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-*.orig -docs/site -coach_env -build -rl_coach.egg* -contrib -test_log_* -dist +*.pyc +.test +experiments diff --git a/README.md b/README.md deleted file mode 100644 index fe63637..0000000 --- a/README.md +++ /dev/null @@ -1,271 +0,0 @@ -# Coach - -[![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://github.com/NervanaSystems/coach/blob/master/LICENSE) -[![Docs](https://img.shields.io/readthedocs/pip/stable.svg)](http://NervanaSystems.github.io/coach/) -[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.1134898.svg)](https://doi.org/10.5281/zenodo.1134898) - -## Overview - -Coach is a python reinforcement learning research framework containing implementation of many state-of-the-art algorithms. - -It exposes a set of easy-to-use APIs for experimenting with new RL algorithms, and allows simple integration of new environments to solve. -Basic RL components (algorithms, environments, neural network architectures, exploration policies, ...) are well decoupled, so that extending and reusing existing components is fairly painless. - -Training an agent to solve an environment is as easy as running: - -```bash -python3 coach.py -p CartPole_DQN -r -``` - -Doom Deathmatch CARLA MontezumaRevenge - -Blog posts from the IntelĀ® AI website: -* [Release 0.8.0](https://ai.intel.com/reinforcement-learning-coach-intel/) (initial release) -* [Release 0.9.0](https://ai.intel.com/reinforcement-learning-coach-carla-qr-dqn/) - -Contacting the Coach development team is also possible through the email [coach@intel.com](coach@intel.com) - -## Table of Contents - -- [Coach](#coach) - * [Overview](#overview) - * [Documentation](#documentation) - * [Installation](#installation) - + [Coach Installer](#coach-installer) - + [TensorFlow GPU Support](#tensorflow-gpu-support) - * [Usage](#usage) - + [Running Coach](#running-coach) - + [Running Coach Dashboard (Visualization)](#running-coach-dashboard-visualization) - + [Parallelizing an Algorithm](#parallelizing-an-algorithm) - * [Supported Environments](#supported-environments) - * [Supported Algorithms](#supported-algorithms) - * [Citation](#citation) - * [Disclaimer](#disclaimer) - -## Documentation - -Framework documentation, algorithm description and instructions on how to contribute a new agent/environment can be found [here](http://NervanaSystems.github.io/coach/). - - -## Installation - -Note: Coach has only been tested on Ubuntu 16.04 LTS, and with Python 3.5. - -### Coach Installer - -Coach's installer will setup all the basics needed to get the user going with running Coach on top of [OpenAI Gym](https://github.com/openai/gym) environments. This can be done by running the following command and then following the on-screen printed instructions: - -```bash -./install.sh -``` - -Coach creates a virtual environment and installs in it to avoid changes to the user's system. - -In order to activate and deactivate Coach's virtual environment: - -```bash -source coach_env/bin/activate -``` - -```bash -deactivate -``` - -In addition to OpenAI Gym, several other environments were tested and are supported. Please follow the instructions in the Supported Environments section below in order to install more environments. - -### TensorFlow GPU Support - -Coach's installer installs [Intel-Optimized TensorFlow](https://software.intel.com/en-us/articles/intel-optimized-tensorflow-wheel-now-available), which does not support GPU, by default. In order to have Coach running with GPU, a GPU supported TensorFlow version must be installed. This can be done by overriding the TensorFlow version: - -```bash -pip3 install tensorflow-gpu -``` - -## Usage - -### Running Coach - -Coach supports both TensorFlow and neon deep learning frameworks. - -Switching between TensorFlow and neon backends is possible by using the `-f` flag. - -Using TensorFlow (default): `-f tensorflow` - -Using neon: `-f neon` - -There are several available presets in presets.py. -To list all the available presets use the `-l` flag. - -To run a preset, use: - -```bash -python3 coach.py -r -p -``` - -For example: -1. CartPole environment using Policy Gradients: - - ```bash - python3 coach.py -r -p CartPole_PG - ``` - -2. Pendulum using Clipped PPO: - - ```bash - python3 coach.py -r -p Pendulum_ClippedPPO -n 8 - ``` - -3. MountainCar using A3C: - - ```bash - python3 coach.py -r -p MountainCar_A3C -n 8 - ``` - -4. Doom basic level using Dueling network and Double DQN algorithm: - - ```bash - python3 coach.py -r -p Doom_Basic_Dueling_DDQN - ``` - -5. Doom health gathering level using Mixed Monte Carlo: - - ```bash - python3 coach.py -r -p Doom_Health_MMC - ``` - -It is easy to create new presets for different levels or environments by following the same pattern as in presets.py - -More usage examples can be found [here](http://NervanaSystems.github.io/coach/usage/index.html). - -### Running Coach Dashboard (Visualization) -Training an agent to solve an environment can be tricky, at times. - -In order to debug the training process, Coach outputs several signals, per trained algorithm, in order to track algorithmic performance. - -While Coach trains an agent, a csv file containing the relevant training signals will be saved to the 'experiments' directory. Coach's dashboard can then be used to dynamically visualize the training signals, and track algorithmic behavior. - -To use it, run: - -```bash -python3 dashboard.py -``` - - - -Coach Design - - -### Parallelizing an Algorithm - -Since the introduction of [A3C](https://arxiv.org/abs/1602.01783) in 2016, many algorithms were shown to benefit from running multiple instances in parallel, on many CPU cores. So far, these algorithms include [A3C](https://arxiv.org/abs/1602.01783), [DDPG](https://arxiv.org/pdf/1704.03073.pdf), [PPO](https://arxiv.org/pdf/1707.06347.pdf), and [NAF](https://arxiv.org/pdf/1610.00633.pdf), and this is most probably only the begining. - -Parallelizing an algorithm using Coach is straight-forward. - -The following method of NetworkWrapper parallelizes an algorithm seamlessly: - -```python -network.train_and_sync_networks(current_states, targets) -``` - -Once a parallelized run is started, the ```train_and_sync_networks``` API will apply gradients from each local worker's network to the main global network, allowing for parallel training to take place. - -Then, it merely requires running Coach with the ``` -n``` flag and with the number of workers to run with. For instance, the following command will set 16 workers to work together to train a MuJoCo Hopper: - -```bash -python3 coach.py -p Hopper_A3C -n 16 -``` - - - -## Supported Environments - -* *OpenAI Gym:* - - Installed by default by Coach's installer. - -* *ViZDoom:* - - Follow the instructions described in the ViZDoom repository - - - https://github.com/mwydmuch/ViZDoom - - Additionally, Coach assumes that the environment variable VIZDOOM_ROOT points to the ViZDoom installation directory. - -* *Roboschool:* - - Follow the instructions described in the roboschool repository - - - https://github.com/openai/roboschool - -* *GymExtensions:* - - Follow the instructions described in the GymExtensions repository - - - https://github.com/Breakend/gym-extensions - - Additionally, add the installation directory to the PYTHONPATH environment variable. - -* *PyBullet:* - - Follow the instructions described in the [Quick Start Guide](https://docs.google.com/document/d/10sXEhzFRSnvFcl3XxNGhnD4N2SedqwdAvK3dsihxVUA) (basically just - 'pip install pybullet') - -* *CARLA:* - - Download release 0.7 from the CARLA repository - - - https://github.com/carla-simulator/carla/releases - - Create a new CARLA_ROOT environment variable pointing to CARLA's installation directory. - - A simple CARLA settings file (```CarlaSettings.ini```) is supplied with Coach, and is located in the ```environments``` directory. - - -## Supported Algorithms - -Coach Design - - - - - -* [Deep Q Network (DQN)](https://www.cs.toronto.edu/~vmnih/docs/dqn.pdf) ([code](agents/dqn_agent.py)) -* [Double Deep Q Network (DDQN)](https://arxiv.org/pdf/1509.06461.pdf) ([code](agents/ddqn_agent.py)) -* [Dueling Q Network](https://arxiv.org/abs/1511.06581) -* [Mixed Monte Carlo (MMC)](https://arxiv.org/abs/1703.01310) ([code](agents/mmc_agent.py)) -* [Persistent Advantage Learning (PAL)](https://arxiv.org/abs/1512.04860) ([code](agents/pal_agent.py)) -* [Categorical Deep Q Network (C51)](https://arxiv.org/abs/1707.06887) ([code](agents/categorical_dqn_agent.py)) -* [Quantile Regression Deep Q Network (QR-DQN)](https://arxiv.org/pdf/1710.10044v1.pdf) ([code](agents/qr_dqn_agent.py)) -* [Bootstrapped Deep Q Network](https://arxiv.org/abs/1602.04621) ([code](agents/bootstrapped_dqn_agent.py)) -* [N-Step Q Learning](https://arxiv.org/abs/1602.01783) | **Distributed** ([code](agents/n_step_q_agent.py)) -* [Neural Episodic Control (NEC)](https://arxiv.org/abs/1703.01988) ([code](agents/nec_agent.py)) -* [Normalized Advantage Functions (NAF)](https://arxiv.org/abs/1603.00748.pdf) | **Distributed** ([code](agents/naf_agent.py)) -* [Policy Gradients (PG)](http://www-anw.cs.umass.edu/~barto/courses/cs687/williams92simple.pdf) | **Distributed** ([code](agents/policy_gradients_agent.py)) -* [Asynchronous Advantage Actor-Critic (A3C)](https://arxiv.org/abs/1602.01783) | **Distributed** ([code](agents/actor_critic_agent.py)) -* [Deep Deterministic Policy Gradients (DDPG)](https://arxiv.org/abs/1509.02971) | **Distributed** ([code](agents/ddpg_agent.py)) -* [Proximal Policy Optimization (PPO)](https://arxiv.org/pdf/1707.06347.pdf) ([code](agents/ppo_agent.py)) -* [Clipped Proximal Policy Optimization](https://arxiv.org/pdf/1707.06347.pdf) | **Distributed** ([code](agents/clipped_ppo_agent.py)) -* [Direct Future Prediction (DFP)](https://arxiv.org/abs/1611.01779) | **Distributed** ([code](agents/dfp_agent.py)) -* Behavioral Cloning (BC) ([code](agents/bc_agent.py)) - - -## Citation - -If you used Coach for your work, please use the following citation: - -``` -@misc{caspi_itai_2017_1134899, - author = {Caspi, Itai and - Leibovich, Gal and - Novik, Gal}, - title = {Reinforcement Learning Coach}, - month = dec, - year = 2017, - doi = {10.5281/zenodo.1134899}, - url = {https://doi.org/10.5281/zenodo.1134899} -} -``` - -## Disclaimer - -Coach is released as a reference code for research purposes. It is not an official Intel product, and the level of quality and support may not be as expected from an official product. -Additional algorithms and environments are planned to be added to the framework. Feedback and contributions from the open source and RL research communities are more than welcome. diff --git a/benchmarks/README.md b/benchmarks/README.md deleted file mode 100644 index ba237e7..0000000 --- a/benchmarks/README.md +++ /dev/null @@ -1,172 +0,0 @@ -# Coach Benchmarks - -The following figures are training curves of some of the presets available through Coach. -The X axis in all the figures is the total steps (for multi-threaded runs, this is the accumulated number of steps over all the workers). -The Y axis in all the figures is the average episode reward with an averaging window of 11 episodes. -These are the results you can expect to get when running the pre-defined presets in Coach. - - -## A3C - -### Breakout_A3C with 16 workers - -```bash -python3 coach.py -p Breakout_A3C -n 16 -r -``` - -Breakout_A3C_16_workers - -### InvertedPendulum_A3C with 16 workers - -```bash -python3 coach.py -p InvertedPendulum_A3C -n 16 -r -``` - -Inverted_Pendulum_A3C_16_workers - -### Hopper_A3C with 16 workers - -```bash -python3 coach.py -p Hopper_A3C -n 16 -r -``` - -Hopper_A3C_16_workers - -### Ant_A3C with 16 workers - -```bash -python3 coach.py -p Ant_A3C -n 16 -r -``` - -Ant_A3C_16_workers - -## Clipped PPO - -### InvertedPendulum_ClippedPPO with 16 workers - -```bash -python3 coach.py -p InvertedPendulum_ClippedPPO -n 16 -r -``` - -InvertedPendulum_ClippedPPO_16_workers - -### Hopper_ClippedPPO with 16 workers - -```bash -python3 coach.py -p Hopper_ClippedPPO -n 16 -r -``` - -Hopper_Clipped_PPO_16_workers - -### Humanoid_ClippedPPO with 16 workers - -```bash -python3 coach.py -p Humanoid_ClippedPPO -n 16 -r -``` - -Humanoid_ClippedPPO_16_workers - -## DQN - -### Pong_DQN - -```bash -python3 coach.py -p Pong_DQN -r -``` - -Pong_DQN - -### Doom_Basic_DQN - -```bash -python3 coach.py -p Doom_Basic_DQN -r -``` - -Doom_Basic_DQN - -## Dueling DDQN - -### Doom_Basic_Dueling_DDQN - -```bash -python3 coach.py -p Doom_Basic_Dueling_DDQN -r -``` - -Doom_Basic_Dueling_DDQN - -## DFP - -### Doom_Health_DFP - -```bash -python3 coach.py -p Doom_Health_DFP -r -``` - -Doom_Health_DFP - -## MMC - -### Doom_Health_MMC - -```bash -python3 coach.py -p Doom_Health_MMC -r -``` - -Doom_Health_MMC - -## NEC - -## Pong_NEC - -```bash -python3 coach.py -p Pong_NEC -r -``` - -Pong_NEC - -## Doom_Basic_NEC - -```bash -python3 coach.py -p Doom_Basic_NEC -r -``` - -Doom_Basic_NEC - -## PG - -### CartPole_PG - -```bash -python3 coach.py -p CartPole_PG -r -``` - -CartPole_PG - -## DDPG - -### Pendulum_DDPG - -```bash -python3 coach.py -p Pendulum_DDPG -r -``` - -Pendulum_DDPG - - -## NAF - -### InvertedPendulum_NAF - -```bash -python3 coach.py -p InvertedPendulum_NAF -r -``` - -InvertedPendulum_NAF - -### Pendulum_NAF - -```bash -python3 coach.py -p Pendulum_NAF -r -``` - -Pendulum_NAF diff --git a/benchmarks/img/Ant_A3C_16_workers.png b/benchmarks/img/Ant_A3C_16_workers.png deleted file mode 100644 index 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    Direct Future Prediction

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    Actions space: Discrete

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    References: Learning to Act by Predicting the Future

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    Network Structure

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    Algorithm Description

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    Choosing an action

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    1. The current states (observations and measurements) and the corresponding goal vector are passed as an input to the network. The output of the network is the predicted future measurements for time-steps and for each possible action.
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    3. For each action, the measurements of each predicted time-step are multiplied by the goal vector, and the result is a single vector of future values for each action.
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    5. Then, a weighted sum of the future values of each action is calculated, and the result is a single value for each action.
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    7. The action values are passed to the exploration policy to decide on the action to use.
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    Training the network

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    Given a batch of transitions, run them through the network to get the current predictions of the future measurements per action, and set them as the initial targets for training the network. For each transition in the batch, the target of the network for the action that was taken, is the actual measurements that were seen in time-steps and . For the actions that were not taken, the targets are the current values.

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    Clipped Proximal Policy Optimization

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    Same as in PPO.

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    Pass the current states through the actor network, and get an action mean vector . While in training phase, use a continuous exploration policy, such as the Ornstein-Uhlenbeck process, to add exploration noise to the action. When testing, use the mean vector as-is.

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    Policy Gradient

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    The policy head loss is defined as . The is used in order to reduce the policy gradient variance, which might be very noisy. This is done in order to reduce the variance of the updates, since noisy gradient updates might destabilize the policy's convergence. The rescaler is a configurable parameter and there are few options to choose from:
    - Total Episode Return - The sum of all the discounted rewards during the episode. - Future Return - Return from each transition until the end of the episode. - Future Return Normalized by Episode - Future returns across the episode normalized by the episode's mean and standard deviation. - Future Return Normalized by Timestep - Future returns normalized using running means and standard deviations, which are calculated seperately for each timestep, across different episodes.

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    Proximal Policy Optimization

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    Run the observation through the policy network, and get the mean and standard deviation vectors for this observation. While in training phase, sample from a multi-dimensional Gaussian distribution with these mean and standard deviation values. When testing, just take the mean values predicted by the network.

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    The current states are used as the input to the network. The network contains several heads, which are used for returning different estimations of the action values. For each episode, the bootstrapped exploration policy selects a single head to play with during the episode. According to the selected head, only the relevant output values are used. Using those values, the exploration policy then selects the action for acting.

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      The Bellman update is projected to the set of atoms representing the values distribution, such that the component of the projected update is calculated as follows: - - where:

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    The network is trained by using the following targets: - -Use the next states as the inputs to the target network and extract the value, from within the head, to get . Then, update the online network using the current states and actions as inputs, and as the targets. -After every training step, use a soft update in order to copy the weights from the online network to the target network.

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    Neural Episodic Control

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    Actions space: Discrete

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    References: Neural Episodic Control

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    Network Structure

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    Algorithm Description

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    Choosing an action

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    1. Use the current state as an input to the online network and extract the state embedding, which is the intermediate output from the middleware.
    2. -
    3. For each possible action , run the DND head using the state embedding and the selected action as inputs. The DND is queried and returns the nearest neighbor keys and values. The keys and values are used to calculate and return the action value from the network.
    4. -
    5. Pass all the values to the exploration policy and choose an action accordingly.
    6. -
    7. Store the state embeddings and actions taken during the current episode in a small buffer , in order to accumulate transitions until it is possible to calculate the total discounted returns over the entire episode.
    8. -
    -

    Finalizing an episode

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    For each step in the episode, the state embeddings and the taken actions are stored in the buffer . When the episode is finished, the replay buffer calculates the -step total return of each transition in the buffer, bootstrapped using the maximum value of the -th transition. Those values are inserted along with the total return into the DND, and the buffer is reset.

    -

    Training the network

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    Train the network only when the DND has enough entries for querying.

    -

    To train the network, the current states are used as the inputs and the -step returns are used as the targets. The -step return used takes into account consecutive steps, and bootstraps the last value from the network if necessary: - -

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    Persistent Advantage Learning

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    Actions space: Discrete

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    References: Increasing the Action Gap: New Operators for Reinforcement Learning

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    Network Structure

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    Algorithm Description

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    Training the network

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      Sample a batch of transitions from the replay buffer.

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      Start by calculating the initial target values in the same manner as they are calculated in DDQN - -

      -
    4. -
    5. The action gap should then be subtracted from each of the calculated targets. To calculate the action gap, run the target network using the current states and get the values for all the actions. Then estimate as the maximum predicted value for the current state: - -
    6. -
    7. For advantage learning (AL), reduce the action gap weighted by a predefined parameter from the targets : - -
    8. -
    9. For persistent advantage learning (PAL), the target network is also used in order to calculate the action gap for the next state: - - where is chosen by running the next states through the online network and choosing the action that has the highest predicted value. Finally, the targets will be defined as - - -
    10. -
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      Train the online network using the current states as inputs, and with the aforementioned targets.

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      Once in every few thousand steps, copy the weights from the online network to the target network.

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    Coach's modularity makes adding an agent a simple and clean task, that involves the following steps:

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      Implement your algorithm in a new file under the agents directory. The agent can inherit base classes such as ValueOptimizationAgent or ActorCriticAgent, or the more generic Agent base class.

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        ValueOptimizationAgent, PolicyOptimizationAgent and Agent are abstract classes. -learn_from_batch() should be overriden with the desired behavior for the algorithm being implemented. If deciding to inherit from Agent, also choose_action() should be overriden.

        -
        def learn_from_batch(self, batch):
        -    """
        -    Given a batch of transitions, calculates their target values and updates the network.
        -    :param batch: A list of transitions
        -    :return: The loss of the training
        -    """
        -    pass
        -
        -def choose_action(self, curr_state, phase=RunPhase.TRAIN):
        -    """
        -    choose an action to act with in the current episode being played. Different behavior might be exhibited when training
        -     or testing.
        -
        -    :param curr_state: the current state to act upon.  
        -    :param phase: the current phase: training or testing.
        -    :return: chosen action, some action value describing the action (q-value, probability, etc)
        -    """
        -    pass
        -
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        Make sure to add your new agent to agents/__init__.py

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      Implement your agent's specific network head, if needed, at the implementation for the framework of your choice. For example architectures/neon_components/heads.py. The head will inherit the generic base class Head. - A new output type should be added to configurations.py, and a mapping between the new head and output type should be defined in the get_output_head() function at architectures/neon_components/general_network.py

      -
    4. -
    5. Define a new configuration class at configurations.py, which includes the new agent name in the type field, the new output type in the output_types field, and assigning default values to hyperparameters.
    6. -
    7. (Optional) Define a preset using the new agent type with a given environment, and the hyperparameters that should be used for training on that environment.
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    Adding a new environment to Coach is as easy as solving CartPole.

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    There are a few simple steps to follow, and we will walk through them one by one.

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      Coach defines a simple API for implementing a new environment which is defined in environment/environment_wrapper.py. - There are several functions to implement, but only some of them are mandatory.

      -

      Here are the important ones:

      -
          def _take_action(self, action_idx):
      -        """
      -        An environment dependent function that sends an action to the simulator.
      -        :param action_idx: the action to perform on the environment.
      -        :return: None
      -        """
      -        pass
      -
      -    def _preprocess_observation(self, observation):
      -        """
      -        Do initial observation preprocessing such as cropping, rgb2gray, rescale etc.
      -        Implementing this function is optional.
      -        :param observation: a raw observation from the environment
      -        :return: the preprocessed observation
      -        """
      -        return observation
      -
      -    def _update_state(self):
      -        """
      -        Updates the state from the environment.
      -        Should update self.observation, self.reward, self.done, self.measurements and self.info
      -        :return: None
      -        """
      -        pass
      -
      -    def _restart_environment_episode(self, force_environment_reset=False):
      -        """
      -        :param force_environment_reset: Force the environment to reset even if the episode is not done yet.
      -        :return:
      -        """
      -        pass
      -
      -    def get_rendered_image(self):
      -        """
      -        Return a numpy array containing the image that will be rendered to the screen.
      -        This can be different from the observation. For example, mujoco's observation is a measurements vector.
      -        :return: numpy array containing the image that will be rendered to the screen
      -        """
      -        return self.observation
      -
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      Make sure to import the environment in environments/__init__.py:

      -
      from doom_environment_wrapper import *
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      Also, a new entry should be added to the EnvTypes enum mapping the environment name to the wrapper's class name:

      -
      Doom = "DoomEnvironmentWrapper"
      -
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    4. -
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      In addition a new configuration class should be implemented for defining the environment's parameters and placed in configurations.py. -For instance, the following is used for Doom:

      -
      class Doom(EnvironmentParameters):
      -    type = 'Doom'
      -    frame_skip = 4
      -    observation_stack_size = 3
      -    desired_observation_height = 60
      -    desired_observation_width = 76
      -
      -
    6. -
    7. -

      And that's it, you're done. Now just add a new preset with your newly created environment, and start training an agent on top of it.

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    Reinforcement learning algorithms are neat. That is - when they work. But when they don't, RL algorithms are often quite tricky to debug.

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    Finding the root cause for why things break in RL is rather difficult. Moreover, different RL algorithms shine in some aspects, but then lack on other. Comparing the algorithms faithfully is also a hard task, which requires the right tools.

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    Coach Dashboard is a visualization tool which simplifies the analysis of the training process. Each run of Coach extracts a lot of information from within the algorithm and stores it in the experiment directory. This information is very valuable for debugging, analyzing and comparing different algorithms. But without a good visualization tool, this information can not be utilized. This is where Coach Dashboard takes place.

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    Visualizing Signals

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    Coach Dashboard exposes a convenient user interface for visualizing the training signals. The signals are dynamically updated - during the agent training. Additionaly, it allows selecting a subset of the available signals, and then overlaying them on top of each other.

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    • Holding the CTRL key, while selecting signals, will allow visualizing more than one signal.
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    Tracking Statistics

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    When running parallel algorithms, such as A3C, it often helps visualizing the learning of all the workers, at the same time. Coach Dashboard allows viewing multiple signals (and even smooth them out, if required) from multiple workers. In addition, it supports viewing the mean and standard deviation of the same signal, across different workers, using Bollinger bands.

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    Comparing Runs

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    Reinforcement learning algorithms are notoriously known as unstable, and suffer from high run-to-run variance. This makes benchmarking and comparing different algorithms even harder. To ease this process, it is common to execute several runs of the same algorithm and average over them. This is easy to do with Coach Dashboard, by centralizing all the experiment directories in a single directory, and then loading them as a single group. Loading several groups of different algorithms then allows comparing the averaged signals, such as the total episode reward.

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    In RL, there are several interesting performance metrics to consider, and this is easy to do by controlling the X-axis units in Coach Dashboard. It is possible to switch between several options such as the total number of steps or the total training time.

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    - -Comparing By Time - - -Comparing Several Algorithms According to the Time Passed - - - - -Comparing By Number of Episodes - - -Comparing Several Algorithms According to the Number of Episodes Played - - -
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    Network Design

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    Each agent has at least one neural network, used as the function approximator, for choosing the actions. The network is designed in a modular way to allow reusability in different agents. It is separated into three main parts:

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      Input Embedders - This is the first stage of the network, meant to convert the input into a feature vector representation. It is possible to combine several instances of any of the supported embedders, in order to allow varied combinations of inputs.

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      Middlewares - The middleware gets the output of the input embedder, and processes it into a different representation domain, before sending it through the output head. The goal of the middleware is to enable processing the combined outputs of several input embedders, and pass them through some extra processing. This, for instance, might include an LSTM or just a plain simple FC layer.

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      Output Heads - The output head is used in order to predict the values required from the network. These might include action-values, state-values or a policy. As with the input embedders, it is possible to use several output heads in the same network. For example, the Actor Critic agent combines two heads - a policy head and a state-value head. - In addition, the output heads defines the loss function according to the head type.

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    Keeping Network Copies in Sync

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    Most of the reinforcement learning agents include more than one copy of the neural network. These copies serve as counterparts of the main network which are updated in different rates, and are often synchronized either locally or between parallel workers. For easier synchronization of those copies, a wrapper around these copies exposes a simplified API, which allows hiding these complexities from the agent.

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    - -Distributed Training - -

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    Supported Algorithms

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    Coach supports many state-of-the-art reinforcement learning algorithms, which are separated into two main classes - value optimization and policy optimization. A detailed description of those algorithms may be found in the algorithms section.

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    - -Supported Algorithms - -

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    • Behavioral Cloning
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    Behavioral Cloning

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    Actions space: Discrete|Continuous

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    Network Structure

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    Algorithm Description

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    Training the network

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    The replay buffer contains the expert demonstrations for the task. -These demonstrations are given as state, action tuples, and with no reward. -The training goal is to reduce the difference between the actions predicted by the network and the actions taken by the expert for each state.

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    1. Sample a batch of transitions from the replay buffer.
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    3. Use the current states as input to the network, and the expert actions as the targets of the network.
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    5. The loss function for the network is MSE, and therefore we use the Q head to minimize this loss.
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        What is Coach?

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        Motivation

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        Train and evaluate reinforcement learning agents by harnessing the power of multi-core CPU processing to achieve state-of-the-art results. Provide a sandbox for easing the development process of new algorithms through a modular design and an elegant set of APIs.

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        Solution

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        Coach is a python environment which models the interaction between an agent and an environment in a modular way. -With Coach, it is possible to model an agent by combining various building blocks, and training the agent on multiple environments. -The available environments allow testing the agent in different practical fields such as robotics, autonomous driving, games and more. -Coach collects statistics from the training process and supports advanced visualization techniques for debugging the agent being trained.

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        Blog post from the IntelĀ® Nervanaā„¢ website can be found here.

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        GitHub repository is here.

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        Design

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        Coach Design

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pmulhuw psadbw pshufw pf2iw pfnacc pfpnacc pi2fw pswapd maskmovdqu clflush movntdq movnti movntpd movdqa movdqu movdq2q movq2dq paddq pmuludq pshufd pshufhw pshuflw pslldq psrldq psubq punpckhqdq punpcklqdq addpd addsd andnpd andpd cmpeqpd cmpeqsd cmplepd cmplesd cmpltpd cmpltsd cmpneqpd cmpneqsd cmpnlepd cmpnlesd cmpnltpd cmpnltsd cmpordpd cmpordsd cmpunordpd cmpunordsd cmppd comisd cvtdq2pd cvtdq2ps cvtpd2dq cvtpd2pi cvtpd2ps cvtpi2pd cvtps2dq cvtps2pd cvtsd2si cvtsd2ss cvtsi2sd cvtss2sd cvttpd2pi cvttpd2dq cvttps2dq cvttsd2si divpd divsd maxpd maxsd minpd minsd movapd movhpd movlpd movmskpd movupd mulpd mulsd orpd shufpd sqrtpd sqrtsd subpd subsd ucomisd unpckhpd unpcklpd xorpd addsubpd addsubps haddpd haddps hsubpd hsubps lddqu movddup movshdup movsldup clgi stgi vmcall vmclear vmfunc vmlaunch vmload vmmcall vmptrld vmptrst vmread vmresume vmrun vmsave vmwrite vmxoff vmxon invept invvpid pabsb pabsw pabsd palignr phaddw phaddd phaddsw phsubw phsubd phsubsw pmaddubsw pmulhrsw pshufb psignb psignw psignd extrq insertq movntsd movntss lzcnt blendpd blendps blendvpd blendvps dppd dpps extractps insertps movntdqa mpsadbw packusdw pblendvb pblendw pcmpeqq pextrb pextrd pextrq phminposuw pinsrb pinsrd pinsrq pmaxsb pmaxsd pmaxud pmaxuw pminsb pminsd pminud pminuw pmovsxbw pmovsxbd pmovsxbq pmovsxwd pmovsxwq pmovsxdq pmovzxbw pmovzxbd pmovzxbq pmovzxwd pmovzxwq pmovzxdq pmuldq pmulld ptest roundpd roundps roundsd roundss crc32 pcmpestri pcmpestrm pcmpistri pcmpistrm pcmpgtq popcnt getsec pfrcpv pfrsqrtv movbe aesenc aesenclast aesdec aesdeclast aesimc aeskeygenassist vaesenc vaesenclast vaesdec vaesdeclast vaesimc vaeskeygenassist vaddpd vaddps vaddsd vaddss vaddsubpd vaddsubps vandpd vandps vandnpd vandnps vblendpd vblendps vblendvpd vblendvps vbroadcastss vbroadcastsd vbroadcastf128 vcmpeq_ospd vcmpeqpd vcmplt_ospd vcmpltpd vcmple_ospd vcmplepd vcmpunord_qpd vcmpunordpd vcmpneq_uqpd vcmpneqpd vcmpnlt_uspd vcmpnltpd vcmpnle_uspd vcmpnlepd vcmpord_qpd vcmpordpd vcmpeq_uqpd vcmpnge_uspd vcmpngepd vcmpngt_uspd vcmpngtpd vcmpfalse_oqpd vcmpfalsepd vcmpneq_oqpd vcmpge_ospd vcmpgepd vcmpgt_ospd vcmpgtpd vcmptrue_uqpd vcmptruepd vcmplt_oqpd vcmple_oqpd vcmpunord_spd vcmpneq_uspd vcmpnlt_uqpd vcmpnle_uqpd vcmpord_spd vcmpeq_uspd vcmpnge_uqpd vcmpngt_uqpd vcmpfalse_ospd vcmpneq_ospd vcmpge_oqpd vcmpgt_oqpd vcmptrue_uspd vcmppd vcmpeq_osps vcmpeqps vcmplt_osps vcmpltps vcmple_osps vcmpleps vcmpunord_qps vcmpunordps vcmpneq_uqps vcmpneqps vcmpnlt_usps vcmpnltps vcmpnle_usps vcmpnleps vcmpord_qps vcmpordps vcmpeq_uqps vcmpnge_usps vcmpngeps vcmpngt_usps vcmpngtps vcmpfalse_oqps vcmpfalseps vcmpneq_oqps vcmpge_osps vcmpgeps vcmpgt_osps vcmpgtps vcmptrue_uqps vcmptrueps vcmplt_oqps vcmple_oqps vcmpunord_sps vcmpneq_usps vcmpnlt_uqps vcmpnle_uqps vcmpord_sps vcmpeq_usps vcmpnge_uqps vcmpngt_uqps vcmpfalse_osps vcmpneq_osps vcmpge_oqps vcmpgt_oqps vcmptrue_usps vcmpps vcmpeq_ossd vcmpeqsd vcmplt_ossd vcmpltsd vcmple_ossd vcmplesd vcmpunord_qsd vcmpunordsd vcmpneq_uqsd vcmpneqsd vcmpnlt_ussd vcmpnltsd vcmpnle_ussd vcmpnlesd vcmpord_qsd vcmpordsd vcmpeq_uqsd vcmpnge_ussd vcmpngesd vcmpngt_ussd vcmpngtsd vcmpfalse_oqsd vcmpfalsesd vcmpneq_oqsd vcmpge_ossd vcmpgesd vcmpgt_ossd vcmpgtsd vcmptrue_uqsd vcmptruesd vcmplt_oqsd vcmple_oqsd vcmpunord_ssd vcmpneq_ussd vcmpnlt_uqsd vcmpnle_uqsd vcmpord_ssd vcmpeq_ussd vcmpnge_uqsd vcmpngt_uqsd vcmpfalse_ossd vcmpneq_ossd vcmpge_oqsd vcmpgt_oqsd vcmptrue_ussd vcmpsd vcmpeq_osss vcmpeqss vcmplt_osss vcmpltss vcmple_osss vcmpless vcmpunord_qss vcmpunordss vcmpneq_uqss vcmpneqss vcmpnlt_usss vcmpnltss vcmpnle_usss vcmpnless vcmpord_qss vcmpordss vcmpeq_uqss vcmpnge_usss vcmpngess vcmpngt_usss vcmpngtss vcmpfalse_oqss vcmpfalsess vcmpneq_oqss vcmpge_osss vcmpgess vcmpgt_osss vcmpgtss vcmptrue_uqss vcmptruess vcmplt_oqss vcmple_oqss vcmpunord_sss vcmpneq_usss vcmpnlt_uqss vcmpnle_uqss vcmpord_sss vcmpeq_usss vcmpnge_uqss vcmpngt_uqss vcmpfalse_osss vcmpneq_osss vcmpge_oqss vcmpgt_oqss vcmptrue_usss vcmpss vcomisd vcomiss vcvtdq2pd vcvtdq2ps vcvtpd2dq vcvtpd2ps vcvtps2dq vcvtps2pd vcvtsd2si vcvtsd2ss vcvtsi2sd vcvtsi2ss vcvtss2sd vcvtss2si vcvttpd2dq vcvttps2dq vcvttsd2si vcvttss2si vdivpd vdivps vdivsd vdivss vdppd vdpps vextractf128 vextractps vhaddpd vhaddps vhsubpd vhsubps vinsertf128 vinsertps vlddqu vldqqu vldmxcsr vmaskmovdqu vmaskmovps vmaskmovpd vmaxpd vmaxps vmaxsd vmaxss vminpd vminps vminsd vminss vmovapd vmovaps vmovd vmovq vmovddup vmovdqa vmovqqa vmovdqu vmovqqu vmovhlps vmovhpd vmovhps vmovlhps vmovlpd vmovlps vmovmskpd vmovmskps vmovntdq vmovntqq vmovntdqa vmovntpd vmovntps vmovsd vmovshdup vmovsldup vmovss vmovupd vmovups vmpsadbw vmulpd vmulps vmulsd vmulss vorpd vorps vpabsb vpabsw vpabsd vpacksswb vpackssdw vpackuswb vpackusdw vpaddb vpaddw vpaddd vpaddq vpaddsb vpaddsw vpaddusb vpaddusw vpalignr vpand vpandn vpavgb vpavgw vpblendvb vpblendw vpcmpestri vpcmpestrm vpcmpistri vpcmpistrm vpcmpeqb vpcmpeqw vpcmpeqd vpcmpeqq vpcmpgtb vpcmpgtw vpcmpgtd vpcmpgtq vpermilpd vpermilps vperm2f128 vpextrb vpextrw vpextrd vpextrq vphaddw vphaddd vphaddsw vphminposuw vphsubw vphsubd vphsubsw vpinsrb vpinsrw vpinsrd vpinsrq vpmaddwd vpmaddubsw vpmaxsb vpmaxsw vpmaxsd vpmaxub vpmaxuw vpmaxud vpminsb vpminsw vpminsd vpminub vpminuw vpminud vpmovmskb vpmovsxbw vpmovsxbd vpmovsxbq vpmovsxwd vpmovsxwq vpmovsxdq vpmovzxbw vpmovzxbd vpmovzxbq vpmovzxwd vpmovzxwq vpmovzxdq vpmulhuw vpmulhrsw vpmulhw vpmullw vpmulld vpmuludq vpmuldq vpor vpsadbw vpshufb vpshufd vpshufhw vpshuflw vpsignb vpsignw vpsignd vpslldq vpsrldq vpsllw vpslld vpsllq vpsraw vpsrad vpsrlw vpsrld vpsrlq vptest vpsubb vpsubw vpsubd vpsubq vpsubsb vpsubsw vpsubusb vpsubusw vpunpckhbw vpunpckhwd vpunpckhdq vpunpckhqdq vpunpcklbw vpunpcklwd vpunpckldq vpunpcklqdq vpxor vrcpps vrcpss vrsqrtps vrsqrtss vroundpd vroundps vroundsd vroundss vshufpd vshufps vsqrtpd vsqrtps vsqrtsd vsqrtss vstmxcsr vsubpd vsubps vsubsd vsubss vtestps vtestpd vucomisd vucomiss vunpckhpd vunpckhps vunpcklpd vunpcklps vxorpd vxorps vzeroall vzeroupper pclmullqlqdq pclmulhqlqdq pclmullqhqdq pclmulhqhqdq pclmulqdq vpclmullqlqdq vpclmulhqlqdq vpclmullqhqdq vpclmulhqhqdq vpclmulqdq vfmadd132ps vfmadd132pd vfmadd312ps vfmadd312pd vfmadd213ps vfmadd213pd vfmadd123ps vfmadd123pd vfmadd231ps vfmadd231pd vfmadd321ps vfmadd321pd vfmaddsub132ps vfmaddsub132pd vfmaddsub312ps vfmaddsub312pd vfmaddsub213ps vfmaddsub213pd vfmaddsub123ps vfmaddsub123pd vfmaddsub231ps vfmaddsub231pd vfmaddsub321ps vfmaddsub321pd vfmsub132ps vfmsub132pd vfmsub312ps vfmsub312pd vfmsub213ps vfmsub213pd vfmsub123ps vfmsub123pd vfmsub231ps vfmsub231pd vfmsub321ps vfmsub321pd vfmsubadd132ps vfmsubadd132pd vfmsubadd312ps vfmsubadd312pd vfmsubadd213ps vfmsubadd213pd vfmsubadd123ps vfmsubadd123pd vfmsubadd231ps vfmsubadd231pd vfmsubadd321ps vfmsubadd321pd vfnmadd132ps vfnmadd132pd vfnmadd312ps vfnmadd312pd vfnmadd213ps vfnmadd213pd vfnmadd123ps vfnmadd123pd vfnmadd231ps vfnmadd231pd vfnmadd321ps vfnmadd321pd vfnmsub132ps vfnmsub132pd vfnmsub312ps vfnmsub312pd vfnmsub213ps vfnmsub213pd vfnmsub123ps vfnmsub123pd vfnmsub231ps vfnmsub231pd vfnmsub321ps vfnmsub321pd vfmadd132ss vfmadd132sd vfmadd312ss vfmadd312sd vfmadd213ss vfmadd213sd vfmadd123ss vfmadd123sd vfmadd231ss vfmadd231sd vfmadd321ss vfmadd321sd vfmsub132ss vfmsub132sd vfmsub312ss vfmsub312sd vfmsub213ss vfmsub213sd vfmsub123ss vfmsub123sd vfmsub231ss vfmsub231sd vfmsub321ss vfmsub321sd vfnmadd132ss vfnmadd132sd vfnmadd312ss vfnmadd312sd vfnmadd213ss vfnmadd213sd vfnmadd123ss vfnmadd123sd vfnmadd231ss vfnmadd231sd vfnmadd321ss vfnmadd321sd vfnmsub132ss vfnmsub132sd vfnmsub312ss vfnmsub312sd vfnmsub213ss vfnmsub213sd vfnmsub123ss vfnmsub123sd vfnmsub231ss vfnmsub231sd vfnmsub321ss vfnmsub321sd rdfsbase rdgsbase rdrand wrfsbase wrgsbase vcvtph2ps vcvtps2ph adcx adox rdseed clac stac xstore xcryptecb xcryptcbc xcryptctr xcryptcfb xcryptofb montmul xsha1 xsha256 llwpcb slwpcb lwpval lwpins vfmaddpd vfmaddps vfmaddsd vfmaddss vfmaddsubpd vfmaddsubps vfmsubaddpd vfmsubaddps vfmsubpd vfmsubps vfmsubsd vfmsubss vfnmaddpd vfnmaddps vfnmaddsd vfnmaddss vfnmsubpd vfnmsubps vfnmsubsd vfnmsubss vfrczpd vfrczps vfrczsd vfrczss vpcmov vpcomb vpcomd vpcomq vpcomub vpcomud vpcomuq vpcomuw vpcomw vphaddbd vphaddbq vphaddbw vphadddq vphaddubd vphaddubq vphaddubw vphaddudq vphadduwd vphadduwq vphaddwd vphaddwq vphsubbw vphsubdq vphsubwd vpmacsdd vpmacsdqh vpmacsdql vpmacssdd vpmacssdqh vpmacssdql vpmacsswd vpmacssww vpmacswd vpmacsww vpmadcsswd vpmadcswd vpperm vprotb vprotd vprotq vprotw vpshab vpshad vpshaq vpshaw vpshlb vpshld vpshlq vpshlw vbroadcasti128 vpblendd vpbroadcastb vpbroadcastw vpbroadcastd vpbroadcastq vpermd vpermpd vpermps vpermq vperm2i128 vextracti128 vinserti128 vpmaskmovd vpmaskmovq vpsllvd vpsllvq vpsravd vpsrlvd vpsrlvq vgatherdpd vgatherqpd vgatherdps vgatherqps vpgatherdd vpgatherqd vpgatherdq vpgatherqq xabort xbegin xend xtest andn bextr blci blcic blsi blsic blcfill blsfill blcmsk blsmsk blsr blcs bzhi mulx pdep pext rorx sarx shlx shrx tzcnt tzmsk t1mskc valignd valignq vblendmpd vblendmps vbroadcastf32x4 vbroadcastf64x4 vbroadcasti32x4 vbroadcasti64x4 vcompresspd vcompressps vcvtpd2udq vcvtps2udq vcvtsd2usi vcvtss2usi vcvttpd2udq vcvttps2udq vcvttsd2usi vcvttss2usi vcvtudq2pd vcvtudq2ps vcvtusi2sd vcvtusi2ss vexpandpd vexpandps vextractf32x4 vextractf64x4 vextracti32x4 vextracti64x4 vfixupimmpd vfixupimmps vfixupimmsd vfixupimmss vgetexppd vgetexpps vgetexpsd vgetexpss vgetmantpd vgetmantps vgetmantsd vgetmantss vinsertf32x4 vinsertf64x4 vinserti32x4 vinserti64x4 vmovdqa32 vmovdqa64 vmovdqu32 vmovdqu64 vpabsq vpandd vpandnd vpandnq vpandq vpblendmd vpblendmq vpcmpltd vpcmpled vpcmpneqd vpcmpnltd vpcmpnled vpcmpd vpcmpltq vpcmpleq vpcmpneqq vpcmpnltq vpcmpnleq vpcmpq vpcmpequd vpcmpltud vpcmpleud vpcmpnequd vpcmpnltud vpcmpnleud vpcmpud vpcmpequq vpcmpltuq vpcmpleuq vpcmpnequq vpcmpnltuq vpcmpnleuq vpcmpuq vpcompressd vpcompressq vpermi2d vpermi2pd vpermi2ps vpermi2q vpermt2d vpermt2pd vpermt2ps vpermt2q vpexpandd vpexpandq vpmaxsq vpmaxuq vpminsq vpminuq vpmovdb vpmovdw vpmovqb vpmovqd vpmovqw vpmovsdb vpmovsdw vpmovsqb vpmovsqd vpmovsqw vpmovusdb vpmovusdw vpmovusqb vpmovusqd vpmovusqw vpord vporq vprold vprolq vprolvd vprolvq vprord vprorq vprorvd vprorvq vpscatterdd vpscatterdq vpscatterqd vpscatterqq vpsraq vpsravq vpternlogd vpternlogq vptestmd vptestmq vptestnmd vptestnmq vpxord vpxorq vrcp14pd vrcp14ps vrcp14sd vrcp14ss vrndscalepd vrndscaleps vrndscalesd vrndscaless vrsqrt14pd vrsqrt14ps vrsqrt14sd vrsqrt14ss vscalefpd vscalefps vscalefsd vscalefss vscatterdpd vscatterdps vscatterqpd vscatterqps vshuff32x4 vshuff64x2 vshufi32x4 vshufi64x2 kandnw kandw kmovw knotw kortestw korw kshiftlw kshiftrw kunpckbw kxnorw kxorw vpbroadcastmb2q vpbroadcastmw2d vpconflictd vpconflictq vplzcntd vplzcntq vexp2pd vexp2ps vrcp28pd vrcp28ps vrcp28sd vrcp28ss vrsqrt28pd vrsqrt28ps vrsqrt28sd vrsqrt28ss vgatherpf0dpd vgatherpf0dps vgatherpf0qpd vgatherpf0qps vgatherpf1dpd vgatherpf1dps vgatherpf1qpd vgatherpf1qps vscatterpf0dpd vscatterpf0dps vscatterpf0qpd vscatterpf0qps vscatterpf1dpd vscatterpf1dps vscatterpf1qpd vscatterpf1qps prefetchwt1 bndmk bndcl bndcu bndcn bndmov bndldx bndstx sha1rnds4 sha1nexte sha1msg1 sha1msg2 sha256rnds2 sha256msg1 sha256msg2 hint_nop0 hint_nop1 hint_nop2 hint_nop3 hint_nop4 hint_nop5 hint_nop6 hint_nop7 hint_nop8 hint_nop9 hint_nop10 hint_nop11 hint_nop12 hint_nop13 hint_nop14 hint_nop15 hint_nop16 hint_nop17 hint_nop18 hint_nop19 hint_nop20 hint_nop21 hint_nop22 hint_nop23 hint_nop24 hint_nop25 hint_nop26 hint_nop27 hint_nop28 hint_nop29 hint_nop30 hint_nop31 hint_nop32 hint_nop33 hint_nop34 hint_nop35 hint_nop36 hint_nop37 hint_nop38 hint_nop39 hint_nop40 hint_nop41 hint_nop42 hint_nop43 hint_nop44 hint_nop45 hint_nop46 hint_nop47 hint_nop48 hint_nop49 hint_nop50 hint_nop51 hint_nop52 hint_nop53 hint_nop54 hint_nop55 hint_nop56 hint_nop57 hint_nop58 hint_nop59 hint_nop60 hint_nop61 hint_nop62 hint_nop63",literal:"ip eip rip al ah bl bh cl ch dl dh sil dil bpl spl r8b r9b r10b r11b r12b r13b r14b r15b ax bx cx dx si di bp sp r8w r9w r10w r11w r12w r13w r14w r15w eax ebx ecx edx esi edi ebp esp eip r8d r9d r10d r11d r12d r13d r14d r15d rax rbx rcx rdx rsi rdi rbp rsp r8 r9 r10 r11 r12 r13 r14 r15 cs ds es fs gs ss st st0 st1 st2 st3 st4 st5 st6 st7 mm0 mm1 mm2 mm3 mm4 mm5 mm6 mm7 xmm0 xmm1 xmm2 xmm3 xmm4 xmm5 xmm6 xmm7 xmm8 xmm9 xmm10 xmm11 xmm12 xmm13 xmm14 xmm15 xmm16 xmm17 xmm18 xmm19 xmm20 xmm21 xmm22 xmm23 xmm24 xmm25 xmm26 xmm27 xmm28 xmm29 xmm30 xmm31 ymm0 ymm1 ymm2 ymm3 ymm4 ymm5 ymm6 ymm7 ymm8 ymm9 ymm10 ymm11 ymm12 ymm13 ymm14 ymm15 ymm16 ymm17 ymm18 ymm19 ymm20 ymm21 ymm22 ymm23 ymm24 ymm25 ymm26 ymm27 ymm28 ymm29 ymm30 ymm31 zmm0 zmm1 zmm2 zmm3 zmm4 zmm5 zmm6 zmm7 zmm8 zmm9 zmm10 zmm11 zmm12 zmm13 zmm14 zmm15 zmm16 zmm17 zmm18 zmm19 zmm20 zmm21 zmm22 zmm23 zmm24 zmm25 zmm26 zmm27 zmm28 zmm29 zmm30 zmm31 k0 k1 k2 k3 k4 k5 k6 k7 bnd0 bnd1 bnd2 bnd3 cr0 cr1 cr2 cr3 cr4 cr8 dr0 dr1 dr2 dr3 dr8 tr3 tr4 tr5 tr6 tr7 r0 r1 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Antialiasing Antisymmetric Apart ApartSquareFree Appearance AppearanceElements AppellF1 Append AppendTo Apply ArcCos ArcCosh ArcCot ArcCoth ArcCsc ArcCsch ArcSec ArcSech ArcSin ArcSinDistribution ArcSinh ArcTan ArcTanh Arg ArgMax ArgMin ArgumentCountQ ARIMAProcess ArithmeticGeometricMean ARMAProcess ARProcess Array ArrayComponents ArrayDepth ArrayFlatten ArrayPad ArrayPlot ArrayQ ArrayReshape ArrayRules Arrays Arrow Arrow3DBox ArrowBox Arrowheads AspectRatio AspectRatioFixed Assert Assuming Assumptions AstronomicalData Asynchronous AsynchronousTaskObject AsynchronousTasks AtomQ Attributes AugmentedSymmetricPolynomial AutoAction AutoDelete AutoEvaluateEvents AutoGeneratedPackage AutoIndent AutoIndentSpacings AutoItalicWords AutoloadPath AutoMatch Automatic AutomaticImageSize AutoMultiplicationSymbol AutoNumberFormatting AutoOpenNotebooks AutoOpenPalettes AutorunSequencing AutoScaling AutoScroll AutoSpacing AutoStyleOptions AutoStyleWords Axes AxesEdge AxesLabel AxesOrigin AxesStyle Axis BabyMonsterGroupB Back Background BackgroundTasksSettings Backslash Backsubstitution Backward Band BandpassFilter BandstopFilter BarabasiAlbertGraphDistribution BarChart BarChart3D BarLegend BarlowProschanImportance BarnesG BarOrigin BarSpacing BartlettHannWindow BartlettWindow BaseForm Baseline BaselinePosition BaseStyle BatesDistribution BattleLemarieWavelet Because BeckmannDistribution Beep Before Begin BeginDialogPacket BeginFrontEndInteractionPacket BeginPackage BellB BellY Below BenfordDistribution BeniniDistribution BenktanderGibratDistribution BenktanderWeibullDistribution BernoulliB BernoulliDistribution BernoulliGraphDistribution BernoulliProcess BernsteinBasis BesselFilterModel BesselI BesselJ BesselJZero BesselK BesselY BesselYZero Beta BetaBinomialDistribution BetaDistribution BetaNegativeBinomialDistribution BetaPrimeDistribution BetaRegularized BetweennessCentrality BezierCurve BezierCurve3DBox BezierCurve3DBoxOptions BezierCurveBox BezierCurveBoxOptions BezierFunction BilateralFilter Binarize BinaryFormat BinaryImageQ BinaryRead BinaryReadList BinaryWrite BinCounts BinLists Binomial BinomialDistribution BinomialProcess BinormalDistribution BiorthogonalSplineWavelet BipartiteGraphQ BirnbaumImportance BirnbaumSaundersDistribution BitAnd BitClear BitGet BitLength BitNot BitOr BitSet BitShiftLeft BitShiftRight BitXor Black BlackmanHarrisWindow BlackmanNuttallWindow BlackmanWindow Blank BlankForm BlankNullSequence BlankSequence Blend Block BlockRandom BlomqvistBeta BlomqvistBetaTest Blue Blur BodePlot BohmanWindow Bold Bookmarks Boole BooleanConsecutiveFunction BooleanConvert BooleanCountingFunction BooleanFunction BooleanGraph BooleanMaxterms BooleanMinimize BooleanMinterms Booleans BooleanTable BooleanVariables BorderDimensions BorelTannerDistribution Bottom BottomHatTransform BoundaryStyle Bounds Box BoxBaselineShift BoxData BoxDimensions Boxed Boxes BoxForm BoxFormFormatTypes BoxFrame BoxID BoxMargins BoxMatrix BoxRatios BoxRotation BoxRotationPoint BoxStyle BoxWhiskerChart Bra BracketingBar BraKet BrayCurtisDistance BreadthFirstScan Break Brown BrownForsytheTest BrownianBridgeProcess BrowserCategory BSplineBasis BSplineCurve BSplineCurve3DBox BSplineCurveBox BSplineCurveBoxOptions BSplineFunction BSplineSurface BSplineSurface3DBox BubbleChart BubbleChart3D BubbleScale BubbleSizes BulletGauge BusinessDayQ ButterflyGraph ButterworthFilterModel Button ButtonBar ButtonBox ButtonBoxOptions ButtonCell ButtonContents ButtonData ButtonEvaluator ButtonExpandable ButtonFrame ButtonFunction ButtonMargins ButtonMinHeight ButtonNote ButtonNotebook ButtonSource ButtonStyle ButtonStyleMenuListing Byte ByteCount ByteOrdering C CachedValue CacheGraphics CalendarData CalendarType CallPacket CanberraDistance Cancel CancelButton CandlestickChart Cap CapForm CapitalDifferentialD CardinalBSplineBasis CarmichaelLambda Cases Cashflow Casoratian Catalan CatalanNumber Catch CauchyDistribution CauchyWindow CayleyGraph CDF CDFDeploy CDFInformation CDFWavelet Ceiling Cell CellAutoOverwrite CellBaseline CellBoundingBox CellBracketOptions CellChangeTimes CellContents CellContext CellDingbat CellDynamicExpression CellEditDuplicate CellElementsBoundingBox CellElementSpacings CellEpilog CellEvaluationDuplicate CellEvaluationFunction CellEventActions CellFrame CellFrameColor CellFrameLabelMargins CellFrameLabels CellFrameMargins CellGroup CellGroupData CellGrouping CellGroupingRules CellHorizontalScrolling CellID CellLabel CellLabelAutoDelete CellLabelMargins CellLabelPositioning CellMargins CellObject CellOpen CellPrint CellProlog Cells CellSize CellStyle CellTags CellularAutomaton CensoredDistribution Censoring Center CenterDot CentralMoment CentralMomentGeneratingFunction CForm ChampernowneNumber ChanVeseBinarize Character CharacterEncoding CharacterEncodingsPath CharacteristicFunction CharacteristicPolynomial CharacterRange Characters ChartBaseStyle ChartElementData ChartElementDataFunction ChartElementFunction ChartElements ChartLabels ChartLayout ChartLegends ChartStyle Chebyshev1FilterModel Chebyshev2FilterModel ChebyshevDistance ChebyshevT ChebyshevU Check CheckAbort CheckAll Checkbox CheckboxBar CheckboxBox CheckboxBoxOptions ChemicalData ChessboardDistance ChiDistribution ChineseRemainder ChiSquareDistribution ChoiceButtons ChoiceDialog CholeskyDecomposition Chop Circle CircleBox CircleDot CircleMinus CirclePlus CircleTimes CirculantGraph CityData Clear ClearAll ClearAttributes ClearSystemCache ClebschGordan ClickPane Clip ClipboardNotebook ClipFill ClippingStyle ClipPlanes ClipRange Clock ClockGauge ClockwiseContourIntegral Close Closed CloseKernels ClosenessCentrality Closing ClosingAutoSave ClosingEvent ClusteringComponents CMYKColor Coarse Coefficient CoefficientArrays CoefficientDomain CoefficientList CoefficientRules CoifletWavelet Collect Colon ColonForm ColorCombine ColorConvert ColorData ColorDataFunction ColorFunction ColorFunctionScaling Colorize ColorNegate ColorOutput ColorProfileData ColorQuantize ColorReplace ColorRules ColorSelectorSettings ColorSeparate ColorSetter ColorSetterBox ColorSetterBoxOptions ColorSlider ColorSpace Column ColumnAlignments ColumnBackgrounds ColumnForm ColumnLines ColumnsEqual ColumnSpacings ColumnWidths CommonDefaultFormatTypes Commonest CommonestFilter CommonUnits CommunityBoundaryStyle CommunityGraphPlot CommunityLabels CommunityRegionStyle CompatibleUnitQ CompilationOptions CompilationTarget Compile Compiled CompiledFunction Complement CompleteGraph CompleteGraphQ CompleteKaryTree CompletionsListPacket Complex Complexes ComplexExpand ComplexInfinity ComplexityFunction ComponentMeasurements ComponentwiseContextMenu Compose ComposeList ComposeSeries Composition CompoundExpression CompoundPoissonDistribution CompoundPoissonProcess CompoundRenewalProcess Compress CompressedData Condition ConditionalExpression Conditioned Cone ConeBox ConfidenceLevel ConfidenceRange ConfidenceTransform ConfigurationPath Congruent Conjugate ConjugateTranspose Conjunction Connect ConnectedComponents ConnectedGraphQ ConnesWindow ConoverTest ConsoleMessage ConsoleMessagePacket ConsolePrint Constant ConstantArray Constants ConstrainedMax ConstrainedMin ContentPadding ContentsBoundingBox ContentSelectable ContentSize Context ContextMenu Contexts ContextToFilename ContextToFileName Continuation Continue ContinuedFraction ContinuedFractionK ContinuousAction ContinuousMarkovProcess ContinuousTimeModelQ ContinuousWaveletData ContinuousWaveletTransform ContourDetect ContourGraphics ContourIntegral ContourLabels ContourLines ContourPlot ContourPlot3D Contours ContourShading ContourSmoothing ContourStyle ContraharmonicMean Control ControlActive ControlAlignment ControllabilityGramian ControllabilityMatrix ControllableDecomposition ControllableModelQ ControllerDuration ControllerInformation ControllerInformationData ControllerLinking ControllerManipulate ControllerMethod ControllerPath ControllerState ControlPlacement ControlsRendering ControlType Convergents ConversionOptions ConversionRules ConvertToBitmapPacket ConvertToPostScript ConvertToPostScriptPacket Convolve ConwayGroupCo1 ConwayGroupCo2 ConwayGroupCo3 CoordinateChartData CoordinatesToolOptions CoordinateTransform CoordinateTransformData CoprimeQ Coproduct CopulaDistribution Copyable CopyDirectory CopyFile CopyTag CopyToClipboard CornerFilter CornerNeighbors Correlation CorrelationDistance CorrelationFunction CorrelationTest Cos Cosh CoshIntegral CosineDistance CosineWindow CosIntegral Cot Coth Count CounterAssignments CounterBox CounterBoxOptions CounterClockwiseContourIntegral CounterEvaluator CounterFunction CounterIncrements CounterStyle CounterStyleMenuListing CountRoots CountryData Covariance CovarianceEstimatorFunction CovarianceFunction CoxianDistribution CoxIngersollRossProcess CoxModel CoxModelFit CramerVonMisesTest CreateArchive CreateDialog CreateDirectory CreateDocument CreateIntermediateDirectories CreatePalette CreatePalettePacket CreateScheduledTask CreateTemporary CreateWindow CriticalityFailureImportance CriticalitySuccessImportance CriticalSection Cross CrossingDetect CrossMatrix Csc Csch CubeRoot Cubics Cuboid CuboidBox Cumulant CumulantGeneratingFunction Cup CupCap Curl CurlyDoubleQuote CurlyQuote CurrentImage CurrentlySpeakingPacket CurrentValue CurvatureFlowFilter CurveClosed Cyan CycleGraph CycleIndexPolynomial Cycles CyclicGroup Cyclotomic Cylinder CylinderBox CylindricalDecomposition D DagumDistribution DamerauLevenshteinDistance DampingFactor Darker Dashed Dashing DataCompression DataDistribution DataRange DataReversed Date DateDelimiters DateDifference DateFunction DateList DateListLogPlot DateListPlot DatePattern DatePlus DateRange DateString DateTicksFormat DaubechiesWavelet DavisDistribution DawsonF DayCount DayCountConvention DayMatchQ DayName DayPlus DayRange DayRound DeBruijnGraph Debug DebugTag Decimal DeclareKnownSymbols DeclarePackage Decompose Decrement DedekindEta Default DefaultAxesStyle DefaultBaseStyle DefaultBoxStyle DefaultButton DefaultColor DefaultControlPlacement DefaultDuplicateCellStyle DefaultDuration DefaultElement DefaultFaceGridsStyle DefaultFieldHintStyle DefaultFont DefaultFontProperties DefaultFormatType DefaultFormatTypeForStyle DefaultFrameStyle DefaultFrameTicksStyle DefaultGridLinesStyle DefaultInlineFormatType DefaultInputFormatType DefaultLabelStyle DefaultMenuStyle DefaultNaturalLanguage DefaultNewCellStyle DefaultNewInlineCellStyle DefaultNotebook DefaultOptions DefaultOutputFormatType DefaultStyle DefaultStyleDefinitions DefaultTextFormatType DefaultTextInlineFormatType DefaultTicksStyle DefaultTooltipStyle DefaultValues Defer DefineExternal DefineInputStreamMethod DefineOutputStreamMethod Definition Degree DegreeCentrality DegreeGraphDistribution DegreeLexicographic DegreeReverseLexicographic Deinitialization Del Deletable Delete DeleteBorderComponents DeleteCases DeleteContents DeleteDirectory DeleteDuplicates DeleteFile DeleteSmallComponents DeleteWithContents DeletionWarning Delimiter DelimiterFlashTime DelimiterMatching Delimiters Denominator DensityGraphics DensityHistogram DensityPlot DependentVariables Deploy Deployed Depth DepthFirstScan Derivative DerivativeFilter DescriptorStateSpace DesignMatrix Det DGaussianWavelet DiacriticalPositioning Diagonal DiagonalMatrix Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DifferenceDelta DifferenceOrder DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralGroup Dilation Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletCharacter DirichletConvolve DirichletDistribution DirichletL DirichletTransform DirichletWindow DisableConsolePrintPacket DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform Discriminant Disjunction Disk DiskBox DiskMatrix Dispatch DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentNotebook DominantColors DOSTextFormat Dot DotDashed DotEqual Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DSolve Dt DualLinearProgramming DualSystemsModel DumpGet DumpSave DuplicateFreeQ Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptions E EccentricityCentrality EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeCost EdgeCount EdgeCoverQ EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData Eliminate EliminationOrder EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EnableConsolePrintPacket Enabled Encode End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfFile EndOfLine EndOfString EndPackage EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entropy EntropyFilter Environment Epilog Equal EqualColumns EqualRows EqualTilde EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerE EulerGamma EulerianGraphQ EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluationCell EvaluationCompletionAction EvaluationElements EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpToTrig ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalCall ExternalDataCharacterEncoding Extract ExtractArchive ExtremeValueDistribution FaceForm FaceGrids FaceGridsStyle Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail FailureDistribution False FARIMAProcess FEDisableConsolePrintPacket FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket Fibonacci FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileDate FileExistsQ FileExtension FileFormat FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileType FilledCurve FilledCurveBox Filling FillingStyle FillingTransform FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindArgMax FindArgMin FindClique FindClusters FindCurvePath FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEulerianCycle FindFaces FindFile FindFit FindGeneratingFunction FindGeoLocation FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMaximum FindMaximumFlow FindMaxValue FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindPermutation FindPostmanTour FindProcessParameters FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindThreshold FindVertexCover FindVertexCut Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstPassageTimeDistribution FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FittedModel FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlatTopWindow FlipView Floor FlushPrintOutputPacket Fold FoldList Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrequencySamplingFilterKernel FresnelC FresnelS Friday FrobeniusNumber FrobeniusSolve FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullOptions FullSimplify Function FunctionExpand FunctionInterpolation FunctionSpace FussellVeselyImportance GaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins Gamma GammaDistribution GammaRegularized GapPenalty Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateConditions GeneratedCell GeneratedParameters GeneratingFunction Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDistance GeoGridPosition GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoPosition GeoPositionENU GeoPositionXYZ GeoProjectionData GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter Graph GraphAssortativity GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel GreatCircleDistance Greater GreaterEqual GreaterEqualLess GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterTilde Green Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain Gudermannian GumbelDistribution HaarWavelet HadamardMatrix HalfNormalDistribution HamiltonianGraphQ HammingDistance HammingWindow HankelH1 HankelH2 HankelMatrix HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash HashTable Haversine HazardFunction Head HeadCompose Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenSurface HighlightGraph HighlightImage HighpassFilter HigmanSimsGroupHS HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HitMissTransform HITSCentrality HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HotellingTSquareDistribution HoytDistribution HTMLSave Hue HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestData I Identity IdentityMatrix If IgnoreCase Im Image Image3D Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageAspectRatio ImageAssemble ImageCache ImageCacheValid ImageCapture ImageChannels ImageClip ImageColorSpace ImageCompose ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDataPacket ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDistance ImageEffect ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageForestingComponents ImageForwardTransformation ImageHistogram ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarkers ImageMeasurements ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImageQ ImageRangeCache ImageReflect ImageRegion ImageResize ImageResolution ImageRotate ImageRotated ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions Implies Import ImportAutoReplacements ImportString ImprovementImportance In IncidenceGraph IncidenceList IncidenceMatrix IncludeConstantBasis IncludeFileExtension IncludePods IncludeSingularTerm Increment Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentUnit IndependentVertexSetQ Indeterminate IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers Infinity Infix Information Inherited InheritScope Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InlineCounterAssignments InlineCounterIncrements InlineRules Inner Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionPointObject InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Install InstallService InString Integer IntegerDigits IntegerExponent IntegerLength IntegerPart IntegerPartitions IntegerQ Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction InterpretTemplate InterquartileRange Interrupt InterruptSettings Intersection Interval IntervalIntersection IntervalMemberQ IntervalUnion Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHaversine InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InversePermutation InverseRadon InverseSeries InverseSurvivalFunction InverseWaveletTransform InverseWeierstrassP InverseZTransform Invisible InvisibleApplication InvisibleTimes IrreduciblePolynomialQ IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcess JaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join Joined JoinedCurve JoinedCurveBox JoinForm JordanDecomposition JordanModelDecomposition K KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelMixtureDistribution KernelObject Kernels Ket Khinchin KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnightTourGraph KnotData KnownUnitQ KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter Label Labeled LabeledSlider LabelingFunction LabelStyle LaguerreL LambdaComponents LambertW LanczosWindow LandauDistribution Language LanguageCategory LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCM LeafCount LeapYearQ LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessFullEqual LessGreater LessLess LessSlantEqual LessTilde LetterCharacter LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox LinearFilter LinearFractionalTransform LinearModelFit LinearOffsetFunction LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBreak LinebreakAdjustments LineBreakChart LineBreakWithin LineColor LineForm LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRead LinkReadHeld LinkReadyQ Links LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot Listen ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalClusteringCoefficient LocalizeVariables LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestAscendingSequence LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow Loopback LoopFreeGraphQ LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LyapunovSolve LyonsGroupLy MachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules MangoldtLambda ManhattanDistance Manipulate Manipulator MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixPlot MatrixPower MatrixQ MatrixRank Max MaxBend MaxDetect MaxExtraBandwidths MaxExtraConditions MaxFeatures MaxFilter Maximize MaxIterations MaxMemoryUsed MaxMixtureKernels MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxValue MaxwellDistribution McLaughlinGroupMcL Mean MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter Median MedianDeviation MedianFilter Medium MeijerG MeixnerDistribution MemberQ MemoryConstrained MemoryInUse Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuPacket MenuSortingValue MenuStyle MenuView MergeDifferences Mesh MeshFunctions MeshRange MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation Method MethodOptions MexicanHatWavelet MeyerWavelet Min MinDetect MinFilter MinimalPolynomial MinimalStateSpaceModel Minimize Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingDataMethod MittagLefflerE MixedRadix MixedRadixQuantity MixtureDistribution Mod Modal Mode Modular ModularLambda Module Modulus MoebiusMu Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction Monday Monitor MonomialList MonomialOrder MonsterGroupM MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform Most MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovingAverage MovingMedian MoyalDistribution MultiedgeStyle MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistribution N NakagamiDistribution NameQ Names NamespaceBox Nand NArgMax NArgMin NBernoulliB NCache NDSolve NDSolveValue Nearest NearestFunction NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeMultinomialDistribution NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestList NestWhile NestWhileList NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextPrime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants None NonlinearModelFit NonlocalMeansFilter NonNegative NonPositive Nor NorlundB Norm Normal NormalDistribution NormalGrouping Normalize NormalizedSquaredEuclideanDistance NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde NotHumpDownHump NotHumpEqual NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess 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NyquistPlot O ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OddQ Off Offset OLEData On ONanGroupON OneIdentity Opacity Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering Orderless OrnsteinUhlenbeckProcess Orthogonalize Out Outer OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OwenT OwnValues PackingMethod PaddedForm Padding PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageWidth PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParetoDistribution Part PartialCorrelationFunction PartialD ParticleData Partition PartitionsP PartitionsQ ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PerformanceGoal PeriodicInterpolation Periodogram PeriodogramArray PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PERTDistribution PetersenGraph PhaseMargins Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest Pink Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarGraphQ Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangePadding PlotRegion PlotStyle Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox PointBox PointFigureChart PointForm PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonBox PolygonBoxOptions PolygonHoleScale PolygonIntersections PolygonScale PolyhedronData PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position Positive PositiveDefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence 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ProgressIndicatorBoxOptions Projection Prolog PromptForm Properties Property PropertyList PropertyValue Proportion Proportional Protect Protected ProteinData Pruning PseudoInverse Purple Put PutAppend Pyramid PyramidBox PyramidBoxOptions QBinomial QFactorial QGamma QHypergeometricPFQ QPochhammer QPolyGamma QRDecomposition QuadraticIrrationalQ Quantile QuantilePlot Quantity QuantityForm QuantityMagnitude QuantityQ QuantityUnit Quartics QuartileDeviation Quartiles QuartileSkewness QueueingNetworkProcess QueueingProcess QueueProperties Quiet Quit Quotient QuotientRemainder RadialityCentrality RadicalBox RadicalBoxOptions RadioButton RadioButtonBar RadioButtonBox RadioButtonBoxOptions Radon RamanujanTau RamanujanTauL RamanujanTauTheta RamanujanTauZ Random RandomChoice RandomComplex RandomFunction RandomGraph RandomImage RandomInteger RandomPermutation RandomPrime RandomReal RandomSample RandomSeed RandomVariate RandomWalkProcess Range RangeFilter RangeSpecification RankedMax RankedMin Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios Raw RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadList ReadProtected Real RealBlockDiagonalForm RealDigits RealExponent Reals Reap Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate RegionBinarize RegionFunction RegionPlot RegionPlot3D RegularExpression Regularization Reinstall Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot Remove RemoveAlphaChannel RemoveAsynchronousTask Removed RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess 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RogersTanimotoDissimilarity Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulerUnits Run RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilarity SameQ SameTest SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveDefinitions SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTaskActiveQ ScheduledTaskData 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SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPrecision SetProperty SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share Sharpen ShearingMatrix ShearingTransform ShenCastanMatrix Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow ShortUpArrow Show ShowAutoStyles ShowCellBracket ShowCellLabel ShowCellTags ShowClosedCellArea ShowContents ShowControls ShowCursorTracker ShowGroupOpenCloseIcon ShowGroupOpener ShowInvisibleCharacters ShowPageBreaks ShowPredictiveInterface ShowSelection ShowShortBoxForm ShowSpecialCharacters ShowStringCharacters ShowSyntaxStyles ShrinkingDelay ShrinkWrapBoundingBox SiegelTheta SiegelTukeyTest Sign Signature SignedRankTest SignificanceLevel SignPadding SignTest SimilarityRules 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SpearmanRankTest SpearmanRho Spectrogram SpectrogramArray Specularity SpellingCorrection SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquaresR SquareSubset SquareSubsetEqual SquareSuperset SquareSupersetEqual SquareUnion SquareWave StabilityMargins StabilityMarginsStyle StableDistribution Stack StackBegin StackComplete StackInhibit StandardDeviation StandardDeviationFilter StandardForm Standardize StandbyDistribution Star 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