Certifed Reduced Basis class. More...

#include <crb.hpp>

Inheritance diagram for Feel::CRB< TruthModelType >:

Public Types
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 CRBSCM< truth_model_type >	scm_type
	scm
typedef boost::shared_ptr < scm_type >	scm_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::theta_vector_type	theta_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 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 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
Public Member Functions
Constructors, destructor
	CRB ()
	default constructor
	CRB (std::string name, po::variables_map const &vm)
	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
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
Methods
void	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) const
void	compareResidualsForTransientProblems (parameter_type const &mu, std::vector< element_ptrtype > const &Un, std::vector< element_ptrtype > const &Unold, std::vector< element_ptrtype > const &Undu, std::vector< element_ptrtype > const &Unduold, std::vector< std::vector< double > > const &primal_residual_coeffs, std::vector< std::vector< double > > const &dual_residual_coeffs) const
void	buildFunctionFromRbCoefficients (std::vector< vectorN_type > const &RBcoeff, wn_type const &WN, std::vector< element_ptrtype > &FEMsolutions)
void	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
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.
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
boost::tuple< double, double, double, double >	run (parameter_type const &mu, double eps=1e-6)
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)
void	saveDB ()
bool	loadDB ()
void	projectionOnPodSpace (const element_ptrtype &u, element_ptrtype &projection, const std::string &name_of_space="primal")
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)
Friends
class	boost::serialization::access

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:

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().

Referenced by Feel::CRB< TruthModelType >::offline().

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

Referenced by Feel::CRB< TruthModelType >::check(), Feel::CRB< TruthModelType >::computeErrorEstimationEfficiencyIndicator(), Feel::CRB< TruthModelType >::maxErrorBounds(), Feel::CRB< TruthModelType >::run(), and Feel::CRB< TruthModelType >::ub().

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().

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 >

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().

Referenced by Feel::CRB< TruthModelType >::offline().

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::CRBDB::name(), and Feel::CRBDB::vm().

Referenced by Feel::CRB< TruthModelType >::check(), Feel::CRB< TruthModelType >::computeErrorEstimationEfficiencyIndicator(), Feel::CRB< TruthModelType >::lb(), Feel::CRB< TruthModelType >::maxErrorBounds(), Feel::CRB< TruthModelType >::run(), and Feel::CRB< TruthModelType >::ub().

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

Referenced by Feel::CRB< TruthModelType >::CRB(), Feel::CRB< TruthModelType >::setOutputIndex(), and Feel::CRB< TruthModelType >::setTruthModel().

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().

Referenced by Feel::CRB< TruthModelType >::offline().

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::Backend< T >::build(), Feel::CRB< TruthModelType >::check(), Feel::CRB< TruthModelType >::exportBasisFunctions(), Feel::inner_product(), Feel::CRB< TruthModelType >::maxErrorBounds(), Feel::CRBDB::name(), Feel::CRB< TruthModelType >::offlineResidual(), Feel::CRB< TruthModelType >::orthonormalize(), Feel::CRB< TruthModelType >::projectionOnPodSpace(), 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

Referenced by Feel::CRB< TruthModelType >::offline().

template<typename TruthModelType >

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

orthonormalize the basis

References Feel::CRBDB::vm().

Referenced by Feel::CRB< TruthModelType >::offline().

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_ptrtype &	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

Referenced by Feel::CRB< TruthModelType >::offline().

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().

Referenced by Feel::CRB< TruthModelType >::loadDB().

template<typename TruthModelType >

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

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().

Referenced by Feel::CRB< TruthModelType >::run().

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().

Referenced by Feel::CRB< TruthModelType >::offline().

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

Referenced by Feel::CRB< TruthModelType >::delta().

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().

Referenced by Feel::CRB< TruthModelType >::ub().

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().

Public Types

Public Member Functions

Friends

Detailed Description

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

Member Function Documentation

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