{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating data points: 100%|██████████| 324/324 [00:11<00:00, 28.10it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoding... done\n"
     ]
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import sys\n",
    "sys.path.insert(0, './Persistent_Homology')\n",
    "\n",
    "from gratings import grating_model\n",
    "from plotting import plot_data, plot_mean_against_index, show_feature\n",
    "from persistence import persistence\n",
    "from decoding import cohomological_parameterization, remove_feature\n",
    "from noisereduction import PCA_reduction, z_cutoff\n",
    "\n",
    "\n",
    "\n",
    "## Generate data\n",
    "data = grating_model(Nn=8, Np=(18,1,18,1), deltaT=55) #, random_neurons=True\n",
    "\n",
    "## Apply noise reduction\n",
    "# data = PCA_reduction(data, 5)\n",
    "# data = z_cutoff(data,2)\n",
    "\n",
    "## Analyze shape\n",
    "# persistence(data,homdim=2,coeff=2)\n",
    "# persistence(data,homdim=2,coeff=3)\n",
    "\n",
    "## Decode first parameter\n",
    "decoding1 = cohomological_parameterization(data, coeff=23)\n",
    "# show_feature(decoding1)\n",
    "# plot_data(data,transformation=\"PCA\", labels=decoding1,\n",
    "#           colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mean_against_index(data,decoding1,\"orientation\")\n",
    "plot_mean_against_index(data,decoding1,\"phase\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoding... done\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Decode second parameter\n",
    "reduced_data = remove_feature(data, decoding1, cut_amplitude=0.5)\n",
    "decoding2 = cohomological_parameterization(reduced_data, coeff=23)\n",
    "# show_feature(decoding2)\n",
    "plot_mean_against_index(data,decoding2,\"orientation\")\n",
    "plot_mean_against_index(data,decoding2,\"phase\")\n",
    "# plot_data(data,transformation=\"PCA\", labels=decoding2,\n",
    "        #   colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Klein bottle\n",
    "R = 25\n",
    "r = 12\n",
    "N = 20\n",
    "data_4D_klein_bottle = []\n",
    "phase = np.linspace(0,2*np.pi, N)\n",
    "orientation = np.linspace(0, np.pi, N)\n",
    "for phi in phase:\n",
    "    for theta in orientation:\n",
    "        x1 = (R + r*np.cos(phi)) *np.cos(2*theta)\n",
    "        x2 = (R + r*np.cos(phi)) *np.sin(2*theta)\n",
    "        x3 = r*np.sin(phi)*np.cos(theta)\n",
    "        x4 = r*np.sin(phi)*np.sin(theta)\n",
    "        data_4D_klein_bottle.append([x1, x2, x3, x4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Klein bottle\n",
    "R = 25\n",
    "P = 8\n",
    "N = 20\n",
    "eps = 0.8\n",
    "data_4D_klein_bottle = []\n",
    "phis = np.linspace(0,2*np.pi, N)\n",
    "vs = np.linspace(0, 2*np.pi, N)\n",
    "param = []\n",
    "for phi in phis:\n",
    "    for v in vs:\n",
    "        param.append([phi, v])\n",
    "        x1 = R * (np.cos(phi/2) * np.cos(v) - np.sin(phi/2)*np.sin(2*v))\n",
    "        x2 = R * (np.sin(phi/2) * np.cos(v) + np.cos(phi/2)*np.sin(2*v))\n",
    "        x3 = P*np.cos(phi)*(1 + eps * np.sin(v))\n",
    "        x4 = P*np.sin(phi)*(1 + eps * np.sin(v))\n",
    "        data_4D_klein_bottle.append([x1, x2, x3, x4])\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x_1 = (R + r\\cos(\\phi))\\cos(\\theta),\\\\\n",
    " x_2 = (R + r\\cos(\\phi))\\sin(\\theta),\\\\\n",
    " x_3 = r\\sin(\\phi)\\cos(\\theta/2)\\\\\n",
    " x_4 = r\\sin(\\phi)\\sin(\\theta/2) $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4D non-intersecting parametrization\n",
    "$ x1 = R(\\cos(\\phi/2) \\cos(v) - \\sin(\\phi/2) \\sin(2v)) \\\\\n",
    "x2 = R(\\sin(\\phi/2) \\cos(v) + \\cos(\\phi/2) \\sin(2v)) \\\\\n",
    "x3 = P\\cos(\\phi)(1+\\epsilon \\sin(v))\\\\\n",
    "x4 = P\\sin(\\phi])(1+\\epsilon \\sin(v))\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_4D_klein_bottle = pd.DataFrame(np.array(data_4D_klein_bottle))\n",
    "param = np.array(param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(400, 4)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_4D_klein_bottle.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "## Apply noise reduction\n",
    "# data = PCA_reduction(data, 5)\n",
    "# data = z_cutoff(data,2)\n",
    "\n",
    "## Analyze shape\n",
    "persistence(data_4D_klein_bottle,homdim=2,coeff=2)\n",
    "persistence(data_4D_klein_bottle,homdim=2,coeff=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoding... done\n"
     ]
    }
   ],
   "source": [
    "## Decode first parameter\n",
    "decoding1 = cohomological_parameterization(data_4D_klein_bottle, coeff=23)\n",
    "# show_feature(decoding1)\n",
    "# plot_mean_against_index(data_4D_klein_bottle,decoding1)\n",
    "# plot_mean_against_index(data,decoding1,\"phase\")\n",
    "# plot_data(data,transformation=\"PCA\", labels=decoding1,\n",
    "#           colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x251304908e0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(param[:,1], decoding1['decoding'][:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoding... done\n"
     ]
    }
   ],
   "source": [
    "\n",
    "## Decode second parameter\n",
    "reduced_data = remove_feature(data_4D_klein_bottle, decoding1, cut_amplitude=0.5)\n",
    "decoding2 = cohomological_parameterization(reduced_data, coeff=23)\n",
    "# show_feature(decoding2)\n",
    "# plot_mean_against_index(data,decoding2,\"orientation\")\n",
    "# plot_mean_against_index(data,decoding2,\"phase\")\n",
    "# plot_data(data,transformation=\"PCA\", labels=decoding2,\n",
    "#           colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x25130ef1dc0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(param[:,1], decoding2['decoding'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "N = 10\n",
    "radius = 10\n",
    "theta_range = np.linspace(0, 2* np.pi, 20)\n",
    "data_circle = [[radius*np.cos(theta), radius*np.sin(theta)] for theta in theta_range]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_circle = pd.DataFrame(np.array(data_circle))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persistence(data_circle, homdim=1, coeff=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decoding... done\n"
     ]
    }
   ],
   "source": [
    "decoding1 = cohomological_parameterization(data_circle, coeff=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a8b5522850>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(theta_range, decoding1['decoding'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Source manifold: coordinates to natural embedding\n",
    "obser"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "source_manifold\n",
    "open_cover\n",
    "patch\n",
    "set of patches\n",
    "coordinate system for each patch\n",
    "observed_embedding\n",
    "homologies give us better candidates for meaningful coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def circle(theta):\n",
    "    \n",
    "def torus(theta, phi):\n",
    "\n",
    "def klein_bottle(theta, phi):\n",
    "\n",
    "def sphere(theta, phi):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "    \n",
    "def hausdorff(data1, data2, homdim, coeff):\n",
    "    \"\"\"Hausdorff metric between two persistence diagrams\"\"\"\n",
    "    dgm1 = (ripser.ripser(data1,maxdim=homdim,coeff=coeff))['dgms']\n",
    "    dgm2 = (ripser.ripser(data2,maxdim=homdim,coeff=coeff))['dgms']\n",
    "    distance = directed_hausdorff(dgm1[homdim], dgm2[homdim])[0]\n",
    "    return distance\n",
    "\n",
    "@multi_input\n",
    "def confidence(X, alpha=0.05, Nsubsamples=20, homdim=1, coeff=2):\n",
    "    \"\"\"\n",
    "    Compute the confidence interval of the persistence diagram of a dataset\n",
    "    \n",
    "    Computation done by subsampling as in arxiv:1303.7117\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: dataframe(n_datapoints, n_features):\n",
    "        Dataframe containing the data\n",
    "    alpha : float between 0 and 1, optional, default 0.05\n",
    "        1-alpha is the confidence\n",
    "    Nsubsamples : int, optional, default 20\n",
    "        The number of subsamples\n",
    "    homdim : int, optional, default 1\n",
    "        The dimension of the homology\n",
    "    coeff : int prime, optional, default 2\n",
    "        The coefficient basis\n",
    "    \"\"\"\n",
    "    N = X.shape[0]\n",
    "    distances = np.zeros(Nsubsamples)\n",
    "    iterator = trange(0, Nsubsamples, position=0, leave=True)\n",
    "    iterator.set_description(\"Computing confidence interval\")\n",
    "    for i in iterator:\n",
    "        subsample = X.iloc[np.random.choice(N, N, replace=True)] # replace = False\n",
    "        distances[i] = hausdorff(X, subsample, homdim, coeff)\n",
    "    distances.sort()\n",
    "    confidence = np.sqrt(2) * 2 * distances[int(alpha*Nsubsamples)]\n",
    "    return confidence\n",
    "\n",
    "@multi_input\n",
    "def persistence(X, homdim=1, coeff=2, threshold=float('inf'),\n",
    "                show_largest_homology=0, distance_matrix=False, Nsubsamples=0,\n",
    "                alpha=0.05, cycle=None, save_path=None):\n",
    "    \"\"\"\n",
    "    Plot the persistence diagram of a dataset using ripser\n",
    "\n",
    "    Also prints the five largest homology components\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: dataframe(n_datapoints, n_features):\n",
    "        Dataframe containing the data\n",
    "    homdim : int, optional, default 1\n",
    "        The dimension of the homology\n",
    "    coeff : int prime, optional, default 2\n",
    "        The coefficient basis\n",
    "    threshold : float, optional, default infinity\n",
    "        The maximum distance in the filtration\n",
    "    show_largest_homology: int, optional, default 0\n",
    "        Print this many of the largest homology components\n",
    "    distance_matrix : bool, optional, default False\n",
    "        When true X will be interepreted as a distance matrix\n",
    "    Nsubsamples : int, optional, default 0\n",
    "        The number of subsamples used in computing the confidence interval\n",
    "        Does not compute the confidence interval when this is 0\n",
    "    alpha : float between 0 and 1, optional, default 0.05\n",
    "        1-alpha is the confidence\n",
    "    cycle : int, optional, default None\n",
    "        If given highlight the homology component in the plot corresponding to\n",
    "        this cycle id\n",
    "    save_path : str, optional, default None\n",
    "        When given save the plot here\n",
    "    \"\"\"\n",
    "    result = ripser.ripser(X, maxdim=homdim, coeff=coeff, do_cocycles=True,\n",
    "                           distance_matrix=distance_matrix, thresh=threshold)\n",
    "    diagrams = result['dgms']\n",
    "    plot_diagrams(diagrams, show=False)\n",
    "    if (Nsubsamples>0):\n",
    "        conf = confidence(X, alpha, Nsubsamples, homdim, 2)\n",
    "        line_length = 10000\n",
    "        plt.plot([0, line_length], [conf, line_length + conf], color='green',\n",
    "                 linestyle='dashed',linewidth=2)\n",
    "    if cycle is not None:\n",
    "        dgm1 = diagrams[1]\n",
    "        plt.scatter(dgm1[cycle, 0], dgm1[cycle, 1], 20, 'k', 'x')\n",
    "    if save_path is not None:\n",
    "        path = save_path + 'Z' + str(coeff)\n",
    "        if (Nsubsamples>0):\n",
    "            path += '_confidence' + str(1-alpha)\n",
    "        path += '.png'\n",
    "        plt.savefig(path)\n",
    "    plt.show()\n",
    "    \n",
    "    if show_largest_homology != 0:\n",
    "        dgm = diagrams[homdim]\n",
    "        largest_indices = np.argsort(dgm[:, 0] - dgm[:, 1])\n",
    "        largest_components = dgm[largest_indices[:show_largest_homology]]\n",
    "        print(f\"Largest {homdim}-homology components:\")\n",
    "        print(largest_components)\n",
    "    return\n",
    "\n",
    "@multi_input\n",
    "def persistence_witness(X, number_of_landmarks=100, max_alpha_square=0.0,\n",
    "                        homdim=1):\n",
    "    \"\"\"\n",
    "    Plot the persistence diagram of a dataset using gudhi\n",
    "\n",
    "    Uses a witness complex allowing it to be used on larger datasets\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: dataframe(n_datapoints, n_features):\n",
    "        Dataframe containing the data\n",
    "    number_of_landmarks : int, optional, default 100\n",
    "        The number of landmarks in the witness complex\n",
    "    max_alpha_square : double, optional, default 0.0\n",
    "        Maximal squared relaxation parameter\n",
    "    homdim : int, optional, default 1\n",
    "        The dimension of the homology\n",
    "    \"\"\"\n",
    "    print(\"Sampling landmarks...\", end=\" \")\n",
    "    \n",
    "    witnesses = X.to_numpy()\n",
    "    landmarks = gudhi.pick_n_random_points(\n",
    "        points=witnesses, nb_points=number_of_landmarks\n",
    "    )\n",
    "    print(\"done\")\n",
    "    message = (\n",
    "        \"EuclideanStrongWitnessComplex with max_edge_length=\"\n",
    "        + repr(max_alpha_square)\n",
    "        + \" - Number of landmarks=\"\n",
    "        + repr(number_of_landmarks)\n",
    "    )\n",
    "    print(message)\n",
    "    witness_complex = gudhi.EuclideanStrongWitnessComplex(\n",
    "        witnesses=witnesses, landmarks=landmarks\n",
    "    )\n",
    "    simplex_tree = witness_complex.create_simplex_tree(\n",
    "        max_alpha_square=max_alpha_square,\n",
    "        limit_dimension=homdim\n",
    "    )\n",
    "    message = \"Number of simplices=\" + repr(simplex_tree.num_simplices())\n",
    "    print(message)\n",
    "    diag = simplex_tree.persistence()\n",
    "    print(\"betti_numbers()=\")\n",
    "    print(simplex_tree.betti_numbers())\n",
    "    gudhi.plot_persistence_diagram(diag, band=0.0)\n",
    "    plt.show()\n",
    "    return\n"
   ]
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