952 lines
212 KiB
Plaintext
952 lines
212 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "269c4188",
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"metadata": {},
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"source": [
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"# Exercise sheet\n",
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"\n",
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"Some general remarks about the exercises:\n",
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"* For your convenience functions from the lecture are included below. Feel free to reuse them without copying to the exercise solution box.\n",
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"* For each part of the exercise a solution box has been added, but you may insert additional boxes. Do not hesitate to add Markdown boxes for textual or LaTeX answers (via `Cell > Cell Type > Markdown`). But make sure to replace any part that says `YOUR CODE HERE` or `YOUR ANSWER HERE` and remove the `raise NotImplementedError()`.\n",
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"* Please make your code readable by humans (and not just by the Python interpreter): choose informative function and variable names and use consistent formatting. Feel free to check the [PEP 8 Style Guide for Python](https://www.python.org/dev/peps/pep-0008/) for the widely adopted coding conventions or [this guide for explanation](https://realpython.com/python-pep8/).\n",
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"* Make sure that the full notebook runs without errors before submitting your work. This you can do by selecting `Kernel > Restart & Run All` in the jupyter menu.\n",
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"* For some exercises test cases have been provided in a separate cell in the form of `assert` statements. When run, a successful test will give no output, whereas a failed test will display an error message.\n",
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"* Each sheet has 100 points worth of exercises. Note that only the grades of sheets number 2, 4, 6, 8 count towards the course examination. Submitting sheets 1, 3, 5, 7 & 9 is voluntary and their grades are just for feedback.\n",
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"\n",
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"Please fill in your name here:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"id": "220d541e",
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"metadata": {},
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"outputs": [],
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"source": [
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"NAME = \"Kees van Kempen\"\n",
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"NAMES_OF_COLLABORATORS = \"\""
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]
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},
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{
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"cell_type": "markdown",
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"id": "b6944e4c",
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"metadata": {},
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"source": [
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"---"
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]
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},
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"cell_type": "markdown",
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"id": "c53fbab6",
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"source": [
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"**Exercise sheet 8**\n",
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"\n",
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"Code from the lectures:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"id": "5e4391a6",
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"metadata": {
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"locked": true,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"rng = np.random.default_rng() \n",
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"import matplotlib.pylab as plt\n",
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"%matplotlib inline\n",
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"\n",
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"def fan_triangulation(n):\n",
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" '''Generates a fan-shaped triangulation of even size n.'''\n",
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" return np.array([[(i-3)%(3*n),i+5,i+4,(i+6)%(3*n),i+2,i+1] \n",
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" for i in range(0,3*n,6)],dtype=np.int32).flatten()\n",
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"\n",
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"def is_fpf_involution(adj):\n",
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" '''Test whether adj defines a fixed-point free involution.'''\n",
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" for x, a in enumerate(adj):\n",
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" if a < 0 or a >= len(adj) or x == a or adj[a] != x:\n",
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" return False\n",
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" return True\n",
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"\n",
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"from collections import deque \n",
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"\n",
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"def triangle_neighbours(adj,i):\n",
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" '''Return the indices of the three neighboring triangles.'''\n",
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" return [j//3 for j in adj[3*i:3*i+3]]\n",
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"\n",
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"def connected_components(adj):\n",
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" '''Calculate the number of connected components of the triangulation.'''\n",
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" n = len(adj)//3 # the number of triangles\n",
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" # array storing the component index of each triangle\n",
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" component = np.full(n,-1,dtype=np.int32) \n",
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" index = 0\n",
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" for i in range(n):\n",
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" if component[i] == -1: # new component found, let us explore it\n",
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" component[i] = index\n",
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" queue = deque([i]) # use an exploration queue for breadth-first search\n",
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" while queue:\n",
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" for nbr in triangle_neighbours(adj,queue.pop()):\n",
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" # the neighboring triangle has not been explored yet\n",
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" if component[nbr] == -1: \n",
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" component[nbr] = index\n",
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" queue.appendleft(nbr) # add it to the exploration queue\n",
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" index += 1\n",
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" return index\n",
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"\n",
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"def next_around_triangle(i):\n",
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" '''Return the label of the side following side i in counter-clockwise direction.'''\n",
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" return i - i%3 + (i+1)%3\n",
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"\n",
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"def prev_around_triangle(i):\n",
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" '''Return the label of the side preceding side i in counter-clockwise direction.'''\n",
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" return i - i%3 + (i-1)%3\n",
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"\n",
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"def vertex_list(adj):\n",
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" '''\n",
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" Return the number of vertices and an array `vertex` of the same size \n",
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" as `adj`, such that `vertex[i]` is the index of the vertex at the \n",
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" start (in ccw order) of the side labeled `i`.\n",
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" '''\n",
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" # a side i that have not been visited yet has vertex[i]==-1\n",
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" vertex = np.full(len(adj),-1,dtype=np.int32) \n",
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" vert_index = 0 \n",
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" for i in range(len(adj)):\n",
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" if vertex[i] == -1:\n",
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" side = i\n",
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" while vertex[side] == -1: # find all sides that share the same vertex\n",
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" vertex[side] = vert_index\n",
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" side = next_around_triangle(adj[side])\n",
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" vert_index += 1\n",
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" return vert_index, vertex\n",
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"\n",
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"def number_of_vertices(adj):\n",
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" '''Calculate the number of vertices in the triangulation.'''\n",
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" return vertex_list(adj)[0]\n",
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"\n",
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"def is_sphere_triangulation(adj):\n",
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" '''Test whether adj defines a triangulation of the 2-sphere.'''\n",
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" if not is_fpf_involution(adj) or connected_components(adj) != 1:\n",
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" return False\n",
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" num_vert = number_of_vertices(adj)\n",
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" num_face = len(adj)//3\n",
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" num_edge = len(adj)//2\n",
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" # verify Euler's formula for the sphere\n",
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" return num_vert - num_edge + num_face == 2\n",
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"\n",
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"def flip_edge(adj,i):\n",
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" if adj[i] == next_around_triangle(i) or adj[i] == prev_around_triangle(i):\n",
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" # flipping an edge that is adjacent to the same triangle on both sides makes no sense\n",
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" return False\n",
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" j = prev_around_triangle(i)\n",
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" k = adj[i]\n",
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" l = prev_around_triangle(k)\n",
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" n = adj[l]\n",
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" adj[i] = n # it is important that we first update\n",
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" adj[n] = i # these adjacencies, before determining m,\n",
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" m = adj[j] # to treat the case j == n appropriately\n",
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" adj[k] = m\n",
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" adj[m] = k\n",
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" adj[j] = l\n",
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" adj[l] = j\n",
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" return True\n",
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"\n",
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"def random_flip(adj):\n",
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" random_side = rng.integers(0,len(adj))\n",
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" return flip_edge(adj,random_side)\n",
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"\n",
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"import networkx as nx\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n",
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"\n",
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"def triangulation_edges(triangulation,vertex):\n",
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" '''Return a list of vertex-id pairs corresponding to the edges in the triangulation.'''\n",
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" return [(vertex[i],vertex[j]) for i,j in enumerate(triangulation) if i < j]\n",
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"\n",
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"def triangulation_triangles(triangulation,vertex):\n",
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" '''Return a list of vertex-id triples corresponding to the triangles in the triangulation.'''\n",
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" return [vertex[i:i+3] for i in range(0,len(triangulation),3)]\n",
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"\n",
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"def plot_triangulation_3d(adj):\n",
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" '''Display an attempt at embedding the triangulation in 3d.'''\n",
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" num_vert, vertex = vertex_list(adj)\n",
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" edges = triangulation_edges(adj,vertex)\n",
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" triangles = triangulation_triangles(adj,vertex)\n",
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" # use the networkX 3d graph layout algorithm to find positions for the vertices\n",
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" pos = np.array(list(nx.spring_layout(nx.Graph(edges),dim=3).values()))\n",
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" fig = plt.figure()\n",
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" ax = fig.add_subplot(111, projection='3d')\n",
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" tris = Poly3DCollection(pos[triangles])\n",
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" tris.set_edgecolor('k')\n",
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" ax.add_collection3d(tris)\n",
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" ax.set_xlim3d(np.amin(pos[:,0]),np.amax(pos[:,0]))\n",
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" ax.set_ylim3d(np.amin(pos[:,1]),np.amax(pos[:,1]))\n",
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" ax.set_zlim3d(np.amin(pos[:,2]),np.amax(pos[:,2]))\n",
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" plt.show()\n",
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" \n",
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"def vertex_neighbors_list(adj):\n",
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" '''Return a list `neighbors` such that `neighbors[v]` is a list of neighbors of the vertex v.'''\n",
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" num_vertices, vertex = vertex_list(adj)\n",
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" neighbors = [[] for _ in range(num_vertices)]\n",
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" for i,j in enumerate(adj):\n",
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" neighbors[vertex[i]].append(vertex[j])\n",
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" return neighbors\n",
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"\n",
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"def vertex_distance_profile(adj,max_distance=30):\n",
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" '''Return array `profile` of size `max_distance` such that `profile[r]` is the number\n",
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" of vertices that have distance r to a randomly chosen initial vertex.'''\n",
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" profile = np.zeros((max_distance),dtype=np.int32)\n",
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" neighbors = vertex_neighbors_list(adj)\n",
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" num_vertices = len(neighbors)\n",
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" start = rng.integers(num_vertices) # random starting vertex\n",
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" distance = np.full(num_vertices,-1,dtype=np.int32) # array tracking the known distances (-1 is unknown)\n",
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" queue = deque([start]) # use an exploration queue for the breadth-first search\n",
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" distance[start] = 0\n",
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" profile[0] = 1 # of course there is exactly 1 vertex at distance 0\n",
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" while queue:\n",
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" current = queue.pop()\n",
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" d = distance[current] + 1 # every unexplored neighbour will have this distance\n",
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" if d >= max_distance:\n",
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" break\n",
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" for nbr in neighbors[current]:\n",
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" if distance[nbr] == -1: # this neighboring vertex has not been explored yet\n",
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" distance[nbr] = d\n",
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" profile[d] += 1\n",
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" queue.appendleft(nbr) # add it to the exploration queue\n",
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" return profile\n",
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" \n",
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"def perform_sweeps(adj,t):\n",
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" '''Perform t sweeps of flip moves, where 1 sweep is N moves.'''\n",
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" for _ in range(len(adj)*t//3):\n",
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" random_flip(adj)\n",
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"\n",
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"def batch_estimate(data,observable,k):\n",
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" '''Devide data into k batches and apply the function observable to each.\n",
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" Returns the mean and standard error.'''\n",
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" batches = np.reshape(data,(k,-1))\n",
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" values = np.apply_along_axis(observable, 1, batches)\n",
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" return np.mean(values), np.std(values)/np.sqrt(k-1)"
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]
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},
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"source": [
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"## Estimating Hausdorff dimensions in various 2D quantum gravity models \n",
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"\n",
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"**(100 Points)**\n",
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"\n",
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"In the lecture we considered the model of two-dimensional Dynamical Triangulations of the 2-sphere. The corresponding partition function is\n",
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"$$ Z^{U}_{S^2,N} = \\sum_T 1, \\tag{1}$$\n",
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"where the sum is over all triangulations of size $N$ with the topology of $S^2$, each of which is represented as an adjacency list $\\operatorname{adj}: \\{0,\\ldots,3N-1\\} \\to \\{0,\\ldots,3N-1\\}$. To emphasize that we are dealing with the **uniform** probability distribution on such triangulations, we have added the label $^U$. It is a lattice model of two-dimensional Euclidean quantum gravity with no coupled matter.\n",
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"\n",
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"One can also consider two-dimensional quantum gravity coupled to matter fields (e.g. a scalar field) supported on the geometry. Formally the corresponding path integral in the continuum reads\n",
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"$$ Z = \\int [\\mathcal{D}g_{ab}]\\int [\\mathcal{D}\\phi] e^{-\\frac{1}{\\hbar}(S_E[g_{ab}] + S_m[\\phi,g_{ab}])} = \\int [\\mathcal{D}g_{ab}]e^{-\\frac{1}{\\hbar}S_E[g_{ab}]} Z^*_m[g_{ab}],$$\n",
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"where $S_m[\\phi,g_{ab}]$ and $Z_m[g_{ab}]$ are the matter action and path integral of the field $\\phi$ on the geometry described by $g_{ab}$. The natural analogue in Dynamical Triangulations is\n",
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"$$Z^*_{S^2,N} = \\sum_T Z^*_m[T],$$\n",
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"where the sum is over the same triangulations as in (1) but now the summand $Z^*_m[T]$ is the lattice partition function of a matter system supported on the triangulation $T$, which generically depends in a non-trivial way on $T$. For instance, the matter system could be an Ising model in which the spin are supported on the triangles of $T$ and $Z^{\\text{Ising}}_m[T]$ would be the corresponding Ising partition function.\n",
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"In other words, when Dynamical Triangulations are coupled to matter the uniform distribution $\\pi^U(T) = 1/Z^U_{S^2,N}$ is changed into a non-uniform distribution $\\pi^*(T) = Z^*_m[T] / Z^*_{S^2,N}$. This can have significant effect on the critical exponents of the random triangulation as $N\\to\\infty$, like the Hausdorff dimension. \n",
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"\n",
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"The goal of this exercise is to estimate the **Hausdorff dimension** of random triangulations in four different models and to conclude based on this that they belong to four different universality classes (i.e. that if they possess well-defined continuum limits that they are described by four different EQFTs): \n",
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"* $Z^{U}_{S^2,N}$: the standard Dynamical Triangulations with **U**niform distribution (U)\n",
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"* $Z^{W}_{S^2,N}$: triangulations coupled to a matter system called a Schnyder **W**ood (W)\n",
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"* $Z^{S}_{S^2,N}$: triangulations coupled to a matter system called a **S**panning tree (S)\n",
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"* $Z^{B}_{S^2,N}$: triangulations coupled to a matter system called a **B**ipolar orientation (B)\n",
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"\n",
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"What these matter systems precisely represent will not be important. We have provided for you a **black box generator** that samples from the corresponding four distributions $\\pi^U(T)$, $\\pi^W(T)$, $\\pi^S(T)$, $\\pi^B(T)$. It does so in an efficient manner (linear time in $N$) using direct Monte Carlo sampling algorithms and therefore returns independent samples with exactly the desired distribution $\\pi^*(T)$ (within numerical precision).\n",
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"\n",
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"The black box generator is provided by the executable program `generator` provided to you on the science server. It can be called directly from this notebook with the following function `generate_random_triangulation`, that takes the desired size $N$ and model (`'U'`,`'W'`, `'S'`, `'B'`) and returns a single random triangulation in the usual form of an adjacency list."
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]
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"data": {
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"text/plain": [
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"True"
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"import subprocess\n",
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"\n",
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"def generate_random_triangulation(n,model):\n",
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" '''\n",
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" Returns a random triangulation generated by the program `generator` in the form \n",
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" of an array of length 3n storing the adjacency information of the triangle sides.\n",
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" Parameters:\n",
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" n - number of triangles in the triangulation, must be positive and even\n",
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" model - a one-letter string specifying the model from which the triangulation is sampled:\n",
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" 'U': Uniform triangulations\n",
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" 'W': Schnyder-Wood-decorated triangulations\n",
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" 'S': Spanning-tree decorated triangulations\n",
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" 'B': Bipolar-oriented triangulations\n",
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" '''\n",
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" program = \"/vol/cursus/NM042B/bin/generator\"\n",
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" output = subprocess.check_output([program,\"-s{}\".format(n),\"-t{}\".format(model)]).decode('ascii').split('\\n')[:-1]\n",
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" return np.array([int(num) for num in output],dtype=np.int32)\n",
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"\n",
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"adj = generate_random_triangulation(100,'B')\n",
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"is_sphere_triangulation(adj)"
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]
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},
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"source": [
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"Recall that the **distance profile** $\\rho_T(r)$ of a triangulation is defined as \n",
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"$$ \\rho_T(r) = \\frac{1}{V} \\sum_{x=0}^{V-1} \\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}},$$\n",
|
|
"where $V = (N+4)/2$ is the number of vertices and $d_T(x,y)$ is the graph distance between the vertices with label $x$ and $y$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
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"id": "d59143f0",
|
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"metadata": {
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"deletable": false,
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"editable": false,
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"nbgrader": {
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"checksum": "afcdbf86f64bd17b8ac9b4f9ec422206",
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}
|
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},
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"source": [
|
|
"**(a)** Let $T$ be a random triangulation of size $N$ and $X$, $Y$ two independent numbers chosen uniformly from $0,\\ldots,V-1$, corresponding to two random vertices in $T$. Explain with a calculation that $\\frac{1}{V}\\mathbb{E}[ \\rho_T(r) ] = \\mathbb{P}(d_T(X,Y) = r)$ and that the expected distance between $X$ and $Y$ is related to the distance profile via\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ]. \\tag{2}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"**(20 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "dd1b43bf",
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"metadata": {
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"deletable": false,
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"nbgrader": {
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"grade": true,
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"grade_id": "cell-f86454063d193cd6",
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"locked": false,
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"points": 20,
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"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**To proof**\n",
|
|
"\n",
|
|
"$\\frac{1}{V}\\mathbb{E}[ \\rho_T(r) ] = \\mathbb{P}(d_T(X,Y) = r)$\n",
|
|
"\n",
|
|
"**Proof**\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{1}{V} \\mathbb{E}\\left[ \\rho_T(r)\\right]\n",
|
|
" = \\frac{1}{V} \\mathbb{E} \\left[\\frac{1}{V} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n",
|
|
" = \\frac{1}{V^2} \\mathbb{E} \\left[ \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n",
|
|
" = \\frac{1}{V^2} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{E} \\left[ \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n",
|
|
"$$\n",
|
|
"\n",
|
|
"The order of summation is changed, as the sum of expectation values is equal to the expectation value of the sum.\n",
|
|
"The latter expectation value of the indicator function is exactly equal to the chance $\\mathbb{P}(d_T(x,y)=r)$ for given $x, y$.\n",
|
|
"For the uniformly distributed $X, Y$, we find $\\mathbb{P}(X = x) = \\frac{1}{V} = \\mathbb{P}(Y = y)$.\n",
|
|
"This allows us to write the right hand side as follows.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\frac{1}{V} \\mathbb{E}\\left[ \\rho_T(r)\\right]\n",
|
|
" = \\frac{1}{V^2} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{P}(d_T(x,y)=r)\n",
|
|
" = \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{P}(X = x) \\mathbb{P}(Y = y) \\mathbb{P}(d_T(x,y)=r)\n",
|
|
" = \\mathbb{P}(d_T(X,Y)=r),\n",
|
|
"$$\n",
|
|
"\n",
|
|
"which is what we sought.\n",
|
|
"\n",
|
|
"Using this result, it is just a matter of writing out the definition of an expectation value to get to the result.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] = \\sum_{r=0}^\\infty r\\, \\mathbb{P}(d_T(X,Y) = r) = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ].\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "29704f5d",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e2cc0493d54bcf087ce14bcb2e8a8d2f",
|
|
"grade": false,
|
|
"grade_id": "cell-aafca9797e5cfee4",
|
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"locked": true,
|
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"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(b)** We will work under the assumption that \n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[\\rho_T(r)] \\approx V^{1-1/d_H} f(r V^{-1/d_H})\n",
|
|
"$$ \n",
|
|
"\n",
|
|
"for a positive real number $d_H$ called the **Hausdorff dimension** and a continuous function $f$ that are both independent of $N$ but do depend on the model. Show that \n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}, \\qquad c = \\int_0^\\infty \\mathrm{d}x\\,x\\,f(x). \\tag{3}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"_Hint:_ Approximate the summation by an integral. **(15 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "0c062ba6",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "2db525e8acbc2412c1c5948052526a15",
|
|
"grade": true,
|
|
"grade_id": "cell-bcf3b38d64a4408d",
|
|
"locked": false,
|
|
"points": 15,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**To proof**\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}, \\qquad c = \\int_0^\\infty \\mathrm{d}x\\,x\\,f(x)\n",
|
|
"$$\n",
|
|
"\n",
|
|
"**Proof**\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E} \\left[ d_T(X,Y) \\right]\n",
|
|
" = \\frac{1}{V} \\sum_{r=0}^\\infty r\\, \\mathbb{E} \\left[ \\rho_T(r) \\right]\n",
|
|
" = \\frac{1}{V} \\sum_{r=0}^\\infty rV^{1-1/d_H}f(rV^{-1/d_H})\n",
|
|
" = \\frac{1}{V} \\sum_{r=0}^\\infty xV^{1/d_H} \\cdot V^{1-1/d_H}f(x)\n",
|
|
" = \\sum_{r=0}^\\infty xf(x),\n",
|
|
"$$\n",
|
|
"where the first equality sign is due to (2), the second due to the given assumption, the third using $x = rV^{-1/d_H}$.\n",
|
|
"\n",
|
|
"Now we approximate the summation by an integral.\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sum_{r=0}^\\infty xf(x)\n",
|
|
" \\approx \\int_{r=0}^\\infty xf(x)dr\n",
|
|
" = V^{1/d_H} \\int_{x=0}^\\infty xf(x)dx\n",
|
|
" = cV^{1/d_H},\n",
|
|
"$$\n",
|
|
"using $\\frac{dr}{dx} = V^{1/d_H}$ for substitution.\n",
|
|
"This yields the desired approximation\n",
|
|
"$$\n",
|
|
" \\mathbb{E} \\left[ d_T(X,Y) \\right] \\approx cV^{1/d_H}.\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "eba53e6d",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "ba14acd8cc24c2dfea35f3b8106cdfc8",
|
|
"grade": false,
|
|
"grade_id": "cell-fcab32195688a5c5",
|
|
"locked": true,
|
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"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(c)** For each of the four models estimate $\\mathbb{E}[d_T(X,Y)]$ with errors for $N = 2^7, 2^8, \\ldots, 2^{12}$ using (2) and based on $100$ samples each. Store your data in the file `qgdimension.hdf5`. Make an estimate of $d_H$ (with errors) for each of the models by fitting the parameters $c$ and $d_H$ of the ansatz (3). For each model, plot the data together with the fit in a log-log plot. **(40 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"id": "ee683060",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "c3664034dec3a350f7fe0533fe2454cb",
|
|
"grade": true,
|
|
"grade_id": "cell-01f5fde55f35f2dc",
|
|
"locked": false,
|
|
"points": 15,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"models = ['U','W','S','B']\n",
|
|
"sizes = [2**k for k in range(7,13)]\n",
|
|
"num_vertices = (np.array(sizes)+4)/2\n",
|
|
"measurements = 100\n",
|
|
"\n",
|
|
"# data gathering and storing in qgdimension.hdf5\n",
|
|
"import h5py\n",
|
|
"\n",
|
|
"max_distance = 15\n",
|
|
"\n",
|
|
"with h5py.File(\"qgdimension.hdf5\", \"a\") as f:\n",
|
|
" if not \"num-vertices\" in f:\n",
|
|
" f.create_dataset(\"num-vertices\",data=num_vertices)\n",
|
|
" \n",
|
|
" for model in models:\n",
|
|
" models_key = f\"distance-profiles-{model}\"\n",
|
|
" if not models_key in f:\n",
|
|
" graph_distance_expectations = np.zeros((len(num_vertices), measurements, max_distance))\n",
|
|
" for idx_N, N in enumerate(num_vertices):\n",
|
|
" for idx_measurement in range(measurements):\n",
|
|
" adj = generate_random_triangulation(N, model)\n",
|
|
" distance_profile = vertex_distance_profile(adj,max_distance)\n",
|
|
" graph_distance_expectations[idx_N][idx_measurement] = distance_profile\n",
|
|
"\n",
|
|
" f.create_dataset(models_key,data=graph_distance_expectations)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"id": "351f7a01",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "000725107fe51acebc0bc68eef8c1c9c",
|
|
"grade": true,
|
|
"grade_id": "cell-9e8f666073e1e2df",
|
|
"locked": false,
|
|
"points": 25,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[[ 1. 1. 9. ... 0. 0. 0.]\n",
|
|
" [ 1. 4. 11. ... 0. 0. 0.]\n",
|
|
" [ 1. 1. 10. ... 0. 0. 0.]\n",
|
|
" ...\n",
|
|
" [ 1. 1. 9. ... 0. 0. 0.]\n",
|
|
" [ 1. 3. 8. ... 0. 0. 0.]\n",
|
|
" [ 1. 3. 12. ... 0. 0. 0.]]\n",
|
|
"()\n"
|
|
]
|
|
},
|
|
{
|
|
"ename": "ValueError",
|
|
"evalue": "matmul: Input operand 0 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)",
|
|
"output_type": "error",
|
|
"traceback": [
|
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
|
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
|
"Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36m<cell line: 22>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m idx_V, V \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(num_vertices):\n\u001b[1;32m 35\u001b[0m \u001b[38;5;28mprint\u001b[39m(profiles[model][idx_V])\n\u001b[0;32m---> 36\u001b[0m mu[idx_V], err[idx_V] \u001b[38;5;241m=\u001b[39m \u001b[43mbatch_estimate\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprofiles\u001b[49m\u001b[43m[\u001b[49m\u001b[43mmodel\u001b[49m\u001b[43m]\u001b[49m\u001b[43m[\u001b[49m\u001b[43midx_V\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 37\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43;01mlambda\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mdistance_profile\u001b[49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[43mexpected_distance\u001b[49m\u001b[43m(\u001b[49m\u001b[43mV\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_distance\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mdistance_profile\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 38\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;241;43m20\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 40\u001b[0m fitfunc \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m V, c, d_H: c\u001b[38;5;241m*\u001b[39mV\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m(\u001b[38;5;241m1\u001b[39m\u001b[38;5;241m/\u001b[39md_H)\n\u001b[1;32m 41\u001b[0m popt, pcov \u001b[38;5;241m=\u001b[39m curve_fit(fitfunc, num_vertices, mu, sigma\u001b[38;5;241m=\u001b[39merr)\n",
|
|
"Input \u001b[0;32mIn [14]\u001b[0m, in \u001b[0;36mbatch_estimate\u001b[0;34m(data, observable, k)\u001b[0m\n\u001b[1;32m 170\u001b[0m \u001b[38;5;124;03m'''Devide data into k batches and apply the function observable to each.\u001b[39;00m\n\u001b[1;32m 171\u001b[0m \u001b[38;5;124;03mReturns the mean and standard error.'''\u001b[39;00m\n\u001b[1;32m 172\u001b[0m batches \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mreshape(data,(k,\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m))\n\u001b[0;32m--> 173\u001b[0m values \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mapply_along_axis\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobservable\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbatches\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 174\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mmean(values), np\u001b[38;5;241m.\u001b[39mstd(values)\u001b[38;5;241m/\u001b[39mnp\u001b[38;5;241m.\u001b[39msqrt(k\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m)\n",
|
|
"File \u001b[0;32m<__array_function__ internals>:5\u001b[0m, in \u001b[0;36mapply_along_axis\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
|
|
"File \u001b[0;32m/opt/jupyter-conda/lib/python3.9/site-packages/numpy/lib/shape_base.py:379\u001b[0m, in \u001b[0;36mapply_along_axis\u001b[0;34m(func1d, axis, arr, *args, **kwargs)\u001b[0m\n\u001b[1;32m 375\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mStopIteration\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m 376\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[1;32m 377\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mCannot apply_along_axis when any iteration dimensions are 0\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m 378\u001b[0m ) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;28mNone\u001b[39m\n\u001b[0;32m--> 379\u001b[0m res \u001b[38;5;241m=\u001b[39m asanyarray(\u001b[43mfunc1d\u001b[49m\u001b[43m(\u001b[49m\u001b[43minarr_view\u001b[49m\u001b[43m[\u001b[49m\u001b[43mind0\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m 381\u001b[0m \u001b[38;5;66;03m# build a buffer for storing evaluations of func1d.\u001b[39;00m\n\u001b[1;32m 382\u001b[0m \u001b[38;5;66;03m# remove the requested axis, and add the new ones on the end.\u001b[39;00m\n\u001b[1;32m 383\u001b[0m \u001b[38;5;66;03m# laid out so that each write is contiguous.\u001b[39;00m\n\u001b[1;32m 384\u001b[0m \u001b[38;5;66;03m# for a tuple index inds, buff[inds] = func1d(inarr_view[inds])\u001b[39;00m\n\u001b[1;32m 385\u001b[0m buff \u001b[38;5;241m=\u001b[39m zeros(inarr_view\u001b[38;5;241m.\u001b[39mshape[:\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m+\u001b[39m res\u001b[38;5;241m.\u001b[39mshape, res\u001b[38;5;241m.\u001b[39mdtype)\n",
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"Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36m<lambda>\u001b[0;34m(distance_profile)\u001b[0m\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m idx_V, V \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(num_vertices):\n\u001b[1;32m 35\u001b[0m \u001b[38;5;28mprint\u001b[39m(profiles[model][idx_V])\n\u001b[1;32m 36\u001b[0m mu[idx_V], err[idx_V] \u001b[38;5;241m=\u001b[39m batch_estimate(profiles[model][idx_V],\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mlambda\u001b[39;00m distance_profile: [expected_distance(V, data, max_distance) \u001b[38;5;28;01mfor\u001b[39;00m data \u001b[38;5;129;01min\u001b[39;00m distance_profile],\n\u001b[1;32m 38\u001b[0m \u001b[38;5;241m20\u001b[39m)\n\u001b[1;32m 40\u001b[0m fitfunc \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m V, c, d_H: c\u001b[38;5;241m*\u001b[39mV\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m(\u001b[38;5;241m1\u001b[39m\u001b[38;5;241m/\u001b[39md_H)\n\u001b[1;32m 41\u001b[0m popt, pcov \u001b[38;5;241m=\u001b[39m curve_fit(fitfunc, num_vertices, mu, sigma\u001b[38;5;241m=\u001b[39merr)\n",
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"Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m idx_V, V \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(num_vertices):\n\u001b[1;32m 35\u001b[0m \u001b[38;5;28mprint\u001b[39m(profiles[model][idx_V])\n\u001b[1;32m 36\u001b[0m mu[idx_V], err[idx_V] \u001b[38;5;241m=\u001b[39m batch_estimate(profiles[model][idx_V],\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mlambda\u001b[39;00m distance_profile: [\u001b[43mexpected_distance\u001b[49m\u001b[43m(\u001b[49m\u001b[43mV\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_distance\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;28;01mfor\u001b[39;00m data \u001b[38;5;129;01min\u001b[39;00m distance_profile],\n\u001b[1;32m 38\u001b[0m \u001b[38;5;241m20\u001b[39m)\n\u001b[1;32m 40\u001b[0m fitfunc \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m V, c, d_H: c\u001b[38;5;241m*\u001b[39mV\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m(\u001b[38;5;241m1\u001b[39m\u001b[38;5;241m/\u001b[39md_H)\n\u001b[1;32m 41\u001b[0m popt, pcov \u001b[38;5;241m=\u001b[39m curve_fit(fitfunc, num_vertices, mu, sigma\u001b[38;5;241m=\u001b[39merr)\n",
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"Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36mexpected_distance\u001b[0;34m(V, distance_profile, max_distance)\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[38;5;124;03m'''\u001b[39;00m\n\u001b[1;32m 15\u001b[0m \u001b[38;5;124;03mCalculates the expectation value of the distance profile given the amount\u001b[39;00m\n\u001b[1;32m 16\u001b[0m \u001b[38;5;124;03mof vertices V, an array distance_profiles of length max_distance,\u001b[39;00m\n\u001b[1;32m 17\u001b[0m \u001b[38;5;124;03mand max_distance as upper limit for the summation for the expectation value.\u001b[39;00m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;124;03m'''\u001b[39;00m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28mprint\u001b[39m(distance_profile\u001b[38;5;241m.\u001b[39mshape)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;241;43m1\u001b[39;49m\u001b[38;5;241;43m/\u001b[39;49m\u001b[43mV\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mdistance_profile\u001b[49m\u001b[38;5;129;43m@np\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43marange\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmax_distance\u001b[49m\u001b[43m)\u001b[49m\n",
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"\u001b[0;31mValueError\u001b[0m: matmul: Input operand 0 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)"
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]
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},
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{
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"data": {
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"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 864x576 with 4 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Fitting and plotting\n",
|
|
"from matplotlib import pyplot as plt\n",
|
|
"from scipy.optimize import curve_fit\n",
|
|
"\n",
|
|
"# Define a dictionary of model names for the plot titles.\n",
|
|
"model_names = {\"U\": \"Uniform triangulations\",\n",
|
|
" \"W\": \"Schnyder-Wood-decorated triangulations\",\n",
|
|
" \"S\": \"Spanning-tree decorated triangulations\",\n",
|
|
" \"B\": \"Bipolar-oriented triangulations\"}\n",
|
|
"\n",
|
|
"d_H_list = {}\n",
|
|
"\n",
|
|
"def expected_distance(V, distance_profile, max_distance=30):\n",
|
|
" '''\n",
|
|
" Calculates the expectation value of the distance profile given the amount\n",
|
|
" of vertices V, an array distance_profiles of length max_distance,\n",
|
|
" and max_distance as upper limit for the summation for the expectation value.\n",
|
|
" '''\n",
|
|
" print(distance_profile.shape)\n",
|
|
" return 1/V*distance_profile@np.arange(max_distance)\n",
|
|
"\n",
|
|
"with h5py.File(\"qgdimension.hdf5\", \"r\") as f:\n",
|
|
" num_vertices = np.array(f[\"num-vertices\"])\n",
|
|
" profiles = {model: np.array(f[f\"distance-profiles-{model}\"]) for model in models}\n",
|
|
" \n",
|
|
" fig, axs = plt.subplots(2, 2, figsize=(12, 8))\n",
|
|
" axs = axs.ravel()\n",
|
|
" fig.suptitle(r\"Graph distance expectation Monte Carlo simulations and Hausdorff dimension $d_H$ fits using $\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}$ for different triangulation models\")\n",
|
|
" \n",
|
|
" for idx_model, model in enumerate(models):\n",
|
|
" # Calculate mean and standard deviation of the expectations.\n",
|
|
" mu = np.zeros(len(num_vertices))\n",
|
|
" err = np.zeros(len(num_vertices))\n",
|
|
" for idx_V, V in enumerate(num_vertices):\n",
|
|
" print(profiles[model][idx_V])\n",
|
|
" mu[idx_V], err[idx_V] = batch_estimate(profiles[model][idx_V],\n",
|
|
" lambda distance_profile: [expected_distance(V, data, max_distance) for data in distance_profile],\n",
|
|
" 20)\n",
|
|
"\n",
|
|
" fitfunc = lambda V, c, d_H: c*V**(1/d_H)\n",
|
|
" popt, pcov = curve_fit(fitfunc, num_vertices, mu, sigma=err)\n",
|
|
" d_H_list[model] = popt[1]\n",
|
|
" num_vertices_fit = np.linspace(np.min(num_vertices)/2, np.max(num_vertices)*2, 1000)\n",
|
|
"\n",
|
|
" ax = axs[idx_model]\n",
|
|
" ax.set_title(f\"{model_names[model]} ({model})\")\n",
|
|
" ax.errorbar(num_vertices, mu, err, label=\"Monte Carlo\",\n",
|
|
" fmt='.', markersize=10, capsize=4)\n",
|
|
" ax.plot(num_vertices_fit, fitfunc(num_vertices_fit, *popt),\n",
|
|
" label=r\"fit: $c = {:.2f}$, $d_H = {:.2f}$\".format(*popt))\n",
|
|
" ax.set_xlabel(r\"$V$\")\n",
|
|
" ax.set_ylabel(r\"$\\mathbb{E}[d_T(X,Y)]$\")\n",
|
|
" ax.set_yscale(\"log\")\n",
|
|
" ax.set_xscale(\"log\")\n",
|
|
" ax.grid(True, which=\"both\", ls=\"-\")\n",
|
|
" ax.legend()\n",
|
|
" \n",
|
|
" fig.tight_layout()\n",
|
|
" fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b505b3cf",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "be7888d11d6b9ca0f2666739857578cb",
|
|
"grade": false,
|
|
"grade_id": "cell-032c7f8d6147d9f9",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(d)** Produce a *collapse* plot for each of the four models as follows: plot \n",
|
|
"$$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)] \\quad\\text{ as function of } x = r / V^{1/d_H},$$ \n",
|
|
"where for $d_H$ you take the estimate obtained in the previous exercise. Show errors in the mean distance profiles via shaded regions (just like in the lecture). Verify that the curves collapse reasonably well. **(25 pts)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"id": "988bfe95",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "7b7eceb7923231bc3710d4e3036265b6",
|
|
"grade": true,
|
|
"grade_id": "cell-faf328e7505cf6a2",
|
|
"locked": false,
|
|
"points": 25,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
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"data": {
|
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"image/png": 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\n",
|
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"text/plain": [
|
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"<Figure size 432x288 with 1 Axes>"
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]
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},
|
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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\n",
|
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
|
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]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
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"data": {
|
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"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"equilibration_sweeps = 500\n",
|
|
"measurement_sweeps = 2\n",
|
|
"measurements = 200\n",
|
|
"\n",
|
|
"max_distance = 15\n",
|
|
"\n",
|
|
"for model in models:\n",
|
|
" d_H = d_H_list[model]\n",
|
|
" \n",
|
|
" # Code mostly copied from lecture 8.\n",
|
|
" mean_profiles = []\n",
|
|
" for size in sizes:\n",
|
|
" #adj = generate_random_triangulation(size, model)\n",
|
|
" #perform_sweeps(adj,equilibration_sweeps)\n",
|
|
" profiles = []\n",
|
|
" for _ in range(measurements):\n",
|
|
" #perform_sweeps(adj,measurement_sweeps)\n",
|
|
" adj = generate_random_triangulation(size, model)\n",
|
|
" profiles.append(vertex_distance_profile(adj,max_distance))\n",
|
|
" mean_profiles.append([batch_estimate(data,np.mean,20) for data in np.transpose(profiles)])\n",
|
|
"\n",
|
|
" #for profile in mean_profiles:\n",
|
|
" # plt.plot([y[0] for y in profile])\n",
|
|
" #for profile in mean_profiles:\n",
|
|
" # plt.fill_between(range(len(profile)),\n",
|
|
" # [y[0]-y[1] for y in profile],[y[0]+y[1] for y in profile],alpha=0.2)\n",
|
|
" #plt.legend(num_vertices, title=\"V\")\n",
|
|
" #plt.xlabel(\"x\")\n",
|
|
" #plt.ylabel(r\"$\\mathbb{E}[\\rho_T(r)]$\")\n",
|
|
" #plt.title(\"Mean distance profile (errors shown as shaded regions)\")\n",
|
|
" #plt.show()\n",
|
|
"\n",
|
|
" for i, profile in enumerate(mean_profiles):\n",
|
|
" rvals = np.arange(len(profile))\n",
|
|
" plt.plot(rvals/num_vertices[i]**(1/d_H),\n",
|
|
" [y[0]*num_vertices[i]**(1/d_H - 1) for y in profile])\n",
|
|
" for i, profile in enumerate(mean_profiles):\n",
|
|
" plt.fill_between(np.arange(len(profile))/num_vertices[i]**(1/d_H),\n",
|
|
" [(y[0]-y[1])*num_vertices[i]**(1/d_H - 1) for y in profile],\n",
|
|
" [(y[0]+y[1])*num_vertices[i]**(1/d_H - 1) for y in profile],\n",
|
|
" alpha=0.2)\n",
|
|
" plt.legend(sizes, title=\"V\")\n",
|
|
" plt.xlabel(r\"$x = r/V^{1/d_H}$\")\n",
|
|
" plt.ylabel(r\"$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)]$\")\n",
|
|
" plt.xlim(0,3)\n",
|
|
" plt.title(f\"Finite-size scaling with Hausdorff dimension $d_H = {d_H:.2f}$\")\n",
|
|
" plt.show()\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d8f25787",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "7f19410ed936f838773ee891b059d1a3",
|
|
"grade": false,
|
|
"grade_id": "cell-65ae9c46ece5b657",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"**(e) Bonus exercise:** Make more robust estimates of $d_H$ by optimizing the quality of the collapse. You could do this (for each model separately) by taking $\\hat{f}(r) = \\mathbb{E}[\\rho_T(r)] / V_0$, where the right-hand side is the mean distance profile for the largest system size with $V_0 = (2^{12} + 4)/2$ vertices. Then according to our assumption, for another size $V \\leq V_0$ we expect $\\mathbb{E}[\\rho_T(r)] / V \\approx k \\hat{f}(kr)$, where $k \\geq 1$ is a scale factor that should be $k\\approx (V_0/V)^{1/d_H}$. Making sure to interpolate the function $\\hat{f}(r)$ (using [`scipy.interpolate.interp1d`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html#scipy.interpolate.interp1d)), this scale factor can be determined by fitting the curve $k \\hat{f}(kr)$ to the data $\\mathbb{E}[\\rho_T(r)] / V$. Then $d_H$ can be estimated by fitting $k$ versus $V$. **(20 bonus points, but note that maximum grade is 10)**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "ed4424ce",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "199ffddc14c77d4174b92a61368cd5c9",
|
|
"grade": true,
|
|
"grade_id": "cell-e24b0602e4e8257d",
|
|
"locked": false,
|
|
"points": 20,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "c9e50c10",
|
|
"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": "3.9.12"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|