{
  "cells": [
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Analysis of the multiorder Laplacian matrix\n",
        "Here we show how to analyze the multiorder Laplacian matrix defined for synchronization in higher-order networks.\n",
        "\n",
        "Source: \n",
        "\n",
        "Lucas M., Cencetti G., Battiston F., _Multiorder Laplacian for synchronization in higher-order networks_, Physical Review Research *2*, 033410 (2020)\n"
      ],
      "id": "e4916749"
    },
    {
      "cell_type": "raw",
      "metadata": {
        "raw_mimetype": "text/restructuredtext"
      },
      "source": [
        ".. admonition:: Definition\n",
        "\n",
        "   Multiorder Laplacians encode coupling at each interaction order for stability analysis.\n"
      ]
    },
    {
      "cell_type": "raw",
      "metadata": {
        "raw_mimetype": "text/restructuredtext"
      },
      "source": [
        ".. admonition:: You will learn\n",
        "\n",
        "   Analyze multiorder Laplacians and relate spectra to synchronization stability.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Overview\n",
        "\n",
        "- Analyze multiorder Laplacian spectra and synchronization properties.\n",
        "- Inspect how interaction order shapes stability.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Setup\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {},
      "execution_count": null,
      "outputs": [],
      "source": [
        "import matplotlib as mpl\n",
        "\n",
        "mpl.rcParams.update({\n",
        "    \"figure.figsize\": (6, 4),\n",
        "    \"figure.dpi\": 120,\n",
        "    \"savefig.dpi\": 150,\n",
        "})\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import sys\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "sys.path.append(\"..\")\n",
        "from hypergraphx.core.hypergraph import Hypergraph\n",
        "from hypergraphx.linalg.linalg import compute_multiorder_laplacian, laplacian_matrices_all_orders\n",
        "from hypergraphx.dynamics.synch import higher_order_MSF\n",
        "\n",
        "from scipy.linalg import eigh\n",
        "\n",
        "from itertools import combinations\n",
        "\n",
        "np.random.seed(123)"
      ],
      "id": "0f51cac7"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "# definition of the higher-order network\n",
        "edge_list = [[0,7],[1,2],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,2,7],[4,5,6],[4,5,7],[4,6,7],[5,6,7],[4,5,6,7]]\n",
        "hypergraph = Hypergraph(edge_list)\n",
        "\n",
        "N = hypergraph.num_nodes()\n",
        "\n",
        "# definition of the coupling coefficients, i.e., the strength of each order of interaction \n",
        "sigmas = [1,1,1]"
      ],
      "id": "51c4dcc7"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
            " [ 0.  2. -1.  0.  0.  0.  0. -1.]\n",
            " [ 0. -1.  2.  0.  0.  0.  0. -1.]\n",
            " [ 0.  0.  0.  0.  0.  0.  0.  0.]\n",
            " [ 0.  0.  0.  0.  6. -2. -2. -2.]\n",
            " [ 0.  0.  0.  0. -2.  6. -2. -2.]\n",
            " [ 0.  0.  0.  0. -2. -2.  6. -2.]\n",
            " [ 0. -1. -1.  0. -2. -2. -2.  8.]]\n"
          ]
        }
      ],
      "source": [
        "# We can compute the Laplacian matrix for the different orders of interaction with\n",
        "laplacians = laplacian_matrices_all_orders(hypergraph)\n",
        "\n",
        "# for instance, the Laplacian matrix of order 2, i.e., the Laplacian matrix for three-body interactions, is given by\n",
        "print(laplacians[2].todense())\n"
      ],
      "id": "1b4427b1"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[ 0.5    0.     0.     0.     0.     0.     0.    -0.5  ]\n",
            " [ 0.     2.067 -1.033  0.     0.     0.     0.    -1.033]\n",
            " [ 0.    -1.033  2.067  0.     0.     0.     0.    -1.033]\n",
            " [ 0.     0.     0.     0.5    0.     0.     0.    -0.5  ]\n",
            " [ 0.     0.     0.     0.     9.7   -3.067 -3.067 -3.567]\n",
            " [ 0.     0.     0.     0.    -3.067  9.7   -3.067 -3.567]\n",
            " [ 0.     0.     0.     0.    -3.067 -3.067  9.7   -3.567]\n",
            " [-0.5   -1.033 -1.033 -0.5   -3.567 -3.567 -3.567 13.767]]\n"
          ]
        }
      ],
      "source": [
        "# We can compute the multiorder Laplacian with\n",
        "multiorder_laplacian = compute_multiorder_laplacian(hypergraph,sigmas)\n",
        "\n",
        "print(multiorder_laplacian.toarray().round(3))"
      ],
      "id": "38aba5a9"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[-9.36750677e-16  5.00000000e-01  6.05839850e-01  1.44725527e+00\n",
            "  3.10000000e+00  1.27666667e+01  1.27666667e+01  1.68135715e+01]\n"
          ]
        }
      ],
      "source": [
        "# The stability of a system of Kuramoto oscillators depends on the spectrum of the multiorder Laplacian\n",
        "spectrum = eigh(multiorder_laplacian.toarray(), eigvals_only=True)\n",
        "\n",
        "print(spectrum)"
      ],
      "id": "01bafedc"
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Master Stability Function\n",
        "Here we show how to evaluate the Master Stability Function for synchronization in higher-order networks.\n",
        "\n",
        "Source: \n",
        "\n",
        "Gambuzza L.V., Di Patti F., Gallo L., Lepri S., Romance M., Criado R., Frasca M., Latora V., Boccaletti S., _Stability of synchronization in simplicial complexes_, Nature Communications *12*(1), 1-13 (2021)\n"
      ],
      "id": "34ea75a6"
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We study synchronization of coupled dynamical systems with higher-order interactions.\n",
        "The model follows a standard multiorder coupling form; the equations below define the dynamics\n",
        "used to compute the master stability function and related spectra.\n"
      ],
      "id": "a67daf6c"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "# To evaluate the MSF we need to define the coupling function F, its Jacobian matrix JF, \n",
        "# as well as the Jacobian matrix of the coupling function, JH.\n",
        "# In this tutorial, we will consider a system of Rossler oscillators, coupled through cubic functions\n",
        "def rossler_system(t, X, a, b, c):\n",
        "    x,y,z = X\n",
        "\n",
        "    dxdt = - y - z\n",
        "    dydt = x + a*y\n",
        "    dzdt = b + z*(x - c)\n",
        "\n",
        "    return np.array([dxdt,dydt,dzdt])\n",
        "\n",
        "def jacobian_rossler(X, a, b, c):\n",
        "    x,y,z = X\n",
        "\n",
        "    dFxdX = [0, -1, -1]\n",
        "    dFydX = [1, a, 0]\n",
        "    dFzdX = [z, 0, x - c] \n",
        "\n",
        "    return np.array([dFxdX, dFydX, dFzdX])\n",
        "\n",
        "def jacobian_coupling(X):\n",
        "    x,y,z = X\n",
        "\n",
        "    dHxdX = [3*(x**2), 0, 0]\n",
        "    dHydX = [0, 0, 0]\n",
        "    dHzdX = [0, 0, 0] \n",
        "\n",
        "    return np.array([dHxdX, dHydX, dHzdX])"
      ],
      "id": "9e53e9bb"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Setting of the isolated system\n",
        "dim = 3\n",
        "F = rossler_system\n",
        "JF = jacobian_rossler\n",
        "params = (0.2, 0.2, 9)\n",
        "\n",
        "# Setting of the coupling\n",
        "sigmas = [0.005, 0.0005, 0.00005]\n",
        "JHs = [jacobian_coupling, jacobian_coupling, jacobian_coupling]\n",
        "\n",
        "# Initial condition of the system\n",
        "X0 = np.random.random(size=(3,))\n",
        "\n",
        "# interval of values on which the MSF is evaluated\n",
        "interval = np.logspace(-4,0.5,100)\n",
        "\n",
        "MSF, hon_MSF, spectrum = higher_order_MSF(hypergraph, dim, F, JF, params, sigmas, JHs, X0, interval, integration_time=8000, integration_step=10**-3, verbose=False)"
      ],
      "id": "bee42f5b"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# We plot the results\n",
        "fig, ax = plt.subplots(figsize=(8, 6))\n",
        "\n",
        "# MSF\n",
        "ax.plot(interval, MSF,\n",
        "        lw=2, c=plt.cm.Blues(0.8), zorder=1,\n",
        "        label=\"MSF, $\\Lambda(\\\\alpha)$\")\n",
        "\n",
        "# Lyapunov exponents associated to the eigenvalues of the Laplacian matrix\n",
        "ax.scatter(spectrum[1:], hon_MSF,\n",
        "        color=plt.cm.Oranges(0.8), zorder=10,\n",
        "        label=\"$\\Lambda(\\lambda_i)$\")\n",
        "\n",
        "ax.hlines(y=0, xmin=10**-4, xmax=10,\n",
        "          colors=plt.cm.Greys(0.9), ls=\"--\")\n",
        "\n",
        "ax.semilogx()\n",
        "ax.set_xlim(10**-4,10**0.5)\n",
        "ax.tick_params(axis='both', which='major', labelsize=13)\n",
        "\n",
        "ax.set_xlabel(\"$\\\\alpha$\", fontsize=15)\n",
        "ax.set_ylabel(\"Master Stability Function, $\\Lambda(\\\\alpha)$\", fontsize=15)\n",
        "ax.legend(fontsize=15, frameon=False, loc=4)\n",
        "\n",
        "plt.show()"
      ],
      "id": "8efa0430"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# We now want to evaluate the MSF for the all-to-all case\n",
        "def rossler_system(t, X, a, b, c):\n",
        "    x,y,z = X\n",
        "\n",
        "    dxdt = - y - z\n",
        "    dydt = x + a*y\n",
        "    dzdt = b + z*(x - c)\n",
        "\n",
        "    return np.array([dxdt,dydt,dzdt])\n",
        "\n",
        "def jacobian_rossler(X, a, b, c):\n",
        "    x,y,z = X\n",
        "\n",
        "    dFxdX = [0, -1, -1]\n",
        "    dFydX = [1, a, 0]\n",
        "    dFzdX = [z, 0, x - c] \n",
        "\n",
        "    return np.array([dFxdX, dFydX, dFzdX])\n",
        "\n",
        "def jacobian_coupling_order1(X):\n",
        "    x,y,z = X\n",
        "\n",
        "    dHxdX = [1, 0, 0]\n",
        "    dHydX = [0, 0, 0]\n",
        "    dHzdX = [0, 0, 0] \n",
        "\n",
        "    return np.array([dHxdX, dHydX, dHzdX])\n",
        "\n",
        "def jacobian_coupling_order2(X):\n",
        "    x,y,z = X\n",
        "\n",
        "    dHxdX = [3 * (x**2), 0, 0]\n",
        "    dHydX = [0, 0, 0]\n",
        "    dHzdX = [0, 0, 0] \n",
        "\n",
        "    return np.array([dHxdX, dHydX, dHzdX])"
      ],
      "id": "18ad3ea6"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# We build the all-to-all hypergraph with hyperedges of size two and three \n",
        "N = 5\n",
        "edge_list = list(combinations(range(N), 2)) + list(combinations(range(N), 3))\n",
        "hypergraph = Hypergraph(edge_list)"
      ],
      "id": "0b4e7a01"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Setting of the isolated system\n",
        "dim = 3\n",
        "F = rossler_system\n",
        "JF = jacobian_rossler\n",
        "params = (0.2, 0.2, 9)\n",
        "\n",
        "# Setting of the coupling\n",
        "sigmas = [0.005, 0.0005]\n",
        "JHs = [jacobian_coupling_order1, jacobian_coupling_order2]\n",
        "\n",
        "# Initial condition of the system\n",
        "X0 = np.random.random(size=(3,))\n",
        "\n",
        "# interval of values on which the MSF is evaluated\n",
        "interval = np.logspace(-4,0.5,100)\n",
        "\n",
        "MSF, hon_MSF, spectrum = higher_order_MSF(hypergraph, dim, F, JF, params, sigmas, JHs, X0, interval, integration_time=6000, integration_step=10**-3, verbose=False)"
      ],
      "id": "e8a2b703"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# We plot the results\n",
        "fig, ax = plt.subplots(figsize=(8, 6))\n",
        "\n",
        "# MSF\n",
        "ax.plot(interval, MSF,\n",
        "        lw=2, c=plt.cm.Blues(0.8), zorder=1,\n",
        "        label=\"MSF, $\\Lambda(\\\\alpha)$\")\n",
        "\n",
        "# Lyapunov exponents associated to the eigenvalues of the Laplacian matrix\n",
        "ax.scatter(spectrum, hon_MSF,\n",
        "        color=plt.cm.Oranges(0.8), zorder=10,\n",
        "        label=\"$\\Lambda(\\lambda_i)$\")\n",
        "\n",
        "ax.hlines(y=0, xmin=10**-4, xmax=10,\n",
        "          colors=plt.cm.Greys(0.9), ls=\"--\")\n",
        "\n",
        "ax.semilogx()\n",
        "ax.set_xlim(10**-4,10**0.5)\n",
        "ax.tick_params(axis='both', which='major', labelsize=13)\n",
        "\n",
        "ax.set_xlabel(\"$\\\\alpha$\", fontsize=15)\n",
        "ax.set_ylabel(\"Master Stability Function, $\\Lambda(\\\\alpha)$\", fontsize=15)\n",
        "ax.legend(fontsize=15, frameon=False, loc=3)\n",
        "\n",
        "plt.show()"
      ],
      "id": "32e0f768"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "base",
      "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": "3.9.9"
    },
    "orig_nbformat": 4,
    "vscode": {
      "interpreter": {
        "hash": "32aaecebd078ebf0fad58c11ce872e322c9fff2b8f0b0f5a9c84d62363eabb98"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}