Main namespace for algorithms that operate on MDPs and RMDPs. More...

Namespaces
	internal
	Internal helper functions.

Classes
class	PolicyDeterministic

class	PolicyNature
	The class abstracts some operations of value / policy iteration in order to generalize to various types of robust MDPs. More...

struct	Solution
	A solution to a plain MDP. More...

struct	SolutionRobust
	A robust solution to a robust or regular MDP. More...

Typedefs
template<class T >
using	NatureResponse = vec_scal_t(*)(numvec const &v, numvec const &p, T threshold)
	Function representing constraints on nature. More...

template<class T >
using	NatureInstance = pair< NatureResponse< T >, T >
	Represents an instance of nature that can be used to directly compute the response.

Functions
template<typename SType , typename Policies >
MatrixXd	transition_mat (const GRMDP< SType > &rmdp, const Policies &policies, bool transpose=false)
	Constructs the transition (or its transpose) matrix for the policy. More...

template<typename SType , typename Policy >
numvec	rewards_vec (const GRMDP< SType > &rmdp, const Policy &policies)
	Constructs the rewards vector for each state for the RMDP. More...

template<typename SType , typename Policies >
numvec	occfreq_mat (const GRMDP< SType > &rmdp, const Transition &init, prec_t discount, const Policies &policies)
	Computes occupancy frequencies using matrix representation of transition probabilities. More...

vec_scal_t	robust_l1 (const numvec &v, const numvec &p, prec_t threshold)
	L1 robust response.

vec_scal_t	optimistic_l1 (const numvec &v, const numvec &p, prec_t threshold)
	L1 optimistic response.

template<class T >
vec_scal_t	robust_unbounded (const numvec &v, const numvec &p, T)
	worst outcome, threshold is ignored

template<class T >
vec_scal_t	optimistic_unbounded (const numvec &v, const numvec &p, T)
	best outcome, threshold is ignored

template<class T >
vec_scal_t	value_action (const RegularAction &action, const numvec &valuefunction, prec_t discount, const NatureInstance< T > &nature)
	Computes an ambiguous value (e.g. More...

template<class T >
vec_scal_t	value_action (const WeightedOutcomeAction &action, numvec const &valuefunction, prec_t discount, const NatureInstance< T > nature)
	Computes the maximal outcome distribution constraints on the nature's distribution. More...

template<class AType , class T >
vec_scal_t	value_fix_state (const SAState< AType > &state, numvec const &valuefunction, prec_t discount, long actionid, const NatureInstance< T > &nature)
	Computes the value of a fixed action and any response of nature. More...

template<typename AType , typename T >
ind_vec_scal_t	value_max_state (const SAState< AType > &state, const numvec &valuefunction, prec_t discount, const NatureInstance< T > &nature)
	Finds the greedy action and its value for the given value function. More...

template<class T >
PolicyNature< T >	uniform_nature (size_t statecount, NatureResponse< T > nature, T threshold)
	A helper function that simply copies a nature specification across all states.

template<class Model , class T >
PolicyNature< T >	uniform_nature (const Model &m, NatureResponse< T > nature, T threshold)
	A helper function that simply copies a nature specification across all states.

template<class SType , class T = prec_t>
auto	rsolve_vi (const GRMDP< SType > &mdp, prec_t discount, const vector< NatureResponse< T >> &nature, const vector< T > &thresholds, numvec valuefunction=numvec(0), const indvec &policy=numvec(0), unsigned long iterations=MAXITER, prec_t maxresidual=SOLPREC)
	Gauss-Seidel variant of value iteration (not parallelized). More...

template<class SType , class T = prec_t>
auto	rsolve_vi (const GRMDP< SType > &mdp, prec_t discount, const NatureResponse< T > &nature, const vector< T > &thresholds, numvec valuefunction=numvec(0), const indvec &policy=numvec(0), unsigned long iterations=MAXITER, prec_t maxresidual=SOLPREC)
	Simplified function call with a single nature for all states.

template<class SType , class T = prec_t>
auto	rsolve_mpi (const GRMDP< SType > &mdp, prec_t discount, const vector< NatureResponse< T >> &nature, const vector< T > &thresholds, const numvec &valuefunction=numvec(0), const indvec &policy=indvec(0), unsigned long iterations_pi=MAXITER, prec_t maxresidual_pi=SOLPREC, unsigned long iterations_vi=MAXITER, prec_t maxresidual_vi=SOLPREC/2, bool print_progress=false)
	Modified policy iteration using Jacobi value iteration in the inner loop. More...

template<class SType , class T = prec_t>
auto	rsolve_mpi (const GRMDP< SType > &mdp, prec_t discount, const NatureResponse< T > &nature, const vector< T > &thresholds, const numvec &valuefunction=numvec(0), const indvec &policy=indvec(0), unsigned long iterations_pi=MAXITER, prec_t maxresidual_pi=SOLPREC, unsigned long iterations_vi=MAXITER, prec_t maxresidual_vi=SOLPREC/2, bool print_progress=false)
	Simplified function call with a single nature for all states.

NatureResponse< prec_t >	string_to_nature (string nature)
	Converts a string representation of nature response to the appropriate nature response call. More...

prec_t	value_action (const RegularAction &action, const numvec &valuefunction, prec_t discount)
	Computes the average value of the action. More...

prec_t	value_action (const RegularAction &action, const numvec &valuefunction, prec_t discount, numvec distribution)
	Computes a value of the action for a given distribution. More...

prec_t	value_action (const WeightedOutcomeAction &action, numvec const &valuefunction, prec_t discount)
	Computes the average outcome using the provided distribution. More...

prec_t	value_action (const WeightedOutcomeAction &action, numvec const &valuefunction, prec_t discount, const numvec &distribution)
	Computes the action value for a fixed index outcome. More...

template<class AType >
pair< long, prec_t >	value_max_state (const SAState< AType > &state, const numvec &valuefunction, prec_t discount)
	Finds the action with the maximal average return. More...

template<class AType >
prec_t	value_fix_state (const SAState< AType > &state, numvec const &valuefunction, prec_t discount, long actionid)
	Computes the value of a fixed (and valid) action. More...

template<class AType >
prec_t	value_fix_state (const SAState< AType > &state, numvec const &valuefunction, prec_t discount, long actionid, numvec distribution)
	Computes the value of a fixed action and fixed response of nature. More...

template<class SType , class ResponseType = PolicyDeterministic>
auto	vi_gs (const GRMDP< SType > &mdp, prec_t discount, numvec valuefunction=numvec(0), const ResponseType &response=PolicyDeterministic(), unsigned long iterations=MAXITER, prec_t maxresidual=SOLPREC)
	Gauss-Seidel variant of value iteration (not parallelized). More...

template<class SType , class ResponseType = PolicyDeterministic>
auto	mpi_jac (const GRMDP< SType > &mdp, prec_t discount, const numvec &valuefunction=numvec(0), const ResponseType &response=PolicyDeterministic(), unsigned long iterations_pi=MAXITER, prec_t maxresidual_pi=SOLPREC, unsigned long iterations_vi=MAXITER, prec_t maxresidual_vi=SOLPREC/2, bool print_progress=false)
	Modified policy iteration using Jacobi value iteration in the inner loop. More...

template<class SType >
auto	solve_vi (const GRMDP< SType > &mdp, prec_t discount, numvec valuefunction=numvec(0), const indvec &policy=numvec(0), unsigned long iterations=MAXITER, prec_t maxresidual=SOLPREC)
	Gauss-Seidel variant of value iteration (not parallelized). More...

template<class SType >
auto	solve_mpi (const GRMDP< SType > &mdp, prec_t discount, const numvec &valuefunction=numvec(0), const indvec &policy=indvec(0), unsigned long iterations_pi=MAXITER, prec_t maxresidual_pi=SOLPREC, unsigned long iterations_vi=MAXITER, prec_t maxresidual_vi=SOLPREC/2, bool print_progress=false)
	Modified policy iteration using Jacobi value iteration in the inner loop. More...

Detailed Description

Main namespace for algorithms that operate on MDPs and RMDPs.

Typedef Documentation

◆ NatureResponse

template<class T >

using craam::algorithms::NatureResponse = typedef vec_scal_t (*)(numvec const& v, numvec const& p, T threshold)

Function representing constraints on nature.

The function computes the best response of nature and can be used in value iteration.

This function represents a nature which computes (in general) a randomized policy (response). If the response is always deterministic, it may be better to define and use a nature that computes and uses a deterministic response.

The parameters are the q-values v, the reference distribution p, and the threshold. The function returns the worst-case solution and the objective value. The threshold can be used to determine the desired robustness of the solution.

Function Documentation

◆ mpi_jac()

template<class SType , class ResponseType = PolicyDeterministic>

auto craam::algorithms::mpi_jac	(	const GRMDP< SType > &	mdp,
		prec_t	discount,
		const numvec &	valuefunction = `numvec(0)`,
		const ResponseType &	response = `PolicyDeterministic()`,
		unsigned long	iterations_pi = `MAXITER`,
		prec_t	maxresidual_pi = `SOLPREC`,
		unsigned long	iterations_vi = `MAXITER`,
		prec_t	maxresidual_vi = `SOLPREC/2`,
		bool	print_progress = `false`
	)

inline

Modified policy iteration using Jacobi value iteration in the inner loop.

See solve_mpi for a simplified interface. This method generalizes modified policy iteration to robust MDPs. In the value iteration step, both the action and the outcome are fixed.

Note that the total number of iterations will be bounded by iterations_pi * iterations_vi

Parameters

type	Type of realization of the uncertainty
discount	Discount factor
valuefunction	Initial value function
response	Using PolicyResponce allows to specify a partial policy. Only the actions that not provided by the partial policy are included in the optimization. Using a class of a different types enables computing other objectives, such as robust or risk averse ones.
iterations_pi	Maximal number of policy iteration steps
maxresidual_pi	Stop the outer policy iteration when the residual drops below this threshold.
iterations_vi	Maximal number of inner loop value iterations
maxresidual_vi	Stop the inner policy iteration when the residual drops below this threshold. This value should be smaller than maxresidual_pi
print_progress	Whether to report on progress during the computation

Returns: Computed (approximate) solution

◆ occfreq_mat()

template<typename SType , typename Policies >

numvec craam::algorithms::occfreq_mat	(	const GRMDP< SType > &	rmdp,
		const Transition &	init,
		prec_t	discount,
		const Policies &	policies
	)

inline

Computes occupancy frequencies using matrix representation of transition probabilities.

This method may not scale well

Template Parameters

SType	Type of the state in the MDP (regular vs robust)
Policy	Type of the policy. Either a single policy for the standard MDP evaluation, or a pair of a deterministic policy and a randomized policy of the nature

Parameters

init	Initial distribution (alpha)
discount	Discount factor (gamma)
policies	The policy (indvec) or the pair of the policy and the policy of nature (pair<indvec,vector<numvec> >). The nature is typically a randomized policy

◆ rewards_vec()

template<typename SType , typename Policy >

numvec craam::algorithms::rewards_vec	(	const GRMDP< SType > &	rmdp,
		const Policy &	policies
	)

inline

Constructs the rewards vector for each state for the RMDP.

Template Parameters

Policy Type of the policy. Either a single policy for the standard MDP evaluation, or a pair of a deterministic policy and a randomized policy of the nature

Parameters

rmdp	Regular or robust MDP
policies	The policy (indvec) or the pair of the policy and the policy of nature (pair<indvec,vector<numvec> >). The nature is typically a randomized policy

◆ rsolve_mpi()

template<class SType , class T = prec_t>

auto craam::algorithms::rsolve_mpi	(	const GRMDP< SType > &	mdp,
		prec_t	discount,
		const vector< NatureResponse< T >> &	nature,
		const vector< T > &	thresholds,
		const numvec &	valuefunction = `numvec(0)`,
		const indvec &	policy = `indvec(0)`,
		unsigned long	iterations_pi = `MAXITER`,
		prec_t	maxresidual_pi = `SOLPREC`,
		unsigned long	iterations_vi = `MAXITER`,
		prec_t	maxresidual_vi = `SOLPREC/2`,
		bool	print_progress = `false`
	)

inline

Modified policy iteration using Jacobi value iteration in the inner loop.

This method generalizes modified policy iteration to robust MDPs. In the value iteration step, both the action and the outcome are fixed.

This is a simplified method interface. Use mpi_jac with PolicyNature for full functionality.

Note that the total number of iterations will be bounded by iterations_pi * iterations_vi

Parameters

type	Type of realization of the uncertainty
discount	Discount factor
nature	Response of nature, one function per state.
thresholds	Parameters passed to nature response functions. One value per state.
valuefunction	Initial value function
policy	Partial policy specification. Optimize only actions that are policy[state] = -1
iterations_pi	Maximal number of policy iteration steps
maxresidual_pi	Stop the outer policy iteration when the residual drops below this threshold.
iterations_vi	Maximal number of inner loop value iterations
maxresidual_vi	Stop the inner policy iteration when the residual drops below this threshold. This value should be smaller than maxresidual_pi
print_progress	Whether to report on progress during the computation

Returns: Computed (approximate) solution

◆ rsolve_vi()

template<class SType , class T = prec_t>

auto craam::algorithms::rsolve_vi	(	const GRMDP< SType > &	mdp,
		prec_t	discount,
		const vector< NatureResponse< T >> &	nature,
		const vector< T > &	thresholds,
		numvec	valuefunction = `numvec(0)`,
		const indvec &	policy = `numvec(0)`,
		unsigned long	iterations = `MAXITER`,
		prec_t	maxresidual = `SOLPREC`
	)

inline

Gauss-Seidel variant of value iteration (not parallelized).

This function is suitable for computing the value function of a finite state MDP. If the states are ordered correctly, one iteration is enough to compute the optimal value function. Since the value function is updated from the last state to the first one, the states should be ordered in the temporal order.

This is a simplified method interface. Use vi_gs with PolicyNature for full functionality.

Parameters

mdp	The MDP to solve
discount	Discount factor.
nature	Response of nature, one function per state.
thresholds	Parameters passed to nature response functions. One value per state.
valuefunction	Initial value function. Passed by value, because it is modified. Optional, use all zeros when not provided. Ignored when size is 0.
policy	Partial policy specification. Optimize only actions that are policy[state] = -1
iterations	Maximal number of iterations to run
maxresidual	Stop when the maximal residual falls below this value.

Returns: Solution that can be used to compute the total return, or the optimal policy.

◆ solve_mpi()

template<class SType >

auto craam::algorithms::solve_mpi	(	const GRMDP< SType > &	mdp,
		prec_t	discount,
		const numvec &	valuefunction = `numvec(0)`,
		const indvec &	policy = `indvec(0)`,
		unsigned long	iterations_pi = `MAXITER`,
		prec_t	maxresidual_pi = `SOLPREC`,
		unsigned long	iterations_vi = `MAXITER`,
		prec_t	maxresidual_vi = `SOLPREC/2`,
		bool	print_progress = `false`
	)

inline

Modified policy iteration using Jacobi value iteration in the inner loop.

This method generalizes modified policy iteration to robust MDPs. In the value iteration step, both the action and the outcome are fixed.

Note that the total number of iterations will be bounded by iterations_pi * iterations_vi

Parameters

type	Type of realization of the uncertainty
discount	Discount factor
valuefunction	Initial value function
policy	Partial policy specification. Optimize only actions that are policy[state] = -1
iterations_pi	Maximal number of policy iteration steps
maxresidual_pi	Stop the outer policy iteration when the residual drops below this threshold.
iterations_vi	Maximal number of inner loop value iterations
maxresidual_vi	Stop the inner policy iteration when the residual drops below this threshold. This value should be smaller than maxresidual_pi
print_progress	Whether to report on progress during the computation

Returns: Computed (approximate) solution

◆ solve_vi()

template<class SType >

auto craam::algorithms::solve_vi	(	const GRMDP< SType > &	mdp,
		prec_t	discount,
		numvec	valuefunction = `numvec(0)`,
		const indvec &	policy = `numvec(0)`,
		unsigned long	iterations = `MAXITER`,
		prec_t	maxresidual = `SOLPREC`
	)

inline

Gauss-Seidel variant of value iteration (not parallelized).

This function is suitable for computing the value function of a finite state MDP. If the states are ordered correctly, one iteration is enough to compute the optimal value function. Since the value function is updated from the last state to the first one, the states should be ordered in the temporal order.

Parameters

mdp	The MDP to solve
discount	Discount factor.
valuefunction	Initial value function. Passed by value, because it is modified. Optional, use all zeros when not provided. Ignored when size is 0.
policy	Partial policy specification. Optimize only actions that are policy[state] = -1
iterations	Maximal number of iterations to run
maxresidual	Stop when the maximal residual falls below this value.

Returns: Solution that can be used to compute the total return, or the optimal policy.

◆ string_to_nature()

NatureResponse<prec_t> craam::algorithms::string_to_nature ( string nature )

inline

Converts a string representation of nature response to the appropriate nature response call.

This function is useful when the code is used within a python or R libraries. The values values correspond to the function definitions, and ones that are currently supported are:

robust_unbounded
optimistic_unbounded
robust_l1
optimistic_l1

◆ transition_mat()

template<typename SType , typename Policies >

MatrixXd craam::algorithms::transition_mat	(	const GRMDP< SType > &	rmdp,
		const Policies &	policies,
		bool	transpose = `false`
	)

inline

Constructs the transition (or its transpose) matrix for the policy.

Template Parameters

SType	Type of the state in the MDP (regular vs robust)
Policy	Type of the policy. Either a single policy for the standard MDP evaluation, or a pair of a deterministic policy and a randomized policy of the nature

Parameters

rmdp	Regular or robust MDP
policies	The policy (indvec) or the pair of the policy and the policy of nature (pair<indvec,vector<numvec> >). The nature is typically a randomized policy
transpose	(optional, false) Whether to return the transpose of the transition matrix. This is useful for computing occupancy frequencies

◆ value_action() [1/6]

prec_t craam::algorithms::value_action	(	const RegularAction &	action,
		const numvec &	valuefunction,
		prec_t	discount
	)

inline

Computes the average value of the action.

Parameters

action	Action for which to compute the value
valuefunction	State value function to use
discount	Discount factor

Returns: Action value

◆ value_action() [2/6]

prec_t craam::algorithms::value_action	(	const RegularAction &	action,
		const numvec &	valuefunction,
		prec_t	discount,
		numvec	distribution
	)

inline

Computes a value of the action for a given distribution.

This function can be used to evaluate a robust solution which may modify the transition probabilities.

The new distribution may be non-zero only for states for which the original distribution is not zero.

Parameters

action	Action for which to compute the value
valuefunction	State value function to use
discount	Discount factor
distribution	New distribution. The length must match the number of states to which the original transition probabilities are strictly greater than 0. The order of states is the same as in the underlying transition.

Returns: Action value

◆ value_action() [3/6]

prec_t craam::algorithms::value_action	(	const WeightedOutcomeAction &	action,
		numvec const &	valuefunction,
		prec_t	discount
	)

inline

Computes the average outcome using the provided distribution.

Parameters

action	Action for which the value is computed
valuefunction	Updated value function
discount	Discount factor

Returns: Mean value of the action

◆ value_action() [4/6]

template<class T >

vec_scal_t craam::algorithms::value_action	(	const RegularAction &	action,
		const numvec &	valuefunction,
		prec_t	discount,
		const NatureInstance< T > &	nature
	)

inline

Computes an ambiguous value (e.g.

robust) of the action, depending on the type of nature that is provided.

Parameters

action	Action for which to compute the value
valuefunction	State value function to use
discount	Discount factor
nature	Method used to compute the response of nature.

◆ value_action() [5/6]

prec_t craam::algorithms::value_action	(	const WeightedOutcomeAction &	action,
		numvec const &	valuefunction,
		prec_t	discount,
		const numvec &	distribution
	)

inline

Computes the action value for a fixed index outcome.

Parameters

action	Action for which the value is computed
valuefunction	Updated value function
discount	Discount factor
distribution	Custom distribution that is selected by nature.

Returns: Value of the action

◆ value_action() [6/6]

template<class T >

vec_scal_t craam::algorithms::value_action	(	const WeightedOutcomeAction &	action,
		numvec const &	valuefunction,
		prec_t	discount,
		const NatureInstance< T >	nature
	)

inline

Computes the maximal outcome distribution constraints on the nature's distribution.

Does not work when the number of outcomes is zero.

Parameters

action	Action for which the value is computed
valuefunction	Value function reference
discount	Discount factor
nature	Method used to compute the response of nature.

Returns: Outcome distribution and the mean value for the choice of the nature

◆ value_fix_state() [1/3]

template<class AType >

prec_t craam::algorithms::value_fix_state	(	const SAState< AType > &	state,
		numvec const &	valuefunction,
		prec_t	discount,
		long	actionid
	)

inline

Computes the value of a fixed (and valid) action.

Performs validity checks.

Parameters

state	State to compute the value for
valuefunction	Value function to use for the following states
discount	Discount factor

Returns: Value of state, 0 if it's terminal regardless of the action index

◆ value_fix_state() [2/3]

template<class AType , class T >

vec_scal_t craam::algorithms::value_fix_state	(	const SAState< AType > &	state,
		numvec const &	valuefunction,
		prec_t	discount,
		long	actionid,
		const NatureInstance< T > &	nature
	)

inline

Computes the value of a fixed action and any response of nature.

Parameters

state	State to compute the value for
valuefunction	Value function to use in computing value of states.
discount	Discount factor
nature	Instance of a nature optimizer

Returns: Value of state, 0 if it's terminal regardless of the action index

◆ value_fix_state() [3/3]

template<class AType >

prec_t craam::algorithms::value_fix_state	(	const SAState< AType > &	state,
		numvec const &	valuefunction,
		prec_t	discount,
		long	actionid,
		numvec	distribution
	)

inline

Computes the value of a fixed action and fixed response of nature.

Parameters

state	State to compute the value for
valuefunction	Value function to use in computing value of states.
discount	Discount factor
distribution	New distribution over states with non-zero nominal probabilities

Returns: Value of state, 0 if it's terminal regardless of the action index

◆ value_max_state() [1/2]

template<class AType >

pair<long,prec_t> craam::algorithms::value_max_state	(	const SAState< AType > &	state,
		const numvec &	valuefunction,
		prec_t	discount
	)

inline

Finds the action with the maximal average return.

The return is 0 with no actions. Such state is assumed to be terminal.

Parameters

state	State to compute the value for
valuefunction	Value function to use for the following states
discount	Discount factor

Returns: (Index of best action, value), returns 0 if the state is terminal.

◆ value_max_state() [2/2]

template<typename AType , typename T >

ind_vec_scal_t craam::algorithms::value_max_state	(	const SAState< AType > &	state,
		const numvec &	valuefunction,
		prec_t	discount,
		const NatureInstance< T > &	nature
	)

inline

Finds the greedy action and its value for the given value function.

This function assumes a robust or optimistic response by nature depending on the provided ambiguity.

When there are no actions, the state is assumed to be terminal and the return is 0.

Parameters

state	State to compute the value for
valuefunction	Value function to use in computing value of states.
discount	Discount factor
nature	Method used to compute the response of nature.

Returns: (Action index, outcome index, value), 0 if it's terminal regardless of the action index

◆ vi_gs()

template<class SType , class ResponseType = PolicyDeterministic>

auto craam::algorithms::vi_gs	(	const GRMDP< SType > &	mdp,
		prec_t	discount,
		numvec	valuefunction = `numvec(0)`,
		const ResponseType &	response = `PolicyDeterministic()`,
		unsigned long	iterations = `MAXITER`,
		prec_t	maxresidual = `SOLPREC`
	)

inline

Gauss-Seidel variant of value iteration (not parallelized).

See solve_vi for a simplified interface.

This function is suitable for computing the value function of a finite state MDP. If the states are ordered correctly, one iteration is enough to compute the optimal value function. Since the value function is updated from the last state to the first one, the states should be ordered in the temporal order.

Parameters

mdp	The mdp to solve
discount	Discount factor.
valuefunction	Initial value function. Passed by value, because it is modified. Optional, use all zeros when not provided. Ignored when size is 0.
response	Using PolicyResponce allows to specify a partial policy. Only the actions that not provided by the partial policy are included in the optimization. Using a class of a different types enables computing other objectives, such as robust or risk averse ones.
iterations	Maximal number of iterations to run
maxresidual	Stop when the maximal residual falls below this value.

Returns: Solution that can be used to compute the total return, or the optimal policy.

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ NatureResponse

Function Documentation

◆ mpi_jac()

◆ occfreq_mat()

◆ rewards_vec()

◆ rsolve_mpi()

◆ rsolve_vi()

◆ solve_mpi()

◆ solve_vi()

◆ string_to_nature()

◆ transition_mat()

◆ value_action() [1/6]

◆ value_action() [2/6]

◆ value_action() [3/6]

◆ value_action() [4/6]

◆ value_action() [5/6]

◆ value_action() [6/6]

◆ value_fix_state() [1/3]

◆ value_fix_state() [2/3]

◆ value_fix_state() [3/3]

◆ value_max_state() [1/2]

◆ value_max_state() [2/2]

◆ vi_gs()