Dakota
Version
Explore and Predict with Confidence
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Method for sequential hybrid iteration using multiple optimization and nonlinear least squares methods on multiple models of varying fidelity. More...
Public Member Functions | |
SeqHybridMetaIterator (ProblemDescDB &problem_db) | |
standard constructor | |
SeqHybridMetaIterator (ProblemDescDB &problem_db, Model &model) | |
alternate constructor | |
~SeqHybridMetaIterator () | |
destructor | |
Public Member Functions inherited from MetaIterator | |
bool | resize () |
reinitializes iterator based on new variable size | |
Public Member Functions inherited from Iterator | |
Iterator (std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
default constructor More... | |
Iterator (ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
standard envelope constructor, which constructs its own model(s) More... | |
Iterator (ProblemDescDB &problem_db, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
alternate envelope constructor which uses the ProblemDescDB but accepts a model from a higher level (meta-iterator) context, instead of constructing its own More... | |
Iterator (const String &method_string, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
alternate envelope constructor for instantiations by name without the ProblemDescDB More... | |
Iterator (const Iterator &iterator) | |
copy constructor More... | |
virtual | ~Iterator () |
destructor | |
Iterator | operator= (const Iterator &iterator) |
assignment operator | |
virtual void | initialize_run () |
utility function to perform common operations prior to pre_run(); typically memory initialization; setting of instance pointers More... | |
virtual void | pre_run () |
pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More... | |
virtual void | finalize_run () |
utility function to perform common operations following post_run(); deallocation and resetting of instance pointers More... | |
virtual void | pre_output () |
write variables to file, following pre-run | |
virtual void | post_input () |
read tabular data for post-run mode | |
virtual void | reset () |
restore initial state for repeated sub-iterator executions | |
virtual void | nested_variable_mappings (const SizetArray &c_index1, const SizetArray &di_index1, const SizetArray &ds_index1, const SizetArray &dr_index1, const ShortArray &c_target2, const ShortArray &di_target2, const ShortArray &ds_target2, const ShortArray &dr_target2) |
set primaryA{CV,DIV,DRV}MapIndices, secondaryA{CV,DIV,DRV}MapTargets within derived Iterators; supports computation of higher-level sensitivities in nested contexts (e.g., derivatives of statistics w.r.t. inserted design variables) | |
virtual void | nested_response_mappings (const RealMatrix &primary_coeffs, const RealMatrix &secondary_coeffs) |
set primaryResponseCoefficients, secondaryResponseCoefficients within derived Iterators; Necessary for scalarization case in MLMC NonDMultilevelSampling to map scalarization in nested context | |
virtual void | unpack_parameters_buffer (MPIUnpackBuffer &recv_buffer, int job_index) |
used by IteratorScheduler to unpack starting data for an iterator run | |
virtual const VariablesArray & | variables_array_results () |
return multiple final iterator solutions (variables). This should only be used if returns_multiple_points() returns true. | |
virtual const ResponseArray & | response_array_results () |
return multiple final iterator solutions (response). This should only be used if returns_multiple_points() returns true. | |
virtual void | response_results_active_set (const ActiveSet &set) |
set the requested data for the final iterator response results | |
virtual const RealSymMatrix & | response_error_estimates () const |
return error estimates associated with the final iterator solution | |
virtual bool | accepts_multiple_points () const |
indicates if this iterator accepts multiple initial points. Default return is false. Override to return true if appropriate. | |
virtual bool | returns_multiple_points () const |
indicates if this iterator returns multiple final points. Default return is false. Override to return true if appropriate. | |
virtual void | initial_point (const Variables &pt) |
sets the initial point for this iterator (user-functions mode for which Model updating is not used) | |
virtual void | initial_point (const RealVector &pt) |
sets the initial point (active continuous variables) for this iterator (user-functions mode for which Model updating is not used) | |
virtual void | initial_points (const VariablesArray &pts) |
sets the multiple initial points for this iterator. This should only be used if accepts_multiple_points() returns true. | |
virtual void | variable_bounds (const RealVector &cv_lower_bnds, const RealVector &cv_upper_bnds) |
assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used) | |
virtual void | linear_constraints (const RealMatrix &lin_ineq_coeffs, const RealVector &lin_ineq_lb, const RealVector &lin_ineq_ub, const RealMatrix &lin_eq_coeffs, const RealVector &lin_eq_tgt) |
assign linear inequality and linear equality constraints for this iterator (user-functions mode for which Model updating is not used) | |
virtual void | nonlinear_constraints (const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt) |
assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used) | |
virtual void | initialize_graphics (int iterator_server_id=1) |
initialize the 2D graphics window and the tabular graphics data More... | |
virtual const Model & | algorithm_space_model () const |
return the result of any recasting or surrogate model recursion layered on top of iteratedModel by the derived Iterator ctor chain | |
virtual void | check_sub_iterator_conflict () |
detect any conflicts due to recursive use of the same Fortran solver More... | |
virtual unsigned short | uses_method () const |
return name of any enabling iterator used by this iterator | |
virtual void | method_recourse () |
perform a method switch, if possible, due to a detected conflict | |
virtual const VariablesArray & | all_variables () |
return the complete set of evaluated variables | |
virtual const RealMatrix & | all_samples () |
return the complete set of evaluated samples | |
virtual const IntResponseMap & | all_responses () const |
return the complete set of computed responses | |
virtual size_t | num_samples () const |
get the current number of samples | |
virtual void | sampling_reset (size_t min_samples, bool all_data_flag, bool stats_flag) |
reset sampling iterator to use at least min_samples | |
virtual void | sampling_reference (size_t samples_ref) |
set reference number of samples, which is a lower bound during reset | |
virtual void | sampling_increment () |
increment to next in sequence of refinement samples | |
virtual void | random_seed (int seed) |
set randomSeed, if present | |
virtual unsigned short | sampling_scheme () const |
return sampling name | |
virtual bool | compact_mode () const |
returns Analyzer::compactMode | |
void | init_communicators (ParLevLIter pl_iter) |
initialize the communicators associated with this Iterator instance | |
void | set_communicators (ParLevLIter pl_iter) |
set the communicators associated with this Iterator instance | |
void | free_communicators (ParLevLIter pl_iter) |
free the communicators associated with this Iterator instance | |
void | resize_communicators (ParLevLIter pl_iter, bool reinit_comms) |
Resize the communicators. This is called from the letter's resize() | |
void | parallel_configuration_iterator (ParConfigLIter pc_iter) |
set methodPCIter | |
ParConfigLIter | parallel_configuration_iterator () const |
return methodPCIter | |
void | parallel_configuration_iterator_map (std::map< size_t, ParConfigLIter > pci_map) |
set methodPCIterMap | |
std::map< size_t, ParConfigLIter > | parallel_configuration_iterator_map () const |
return methodPCIterMap | |
void | run (ParLevLIter pl_iter) |
invoke set_communicators(pl_iter) prior to run() | |
void | run () |
orchestrate initialize/pre/core/post/finalize phases More... | |
void | assign_rep (std::shared_ptr< Iterator > iterator_rep) |
replaces existing letter with a new one More... | |
void | iterated_model (const Model &model) |
set the iteratedModel (iterators and meta-iterators using a single model instance) | |
Model & | iterated_model () |
return the iteratedModel (iterators & meta-iterators using a single model instance) | |
ProblemDescDB & | problem_description_db () const |
return the problem description database (probDescDB) | |
ParallelLibrary & | parallel_library () const |
return the parallel library (parallelLib) | |
void | method_name (unsigned short m_name) |
set the method name to an enumeration value | |
unsigned short | method_name () const |
return the method name via its native enumeration value | |
void | method_string (const String &m_str) |
set the method name by string | |
String | method_string () const |
return the method name by string | |
String | method_enum_to_string (unsigned short method_enum) const |
convert a method name enumeration value to a string | |
unsigned short | method_string_to_enum (const String &method_str) const |
convert a method name string to an enumeration value | |
String | submethod_enum_to_string (unsigned short submethod_enum) const |
convert a sub-method name enumeration value to a string | |
const String & | method_id () const |
return the method identifier (methodId) | |
int | maximum_evaluation_concurrency () const |
return the maximum evaluation concurrency supported by the iterator | |
void | maximum_evaluation_concurrency (int max_conc) |
set the maximum evaluation concurrency supported by the iterator | |
size_t | maximum_iterations () const |
return the maximum iterations for this iterator | |
void | maximum_iterations (size_t max_iter) |
set the maximum iterations for this iterator | |
void | convergence_tolerance (Real conv_tol) |
set the method convergence tolerance (convergenceTol) | |
Real | convergence_tolerance () const |
return the method convergence tolerance (convergenceTol) | |
void | output_level (short out_lev) |
set the method output level (outputLevel) | |
short | output_level () const |
return the method output level (outputLevel) | |
void | summary_output (bool summary_output_flag) |
Set summary output control; true enables evaluation/results summary. | |
size_t | num_final_solutions () const |
return the number of solutions to retain in best variables/response arrays | |
void | num_final_solutions (size_t num_final) |
set the number of solutions to retain in best variables/response arrays | |
void | active_set (const ActiveSet &set) |
set the default active set (for use with iterators that employ evaluate_parameter_sets()) | |
const ActiveSet & | active_set () const |
return the default active set (used by iterators that employ evaluate_parameter_sets()) | |
void | active_set_request_vector (const ShortArray &asv) |
return the default active set request vector (used by iterators that employ evaluate_parameter_sets()) | |
const ShortArray & | active_set_request_vector () const |
return the default active set request vector (used by iterators that employ evaluate_parameter_sets()) | |
void | active_set_request_values (short asv_val) |
return the default active set request vector (used by iterators that employ evaluate_parameter_sets()) | |
void | sub_iterator_flag (bool si_flag) |
set subIteratorFlag (and update summaryOutputFlag if needed) | |
bool | is_null () const |
function to check iteratorRep (does this envelope contain a letter?) | |
std::shared_ptr< Iterator > | iterator_rep () const |
returns iteratorRep for access to derived class member functions that are not mapped to the top Iterator level | |
virtual void | eval_tag_prefix (const String &eval_id_str) |
set the hierarchical eval ID tag prefix More... | |
std::shared_ptr< TraitsBase > | traits () const |
returns methodTraits for access to derived class member functions that are not mapped to the top TraitsBase level | |
bool | top_level () |
Return whether the iterator is the top level iterator. | |
void | top_level (bool tflag) |
Set the iterator's top level flag. | |
Protected Member Functions | |
void | core_run () |
Performs the hybrid iteration by executing a sequence of iterators, using a similar sequence of models that may vary in fidelity. | |
void | print_results (std::ostream &s, short results_state=FINAL_RESULTS) |
print the final iterator results More... | |
void | derived_init_communicators (ParLevLIter pl_iter) |
derived class contributions to initializing the communicators associated with this Iterator instance | |
void | derived_set_communicators (ParLevLIter pl_iter) |
derived class contributions to setting the communicators associated with this Iterator instance | |
void | derived_free_communicators (ParLevLIter pl_iter) |
derived class contributions to freeing the communicators associated with this Iterator instance | |
IntIntPair | estimate_partition_bounds () |
estimate the minimum and maximum partition sizes that can be utilized by this Iterator | |
const Variables & | variables_results () const |
return the final solution from selectedIterators (variables) | |
const Response & | response_results () const |
return the final solution from selectedIterators (response) | |
void | initialize_iterator (int job_index) |
used by IteratorScheduler to set the starting data for a run | |
void | pack_parameters_buffer (MPIPackBuffer &send_buffer, int job_index) |
used by IteratorScheduler to pack starting data for an iterator run | |
void | unpack_parameters_initialize (MPIUnpackBuffer &recv_buffer, int job_index) |
used by IteratorScheduler to unpack starting data and initialize an iterator run | |
void | pack_results_buffer (MPIPackBuffer &send_buffer, int job_index) |
used by IteratorScheduler to pack results data from an iterator run | |
void | unpack_results_buffer (MPIUnpackBuffer &recv_buffer, int job_index) |
used by IteratorScheduler to unpack results data from an iterator run | |
void | update_local_results (int job_index) |
used by IteratorScheduler to update local results arrays | |
void | declare_sources () |
Declare sources to the evaluations database. | |
Protected Member Functions inherited from MetaIterator | |
MetaIterator (ProblemDescDB &problem_db) | |
standard constructor | |
MetaIterator (ProblemDescDB &problem_db, Model &model) | |
alternate constructor | |
~MetaIterator () | |
destructor | |
void | post_run (std::ostream &s) |
post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way More... | |
void | check_model (const String &method_ptr, const String &model_ptr) |
check that a model identified by pointer has the same id as the iteratedModel passed through the ctor chain | |
void | allocate_by_pointer (const String &method_ptr, Iterator &the_iterator, Model &the_model) |
initialize the_iterator and the_model based on method_ptr | |
void | allocate_by_name (const String &method_string, const String &model_ptr, Iterator &the_iterator, Model &the_model) |
initialize the_iterator based on method_string | |
std::pair< int, int > | estimate_by_pointer (const String &method_ptr, Iterator &the_iterator, Model &the_model) |
estimate minimum and maximum processors per iterator needed for init_iterator_parallelism(); instantiates the_iterator and the_model as needed, but on minimal processor ranks (is later augmented by allocate_by_pointer()) | |
std::pair< int, int > | estimate_by_name (const String &method_string, const String &model_ptr, Iterator &the_iterator, Model &the_model) |
estimate minimum and maximum processors per iterator needed for init_iterator_parallelism(); instantiates the_iterator and the_model as needed, but on minimal processor ranks (is later augmented by allocate_by_name()) | |
Protected Member Functions inherited from Iterator | |
Iterator (BaseConstructor, ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More... | |
Iterator (NoDBBaseConstructor, unsigned short method_name, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
alternate constructor for base iterator classes constructed on the fly More... | |
Iterator (NoDBBaseConstructor, unsigned short method_name, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
alternate constructor for base iterator classes constructed on the fly More... | |
Iterator (NoDBBaseConstructor, Model &model, size_t max_iter, size_t max_eval, Real conv_tol, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase())) | |
alternate envelope constructor for instantiations without ProblemDescDB More... | |
virtual void | update_from_model (const Model &model) |
set inherited data attributes based on extractions from incoming model | |
virtual const VariablesArray & | initial_points () const |
gets the multiple initial points for this iterator. This will only be meaningful after a call to initial_points mutator. | |
StrStrSizet | run_identifier () const |
get the unique run identifier based on method name, id, and number of executions | |
void | initialize_model_graphics (Model &model, int iterator_server_id) |
helper function that encapsulates initialization operations, modular on incoming Model instance More... | |
void | export_final_surrogates (Model &data_fit_surr_model) |
export final surrogates generated, e.g., GP in EGO and friends More... | |
Private Member Functions | |
void | run_sequential () |
run a sequential hybrid More... | |
void | run_sequential_adaptive () |
run a sequential adaptive hybrid More... | |
void | partition_sets (size_t num_sets, int job_index, size_t &start_index, size_t &job_size) |
convert num_sets and job_index into a start_index and job_size for extraction from parameterSets | |
void | extract_parameter_sets (int job_index, VariablesArray &partial_param_sets) |
extract partial_param_sets from parameterSets based on job_index More... | |
void | update_local_results (PRPArray &prp_results, int job_id) |
update the partial set of final results from the local iterator execution | |
void | initialize_iterator (const VariablesArray ¶m_sets) |
called by unpack_parameters_initialize(MPIUnpackBuffer) and initialize_iterator(int) to update the active Model and Iterator | |
Private Attributes | |
String | seqHybridType |
empty (default) or "adaptive" | |
StringArray | methodStrings |
the list of method pointer or method name identifiers | |
StringArray | modelStrings |
the list of model pointer identifiers for method identification by name | |
bool | lightwtMethodCtor |
use of lightweight Iterator construction by name | |
bool | singlePassedModel |
use of constructor that enforces use of a single passed Model | |
IteratorArray | selectedIterators |
the set of iterators, one for each entry in methodStrings | |
ModelArray | selectedModels |
the set of models, one for each iterator (if not lightweight construction) | |
size_t | seqCount |
hybrid sequence counter: 0 to numIterators-1 | |
Real | progressThreshold |
when the progress metric falls below this threshold, the sequential adaptive hybrid switches to the next method | |
PRP2DArray | prpResults |
2-D array of results corresponding to numIteratorJobs, one set of results per job (iterators may return multiple final solutions) | |
VariablesArray | parameterSets |
1-D array of variable starting points for the iterator jobs | |
Friends | |
class | IteratorScheduler |
protect scheduler callback functions from general access | |
Additional Inherited Members | |
Static Protected Member Functions inherited from Iterator | |
static void | gnewton_set_recast (const Variables &recast_vars, const ActiveSet &recast_set, ActiveSet &sub_model_set) |
conversion of request vector values for the Gauss-Newton Hessian approximation More... | |
Protected Attributes inherited from MetaIterator | |
IteratorScheduler | iterSched |
scheduler for concurrent execution of Iterators | |
int | maxIteratorConcurrency |
maximum number of concurrent sub-iterator executions | |
Protected Attributes inherited from Iterator | |
ProblemDescDB & | probDescDB |
class member reference to the problem description database More... | |
ParallelLibrary & | parallelLib |
class member reference to the parallel library | |
ParConfigLIter | methodPCIter |
the active ParallelConfiguration used by this Iterator instance | |
Model | iteratedModel |
the model to be iterated (for iterators and meta-iterators employing a single model instance) | |
size_t | myModelLayers |
number of Models locally (in Iterator or derived classes) wrapped around the initially passed in Model | |
unsigned short | methodName |
name of the iterator (the user's method spec) | |
Real | convergenceTol |
iteration convergence tolerance | |
size_t | maxIterations |
maximum number of iterations for the method | |
size_t | maxFunctionEvals |
maximum number of fn evaluations for the method | |
int | maxEvalConcurrency |
maximum number of concurrent model evaluations More... | |
ActiveSet | activeSet |
the response data requirements on each function evaluation | |
size_t | numFinalSolutions |
number of solutions to retain in best variables/response arrays | |
VariablesArray | bestVariablesArray |
collection of N best solution variables found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone) | |
ResponseArray | bestResponseArray |
collection of N best solution responses found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone) | |
bool | subIteratorFlag |
flag indicating if this Iterator is a sub-iterator (NestedModel::subIterator or DataFitSurrModel::daceIterator) | |
short | outputLevel |
output verbosity level: {SILENT,QUIET,NORMAL,VERBOSE,DEBUG}_OUTPUT | |
bool | summaryOutputFlag |
flag for summary output (evaluation stats, final results); default true, but false for on-the-fly (helper) iterators and sub-iterator use cases | |
ResultsManager & | resultsDB |
reference to the global iterator results database | |
EvaluationStore & | evaluationsDB |
reference to the global evaluation database | |
EvaluationsDBState | evaluationsDBState |
State of evaluations DB for this iterator. | |
ResultsNames | resultsNames |
valid names for iterator results | |
std::shared_ptr< TraitsBase > | methodTraits |
pointer that retains shared ownership of a TraitsBase object, or child thereof | |
bool | topLevel |
Whether this is the top level iterator. | |
bool | exportSurrogate = false |
whether to export final surrogates | |
String | surrExportPrefix |
base filename for exported surrogates | |
unsigned short | surrExportFormat = NO_MODEL_FORMAT |
(bitwise) format(s) to export | |
Method for sequential hybrid iteration using multiple optimization and nonlinear least squares methods on multiple models of varying fidelity.
Sequential hybrid meta-iteration supports two approaches: (1) the non-adaptive sequential hybrid runs one method to completion, passes its best results as the starting point for a subsequent method, and continues this succession until all methods have been executed (the stopping rules are controlled internally by each iterator), and (2) the adaptive sequential hybrid uses adaptive stopping rules for the iterators that are controlled externally by this method. Any iterator may be used so long as it defines the notion of a final solution which can be passed as starting data for subsequent iterators.
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protectedvirtual |
print the final iterator results
This virtual function provides additional iterator-specific final results outputs beyond the function evaluation summary printed in finalize_run().
Reimplemented from Iterator.
References Response::function_values(), Response::is_null(), Variables::is_null(), MetaIterator::iterSched, IteratorScheduler::messagePass, and SeqHybridMetaIterator::prpResults.
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private |
run a sequential hybrid
In the sequential nonadaptive case, there is no interference with the iterators. Each runs until its own convergence criteria is satisfied. Status: fully operational.
References Iterator::accepts_multiple_points(), ParallelLibrary::bcast(), ParallelLibrary::bcast_hs(), Iterator::initialize_graphics(), Model::interface_id(), Iterator::iteratedModel, IteratorScheduler::iterator_message_lengths(), IteratorScheduler::iteratorCommRank, IteratorScheduler::iteratorCommSize, IteratorScheduler::iteratorScheduling, IteratorScheduler::iteratorServerId, MetaIterator::iterSched, IteratorScheduler::messagePass, Iterator::methodPCIter, SeqHybridMetaIterator::methodStrings, IteratorScheduler::miPLIndex, Iterator::num_final_solutions(), IteratorScheduler::numIteratorJobs, IteratorScheduler::numIteratorServers, SeqHybridMetaIterator::pack_parameters_buffer(), Iterator::parallelLib, SeqHybridMetaIterator::parameterSets, SeqHybridMetaIterator::prpResults, ParallelLibrary::recv(), Iterator::response_results(), IteratorScheduler::schedule_iterators(), SeqHybridMetaIterator::selectedIterators, SeqHybridMetaIterator::selectedModels, ParallelLibrary::send(), SeqHybridMetaIterator::seqCount, SeqHybridMetaIterator::singlePassedModel, MPIPackBuffer::size(), Iterator::summaryOutputFlag, and Iterator::variables_results().
Referenced by SeqHybridMetaIterator::core_run().
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private |
run a sequential adaptive hybrid
In the sequential adaptive case, there is interference with the iterators through the use of the ++ overloaded operator. iterator++ runs the iterator for one cycle, after which a progress_metric is computed. This progress metric is used to dictate method switching instead of each iterator's internal convergence criteria. Status: incomplete.
References Iterator::finalize_run(), Iterator::initialize_graphics(), Iterator::initialize_run(), IteratorScheduler::iteratorCommRank, IteratorScheduler::iteratorServerId, MetaIterator::iterSched, SeqHybridMetaIterator::methodStrings, IteratorScheduler::numIteratorServers, SeqHybridMetaIterator::progressThreshold, Iterator::response_results(), SeqHybridMetaIterator::selectedIterators, SeqHybridMetaIterator::selectedModels, SeqHybridMetaIterator::seqCount, Iterator::summaryOutputFlag, and Iterator::variables_results().
Referenced by SeqHybridMetaIterator::core_run().
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inlineprivate |
extract partial_param_sets from parameterSets based on job_index
This convenience function is executed on an iterator master (static scheduling) or a meta-iterator master (self scheduling) at run initialization time and has access to the full parameterSets array (this is All-Reduced for all peers at the completion of each cycle in run_sequential()).
References SeqHybridMetaIterator::parameterSets, and SeqHybridMetaIterator::partition_sets().
Referenced by SeqHybridMetaIterator::initialize_iterator(), and SeqHybridMetaIterator::pack_parameters_buffer().