explore_eval_gtr

0110_pyc_test/0110_pyc_test.py

@@ -0,0 +1,11 @@
+import numpy as np
+# A, B로 나뉘어진 현시시간을 (4현시) 세부현시시간(5현시)로 바꾸는 코드
+durs_A = np.array([37, 55, 45, 23])
+durs_B = np.array([37, 55, 28, 40])
+cums_A = durs_A.cumsum()
+cums_B = durs_B.cumsum()
+cycle = durs_A.sum()
+detailed_cums = []
+combined_row = np.unique(np.concatenate((cums_A, cums_B)))
+detailed_durations = np.concatenate(([combined_row[0]], np.diff(combined_row)))
+print(detailed_durations)

0110_pyc_test/0110_pyc_test_decompiled.py

@@ -0,0 +1,24 @@
+import numpy as np
+
+# 두 개의 배열 생성
+durs_A = np.array([37, 55, 45, 23])
+durs_B = np.array([37, 55, 28, 40])
+
+# 두 배열의 누적합 계산
+cums_A = durs_A.cumsum()
+cums_B = durs_B.cumsum()
+
+# durs_A의 합계를 cycle에 저장
+cycle = durs_A.sum()
+
+# 빈 리스트 생성
+detailed_cums = []
+
+# cums_A와 cums_B의 고유한 요소들을 결합
+combined_row = np.unique(np.concatenate((cums_A, cums_B)))
+
+# combined_row의 각 요소 간 차이 계산
+detailed_durations = np.concatenate(([combined_row[0]], np.diff(combined_row)))
+
+# 결과 출력
+print(detailed_durations)

0110_pyc_test/env.py

@@ -0,0 +1,189 @@
+import os
+import sys
+import numpy as np
+
+from sumolib import checkBinary
+
+from args import Args
+
+
+class Env:
+    '''This class is responsible for handling the traffic light optimization environment.'''
+    def __init__(self, infos, path_config, name=0):
+        '''
+        Initializes the environment with given information,
+        configuration path and initial state path.
+        '''
+        self.path_config = path_config
+        self.infos = infos
+        self.node_ids = Args.node_ids
+        assert list(self.node_ids) == list(self.infos)
+        self.path_init_state = f'data/init_state_{name}'
+        assert not os.path.exists(self.path_init_state)
+        self.gui = Args.gui
+
+        self.e2_length      = Args.e2_length
+        self.yellow_length  = Args.yellow_length
+        self.step_length    = Args.step_length
+        self.rest_length    = self.step_length - self.yellow_length
+        self.episode_length = Args.episode_length
+        self.episode_step   = Args.episode_step
+
+        self.name = name
+
+
+    def _start(self):
+        '''
+        Starts the simulation.
+        https://sumo.dlr.de/docs/TraCI/Interfacing_TraCI_from_Python.html#importing_traci_in_a_script
+        '''
+        import traci
+        if 'SUMO_HOME' in os.environ:
+            tools = os.path.join(os.environ['SUMO_HOME'], 'tools')
+            sys.path.append(tools)
+        else:
+            sys.exit("please declare environment variable 'SUMO_HOME'")
+
+        sumo_binary = checkBinary('sumo-gui' if self.gui else 'sumo')
+        cmd = [sumo_binary, '-c', self.path_config]
+        traci.start(cmd, label=self.name)
+        self.conn = traci.getConnection(self.name)
+
+
+    def close(self):
+        '''Closes the simulation.'''
+        self.conn.close()
+        if os.path.exists(self.path_init_state):
+            os.remove(self.path_init_state)
+
+
+    def _save(self):
+        '''
+        Saves the current state of the simulation.
+        https://sumo.dlr.de/docs/TraCI/Change_Simulation_State.html
+        '''
+        self.conn.simulation.saveState(self.path_init_state)
+
+
+    def _load(self):
+        '''
+        Loads the saved state of the simulation.
+        https://sumo.dlr.de/docs/TraCI/Change_Simulation_State.html
+        '''
+        self.conn.simulation.loadState(self.path_init_state)
+
+
+    def _step(self, step_length):
+        '''Advances the simulation by a given number of steps.'''
+        for _ in range(step_length):
+            self.conn.simulationStep()
+
+
+    def _get_occupancy(self, detector_id):
+        '''
+        Returns the occupancy of a given detector.
+        https://sumo.dlr.de/docs/TraCI/Lane_Area_Detector_Value_Retrieval.html
+        '''
+        return self.conn.lanearea.getLastStepOccupancy(detector_id) / 100
+
+
+    def _get_queue(self, detector_id):
+        '''
+        Returns the queue length at a given detector.
+        https://sumo.dlr.de/docs/TraCI/Lane_Area_Detector_Value_Retrieval.html
+        '''
+        return self.conn.lanearea.getJamLengthMeters(detector_id) / self.e2_length
+
+
+    def _get_values(self):
+        '''Retrieves the occupancy, queue and phase for each node.'''
+        node2values = {}
+        for node_id, info in self.infos.items():
+            values = {}
+            values['occupancy'] = [self._get_occupancy(d) for d in info['detectors']]
+            values['queue'] = [self._get_queue(d) for d in info['detectors']]
+            values['phase'] = [self.prev_phase_indexes[node_id]]
+            node2values[node_id] = values
+
+        states, rewards = [], []
+        global_reward = 0
+        for node_id, info in self.infos.items():
+            occupancy = [node2values[node_id]['occupancy']]
+            queue = [node2values[node_id]['queue']]
+            phase = [node2values[node_id]['phase']]
+            reward = -np.sum(node2values[node_id]['queue'])
+            global_reward -= np.sum(node2values[node_id]['queue'])
+            for nnode_id in info['neighbors']:
+                occupancy.append(node2values[nnode_id]['occupancy'])
+                queue.append(node2values[nnode_id]['queue'])
+                phase.append(node2values[nnode_id]['phase'])
+                reward -= np.sum(node2values[nnode_id]['queue']) * 0.5
+
+            states.append(np.concatenate(occupancy + queue + phase, dtype=np.float32))
+            rewards.append(reward)
+            
+        return states, rewards, global_reward
+
+
+    def _set_yellows(self, actions):
+        '''Sets the yellow phase for nodes based on the given actions.'''
+        for node_id, action in zip(self.node_ids, actions):
+
+            if action == 0:
+                continue
+
+            info = self.infos[node_id]
+            prev_idx = self.prev_phase_indexes[node_id]
+            idx = (prev_idx + 1) % len(info['phases']['green'])
+            self.prev_phase_indexes[node_id] = idx
+
+            y = info['phases']['yellow'][prev_idx]
+            self._set_phase(node_id, y)
+
+
+    def _set_greens(self):
+        '''Sets the green phase for each node.'''
+        for node_id, info in self.infos.items():
+            idx = self.prev_phase_indexes[node_id]
+            g = info['phases']['green'][idx]
+            self._set_phase(node_id, g)
+
+
+    def _set_phase(self, node_id, phase):
+        '''Sets the phase for a specific node.'''
+        if self.prev_phases.get(node_id) != phase:
+            self.conn.trafficlight.setRedYellowGreenState(node_id, phase)
+            self.prev_phases[node_id] = phase
+
+
+    def step(self, actions):
+        '''Performs a step in the simulation based on the given actions.'''
+        
+        self._set_yellows(actions)
+        self._step(self.yellow_length)
+        self._set_greens()
+        self._step(self.rest_length)
+        self.curr_step += 1
+
+        states, rewards, global_reward = self._get_values()
+        done = self.curr_step >= self.episode_step
+        return states, rewards, done, global_reward
+
+
+    def reset(self):
+        '''Resets the simulation to its initial state.'''
+
+        # Initialize simulation
+        if not os.path.exists(self.path_init_state):
+            self._start()
+            self._save()
+        self._load()
+
+        self.curr_step = 0
+        self.prev_phases = {n:'none' for n in self.node_ids}
+        self.prev_phase_indexes = {n:0 for n in self.node_ids}
+
+        self._set_greens()
+        self._step(1)
+        states, _, _ = self._get_values()
+        return states

0110_pyc_test/env_decompiled.py

@@ -0,0 +1,171 @@
+# uncompyle6 version 3.9.0
+# Python bytecode version base 3.8.0 (3413)
+# Decompiled from: Python 3.8.10 (tags/v3.8.10:3d8993a, May  3 2021, 11:48:03) [MSC v.1928 64 bit (AMD64)]
+# Embedded file name: .\env.py
+# Compiled at: 2024-01-10 13:34:11
+# Size of source mod 2**32: 6588 bytes
+import os, sys, numpy as np
+from sumolib import checkBinary
+from args import Args
+
+class Env:
+    __doc__ = 'This class is responsible for handling the traffic light optimization environment.'
+
+    def __init__(self, infos, path_config, name=0):
+        """
+        Initializes the environment with given information,
+        configuration path and initial state path.
+        """
+        self.path_config = path_config
+        self.infos = infos
+        self.node_ids = Args.node_ids
+        assert list(self.node_ids) == list(self.infos)
+        self.path_init_state = f"data/init_state_{name}"
+        assert not os.path.exists(self.path_init_state)
+        self.gui = Args.gui
+        self.e2_length = Args.e2_length
+        self.yellow_length = Args.yellow_length
+        self.step_length = Args.step_length
+        self.rest_length = self.step_length - self.yellow_length
+        self.episode_length = Args.episode_length
+        self.episode_step = Args.episode_step
+        self.name = name
+
+    def _start(self):
+        """
+        Starts the simulation.
+        https://sumo.dlr.de/docs/TraCI/Interfacing_TraCI_from_Python.html#importing_traci_in_a_script
+        """
+        import traci
+        if 'SUMO_HOME' in os.environ:
+            tools = os.path.join(os.environ['SUMO_HOME'], 'tools')
+            sys.path.append(tools)
+        else:
+            sys.exit("please declare environment variable 'SUMO_HOME'")
+        sumo_binary = checkBinary('sumo-gui' if self.gui else 'sumo')
+        cmd = [sumo_binary, '-c', self.path_config]
+        traci.start(cmd, label=(self.name))
+        self.conn = traci.getConnection(self.name)
+
+    def close(self):
+        """Closes the simulation."""
+        self.conn.close()
+        if os.path.exists(self.path_init_state):
+            os.remove(self.path_init_state)
+
+    def _save(self):
+        """
+        Saves the current state of the simulation.
+        https://sumo.dlr.de/docs/TraCI/Change_Simulation_State.html
+        """
+        self.conn.simulation.saveState(self.path_init_state)
+
+    def _load(self):
+        """
+        Loads the saved state of the simulation.
+        https://sumo.dlr.de/docs/TraCI/Change_Simulation_State.html
+        """
+        self.conn.simulation.loadState(self.path_init_state)
+
+    def _step(self, step_length):
+        """Advances the simulation by a given number of steps."""
+        for _ in range(step_length):
+            self.conn.simulationStep()
+
+    def _get_occupancy(self, detector_id):
+        """
+        Returns the occupancy of a given detector.
+        https://sumo.dlr.de/docs/TraCI/Lane_Area_Detector_Value_Retrieval.html
+        """
+        return self.conn.lanearea.getLastStepOccupancy(detector_id) / 100
+
+    def _get_queue(self, detector_id):
+        """
+        Returns the queue length at a given detector.
+        https://sumo.dlr.de/docs/TraCI/Lane_Area_Detector_Value_Retrieval.html
+        """
+        return self.conn.lanearea.getJamLengthMeters(detector_id) / self.e2_length
+
+    def _get_values(self):
+        """Retrieves the occupancy, queue and phase for each node."""
+        node2values = {}
+        for node_id, info in self.infos.items():
+            values = {}
+            values['occupancy'] = [self._get_occupancy(d) for d in info['detectors']]
+            values['queue'] = [self._get_queue(d) for d in info['detectors']]
+            values['phase'] = [self.prev_phase_indexes[node_id]]
+            node2values[node_id] = values
+        else:
+            states, rewards = [], []
+            global_reward = 0
+            for node_id, info in self.infos.items():
+                occupancy = [
+                 node2values[node_id]['occupancy']]
+                queue = [node2values[node_id]['queue']]
+                phase = [node2values[node_id]['phase']]
+                reward = -np.sum(node2values[node_id]['queue'])
+                global_reward -= np.sum(node2values[node_id]['queue'])
+                for nnode_id in info['neighbors']:
+                    occupancy.append(node2values[nnode_id]['occupancy'])
+                    queue.append(node2values[nnode_id]['queue'])
+                    phase.append(node2values[nnode_id]['phase'])
+                    reward -= np.sum(node2values[nnode_id]['queue']) * 0.5
+                else:
+                    states.append(np.concatenate((occupancy + queue + phase), dtype=(np.float32)))
+                    rewards.append(reward)
+
+            else:
+                return (
+                 states, rewards, global_reward)
+
+    def _set_yellows(self, actions):
+        """Sets the yellow phase for nodes based on the given actions."""
+        for node_id, action in zip(self.node_ids, actions):
+            if action == 0:
+                pass
+            else:
+                info = self.infos[node_id]
+                prev_idx = self.prev_phase_indexes[node_id]
+                idx = (prev_idx + 1) % len(info['phases']['green'])
+                self.prev_phase_indexes[node_id] = idx
+                y = info['phases']['yellow'][prev_idx]
+                self._set_phase(node_id, y)
+
+    def _set_greens(self):
+        """Sets the green phase for each node."""
+        for node_id, info in self.infos.items():
+            idx = self.prev_phase_indexes[node_id]
+            g = info['phases']['green'][idx]
+            self._set_phase(node_id, g)
+
+    def _set_phase(self, node_id, phase):
+        """Sets the phase for a specific node."""
+        if self.prev_phases.get(node_id) != phase:
+            self.conn.trafficlight.setRedYellowGreenState(node_id, phase)
+            self.prev_phases[node_id] = phase
+
+    def step(self, actions):
+        """Performs a step in the simulation based on the given actions."""
+        self._set_yellows(actions)
+        self._step(self.yellow_length)
+        self._set_greens()
+        self._step(self.rest_length)
+        self.curr_step += 1
+        states, rewards, global_reward = self._get_values()
+        done = self.curr_step >= self.episode_step
+        return (states, rewards, done, global_reward)
+
+    def reset(self):
+        """Resets the simulation to its initial state."""
+        if not os.path.exists(self.path_init_state):
+            self._start()
+            self._save()
+        self._load()
+        self.curr_step = 0
+        self.prev_phases = {n: 'none' for n in self.node_ids}
+        self.prev_phase_indexes = {n: 0 for n in self.node_ids}
+        self._set_greens()
+        self._step(1)
+        states, _, _ = self._get_values()
+        return states
+# okay decompiling .\env.cpython-38.pyc

0217_explore_eval_gtr/0217_explore_eval_gtr.ipynb

@@ -0,0 +1,122 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "`node_id = '11053'`는 총 4현시로 구성되어 있고, 1현시와 2현시에서 오버랩이 일어난다.\n",
+    "\n",
+    "#### single ring\n",
+    "\n",
+    "3현시는 오버랩현시에 포함되지 않으므로\n",
+    "$a_3=b_3$\n",
+    "이어야 한다. (단, $a_3$은 A링 3현시의 현시시간.)\n",
+    "그런데\n",
+    "\\begin{align*}\n",
+    "a_3&=ag_3+ar_3+ay_3\\\\\n",
+    "b_3&=bg_3+br_3+by_3\n",
+    "\\end{align*}\n",
+    "에서\n",
+    "\\begin{align*}\n",
+    "ag_3+ar_3+ay_3 &= bg_3+br_3+by_3\\\\\n",
+    "ag_3 - bg_3 &= -ar_3+br_3 -ay_3+by_3\\\\\n",
+    "\\begin{bmatrix}0\\\\0\\\\1\\\\0\\\\0\\\\0\\\\-1\\\\0\\end{bmatrix}^T\n",
+    "\\begin{bmatrix}ag_1\\\\ag_2\\\\ag_3\\\\ag_4\\\\bg_1\\\\bg_2\\\\bg_3\\\\bg_4\\end{bmatrix}\n",
+    "&= (-1)((ar_3+ay_3)-(br_3+by_3))\\tag{$*$}\n",
+    "\\end{align*}\n",
+    "이어야 한다.\n",
+    "한편\n",
+    "\\begin{align*}\n",
+    "\\texttt{loss\\_lst}\n",
+    "&= \\texttt{r\\_lst} + \\texttt{y\\_loss\\_lst} + \\texttt{y\\_lst}\\\\\n",
+    "&=\\begin{bmatrix}ar_1\\\\ar_2\\\\ar_3\\\\ar_4\\\\br_1\\\\br_2\\\\br_3\\\\br_4\\end{bmatrix}\n",
+    "+\\begin{bmatrix}0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\end{bmatrix}\n",
+    "+\\begin{bmatrix}ay_1\\\\ay_2\\\\ay_3\\\\ay_4\\\\by_1\\\\by_2\\\\by_3\\\\by_4\\end{bmatrix}\n",
+    "\\end{align*}\n",
+    "이다. ($\\texttt{y\\_loss\\_lst}$는 편의상 0.3으로 이루어진 벡터로 표현함.)\n",
+    "따라서 식 $(*)$의 우변은\n",
+    "$$\n",
+    "(-1)((ar_3+ay_3)-(br_3+by_3))\n",
+    "=(-1)\\begin{bmatrix}0\\\\0\\\\1\\\\0\\\\0\\\\0\\\\-1\\\\0\\end{bmatrix}^T\\texttt{loss\\_lst}\n",
+    "$$\n",
+    "으로 쓸 수 있고, 따라서 식 $(*)$은 \n",
+    "\n",
+    "$$\n",
+    "\\begin{bmatrix}0\\\\0\\\\1\\\\0\\\\0\\\\0\\\\-1\\\\0\\end{bmatrix}^T\n",
+    "\\begin{bmatrix}ag_1\\\\ag_2\\\\ag_3\\\\ag_4\\\\bg_1\\\\bg_2\\\\bg_3\\\\bg_4\\end{bmatrix}\n",
+    " = (-1)\\begin{bmatrix}0\\\\0\\\\1\\\\0\\\\0\\\\0\\\\-1\\\\0\\end{bmatrix}^T\\texttt{loss\\_lst}\n",
+    "$$\n",
+    "\n",
+    "이다.\n",
+    "A링과 B링의 황색/적색시간이 같으면 ($ar_i=br_i$, $ay_i=by_i$ ; 대부분의 경우에 이것이 성립한다.) 위 식의 우변은 0이다.\n",
+    "이것은 $ag_3=bg_3$이라는 의미이다.\n",
+    "\n",
+    "\n",
+    "이상이 `evaluation_green_time_ratio.py`의 368, 369번째 줄의 의미이다."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### dual ring\n",
+    "\n",
+    "1현시와 2현시는 오버랩되므로\n",
+    "$a_1+a_2=b_1+b_2$\n",
+    "이어야 한다.\n",
+    "그러면\n",
+    "\\begin{align*}\n",
+    "ag_1+ar_1+ay_1+ag_2+ar_2+ay_2 &= bg_1+br_1+by_1+bg_2+br_2+by_2\\\\\n",
+    "ag_1 + ag_2 - bg_1 - bg_2 &= -ar_1-ay_1-ar_2-ay_2+br_1+by_1+br_2+by_2\\\\\n",
+    "\\begin{bmatrix}1\\\\1\\\\0\\\\0\\\\-1\\\\-1\\\\0\\\\0\\end{bmatrix}^T\n",
+    "\\begin{bmatrix}ag_1\\\\ag_2\\\\ag_3\\\\ag_4\\\\bg_1\\\\bg_2\\\\bg_3\\\\bg_4\\end{bmatrix}\n",
+    "&= (-1)((ar_1+ay_1+ar_2+ay_2)-(br_1+by_1+br_2+by_2))\\tag{$**$}\n",
+    "\\end{align*}\n",
+    "이어야 한다.\n",
+    "한편\n",
+    "\\begin{align*}\n",
+    "\\texttt{loss\\_lst}\n",
+    "&= \\texttt{r\\_lst} + \\texttt{y\\_loss\\_lst} + \\texttt{y\\_lst}\\\\\n",
+    "&=\\begin{bmatrix}ar_1\\\\ar_2\\\\ar_3\\\\ar_4\\\\br_1\\\\br_2\\\\br_3\\\\br_4\\end{bmatrix}\n",
+    "+\\begin{bmatrix}0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\\\0.3 \\end{bmatrix}\n",
+    "+\\begin{bmatrix}ay_1\\\\ay_2\\\\ay_3\\\\ay_4\\\\by_1\\\\by_2\\\\by_3\\\\by_4\\end{bmatrix}\n",
+    "\\end{align*}\n",
+    "에서 식 $(**)$의 우변은\n",
+    "$$\n",
+    "(-1)((ar_1+ay_1+ar_2+ay_2)-(br_1+by_1+br_2+by_2))\n",
+    "=(-1)\\begin{bmatrix}1\\\\1\\\\0\\\\0\\\\-1\\\\-1\\\\0\\\\0\\end{bmatrix}^T\\texttt{loss\\_lst}\n",
+    "$$\n",
+    "으로 쓸 수 있고, 따라서 식 $(*)$은 \n",
+    "\n",
+    "$$\n",
+    "\\begin{bmatrix}1\\\\1\\\\0\\\\0\\\\-1\\\\-1\\\\0\\\\0\\end{bmatrix}^T\n",
+    "\\begin{bmatrix}ag_1\\\\ag_2\\\\ag_3\\\\ag_4\\\\bg_1\\\\bg_2\\\\bg_3\\\\bg_4\\end{bmatrix}\n",
+    " = (-1)\\begin{bmatrix}1\\\\1\\\\0\\\\0\\\\-1\\\\-1\\\\0\\\\0\\end{bmatrix}^T\\texttt{loss\\_lst}\n",
+    "$$\n",
+    "\n",
+    "이다. 이것이 `evaluation_green_time_ratio.py`의 380, 381번째 줄의 의미이다."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "sts",
+   "language": "python",
+   "name": "sts"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

0217_explore_eval_gtr/0217_explore_eval_gtr.md

@@ -0,0 +1,87 @@
+`node_id = '11053'`는 총 4현시로 구성되어 있고, 1현시와 2현시에서 오버랩이 일어난다.
+
+#### single ring
+
+3현시는 오버랩현시에 포함되지 않으므로
+$a_3=b_3$
+이어야 한다. (단, $a_3$은 A링 3현시의 현시시간.)
+그런데
+\begin{align*}
+a_3&=ag_3+ar_3+ay_3\\
+b_3&=bg_3+br_3+by_3
+\end{align*}
+에서
+\begin{align*}
+ag_3+ar_3+ay_3 &= bg_3+br_3+by_3\\
+ag_3 - bg_3 &= -ar_3+br_3 -ay_3+by_3\\
+\begin{bmatrix}0\\0\\1\\0\\0\\0\\-1\\0\end{bmatrix}^T
+\begin{bmatrix}ag_1\\ag_2\\ag_3\\ag_4\\bg_1\\bg_2\\bg_3\\bg_4\end{bmatrix}
+&= (-1)((ar_3+ay_3)-(br_3+by_3))\tag{$*$}
+\end{align*}
+이어야 한다.
+한편
+\begin{align*}
+\texttt{loss\_lst}
+&= \texttt{r\_lst} + \texttt{y\_loss\_lst} + \texttt{y\_lst}\\
+&=\begin{bmatrix}ar_1\\ar_2\\ar_3\\ar_4\\br_1\\br_2\\br_3\\br_4\end{bmatrix}
++\begin{bmatrix}0.3 \\0.3 \\0.3 \\0.3 \\0.3 \\0.3 \\0.3 \\0.3 \end{bmatrix}
++\begin{bmatrix}ay_1\\ay_2\\ay_3\\ay_4\\by_1\\by_2\\by_3\\by_4\end{bmatrix}
+\end{align*}
+이다. ($\texttt{y\_loss\_lst}$는 편의상 0.3으로 이루어진 벡터로 표현함.)
+따라서 식 $(*)$의 우변은
+$$
+(-1)((ar_3+ay_3)-(br_3+by_3))
+=(-1)\begin{bmatrix}0\\0\\1\\0\\0\\0\\-1\\0\end{bmatrix}^T\texttt{loss\_lst}
+$$
+으로 쓸 수 있고, 따라서 식 $(*)$은 
+
+$$
+\begin{bmatrix}0\\0\\1\\0\\0\\0\\-1\\0\end{bmatrix}^T
+\begin{bmatrix}ag_1\\ag_2\\ag_3\\ag_4\\bg_1\\bg_2\\bg_3\\bg_4\end{bmatrix}
+ = (-1)\begin{bmatrix}0\\0\\1\\0\\0\\0\\-1\\0\end{bmatrix}^T\texttt{loss\_lst}
+$$
+
+이다.
+A링과 B링의 황색/적색시간이 같으면 ($ar_i=br_i$, $ay_i=by_i$ ; 대부분의 경우에 이것이 성립한다.) 위 식의 우변은 0이다.
+이것은 $ag_3=bg_3$이라는 의미이다.
+
+
+이상이 `evaluation_green_time_ratio.py`의 368, 369번째 줄의 의미이다.
+
+
+#### dual ring
+
+1현시와 2현시는 오버랩되므로
+$a_1+a_2=b_1+b_2$
+이어야 한다.
+그러면
+\begin{align*}
+ag_1+ar_1+ay_1+ag_2+ar_2+ay_2 &= bg_1+br_1+by_1+bg_2+br_2+by_2\\
+ag_1 + ag_2 - bg_1 - bg_2 &= -ar_1-ay_1-ar_2-ay_2+br_1+by_1+br_2+by_2\\
+\begin{bmatrix}1\\1\\0\\0\\-1\\-1\\0\\0\end{bmatrix}^T
+\begin{bmatrix}ag_1\\ag_2\\ag_3\\ag_4\\bg_1\\bg_2\\bg_3\\bg_4\end{bmatrix}
+&= (-1)((ar_1+ay_1+ar_2+ay_2)-(br_1+by_1+br_2+by_2))\tag{$**$}
+\end{align*}
+이어야 한다.
+한편
+\begin{align*}
+\texttt{loss\_lst}
+&= \texttt{r\_lst} + \texttt{y\_loss\_lst} + \texttt{y\_lst}\\
+&=\begin{bmatrix}ar_1\\ar_2\\ar_3\\ar_4\\br_1\\br_2\\br_3\\br_4\end{bmatrix}
++\begin{bmatrix}0.3 \\0.3 \\0.3 \\0.3 \\0.3 \\0.3 \\0.3 \\0.3 \end{bmatrix}
++\begin{bmatrix}ay_1\\ay_2\\ay_3\\ay_4\\by_1\\by_2\\by_3\\by_4\end{bmatrix}
+\end{align*}
+에서 식 $(**)$의 우변은
+$$
+(-1)((ar_1+ay_1+ar_2+ay_2)-(br_1+by_1+br_2+by_2))
+=(-1)\begin{bmatrix}1\\1\\0\\0\\-1\\-1\\0\\0\end{bmatrix}^T\texttt{loss\_lst}
+$$
+으로 쓸 수 있고, 따라서 식 $(*)$은 
+
+$$
+\begin{bmatrix}1\\1\\0\\0\\-1\\-1\\0\\0\end{bmatrix}^T
+\begin{bmatrix}ag_1\\ag_2\\ag_3\\ag_4\\bg_1\\bg_2\\bg_3\\bg_4\end{bmatrix}
+ = (-1)\begin{bmatrix}1\\1\\0\\0\\-1\\-1\\0\\0\end{bmatrix}^T\texttt{loss\_lst}
+$$
+
+이다. 이것이 `evaluation_green_time_ratio.py`의 380, 381번째 줄의 의미이다.