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SG++-Doxygen-Documentation
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Class that stores, generates and manipulates a density function during online phase in on/off learning. More...
#include <DBMatOnlineDE.hpp>
Public Member Functions | |
void | computeDensityDifferenceFunction (DataVector &alpha, DataMatrix &mp, DataMatrix &mq, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool save_b=false, bool do_cv=false) |
Computes the density difference function for two data matrix instances. | |
void | computeDensityDifferenceFunction (DataVector &alpha, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool do_cv=false) |
Computes the density difference function again based on the saved b's (only applicable for streaming) | |
void | computeDensityFunction (DataVector &alpha, DataMatrix &m, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool save_b=false, bool do_cv=false) |
Computes the density function for a certain data matrix. | |
void | computeDensityFunction (DataVector &alpha, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool do_cv=false) |
Computes the density function again based on the saved b's (only applicable for streaming) | |
void | computeDensityFunctionParallel (DataVectorDistributed &alpha, DataMatrix &m, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, const ParallelConfiguration ¶llelConfig, std::shared_ptr< BlacsProcessGrid > processGrid, bool save_b=false, bool do_cv=false, std::list< size_t > *deletedPoints=nullptr, size_t newPoints=0) |
Computes the density function for a certain data matrix in parallel using ScaLAPACK. | |
void | computeDensityFunctionParallel (DataVectorDistributed &alpha, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, const ParallelConfiguration ¶llelConfig, std::shared_ptr< BlacsProcessGrid > processGrid, bool do_cv=false) |
Computes the density function again based on the saved b's (only applicable for streaming) in parallel on a cluster using ScaLAPACK. | |
DataVector | computeWeightedBFromBatch (DataMatrix &m, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool weighted) |
Computes/updates the b vector for the given batch of data. | |
DataVectorDistributed | computeWeightedBFromBatchParallel (DataMatrix &m, Grid &grid, const DensityEstimationConfiguration &densityEstimationConfig, const ParallelConfiguration ¶llelConfig, std::shared_ptr< BlacsProcessGrid > processGrid, bool weighted) |
Computes/updates the b vector for the given batch of data in parallel using ScaLAPACK. | |
std::vector< DataVector > | computeWeightedBFromBatchTwoDatasets (DataMatrix &mp, DataMatrix &mq, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool weighted) |
Initializes the b vector for the given batch of data in two datasets scenarios. | |
DBMatOnlineDE (DBMatOffline &offline, Grid &grid, double lambda, double beta=0.) | |
Constructor. | |
double | eval (DataVector &alpha, const DataVector &p, Grid &grid, bool force=false) |
Evaluates the density function at a certain point. | |
void | eval (DataVector &alpha, DataMatrix &values, DataVector &results, Grid &grid, bool force=false) |
Evaluates the density function on multiple points. | |
void | evalParallel (DataVector &alpha, DataMatrix &values, DataVectorDistributed &results, Grid &grid, bool force=false) |
Evaluates the density function on multiple points using parallelization. | |
double | getBeta () |
Returns the current weighting factor. | |
bool | isComputed () |
Returns if the surplus has already been computed. | |
double | normalize (DataVector &alpha, Grid &grid, size_t samples=1000) |
Normalize the Density. | |
double | normalizeQuadrature (DataVector &alpha, Grid &grid) |
Normalize the Density using Quadrature. | |
void | resetTraining () |
Resets the training state of the model. | |
void | setBeta (double beta) |
Sets the weighting factor. | |
virtual void | syncDistributedDecomposition (std::shared_ptr< BlacsProcessGrid > processGrid, const ParallelConfiguration ¶llelConfig) |
Synchronizes the distributed decomposition, only has an effect if ScaLAPACK is used. | |
void | updateRhs (size_t gridSize, std::vector< size_t > &deletedPoints) |
Restructures the rhs (b vector) of the system matrix. | |
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DBMatOnline (const DBMatOnline &rhs)=delete | |
DBMatOnline (DBMatOffline &o) | |
Constructor. | |
DBMatOnline (DBMatOnline &&rhs)=default | |
DBMatOffline & | getOfflineObject () |
Returns a reference to the offline object. | |
const DBMatOffline & | getOfflineObject () const |
DBMatOnline & | operator= (const DBMatOnline &rhs)=delete |
DBMatOnline & | operator= (DBMatOnline &&rhs)=delete |
void | setLambda (double lambda) |
virtual std::vector< size_t > | updateSystemMatrixDecomposition (DensityEstimationConfiguration &densityEstimationConfig, Grid &grid, size_t numAddedGridPoints, std::vector< size_t > &deletedGridPointIndices, double lambda) |
Update the system matrix decomposition after the grid has been modified. | |
virtual | ~DBMatOnline ()=default |
Destructor. | |
Protected Member Functions | |
double | computeL2Error (DataVector &alpha, Grid &grid) |
double | resDensity (DataVector &alpha, Grid &grid) |
virtual void | solveSLE (DataVector &alpha, DataVector &b, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool do_cv)=0 |
virtual void | solveSLEParallel (DataVectorDistributed &alpha, DataVectorDistributed &b, Grid &grid, DensityEstimationConfiguration &densityEstimationConfig, bool do_cv=0)=0 |
Protected Attributes | |
double | beta |
DataVector | bSave |
std::unique_ptr< DataVectorDistributed > | bSaveDistributed |
DataVector | bSaveExtra |
DataVector | bTotalPoints |
std::unique_ptr< DataVectorDistributed > | bTotalPointsDistributed |
DataVector | bTotalPointsExtra |
bool | distributedVectorsInitialized |
bool | functionComputed |
double | lambda |
bool | localVectorsInitialized |
double | normFactor |
size_t | oDim |
DataMatrix * | testMat |
DataMatrix * | testMatRes |
bool | useExtraLocalVectors |
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DBMatOffline & | offlineObject |
Class that stores, generates and manipulates a density function during online phase in on/off learning.
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explicit |
Constructor.
offline | The offline object we base our evaluations on. |
grid | The underlying grid (TODO(fuchsgruber) do we need this?) |
lambda | The regularization strength (TODO(fuchsgruber) remove this) |
beta | The initial weighting factor |
References functionComputed, grid(), and oDim.
void sgpp::datadriven::DBMatOnlineDE::computeDensityDifferenceFunction | ( | DataVector & | alpha, |
DataMatrix & | mp, | ||
DataMatrix & | mq, | ||
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
bool | save_b = false , |
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bool | do_cv = false |
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Computes the density difference function for two data matrix instances.
alpha | the vector where surplusses for the density function will be stored |
mp | the matrix that contains the data points for the first input dataset |
mq | the matrix that contains the data points for the second input dataset |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation |
save_b | Indicates whether the old right hand side should be saved and combined with the new right hand side (aka streaming) |
do_cv | Indicates whether crossvalidation should take place |
References alpha, beta, bSave, bSaveExtra, bTotalPoints, bTotalPointsExtra, computeWeightedBFromBatchTwoDatasets(), functionComputed, sgpp::base::DataVector::get(), sgpp::datadriven::DBMatOffline::getDecomposedMatrix(), sgpp::base::DataMatrix::getNcols(), sgpp::base::DataMatrix::getNrows(), grid(), localVectorsInitialized, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::base::DataVector::set(), solveSLE(), and useExtraLocalVectors.
void sgpp::datadriven::DBMatOnlineDE::computeDensityDifferenceFunction | ( | DataVector & | alpha, |
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
bool | do_cv = false |
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Computes the density difference function again based on the saved b's (only applicable for streaming)
alpha | the vector where surplusses for the density function will be stored |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation combined with the new right hand side (aka streaming) |
do_cv | Indicates whether crossvalidation should take place |
References alpha, bSave, bSaveExtra, bTotalPoints, bTotalPointsExtra, functionComputed, sgpp::base::DataVector::get(), grid(), and solveSLE().
void sgpp::datadriven::DBMatOnlineDE::computeDensityFunction | ( | DataVector & | alpha, |
DataMatrix & | m, | ||
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
bool | save_b = false , |
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bool | do_cv = false |
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Computes the density function for a certain data matrix.
alpha | the vector where surplusses for the density function will be stored |
m | the matrix that contains the data points |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation |
save_b | Indicates whether the old right hand side should be saved and combined with the new right hand side (aka streaming) |
do_cv | Indicates whether crossvalidation should take place |
References alpha, beta, bSave, bTotalPoints, computeWeightedBFromBatch(), functionComputed, sgpp::base::DataVector::get(), sgpp::datadriven::DBMatOffline::getDecomposedMatrix(), sgpp::base::DataMatrix::getNcols(), grid(), localVectorsInitialized, m, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::base::DataVector::set(), and solveSLE().
void sgpp::datadriven::DBMatOnlineDE::computeDensityFunction | ( | DataVector & | alpha, |
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
bool | do_cv = false |
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) |
Computes the density function again based on the saved b's (only applicable for streaming)
alpha | the vector where surplusses for the density function will be stored |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation combined with the new right hand side (aka streaming) |
do_cv | Indicates whether crossvalidation should take place |
References alpha, bSave, bTotalPoints, functionComputed, sgpp::base::DataVector::get(), grid(), and solveSLE().
void sgpp::datadriven::DBMatOnlineDE::computeDensityFunctionParallel | ( | DataVectorDistributed & | alpha, |
DataMatrix & | m, | ||
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
const ParallelConfiguration & | parallelConfig, | ||
std::shared_ptr< BlacsProcessGrid > | processGrid, | ||
bool | save_b = false , |
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bool | do_cv = false , |
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std::list< size_t > * | deletedPoints = nullptr , |
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size_t | newPoints = 0 |
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Computes the density function for a certain data matrix in parallel using ScaLAPACK.
alpha | the distributed vector where surplusses for the density function will be stored |
m | the matrix that contains the data points, currently every process has to have the data points |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation |
parallelConfig | configuration for ScaLAPACK |
processGrid | pointer to BlacsProcessGrid |
save_b | Indicates whether the old right hand side should be saved and combined with the new right hand side (aka streaming) |
do_cv | Indicates whether crossvalidation should take place |
deletedPoints | indicates the indices of removed grid points due to coarsening |
newPoints | indicates the amount of added points due to refinement |
References alpha, beta, bSaveDistributed, bTotalPointsDistributed, computeWeightedBFromBatchParallel(), distributedVectorsInitialized, functionComputed, sgpp::datadriven::DBMatOffline::getDecomposedMatrix(), sgpp::base::DataMatrix::getNcols(), grid(), m, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::datadriven::ParallelConfiguration::rowBlockSize_, and solveSLEParallel().
void sgpp::datadriven::DBMatOnlineDE::computeDensityFunctionParallel | ( | DataVectorDistributed & | alpha, |
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
const ParallelConfiguration & | parallelConfig, | ||
std::shared_ptr< BlacsProcessGrid > | processGrid, | ||
bool | do_cv = false |
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) |
Computes the density function again based on the saved b's (only applicable for streaming) in parallel on a cluster using ScaLAPACK.
alpha | the vector where surplusses for the density function will be stored |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation combined with the new right hand side (aka streaming) |
parallelConfig | configuration for ScaLAPACK |
processGrid | pointer to BlacsProcessGrid |
do_cv | Indicates whether crossvalidation should take place |
References alpha, bSaveDistributed, bTotalPointsDistributed, functionComputed, grid(), sgpp::datadriven::ParallelConfiguration::rowBlockSize_, and solveSLEParallel().
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DataVector sgpp::datadriven::DBMatOnlineDE::computeWeightedBFromBatch | ( | DataMatrix & | m, |
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
bool | weighted | ||
) |
Computes/updates the b vector for the given batch of data.
m | the matrix that contains the data points |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation |
weighted | Flag to decide whether to weight the b vector with the no. of points |
References sgpp::op_factory::createOperationMultipleEval(), sgpp::op_factory::createOperationMultipleEvalInter(), sgpp::datadriven::DensityEstimationConfiguration::decomposition_, sgpp::datadriven::DBMatOnlineDE_SMW::getB(), sgpp::datadriven::DBMatOnlineDEOrthoAdapt::getB(), sgpp::datadriven::DBMatOffline::getDecomposedMatrix(), sgpp::base::DataMatrix::getNcols(), grid(), sgpp::datadriven::DBMatOffline::interactions, sgpp::datadriven::LU, m, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::datadriven::OrthoAdapt, sgpp::datadriven::SMW_chol, and sgpp::datadriven::SMW_ortho.
Referenced by computeDensityFunction().
DataVectorDistributed sgpp::datadriven::DBMatOnlineDE::computeWeightedBFromBatchParallel | ( | DataMatrix & | m, |
Grid & | grid, | ||
const DensityEstimationConfiguration & | densityEstimationConfig, | ||
const ParallelConfiguration & | parallelConfig, | ||
std::shared_ptr< BlacsProcessGrid > | processGrid, | ||
bool | weighted | ||
) |
Computes/updates the b vector for the given batch of data in parallel using ScaLAPACK.
m | the matrix that contains the data points, currently every process has to have the data points |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation |
parallelConfig | ScaLAPACK configuration |
processGrid | process grid for ScaLAPACK |
weighted | Flag to decide whether to weight the b vector with the no. of points |
References sgpp::op_factory::createOperationMultipleEval(), sgpp::datadriven::DensityEstimationConfiguration::decomposition_, sgpp::datadriven::DBMatOnlineDEOrthoAdapt::getB(), sgpp::datadriven::DBMatOnlineDE_SMW::getBDistributed(), sgpp::datadriven::DBMatOffline::getDecomposedMatrix(), sgpp::datadriven::DataMatrixDistributed::getGlobalCols(), sgpp::base::DataMatrix::getNcols(), grid(), sgpp::datadriven::DBMatOffline::interactions, m, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::datadriven::OrthoAdapt, sgpp::datadriven::ParallelConfiguration::rowBlockSize_, sgpp::datadriven::SCALAPACK, sgpp::datadriven::SMW_chol, and sgpp::datadriven::SMW_ortho.
Referenced by computeDensityFunctionParallel().
std::vector< DataVector > sgpp::datadriven::DBMatOnlineDE::computeWeightedBFromBatchTwoDatasets | ( | DataMatrix & | mp, |
DataMatrix & | mq, | ||
Grid & | grid, | ||
DensityEstimationConfiguration & | densityEstimationConfig, | ||
bool | weighted | ||
) |
Initializes the b vector for the given batch of data in two datasets scenarios.
Does not compute the actual b, but initializes it and computes the two dataset contributions bp and bq. All these three vectors are returned, in this order, if weighted is false. Otherwise, only the final b is returned and usable in the std::vector.
mp | the matrix that contains the first data points |
mq | the matrix that contains the second data points |
grid | The underlying grid |
densityEstimationConfig | Configuration for the density estimation |
weighted | Flag to decide whether to weight the b vector with the no. of points |
References sgpp::op_factory::createOperationMultipleEval(), sgpp::op_factory::createOperationMultipleEvalInter(), sgpp::datadriven::DensityEstimationConfiguration::decomposition_, sgpp::base::DataVector::get(), sgpp::datadriven::DBMatOnlineDE_SMW::getB(), sgpp::datadriven::DBMatOnlineDEOrthoAdapt::getB(), sgpp::datadriven::DBMatOffline::getDecomposedMatrix(), sgpp::base::DataMatrix::getNcols(), sgpp::base::DataMatrix::getNrows(), grid(), sgpp::datadriven::DBMatOffline::interactions, sgpp::datadriven::LU, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::datadriven::OrthoAdapt, sgpp::base::DataVector::setAll(), sgpp::datadriven::SMW_chol, and sgpp::datadriven::SMW_ortho.
Referenced by computeDensityDifferenceFunction().
double sgpp::datadriven::DBMatOnlineDE::eval | ( | DataVector & | alpha, |
const DataVector & | p, | ||
Grid & | grid, | ||
bool | force = false |
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Evaluates the density function at a certain point.
alpha | the vector of surplusses |
p | the point at which the function is evaluated |
grid | the underlying grid |
force | if set, it will even try to evaluate if the internal state recommends otherwise |
References alpha, sgpp::op_factory::createOperationEval(), functionComputed, grid(), and normFactor.
Referenced by computeL2Error(), python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), and normalize().
void sgpp::datadriven::DBMatOnlineDE::eval | ( | DataVector & | alpha, |
DataMatrix & | values, | ||
DataVector & | results, | ||
Grid & | grid, | ||
bool | force = false |
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) |
Evaluates the density function on multiple points.
alpha | the vector of surplusses |
values | the points at which the function is evaluated |
results | the result of the evaluation |
grid | the underlying grid |
force | if set, it will even try to evaluate if the internal state recommends otherwise |
References alpha, sgpp::op_factory::createOperationMultipleEval(), sgpp::op_factory::createOperationMultipleEvalInter(), functionComputed, grid(), sgpp::datadriven::DBMatOffline::interactions, sgpp::base::DataVector::mult(), normFactor, and sgpp::datadriven::DBMatOnline::offlineObject.
Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity().
void sgpp::datadriven::DBMatOnlineDE::evalParallel | ( | DataVector & | alpha, |
DataMatrix & | values, | ||
DataVectorDistributed & | results, | ||
Grid & | grid, | ||
bool | force = false |
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Evaluates the density function on multiple points using parallelization.
alpha | the vector of surplusses |
values | the points at which the function is evaluated |
results | the result of the evaluation |
grid | the underlying grid |
force | if set, it will even try to evaluate if the internal state recommends otherwise |
References alpha, sgpp::op_factory::createOperationMultipleEval(), functionComputed, grid(), sgpp::datadriven::DBMatOffline::interactions, normFactor, sgpp::datadriven::DBMatOnline::offlineObject, sgpp::datadriven::SCALAPACK, and sgpp::datadriven::DataVectorDistributed::scale().
double sgpp::datadriven::DBMatOnlineDE::getBeta | ( | ) |
Returns the current weighting factor.
References beta.
bool sgpp::datadriven::DBMatOnlineDE::isComputed | ( | ) |
Returns if the surplus has already been computed.
References functionComputed.
double sgpp::datadriven::DBMatOnlineDE::normalize | ( | DataVector & | alpha, |
Grid & | grid, | ||
size_t | samples = 1000 |
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) |
Normalize the Density.
alpha | the vector of surplusses |
grid | the underlying grid |
samples | number of samples to be used for MC quadrature |
References eval(), grid(), normFactor, and oDim.
double sgpp::datadriven::DBMatOnlineDE::normalizeQuadrature | ( | DataVector & | alpha, |
Grid & | grid | ||
) |
Normalize the Density using Quadrature.
alpha | the vector of surplusses |
grid | the underlying grid |
References alpha, sgpp::op_factory::createOperationQuadrature(), sgpp::base::OperationQuadrature::doQuadrature(), grid(), and normFactor.
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void sgpp::datadriven::DBMatOnlineDE::resetTraining | ( | ) |
Resets the training state of the model.
References distributedVectorsInitialized, functionComputed, and localVectorsInitialized.
void sgpp::datadriven::DBMatOnlineDE::setBeta | ( | double | beta | ) |
Sets the weighting factor.
beta | the new weighting factor. If set to 0, no plasticity takes place. |
References beta.
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protectedpure virtual |
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protectedpure virtual |
Implemented in sgpp::datadriven::DBMatOnlineDE_SMW, sgpp::datadriven::DBMatOnlineDEChol, and sgpp::datadriven::DBMatOnlineDEOrthoAdapt.
Referenced by computeDensityFunctionParallel(), and computeDensityFunctionParallel().
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Synchronizes the distributed decomposition, only has an effect if ScaLAPACK is used.
Reimplemented in sgpp::datadriven::DBMatOnlineDE_SMW, and sgpp::datadriven::DBMatOnlineDEOrthoAdapt.
References sgpp::datadriven::DBMatOnline::offlineObject, and sgpp::datadriven::DBMatOffline::syncDistributedDecomposition().
void sgpp::datadriven::DBMatOnlineDE::updateRhs | ( | size_t | gridSize, |
std::vector< size_t > & | deletedPoints | ||
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Restructures the rhs (b vector) of the system matrix.
This is only availible for streaming, i.e. when computeDensityFunction was called with save_b = true. First b is coarsened, then extended according to the new grid size (refinement).
gridSize | grid size after coarsening and refinement (inherently gives the number of points added during refinement after coarsening) |
deletedPoints | pointer to list of indexes that will be removed from b |
References bSave, bSaveDistributed, bSaveExtra, bTotalPoints, bTotalPointsDistributed, bTotalPointsExtra, distributedVectorsInitialized, functionComputed, localVectorsInitialized, sgpp::base::DataVector::remove(), sgpp::base::DataVector::resizeZero(), and useExtraLocalVectors.
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Referenced by computeDensityDifferenceFunction(), computeDensityFunction(), computeDensityFunctionParallel(), getBeta(), and setBeta().
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Referenced by computeDensityFunctionParallel(), computeDensityFunctionParallel(), and updateRhs().
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Referenced by computeDensityDifferenceFunction(), computeDensityDifferenceFunction(), and updateRhs().
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Referenced by computeDensityFunctionParallel(), computeDensityFunctionParallel(), and updateRhs().
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Referenced by computeDensityDifferenceFunction(), computeDensityDifferenceFunction(), and updateRhs().
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Referenced by computeDensityFunctionParallel(), resetTraining(), and updateRhs().
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Referenced by computeDensityDifferenceFunction(), computeDensityDifferenceFunction(), computeDensityFunction(), computeDensityFunction(), computeDensityFunctionParallel(), computeDensityFunctionParallel(), DBMatOnlineDE(), eval(), eval(), evalParallel(), isComputed(), resetTraining(), and updateRhs().
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Referenced by sgpp::datadriven::DBMatOnlineDEChol::buildCholSolver(), sgpp::datadriven::DBMatOnlineDEChol::solveSLE(), sgpp::datadriven::DBMatOnlineDEChol::solveSLEParallel(), sgpp::datadriven::DBMatOnlineDE_SMW::updateSystemMatrixDecomposition(), sgpp::datadriven::DBMatOnlineDEChol::updateSystemMatrixDecomposition(), sgpp::datadriven::DBMatOnlineDEOrthoAdapt::updateSystemMatrixDecomposition(), and sgpp::datadriven::DBMatOnlineDE_SMW::updateSystemMatrixDecompositionParallel().
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Referenced by computeDensityDifferenceFunction(), computeDensityFunction(), resetTraining(), and updateRhs().
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Referenced by eval(), eval(), evalParallel(), normalize(), and normalizeQuadrature().
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Referenced by DBMatOnlineDE(), and normalize().
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Referenced by computeL2Error(), and resDensity().
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Referenced by computeL2Error().
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Referenced by computeDensityDifferenceFunction(), and updateRhs().