{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IFN Tutorial\n",
    "\n",
    "by [*Kardi Teknomo*](https://people.revoledu.com/kardi/)\n",
    "\n",
    "IFN is reusable Python library for Ideal Flow Network (IFN). The library of IFN itself is quite generic that it can be useful for any network, not just IFN. If you are interested in using IFN for general network, refer to [IFN Tutorial for General Network](tutorial.html).\n",
    "\n",
    "In this tutorial, our focus is on the Ideal Flow Network (IFN) itself.\n",
    "\n",
    "\n",
    "To use IFN module, we first need to import it. We also need to se numpy, thus, we also import it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IFN\n",
      "{}\n"
     ]
    }
   ],
   "source": [
    "import IdealFlow.Network as net\n",
    "import numpy as np\n",
    "\n",
    "n = net.IFN(name=\"IFN\")\n",
    "print(n.name)\n",
    "print(n)  # print the string of adjacency list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IFN from Links\n",
    "\n",
    "Can create a network add links. A link is a directed edge from start node to end node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n.add_link(\"a\",\"b\")\n",
    "n.add_link(\"a\",\"c\")\n",
    "n.add_link(\"a\",\"d\")\n",
    "n.add_link(\"d\",\"e\")\n",
    "n.add_link(\"e\",\"a\")\n",
    "n.add_link(\"e\",\"d\")\n",
    "n.add_link(\"c\",\"b\")\n",
    "n.add_link(\"b\",\"d\")\n",
    "n.add_link(\"e\",\"c\")\n",
    "n.show(\"Circular\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The capacity matrix is shown as follow. The positive numbers represent the number of lanes in the links. Zero means no links between nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "list_nodes: ['a', 'b', 'c', 'd', 'e']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[[0, 1, 1, 1, 0],\n",
       " [0, 0, 0, 1, 0],\n",
       " [0, 1, 0, 0, 0],\n",
       " [0, 0, 0, 0, 1],\n",
       " [1, 0, 1, 1, 0]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C, list_nodes = n.get_matrix()\n",
    "print('list_nodes:', list_nodes)\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The adjacency matrix of the capacity matrix that is strongly connected is always irreducible matrix. Let us test using the following code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is irreducible? True\n",
      "A [[0 1 1 1 0]\n",
      " [0 0 0 1 0]\n",
      " [0 1 0 0 0]\n",
      " [0 0 0 0 1]\n",
      " [1 0 1 1 0]]\n"
     ]
    }
   ],
   "source": [
    "A=n.capacity_to_adjacency(C)\n",
    "print('Is irreducible?',n.is_irreducible_matrix(A))\n",
    "print('A',A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the Capacity matrix, we can compute the Stochastic matrix as follow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stochastic matrix=\n",
      " [[0.         0.33333333 0.33333333 0.33333333 0.        ]\n",
      " [0.         0.         0.         1.         0.        ]\n",
      " [0.         1.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         1.        ]\n",
      " [0.33333333 0.         0.33333333 0.33333333 0.        ]]\n"
     ]
    }
   ],
   "source": [
    "S=n.capacity_to_stochastic(C)\n",
    "print('stochastic matrix=\\n',S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check network efficiency based on the entropy ratio. A network is efficient if it has maximum entropy. Efficient network happens if the outflow probability distribution in each node is uniformly distributed in term of time and space. In this example the network efficiency is the same as the entropy ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropy= 2.197224577336219\n",
      "Entropy ratio= 1.0\n"
     ]
    }
   ],
   "source": [
    "print('Entropy=', n.stochastic_to_network_entropy(S))\n",
    "print('Entropy ratio=', n.stochastic_to_entropy_ratio(S))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the ideal flow matrix F that represents the steady state flow in each link."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ideal Flow matrix=\n",
      " [[0.         0.03333333 0.03333333 0.03333333 0.        ]\n",
      " [0.         0.         0.         0.16666667 0.        ]\n",
      " [0.         0.13333333 0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.3       ]\n",
      " [0.1        0.         0.1        0.1        0.        ]]\n"
     ]
    }
   ],
   "source": [
    "F=n.capacity_to_ideal_flow(C)\n",
    "print('Ideal Flow matrix=\\n', F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the sum of rows and sum of columns of an ideal flow matrix are always the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum of row= [0.1        0.16666667 0.13333333 0.3        0.3       ] \n",
      "\n",
      "sum of columns= [0.1        0.16666667 0.13333333 0.3        0.3       ] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "sR=n.sum_of_row(F)\n",
    "sC=n.sum_of_col(F)\n",
    "print('sum of row=',sR,'\\n')\n",
    "print('sum of columns=',sC,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Premagic matrix means the matrix has exactly the same sum of rows as the sum of columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "isPremagic(F)= True\n"
     ]
    }
   ],
   "source": [
    "print('isPremagic(F)=',n.is_premagic_matrix(F))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ideal flow matrix is defined as premagic (the flow are conserved) and strongly connected (irreducible)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "isIrreducible(F)= True\n",
      "is Ideal Flow(F)= True\n"
     ]
    }
   ],
   "source": [
    "print('isIrreducible(F)=', n.is_irreducible_matrix(F))\n",
    "print('is Ideal Flow(F)=', n.is_ideal_flow_matrix(F))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IFN from Matrix\n",
    "\n",
    "In the following example, we will examine an efficient network. Let us define an adjacency matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 1, 1],\n",
       "       [1, 0, 0, 0],\n",
       "       [0, 1, 0, 1],\n",
       "       [0, 1, 0, 0]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#   a  b  c  d  \n",
    "A=[[0, 0, 1, 1],   # a\n",
    "   [1, 0, 0, 0],   # b\n",
    "   [0, 1, 0, 1],   # c\n",
    "   [0, 1, 0, 0],   # d\n",
    "  ]\n",
    "A=np.asarray(A)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can put this matrix into network by setting the list of nodes and set the matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = net.IFN(name=\"IFN from Matrix\")  # new network\n",
    "num_nodes=4\n",
    "list_nodes=n.alphabet_list(num_nodes)\n",
    "n.set_matrix(A,list_nodes)\n",
    "n.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can obtain the ideal flow directly from adjacency matrix and the outflow probability distribution of each node would be equal (uniform distribution)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F= [[0.         0.         0.15384615 0.15384615]\n",
      " [0.30769231 0.         0.         0.        ]\n",
      " [0.         0.07692308 0.         0.07692308]\n",
      " [0.         0.23076923 0.         0.        ]] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "F=n.adjacency_to_ideal_flow(A)\n",
    "print('F=',F,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sum of rows of ideal flow matrix is always equal to the sum of columns. This property is called *premagic* property."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum of row=\n",
      " [0.30769231 0.30769231 0.15384615 0.23076923]\n",
      "sum of columns=\n",
      " [0.30769231 0.30769231 0.15384615 0.23076923]\n",
      "isPremagic(F)= True\n"
     ]
    }
   ],
   "source": [
    "sR=n.sum_of_row(F)\n",
    "sC=n.sum_of_col(F)\n",
    "print('sum of row=\\n',sR)\n",
    "print('sum of columns=\\n',sC)\n",
    "print('isPremagic(F)=',n.is_premagic_matrix(F))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily scale ideal flow matrix by a scaling factor, kappa $\\kappa$, which is the same as the total flow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F=\n",
      " [[  0.           0.         153.84615385 153.84615385]\n",
      " [307.69230769   0.           0.           0.        ]\n",
      " [  0.          76.92307692   0.          76.92307692]\n",
      " [  0.         230.76923077   0.           0.        ]]\n"
     ]
    }
   ],
   "source": [
    "kappa=1000\n",
    "F=n.adjacency_to_ideal_flow(A, kappa)\n",
    "print('F=\\n',F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get back the stochastic matrix based on ideal flow matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S=\n",
      " [[0.  0.  0.5 0.5]\n",
      " [1.  0.  0.  0. ]\n",
      " [0.  0.5 0.  0.5]\n",
      " [0.  1.  0.  0. ]]\n"
     ]
    }
   ],
   "source": [
    "S=n.ideal_flow_to_stochastic(F)\n",
    "print('S=\\n',S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that our entropy ratio is 1, that means a network with uniform distribution of outflow is the most efficient network. The proof of this theorem can be found in a paper in [EASTS journal](https://www.jstage.jst.go.jp/article/easts/12/0/12_939/_pdf/-char/en)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropy= 1.3862943611198906\n",
      "Entropy ratio= 1.0\n"
     ]
    }
   ],
   "source": [
    "print('Entropy=', n.stochastic_to_network_entropy(S))\n",
    "print('Entropy ratio=', n.stochastic_to_entropy_ratio(S))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IFN from Trajectories\n",
    "\n",
    "One of many novelty point of IFN is the idea of expandable network based on trajectories.\n",
    "Trajectories are sequences of points in the feature space that are connected by edges.\n",
    "In IFN, trajectories are represented by a path or a node sequence.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': {'b': 1}, 'b': {'c': 1}, 'c': {'d': 1}, 'd': {}}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = net.IFN(name=\"IFN from Tajectories\")  # new network\n",
    "tr1 = ['a','b','c', 'd']\n",
    "n.set_path(tr1)\n",
    "print(n)  # print the string of adjacency list\n",
    "n.show(); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can test if our network is connected. Pretend the arrows are ignored for a moment, is there any path from any node to any other node?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is connected? True\n"
     ]
    }
   ],
   "source": [
    "print('is connected?',n.is_connected)  # if two ways/undirected"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "our network is not connected yet.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having a network does not mean it is an Ideal Flow Network (IFN). We can test if our network is already an ideal flow. An ideal flow network is a network which is both strongly connected and premagic. Let us test whether it is strongly connected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is strongly connected? False\n"
     ]
    }
   ],
   "source": [
    "print('is strongly connected?',n.is_strongly_connected)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Premagic means balance of flow. A flow is balance when in each node, the sum of inflows is exactly equal to the sum of outflows. Let us test whether our network is premagic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is premagic? False\n"
     ]
    }
   ],
   "source": [
    "print('is premagic?',n.is_premagic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can test whether our network is an ideal flow type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is Ideal Flow? False\n"
     ]
    }
   ],
   "source": [
    "print('is Ideal Flow?',n.is_ideal_flow)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can add more trajectory to expand the network. Then we test the updated network again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': {'b': 1}, 'b': {'c': 1, 'e': 1}, 'c': {'d': 1, 'b': 1}, 'd': {'c': 1}, 'e': {'d': 1}}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is connected? True \n",
      "\n",
      "is strongly connected? False \n",
      "\n",
      "is premagic? False \n",
      "\n",
      "is Ideal Flow? False \n",
      "\n"
     ]
    }
   ],
   "source": [
    "tr2 = ['e', 'd', 'c', 'b', 'e']\n",
    "n.set_path(tr2)\n",
    "print(n)  # print the string of adjacency list\n",
    "n.show(); \n",
    "print('is connected?',n.is_connected,'\\n')  # if two ways/undirected\n",
    "print('is strongly connected?',n.is_strongly_connected,'\\n') # if we follow the arrows\n",
    "print('is premagic?',n.is_premagic,'\\n')\n",
    "print('is Ideal Flow?',n.is_ideal_flow,'\\n')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our network is still weakly connected. If the ignore the directional arrows, it is connected but wen we follow the directional arrows, it is not connected. \n",
    "\n",
    "\n",
    "To make a connected network into a strongly connected network, we add a cloud node and dummy link from sink node to the cloud node, and from the cloud node to source node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can see that the network is indeed strongly connected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is strongly connected? False \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('is strongly connected?',n.is_strongly_connected,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we test if it premagic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is premagic? False \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('is premagic?',n.is_premagic,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make the network connected, we can add link from any node of the component 'bedc' to the sink node 'a'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': {'b': 1}, 'b': {'c': 1, 'e': 1}, 'c': {'d': 1, 'b': 1, 'a': 1}, 'd': {'c': 1}, 'e': {'d': 1}}\n",
      "is connected? True \n",
      "\n",
      "is strongly connected? True \n",
      "\n",
      "is premagic? False \n",
      "\n",
      "is Ideal Flow? False \n",
      "\n"
     ]
    }
   ],
   "source": [
    "n.add_link('c', 'a')\n",
    "n.show(); \n",
    "print(n)  # print the string of adjacency list\n",
    "print('is connected?',n.is_connected,'\\n')  # if two ways/undirected\n",
    "print('is strongly connected?',n.is_strongly_connected,'\\n') # if we follow the arrows\n",
    "print('is premagic?',n.is_premagic,'\\n')\n",
    "print('is Ideal Flow?',n.is_ideal_flow,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By now, our network is already strongly connected but still not premagic yet.\n",
    "We need to add more trajectories to make it premagic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': {'b': 1, 'c': 1}, 'b': {'c': 1, 'e': 1}, 'c': {'d': 1, 'b': 1, 'a': 1}, 'd': {'c': 1, 'a': 1}, 'e': {'d': 1}}\n",
      "is connected? True \n",
      "\n",
      "is strongly connected? True \n",
      "\n",
      "is premagic? True \n",
      "\n",
      "is Ideal Flow? True \n",
      "\n"
     ]
    }
   ],
   "source": [
    "tr3 = ['d', 'a', 'c']\n",
    "n.set_path(tr3)\n",
    "n.show(); \n",
    "print(n)  # print the string of adjacency list\n",
    "\n",
    "print('is connected?',n.is_connected,'\\n')  # if two ways/undirected\n",
    "print('is strongly connected?',n.is_strongly_connected,'\\n') # if we follow the arrows\n",
    "print('is premagic?',n.is_premagic,'\\n')\n",
    "print('is Ideal Flow?',n.is_ideal_flow,'\\n')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By now our network is already an ideal flow network (IFN).\n",
    "\n",
    "How do we get the last trajectory (*tr3*) that make it into an ideal flow? Is it by trial and error? No, it actually can be formed easily by making cycles from the existing trajectories. Observed that *tr2 = ['e', 'd', 'c', 'b', 'e']* is already a cycle, thus we can simply ignore.\n",
    "\n",
    "> tr1 = ['a','b','c', 'd']\n",
    "\n",
    "and then we added a branch by \n",
    "\n",
    "> n.add_link('c', 'a')\n",
    "\n",
    "We have link'ca' and 'abc' (from *tr1*) that forms a cycle.\n",
    "\n",
    "The remaining path to make the cycle within the existing network is 'dac'. Thus,\n",
    "> tr3 = ['d', 'a', 'c']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IFN from Cycles\n",
    "\n",
    "In the last section, how do we know that we need to form cycles in order to create IFN? It is based on the [Ideal Flow mathematical theory](https://arxiv.org/abs/2408.06344) that when we merge any cycles with certain pivot (i.e. connecting node, link, or path), it would always form an strongly connected network which is premagic.\n",
    "\n",
    "In this section let us demonstrate that we can create IFN by merging cycles.\n",
    "We will use the following example to demonstrate this.\n",
    "\n",
    "Let us create a new network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IFN from Cycles\n",
      "{}\n"
     ]
    }
   ],
   "source": [
    "n = net.IFN(name=\"IFN from Cycles\")\n",
    "print(n.name)\n",
    "print(n)  # print the string of adjacency list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Equivalent IFN\n",
    "\n",
    "To make a strongly connected network into ideal flow network, first, let us assume the existing weight as capacity matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Design Total Nodes: 5 \n",
      "Design Total Links: 8\n",
      "C [[0 1 1 0 0]\n",
      " [0 1 0 1 0]\n",
      " [0 1 0 0 0]\n",
      " [0 0 0 0 1]\n",
      " [1 0 0 1 0]]\n",
      "{'a': {'b': np.int64(1), 'c': np.int64(1)}, 'b': {'b': np.int64(1), 'd': np.int64(1)}, 'c': {'b': np.int64(1)}, 'd': {'e': np.int64(1)}, 'e': {'a': np.int64(1), 'd': np.int64(1)}}\n"
     ]
    }
   ],
   "source": [
    "n = net.IFN(\"Random Irreducible Network\")\n",
    "numNode=5                         # number of nodes\n",
    "numLink=numNode+int(3*numNode/4)  # number of links\n",
    "print(\"Design Total Nodes:\",numNode,'\\nDesign Total Links:',numLink)\n",
    "\n",
    "# using static methods to generate matrix and test matrix\n",
    "C=n.rand_irreducible(numNode,numLink)       # generate random irreducible matrix\n",
    "print('C',C)\n",
    "list_nodes = n.alphabet_list(numNode)       # generate list of nodes \n",
    "n.set_matrix(C,list_nodes)\n",
    "print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C =\n",
      " [[0 1 1 0 0]\n",
      " [0 1 0 1 0]\n",
      " [0 1 0 0 0]\n",
      " [0 0 0 0 1]\n",
      " [1 0 0 1 0]]\n",
      "listNodes =\n",
      " ['a', 'b', 'c', 'd', 'e']\n"
     ]
    }
   ],
   "source": [
    "# we can also see it back\n",
    "C,listNodes=n.get_matrix()\n",
    "print('C =\\n',np.array(C))\n",
    "print('listNodes =\\n',listNodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the network is strongly connected, then the matrix must be irreducible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is C irreducible? True\n"
     ]
    }
   ],
   "source": [
    "print('is C irreducible?',n.is_irreducible_matrix(C))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we compute the ideal flow from capacity matrix. These values represent link probabilities of flows in the network. The total values is one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Flow 1.0000000000000007\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.06666667, 0.06666667, 0.        , 0.        ],\n",
       "       [0.        , 0.13333333, 0.        , 0.13333333, 0.        ],\n",
       "       [0.        , 0.06666667, 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.        , 0.26666667],\n",
       "       [0.13333333, 0.        , 0.        , 0.13333333, 0.        ]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F=n.capacity_to_ideal_flow(C)\n",
    "n.set_matrix(F,listNodes)\n",
    "print('Total Flow', n.total_flow)\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The characteristics of ideal flow is irreducible and premagic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is F irreducible? True \n",
      "\n",
      "is F premagic? True \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('is F irreducible?',n.is_irreducible_matrix(F),'\\n')\n",
    "print('is F premagic?',n.is_premagic_matrix(F),'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ideal Flow matrix contain rational numbers which are also scalable. We can get the equivalent ideal flow matrix by multiplying it with some global scalling factor. One important scaling is to make the ideal flow into minimum integer. This is also called the *basis network*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling= 15\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 1., 0., 0.],\n",
       "       [0., 2., 0., 2., 0.],\n",
       "       [0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 4.],\n",
       "       [2., 0., 0., 2., 0.]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaling=n.global_scaling(F,scaling_type='int')\n",
    "print('scaling=',scaling)\n",
    "F=n.equivalent_ifn(F,scaling)\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we replace the weights of capacity into flow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, np.float64(1.000000000000003), np.float64(1.000000000000003), 0, 0],\n",
       " [0, np.float64(1.9999999999999991), 0, np.float64(1.9999999999999991), 0],\n",
       " [0, np.float64(1.0000000000000016), 0, 0, 0],\n",
       " [0, 0, 0, 0, np.float64(4.000000000000003)],\n",
       " [np.float64(2.0000000000000004), 0, 0, np.float64(2.0000000000000004), 0]]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.set_matrix(F,listNodes)\n",
    "M,_=n.get_matrix()\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us test again, to make sure all of the properties are satisfied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is M irreducible? True \n",
      "\n",
      "is ideal flow? True \n",
      "\n",
      "is strongly connected? True \n",
      "\n",
      "is M premagic? True \n",
      "\n",
      "is premagic network? True \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('is M irreducible?',n.is_irreducible_matrix(M),'\\n')\n",
    "print('is ideal flow?',n.is_ideal_flow,'\\n')\n",
    "print('is strongly connected?',n.is_strongly_connected,'\\n')\n",
    "print('is M premagic?',n.is_premagic_matrix(M),'\\n')\n",
    "print('is premagic network?',n.is_premagic,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equivalent IFN\n",
    "\n",
    "We can scale our ideal flow matrix into an equivalent ideal flow matrix such that the minimum is some predefined value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling= 99.99999999999984\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[  0., 100., 100.,   0.,   0.],\n",
       "       [  0., 200.,   0., 200.,   0.],\n",
       "       [  0., 100.,   0.,   0.,   0.],\n",
       "       [  0.,   0.,   0.,   0., 400.],\n",
       "       [200.,   0.,   0., 200.,   0.]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaling=n.global_scaling(F,scaling_type='min',val=100)\n",
    "print('scaling=',scaling)\n",
    "F1=n.equivalent_ifn(F,scaling)\n",
    "F1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can scale our ideal flow matrix into an equivalent ideal flow matrix such that the maximum is some predefined value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling= 2.4999999999999982\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0. ,  2.5,  2.5,  0. ,  0. ],\n",
       "       [ 0. ,  5. ,  0. ,  5. ,  0. ],\n",
       "       [ 0. ,  2.5,  0. ,  0. ,  0. ],\n",
       "       [ 0. ,  0. ,  0. ,  0. , 10. ],\n",
       "       [ 5. ,  0. ,  0. ,  5. ,  0. ]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaling=n.global_scaling(F,scaling_type='max',val=10)\n",
    "print('scaling=',scaling)\n",
    "F1=n.equivalent_ifn(F,scaling)\n",
    "F1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can scale our ideal flow matrix into an equivalent ideal flow matrix such that the sum of flow  is some predefined value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling= 66.66666666666661\n",
      "sum:  999.9999999999999\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[  0.        ,  66.66666667,  66.66666667,   0.        ,\n",
       "          0.        ],\n",
       "       [  0.        , 133.33333333,   0.        , 133.33333333,\n",
       "          0.        ],\n",
       "       [  0.        ,  66.66666667,   0.        ,   0.        ,\n",
       "          0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ,   0.        ,\n",
       "        266.66666667],\n",
       "       [133.33333333,   0.        ,   0.        , 133.33333333,\n",
       "          0.        ]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaling=n.global_scaling(F,scaling_type='sum',val=1000)\n",
    "print('scaling=',scaling)\n",
    "F1=n.equivalent_ifn(F,scaling)\n",
    "print('sum: ',np.sum(F1))\n",
    "F1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, we can also find global scaling to make *basis network*, which is IFN with minimum integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scaling= 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 1., 0., 0.],\n",
       "       [0., 2., 0., 2., 0.],\n",
       "       [0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 4.],\n",
       "       [2., 0., 0., 2., 0.]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaling=n.global_scaling(F,scaling_type='int')\n",
    "print('scaling=',scaling)\n",
    "F=n.equivalent_ifn(F,scaling)\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To set the link values based on the ideal flow matrix, we apply the matrix. Since we want to compare the two IFNs later, instead of replace it in the same network, now we create a new network to be filled with integer IFN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([[0, np.float64(1.0), np.float64(1.0), 0, 0],\n",
       "  [0, np.float64(2.0), 0, np.float64(2.0), 0],\n",
       "  [0, np.float64(1.0), 0, 0, 0],\n",
       "  [0, 0, 0, 0, np.float64(4.0)],\n",
       "  [np.float64(2.0), 0, 0, np.float64(2.0), 0]],\n",
       " ['a', 'b', 'c', 'd', 'e'])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n2=net.IFN(name=\"Ideal Flow\")  # create new network\n",
    "n2.set_matrix(np.around(F),listNodes)\n",
    "n2.get_matrix()                     # check if it is correctly applied"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us test the properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "is ideal flow True \n",
      "\n",
      "is strongly connected True \n",
      "\n",
      "is premagic True \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('is ideal flow',n2.is_ideal_flow,'\\n')\n",
    "print('is strongly connected',n2.is_strongly_connected,'\\n')\n",
    "print('is premagic',n2.is_premagic,'\\n')\n",
    "n2.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Equivalent IFNs would have exactly the same stochastic matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S=n.capacity_to_stochastic(F)\n",
    "S1=n.capacity_to_stochastic(F1)\n",
    "np.array_equal(S1,S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Equivalent ideal flow would have the same coeficient of variation of flow. Coeffcient of variation is the standard deviation divided by the average. The difference here is due to rounding off error. The total flow of n1 must be 1 but due to round off error, it is not exactly one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total flow of n1: 15.000000000000009 \n",
      "\n",
      "total flow of n2: 15.0 \n",
      "\n",
      "coef. variation of n1: 0.17480147469502513 \n",
      "\n",
      "coef. variation of n2: 0.17480147469502524 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('total flow of n1:',n.total_flow,'\\n')\n",
    "print('total flow of n2:',n2.total_flow,'\\n')\n",
    "print('coef. variation of n1:',n.cov_flow,'\\n')\n",
    "print('coef. variation of n2:',n2.cov_flow,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observed that the two network is equivalent IFN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.is_equivalent_ifn(n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just in case when our network contains a cloud node, if we want to get the total flow, however, our original network was not include the cloud node. Thus, our total flow in the network is not correct yet because it includes the flow in the dummy links. We have to get the network without cloud node and dummy links (which is not an IFN anymore but we have calculated the ideal flow anyway)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n3=n2.network_delete_cloud()\n",
    "n3.show(\"Circular\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can get the correct total flow of the original network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(15.0)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n3.total_flow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First update: [Sept 2017](http://people.revoledu.com/kardi/tutorial/Python/Ideal+Flow.html)\n",
    "\n",
    "Last Update: Oct 2024\n",
    "\n",
    "Cite this tutorial as:\n",
    "\n",
    "> Teknomo,K. (2024) Ideal Flow Network Anaysis using Python \n",
    "\n",
    "See Also: [Resources on Ideal Flow Network](https://people.revoledu.com/kardi/research/trajectory/ifn/index.html), [IFN Tutorial](https://people.revoledu.com/kardi/tutorial/IFN/)\n",
    "\n",
    "Copyright © 2024 Kardi Teknomo"
   ]
  }
 ],
 "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}