{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "269c4188",
   "metadata": {},
   "source": [
    "# Exercise sheet\n",
    "\n",
    "Some general remarks about the exercises:\n",
    "* For your convenience functions from the lecture are included below. Feel free to reuse them without copying to the exercise solution box.\n",
    "* 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",
    "* 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",
    "* 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",
    "* 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",
    "* 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",
    "\n",
    "Please fill in your name here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "220d541e",
   "metadata": {},
   "outputs": [],
   "source": [
    "NAME = \"Kees van Kempen\"\n",
    "NAMES_OF_COLLABORATORS = \"\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6944e4c",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c53fbab6",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "da0f2845f08ee29eb0450f8eff343e98",
     "grade": false,
     "grade_id": "cell-3cb26b1434512d8d",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "**Exercise sheet 8**\n",
    "\n",
    "Code from the lectures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5e4391a6",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "1814f5ba5f2d71b14a4c534cfe3ad7ff",
     "grade": false,
     "grade_id": "cell-40c62687f6a2c579",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "rng = np.random.default_rng()  \n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def fan_triangulation(n):\n",
    "    '''Generates a fan-shaped triangulation of even size n.'''\n",
    "    return np.array([[(i-3)%(3*n),i+5,i+4,(i+6)%(3*n),i+2,i+1] \n",
    "                     for i in range(0,3*n,6)],dtype=np.int32).flatten()\n",
    "\n",
    "def is_fpf_involution(adj):\n",
    "    '''Test whether adj defines a fixed-point free involution.'''\n",
    "    for x, a in enumerate(adj):\n",
    "        if a < 0 or a >= len(adj) or x == a or adj[a] != x:\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "from collections import deque \n",
    "\n",
    "def triangle_neighbours(adj,i):\n",
    "    '''Return the indices of the three neighboring triangles.'''\n",
    "    return [j//3 for j in adj[3*i:3*i+3]]\n",
    "\n",
    "def connected_components(adj):\n",
    "    '''Calculate the number of connected components of the triangulation.'''\n",
    "    n = len(adj)//3   # the number of triangles\n",
    "    # array storing the component index of each triangle\n",
    "    component = np.full(n,-1,dtype=np.int32)   \n",
    "    index = 0\n",
    "    for i in range(n):\n",
    "        if component[i] == -1:    # new component found, let us explore it\n",
    "            component[i] = index\n",
    "            queue = deque([i])   # use an exploration queue for breadth-first search\n",
    "            while queue:\n",
    "                for nbr in triangle_neighbours(adj,queue.pop()):\n",
    "                    # the neighboring triangle has not been explored yet\n",
    "                    if component[nbr] == -1:  \n",
    "                        component[nbr] = index\n",
    "                        queue.appendleft(nbr)   # add it to the exploration queue\n",
    "            index += 1\n",
    "    return index\n",
    "\n",
    "def next_around_triangle(i):\n",
    "    '''Return the label of the side following side i in counter-clockwise direction.'''\n",
    "    return i - i%3 + (i+1)%3\n",
    "\n",
    "def prev_around_triangle(i):\n",
    "    '''Return the label of the side preceding side i in counter-clockwise direction.'''\n",
    "    return i - i%3 + (i-1)%3\n",
    "\n",
    "def vertex_list(adj):\n",
    "    '''\n",
    "    Return the number of vertices and an array `vertex` of the same size \n",
    "    as `adj`, such that `vertex[i]` is the index of the vertex at the \n",
    "    start (in ccw order) of the side labeled `i`.\n",
    "    '''\n",
    "    # a side i that have not been visited yet has vertex[i]==-1\n",
    "    vertex = np.full(len(adj),-1,dtype=np.int32)  \n",
    "    vert_index = 0 \n",
    "    for i in range(len(adj)):\n",
    "        if vertex[i] == -1:\n",
    "            side = i\n",
    "            while vertex[side] == -1:  # find all sides that share the same vertex\n",
    "                vertex[side] = vert_index\n",
    "                side = next_around_triangle(adj[side])\n",
    "            vert_index += 1\n",
    "    return vert_index, vertex\n",
    "\n",
    "def number_of_vertices(adj):\n",
    "    '''Calculate the number of vertices in the triangulation.'''\n",
    "    return vertex_list(adj)[0]\n",
    "\n",
    "def is_sphere_triangulation(adj):\n",
    "    '''Test whether adj defines a triangulation of the 2-sphere.'''\n",
    "    if not is_fpf_involution(adj) or connected_components(adj) != 1:\n",
    "        return False\n",
    "    num_vert = number_of_vertices(adj)\n",
    "    num_face = len(adj)//3\n",
    "    num_edge = len(adj)//2\n",
    "    # verify Euler's formula for the sphere\n",
    "    return num_vert - num_edge + num_face == 2\n",
    "\n",
    "def flip_edge(adj,i):\n",
    "    if adj[i] == next_around_triangle(i) or adj[i] == prev_around_triangle(i):\n",
    "        # flipping an edge that is adjacent to the same triangle on both sides makes no sense\n",
    "        return False\n",
    "    j = prev_around_triangle(i)\n",
    "    k = adj[i]\n",
    "    l = prev_around_triangle(k)\n",
    "    n = adj[l]\n",
    "    adj[i] = n  # it is important that we first update\n",
    "    adj[n] = i  # these adjacencies, before determining m,\n",
    "    m = adj[j]  # to treat the case j == n appropriately\n",
    "    adj[k] = m\n",
    "    adj[m] = k\n",
    "    adj[j] = l\n",
    "    adj[l] = j\n",
    "    return True\n",
    "\n",
    "def random_flip(adj):\n",
    "    random_side = rng.integers(0,len(adj))\n",
    "    return flip_edge(adj,random_side)\n",
    "\n",
    "import networkx as nx\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n",
    "\n",
    "def triangulation_edges(triangulation,vertex):\n",
    "    '''Return a list of vertex-id pairs corresponding to the edges in the triangulation.'''\n",
    "    return [(vertex[i],vertex[j]) for i,j in enumerate(triangulation) if i < j]\n",
    "\n",
    "def triangulation_triangles(triangulation,vertex):\n",
    "    '''Return a list of vertex-id triples corresponding to the triangles in the triangulation.'''\n",
    "    return [vertex[i:i+3] for i in range(0,len(triangulation),3)]\n",
    "\n",
    "def plot_triangulation_3d(adj):\n",
    "    '''Display an attempt at embedding the triangulation in 3d.'''\n",
    "    num_vert, vertex = vertex_list(adj)\n",
    "    edges = triangulation_edges(adj,vertex)\n",
    "    triangles = triangulation_triangles(adj,vertex)\n",
    "    # use the networkX 3d graph layout algorithm to find positions for the vertices\n",
    "    pos = np.array(list(nx.spring_layout(nx.Graph(edges),dim=3).values()))\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    tris = Poly3DCollection(pos[triangles])\n",
    "    tris.set_edgecolor('k')\n",
    "    ax.add_collection3d(tris)\n",
    "    ax.set_xlim3d(np.amin(pos[:,0]),np.amax(pos[:,0]))\n",
    "    ax.set_ylim3d(np.amin(pos[:,1]),np.amax(pos[:,1]))\n",
    "    ax.set_zlim3d(np.amin(pos[:,2]),np.amax(pos[:,2]))\n",
    "    plt.show()\n",
    "    \n",
    "def vertex_neighbors_list(adj):\n",
    "    '''Return a list `neighbors` such that `neighbors[v]` is a list of neighbors of the vertex v.'''\n",
    "    num_vertices, vertex = vertex_list(adj)\n",
    "    neighbors = [[] for _ in range(num_vertices)]\n",
    "    for i,j in enumerate(adj):\n",
    "        neighbors[vertex[i]].append(vertex[j])\n",
    "    return neighbors\n",
    "\n",
    "def vertex_distance_profile(adj,max_distance=30):\n",
    "    '''Return array `profile` of size `max_distance` such that `profile[r]` is the number\n",
    "    of vertices that have distance r to a randomly chosen initial vertex.'''\n",
    "    profile = np.zeros((max_distance),dtype=np.int32)\n",
    "    neighbors = vertex_neighbors_list(adj)\n",
    "    num_vertices = len(neighbors)\n",
    "    start = rng.integers(num_vertices) # random starting vertex\n",
    "    distance = np.full(num_vertices,-1,dtype=np.int32)  # array tracking the known distances (-1 is unknown)\n",
    "    queue = deque([start])   # use an exploration queue for the breadth-first search\n",
    "    distance[start] = 0\n",
    "    profile[0] = 1  # of course there is exactly 1 vertex at distance 0\n",
    "    while queue:\n",
    "        current = queue.pop()\n",
    "        d = distance[current] + 1  # every unexplored neighbour will have this distance\n",
    "        if d >= max_distance:\n",
    "            break\n",
    "        for nbr in neighbors[current]:\n",
    "            if distance[nbr] == -1:  # this neighboring vertex has not been explored yet\n",
    "                distance[nbr] = d\n",
    "                profile[d] += 1\n",
    "                queue.appendleft(nbr)   # add it to the exploration queue\n",
    "    return profile\n",
    "    \n",
    "def perform_sweeps(adj,t):\n",
    "    '''Perform t sweeps of flip moves, where 1 sweep is N moves.'''\n",
    "    for _ in range(len(adj)*t//3):\n",
    "        random_flip(adj)\n",
    "\n",
    "def batch_estimate(data,observable,k):\n",
    "    '''Devide data into k batches and apply the function observable to each.\n",
    "    Returns the mean and standard error.'''\n",
    "    batches = np.reshape(data,(k,-1))\n",
    "    values = np.apply_along_axis(observable, 1, batches)\n",
    "    return np.mean(values), np.std(values)/np.sqrt(k-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bed55184",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "8c9a6c198119d4649dd87308e8933611",
     "grade": false,
     "grade_id": "cell-5f5adc7840fea9ad",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Estimating Hausdorff dimensions in various 2D quantum gravity models \n",
    "\n",
    "**(100 Points)**\n",
    "\n",
    "In the lecture we considered the model of two-dimensional Dynamical Triangulations of the 2-sphere. The corresponding partition function is\n",
    "$$ Z^{U}_{S^2,N} = \\sum_T 1, \\tag{1}$$\n",
    "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",
    "\n",
    "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",
    "$$ Z = \\int [\\mathcal{D}g_{ab}]\\int [\\mathcal{D}\\phi] e^{-\\frac{1}{\\hbar}(S_E[g_{ab}] + S_m[\\phi,g_{ab}])} = \\int [\\mathcal{D}g_{ab}]e^{-\\frac{1}{\\hbar}S_E[g_{ab}]} Z^*_m[g_{ab}],$$\n",
    "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",
    "$$Z^*_{S^2,N} = \\sum_T Z^*_m[T],$$\n",
    "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",
    "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",
    "\n",
    "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",
    "* $Z^{U}_{S^2,N}$: the standard Dynamical Triangulations with **U**niform distribution (U)\n",
    "* $Z^{W}_{S^2,N}$: triangulations coupled to a matter system called a Schnyder **W**ood (W)\n",
    "* $Z^{S}_{S^2,N}$: triangulations coupled to a matter system called a **S**panning tree (S)\n",
    "* $Z^{B}_{S^2,N}$: triangulations coupled to a matter system called a **B**ipolar orientation (B)\n",
    "\n",
    "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",
    "\n",
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bcc7acba",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "7d6abad00aa217998ca44ecc5e89f423",
     "grade": false,
     "grade_id": "cell-266ff66f880583d7",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import subprocess\n",
    "\n",
    "def generate_random_triangulation(n,model):\n",
    "    '''\n",
    "    Returns a random triangulation generated by the program `generator` in the form \n",
    "    of an array of length 3n storing the adjacency information of the triangle sides.\n",
    "    Parameters:\n",
    "      n - number of triangles in the triangulation, must be positive and even\n",
    "      model - a one-letter string specifying the model from which the triangulation is sampled:\n",
    "         'U': Uniform triangulations\n",
    "         'W': Schnyder-Wood-decorated triangulations\n",
    "         'S': Spanning-tree decorated triangulations\n",
    "         'B': Bipolar-oriented triangulations\n",
    "    '''\n",
    "    program = \"/vol/cursus/NM042B/bin/generator\"\n",
    "    output = subprocess.check_output([program,\"-s{}\".format(n),\"-t{}\".format(model)]).decode('ascii').split('\\n')[:-1]\n",
    "    return np.array([int(num) for num in output],dtype=np.int32)\n",
    "\n",
    "adj = generate_random_triangulation(100,'B')\n",
    "is_sphere_triangulation(adj)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4518f51f",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "37e92f3a59f2d5c6d117868d04d8f0d4",
     "grade": false,
     "grade_id": "cell-6aacf5fa6d8c4eb9",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Recall that the **distance profile** $\\rho_T(r)$ of a triangulation is defined as \n",
    "$$ \\rho_T(r) = \\frac{1}{V} \\sum_{x=0}^{V-1} \\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}},$$\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": 119,
   "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": 120,
   "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, V_space, 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": 111,
   "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": {
      "text/plain": [
       "{'U': 3.569451122838096,\n",
       " 'W': 2.7064403223694575,\n",
       " 'S': 3.143472808640101,\n",
       " 'B': 2.9010605067214215}"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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
}