Characterization of PH1 Example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bc250adc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 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"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inverse barcode problem solution X_0 [0.         0.08231514 0.14959482 0.23581218 0.30803434 0.36900613\n",
      " 0.44846321 0.51686192 0.60364243 0.65742649 0.71956152 0.77038877\n",
      " 0.86928074 0.93469511]\n",
      "Inverse barcode problem solution X_1: [0.         0.32863348 0.42900004 0.54690613 0.64673519 0.73201159\n",
      " 0.83406104 0.91972856 1.01563425 1.07561804 1.14025847 1.19312963\n",
      " 1.29295719 1.35908684]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import gudhi as gd\n",
    "from gudhi import RipsComplex\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# Parameters\n",
    "radius = 0.25\n",
    "center = np.array([0.5, 0.5])\n",
    "num_points = 100  # Total number of points\n",
    "noise_level = 0.05  # Amount of noise to add\n",
    "\n",
    "# Generate points on a perfect circle\n",
    "angles = np.linspace(0, 2*np.pi, num_points, endpoint=False)\n",
    "x = center[0] + radius * np.cos(angles)\n",
    "y = center[1] + radius * np.sin(angles)\n",
    "perfect_circle = np.column_stack((x, y))\n",
    "\n",
    "# Add Gaussian noise to make it a noisy circle\n",
    "noisy_circle = perfect_circle + np.random.normal(scale=noise_level, size=(num_points, 2))\n",
    "\n",
    "# Plot the points\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.scatter(noisy_circle[:, 0], noisy_circle[:, 1], s=10, c='blue')\n",
    "plt.title('Noisy Circle Point Cloud')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.grid(True)\n",
    "plt.axis('equal')  # Keep aspect ratio equal\n",
    "plt.show()\n",
    "\n",
    "# Crear complejo de Rips\n",
    "rips_complex = gd.RipsComplex(points=noisy_circle, max_edge_length=2.0)\n",
    "simplex_tree = rips_complex.create_simplex_tree(max_dimension=2)\n",
    "\n",
    "# Calcular persistencia\n",
    "simplex_tree.compute_persistence()\n",
    "\n",
    "# Graficar el barcode de persistencia\n",
    "gd.plot_persistence_barcode(simplex_tree.persistence())\n",
    "plt.title(\"Pointcloud's Barcode\")\n",
    "plt.show()\n",
    "# Extraer los pares de nacimiento y muerte de la persistencia\n",
    "persistence = simplex_tree.persistence()\n",
    "\n",
    "finite_deaths = [death for (dim, (birth, death)) in persistence if np.isfinite(death)]\n",
    "max_filtration = max(finite_deaths) + 0.1 if finite_deaths else 0.5\n",
    "\n",
    "\n",
    "# Extraer características de dimensión 1 (ciclos)\n",
    "dim_1_pairs = [pair[1] for pair in persistence if pair[0] == 1]\n",
    "bd_array = np.array(dim_1_pairs)\n",
    "\n",
    "# Graficar solo la barcode de dimensión 1 (horizontal)\n",
    "plt.figure(figsize=(8, 4))\n",
    "for i, (birth, death) in enumerate(bd_array):\n",
    "    plt.hlines(y=i, xmin=birth, xmax=death, color='steelblue', linewidth=10)\n",
    "plt.xlim(0, max_filtration)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Graficar solo la barcode de dimensión 1 (horizontal)\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.hlines(y=12, xmin=0, xmax=70, color='steelblue', linewidth=10)\n",
    "for i, (birth, death) in enumerate(bd_array):\n",
    "    # Start the bars at 0 instead of 'birth'\n",
    "    plt.xlim(0, max_filtration)\n",
    "    plt.hlines(y=i, xmin=0, xmax=death, color='steelblue', linewidth=10)\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.hlines(y=12, xmin=0, xmax=70, color='steelblue', linewidth=10)\n",
    "for i, (birth, death) in enumerate(bd_array):\n",
    "    # Start the bars at 0 instead of 'birth'\n",
    "    plt.xlim(0, max_filtration)\n",
    "    plt.hlines(y=i, xmin=0, xmax=birth, color='steelblue', linewidth=10)\n",
    "    \n",
    "# Cálculo de suma acumulativa de birth y death de los ciclos H1\n",
    "if dim_1_pairs:\n",
    "    births = [birth for (birth, death) in dim_1_pairs]\n",
    "    deaths = [death if np.isfinite(death) else max_filtration for (birth, death) in dim_1_pairs]\n",
    "\n",
    "    # Añadir el 0 al principio\n",
    "    births = [0] + births\n",
    "    deaths = [0] + deaths\n",
    "\n",
    "    # Sumas acumulativas\n",
    "    cumulative_births = np.cumsum(births)\n",
    "    cumulative_deaths = np.cumsum(deaths)\n",
    "\n",
    "    # Puntos 2D para graficar como una línea real 1D\n",
    "    birth_points_2d = np.array([[x, 0] for x in cumulative_births])\n",
    "    death_points_2d = np.array([[x, 0] for x in cumulative_deaths])\n",
    "\n",
    "    # Definir límites comunes para el eje X\n",
    "    x_max = max(cumulative_births[-1], cumulative_deaths[-1])\n",
    "    x_lim = (0, x_max * 1.05)  # Un pequeño margen a la derecha\n",
    "\n",
    "    # Gráfico de puntos acumulados de birth\n",
    "    plt.figure(figsize=(8, 2))\n",
    "    plt.scatter(birth_points_2d[:, 0], birth_points_2d[:, 1], color='green', s=100, label='Cumulative Births')\n",
    "    plt.axhline(0, color='black', linewidth=1)\n",
    "    plt.yticks([])\n",
    "    plt.xlim(x_lim)\n",
    "    plt.xlabel(\"Inverse barcode problem solution X_0\")\n",
    "    plt.title(\"Cumulative Births (H1)\")\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "    # Gráfico de puntos acumulados de death\n",
    "    plt.figure(figsize=(8, 2))\n",
    "    plt.scatter(death_points_2d[:, 0], death_points_2d[:, 1], color='purple', s=100, label='Cumulative Deaths')\n",
    "    plt.axhline(0, color='black', linewidth=1)\n",
    "    plt.yticks([])\n",
    "    plt.xlim(x_lim)\n",
    "    plt.xlabel(\"Inverse barcode problem solution X_1\")\n",
    "    plt.title(\"Cumulative Deaths (H1)\")\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "    # Imprimir resultados\n",
    "    print(\"Inverse barcode problem solution X_0\", cumulative_births)\n",
    "    print(\"Inverse barcode problem solution X_1:\", cumulative_deaths)\n",
    "\n"
   ]
  }
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