Source code for ding.policy.ppo

from typing import List, Dict, Any, Tuple, Union
from collections import namedtuple
import torch
import copy
import numpy as np
from torch.distributions import Independent, Normal

from ding.torch_utils import Adam, to_device
from ding.rl_utils import ppo_data, ppo_error, ppo_policy_error, ppo_policy_data, get_gae_with_default_last_value, \
    v_nstep_td_data, v_nstep_td_error, get_nstep_return_data, get_train_sample, gae, gae_data, ppo_error_continuous, \
    get_gae
from ding.model import model_wrap
from ding.utils import POLICY_REGISTRY, split_data_generator, RunningMeanStd
from ding.utils.data import default_collate, default_decollate
from .base_policy import Policy
from .common_utils import default_preprocess_learn
from ding.utils import dicts_to_lists, lists_to_dicts


[docs]@POLICY_REGISTRY.register('ppo') class PPOPolicy(Policy): r""" Overview: Policy class of on policy version PPO algorithm. """ config = dict( # (str) RL policy register name (refer to function "POLICY_REGISTRY"). type='ppo', # (bool) Whether to use cuda for network. cuda=False, # (bool) Whether the RL algorithm is on-policy or off-policy. (Note: in practice PPO can be off-policy used) on_policy=True, # (bool) Whether to use priority(priority sample, IS weight, update priority) priority=False, # (bool) Whether use Importance Sampling Weight to correct biased update. If True, priority must be True. priority_IS_weight=False, recompute_adv=True, continuous=True, nstep_return=False, multi_agent=False, # (bool) Whether to need policy data in process transition transition_with_policy_data=True, learn=dict( # (bool) Whether to use multi gpu multi_gpu=False, epoch_per_collect=10, batch_size=64, learning_rate=3e-4, # ============================================================== # The following configs is algorithm-specific # ============================================================== # (float) The loss weight of value network, policy network weight is set to 1 value_weight=0.5, # (float) The loss weight of entropy regularization, policy network weight is set to 1 entropy_weight=0.0, # (float) PPO clip ratio, defaults to 0.2 clip_ratio=0.2, # (bool) Whether to use advantage norm in a whole training batch adv_norm=True, value_norm=True, ppo_param_init=True, grad_clip_type='clip_norm', grad_clip_value=0.5, ignore_done=False, ), collect=dict( # (int) Only one of [n_sample, n_episode] shoule be set # n_sample=64, # (int) Cut trajectories into pieces with length "unroll_len". unroll_len=1, # ============================================================== # The following configs is algorithm-specific # ============================================================== # (float) Reward's future discount factor, aka. gamma. discount_factor=0.99, # (float) GAE lambda factor for the balance of bias and variance(1-step td and mc) gae_lambda=0.95, ), eval=dict(), ) def _init_learn(self) -> None: r""" Overview: Learn mode init method. Called by ``self.__init__``. Init the optimizer, algorithm config and the main model. """ self._priority = self._cfg.priority self._priority_IS_weight = self._cfg.priority_IS_weight assert not self._priority and not self._priority_IS_weight, "Priority is not implemented in PPO" self._continuous = self._cfg.continuous if self._cfg.learn.ppo_param_init: for n, m in self._model.named_modules(): if isinstance(m, torch.nn.Linear): torch.nn.init.orthogonal_(m.weight) torch.nn.init.zeros_(m.bias) if self._continuous: # init log sigma if hasattr(self._model.actor_head, 'log_sigma_param'): torch.nn.init.constant_(self._model.actor_head.log_sigma_param, -0.5) for m in list(self._model.critic.modules()) + list(self._model.actor.modules()): if isinstance(m, torch.nn.Linear): # orthogonal initialization torch.nn.init.orthogonal_(m.weight, gain=np.sqrt(2)) torch.nn.init.zeros_(m.bias) # do last policy layer scaling, this will make initial actions have (close to) # 0 mean and std, and will help boost performances, # see https://arxiv.org/abs/2006.05990, Fig.24 for details for m in self._model.actor.modules(): if isinstance(m, torch.nn.Linear): torch.nn.init.zeros_(m.bias) m.weight.data.copy_(0.01 * m.weight.data) # Optimizer self._optimizer = Adam( self._model.parameters(), lr=self._cfg.learn.learning_rate, grad_clip_type=self._cfg.learn.grad_clip_type, clip_value=self._cfg.learn.grad_clip_value ) self._learn_model = model_wrap(self._model, wrapper_name='base') # Algorithm config self._value_weight = self._cfg.learn.value_weight self._entropy_weight = self._cfg.learn.entropy_weight self._clip_ratio = self._cfg.learn.clip_ratio self._adv_norm = self._cfg.learn.adv_norm self._value_norm = self._cfg.learn.value_norm if self._value_norm: self._running_mean_std = RunningMeanStd(epsilon=1e-4, device=self._device) self._gamma = self._cfg.collect.discount_factor self._gae_lambda = self._cfg.collect.gae_lambda self._recompute_adv = self._cfg.recompute_adv # Main model self._learn_model.reset() def _forward_learn(self, data: Dict[str, Any]) -> Dict[str, Any]: r""" Overview: Forward and backward function of learn mode. Arguments: - data (:obj:`dict`): Dict type data Returns: - info_dict (:obj:`Dict[str, Any]`): Including current lr, total_loss, policy_loss, value_loss, entropy_loss, \ adv_abs_max, approx_kl, clipfrac """ data = default_preprocess_learn(data, ignore_done=self._cfg.learn.ignore_done, use_nstep=False) if self._cuda: data = to_device(data, self._device) # ==================== # PPO forward # ==================== return_infos = [] self._learn_model.train() for epoch in range(self._cfg.learn.epoch_per_collect): if self._recompute_adv: # new v network compute new value with torch.no_grad(): value = self._learn_model.forward(data['obs'], mode='compute_critic')['value'] next_value = self._learn_model.forward(data['next_obs'], mode='compute_critic')['value'] if self._value_norm: value *= self._running_mean_std.std next_value *= self._running_mean_std.std compute_adv_data = gae_data(value, next_value, data['reward'], data['done'], data['traj_flag']) data['adv'] = gae(compute_adv_data, self._gamma, self._gae_lambda) unnormalized_returns = value + data['adv'] if self._value_norm: data['value'] = value / self._running_mean_std.std data['return'] = unnormalized_returns / self._running_mean_std.std self._running_mean_std.update(unnormalized_returns.cpu().numpy()) else: data['value'] = value data['return'] = unnormalized_returns else: # don't recompute adv if self._value_norm: unnormalized_return = data['adv'] + data['value'] * self._running_mean_std.std data['return'] = unnormalized_return / self._running_mean_std.std self._running_mean_std.update(unnormalized_return.cpu().numpy()) else: data['return'] = data['adv'] + data['value'] for batch in split_data_generator(data, self._cfg.learn.batch_size, shuffle=True): output = self._learn_model.forward(batch['obs'], mode='compute_actor_critic') adv = batch['adv'] if self._adv_norm: # Normalize advantage in a train_batch adv = (adv - adv.mean()) / (adv.std() + 1e-8) # Calculate ppo error if self._continuous: ppo_batch = ppo_data( output['logit'], batch['logit'], batch['action'], output['value'], batch['value'], adv, batch['return'], batch['weight'] ) ppo_loss, ppo_info = ppo_error_continuous(ppo_batch, self._clip_ratio) else: ppo_batch = ppo_data( output['logit'], batch['logit'], batch['action'], output['value'], batch['value'], adv, batch['return'], batch['weight'] ) ppo_loss, ppo_info = ppo_error(ppo_batch, self._clip_ratio) wv, we = self._value_weight, self._entropy_weight total_loss = ppo_loss.policy_loss + wv * ppo_loss.value_loss - we * ppo_loss.entropy_loss self._optimizer.zero_grad() total_loss.backward() self._optimizer.step() return_info = { 'cur_lr': self._optimizer.defaults['lr'], 'total_loss': total_loss.item(), 'policy_loss': ppo_loss.policy_loss.item(), 'value_loss': ppo_loss.value_loss.item(), 'entropy_loss': ppo_loss.entropy_loss.item(), 'adv_max': adv.max().item(), 'adv_mean': adv.mean().item(), 'value_mean': output['value'].mean().item(), 'value_max': output['value'].max().item(), 'approx_kl': ppo_info.approx_kl, 'clipfrac': ppo_info.clipfrac, 'act': batch['action'].float().mean().item(), } if self._continuous: return_info.update( { 'mu_mean': output['logit'][0].mean().item(), 'sigma_mean': output['logit'][1].mean().item(), } ) return_infos.append(return_info) return return_infos def _state_dict_learn(self) -> Dict[str, Any]: return { 'model': self._learn_model.state_dict(), 'optimizer': self._optimizer.state_dict(), } def _load_state_dict_learn(self, state_dict: Dict[str, Any]) -> None: self._learn_model.load_state_dict(state_dict['model']) self._optimizer.load_state_dict(state_dict['optimizer']) def _init_collect(self) -> None: r""" Overview: Collect mode init method. Called by ``self.__init__``. Init traj and unroll length, collect model. """ self._unroll_len = self._cfg.collect.unroll_len self._continuous = self._cfg.continuous if self._continuous: self._collect_model = model_wrap(self._model, wrapper_name='base') else: self._collect_model = model_wrap(self._model, wrapper_name='multinomial_sample') self._collect_model.reset() self._gamma = self._cfg.collect.discount_factor self._gae_lambda = self._cfg.collect.gae_lambda self._recompute_adv = self._cfg.recompute_adv def _forward_collect(self, data: dict) -> dict: r""" Overview: Forward function of collect mode. Arguments: - data (:obj:`Dict[str, Any]`): Dict type data, stacked env data for predicting policy_output(action), \ values are torch.Tensor or np.ndarray or dict/list combinations, keys are env_id indicated by integer. Returns: - output (:obj:`Dict[int, Any]`): Dict type data, including at least inferred action according to input obs. ReturnsKeys - necessary: ``action`` """ data_id = list(data.keys()) data = default_collate(list(data.values())) if self._cuda: data = to_device(data, self._device) self._collect_model.eval() with torch.no_grad(): output = self._collect_model.forward(data, mode='compute_actor_critic') if self._continuous: (mu, sigma), value = output['logit'], output['value'] dist = Independent(Normal(mu, sigma), 1) output['action'] = dist.sample() if self._cuda: output = to_device(output, 'cpu') output = default_decollate(output) return {i: d for i, d in zip(data_id, output)} def _process_transition(self, obs: Any, model_output: dict, timestep: namedtuple) -> dict: """ Overview: Generate dict type transition data from inputs. Arguments: - obs (:obj:`Any`): Env observation - model_output (:obj:`dict`): Output of collect model, including at least ['action'] - timestep (:obj:`namedtuple`): Output after env step, including at least ['obs', 'reward', 'done']\ (here 'obs' indicates obs after env step). Returns: - transition (:obj:`dict`): Dict type transition data. """ transition = { 'obs': obs, 'next_obs': timestep.obs, 'action': model_output['action'], 'logit': model_output['logit'], 'value': model_output['value'], 'reward': timestep.reward, 'done': timestep.done, } return transition def _get_train_sample(self, data: list) -> Union[None, List[Any]]: r""" Overview: Get the trajectory and calculate GAE, return one data to cache for next time calculation Arguments: - data (:obj:`list`): The trajectory's cache Returns: - samples (:obj:`dict`): The training samples generated """ data = to_device(data, self._device) for transition in data: transition['traj_flag'] = copy.deepcopy(transition['done']) data[-1]['traj_flag'] = True if self._cfg.learn.ignore_done: data[-1]['done'] = False if data[-1]['done']: last_value = torch.zeros_like(data[-1]['value']) else: if self._cfg.multi_agent: with torch.no_grad(): last_value = self._collect_model.forward( { 'agent_state': data[-1]['next_obs']['agent_state'].unsqueeze(0), 'global_state': data[-1]['next_obs']['global_state'].unsqueeze(0), 'action_mask': data[-1]['next_obs']['action_mask'].unsqueeze(0) }, mode='compute_actor_critic' )['value'] last_value = last_value.squeeze(0) else: with torch.no_grad(): last_value = self._collect_model.forward( data[-1]['next_obs'].unsqueeze(0), mode='compute_actor_critic' )['value'] if self._value_norm: last_value *= self._running_mean_std.std for i in range(len(data)): data[i]['value'] *= self._running_mean_std.std data = get_gae( data, to_device(last_value, self._device), gamma=self._gamma, gae_lambda=self._gae_lambda, cuda=False, ) if self._value_norm: for i in range(len(data)): data[i]['value'] /= self._running_mean_std.std # remove next_obs for save memory when not recompute adv if not self._recompute_adv: for i in range(len(data)): data[i].pop('next_obs') return get_train_sample(data, self._unroll_len) def _init_eval(self) -> None: r""" Overview: Evaluate mode init method. Called by ``self.__init__``. Init eval model with argmax strategy. """ self._continuous = self._cfg.continuous if self._continuous: self._eval_model = model_wrap(self._model, wrapper_name='base') else: self._eval_model = model_wrap(self._model, wrapper_name='argmax_sample') self._eval_model.reset() def _forward_eval(self, data: dict) -> dict: r""" Overview: Forward function of eval mode, similar to ``self._forward_collect``. Arguments: - data (:obj:`Dict[str, Any]`): Dict type data, stacked env data for predicting policy_output(action), \ values are torch.Tensor or np.ndarray or dict/list combinations, keys are env_id indicated by integer. Returns: - output (:obj:`Dict[int, Any]`): The dict of predicting action for the interaction with env. ReturnsKeys - necessary: ``action`` """ data_id = list(data.keys()) data = default_collate(list(data.values())) if self._cuda: data = to_device(data, self._device) self._eval_model.eval() with torch.no_grad(): output = self._eval_model.forward(data, mode='compute_actor') if self._continuous: (mu, sigma) = output['logit'] output.update({'action': mu}) if self._cuda: output = to_device(output, 'cpu') output = default_decollate(output) return {i: d for i, d in zip(data_id, output)} def default_model(self) -> Tuple[str, List[str]]: if self._cfg.multi_agent: return 'mavac', ['ding.model.template.mavac'] else: return 'vac', ['ding.model.template.vac'] def _monitor_vars_learn(self) -> List[str]: variables = super()._monitor_vars_learn() + [ 'policy_loss', 'value_loss', 'entropy_loss', 'adv_max', 'adv_mean', 'approx_kl', 'clipfrac', 'value_max', 'value_mean', ] if self._continuous: variables += ['mu_mean', 'sigma_mean', 'sigma_grad', 'act'] return variables
@POLICY_REGISTRY.register('ppo_offpolicy') class PPOOffPolicy(Policy): r""" Overview: Policy class of PPO algorithm. """ config = dict( # (str) RL policy register name (refer to function "POLICY_REGISTRY"). type='ppo', # (bool) Whether to use cuda for network. cuda=False, on_policy=False, # (bool) Whether to use priority(priority sample, IS weight, update priority) priority=False, # (bool) Whether use Importance Sampling Weight to correct biased update. If True, priority must be True. priority_IS_weight=False, # (bool) Whether to use nstep_return for value loss nstep_return=False, nstep=3, # (bool) Whether to need policy data in process transition transition_with_policy_data=True, learn=dict( # (bool) Whether to use multi gpu multi_gpu=False, # How many updates(iterations) to train after collector's one collection. # Bigger "update_per_collect" means bigger off-policy. # collect data -> update policy-> collect data -> ... update_per_collect=5, batch_size=64, learning_rate=0.001, # ============================================================== # The following configs is algorithm-specific # ============================================================== # (float) The loss weight of value network, policy network weight is set to 1 value_weight=0.5, # (float) The loss weight of entropy regularization, policy network weight is set to 1 entropy_weight=0.01, # (float) PPO clip ratio, defaults to 0.2 clip_ratio=0.2, # (bool) Whether to use advantage norm in a whole training batch adv_norm=False, ignore_done=False, ), collect=dict( # (int) Only one of [n_sample, n_episode] shoule be set # n_sample=64, # (int) Cut trajectories into pieces with length "unroll_len". unroll_len=1, # ============================================================== # The following configs is algorithm-specific # ============================================================== # (float) Reward's future discount factor, aka. gamma. discount_factor=0.99, # (float) GAE lambda factor for the balance of bias and variance(1-step td and mc) gae_lambda=0.95, ), eval=dict(), other=dict(replay_buffer=dict(replay_buffer_size=10000, ), ), ) def _init_learn(self) -> None: r""" Overview: Learn mode init method. Called by ``self.__init__``. Init the optimizer, algorithm config and the main model. """ self._priority = self._cfg.priority self._priority_IS_weight = self._cfg.priority_IS_weight assert not self._priority and not self._priority_IS_weight, "Priority is not implemented in PPO" # Orthogonal init for m in self._model.modules(): if isinstance(m, torch.nn.Conv2d): torch.nn.init.orthogonal_(m.weight) if isinstance(m, torch.nn.Linear): torch.nn.init.orthogonal_(m.weight) # Optimizer self._optimizer = Adam(self._model.parameters(), lr=self._cfg.learn.learning_rate) self._learn_model = model_wrap(self._model, wrapper_name='base') # Algorithm config self._value_weight = self._cfg.learn.value_weight self._entropy_weight = self._cfg.learn.entropy_weight self._clip_ratio = self._cfg.learn.clip_ratio self._adv_norm = self._cfg.learn.adv_norm self._nstep = self._cfg.nstep self._nstep_return = self._cfg.nstep_return # Main model self._learn_model.reset() def _forward_learn(self, data: dict) -> Dict[str, Any]: r""" Overview: Forward and backward function of learn mode. Arguments: - data (:obj:`dict`): Dict type data Returns: - info_dict (:obj:`Dict[str, Any]`): Including current lr, total_loss, policy_loss, value_loss, entropy_loss, \ adv_abs_max, approx_kl, clipfrac """ data = default_preprocess_learn(data, ignore_done=self._cfg.learn.ignore_done, use_nstep=self._nstep_return) if self._cuda: data = to_device(data, self._device) # ==================== # PPO forward # ==================== self._learn_model.train() # normal ppo if not self._nstep_return: output = self._learn_model.forward(data['obs'], mode='compute_actor_critic') adv = data['adv'] return_ = data['value'] + adv if self._adv_norm: # Normalize advantage in a total train_batch adv = (adv - adv.mean()) / (adv.std() + 1e-8) # Calculate ppo error ppodata = ppo_data( output['logit'], data['logit'], data['action'], output['value'], data['value'], adv, return_, data['weight'] ) ppo_loss, ppo_info = ppo_error(ppodata, self._clip_ratio) wv, we = self._value_weight, self._entropy_weight total_loss = ppo_loss.policy_loss + wv * ppo_loss.value_loss - we * ppo_loss.entropy_loss else: output = self._learn_model.forward(data['obs'], mode='compute_actor') adv = data['adv'] if self._adv_norm: # Normalize advantage in a total train_batch adv = (adv - adv.mean()) / (adv.std() + 1e-8) # Calculate ppo error ppodata = ppo_policy_data(output['logit'], data['logit'], data['action'], adv, data['weight']) ppo_policy_loss, ppo_info = ppo_policy_error(ppodata, self._clip_ratio) wv, we = self._value_weight, self._entropy_weight next_obs = data.get('next_obs') value_gamma = data.get('value_gamma') reward = data.get('reward') # current value value = self._learn_model.forward(data['obs'], mode='compute_critic') # target value next_data = {'obs': next_obs} target_value = self._learn_model.forward(next_data['obs'], mode='compute_critic') # TODO what should we do here to keep shape assert self._nstep > 1 td_data = v_nstep_td_data( value['value'], target_value['value'], reward, data['done'], data['weight'], value_gamma ) # calculate v_nstep_td critic_loss critic_loss, td_error_per_sample = v_nstep_td_error(td_data, self._gamma, self._nstep) ppo_loss_data = namedtuple('ppo_loss', ['policy_loss', 'value_loss', 'entropy_loss']) ppo_loss = ppo_loss_data(ppo_policy_loss.policy_loss, critic_loss, ppo_policy_loss.entropy_loss) total_loss = ppo_policy_loss.policy_loss + wv * critic_loss - we * ppo_policy_loss.entropy_loss # ==================== # PPO update # ==================== self._optimizer.zero_grad() total_loss.backward() self._optimizer.step() return { 'cur_lr': self._optimizer.defaults['lr'], 'total_loss': total_loss.item(), 'policy_loss': ppo_loss.policy_loss.item(), 'value_loss': ppo_loss.value_loss.item(), 'entropy_loss': ppo_loss.entropy_loss.item(), 'adv_abs_max': adv.abs().max().item(), 'approx_kl': ppo_info.approx_kl, 'clipfrac': ppo_info.clipfrac, } def _state_dict_learn(self) -> Dict[str, Any]: return { 'model': self._learn_model.state_dict(), 'optimizer': self._optimizer.state_dict(), } def _load_state_dict_learn(self, state_dict: Dict[str, Any]) -> None: self._learn_model.load_state_dict(state_dict['model']) self._optimizer.load_state_dict(state_dict['optimizer']) def _init_collect(self) -> None: r""" Overview: Collect mode init method. Called by ``self.__init__``. Init traj and unroll length, collect model. """ self._unroll_len = self._cfg.collect.unroll_len self._collect_model = model_wrap(self._model, wrapper_name='multinomial_sample') self._collect_model.reset() self._gamma = self._cfg.collect.discount_factor self._gae_lambda = self._cfg.collect.gae_lambda self._nstep = self._cfg.nstep self._nstep_return = self._cfg.nstep_return def _forward_collect(self, data: dict) -> dict: r""" Overview: Forward function of collect mode. Arguments: - data (:obj:`Dict[str, Any]`): Dict type data, stacked env data for predicting policy_output(action), \ values are torch.Tensor or np.ndarray or dict/list combinations, keys are env_id indicated by integer. Returns: - output (:obj:`Dict[int, Any]`): Dict type data, including at least inferred action according to input obs. ReturnsKeys - necessary: ``action`` """ data_id = list(data.keys()) data = default_collate(list(data.values())) if self._cuda: data = to_device(data, self._device) self._collect_model.eval() with torch.no_grad(): output = self._collect_model.forward(data, mode='compute_actor_critic') if self._cuda: output = to_device(output, 'cpu') output = default_decollate(output) return {i: d for i, d in zip(data_id, output)} def _process_transition(self, obs: Any, model_output: dict, timestep: namedtuple) -> dict: """ Overview: Generate dict type transition data from inputs. Arguments: - obs (:obj:`Any`): Env observation - model_output (:obj:`dict`): Output of collect model, including at least ['action'] - timestep (:obj:`namedtuple`): Output after env step, including at least ['obs', 'reward', 'done']\ (here 'obs' indicates obs after env step). Returns: - transition (:obj:`dict`): Dict type transition data. """ transition = { 'obs': obs, 'next_obs': timestep.obs, 'logit': model_output['logit'], 'action': model_output['action'], 'value': model_output['value'], 'reward': timestep.reward, 'done': timestep.done, } return transition def _get_train_sample(self, data: list) -> Union[None, List[Any]]: r""" Overview: Get the trajectory and calculate GAE, return one data to cache for next time calculation Arguments: - data (:obj:`list`): The trajectory's cache Returns: - samples (:obj:`dict`): The training samples generated """ data = get_gae_with_default_last_value( data, data[-1]['done'], gamma=self._gamma, gae_lambda=self._gae_lambda, cuda=False, ) if not self._nstep_return: return get_train_sample(data, self._unroll_len) else: return get_nstep_return_data(data, self._nstep) def _init_eval(self) -> None: r""" Overview: Evaluate mode init method. Called by ``self.__init__``. Init eval model with argmax strategy. """ self._eval_model = model_wrap(self._model, wrapper_name='argmax_sample') self._eval_model.reset() def _forward_eval(self, data: dict) -> dict: r""" Overview: Forward function of eval mode, similar to ``self._forward_collect``. Arguments: - data (:obj:`Dict[str, Any]`): Dict type data, stacked env data for predicting policy_output(action), \ values are torch.Tensor or np.ndarray or dict/list combinations, keys are env_id indicated by integer. Returns: - output (:obj:`Dict[int, Any]`): The dict of predicting action for the interaction with env. ReturnsKeys - necessary: ``action`` """ data_id = list(data.keys()) data = default_collate(list(data.values())) if self._cuda: data = to_device(data, self._device) self._eval_model.eval() with torch.no_grad(): output = self._eval_model.forward(data, mode='compute_actor') if self._cuda: output = to_device(output, 'cpu') output = default_decollate(output) return {i: d for i, d in zip(data_id, output)} def default_model(self) -> Tuple[str, List[str]]: return 'vac', ['ding.model.template.vac'] def _monitor_vars_learn(self) -> List[str]: return super()._monitor_vars_learn() + [ 'policy_loss', 'value_loss', 'entropy_loss', 'adv_abs_max', 'approx_kl', 'clipfrac' ]