prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  [rllib] [docs] Document multi-agent support
  We should document the new multi-agent support in rllib and have some examples in readthedocs. It would be good to cover the supported cases and which ones are not yet supported (or provide workarounds).
  
  </issue>
  <code>
  [start of python/ray/rllib/examples/multiagent_pendulum_env.py]
  1 from gym.spaces import Box, Tuple
  2 from gym.utils import seeding
  3 from gym.envs.classic_control.pendulum import PendulumEnv
  4 import numpy as np
  5 
  6 """
  7  Multiagent pendulum that sums its torques to generate an action
  8 """
  9 
  10 
  11 class MultiAgentPendulumEnv(PendulumEnv):
  12     metadata = {
  13       'render.modes': ['human', 'rgb_array'],
  14       'video.frames_per_second': 30
  15     }
  16 
  17     def __init__(self):
  18         self.max_speed = 8
  19         self.max_torque = 2.
  20         self.dt = .05
  21         self.viewer = None
  22 
  23         high = np.array([1., 1., self.max_speed])
  24         self.action_space = [Box(low=-self.max_torque / 2,
  25                                  high=self.max_torque / 2, shape=(1,))
  26                              for _ in range(2)]
  27         self.observation_space = Tuple(tuple(Box(low=-high, high=high)
  28                                              for _ in range(2)))
  29 
  30         self._seed()
  31 
  32     def _seed(self, seed=None):
  33         self.np_random, seed = seeding.np_random(seed)
  34         return [seed]
  35 
  36     def _step(self, u):
  37         th, thdot = self.state  # th := theta
  38 
  39         summed_u = np.sum(u)
  40         g = 10.
  41         m = 1.
  42         length = 1.
  43         dt = self.dt
  44 
  45         summed_u = np.clip(summed_u, -self.max_torque, self.max_torque)
  46         self.last_u = summed_u  # for rendering
  47         costs = self.angle_normalize(th) ** 2 + .1 * thdot ** 2 + \
  48             .001 * (summed_u ** 2)
  49 
  50         newthdot = thdot + (-3 * g / (2 * length) * np.sin(th + np.pi) +
  51                             3. / (m * length ** 2) * summed_u) * dt
  52         newth = th + newthdot * dt
  53         newthdot = np.clip(newthdot, -self.max_speed, self.max_speed)
  54 
  55         self.state = np.array([newth, newthdot])
  56         return self._get_obs(), -costs, False, {}
  57 
  58     def _reset(self):
  59         high = np.array([np.pi, 1])
  60         self.state = self.np_random.uniform(low=-high, high=high)
  61         self.last_u = None
  62         return self._get_obs()
  63 
  64     def _get_obs(self):
  65         theta, thetadot = self.state
  66         return [np.array([np.cos(theta), np.sin(theta), thetadot])
  67                 for _ in range(2)]
  68 
  69     def angle_normalize(self, x):
  70         return (((x + np.pi) % (2 * np.pi)) - np.pi)
  71
  [end of python/ray/rllib/examples/multiagent_pendulum_env.py]
  [start of python/ray/rllib/examples/multiagent_mountaincar_env.py]
  1 import math
  2 from gym.spaces import Box, Tuple, Discrete
  3 import numpy as np
  4 from gym.envs.classic_control.mountain_car import MountainCarEnv
  5 
  6 """
  7 Multiagent mountain car that sums and then
  8 averages its actions to produce the velocity
  9 """
  10 
  11 
  12 class MultiAgentMountainCarEnv(MountainCarEnv):
  13     def __init__(self):
  14         self.min_position = -1.2
  15         self.max_position = 0.6
  16         self.max_speed = 0.07
  17         self.goal_position = 0.5
  18 
  19         self.low = np.array([self.min_position, -self.max_speed])
  20         self.high = np.array([self.max_position, self.max_speed])
  21 
  22         self.viewer = None
  23 
  24         self.action_space = [Discrete(3) for _ in range(2)]
  25         self.observation_space = Tuple(tuple(Box(self.low, self.high)
  26                                              for _ in range(2)))
  27 
  28         self._seed()
  29         self.reset()
  30 
  31     def _step(self, action):
  32         summed_act = 0.5 * np.sum(action)
  33 
  34         position, velocity = self.state
  35         velocity += (summed_act - 1) * 0.001
  36         velocity += math.cos(3 * position) * (-0.0025)
  37         velocity = np.clip(velocity, -self.max_speed, self.max_speed)
  38         position += velocity
  39         position = np.clip(position, self.min_position, self.max_position)
  40         if (position == self.min_position and velocity < 0):
  41             velocity = 0
  42 
  43         done = bool(position >= self.goal_position)
  44 
  45         reward = position
  46 
  47         self.state = (position, velocity)
  48         return [np.array(self.state) for _ in range(2)], reward, done, {}
  49 
  50     def _reset(self):
  51         self.state = np.array([self.np_random.uniform(low=-0.6, high=-0.4), 0])
  52         return [np.array(self.state) for _ in range(2)]
  53
  [end of python/ray/rllib/examples/multiagent_mountaincar_env.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/python/ray/rllib/examples/multiagent_mountaincar_env.py b/python/ray/rllib/examples/multiagent_mountaincar_env.py
  --- a/python/ray/rllib/examples/multiagent_mountaincar_env.py
  +++ b/python/ray/rllib/examples/multiagent_mountaincar_env.py
  @@ -22,8 +22,8 @@
           self.viewer = None
   
           self.action_space = [Discrete(3) for _ in range(2)]
  -        self.observation_space = Tuple(tuple(Box(self.low, self.high)
  -                                             for _ in range(2)))
  +        self.observation_space = Tuple([
  +            Box(self.low, self.high) for _ in range(2)])
   
           self._seed()
           self.reset()
  diff --git a/python/ray/rllib/examples/multiagent_pendulum_env.py b/python/ray/rllib/examples/multiagent_pendulum_env.py
  --- a/python/ray/rllib/examples/multiagent_pendulum_env.py
  +++ b/python/ray/rllib/examples/multiagent_pendulum_env.py
  @@ -24,8 +24,8 @@
           self.action_space = [Box(low=-self.max_torque / 2,
                                    high=self.max_torque / 2, shape=(1,))
                                for _ in range(2)]
  -        self.observation_space = Tuple(tuple(Box(low=-high, high=high)
  -                                             for _ in range(2)))
  +        self.observation_space = Tuple([
  +            Box(low=-high, high=high) for _ in range(2)])
   
           self._seed()
  
verification_info: {"golden_diff": "diff --git a/python/ray/rllib/examples/multiagent_mountaincar_env.py b/python/ray/rllib/examples/multiagent_mountaincar_env.py\n--- a/python/ray/rllib/examples/multiagent_mountaincar_env.py\n+++ b/python/ray/rllib/examples/multiagent_mountaincar_env.py\n@@ -22,8 +22,8 @@\n         self.viewer = None\n \n         self.action_space = [Discrete(3) for _ in range(2)]\n-        self.observation_space = Tuple(tuple(Box(self.low, self.high)\n-                                             for _ in range(2)))\n+        self.observation_space = Tuple([\n+            Box(self.low, self.high) for _ in range(2)])\n \n         self._seed()\n         self.reset()\ndiff --git a/python/ray/rllib/examples/multiagent_pendulum_env.py b/python/ray/rllib/examples/multiagent_pendulum_env.py\n--- a/python/ray/rllib/examples/multiagent_pendulum_env.py\n+++ b/python/ray/rllib/examples/multiagent_pendulum_env.py\n@@ -24,8 +24,8 @@\n         self.action_space = [Box(low=-self.max_torque / 2,\n                                  high=self.max_torque / 2, shape=(1,))\n                              for _ in range(2)]\n-        self.observation_space = Tuple(tuple(Box(low=-high, high=high)\n-                                             for _ in range(2)))\n+        self.observation_space = Tuple([\n+            Box(low=-high, high=high) for _ in range(2)])\n \n         self._seed()\n", "issue": "[rllib] [docs] Document multi-agent support\nWe should document the new multi-agent support in rllib and have some examples in readthedocs. It would be good to cover the supported cases and which ones are not yet supported (or provide workarounds).\n", "before_files": [{"content": "from gym.spaces import Box, Tuple\nfrom gym.utils import seeding\nfrom gym.envs.classic_control.pendulum import PendulumEnv\nimport numpy as np\n\n\"\"\"\n Multiagent pendulum that sums its torques to generate an action\n\"\"\"\n\n\nclass MultiAgentPendulumEnv(PendulumEnv):\n    metadata = {\n      'render.modes': ['human', 'rgb_array'],\n      'video.frames_per_second': 30\n    }\n\n    def __init__(self):\n        self.max_speed = 8\n        self.max_torque = 2.\n        self.dt = .05\n        self.viewer = None\n\n        high = np.array([1., 1., self.max_speed])\n        self.action_space = [Box(low=-self.max_torque / 2,\n                                 high=self.max_torque / 2, shape=(1,))\n                             for _ in range(2)]\n        self.observation_space = Tuple(tuple(Box(low=-high, high=high)\n                                             for _ in range(2)))\n\n        self._seed()\n\n    def _seed(self, seed=None):\n        self.np_random, seed = seeding.np_random(seed)\n        return [seed]\n\n    def _step(self, u):\n        th, thdot = self.state  # th := theta\n\n        summed_u = np.sum(u)\n        g = 10.\n        m = 1.\n        length = 1.\n        dt = self.dt\n\n        summed_u = np.clip(summed_u, -self.max_torque, self.max_torque)\n        self.last_u = summed_u  # for rendering\n        costs = self.angle_normalize(th) ** 2 + .1 * thdot ** 2 + \\\n            .001 * (summed_u ** 2)\n\n        newthdot = thdot + (-3 * g / (2 * length) * np.sin(th + np.pi) +\n                            3. / (m * length ** 2) * summed_u) * dt\n        newth = th + newthdot * dt\n        newthdot = np.clip(newthdot, -self.max_speed, self.max_speed)\n\n        self.state = np.array([newth, newthdot])\n        return self._get_obs(), -costs, False, {}\n\n    def _reset(self):\n        high = np.array([np.pi, 1])\n        self.state = self.np_random.uniform(low=-high, high=high)\n        self.last_u = None\n        return self._get_obs()\n\n    def _get_obs(self):\n        theta, thetadot = self.state\n        return [np.array([np.cos(theta), np.sin(theta), thetadot])\n                for _ in range(2)]\n\n    def angle_normalize(self, x):\n        return (((x + np.pi) % (2 * np.pi)) - np.pi)\n", "path": "python/ray/rllib/examples/multiagent_pendulum_env.py"}, {"content": "import math\nfrom gym.spaces import Box, Tuple, Discrete\nimport numpy as np\nfrom gym.envs.classic_control.mountain_car import MountainCarEnv\n\n\"\"\"\nMultiagent mountain car that sums and then\naverages its actions to produce the velocity\n\"\"\"\n\n\nclass MultiAgentMountainCarEnv(MountainCarEnv):\n    def __init__(self):\n        self.min_position = -1.2\n        self.max_position = 0.6\n        self.max_speed = 0.07\n        self.goal_position = 0.5\n\n        self.low = np.array([self.min_position, -self.max_speed])\n        self.high = np.array([self.max_position, self.max_speed])\n\n        self.viewer = None\n\n        self.action_space = [Discrete(3) for _ in range(2)]\n        self.observation_space = Tuple(tuple(Box(self.low, self.high)\n                                             for _ in range(2)))\n\n        self._seed()\n        self.reset()\n\n    def _step(self, action):\n        summed_act = 0.5 * np.sum(action)\n\n        position, velocity = self.state\n        velocity += (summed_act - 1) * 0.001\n        velocity += math.cos(3 * position) * (-0.0025)\n        velocity = np.clip(velocity, -self.max_speed, self.max_speed)\n        position += velocity\n        position = np.clip(position, self.min_position, self.max_position)\n        if (position == self.min_position and velocity < 0):\n            velocity = 0\n\n        done = bool(position >= self.goal_position)\n\n        reward = position\n\n        self.state = (position, velocity)\n        return [np.array(self.state) for _ in range(2)], reward, done, {}\n\n    def _reset(self):\n        self.state = np.array([self.np_random.uniform(low=-0.6, high=-0.4), 0])\n        return [np.array(self.state) for _ in range(2)]\n", "path": "python/ray/rllib/examples/multiagent_mountaincar_env.py"}]}