242 lines
11 KiB
Markdown
242 lines
11 KiB
Markdown
Simulation Configuration
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==
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## Introduction
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Given a **Simulation Configuration**, cadCAD produces datasets that represent the evolution of the state of a system
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over [discrete time](https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time). The state of the
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system is described by a set of [State Variables](#State-Variables). The dynamic of the system is described by
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[Policy Functions](#Policy-Functions) and [State Update Functions](#State-Update-Functions), which are evaluated by
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cadCAD according to the definitions set by the user in [Partial State Update Blocks](#Partial-State-Update-Blocks).
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A Simulation Configuration is comprised of a [System Model](#System-Model) and a set of
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[Simulation Properties](#Simulation-Properties)
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`append_configs`, stores a **Simulation Configuration** to be [Executed](/JS4Q9oayQASihxHBJzz4Ug) by cadCAD
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```python
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from cadCAD.configuration import append_configs
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append_configs(
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initial_state = ..., # System Model
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partial_state_update_blocks = .., # System Model
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policy_ops = ..., # System Model
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sim_configs = ... # Simulation Properties
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)
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```
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Parameters:
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* **initial_state** : _dict_ - [State Variables](#State-Variables) and their initial values
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* **partial_state_update_blocks** : List[dict[dict]] - List of [Partial State Update Blocks](#Partial-State-Update-Blocks)
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* **policy_ops** : List[functions] - See [Policy Aggregation](/63k2ncjITuqOPCUHzK7Viw)
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* **sim_configs** - See [System Model Parameter Sweep](/4oJ_GT6zRWW8AO3yMhFKrg)
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## Simulation Properties
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Simulation properties are passed to `append_configs` in the `sim_configs` parameter. To construct this parameter, we
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use the `config_sim` function in `cadCAD.configuration.utils`
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```python
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from cadCAD.configuration.utils import config_sim
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c = config_sim({
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"N": ...,
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"T": range(...),
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"M": ...
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})
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append_configs(
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...
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sim_configs = c # Simulation Properties
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)
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```
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### T - Simulation Length
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Computer simulations run in discrete time:
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>Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being
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unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. (...)
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This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a
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new fixed reading of 10:38, etc.
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([source: Wikipedia](https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time))
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As is common in many simulation tools, in cadCAD too we refer to each discrete unit of time as a **timestep**. cadCAD
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increments a "time counter", and at each step it updates the state variables according to the equations that describe
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the system.
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The main simulation property that the user must set when creating a Simulation Configuration is the number of timesteps
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in the simulation. In other words, for how long do they want to simulate the system that has been modeled.
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### N - Number of Runs
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cadCAD facilitates running multiple simulations of the same system sequentially, reporting the results of all those
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runs in a single dataset. This is especially helpful for running
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[Monte Carlo Simulations](../tutorials/robot-marbles-part-4/robot-marbles-part-4.ipynb).
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### M - Parameters of the System
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Parameters of the system, passed to the state update functions and the policy functions in the `params` parameter are
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defined here. See [System Model Parameter Sweep](/4oJ_GT6zRWW8AO3yMhFKrg) for more information.
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## System Model
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The System Model describes the system that will be simulated in cadCAD. It is comprised of a set of
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[State Variables](###Sate-Variables) and the [State Update Functions](#State-Update-Functions) that determine the
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evolution of the state of the system over time. [Policy Functions](#Policy-Functions) (representations of user policies
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or internal system control policies) may also be part of a System Model.
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### State Variables
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>A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical
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system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the
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absence of any external forces affecting the system. ([source: Wikipedia](https://en.wikipedia.org/wiki/State_variable))
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cadCAD can handle state variables of any Python data type, including custom classes. It is up to the user of cadCAD to
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determine the state variables needed to **sufficiently and accurately** describe the system they are interested in.
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State Variables are passed to `append_configs` along with its initial values, as a Python `dict` where the `dict_keys`
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are the names of the variables and the `dict_values` are their initial values.
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```python
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from cadCAD.configuration import append_configs
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genesis_states = {
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'state_variable_1': 0,
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'state_variable_2': 0,
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'state_variable_3': 1.5,
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'timestamp': '2019-01-01 00:00:00'
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}
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append_configs(
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initial_state = genesis_states,
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...
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)
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```
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### State Update Functions
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State Update Functions represent equations according to which the state variables change over time. Each state update
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function must return a tuple containing a string with the name of the state variable being updated and its new value.
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Each state update function can only modify a single state variable. The general structure of a state update function is:
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```python
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def state_update_function_A(_params, substep, sH, s, _input):
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...
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return 'state_variable_name', new_value
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```
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Parameters:
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* **_params** : _dict_ - [System parameters](/4oJ_GT6zRWW8AO3yMhFKrg)
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* **substep** : _int_ - Current [substep](#Substep)
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* **sH** : _list[list[dict_]] - Historical values of all state variables for the simulation. See
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[Historical State Access](/smiyQTnATtC9xPwvF8KbBQ) for details
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* **s** : _dict_ - Current state of the system, where the `dict_keys` are the names of the state variables and the
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`dict_values` are their current values.
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* **_input** : _dict_ - Aggregation of the signals of all policy functions in the current
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[Partial State Update Block](#Partial-State-Update-Block)
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Return:
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* _tuple_ containing a string with the name of the state variable being updated and its new value.
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State update functions should not modify any of the parameters passed to it, as those are mutable Python objects that
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cadCAD relies on in order to run the simulation according to the specifications.
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### Policy Functions
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A Policy Function computes one or more signals to be passed to [State Update Functions](#State-Update-Functions)
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(via the _\_input_ parameter). Read
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[this article](../tutorials/robot-marbles-part-2/robot-marbles-part-2.ipynb)
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for details on why and when to use policy functions.
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<!-- We would then expand the tutorials with these kind of concepts
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#### Policies
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Policies consist of the potential action made available through mechanisms. The action taken is expected to be the
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result of a conditional determination of the past state.
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While executed the same, the modeller can approach policies dependent on the availability of a mechanism to a population.
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- ***Control Policy***
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When the controlling or deploying entity has the ability to act in order to affect some aspect of the system, this is a
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control policy.
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- ***User Policy*** model agent behaviors in reaction to state variables and exogenous variables. The resulted user
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action will become an input to PSUs. Note that user behaviors should not directly update value of state variables.
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The action taken, as well as the potential to act, through a mechanism is a behavior. -->
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The general structure of a policy function is:
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```python
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def policy_function_1(_params, substep, sH, s):
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...
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return {'signal_1': value_1, ..., 'signal_N': value_N}
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```
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Parameters:
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* **_params** : _dict_ - [System parameters](/4oJ_GT6zRWW8AO3yMhFKrg)
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* **substep** : _int_ - Current [substep](#Substep)
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* **sH** : _list[list[dict_]] - Historical values of all state variables for the simulation. See
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[Historical State Access](/smiyQTnATtC9xPwvF8KbBQ) for details
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* **s** : _dict_ - Current state of the system, where the `dict_keys` are the names of the state variables and the
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`dict_values` are their current values.
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Return:
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* _dict_ of signals to be passed to the state update functions in the same
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[Partial State Update Block](#Partial-State-Update-Blocks)
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Policy functions should not modify any of the parameters passed to it, as those are mutable Python objects that cadCAD
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relies on in order to run the simulation according to the specifications.
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At each [Partial State Update Block](#Partial-State-Update-Blocks) (PSUB), the `dicts` returned by all policy functions
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within that PSUB dictionaries are aggregated into a single `dict` using an initial reduction function
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(a key-wise operation, default: `dic1['keyA'] + dic2['keyA']`) and optional subsequent map functions. The resulting
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aggregated `dict` is then passed as the `_input` parameter to the state update functions in that PSUB. For more
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information on how to modify the aggregation method, see [Policy Aggregation](/63k2ncjITuqOPCUHzK7Viw).
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### Partial State Update Blocks
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A **Partial State Update Block** (PSUB) is a set of State Update Functions and Policy Functions such that State Update
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Functions in the set are independent from each other and Policies in the set are independent from each other and from
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the State Update Functions in the set. In other words, if a state variable is updated in a PSUB, its new value cannot
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impact the State Update Functions and Policy Functions in that PSUB - only those in the next PSUB.
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Partial State Update Blocks are passed to `append_configs` as a List of Python `dicts` where the `dict_keys` are named
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`"policies"` and `"variables"` and the values are also Python `dicts` where the keys are the names of the policy and
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state update functions and the values are the functions.
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```python
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PSUBs = [
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{
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"policies": {
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"b_1": policy_function_1,
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...
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"b_J": policy_function_J
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},
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"variables": {
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"s_1": state_update_function_1,
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...
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"s_K": state_update_function_K
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}
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}, #PSUB_1,
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{...}, #PSUB_2,
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...
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{...} #PSUB_M
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]
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append_configs(
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...
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partial_state_update_blocks = PSUBs,
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...
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)
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```
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#### Substep
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At each timestep, cadCAD iterates over the `partial_state_update_blocks` list. For each Partial State Update Block,
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cadCAD returns a record containing the state of the system at the end of that PSUB. We refer to that subdivision of a
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timestep as a `substep`.
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## Result Dataset
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cadCAD returns a dataset containing the evolution of the state variables defined by the user over time, with three `int`
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indexes:
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* `run` - id of the [run](#N-Number-of-Runs)
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* `timestep` - discrete unit of time (the total number of timesteps is defined by the user in the
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[T Simulation Parameter](#T-Simulation-Length))
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* `substep` - subdivision of timestep (the number of [substeps](#Substeps) is the same as the number of Partial State
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Update Blocks)
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Therefore, the total number of records in the resulting dataset is `N` x `T` x `len(partial_state_update_blocks)`
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#### [System Simulation Execution](Simulation_Execution.md)
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