#include <crb.hpp>

Detailed Description

template<typename TruthModelType>
class Feel::CRB< TruthModelType >

Certifed Reduced Basis class.

Implements the certified reduced basis method

Author: Christophe Prud'homme

See Also

Inheritance diagram for Feel::CRB< TruthModelType >:

Public Member Functions
Constructors, destructor
	CRB ()
	default constructor

	CRB (std::string name, po::variables_map const &vm)
	constructor from command line options

	CRB (std::string name, po::variables_map const &vm, truth_model_ptrtype const &model)
	constructor from command line options

	CRB (CRB const &o)
	copy constructor

	~CRB ()
	destructor

Operator overloads
CRB &	operator= (CRB const &o)
	copy operator

Accessors
int	factor () const
	return factor

int	maxIter () const

parameterspace_ptrtype	Dmu () const

int	outputIndex () const

int	dimension () const

sampling_ptrtype	trainSampling () const

CRBErrorType	errorType () const

scm_ptrtype	scm () const

void	loadSCMDB ()

Mutators
void	setOutputIndex (uint16_type oindex)
	set the output index

void	setCRBErrorType (CRBErrorType error)
	set the crb error type

void	setTolerance (double tolerance)
	set offline tolerance

void	setTruthModel (truth_model_ptrtype const &model)
	set the truth offline model

void	setMaxIter (int K)
	set max iteration number

void	setFactor (int Factor)
	set factor

void	setOfflineStep (bool b)
	set boolean indicates if we are in offline_step or not

Methods
double	orthonormalize (size_type N, wn_type &wn, int Nm=1)

void	checkResidual (parameter_type const &mu, std::vector< std::vector< double > > const &primal_residual_coeffs, std::vector< std::vector< double > > const &dual_residual_coeffs, element_type &u, element_type &udu) const

void	compareResidualsForTransientProblems (int N, parameter_type const &mu, std::vector< element_type > const &Un, std::vector< element_type > const &Unold, std::vector< element_type > const &Undu, std::vector< element_type > const &Unduold, std::vector< std::vector< double > > const &primal_residual_coeffs, std::vector< std::vector< double > > const &dual_residual_coeffs) const

void	buildFunctionFromRbCoefficients (int N, std::vector< vectorN_type > const &RBcoeff, wn_type const &WN, std::vector< element_ptrtype > &FEMsolutions)

double	checkOrthonormality (int N, const wn_type &wn) const

void	check (size_type N) const

void	computeErrorEstimationEfficiencyIndicator (parameterspace_ptrtype const &Dmu, double &max_ei, double &min_ei, int N=4)

void	exportBasisFunctions (const export_vector_wn_type &wn) const

boost::tuple< double, double >	lb (size_type N, parameter_type const &mu, std::vector< vectorN_type > &uN, std::vector< vectorN_type > &uNdu, std::vector< vectorN_type > &uNold, std::vector< vectorN_type > &uNduold, int K=0) const

void	updateJacobian (const map_dense_vector_type &map_X, map_dense_matrix_type &map_J, const parameter_type &mu, int N) const

void	updateResidual (const map_dense_vector_type &map_X, map_dense_vector_type &map_R, const parameter_type &mu, int N) const

void	computeProjectionInitialGuess (const parameter_type &mu, int N, vectorN_type &initial_guess) const

void	newton (size_type N, parameter_type const &mu, vectorN_type &uN, double &condition_number, double &output) const

element_type	offlineFixedPointPrimal (parameter_type const &mu, sparse_matrix_ptrtype &A, bool zero_iteration)

element_type	offlineFixedPointDual (parameter_type const &mu, element_ptrtype &dual_initial_field, const sparse_matrix_ptrtype &A, const element_type &u, bool zero_iteration)

void	fixedPointPrimal (size_type N, parameter_type const &mu, std::vector< vectorN_type > &uN, std::vector< vectorN_type > &uNold, double &condition_number, std::vector< double > &output_vector, int K=0) const

void	fixedPointDual (size_type N, parameter_type const &mu, std::vector< vectorN_type > &uNdu, std::vector< vectorN_type > &uNduold, std::vector< double > &output_vector, int K=0) const

void	fixedPoint (size_type N, parameter_type const &mu, std::vector< vectorN_type > &uN, std::vector< vectorN_type > &uNdu, std::vector< vectorN_type > &uNold, std::vector< vectorN_type > &uNduold, double &condition_number, std::vector< double > &output_vector, int K=0) const

double	computeConditioning (matrixN_type &A) const

boost::tuple< double, double >	lb (parameter_ptrtype const &mu, size_type N, std::vector< vectorN_type > &uN, std::vector< vectorN_type > &uNdu) const

value_type	ub (size_type N, parameter_type const &mu, std::vector< vectorN_type > &uN, std::vector< vectorN_type > &uNdu) const

value_type	delta (size_type N, parameter_ptrtype const &mu, std::vector< vectorN_type > const &uN, std::vector< vectorN_type > const &uNdu, std::vector< vectorN_type > const &uNold, std::vector< vectorN_type > const &uNduold, int k=0) const

error_estimation_type	delta (size_type N, parameter_type const &mu, std::vector< vectorN_type > const &uN, std::vector< vectorN_type > const &uNdu, std::vector< vectorN_type > const &uNold, std::vector< vectorN_type > const &uNduold, int k=0) const

value_type	ub (size_type K, parameter_ptrtype const &mu, std::vector< vectorN_type > &uN, std::vector< vectorN_type > &uNdu) const

convergence_type	offline ()

max_error_type	maxErrorBounds (size_type N) const
	Retuns maximum value of the relative error. More...

residual_error_type	transientPrimalResidual (int Ncur, parameter_type const &mu, vectorN_type const &Un, vectorN_type const &Unold=vectorN_type(), double time_step=1, double time=1e30) const

residual_error_type	steadyPrimalResidual (int Ncur, parameter_type const &mu, vectorN_type const &Un, double time=0) const

residual_error_type	transientDualResidual (int Ncur, parameter_type const &mu, vectorN_type const &Un, vectorN_type const &Unold=vectorN_type(), double time_step=1, double time=1e30) const

residual_error_type	steadyDualResidual (int Ncur, parameter_type const &mu, vectorN_type const &Un, double time=0) const

value_type	initialDualResidual (int Ncur, parameter_type const &mu, vectorN_type const &Uduini, double time_step) const

void	offlineResidual (int Ncur, int number_of_added_elements=1)

void	offlineResidual (int Ncur, mpl::bool_< true >, int number_of_added_elements=1)

void	offlineResidual (int Ncur, mpl::bool_< false >, int number_of_added_elements=1)

value_type	empiricalErrorEstimation (int Ncur, parameter_type const &mu, int k) const

element_type	expansion (parameter_type const &mu, int N=-1, int time_index=-1)

element_type	expansion (vectorN_type const &u, int const N, wn_type const &WN) const

void	checkInitialGuess (const element_type expansion_uN, parameter_type const &mu, vectorN_type &error) const

void	checkInitialGuess (const element_type expansion_uN, parameter_type const &mu, vectorN_type &error, mpl::bool_< true >) const

void	checkInitialGuess (const element_type expansion_uN, parameter_type const &mu, vectorN_type &error, mpl::bool_< false >) const

boost::tuple< double, double, solutions_tuple, double, double, double, upper_bounds_tuple >	run (parameter_type const &mu, double eps=1e-6, int N=-1)

void	run (const double X, unsigned long N, double Y, unsigned long P)

void	run (const double X, unsigned long N, double Y, unsigned long P, mpl::bool_< true >)

void	run (const double X, unsigned long N, double Y, unsigned long P, mpl::bool_< false >)

sampling_type	randomSampling (int N)

sampling_type	equidistributedSampling (int N)

sampling_ptrtype	wnmu () const

wn_type	wn () const

wn_type	wndu () const

void	saveDB ()

bool	loadDB ()

void	projectionOnPodSpace (const element_type &u, element_ptrtype &projection, const std::string &name_of_space="primal")

bool	useWNmu ()

bool	rebuildDB ()

bool	showMuSelection ()

bool	printErrorDuringOfflineStep ()

void	printMuSelection (void)

void	printErrorsDuringRbConstruction (void)

double	correctionTerms (parameter_type const &mu, std::vector< vectorN_type > const &uN, std::vector< vectorN_type > const &uNdu, std::vector< vectorN_type > const &uNold, int const K=0) const

void	buildVarianceMatrixPhi (int const N)

void	buildVarianceMatrixPhi (int const N, mpl::bool_< true >)

void	buildVarianceMatrixPhi (int const N, mpl::bool_< false >)

WorldComm const &	worldComm () const

void	computationalTimeStatistics (std::string appname)

Public Member Functions inherited from Feel::CRBDB
	CRBDB ()
	default constructor

	CRBDB (std::string prefixdir, std::string name, std::string dbprefix, po::variables_map const &vm)
	constructor from command line options

	CRBDB (CRBDB const &)
	copy constructor

virtual	~CRBDB ()
	destructor

CRBDB &	operator= (CRBDB const &o)
	copy operator

std::string const &	prefixDirectory () const

std::string const &	name () const

std::string const &	dbFilename () const

fs::path	dbLocalPath () const

fs::path	dbSystemPath () const

fs::path	lookForDB () const

po::variables_map	vm ()

po::variables_map	vm () const

bool	isDBLoaded () const

void	setDBFilename (std::string const &filename)
	set the DB filename

Friends
class	boost::serialization::access

Typedefs
typedef TruthModelType	truth_model_type

typedef truth_model_type	model_type

typedef boost::shared_ptr < truth_model_type >	truth_model_ptrtype

typedef double	value_type

typedef boost::tuple< double, double >	bounds_type

typedef ParameterSpace < TruthModelType::ParameterSpaceDimension >	parameterspace_type

typedef boost::shared_ptr < parameterspace_type >	parameterspace_ptrtype

typedef parameterspace_type::element_type	parameter_type

typedef parameterspace_type::element_ptrtype	parameter_ptrtype

typedef parameterspace_type::sampling_type	sampling_type

typedef parameterspace_type::sampling_ptrtype	sampling_ptrtype

typedef boost::tuple< double, parameter_type, size_type, double, double >	relative_error_type

typedef relative_error_type	max_error_type

typedef boost::tuple< double, std::vector< std::vector < double > >, std::vector < std::vector< double > >, double, double >	error_estimation_type

typedef boost::tuple< double, std::vector< double > >	residual_error_type

typedef boost::bimap< int, boost::tuple< double, double, double > >	convergence_type

typedef convergence_type::value_type	convergence

typedef CRB	self_type

typedef CRBSCM< truth_model_type >	scm_type
	scm

typedef boost::shared_ptr < scm_type >	scm_ptrtype

typedef CRBElementsDB < truth_model_type >	crb_elements_db_type
	elements database

typedef boost::shared_ptr < crb_elements_db_type >	crb_elements_db_ptrtype

typedef POD< truth_model_type >	pod_type
	POD.

typedef boost::shared_ptr < pod_type >	pod_ptrtype

typedef model_type::functionspace_type	functionspace_type
	function space type

typedef model_type::functionspace_ptrtype	functionspace_ptrtype

typedef model_type::element_type	element_type
	element of the functionspace type

typedef model_type::element_ptrtype	element_ptrtype

typedef model_type::backend_type	backend_type

typedef boost::shared_ptr < backend_type >	backend_ptrtype

typedef model_type::sparse_matrix_ptrtype	sparse_matrix_ptrtype

typedef model_type::vector_ptrtype	vector_ptrtype

typedef model_type::beta_vector_type	beta_vector_type

typedef Eigen::VectorXd	y_type

typedef std::vector< y_type >	y_set_type

typedef std::vector < boost::tuple< double, double > >	y_bounds_type

typedef std::vector< element_type >	wn_type

typedef boost::tuple < std::vector< wn_type > , std::vector< std::string > >	export_vector_wn_type

typedef std::vector< double >	vector_double_type

typedef boost::shared_ptr < vector_double_type >	vector_double_ptrtype

typedef Eigen::VectorXd	vectorN_type

typedef Eigen::MatrixXd	matrixN_type

typedef Eigen::Map < Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > >	map_dense_matrix_type

typedef Eigen::Map < Eigen::Matrix< double, Eigen::Dynamic, 1 > >	map_dense_vector_type

typedef boost::tuple < std::vector< vectorN_type > , std::vector< vectorN_type > , std::vector< vectorN_type > , std::vector< vectorN_type > >	solutions_tuple

typedef boost::tuple< double, double, double, std::vector < std::vector< double > >, std::vector< std::vector < double > > >	upper_bounds_tuple

typedef std::vector< element_type >	mode_set_type

typedef boost::shared_ptr < mode_set_type >	mode_set_ptrtype

typedef boost::multi_array < value_type, 2 >	array_2_type

typedef boost::multi_array < vectorN_type, 2 >	array_3_type

typedef boost::multi_array < matrixN_type, 2 >	array_4_type

typedef model_type::mesh_type	mesh_type
	mesh type

typedef boost::shared_ptr < mesh_type >	mesh_ptrtype

typedef model_type::space_type	space_type
	space type

typedef boost::shared_ptr < space_type >	space_ptrtype

typedef Bdf< space_type >	bdf_type
	time discretization

typedef boost::shared_ptr < bdf_type >	bdf_ptrtype

typedef Exporter< mesh_type >	export_type

typedef boost::shared_ptr < export_type >	export_ptrtype

typedef Preconditioner< double >	preconditioner_type

typedef boost::shared_ptr < preconditioner_type >	preconditioner_ptrtype

typedef mpl::if_ < boost::is_same< mpl::int_ < nb_spaces >, mpl::int_ < 2 > >, fusion::vector < mpl::int_< 0 >, mpl::int_ < 1 > >, typename mpl::if_ < boost::is_same< mpl::int_ < nb_spaces >, mpl::int_ < 3 > >, fusion::vector < mpl::int_< 0 >, mpl::int_ < 1 >, mpl::int_ < 2 > >, typename mpl::if_ < boost::is_same< mpl::int_ < nb_spaces >, mpl::int_ < 4 > >, fusion::vector < mpl::int_< 0 >, mpl::int_ < 1 >, mpl::int_ < 2 >, mpl::int_ < 3 > >, fusion::vector < mpl::int_< 0 >, mpl::int_ < 1 >, mpl::int_ < 2 >, mpl::int_ < 3 >, mpl::int_ < 4 > > >::type >::type > ::type	index_vector_type

static const int	nb_spaces = functionspace_type::nSpaces

Additional Inherited Members
Protected Member Functions inherited from Feel::CRBDB
template<class Archive >
void	load (Archive &ar, const unsigned int version)

template<class Archive >
void	save (Archive &ar, const unsigned int version) const

void	setIsLoaded (bool isloaded)

Member Function Documentation

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::check ( size_type N ) const

check the reduced basis space invariant properties

Parameters

N	dimension of

References Feel::CRB< TruthModelType >::delta(), Feel::CRB< TruthModelType >::lb(), and Feel::CRBDB::vm().

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::computationalTimeStatistics ( std::string appname )

evaluate online time via the option crb.computational-time-neval

References Feel::CRB< TruthModelType >::dimension(), and Feel::CRB< TruthModelType >::run().

template<typename TruthModelType >

double Feel::CRB< TruthModelType >::computeConditioning ( matrixN_type & A ) const

computation of the conditioning number of a given matrix

Parameters

A	: reduced matrix

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::computeErrorEstimationEfficiencyIndicator	(	parameterspace_ptrtype const &	Dmu,
		double &	max_ei,
		double &	min_ei,
		int	N = `4`
	)

compute effectivity indicator of the error estimation overall a given parameter space

Parameters

max_ei	: maximum efficiency indicator (output)
min_ei	: minimum efficiency indicator (output)
Dmu	(input) parameter space
N	: sampling size (optional input with default value)

References Feel::CRB< TruthModelType >::delta(), and Feel::CRB< TruthModelType >::lb().

template<typename TruthModelType>

value_type Feel::CRB< TruthModelType >::delta	(	size_type	N,
		parameter_ptrtype const &	mu,
		std::vector< vectorN_type > const &	uN,
		std::vector< vectorN_type > const &	uNdu,
		std::vector< vectorN_type > const &	uNold,
		std::vector< vectorN_type > const &	uNduold,
		int	k = `0`
	)		const

inline

Returns the error bound on the output

Parameters

mu	$\mu$ the parameter at which to evaluate the output
N	the size of the reduced basis space to use
uN	primal solution
uNdu	dual solution

Returns: compute online the lower bound

template<typename TruthModelType >

CRB< TruthModelType >::error_estimation_type Feel::CRB< TruthModelType >::delta	(	size_type	N,
		parameter_type const &	mu,
		std::vector< vectorN_type > const &	uN,
		std::vector< vectorN_type > const &	uNdu,
		std::vector< vectorN_type > const &	uNold,
		std::vector< vectorN_type > const &	uNduold,
		int	k = `0`
	)		const

Returns the error bound on the output associed to $\mu$

Parameters

mu	$\mu$ the parameter at which to evaluate the output
N	the dimension of
uN	primal solution
uNdu	dual solution

Returns: compute online the lower bound

References Feel::CRB< TruthModelType >::transientPrimalResidual(), and Feel::CRBDB::vm().

template<typename TruthModelType>

int Feel::CRB< TruthModelType >::dimension ( ) const

inline

Returns: the dimension of the reduced basis space

template<typename TruthModelType>

parameterspace_ptrtype Feel::CRB< TruthModelType >::Dmu ( ) const

inline

Returns: the parameter space

template<typename TruthModelType>

sampling_type Feel::CRB< TruthModelType >::equidistributedSampling ( int N )

inline

Returns: a equidistributed sampling

template<typename TruthModelType>

CRBErrorType Feel::CRB< TruthModelType >::errorType ( ) const

inline

Returns: the error type

template<typename TruthModelType >

CRB< TruthModelType >::element_type Feel::CRB< TruthModelType >::expansion	(	parameter_type const &	mu,
		int	N = `-1`,
		int	time_index = `-1`
	)

return the crb expansion at parameter , ie $\sum_{i=0}^N u^N_i \phi_i$ where $, i=1...N$ are the basis function of the reduced basis space if N>0 take the N^th first elements, else take all elements

References Feel::CRB< TruthModelType >::lb().

template<typename TruthModelType >

CRB< TruthModelType >::element_type Feel::CRB< TruthModelType >::expansion	(	vectorN_type const &	u,
		int const	N,
		wn_type const &	WN
	)		const

return the crb expansion at parameter , ie $\sum_{i=0}^N u^N_i \phi_i$ where $, i=1...N$ are the basis function of the reduced basis space

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::exportBasisFunctions ( const export_vector_wn_type & wn ) const

export basis functions to visualize it

Parameters

wn	: tuple composed of a vector of wn_type and a vector of string (used to name basis)

References Feel::CRBDB::name().

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::fixedPoint	(	size_type	N,
		parameter_type const &	mu,
		std::vector< vectorN_type > &	uN,
		std::vector< vectorN_type > &	uNdu,
		std::vector< vectorN_type > &	uNold,
		std::vector< vectorN_type > &	uNduold,
		double &	condition_number,
		std::vector< double > &	output_vector,
		int	K = `0`
	)		const

fixed point ( main ) - ONLINE step

Parameters

N	: dimension of the reduced basis
mu	:current parameter
uN	: dual reduced solution ( vectorN_type )
uNdu	: dual reduced solution ( vectorN_type )
uNold	: dual old reduced solution ( vectorN_type )
uNduold	: dual old reduced solution ( vectorN_type )
output	: vector of outpus at each time step
K	: number of time step ( default value, must be >0 if used )

References Feel::CRBDB::vm().

template<typename TruthModelType >

boost::tuple< double, double > Feel::CRB< TruthModelType >::lb	(	size_type	N,
		parameter_type const &	mu,
		std::vector< vectorN_type > &	uN,
		std::vector< vectorN_type > &	uNdu,
		std::vector< vectorN_type > &	uNold,
		std::vector< vectorN_type > &	uNduold,
		int	K = `0`
	)		const

Returns the lower bound of the output

Parameters

mu	$\mu$ the parameter at which to evaluate the output
N	the size of the reduced basis space to use
uN	primal solution
uNdu	dual solution
K	: index of time ( time = K*dt) at which we want to evaluate the output Note : K as a default value for non time-dependent problems

Returns: compute online the lower bound also condition number of matrix A

References Feel::CRB< TruthModelType >::fixedPoint(), Feel::CRBDB::name(), and Feel::CRBDB::vm().

template<typename TruthModelType>

boost::tuple<double,double> Feel::CRB< TruthModelType >::lb	(	parameter_ptrtype const &	mu,
		size_type	N,
		std::vector< vectorN_type > &	uN,
		std::vector< vectorN_type > &	uNdu
	)		const

inline

Returns the lower bound of the output

Parameters

mu	$\mu$ the parameter at which to evaluate the output
N	the size of the reduced basis space to use
uN	primal solution
uNdu	dual solution

Returns: compute online the lower bound and condition number of matrix A

References Feel::CRB< TruthModelType >::lb().

template<typename TruthModelType >

bool Feel::CRB< TruthModelType >::loadDB ( )

virtual

load the CRB database

Reimplemented from Feel::CRBDB.

References Feel::CRBDB::isDBLoaded(), Feel::CRBDB::lookForDB(), and Feel::CRB< TruthModelType >::rebuildDB().

template<typename TruthModelType >

CRB< TruthModelType >::max_error_type Feel::CRB< TruthModelType >::maxErrorBounds ( size_type N ) const

Retuns maximum value of the relative error.

Parameters

N	number of elements in the reduced basis <=> M_N

References Feel::CRB< TruthModelType >::delta(), Feel::CRB< TruthModelType >::lb(), and Feel::CRBDB::vm().

template<typename TruthModelType>

int Feel::CRB< TruthModelType >::maxIter ( ) const

inline

Returns: max iterations

template<typename TruthModelType >

CRB< TruthModelType >::convergence_type Feel::CRB< TruthModelType >::offline ( )

Offline computation

Returns: the convergence history (max error)

References Feel::CRB< TruthModelType >::check(), Feel::CRB< TruthModelType >::exportBasisFunctions(), Feel::inner_product(), Feel::CRB< TruthModelType >::maxErrorBounds(), Feel::CRB< TruthModelType >::offlineResidual(), Feel::CRB< TruthModelType >::orthonormalize(), Feel::CRB< TruthModelType >::saveDB(), and Feel::CRBDB::vm().

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::offlineResidual	(	int	Ncur,
		int	number_of_added_elements = `1`
	)

generate offline the residual

template<typename TruthModelType >

double Feel::CRB< TruthModelType >::orthonormalize	(	size_type	N,
		wn_type &	wn,
		int	Nm = `1`
	)

orthonormalize the basis return the norm of the matrix A(i,j)=M_model->scalarProduct( WN[j], WN[i] ), should be 0

template<typename TruthModelType>

int Feel::CRB< TruthModelType >::outputIndex ( ) const

inline

Returns: the output index

template<typename TruthModelType >

bool Feel::CRB< TruthModelType >::printErrorDuringOfflineStep ( )

if true, print the max error (absolute) during the offline stage

References Feel::CRBDB::vm().

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::printErrorsDuringRbConstruction ( void )

print max errors (total error and also primal and dual contributions) during offline stage

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::printMuSelection ( void )

print parameters set mu selected during the offline stage

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::projectionOnPodSpace	(	const element_type &	u,
		element_ptrtype &	projection,
		const std::string &	name_of_space = `"primal"`
	)

do the projection on the POD space of u (for transient problems)

Parameters

u	: the solution to project (input parameter)
projection	: the projection (output parameter)
name_of_space	: primal or dual

template<typename TruthModelType>

sampling_type Feel::CRB< TruthModelType >::randomSampling ( int N )

inline

Returns: a random sampling

template<typename TruthModelType >

bool Feel::CRB< TruthModelType >::rebuildDB ( )

if true, rebuild the database (if already exist)

References Feel::CRBDB::vm().

template<typename TruthModelType >

boost::tuple< double, double, typename CRB< TruthModelType >::solutions_tuple, double, double, double, typename CRB< TruthModelType >::upper_bounds_tuple > Feel::CRB< TruthModelType >::run	(	parameter_type const &	mu,
		double	eps = `1e-6`,
		int	N = `-1`
	)

run the certified reduced basis with P parameters and returns 1 output

References Feel::CRB< TruthModelType >::delta(), Feel::CRB< TruthModelType >::lb(), and Feel::CRBDB::vm().

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::run	(	const double *	X,
		unsigned long	N,
		double *	Y,
		unsigned long	P
	)

run the certified reduced basis with P parameters and returns 1 output

References Feel::CRB< TruthModelType >::run().

template<typename TruthModelType >

void Feel::CRB< TruthModelType >::saveDB ( )

virtual

save the CRB database

Reimplemented from Feel::CRBDB.

References Feel::CRBDB::dbFilename(), and Feel::CRBDB::dbLocalPath().

template<typename TruthModelType>

scm_ptrtype Feel::CRB< TruthModelType >::scm ( ) const

inline

Returns: the scm object

template<typename TruthModelType >

bool Feel::CRB< TruthModelType >::showMuSelection ( )

if true, show the mu selected during the offline stage

References Feel::CRBDB::vm().

template<typename TruthModelType>

sampling_ptrtype Feel::CRB< TruthModelType >::trainSampling ( ) const

inline

Returns: the train sampling used to generate the reduced basis space

template<typename TruthModelType >

CRB< TruthModelType >::residual_error_type Feel::CRB< TruthModelType >::transientPrimalResidual	(	int	Ncur,
		parameter_type const &	mu,
		vectorN_type const &	Un,
		vectorN_type const &	Unold = `vectorN_type()`,
		double	time_step = `1`,
		double	time = `1e30`
	)		const

evaluate online the residual

template<typename TruthModelType>

value_type Feel::CRB< TruthModelType >::ub	(	size_type	N,
		parameter_type const &	mu,
		std::vector< vectorN_type > &	uN,
		std::vector< vectorN_type > &	uNdu
	)		const

inline

Returns the upper bound of the output associed to $\mu$

Parameters

mu	$\mu$ the parameter at which to evaluate the output
N	the dimension of
uN	primal solution
uNdu	dual solution

Returns: compute online the lower bound

References Feel::CRB< TruthModelType >::delta(), and Feel::CRB< TruthModelType >::lb().

template<typename TruthModelType>

value_type Feel::CRB< TruthModelType >::ub	(	size_type	K,
		parameter_ptrtype const &	mu,
		std::vector< vectorN_type > &	uN,
		std::vector< vectorN_type > &	uNdu
	)		const

inline

Returns the upper bound of the output associed to $\mu$

Parameters

mu	$\mu$ the parameter at which to evaluate the output
N	the dimension of

Returns: compute online the lower bound

References Feel::CRB< TruthModelType >::ub().

The documentation for this class was generated from the following file:

crb.hpp

Detailed Description

template<typename TruthModelType> class Feel::CRB< TruthModelType >

Public Member Functions

Friends

Typedefs

Additional Inherited Members

Member Function Documentation

template<typename TruthModelType>
class Feel::CRB< TruthModelType >