1,:],s=20, c=color, cmap=\"hsv\")\n",
    "#plot(*edges_constant.T, c='k')\n",
    "plot(edges_constant.T[0,:],edges_constant.T[1,:], c='k')\n",
    "edges_constant.shape\n",
    "plt.axis('equal')\n",
    "plt.title('Visualizing constant edges')\n",
    "plt.show()"
   ]
  },
  {
   "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",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}