753 lines
109 KiB
Plaintext
753 lines
109 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": 1,
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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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"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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"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",
|
|
"id": "d59143f0",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "afcdbf86f64bd17b8ac9b4f9ec422206",
|
|
"grade": false,
|
|
"grade_id": "cell-8e6d6fcefb5ab644",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"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",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "74963ed3d7cbd9eaa06be2e66a8f939e",
|
|
"grade": true,
|
|
"grade_id": "cell-f86454063d193cd6",
|
|
"locked": false,
|
|
"points": 20,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"YOUR ANSWER HERE"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "29704f5d",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e2cc0493d54bcf087ce14bcb2e8a8d2f",
|
|
"grade": false,
|
|
"grade_id": "cell-aafca9797e5cfee4",
|
|
"locked": true,
|
|
"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": [
|
|
"YOUR ANSWER HERE"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "eba53e6d",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "ba14acd8cc24c2dfea35f3b8106cdfc8",
|
|
"grade": false,
|
|
"grade_id": "cell-fcab32195688a5c5",
|
|
"locked": true,
|
|
"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": 4,
|
|
"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 = 30\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\"expectation-graph-distance-{model}\"\n",
|
|
" if not models_key in f:\n",
|
|
" graph_distance_expectations = np.zeros((len(num_vertices), measurements))\n",
|
|
" for idx_N, N in enumerate(num_vertices):\n",
|
|
" V = (N + 4)/2\n",
|
|
" for idx_measurement in range(measurements):\n",
|
|
" adj = generate_random_triangulation(N, model)\n",
|
|
" expectation = 1/V * vertex_distance_profile(adj,max_distance)@np.arange(max_distance)\n",
|
|
" graph_distance_expectations[idx_N][idx_measurement] = expectation\n",
|
|
"\n",
|
|
" f.create_dataset(models_key,data=graph_distance_expectations)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"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": [
|
|
{
|
|
"data": {
|
|
"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",
|
|
"with h5py.File(\"qgdimension.hdf5\", \"r\") as f:\n",
|
|
" num_vertices = np.array(f[\"num-vertices\"])\n",
|
|
" expectations = {model: np.array(f[f\"expectation-graph-distance-{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.mean(expectations[model], 1)\n",
|
|
" sigma = np.std(expectations[model], 1)\n",
|
|
"\n",
|
|
" fitfunc = lambda V, c, d_H: c*V**(1/d_H)\n",
|
|
" popt, pcov = curve_fit(fitfunc, num_vertices, mu, sigma=sigma)\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, sigma, 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": null,
|
|
"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": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"d_H_list"
|
|
]
|
|
},
|
|
{
|
|
"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
|
|
}
|