Comparing_Extremal_Bounds.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Required Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import required libraries\n",
    "import networkx as nx\n",
    "from networkx.generators.random_graphs import erdos_renyi_graph\n",
    "from networkx.generators import cycle_graph,star_graph,complete_graph\n",
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing Bounds "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Generate Erdos Reyni Random Graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_graph(n,p, lap_type,seed):\n",
    "    np.random.seed(seed)\n",
    "\n",
    "    #seed is set equal to the no. of vertices\n",
    "    G = erdos_renyi_graph(n, p,seed=seed)\n",
    "    \n",
    "    #edges\n",
    "    edges = defaultdict(list)\n",
    "    [edges[i].append(j) for i,j in G.edges()]\n",
    "\n",
    "    # generate random gains of unit modulus\n",
    "    gains = np.exp(1j*np.random.rand(n,n))\n",
    "\n",
    "    # adjacency matrix for the underlying graph\n",
    "    Adj = nx.to_numpy_array(G)\n",
    "\n",
    "    # calculate degree diagonal matrix\n",
    "    D_vec = np.sum(Adj,1)\n",
    "    D = np.diag(np.sum(Adj,1))\n",
    "    delta, Delta = np.min(D_vec),np.max(D_vec)\n",
    "    \n",
    "    #no of edges\n",
    "    m = G.number_of_edges()\n",
    "    \n",
    "    #signless lapalcian\n",
    "    Q = D+Adj\n",
    "    \n",
    "    #signless normalized lapalcian\n",
    "    Q_norm = np.identity(n) + np.diag(D_vec**(-.5))@Adj@np.diag(D_vec**(-.5))\n",
    "\n",
    "    # adjacency matrix for the gain graph\n",
    "    temp = np.multiply(gains,Adj)\n",
    "    temp = (temp+temp.conj().T)\n",
    "    abs_mat = np.absolute(temp)\n",
    "    abs_mat = np.where(abs_mat==0,1,abs_mat)\n",
    "    gain_Adj = temp/abs_mat\n",
    "    \n",
    "    # Laplacian matrix for the gain graph\n",
    "    if lap_type == 'laplacian':\n",
    "        return G, m, D,delta, Delta, gain_Adj, D - gain_Adj,Q,edges\n",
    "    if lap_type == 'norm-laplacian':\n",
    "        return G, m, D,delta, Delta, gain_Adj, (np.identity(n) - np.diag(D_vec**(-.5))@gain_Adj@np.diag(D_vec**(-.5))),Q_norm,edges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Upper bounds for $\\lambda_1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=6,p=0.5781364298824675,m=8,delta=1.0, Delta=4.0\n",
      "a(phi): 0.02805532705504743, chromatic number: 3\n",
      "B_6 = 1.000 | B_7 = 0.586 | B_1 = 1.907 | B_2 = 1.838 | B_3 = 1.936 | B_4 = 0.075 | B_5 = 3.963 | lambda_1 = 0.013\n",
      "\n",
      "n=7,p=0.8539337505004864,m=19,delta=4.0, Delta=6.0\n",
      "a(phi): 0.015191299076208975, chromatic number: 6\n",
      "B_6 = 4.000 | B_7 = 3.586 | B_1 = 4.456 | B_2 = 4.446 | B_3 = 4.477 | B_4 = 0.082 | B_5 = 6.498 | lambda_1 = 0.063\n",
      "\n",
      "n=8,p=0.06809727353795003,m=2,delta=0.0, Delta=1.0\n",
      "a(phi): 0.00034019067282375914, chromatic number: 2\n",
      "B_6 = 0.000 | B_7 = 0.000 | B_1 = 0.173 | B_2 = 0.217 | B_3 = 0.233 | B_4 = 0.000 | B_5 = 1.000 | lambda_1 = -0.000\n",
      "\n",
      "n=9,p=0.46453080777933253,m=20,delta=2.0, Delta=7.0\n",
      "a(phi): 0.010478711214162661, chromatic number: 4\n",
      "B_6 = 2.500 | B_7 = 1.697 | B_1 = 3.679 | B_2 = 3.590 | B_3 = 3.699 | B_4 = 0.047 | B_5 = 5.910 | lambda_1 = 0.036\n",
      "\n",
      "n=10,p=0.7819491186191484,m=35,delta=5.0, Delta=9.0\n",
      "a(phi): 0.01740076650314637, chromatic number: 6\n",
      "B_6 = 5.000 | B_7 = 4.586 | B_1 = 6.118 | B_2 = 6.069 | B_3 = 6.118 | B_4 = 0.122 | B_5 = 8.376 | lambda_1 = 0.085\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def upper_bound_lambda(G, n, D, gain_Adj, L,edges,m,delta, Delta):\n",
    "    \n",
    "    #Diagonal Matrix\n",
    "    D_vec = np.diagonal(D)\n",
    "    \n",
    "    #For calculating average 2-degree bounds\n",
    "    def adj_degree_expres(i,L,power_i,power_j):\n",
    "        return (D_vec[i]**power_i)*(np.sum(D_vec[(gain_Adj[i]!=0)]**power_j))\n",
    "    \n",
    "    #For calculating a(Phi)\n",
    "    def real_part_gains(gain_Adj):\n",
    "        return np.real((1-(np.ones(n).T@gain_Adj@np.ones(n))/(2*m)))\n",
    "    \n",
    "     #For calculating chromatic number\n",
    "    def chrom_num(G):\n",
    "        return len(set(nx.coloring.greedy_color(G, strategy=\"largest_first\").values()))\n",
    "    \n",
    "    #Bounds expressions\n",
    "    def expression(s,t,n,exp_ind, tr):\n",
    "\n",
    "        p = (2*m)//n\n",
    "        \n",
    "        if exp_ind==1:\n",
    "            return (1/n)*(2*m -np.sqrt((4*m*(n-m+n*p)-n**2*p*(p+1))/(n-1)))\n",
    "        \n",
    "        if exp_ind==2:\n",
    "            return (1/n)*(2*m - np.sqrt((2*m*(n-2)*(n-2*m)+n*(n-2)*(delta**2+Delta**2)+n*(2*m-delta-Delta)**2)/((n-1)*(n-2))))\n",
    "\n",
    "        if exp_ind==3:\n",
    "            return (1/n)*(2*m -np.sqrt((2*m*n)/(n-1)))\n",
    "        \n",
    "        if exp_ind==4:\n",
    "            print(f'a(phi): {real_part_gains(gain_Adj)}, chromatic number: {chrom_num(G)}')\n",
    "            return ((2*m)/n)*(real_part_gains(gain_Adj))\n",
    "        \n",
    "        if exp_ind==5:\n",
    "            return ((2*m)/n)*(1 -(real_part_gains(gain_Adj)-1)/(chrom_num(G)-1))\n",
    "            \n",
    "        if exp_ind==6:\n",
    "            return 0.5*(D_vec[s]+D_vec[t]-2)\n",
    "        \n",
    "        if exp_ind==7:\n",
    "            return 0.5*(D_vec[s]+D_vec[t]-np.sqrt((D_vec[s]-D_vec[t])**2+4))\n",
    "\n",
    "    \n",
    "    indices = list(np.zeros(6))\n",
    "    tuples = [0,0]\n",
    "\n",
    "    \n",
    "    for exp_ind in range(1,8):\n",
    "        \n",
    "        if exp_ind == 6 or exp_ind == 7:\n",
    "            prev_d_min = n+1\n",
    "            \n",
    "            for i in range(n):\n",
    "                for j in edges[i]:\n",
    "                    next_d_min = expression(i,j,n,exp_ind, tr=2)\n",
    "\n",
    "                    if next_d_min <= prev_d_min:\n",
    "                        prev_d_min = next_d_min\n",
    "                        tuples[exp_ind-6] = [i,j]\n",
    "                        \n",
    "    return [expression(indices[0],0,n,1,2),expression(indices[1],0,n,2,2), expression(indices[2],0,n,3,2),\n",
    "            expression(indices[3],0,n,4,2),expression(indices[4],0,n,5,2),expression(tuples[0][0],tuples[0][1],n,6,2),\n",
    "            expression(tuples[1][0],tuples[1][1],n,7,2)]\n",
    "\n",
    "\n",
    "\n",
    "p_list = np.random.rand(5)\n",
    "for i,nodes in enumerate(range(6,11)):\n",
    "    n = nodes\n",
    "    G, m, D,delta, Delta, gain_Adj, L,Q,edges = generate_graph(n, p_list[i], 'laplacian',n)\n",
    "    print(f'n={n},p={p_list[i]},m={m},delta={delta}, Delta={Delta}')\n",
    "    \n",
    "    #calculating eigenvalues of Laplacian\n",
    "    eig, eigv = np.linalg.eigh(L)\n",
    "    \n",
    "    #Bound values \n",
    "    B_1,B_2,B_3,B_4,B_5,B_6,B_7 = upper_bound_lambda(G, n, D, gain_Adj, L,edges,m,delta, Delta)\n",
    "    \n",
    "    \n",
    "    print( f'B_6 = {B_6:.3f} | B_7 = {B_7:.3f} | B_1 = {B_1:.3f} | B_2 = {B_2:.3f} | B_3 = {B_3:.3f} | B_4 = {B_4:.3f} | B_5 = {B_5:.3f} | lambda_1 = {np.min(eig):.3f}',end='\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bounds for $\\lambda_n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def using_svd(L,iterations,type_):\n",
    "    # calculate Delta \n",
    "    d_max = np.real(np.max(np.diagonal(L)))\n",
    "    \n",
    "    #svd \n",
    "    U, lamb, U_conj = np.linalg.svd(L)\n",
    "    \n",
    "    for k in range(1,iterations+1):\n",
    "        \n",
    "        # For powers of Laplacian\n",
    "        if type_ == 'laplacian':\n",
    "            expression = np.real((np.max(np.diagonal(U@np.diag(lamb**k)@U_conj)))**(1/k))\n",
    "            if expression >= d_max+1:\n",
    "                return k, expression\n",
    "            \n",
    "        # For powers of Traces\n",
    "        if type_ == 'trace':\n",
    "            L_k = U@np.diag(lamb**k)@U_conj\n",
    "            L_2k = L_k@L_k\n",
    "            trace_L_k = np.trace(L_k)\n",
    "            expression = np.real((trace_L_k/n+np.sqrt((1/(n**3-n**2))*(n*np.trace(L_2k)-trace_L_k**2)))**(1/k))\n",
    "\n",
    "            if expression >= d_max+1:\n",
    "                return k, expression\n",
    "    else:\n",
    "        print('Could not find such a k yet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Gergorian Bounds "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def adj_degree_expres(D_vec, i,gain_Adj,power_i,power_j):\n",
    "    return (D_vec[i]**power_i)*(np.sum(D_vec[np.where(gain_Adj[i]!=0)]**power_j))\n",
    "\n",
    "# ***********************************************************************************\n",
    "def d_m_power_k(D,n,L, iterations):\n",
    "    bounds = []\n",
    "    delta = np.min(np.diagonal(D))\n",
    "    D = D-.6435*np.identity(n)\n",
    "    min_k,ind = np.inf,0\n",
    "    for k in range(iterations):   \n",
    "        jn = np.ones(n)\n",
    "        D_vec = np.diagonal(D)\n",
    "        Ah = np.abs((np.diag(D_vec**(-1)))@np.abs(L)@(np.diag(D_vec)))\n",
    "        d = Ah@jn\n",
    "        bound = max(d)\n",
    "#         print(bound)\n",
    "        bounds.append(bound)\n",
    "        D = np.diag(d)\n",
    "\n",
    "        if  bound <= min_k:\n",
    "                min_k = bound\n",
    "                ind = k\n",
    "        \n",
    "    return ind, min_k, bounds\n",
    "\n",
    "# ***********************************************************************************\n",
    "def d_n_power_k(D,n,L,iterations):\n",
    "    bounds = []\n",
    "    min_k,ind = np.inf,0\n",
    "    Delta = np.max(D)\n",
    "    for k in range(iterations):\n",
    "        jn = np.ones(n)\n",
    "        D_vec = np.diagonal(D)- (2*Delta-2)*np.ones(n) #epsilon = (29/45) for cycle\n",
    "        Ah = np.abs((np.diag(D_vec**(-1)))@(np.abs(L))@(np.diag(D_vec)))\n",
    "        d = Ah@jn\n",
    "        bound = max(d)\n",
    "        bounds.append(bound)\n",
    "        D = np.diag(d)\n",
    "\n",
    "        if  bound <= min_k:\n",
    "                min_k = bound\n",
    "                ind = k\n",
    "    return ind, min_k,bounds\n",
    "\n",
    "# ***********************************************************************************\n",
    "def d_l_power_k(D,n,gain_Adj,L,iterations):\n",
    "    bounds = []\n",
    "    l_k_2 = list(np.zeros(n))\n",
    "    l_k_1 = [adj_degree_expres(np.diagonal(D),k,gain_Adj,-1,1) for k in range(n)]\n",
    "    \n",
    "    min_k,ind = np.inf,0\n",
    "    \n",
    "    for k in range(iterations):\n",
    "        \n",
    "        jn = np.ones(n)\n",
    "        D_vec = np.diagonal(D)+l_k_1-l_k_2\n",
    "        Ah = np.abs((np.diag(D_vec**(-1)))@(np.abs(L))@(np.diag(D_vec)))\n",
    "        d = Ah@jn\n",
    "        bound = max(d)\n",
    "        \n",
    "        l_k_2 = l_k_1\n",
    "        l_k_1 = d\n",
    "        \n",
    "        bounds.append(bound)\n",
    "        D = np.diag(d)\n",
    "\n",
    "        if  bound <= min_k:\n",
    "                min_k = bound\n",
    "                ind = k\n",
    "    return ind, min_k,bounds\n",
    "# d_m_power_k(D_vec,n, gain_Adj,iterations=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Upper Bounds for $\\lambda_n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def upper_bound_lambda(G, n, D, gain_Adj, L,edges,m,delta, Delta):\n",
    "    D_vec = np.diagonal(D)\n",
    "    tuples = [0,0,0]\n",
    "    t_d,b_d = 0,0\n",
    "    \n",
    "    def expression(s,t,n,exp_ind,D_vec,gain_Adj):\n",
    "\n",
    "        p = (2*m)//n\n",
    "        \n",
    "        if exp_ind==1:\n",
    "            return using_svd(L, 10000,'laplacian')\n",
    "        \n",
    "        if exp_ind==2:\n",
    "            return using_svd(L, 10000,'trace')\n",
    "\n",
    "        if exp_ind==3:\n",
    "            _,bound_m_k,_ = d_m_power_k(D,n,L,iterations=100)\n",
    "            return bound_m_k \n",
    "        \n",
    "        if exp_ind==4:\n",
    "            _,bound_n_k,_ = d_n_power_k(D,n,L,iterations=100)\n",
    "            return bound_n_k\n",
    "        \n",
    "        if exp_ind==5:\n",
    "            _,bound_l_k,_ = d_l_power_k(D,n, gain_Adj,L,iterations=100)\n",
    "            return bound_l_k\n",
    "            \n",
    "        if exp_ind==6:\n",
    "            return (D_vec[s]+D_vec[t])\n",
    "        \n",
    "        if exp_ind==7:\n",
    "            m_s = adj_degree_expres(D_vec,s,gain_Adj,-1,1)\n",
    "            m_t = adj_degree_expres(D_vec,t,gain_Adj,-1,1)\n",
    "            return (D_vec[s]*(D_vec[s]+m_s)+D_vec[t]*(D_vec[t]+m_t))/(D_vec[s]+D_vec[t])\n",
    "        \n",
    "        if exp_ind==8:\n",
    "#             print(t_d,b_d)\n",
    "            return 2+np.sqrt((t_d-2)*(b_d-2))\n",
    "\n",
    "\n",
    "    \n",
    "    for exp_ind in range(1,9):\n",
    "        \n",
    "        if exp_ind in [6,7,8]:\n",
    "            prev_d_max = -1*(n+1)\n",
    "            \n",
    "            if exp_ind==8:  \n",
    "                g,d = gain_Adj.copy(),D_vec.copy()\n",
    "                g[tuples[1][0]][tuples[1][1]],g[tuples[1][1]][tuples[1][0]] = 0,0\n",
    "                d[tuples[1][0]] = D_vec[tuples[1][0]]-1\n",
    "                d[tuples[1][1]] = D_vec[tuples[1][1]]-1\n",
    "            \n",
    "                for i in range(n):\n",
    "                    for j in edges[i]: \n",
    "                        if i!= tuples[1][0] and j!= tuples[1][1]:\n",
    "                            next_d_max = expression(i,j,n,7,d,g)\n",
    "\n",
    "                            if next_d_max >= prev_d_max:\n",
    "                                prev_d_max = next_d_max\n",
    "                                tuples[exp_ind-6] = [i,j]\n",
    "                \n",
    "            else:\n",
    "                for i in range(n):\n",
    "                    for j in edges[i]:                        \n",
    "                        next_d_max = expression(i,j,n,exp_ind,D_vec,gain_Adj)\n",
    "\n",
    "                        if next_d_max >= prev_d_max:\n",
    "                            prev_d_max = next_d_max\n",
    "                            tuples[exp_ind-6] = [i,j]\n",
    "\n",
    "    t_d = expression(tuples[1][0],tuples[1][1],n,7,D_vec,gain_Adj)\n",
    "    b_d = expression(tuples[2][0],tuples[2][1],n,7,D_vec,gain_Adj)\n",
    "                        \n",
    "    return [expression(0,0,n,1,D_vec,gain_Adj),expression(0,0,n,2,D_vec,gain_Adj), expression(0,0,n,3,D_vec,gain_Adj),\n",
    "            expression(0,0,n,4,D_vec,gain_Adj),expression(0,0,n,5,D_vec,gain_Adj),expression(tuples[0][0],tuples[0][1],n,6,D_vec,gain_Adj),\n",
    "            expression(tuples[1][0],tuples[1][1],n,7,D_vec,gain_Adj),expression(0,0,n,8,D_vec,gain_Adj)]\n",
    "\n",
    "\n",
    "p_list = np.random.rand(5)\n",
    "for i,nodes in enumerate(range(6,11)):\n",
    "    n = nodes\n",
    "    G, m, D,delta, Delta, gain_Adj, L,Q,edges = generate_graph(n, p_list[i], 'laplacian',n)\n",
    "    epsilon, epsilon_bounds = d_n_power_k_epsilon(D,n,L, iterations=500)\n",
    "    print(f'n={n},p={p_list[i]},m={m},delta={delta}, Delta={Delta}')\n",
    "\n",
    "    D_vec = np.diagonal(D)\n",
    "    m_i_s = [adj_degree_expres(D_vec,k,gain_Adj,-1,1) for k in range(n)]\n",
    "    \n",
    "    #calculating eigenvalues of Laplacian\n",
    "    eig, eigv = np.linalg.eigh(L)\n",
    "    \n",
    "    #calculating eigenvalues of Laplacian\n",
    "    # For +1 gain\n",
    "    eig_q, eigv_q = np.linalg.eigh(Q-2*np.ones((n,n))+2*np.identity(n))\n",
    "    \n",
    "    B_1,B_2,B_3,B_4,B_5,B_6,B_7,B_8 = upper_bound_lambda(G, n, D, gain_Adj, L,edges,m,delta, Delta)\n",
    "    \n",
    "    def degree_conj(D_vec,k):\n",
    "        return np.sum(sorted(D_vec)[::-1][:k])/k\n",
    "\n",
    "    print( f'B_1 = ({B_1[0]},{B_1[1]:.3f}) | B_2 = ({B_2[0]},{B_2[1]:.3f}) | B_6 = {B_6:.3f} | B_3 = {B_3:.3f} | B_4 = {epsilon:.3f}, {min(epsilon_bounds):.3f} | B_5 = {B_5:.3f} | B_7 = {B_7:.3f} | B_8 = {B_8:.3f} | d_i+m_i = {np.max(D_vec + m_i_s):.3f} | d_conj_lower = {degree_conj(D_vec,2):.3f}| lambda_n = {np.max(eig):.3f} | q_n = {np.max(eig_q):.3f}',end='\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Triangle Upper Bounds for $\\lambda_1$  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=6,p=0.5488135039273248,m=8,delta=1.0, Delta=4.0\n",
      "a(phi): 0.028 | b(phi): 1.101 | chromatic number: 3\n",
      "T1 = 1.013 | T2 = 0.873 | T3 = 1.013 | T4 = 0.379\n",
      "P1 = 1.000 | P2 = 0.775 | P3 = 0.634 | P4 = 0.363\n",
      "chromatic bound: 0.065\n",
      "\n",
      "n=7,p=0.7151893663724195,m=18,delta=4.0, Delta=6.0\n",
      "a(phi): 0.015 | b(phi): 0.982 | chromatic number: 5\n",
      "T1 = 3.000 | T2 = 2.814 | T3 = 2.865 | T4 = 3.004\n",
      "P1 = 3.333 | P2 = 3.293 | P3 = 3.219 | P4 = 3.268\n",
      "chromatic bound: 0.079\n",
      "\n",
      "n=8,p=0.6027633760716439,m=19,delta=4.0, Delta=6.0\n",
      "a(phi): 0.017 | b(phi): 1.041 | chromatic number: 5\n",
      "T1 = 2.005 | T2 = 2.005 | T3 = 2.005 | T4 = 2.005\n",
      "P1 = 3.000 | P2 = 2.775 | P3 = 2.775 | P4 = 2.814\n",
      "chromatic bound: 0.080\n",
      "\n",
      "n=9,p=0.5448831829968969,m=22,delta=4.0, Delta=7.0\n",
      "a(phi): 0.010 | b(phi): 0.984 | chromatic number: 4\n",
      "T1 = 2.020 | T2 = 2.020 | T3 = 2.020 | T4 = 2.020\n",
      "P1 = 3.000 | P2 = 2.775 | P3 = 2.775 | P4 = 2.814\n",
      "chromatic bound: 0.051\n",
      "\n",
      "n=10,p=0.4236547993389047,m=19,delta=1.0, Delta=6.0\n",
      "a(phi): 0.014 | b(phi): 0.977 | chromatic number: 4\n",
      "T1 = 2.012 | T2 = 1.872 | T3 = 1.827 | T4 = 1.517\n",
      "P1 = 1.667 | P2 = 0.411 | P3 = 0.775 | P4 = 0.551\n",
      "chromatic bound: 0.053\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import itertools\n",
    "np.random.seed(0)\n",
    "p_list = np.random.rand(5)\n",
    "\n",
    "# for calculating a(Phi) and b(Phi)\n",
    "def a_b_Phi(gain_Adj,string):\n",
    "    if string=='real':\n",
    "        return np.real((1-(np.ones(n).T@gain_Adj@np.ones(n))/(2*m)))\n",
    "    elif string=='img':\n",
    "        igain_adj = np.conjugate(np.triu(-1j*gain_Adj)).T+np.triu(-1j*gain_Adj)\n",
    "        return np.real((1-(np.ones(n).T@igain_adj@np.ones(n))/(2*m)))\n",
    "    \n",
    "def chrom_num(G):\n",
    "    return len(set(nx.coloring.greedy_color(G, strategy=\"largest_first\").values()))\n",
    "    \n",
    "    \n",
    "for i,nodes in enumerate(range(6,11)):\n",
    "    n = nodes\n",
    "    #Fetching graph parameters\n",
    "    G, m, D,delta, Delta, gain_Adj, L,Q,edges = generate_graph(n, p_list[i], 'laplacian',n)\n",
    "    print(f'n={n},p={p_list[i]},m={m},delta={delta}, Delta={Delta}')\n",
    "    a_phi,b_phi,chi = a_b_Phi(gain_Adj,'real'),a_b_Phi(gain_Adj,'img'),chrom_num(G)\n",
    "    print(f'a(phi): {a_phi:.3f} | b(phi): {b_phi:.3f} | chromatic number: {chi}')\n",
    "\n",
    "    D_vec = np.diagonal(D)\n",
    "    \n",
    "    #calculating eigenvalues of Laplacian\n",
    "    eig, eigv = np.linalg.eigh(L)\n",
    "    \n",
    "    np.random.seed(5)\n",
    "    #calculate frobenius bound\n",
    "    D_inv = np.linalg.inv(D)\n",
    "    \n",
    "    \n",
    "    #calculating eigenvalues of Laplacian\n",
    "    eig_q, eigv_q = np.linalg.eigh(L)\n",
    "\n",
    "    \n",
    "    igain_adj = np.conjugate(np.triu(-1j*gain_Adj)).T+np.triu(-1j*gain_Adj)\n",
    "    L_b  = D-igain_adj\n",
    "    \n",
    "    cliques = nx.find_cliques(G)\n",
    "    cliques3 = list(set(sum([list(itertools.combinations(set(clq), 3)) for clq in cliques if len(clq)>=3],[])))\n",
    "#     print(f'cliques3: {cliques3}', end='\\n')\n",
    "\n",
    "    \n",
    "    def d3_degree_bounds(objects, type_):\n",
    "        B1,B2,B3,B4 = [],[],[],[]\n",
    "        for object_ in objects:\n",
    "            s,t,r = sorted(object_)\n",
    "\n",
    "            if type_ == 'triangle':\n",
    "                costheta = np.real(gain_Adj[s][t]*gain_Adj[s][r]*gain_Adj[t][r])\n",
    "            elif type_ == 'tree':\n",
    "                costheta = 0\n",
    "\n",
    "            B1.append((D_vec[s]+D_vec[t]+D_vec[r]-2*costheta-4)/3)\n",
    "            B2.append((D_vec[s]+D_vec[t]+2*D_vec[r]-2-np.sqrt((D_vec[s]+D_vec[t]-2*D_vec[r]-2)**2+8*(costheta+1)**2))/4)\n",
    "            B3.append((D_vec[s]+2*D_vec[t]+D_vec[r]-2-np.sqrt((D_vec[s]-2*D_vec[t]+D_vec[r]-2)**2+8*(costheta+1)**2))/4)\n",
    "            B4.append((2*D_vec[s]+D_vec[t]+D_vec[r]-2*costheta-np.sqrt((2*D_vec[s]-D_vec[t]-D_vec[r]-2*costheta)**2+32))/4)\n",
    "\n",
    "        return B1,B2,B3,B4\n",
    "\n",
    "\n",
    "    #for triangle\n",
    "    T1,T2,T3,T4 = d3_degree_bounds(cliques3,'triangle')\n",
    "#     print(T1)\n",
    "    \n",
    "    #for trees\n",
    "    paths = []\n",
    "    for i in range(n):\n",
    "        for j in list(set(list(range(n)))-set(edges[i])):\n",
    "            for path in nx.all_simple_paths(G, source=i, target=j, cutoff=2):\n",
    "                paths.append(sorted(path))\n",
    "    paths3 = list((set(map(tuple, [path for path in paths if len(path)==3]))) - set(cliques3))\n",
    "#     print(f'paths3: {paths3}',end='\\n\\n')\n",
    "    \n",
    "    P1,P2,P3,P4 = d3_degree_bounds(paths3,'tree')\n",
    "\n",
    "    \n",
    "    #for triangle\n",
    "    print( f'T1 = {sorted(T1)[0]:.3f} | T2 = {sorted(T2)[0]:.3f} | T3 = {sorted(T3)[0]:.3f} | T4 = {sorted(T4)[0]:.3f}',end='\\n')\n",
    "    \n",
    "    #for tree\n",
    "    print( f'P1 = {sorted(P1)[0]:.3f} | P2 = {sorted(P2)[0]:.3f} | P3 = {sorted(P3)[0]:.3f} | P4 = {sorted(P4)[0]:.3f}',end='\\n')\n",
    "    \n",
    "    #chromatic bound a(phi) and b(phi)\n",
    "    bound = (m/n)*(a_phi+1-(a_phi-1)/(chi-1)-np.sqrt(chi**2*(a_phi-1)**2+4*(chi-1)*(b_phi-1)**2)/(chi-1))\n",
    "    print(f'chromatic bound: {bound:.3f}',end='\\n\\n')\n",
    "    \n",
    "    theta = np.array([round(np.angle(gain_Adj[i][j]),3) if gain_Adj[i][j]!=0 else 0 for i in range(n) for j in range(n)]).reshape(n,n)\n",
    "    G = nx.from_numpy_matrix(theta)\n",
    "    pos=nx.get_node_attributes(G,'pos')\n",
    "#     nx.draw(G,pos)\n",
    "    labels = nx.get_edge_attributes(G,'weight')\n",
    "#     nx.draw_networkx_edge_labels(G,pos,edge_labels=labels)\n",
    "    \n",
    "    #  -----------------------------------------------------------------\n",
    "#     plt.savefig(f'erdos_reyni/{n}.eps',format='eps',dps=200)\n",
    "    #  -----------------------------------------------------------------\n",
    "#     plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bipartite graph bound for randomly generated Erdos-Reyni Bipartite graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=10,p=0.7,m=17,delta=2.0, Delta=5.0\n",
      "a(phi): 0.017 | b(phi): 0.958 | chromatic number: 2\n",
      "\n",
      "Bipartite chromatic bound: 0.059 | 2mn*a(phi): 0.059 | lambda_1 = 0.018\n",
      "Bipartite chromatic bound: 2.818 | 2mn*b(phi): 3.257 | lambda_1 = 0.018\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=12,p=0.7,m=22,delta=2.0, Delta=6.0\n",
      "a(phi): 0.025 | b(phi): 0.977 | chromatic number: 2\n",
      "\n",
      "Bipartite chromatic bound: 0.093 | 2mn*a(phi): 0.093 | lambda_1 = 0.042\n",
      "Bipartite chromatic bound: 3.137 | 2mn*b(phi): 3.581 | lambda_1 = 0.042\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=14,p=0.7,m=31,delta=2.0, Delta=6.0\n",
      "a(phi): 0.018 | b(phi): 0.991 | chromatic number: 2\n",
      "\n",
      "Bipartite chromatic bound: 0.078 | 2mn*a(phi): 0.078 | lambda_1 = 0.050\n",
      "Bipartite chromatic bound: 3.874 | 2mn*b(phi): 4.388 | lambda_1 = 0.050\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_bipartite_graph(n1,n2,p, lap_type,seed):\n",
    "    np.random.seed(seed)\n",
    "\n",
    "    n = n1+n2\n",
    "    G = nx.bipartite.random_graph(n1,n2,p, seed = 0) \n",
    "\n",
    "    \n",
    "    #edges\n",
    "    edges = defaultdict(list)\n",
    "    [edges[i].append(j) for i,j in G.edges()]\n",
    "\n",
    "    # generate random gains of unit modulus\n",
    "    gains = np.exp(1j*np.random.rand(n,n))\n",
    "\n",
    "    # adjacency matrix for the underlying graph\n",
    "    Adj = nx.to_numpy_array(G)\n",
    "\n",
    "    # calculate degree diagonal matrix\n",
    "    D_vec = np.sum(Adj,1)\n",
    "    D = np.diag(np.sum(Adj,1))\n",
    "    delta, Delta = np.min(D_vec),np.max(D_vec)\n",
    "    \n",
    "    #no of edges\n",
    "    m = G.number_of_edges()\n",
    "    \n",
    "    #signless lapalcian\n",
    "    Q = D+Adj\n",
    "    \n",
    "    #signless normalized lapalcian\n",
    "    Q_norm = np.identity(n) + np.diag(D_vec**(-.5))@Adj@np.diag(D_vec**(-.5))\n",
    "\n",
    "    # adjacency matrix for the gain graph\n",
    "    temp = np.multiply(gains,Adj)\n",
    "    temp = (temp+temp.conj().T)\n",
    "    abs_mat = np.absolute(temp)\n",
    "    abs_mat = np.where(abs_mat==0,1,abs_mat)\n",
    "    gain_Adj = temp/abs_mat\n",
    "    \n",
    "    # Laplacian matrix for the gain graph\n",
    "    if lap_type == 'laplacian':\n",
    "        return G, m, D,delta, Delta, gain_Adj, D - gain_Adj,Q,edges\n",
    "    if lap_type == 'norm-laplacian':\n",
    "        return G, m, D,delta, Delta, gain_Adj, (np.identity(n) - np.diag(D_vec**(-.5))@gain_Adj@np.diag(D_vec**(-.5))),Q_norm,edges\n",
    "    \n",
    "    \n",
    "# ************************************************************************************\n",
    "# np.random.seed(0)\n",
    "# p_list = np.random.rand(3)\n",
    "for n1 in range(4,7):\n",
    "    n = 2*n1+2\n",
    "    G, m, D,delta, Delta, gain_Adj, L,Q,edges = generate_bipartite_graph(n1,n1+2,0.7, 'laplacian',seed=0)\n",
    "    \n",
    "    igain_adj = np.conjugate(np.triu(-1j*gain_Adj)).T+np.triu(-1j*gain_Adj)\n",
    "    L_b  = D-igain_adj\n",
    "    eig, eigv = np.linalg.eigh(L)\n",
    "    eig_b, eigv_b = np.linalg.eigh(L_b)\n",
    "#     print(eig,eig_b)\n",
    "#     print(igain_adj-gain_Adj,end='\\n\\n')\n",
    "#     print(np.linalg.eigvals(L_b)-np.linalg.eigvals(L))\n",
    "    \n",
    "    print(f'n={n},p={0.7},m={m},delta={delta}, Delta={Delta}')\n",
    "    a_phi,b_phi,chi = a_b_Phi(gain_Adj,'real'),a_b_Phi(gain_Adj,'img'),chrom_num(G)\n",
    "    print(f'a(phi): {a_phi:.3f} | b(phi): {b_phi:.3f} | chromatic number: {chi}',end='\\n\\n')\n",
    "    \n",
    "    \n",
    "    #Bipartite chromatic bound a(phi) \n",
    "    bound_a_phi = (m/(2*n1*(n1+2)))*(n-np.sqrt(n**2-4*a_phi*(2-a_phi)*n1*(n1+2)))\n",
    "    #Bipartite chromatic bound b(phi)\n",
    "    bound_b_phi = (m/(2*n1*(n1+2)))*(n-np.sqrt(n**2-4*b_phi*(2-b_phi)*n1*(n1+2)))\n",
    "    print(f'Bipartite chromatic bound: {bound_a_phi:.3f} | 2mn*a(phi): {(2*m/n)*a_phi:.3f} | lambda_1 = {np.min(eig):.3f}')\n",
    "    print(f'Bipartite chromatic bound: {bound_b_phi:.3f} | 2mn*b(phi): {(2*m/n)*b_phi:.3f} | lambda_1 = {np.min(eig):.3f}',end='\\n\\n')\n",
    "    \n",
    "#     theta = np.array([round(np.angle(gain_Adj[i][j]),3) if gain_Adj[i][j]!=0 else 0 for i in range(n) for j in range(n)]).reshape(n,n)\n",
    "#     G = nx.from_numpy_matrix(theta)\n",
    "    nx.draw(G,pos=nx.spring_layout(G),with_labels = True,fontsize = 30)\n",
    "    #  -----------------------------------------------------------------\n",
    "    plt.savefig(f'bipartite/{n}.eps',format='eps',dps=200)\n",
    "    #  -----------------------------------------------------------------\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bipartite bound for the bipartite adjacency matrix defined in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda_1 = 3.597, Bipartite bound = 3.982, m_n_a_phi = 4.600, a_phi = 0.613\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1 ,-1 ,1 ,1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1],\n",
    "[1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1],\n",
    "[1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1],\n",
    "[1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1],\n",
    "[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1]])\n",
    "\n",
    "# G=nx.from_numpy_matrix(np.abs(Adj))\n",
    "# nx.draw(G,pos=nx.spring_layout(G),with_labels = True,fontsize = 30)\n",
    "\n",
    "Adj = np.block([\n",
    "    [np.zeros((5,5)),   A],\n",
    "    [A.T, np.zeros((15,15))]])\n",
    "\n",
    "D_vec = np.sum(np.abs(Adj), axis=1)\n",
    "Delta = max(D_vec)\n",
    "\n",
    "L = np.diag(D_vec)- Adj\n",
    "eig, _ = np.linalg.eigh(L)\n",
    "# print(f'lambda_1 = {eig[0]}, Bipartite bound = {bound_a_phi}')\n",
    "\n",
    "n, n1, n2, m = 20, 5, 15, np.sum(D_vec)/2\n",
    "\n",
    "\n",
    "a_phi = (1-(np.ones(n).T@Adj@np.ones(n))/(2*m))\n",
    "m_n_a_phi = (2*m/n)*a_phi\n",
    "bound_a_phi = (m/(2*n1*n2))*(n-np.sqrt(n**2-4*a_phi*(2-a_phi)*n1*(n2)))\n",
    "print(f'lambda_1 = {eig[0]:.3f}, Bipartite bound = {bound_a_phi:.3f}, m_n_a_phi = {m_n_a_phi:.3f}, a_phi = {a_phi:.3f}')\n",
    "\n",
    "# frustration bound\n",
    "# frus_bound = n*np.sqrt(bound_a_phi*Delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supplementary: An Analysis of Gershgorian Bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lambda_n = 5.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from networkx.generators import star_graph\n",
    "\n",
    "n = 5\n",
    "# G = star_graph(n-1)\n",
    "G = cycle_graph(n)\n",
    "\n",
    "# graph = 'star'\n",
    "graph = 'wheel'\n",
    "\n",
    "G.add_edge(0, 2)\n",
    "G.add_edge(0, 3)\n",
    "# G.add_edge(1, 3)\n",
    "\n",
    "# n = 7\n",
    "# G = erdos_renyi_graph(n, p_list[1],seed=n)\n",
    "\n",
    "# adjacency matrix for the underlying graph\n",
    "Adj = nx.to_numpy_array(G)\n",
    "\n",
    "# calculate degree diagonal matrix\n",
    "D_vec = np.sum(Adj,1)\n",
    "D = np.diag(np.sum(Adj,1))\n",
    "\n",
    "# Laplacian matrix for the gain graph\n",
    "L = D - Adj\n",
    "\n",
    "edges = defaultdict(list)\n",
    "[edges[i].append(j) for i,j in G.edges()]\n",
    "# edges\n",
    "\n",
    "\n",
    "eig, eigv = np.linalg.eigh(L)\n",
    "lambda_n = np.max(eig)\n",
    "print(f'Lambda_n = {lambda_n}')\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "nx.draw(G,pos = nx.spectral_layout(G), node_size = 1000, with_labels = True, font_size=20)\n",
    "\n",
    "#  -----------------------------------------------------------------\n",
    "plt.savefig(f'{graph}.eps',format='eps',dps=200)\n",
    "#  -----------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unfolding the recurrence relation for gershgorian bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ind,m_min,bounds_m = d_m_power_k(D,n, L,iterations=100)\n",
    "plt.plot(list(range(100)),bounds_m)\n",
    "plt.xlabel('k',fontsize=16)\n",
    "plt.ylabel('value',fontsize=16)\n",
    "plt.title(f'Min Bound Value: {m_min:.3f}, k = {ind}',fontsize=16)\n",
    "#  -----------------------------------------------------------------\n",
    "# plt.savefig(f'm_k_{graph}.eps',format='eps',dps=200)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.show()\n",
    "\n",
    "_,n_min,bounds_n = d_n_power_k(D,n, L,iterations=100)\n",
    "plt.plot(list(range(100)),bounds_n)\n",
    "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(0,0))\n",
    "plt.xlabel('k',fontsize=16)\n",
    "plt.ylabel('value',fontsize=16)\n",
    "plt.title(f'Min Bound Value: {n_min:.3f}, k = {ind}',fontsize=16)\n",
    "#  -----------------------------------------------------------------\n",
    "# plt.savefig(f'n_k_{graph}.eps',format='eps',dps=200)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.show()\n",
    "\n",
    "_,l_min,bounds_l = d_l_power_k(D,n,Adj,L,iterations=100)\n",
    "plt.plot(list(range(100)),bounds_l)\n",
    "plt.xlabel('k',fontsize=16)\n",
    "plt.ylabel('value',fontsize=16)\n",
    "plt.title(f'Min Bound Value: {l_min:.3f}, k = {ind}',fontsize=16)\n",
    "#  -----------------------------------------------------------------\n",
    "# plt.savefig(f'l_k_{graph}.eps',format='eps',dps=200)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# epsilons = np.linspace(-2,10,100) #1.218\n",
    "# epsilons = np.linspace(5.9,6,1000) #1.218\n",
    "# epsilons = np.linspace(0,1.218,400) #1.218\n",
    "epsilons = np.linspace(0,0.99,1000) #1.218\n",
    "# ***********************************************************************************\n",
    "def d_n_power_k_epsilon(D,n,L,iterations):\n",
    "    bounds = []\n",
    "#     epsilons = 0.2*np.ones(10)\n",
    "    jn = np.ones(n)\n",
    "    orig = D\n",
    "    for epsilon in epsilons:\n",
    "        min_k,ind = np.inf,0\n",
    "        D = orig\n",
    "        for k in range(iterations):\n",
    "            D_vec = np.diagonal(D)-epsilon*np.ones(n)\n",
    "            Ah = np.abs((np.diag(D_vec**(-1)))@(np.abs(L))@(np.diag(D_vec)))\n",
    "            d = Ah@jn\n",
    "            bound = max(d)\n",
    "            D = np.diag(d)\n",
    "\n",
    "            if  bound <= min_k:\n",
    "                    min_k = bound\n",
    "                    ind = k\n",
    "        bounds.append(min_k)\n",
    "    bounds = np.array(bounds)\n",
    "    return epsilons[bounds == np.min(bounds)][0], bounds\n",
    "# d_n_power_k(D,n,L,iterations=100)\n",
    "\n",
    "\n",
    "k, bounds_n = d_n_power_k_epsilon(D,n, L,iterations=100)\n",
    "plt.plot(epsilons,bounds_n)\n",
    "plt.xlabel(r'$\\epsilon$',fontsize = 16)\n",
    "plt.ylabel(r'$B(\\epsilon)$',fontsize = 16)\n",
    "plt.title(f'Min Bound Value: {min(bounds_n):.3f}, $\\epsilon$ = {k:.3f}',fontsize=16)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.savefig(f'n_k_epsilon-{graph}.eps',format='eps',dps=200)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\eta$ analysis for $m^k$ bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "etas = np.linspace(0,0.99,1000) #1.218\n",
    "# ***********************************************************************************\n",
    "def d_m_power_k_eta(D,n,L,iterations):\n",
    "    bounds = []\n",
    "    orig = D\n",
    "    jn = np.ones(n)\n",
    "    \n",
    "    for eta in etas:\n",
    "        min_k,ind = np.inf,0\n",
    "        \n",
    "        D = orig\n",
    "        #delta = np.min(np.diagonal(D))\n",
    "        D = D-eta*np.identity(n)\n",
    "        #D = 2*(np.max(D)+1)*np.identity(n)\n",
    "        \n",
    "        for k in range(iterations):\n",
    "            D_vec = np.diagonal(D)\n",
    "            Ah = np.abs((np.diag(D_vec**(-1)))@np.abs(L)@(np.diag(D_vec)))\n",
    "            d = Ah@jn\n",
    "            bound = max(d)\n",
    "            D = np.diag(d)\n",
    "\n",
    "            if  bound <= min_k:\n",
    "                    min_k = bound\n",
    "                    ind = k\n",
    "        bounds.append(min_k)\n",
    "    bounds = np.array(bounds)\n",
    "    return etas[bounds == np.min(bounds)][0], bounds\n",
    "\n",
    "\n",
    "k, bounds_n = d_m_power_k_eta(D,n, L,iterations=100)\n",
    "plt.plot(etas,bounds_n)\n",
    "plt.xlabel(r'$\\eta$',fontsize = 16)\n",
    "plt.ylabel(r'$B(\\eta)$',fontsize = 16)\n",
    "plt.title(f'Min Bound Value: {min(bounds_n):.3f}, $\\eta$ = {k:.3f}',fontsize=16)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.savefig(f'm_k_eta-{graph}.eps',format='eps',dps=200)\n",
    "#  -----------------------------------------------------------------\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}