Effective_Resistance_WSPD.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "f9Q5bWg5sPQ_",
      "metadata": {
        "id": "f9Q5bWg5sPQ_"
      },
      "source": [
        "## Utils"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "AI_Zc5K9KhrN",
      "metadata": {
        "id": "AI_Zc5K9KhrN"
      },
      "outputs": [],
      "source": [
        "from Network import *"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "X7BfiQWlo_oi",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X7BfiQWlo_oi",
        "outputId": "d25d4ad1-5460-402d-ba1b-647541584c06"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1.13.1+cu117\n"
          ]
        }
      ],
      "source": [
        "! python -c \"import torch; print(torch.__version__)\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "5QoemF-xPH1k",
      "metadata": {
        "id": "5QoemF-xPH1k"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import networkx as nx\n",
        "import pydot\n",
        "from networkx.drawing.nx_pydot import graphviz_layout\n",
        "import numpy as np\n",
        "import wspd\n",
        "import time\n",
        "\n",
        "\n",
        "import torch\n",
        "import torch_geometric\n",
        "from torch_geometric.transforms import BaseTransform\n",
        "from torch_geometric.data.datapipes import functional_transform\n",
        "\n",
        "import networkx as nx\n",
        "from functools import reduce\n",
        "\n",
        "\n",
        "def make_binary_tree_graph(r, h):\n",
        "    T = nx.balanced_tree(r, h)\n",
        "    # print(\"Graph Nodes:\", list(T.nodes))\n",
        "    # print(\"Graph Edges:\", list(T.edges))\n",
        "    TT = nx.adjacency_matrix(T)\n",
        "    # print(\"Adjacency Matrix:\", TT.todense())\n",
        "\n",
        "    # pos = graphviz_layout(T, prog=\"dot\")\n",
        "    # nx.draw(T, pos)\n",
        "    # plt.show()\n",
        "\n",
        "    matrix = nx.linalg.graphmatrix.adjacency_matrix(T).todense()\n",
        "    print(type(matrix))\n",
        "    matrix = np.array(matrix).astype(float)\n",
        "    return matrix, T\n",
        "\n",
        "\n",
        "def make_2d_graph(m, n, periodic=False, return_pos=False):\n",
        "    network = nx.grid_2d_graph(m, n, periodic=False, create_using=None)\n",
        "    matrix = nx.linalg.graphmatrix.adjacency_matrix(network).todense()\n",
        "    matrix = np.array(matrix).astype(float)\n",
        "\n",
        "    pos = graphviz_layout(network, prog=\"dot\")\n",
        "    nx.draw(network, pos)\n",
        "    plt.show()\n",
        "\n",
        "    return matrix, network\n",
        "\n",
        "\n",
        "def make_path_graph(n):\n",
        "    parent = [i for i in range(n-1)]\n",
        "    children = [i+1 for i in range(n-1)]\n",
        "    external = [1, n]\n",
        "\n",
        "    P = nx.path_graph(n)\n",
        "\n",
        "    # print(\"Parent:\", parent)\n",
        "    # print(\"Children:\", children)\n",
        "    # print(\"External:\", external)\n",
        "    # print(\"Graph Nodes:\", list(P.nodes))\n",
        "    # print(\"Graph Edges:\", list(P.edges))\n",
        "    # Adj_P = nx.adjacency_matrix(P)\n",
        "    # print(\"Adjacency Matrix:\", Adj_P.todense())\n",
        "\n",
        "    pos = graphviz_layout(P, prog=\"dot\")\n",
        "    nx.draw(P, pos)\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "    matrix = nx.linalg.graphmatrix.adjacency_matrix(P).todense()\n",
        "    Adj_P = np.array(matrix).astype(float)\n",
        "    # return Adj_P, parent, children, n, external\n",
        "    return Adj_P, P\n",
        "\n",
        "def calc_ef_embedding(graph):\n",
        "  laplacian = torch.tensor(nx.laplacian_matrix(graph).todense().astype(\"float\"))\n",
        "  pinv = torch.linalg.pinv(laplacian, hermitian=True)\n",
        "  squared_pinv = pinv @ pinv\n",
        "\n",
        "\n",
        "  # The entries resistance_matrix[s,t] are the effective resistance  between s and t.\n",
        "  pinv_diagonal = torch.diagonal(pinv)\n",
        "  resistance_matrix = pinv_diagonal.unsqueeze(0) + pinv_diagonal.unsqueeze(1) - 2*pinv\n",
        "  return resistance_matrix\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "nfW_pZAAq4UQ",
      "metadata": {
        "id": "nfW_pZAAq4UQ"
      },
      "source": [
        "## Path"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "9pnvsGQUTIyh",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "9pnvsGQUTIyh",
        "outputId": "b5ff60fd-4747-4acc-daa7-aded8835334c"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_182487/3698167580.py:63: DeprecationWarning: nx.nx_pydot.graphviz_layout depends on the pydot package, which hasknown issues and is not actively maintained. Consider usingnx.nx_agraph.graphviz_layout instead.\n",
            "\n",
            "See https://github.com/networkx/networkx/issues/5723\n",
            "  pos = graphviz_layout(P, prog=\"dot\")\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "n= 10\n",
        "adj_path, path_graph = make_path_graph(n)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "3Oam1rR0r6xp",
      "metadata": {
        "id": "3Oam1rR0r6xp"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tensor([[0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000, 6.0000, 7.0000, 8.0000,\n",
            "         9.0000],\n",
            "        [1.0000, 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000, 6.0000, 7.0000,\n",
            "         8.0000],\n",
            "        [2.0000, 1.0000, 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000, 6.0000,\n",
            "         7.0000],\n",
            "        [3.0000, 2.0000, 1.0000, 0.0000, 1.0000, 2.0000, 3.0000, 4.0000, 5.0000,\n",
            "         6.0000],\n",
            "        [4.0000, 3.0000, 2.0000, 1.0000, 0.0000, 1.0000, 2.0000, 3.0000, 4.0000,\n",
            "         5.0000],\n",
            "        [5.0000, 4.0000, 3.0000, 2.0000, 1.0000, 0.0000, 1.0000, 2.0000, 3.0000,\n",
            "         4.0000],\n",
            "        [6.0000, 5.0000, 4.0000, 3.0000, 2.0000, 1.0000, 0.0000, 1.0000, 2.0000,\n",
            "         3.0000],\n",
            "        [7.0000, 6.0000, 5.0000, 4.0000, 3.0000, 2.0000, 1.0000, 0.0000, 1.0000,\n",
            "         2.0000],\n",
            "        [8.0000, 7.0000, 6.0000, 5.0000, 4.0000, 3.0000, 2.0000, 1.0000, 0.0000,\n",
            "         1.0000],\n",
            "        [9.0000, 8.0000, 7.0000, 6.0000, 5.0000, 4.0000, 3.0000, 2.0000, 1.0000,\n",
            "         0.0000]], dtype=torch.float64)\n"
          ]
        }
      ],
      "source": [
        "ef_embedding_path = calc_ef_embedding(path_graph)\n",
        "print(ef_embedding_path)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "9d3c10c7",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<function Tensor.type>"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ef_embedding_path.type"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "aj4dXtLSfqB-",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "aj4dXtLSfqB-",
        "outputId": "0faf2453-e278-4742-9d23-6c078b873e34"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "n = 4\n",
        "m = 4\n",
        "adj_grid, grid_graph = make_2d_graph(n,m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "id": "Ho4I-gr5TNEJ",
      "metadata": {
        "id": "Ho4I-gr5TNEJ"
      },
      "outputs": [],
      "source": [
        "network = Network(None, None, path_graph)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "id": "z2c16AZTThDu",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z2c16AZTThDu",
        "outputId": "2a48058e-ad39-4eb1-9616-f64262e9791c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<Network.Network at 0x7ac4edf869e0>"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "network"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "aXYvmtvwTEmw",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aXYvmtvwTEmw",
        "outputId": "83ff3a79-ae3b-4bd4-ff26-a8d01464ac4f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
            "[[ 0.04743416  0.20554805  0.04743416 -0.11067972  0.04743416 -0.11067972\n",
            "   0.04743416 -0.11067972  0.04743416 -0.11067972]\n",
            " [ 0.23717082  0.39528471  0.23717082  0.07905694 -0.07905694 -0.23717082\n",
            "  -0.39528471 -0.23717082 -0.07905694  0.07905694]\n",
            " [-0.14230249 -0.30041638 -0.14230249 -0.30041638 -0.14230249  0.01581139\n",
            "   0.17392527  0.33203915  0.17392527  0.33203915]\n",
            " [-0.20554805 -0.04743416  0.11067972  0.2687936   0.11067972 -0.04743416\n",
            "   0.11067972 -0.04743416 -0.20554805 -0.04743416]\n",
            " [-0.07905694  0.07905694 -0.07905694  0.07905694 -0.07905694  0.07905694\n",
            "   0.23717082  0.07905694 -0.07905694 -0.23717082]\n",
            " [ 0.11067972  0.2687936   0.11067972 -0.04743416 -0.20554805 -0.36366193\n",
            "  -0.20554805 -0.04743416  0.11067972  0.2687936 ]\n",
            " [-0.23717082 -0.07905694  0.07905694 -0.07905694  0.07905694  0.23717082\n",
            "   0.07905694 -0.07905694  0.07905694 -0.07905694]\n",
            " [-0.33203915 -0.17392527 -0.33203915 -0.17392527 -0.01581139  0.14230249\n",
            "  -0.01581139  0.14230249  0.30041638  0.45853026]\n",
            " [-0.14230249 -0.30041638 -0.14230249  0.01581139 -0.14230249  0.01581139\n",
            "   0.17392527  0.01581139  0.17392527  0.33203915]\n",
            " [-0.01581139  0.14230249  0.30041638  0.14230249 -0.01581139 -0.17392527\n",
            "  -0.33203915 -0.17392527 -0.01581139  0.14230249]\n",
            " [ 0.33203915  0.17392527  0.33203915  0.17392527  0.01581139 -0.14230249\n",
            "  -0.30041638 -0.14230249 -0.30041638 -0.14230249]\n",
            " [-0.39528471 -0.23717082 -0.07905694  0.07905694 -0.07905694  0.07905694\n",
            "  -0.07905694  0.07905694  0.23717082  0.39528471]\n",
            " [-0.2687936  -0.11067972  0.04743416 -0.11067972  0.04743416  0.20554805\n",
            "   0.04743416 -0.11067972  0.04743416  0.20554805]\n",
            " [ 0.17392527  0.01581139 -0.14230249  0.01581139 -0.14230249  0.01581139\n",
            "  -0.14230249  0.01581139  0.17392527  0.01581139]\n",
            " [-0.45853026 -0.30041638 -0.14230249  0.01581139  0.17392527  0.33203915\n",
            "   0.17392527  0.01581139  0.17392527  0.01581139]\n",
            " [-0.04743416  0.11067972 -0.04743416  0.11067972 -0.04743416  0.11067972\n",
            "  -0.04743416 -0.20554805 -0.04743416  0.11067972]\n",
            " [ 0.17392527  0.01581139 -0.14230249  0.01581139 -0.14230249  0.01581139\n",
            "   0.17392527  0.01581139 -0.14230249  0.01581139]\n",
            " [-0.11067972  0.04743416  0.20554805  0.04743416 -0.11067972  0.04743416\n",
            "  -0.11067972  0.04743416 -0.11067972  0.04743416]\n",
            " [-0.14230249 -0.30041638 -0.14230249  0.01581139  0.17392527  0.01581139\n",
            "  -0.14230249  0.01581139  0.17392527  0.33203915]\n",
            " [ 0.07905694 -0.07905694 -0.23717082 -0.07905694  0.07905694 -0.07905694\n",
            "   0.07905694 -0.07905694  0.07905694  0.23717082]\n",
            " [ 0.23717082  0.07905694 -0.07905694  0.07905694  0.23717082  0.07905694\n",
            "  -0.07905694 -0.23717082 -0.07905694 -0.23717082]\n",
            " [-0.30041638 -0.14230249  0.01581139  0.17392527  0.33203915  0.17392527\n",
            "   0.01581139 -0.14230249  0.01581139 -0.14230249]\n",
            " [ 0.20554805  0.04743416 -0.11067972  0.04743416  0.20554805  0.04743416\n",
            "  -0.11067972 -0.2687936  -0.11067972  0.04743416]\n",
            " [-0.14230249  0.01581139 -0.14230249 -0.30041638 -0.14230249  0.01581139\n",
            "   0.17392527  0.33203915  0.17392527  0.01581139]\n",
            " [-0.33203915 -0.17392527 -0.01581139 -0.17392527 -0.01581139 -0.17392527\n",
            "  -0.01581139  0.14230249  0.30041638  0.45853026]\n",
            " [-0.07905694 -0.23717082 -0.07905694 -0.23717082 -0.07905694  0.07905694\n",
            "  -0.07905694  0.07905694  0.23717082  0.39528471]\n",
            " [ 0.39528471  0.55339859  0.39528471  0.23717082  0.07905694 -0.07905694\n",
            "  -0.23717082 -0.39528471 -0.55339859 -0.39528471]\n",
            " [-0.11067972  0.04743416 -0.11067972 -0.2687936  -0.11067972  0.04743416\n",
            "   0.20554805  0.04743416  0.20554805  0.04743416]\n",
            " [ 0.04743416 -0.11067972 -0.2687936  -0.42690748 -0.2687936  -0.11067972\n",
            "   0.04743416  0.20554805  0.36366193  0.52177581]\n",
            " [ 0.14230249  0.30041638  0.14230249  0.30041638  0.14230249 -0.01581139\n",
            "  -0.17392527 -0.33203915 -0.17392527 -0.33203915]\n",
            " [-0.01581139 -0.17392527 -0.01581139  0.14230249  0.30041638  0.14230249\n",
            "  -0.01581139 -0.17392527 -0.01581139 -0.17392527]\n",
            " [ 0.17392527  0.01581139  0.17392527  0.01581139  0.17392527  0.01581139\n",
            "  -0.14230249 -0.30041638 -0.14230249  0.01581139]\n",
            " [-0.14230249 -0.30041638 -0.14230249  0.01581139  0.17392527  0.01581139\n",
            "  -0.14230249  0.01581139  0.17392527  0.33203915]\n",
            " [-0.36366193 -0.20554805 -0.36366193 -0.20554805 -0.04743416  0.11067972\n",
            "   0.2687936   0.42690748  0.2687936   0.11067972]\n",
            " [-0.07905694 -0.23717082 -0.07905694  0.07905694 -0.07905694 -0.23717082\n",
            "  -0.07905694  0.07905694  0.23717082  0.39528471]\n",
            " [-0.2687936  -0.11067972  0.04743416  0.20554805  0.04743416 -0.11067972\n",
            "   0.04743416  0.20554805  0.04743416 -0.11067972]\n",
            " [ 0.33203915  0.17392527  0.01581139  0.17392527  0.01581139 -0.14230249\n",
            "  -0.30041638 -0.14230249  0.01581139 -0.14230249]\n",
            " [ 0.39528471  0.23717082  0.39528471  0.23717082  0.07905694 -0.07905694\n",
            "  -0.23717082 -0.39528471 -0.23717082 -0.39528471]\n",
            " [ 0.33203915  0.17392527  0.01581139  0.17392527  0.01581139 -0.14230249\n",
            "   0.01581139 -0.14230249 -0.30041638 -0.14230249]\n",
            " [ 0.14230249 -0.01581139  0.14230249  0.30041638  0.14230249 -0.01581139\n",
            "  -0.17392527 -0.33203915 -0.17392527 -0.01581139]]\n"
          ]
        }
      ],
      "source": [
        "network = Network(None, None, path_graph)\n",
        "epsilon=0.1\n",
        "method='spl' #spl #ext\n",
        "Effective_R , Z_embedding = network.effR(epsilon, method)\n",
        "print(Effective_R)\n",
        "print(Z_embedding)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "7d3cf351",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(10, 40)"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Z_emb_T = Z_embedding.transpose()\n",
        "Z_emb_T.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "id": "6EvKmnHmq-Xg",
      "metadata": {
        "id": "6EvKmnHmq-Xg"
      },
      "outputs": [],
      "source": [
        "def get_and_add_box(dumbell_indices,boxes,data, i):\n",
        "    l,r = dumbell_indices[i]\n",
        "    # loop loop loop loop\n",
        "    lbox = np.array([[min(x),max(x)] for x in data[l].T]).T\n",
        "    rbox = np.array([[min(x),max(x)] for x in data[r].T]).T\n",
        "    boxes.append([lbox,rbox])\n",
        "\n",
        "def compute_centers(boxes, lcenters, rcenters, i):\n",
        "    lc, rc = boxes[i]\n",
        "    lcenters.append( (lc[0,:] + lc[1,:])/2)\n",
        "    rcenters.append( (rc[0,:] + rc[1,:])/2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "PNVhfzRorTdp",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "id": "PNVhfzRorTdp",
        "outputId": "6481db08-272c-4536-c43b-911e87b73202"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "number of points: 10\n",
            "point dimension: 40\n",
            "WSPD construction in  0.0012 seconds and size 35\n",
            "[([3], [2]), ([3], [4]), ([2], [4]), ([1], [0]), ([3], [1]), ([2], [1]), ([3], [0]), ([2], [0]), ([4], [1]), ([4], [0]), ([7], [6]), ([7], [5]), ([6], [5]), ([8], [9]), ([7], [8]), ([6], [8]), ([7], [9]), ([6], [9]), ([5], [8]), ([5], [9]), ([3], [7]), ([3], [6]), ([2], [7, 6]), ([4], [7]), ([4], [6]), ([3], [5]), ([2], [5]), ([4], [5]), ([1, 0], [7, 6]), ([1], [5]), ([0], [5]), ([3, 2], [8, 9]), ([4], [8]), ([4], [9]), ([1, 0], [8, 9])]\n"
          ]
        }
      ],
      "source": [
        "S = 2.0 # separation constant\n",
        "\n",
        "# Don't provide multiple copies of the same point in the data. The copies will get anyways removed in build_wspd() call.\n",
        "data = np.array(Z_emb_T)\n",
        "data_pts = data.tolist()\n",
        "\n",
        "\n",
        "nr_pts = len(data_pts) # number of points\n",
        "print(\"number of points: \" f'{nr_pts}')\n",
        "dim = len(data_pts[0]) # point dimension\n",
        "print(\"point dimension: \" f'{dim}')\n",
        "\n",
        "data_pts = [wspd.point(p) for p in data_pts] # move points to point class objects\n",
        "\n",
        "tic = time.perf_counter()\n",
        "dumbells = wspd.build_wspd(nr_pts, dim, S, data_pts) # compute WSPD\n",
        "toc = time.perf_counter()\n",
        "\n",
        "print(f\"WSPD construction in  {toc - tic:0.4f} seconds and size {len(dumbells)}\")\n",
        "print(dumbells)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "gYdi_1YLrCkm",
      "metadata": {
        "id": "gYdi_1YLrCkm"
      },
      "source": [
        "## Grid"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "XMDX5NzUTIWM",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 585
        },
        "id": "XMDX5NzUTIWM",
        "outputId": "2272f3ab-7d6b-4d84-d02f-0a460b6a3169"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "<ipython-input-27-72dc02e35509>:39: DeprecationWarning: nx.nx_pydot.graphviz_layout depends on the pydot package, which has known issues and is not actively maintained. Consider using nx.nx_agraph.graphviz_layout instead.\n",
            "\n",
            "See https://github.com/networkx/networkx/issues/5723\n",
            "  pos = graphviz_layout(network, prog=\"dot\")\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "n = 3\n",
        "m = 3\n",
        "adj_grid, grid_graph = make_2d_graph(n,m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9MZ-N2GFAz6o",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9MZ-N2GFAz6o",
        "outputId": "99a907e3-3c67-4f3d-9949-1b830bf9cf8c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tensor([[0.0000, 0.7083, 1.2500, 0.7083, 0.8750, 1.2083, 1.2500, 1.2083, 1.5000],\n",
            "        [0.7083, 0.0000, 0.7083, 0.8333, 0.5833, 0.8333, 1.2083, 1.0000, 1.2083],\n",
            "        [1.2500, 0.7083, 0.0000, 1.2083, 0.8750, 0.7083, 1.5000, 1.2083, 1.2500],\n",
            "        [0.7083, 0.8333, 1.2083, 0.0000, 0.5833, 1.0000, 0.7083, 0.8333, 1.2083],\n",
            "        [0.8750, 0.5833, 0.8750, 0.5833, 0.0000, 0.5833, 0.8750, 0.5833, 0.8750],\n",
            "        [1.2083, 0.8333, 0.7083, 1.0000, 0.5833, 0.0000, 1.2083, 0.8333, 0.7083],\n",
            "        [1.2500, 1.2083, 1.5000, 0.7083, 0.8750, 1.2083, 0.0000, 0.7083, 1.2500],\n",
            "        [1.2083, 1.0000, 1.2083, 0.8333, 0.5833, 0.8333, 0.7083, 0.0000, 0.7083],\n",
            "        [1.5000, 1.2083, 1.2500, 1.2083, 0.8750, 0.7083, 1.2500, 0.7083, 0.0000]],\n",
            "       dtype=torch.float64)\n"
          ]
        }
      ],
      "source": [
        "\n",
        "ef_embedding_grid = calc_ef_embedding(grid_graph)\n",
        "print(ef_embedding_grid)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "VO28ynbNX-_4",
      "metadata": {
        "id": "VO28ynbNX-_4"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "def get_and_add_box(dumbell_indices,boxes,data, i):\n",
        "    l,r = dumbell_indices[i]\n",
        "    # loop loop loop loop\n",
        "    lbox = np.array([[min(x),max(x)] for x in data[l].T]).T\n",
        "    rbox = np.array([[min(x),max(x)] for x in data[r].T]).T\n",
        "    boxes.append([lbox,rbox])\n",
        "\n",
        "def compute_centers(boxes, lcenters, rcenters, i):\n",
        "    lc, rc = boxes[i]\n",
        "    lcenters.append( (lc[0,:] + lc[1,:])/2)\n",
        "    rcenters.append( (rc[0,:] + rc[1,:])/2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "cE5z7ihuYJ1k",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cE5z7ihuYJ1k",
        "outputId": "08b0c37e-02d8-402e-aed6-ebecfaaabfdd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "number of points: 9\n",
            "point dimension: 9\n",
            "WSPD construction in  0.0003 seconds and size 36\n",
            "[([8], [7]), ([8], [4]), ([7], [4]), ([8], [6]), ([7], [6]), ([4], [6]), ([5], [2]), ([8], [5]), ([8], [2]), ([7], [5]), ([7], [2]), ([4], [5]), ([4], [2]), ([6], [5]), ([6], [2]), ([0], [3]), ([0], [1]), ([3], [1]), ([8], [0]), ([8], [3]), ([7], [0]), ([7], [3]), ([8], [1]), ([7], [1]), ([4], [0]), ([4], [3]), ([4], [1]), ([6], [0]), ([6], [3]), ([6], [1]), ([5], [0]), ([5], [3]), ([2], [0]), ([2], [3]), ([5], [1]), ([2], [1])]\n"
          ]
        }
      ],
      "source": [
        "S = 2.0 # separation constant\n",
        "\n",
        "# Don't provide multiple copies of the same point in the data. The copies will get anyways removed in build_wspd() call.\n",
        "data = np.array(ef_embedding_grid)\n",
        "data_pts = data.tolist()\n",
        "\n",
        "nr_pts = len(data_pts) # number of points\n",
        "print(\"number of points: \" f'{nr_pts}')\n",
        "dim = len(data_pts[0]) # point dimension\n",
        "print(\"point dimension: \" f'{dim}')\n",
        "\n",
        "data_pts = [wspd.point(p) for p in data_pts] # move points to point class objects\n",
        "\n",
        "tic = time.perf_counter()\n",
        "dumbells = wspd.build_wspd(nr_pts, dim, S, data_pts) # compute WSPD\n",
        "toc = time.perf_counter()\n",
        "\n",
        "print(f\"WSPD construction in  {toc - tic:0.4f} seconds and size {len(dumbells)}\")\n",
        "print(dumbells)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [
        "f9Q5bWg5sPQ_"
      ],
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.8.17"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}