adding introduction notebook

440f44ed · shawk masboob · 8e8bb9c7 · 440f44ed
Commit 440f44ed authored 4 years ago by shawk masboob
--- a/TDA_Introduction.ipynb
+++ b/TDA_Introduction.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h1><center>Topological Data Analysis</center></h1>\n",
+    "\n",
+    "![Url](https://thumbs.gfycat.com/DisgustingBlandDromedary-size_restricted.gif)\n",
+    "\n",
+    "<p style=\"text-align: center;\">Gif from: https://gfycat.com/disgustingblanddromedary</p>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from ripser import ripser\n",
+    "from persim import plot_diagrams\n",
+    "\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Background"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Simplicial Complex"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Homology"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Betti Number"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Euler-Poincare Formula"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Persistent Homology"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "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"
+    }
+   ],
+   "source": [
+    "N = 25\n",
+    "\n",
+    "r = np.random.uniform(-0.2, 0.2, N) # radious\n",
+    "theta = np.random.uniform(-np.pi, np.pi, N) # angles\n",
+    "\n",
+    "x = (1+r)*np.cos(theta) # x-corodinate\n",
+    "y = (1+r)*np.sin(theta) # y-coordinate\n",
+    "\n",
+    "X = np.column_stack((x,y)) # data set\n",
+    "\n",
+    "plt.scatter(X[:,0], X[:,1])\n",
+    "\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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JRBSRMImIIhImEVFEwiQiikiYREQRCZOIKKKxMJF0gqT76++AXSBp3z7a7S3pLkmLJB3bVD0R0axGvgO2xam2v9LXTEnrAGcA7wSWADdKmm379obriojCRno3ZyqwyPa9tp8DLgSmjXBNEbEWmg6ToyTdImmWpI07zJ8I3NcyvqSetpp0Dxoxug0pTCRdLWlhh8c04FvAa4ApwAPAVzutosO0vnr/m2m7x3bP+PHjh1J2RDRgSMdMBuoitJeks4CfdJi1BJjcMj4JWDqUmiJiZDR5NmfLltH96dz1543AdpK2lbQeMB2Y3VRNEdGcJs/mnCJpCtVuy2LgCKi6CAW+Y3tf2yslHQVcCawDzLJ9W4M1RURDGgsT2x/sY/qqLkLr8TnAnE5tI6J7jPSp4YgYIxImEVFEwiQiikiYREQRCZOIKCJhEhFFJEwiooiESUQUkTCJiCISJhFRRMIkIopImEREEQmTiCgiYRIRRSRMIqKIhElEFJEwiYgiEiYRUUQjX9so6SJg+3p0I+AJ21M6tFsMPAk8D6y03dNEPRHRvEbCxPbf9Q5L+iqwvJ/mu9t+pIk6ImL4NNrXsCQBHwDe0eTzRMTIa/qYyduAh2zf3cd8A1dJmi9pRsO1RESD1nrLRNLVwBYdZh1n+0f18EHABf2sZlfbSyVtDsyVdKfta/p4vhnADICtt956bcuOiIbI7ti179BXLK0L3A/sYnvJINqfADxl+ysDte3p6fG8efOGXmREdCRp/pqeEGlyN2dP4M6+gkTSOEkb9A4De9G5C9GI6AJNhsl02nZxJG0lqbf3vgnAdZJuBn4NXGb7igbriYgGNdk96Ic6TFvVNajte4Gdm3r+iBheuQI2IopImEREEQmTiCgiYRIRRSRMIqKIhElEFJEwiYgiEiYRUUTCJCKKSJhERBEJk4goImESEUUkTCKiiIRJRBSRMImIIhImEVFEwiQiikiYREQRCZOIKGJIYSLpQEm3SfqTpJ62eZ+WtEjSXZLe1cfy20q6QdLdki6StN5Q6omIkTPULZOFwPuBF3WcJWlHqm+n3wnYG/impHU6LH8ycKrt7YDHgcOHWE9EjJAhhYntO2zf1WHWNOBC28/a/i2wCJja2qDuh/gdwA/rSecC7xtKPRExcprq6mIicH3L+JJ6WqtNgSdsr+ynzSqt3YMCz0oaix12bQY8MtJFNGCsvi4Yu69t+zVdYMAwGWSfwqst1mFaez+kg2nzwgx7JjCzrmnemnZd2A3yurrPWH1tkta4/90Bw8T2nmtRyxJgcsv4JGBpW5tHgI0krVtvnXRqExFdoqlTw7OB6ZLWl7QtsB1VF6CruOox/efAAfWkQ4G+tnQiYpQb6qnh/SUtAd4CXCbpSgDbtwE/AG4HrgA+Zvv5epk5kraqV3EM8E+SFlEdQzl7kE89cyh1j2J5Xd1nrL62NX5dqjYQIiKGJlfARkQRCZOIKKJrwmSol+53C0knSLpf0oL6se9I1zQUkvauP5dFko4d6XpKkbRY0q31Z7TGp1FHE0mzJC1rvXZL0iaS5ta3usyVtPFA6+maMGHol+53k1NtT6kfc0a6mLVVfw5nAPsAOwIH1Z/XWLF7/Rl1+3Um51D97bQ6FvhpfavLT+vxfnVNmAzl0v0YMVOBRbbvtf0ccCHV5xWjiO1rgMfaJk+jusUFBnmrS9eEST8mAve1jPd7WX6XOErSLfXm54Cbl6PYWPxsehm4StL8+laPsWaC7QcA6p+bD7RAU/fmrJUGL90fVfp7ncC3gBOpXsOJwFeBDw9fdUV13WezBna1vVTS5sBcSXfW/+FfskZVmDR46f6oMtjXKeks4CcNl9OkrvtsBsv20vrnMkmXUO3SjaUweUjSlrYfkLQlsGygBcbCbs6Al+53k/qD67U/1YHnbnUjsF39JVjrUR0onz3CNQ2ZpHGSNugdBvaiuz+nTmZT3eICg7zVZVRtmfRH0v7AacB4qkv3F9h+l+3bJPVeur+Slkv3u9QpkqZQ7Q4sBo4Y2XLWnu2Vko4CrgTWAWbVt1p0uwnAJdVX8rAu8H3bV4xsSWtP0gXAbsBm9e0xnwdOAn4g6XDg/4ADB1xPLqePiBLGwm5ORIwCCZOIKCJhEhFFJEwiooiESUQUkTCJiCISJhFRxP8DMfVsixEHCoIAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from matplotlib import pyplot as plt\n",
+    "from matplotlib import animation\n",
+    "def create_circle():\n",
+    "    circle = plt.Circle((0, 0), 0.05)\n",
+    "    return circle\n",
+    "def update_radius(i, circle):\n",
+    "    circle.radius = i*0.5\n",
+    "    return circle,\n",
+    "def create_animation():\n",
+    "    fig = plt.gcf()\n",
+    "    ax = plt.axes(xlim=(-10, 10), ylim=(-10, 10))\n",
+    "    ax.set_aspect('equal')\n",
+    "    circle = create_circle()\n",
+    "    ax.add_patch(circle)\n",
+    "    anim = animation.FuncAnimation(\n",
+    "        fig, update_radius, fargs = (circle,), frames=30, interval=50)\n",
+    "    plt.title('Simple Circle Animation')\n",
+    "    plt.show()\n",
+    "if __name__ == '__main__':\n",
+    "    create_animation()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### References"
+   ]
+  },
+  {
+   "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:markdown id: tags:
+
+<h1><center>Topological Data Analysis</center></h1>
+
+![Url](https://thumbs.gfycat.com/DisgustingBlandDromedary-size_restricted.gif)
+
+<p style="text-align: center;">Gif from: https://gfycat.com/disgustingblanddromedary</p>
+
+%% Cell type:code id: tags:
+
+``` python
+import numpy as np
+import matplotlib.pyplot as plt
+from ripser import ripser
+from persim import plot_diagrams
+
+%matplotlib inline
+```
+
+%% Cell type:markdown id: tags:
+
+### Background
+
+%% Cell type:markdown id: tags:
+
+### Simplicial Complex
+
+%% Cell type:markdown id: tags:
+
+### Homology
+
+%% Cell type:markdown id: tags:
+
+#### Betti Number
+
+%% Cell type:markdown id: tags:
+
+#### Euler-Poincare Formula
+
+%% Cell type:markdown id: tags:
+
+### Persistent Homology
+
+%% Cell type:code id: tags:
+
+``` python
+N = 25
+
+r = np.random.uniform(-0.2, 0.2, N) # radious
+theta = np.random.uniform(-np.pi, np.pi, N) # angles
+
+x = (1+r)*np.cos(theta) # x-corodinate
+y = (1+r)*np.sin(theta) # y-coordinate
+
+X = np.column_stack((x,y)) # data set
+
+plt.scatter(X[:,0], X[:,1])
+
+plt.show()
+```
+
+%% Output
+
+
+
+%% Cell type:code id: tags:
+
+``` python
+from matplotlib import pyplot as plt
+from matplotlib import animation
+def create_circle():
+    circle = plt.Circle((0, 0), 0.05)
+    return circle
+def update_radius(i, circle):
+    circle.radius = i*0.5
+    return circle,
+def create_animation():
+    fig = plt.gcf()
+    ax = plt.axes(xlim=(-10, 10), ylim=(-10, 10))
+    ax.set_aspect('equal')
+    circle = create_circle()
+    ax.add_patch(circle)
+    anim = animation.FuncAnimation(
+        fig, update_radius, fargs = (circle,), frames=30, interval=50)
+    plt.title('Simple Circle Animation')
+    plt.show()
+if __name__ == '__main__':
+    create_animation()
+```
+
+%% Output
+
+
+
+%% Cell type:markdown id: tags:
+
+### References
+
+%% Cell type:code id: tags:
+
+``` python
+```