#include <IncrementalSVD.h>

Inheritance diagram for CAROM::IncrementalSVD:

Public Member Functions
	IncrementalSVD (Options options, const std::string &basis_file_name)
	Constructor. More...

virtual	~IncrementalSVD ()
	Destructor.

virtual bool	takeSample (double *u_in, double time, bool add_without_increase=false)
	Sample new state, u_in, at the given time. More...

virtual const Matrix *	getSpatialBasis ()
	Returns the basis vectors for the current time interval as a Matrix. More...

virtual const Matrix *	getTemporalBasis ()
	Returns the temporal basis vectors for the current time interval as a Matrix. More...

virtual const Vector *	getSingularValues ()
	Returns the singular values for the current time interval. More...

virtual const Matrix *	getSnapshotMatrix ()
	Returns the snapshot matrix for the current time interval. More...

Public Member Functions inherited from CAROM::SVD
	SVD (Options options)
	Constructor. More...

	~SVD ()

int	getDim () const
	Returns the dimension of the system on this processor. More...

int	getNumBasisTimeIntervals () const
	Returns the number of time intervals on which different sets of basis vectors are defined. More...

double	getBasisIntervalStartTime (int which_interval) const
	Returns the start time for the requested time interval. More...

bool	isNewTimeInterval () const
	Returns true if the next sample will result in a new time interval. More...

void	increaseTimeInterval ()
	Increase the number of time intervals by one.

int	getNumSamples () const
	Get the number of samples taken.

Protected Member Functions
virtual void	buildInitialSVD (double *u, double time)=0
	Constructs the first SVD. More...

virtual bool	buildIncrementalSVD (double *u, bool add_without_increase=false)
	Adds the new sampled the state vector, u, to the system. More...

virtual void	computeBasis ()=0
	Computes the current basis vectors.

void	constructQ (double &Q, const Vector l, double k)
	Construct the matrix Q whose SVD is needed. More...

bool	svd (double A, Matrix &U, Matrix &S, Matrix &V)
	Given a matrix, A, returns 2 of the 3 components of its singular value decomposition. The right singular vectors are not needed and therefore not returned. More...

virtual void	addLinearlyDependentSample (const Matrix A, const Matrix W, const Matrix *sigma)=0
	Add a linearly dependent sample to the SVD. More...

virtual void	addNewSample (const Vector j, const Matrix A, const Matrix W, Matrix sigma)=0
	Add a new, unique sample to the SVD. More...

int	numSamples ()
	The number of samples stored. More...

double	checkOrthogonality (const Matrix *m)
	Computes and returns the orthogonality of m. More...

void	reOrthogonalize (Matrix *m)
	Reorthogonalizes m. More...

Protected Attributes
double	d_linearity_tol
	Tolerance to determine whether or not a sample is linearly dependent.

bool	d_skip_linearly_dependent
	Whether to skip linearly dependent samples.

int	d_max_basis_dimension
	The maximum basis dimension.

int	d_size
	The total number of processors.

int	d_rank
	The rank of the processor owning this object.

std::vector< int >	d_proc_dims
	The dimension of the system on each processor.

long int	d_total_dim
	The total dimension of the system.

bool	d_save_state
	If true the state of the SVD will be written to disk when the object is deleted. If there are multiple time intervals then the state will not be saved as restoring such a state makes no sense.

bool	d_update_right_SV
	Whether to update the right singular vectors.

Database *	d_state_database
	Pointer to the database that will hold saved state data if the state is to be saved.

std::string	d_state_file_name
	The name of file to which state is saved or restored from.

Protected Attributes inherited from CAROM::SVD
int	d_dim
	Dimension of the system.

int	d_num_samples
	Number of samples stored for the current time interval.

int	d_num_rows_of_W
	Number of rows in right singular matrix.

const int	d_samples_per_time_interval
	The maximum number of samples to be collected for a time interval.

const int	d_max_time_intervals
	The maximum number of time intervals.

Matrix *	d_basis
	The globalized basis vectors for the current time interval. More...

Matrix *	d_basis_right
	The globalized right basis vectors for the current time interval. More...

Matrix *	d_U
	The matrix U which is large. More...

Matrix *	d_W
	The matrix U which is large. More...

Vector *	d_S
	The vector S which is small. More...

Matrix *	d_snapshots
	The globalized snapshot vectors for the current time interval. More...

std::vector< double >	d_time_interval_start_times
	The simulation time at which each time interval starts.

bool	d_debug_algorithm
	Flag to indicate if results of algorithm should be printed for debugging purposes.

Static Protected Attributes
static const int	COMMUNICATE_U
	MPI message tag.

Detailed Description

Abstract class IncrementalSVD defines the internal API of the incremental SVD algorithm.

Constructor & Destructor Documentation

CAROM::IncrementalSVD::IncrementalSVD	(	Options	options,
		const std::string &	basis_file_name
	)

Constructor.

Parameters

[in]	options	The struct containing the options for this abstract SVD class.
[in]	basis_file_name	The base part of the name of the file containing the basis vectors. Each process will append its process ID to this base name.

See Also: Options

Member Function Documentation

virtual void CAROM::IncrementalSVD::addLinearlyDependentSample	(	const Matrix *	A,
		const Matrix *	W,
		const Matrix *	sigma
	)

protectedpure virtual

Add a linearly dependent sample to the SVD.

Precondition: A != 0; sigma != 0

Parameters

[in]	A	The left singular vectors.
[in]	W	The right singular vectors.
[in]	sigma	The singular values.

virtual void CAROM::IncrementalSVD::addNewSample	(	const Vector *	j,
		const Matrix *	A,
		const Matrix *	W,
		Matrix *	sigma
	)

protectedpure virtual

Add a new, unique sample to the SVD.

Precondition: j != 0; A != 0; sigma != 0

Parameters

[in]	j	The new column of d_U.
[in]	A	The left singular vectors.
[in]	W	The right singular vectors.
[in]	sigma	The singular values.

virtual bool CAROM::IncrementalSVD::buildIncrementalSVD	(	double *	u,
		bool	add_without_increase = `false`
	)

protectedvirtual

Adds the new sampled the state vector, u, to the system.

Precondition: u != 0

Parameters

[in]	u	The new state.
[in]	add_without_increase	If true, addLinearlyDependent is invoked.

Returns: True if building the incremental SVD was successful.

virtual void CAROM::IncrementalSVD::buildInitialSVD	(	double *	u,
		double	time
	)

protectedpure virtual

Constructs the first SVD.

Precondition: u != 0; time >= 0.0

Parameters

[in]	u	The first state.
[in]	time	The simulation time for the first state.

double CAROM::IncrementalSVD::checkOrthogonality ( const Matrix * m )

protected

Computes and returns the orthogonality of m.

Precondition: m != 0

Parameters

[in] m The matrix to check.

Returns: The orthogonality of m.

void CAROM::IncrementalSVD::constructQ	(	double *&	Q,
		const Vector *	l,
		double	k
	)

protected

Construct the matrix Q whose SVD is needed.

Precondition: l != 0; l.dim() == numSamples()

Parameters

[out]	Q	The matrix to be constructed. [d_S,l; 0,k]
[in]	l	The last column of Q.
[in]	k	The lower right element of Q.

virtual const Vector* CAROM::IncrementalSVD::getSingularValues ( )

virtual

Returns the singular values for the current time interval.

Returns: The singular values for the current time interval.

Implements CAROM::SVD.

virtual const Matrix* CAROM::IncrementalSVD::getSnapshotMatrix ( )

virtual

Returns the snapshot matrix for the current time interval.

Returns: The snapshot matrix for the current time interval.

Implements CAROM::SVD.

virtual const Matrix* CAROM::IncrementalSVD::getSpatialBasis ( )

virtual

Returns the basis vectors for the current time interval as a Matrix.

Returns: The basis vectors for the current time interval.

Implements CAROM::SVD.

virtual const Matrix* CAROM::IncrementalSVD::getTemporalBasis ( )

virtual

Returns the temporal basis vectors for the current time interval as a Matrix.

Returns: The temporal basis vectors for the current time interval.

Implements CAROM::SVD.

int CAROM::IncrementalSVD::numSamples ( )

inlineprotected

The number of samples stored.

Returns: The number of samples stored.

void CAROM::IncrementalSVD::reOrthogonalize ( Matrix * m )

protected

Reorthogonalizes m.

Precondition: m != 0

Parameters

[in,out] m The matrix to reorthogonalize.

bool CAROM::IncrementalSVD::svd	(	double *	A,
		Matrix *&	U,
		Matrix *&	S,
		Matrix *&	V
	)

protected

Given a matrix, A, returns 2 of the 3 components of its singular value decomposition. The right singular vectors are not needed and therefore not returned.

Precondition: A != 0

Parameters

[in]	A	The matrix whose SVD is needed.
[out]	U	The left singular vectors of A.
[out]	S	The singular values of A.
[out]	V	The right singular vectors of A.

Returns: True if the SVD succeeded.

virtual bool CAROM::IncrementalSVD::takeSample	(	double *	u_in,
		double	time,
		bool	add_without_increase = `false`
	)

virtual

Sample new state, u_in, at the given time.

Precondition: u_in != 0; time >= 0.0

Parameters

[in]	u_in	The state at the specified time.
[in]	time	The simulation time for the state.
[in]	add_without_increase	If true, addLinearlyDependent is invoked.

Returns: True if the sampling was successful.

Implements CAROM::SVD.

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

lib/linalg/svd/IncrementalSVD.h

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation