Solver state

Given an AbstractManoptProblem, that is a certain optimisation task, the state specifies the solver to use. It contains the parameters of a solver and all fields necessary during the algorithm, for example the current iterate, a StoppingCriterion or a Stepsize.

Manopt.AbstractManoptSolverStateType
AbstractManoptSolverState

A general super type for all solver states.

Fields

The following fields are assumed to be default. If you use different ones, provide the access functions accordingly

source
Manopt.get_stateFunction
get_state(s::AbstractManoptSolverState, recursive::Bool=true)

return the (one step) undecorated AbstractManoptSolverState of the (possibly) decorated s. As long as your decorated state stores the state within s.state and the dispatch_objective_decorator is set to Val{true}, the internal state are extracted automatically.

By default the state that is stored within a decorated state is assumed to be at s.state. Overwrite _get_state(s, ::Val{true}, recursive) to change this behaviour for your states` for both the recursive and the direct case.

If recursive is set to false, only the most outer decorator is taken away instead of all.

source
Manopt.get_countFunction
get_count(ams::AbstractManoptSolverState, ::Symbol)

Obtain the count for a certain countable size, for example the :Iterations. This function returns 0 if there was nothing to count

Available symbols from within the solver state

  • :Iterations is passed on to the stop field to obtain the iteration at which the solver stopped.
source
get_count(co::ManifoldCountObjective, s::Symbol, mode::Symbol=:None)

Get the number of counts for a certain symbol s.

Depending on the mode different results appear if the symbol does not exist in the dictionary

  • :None: (default) silent mode, returns -1 for non-existing entries
  • :warn: issues a warning if a field does not exist
  • :error: issues an error if a field does not exist
source

Since every subtype of an AbstractManoptSolverState directly relate to a solver, the concrete states are documented together with the corresponding solvers. This page documents the general features available for every state.

A first example is to obtain or set, the current iterate. This might be useful to continue investigation at the current iterate, or to set up a solver for a next experiment, respectively.

Manopt.get_iterateFunction
get_iterate(O::AbstractManoptSolverState)

return the (last stored) iterate within AbstractManoptSolverStates`. This should usually refer to a single point on the manifold the solver is working on

By default this also removes all decorators of the state beforehand.

source
get_iterate(agst::AbstractGradientSolverState)

return the iterate stored within gradient options. THe default returns agst.p.

source

An internal function working on the state and elements within a state is used to pass messages from (sub) activities of a state to the corresponding DebugMessages

Manopt.get_messageFunction
get_message(du::AbstractManoptSolverState)

get a message (String) from internal functors, in a summary. This should return any message a sub-step might have issued as well.

source

Furthermore, to access the stopping criterion use

Decorators for AbstractManoptSolverStates

A solver state can be decorated using the following trait and function to initialize

Manopt.dispatch_state_decoratorFunction
dispatch_state_decorator(s::AbstractManoptSolverState)

Indicate internally, whether an AbstractManoptSolverStates is of decorating type, and stores (encapsulates) a state in itself, by default in the field s.state.

Decorators indicate this by returning Val{true} for further dispatch.

The default is Val{false}, so by default a state is not decorated.

source
Manopt.decorate_state!Function
decorate_state!(s::AbstractManoptSolverState)

decorate the AbstractManoptSolverStates with specific decorators.

Optional arguments

optional arguments provide necessary details on the decorators.

  • debug: (Array{Union{Symbol,DebugAction,String,Int},1}()) a set of symbols representing DebugActions, Strings used as dividers and a sub-sampling integer. These are passed as a DebugGroup within :Iteration to the DebugSolverState decorator dictionary. Only exception is :Stop that is passed to :Stop.
  • record: (Array{Union{Symbol,RecordAction,Int},1}()) specify recordings by using Symbols or RecordActions directly. An integer can again be used for only recording every $i$th iteration.
  • return_state: (false) indicate whether to wrap the options in a ReturnSolverState, indicating that the solver should return options and not (only) the minimizer.

other keywords are ignored.

See also

DebugSolverState, RecordSolverState, ReturnSolverState

source

A simple example is the

as well as DebugSolverState and RecordSolverState.

State actions

A state action is a struct for callback functions that can be attached within for example the just mentioned debug decorator or the record decorator.

Several state decorators or actions might store intermediate values like the (last) iterate to compute some change or the last gradient. In order to minimise the storage of these, there is a generic StoreStateAction that acts as generic common storage that can be shared among different actions.

Manopt.StoreStateActionType
StoreStateAction <: AbstractStateAction

internal storage for AbstractStateActions to store a tuple of fields from an AbstractManoptSolverStates

This functor possesses the usual interface of functions called during an iteration and acts on (p, s, i), where p is a AbstractManoptProblem, s is an AbstractManoptSolverState and i is the current iteration.

Fields

  • values: a dictionary to store interim values based on certain Symbols
  • keys: a Vector of Symbols to refer to fields of AbstractManoptSolverState
  • point_values: a NamedTuple of mutable values of points on a manifold to be stored in StoreStateAction. Manifold is later determined by AbstractManoptProblem passed to update_storage!.
  • point_init: a NamedTuple of boolean values indicating whether a point in point_values with matching key has been already initialized to a value. When it is false, it corresponds to a general value not being stored for the key present in the vector keys.
  • vector_values: a NamedTuple of mutable values of tangent vectors on a manifold to be stored in StoreStateAction. Manifold is later determined by AbstractManoptProblem passed to update_storage!. It is not specified at which point the vectors are tangent but for storage it should not matter.
  • vector_init: a NamedTuple of boolean values indicating whether a tangent vector in vector_values: with matching key has been already initialized to a value. When it is false, it corresponds to a general value not being stored for the key present in the vector keys.
  • once: whether to update the internal values only once per iteration
  • lastStored: last iterate, where this AbstractStateAction was called (to determine once)

To handle the general storage, use get_storage and has_storage with keys as Symbols. For the point storage use PointStorageKey. For tangent vector storage use VectorStorageKey. Point and tangent storage have been optimized to be more efficient.

Constructors

StoreStateAction(s::Vector{Symbol})

This is equivalent as providing s to the keyword store_fields, just that here, no manifold is necessity for the construction.

StoreStateAction(M)

Keyword arguments

  • store_fields (Symbol[])
  • store_points (Symbol[])
  • store_vectors (Symbol[])

as vectors of symbols each referring to fields of the state (lower case symbols) or semantic ones (upper case).

  • p_init (rand(M))
  • X_init (zero_vector(M, p_init))

are used to initialize the point and vector storage, change these if you use other types (than the default) for your points/vectors on M.

  • once (true) whether to update internal storage only once per iteration or on every update call
source
Manopt.get_storageFunction
get_storage(a::AbstractStateAction, key::Symbol)

Return the internal value of the AbstractStateActiona at the Symbolkey.

source
get_storage(a::AbstractStateAction, ::PointStorageKey{key}) where {key}

Return the internal value of the AbstractStateActiona at the Symbolkey that represents a point.

source
get_storage(a::AbstractStateAction, ::VectorStorageKey{key}) where {key}

Return the internal value of the AbstractStateActiona at the Symbolkey that represents a vector.

source
Manopt.has_storageFunction
has_storage(a::AbstractStateAction, key::Symbol)

Return whether the AbstractStateActiona has a value stored at the Symbolkey.

source
has_storage(a::AbstractStateAction, ::PointStorageKey{key}) where {key}

Return whether the AbstractStateActiona has a point value stored at the Symbolkey.

source
has_storage(a::AbstractStateAction, ::VectorStorageKey{key}) where {key}

Return whether the AbstractStateActiona has a point value stored at the Symbolkey.

source
Manopt.update_storage!Function
update_storage!(a::AbstractStateAction, amp::AbstractManoptProblem, s::AbstractManoptSolverState)

Update the AbstractStateActiona internal values to the ones given on the AbstractManoptSolverStates. Optimized using the information from amp

source
update_storage!(a::AbstractStateAction, d::Dict{Symbol,<:Any})

Update the AbstractStateActiona internal values to the ones given in the dictionary d. The values are merged, where the values from d are preferred.

source

as well as two internal functions

Abstract states

In a few cases it is useful to have a hierarchy of types. These are

For the sub problem state, there are two access functions

Manopt.get_sub_problemFunction
get_sub_problem(ams::AbstractSubProblemSolverState)

Access the sub problem of a solver state that involves a sub optimisation task. By default this returns ams.sub_problem.

source
Manopt.get_sub_stateFunction
get_sub_state(ams::AbstractSubProblemSolverState)

Access the sub state of a solver state that involves a sub optimisation task. By default this returns ams.sub_state.

source