Inheritance diagram for CAROM::SnapshotDMD:

Public Member Functions
	SnapshotDMD (int dim, double dt, bool alt_output_basis=false, std::shared_ptr< Vector > state_offset=nullptr)
	Constructor. Basic DMD with uniform time step size. Inherited directly from base DMD class. More...

	SnapshotDMD (std::string base_file_name)
	Constructor. DMD from saved models. Inherited directly from base DMD class. More...

	~SnapshotDMD ()
	Destroy the SnapshotDMD object.

void	interpolateToNSnapshots (int n)
	Interpolate the current snapshots to n, new snapshots distributed uniformly over the currently sampled time domain. More...

void	train (int k, const Matrix *W0=NULL, double linearity_tol=0.0)
	Train the DMD model with specified reduced dimension. If k is too large then new snapshots are computed using interpolateToNSnapshots(k+1). More...

void	train (double energy_fraction, const Matrix *W0=NULL, double linearity_tol=0.0)
	Train the DMD model with energy fraction criterion. More...

std::vector< std::shared_ptr< Vector > >	getSnapshotVectors ()
	Returns a copy of the current snapshot vector "d_snapshots".

Public Member Functions inherited from CAROM::DMD
	DMD (int dim, double dt, bool alt_output_basis=false, std::shared_ptr< Vector > state_offset=nullptr)
	Constructor. Basic DMD with uniform time step size. More...

	DMD (std::string base_file_name)
	Constructor. DMD from saved models. More...

virtual	~DMD ()
	Destroy the DMD object.

virtual void	setOffset (std::shared_ptr< Vector > &offset_vector, int order)
	Set the offset of a certain order.

virtual void	takeSample (double *u_in, double t)
	Sample the new state, u_in. Any samples in d_snapshots taken at the same or later time will be erased. More...

void	projectInitialCondition (const Vector &init, double t_offset=-1.0)
	Project new initial condition using d_phi. Calculate pinv(phi) x init, or more precisely, (phi* x phi)^{-1} x phi* x init, where phi* is the conjugate transpose. More...

std::unique_ptr< Vector >	predict (double t, int deg=0)
	Predict state given a time. Uses the projected initial condition of the training dataset (the first column). More...

double	getTimeOffset () const
	Get the time offset contained within d_t_offset.

int	getNumSamples () const
	Returns the number of samples taken. More...

int	getDimension () const

std::unique_ptr< const Matrix >	getSnapshotMatrix ()
	Get the snapshot matrix contained within d_snapshots.

virtual void	load (std::string base_file_name)
	Load the object state from a file. More...

void	load (const char *base_file_name)
	Load the object state from a file. More...

virtual void	save (std::string base_file_name)
	Save the object state to a file. More...

void	save (const char *base_file_name)
	Save the object state to a file. More...

void	summary (std::string base_file_name)
	Output the DMD record in CSV files.

Protected Member Functions
	SnapshotDMD (std::vector< std::complex< double >> &eigs, std::shared_ptr< Matrix > &phi_real, std::shared_ptr< Matrix > &phi_imaginary, int k, double dt, double t_offset, std::shared_ptr< Vector > &state_offset)
	Constructor. More...

Protected Member Functions inherited from CAROM::DMD
	DMD (int dim, bool alt_output_basis=false, std::shared_ptr< Vector > state_offset=nullptr)
	Constructor. Variant of DMD with non-uniform time step size. More...

	DMD (std::vector< std::complex< double >> &eigs, std::shared_ptr< Matrix > &phi_real, std::shared_ptr< Matrix > &phi_imaginary, int k, double dt, double t_offset, std::shared_ptr< Vector > &state_offset)
	Constructor. Specified from DMD components. More...

	DMD ()
	Unimplemented default constructor.

	DMD (const DMD &other)
	Unimplemented copy constructor.

DMD &	operator= (const DMD &rhs)
	Unimplemented assignment operator.

std::pair< std::shared_ptr< Matrix >, std::shared_ptr< Matrix > >	phiMultEigs (double t, int deg=0)
	Internal function to multiply d_phi with the eigenvalues.

void	constructDMD (const Matrix &f_snapshots, int rank, int num_procs, const Matrix *W0, double linearity_tol)
	Construct the DMD object.

virtual std::pair< Matrix , Matrix >	computeDMDSnapshotPair (const Matrix &snapshots)
	Returns a pair of pointers to the minus and plus snapshot matrices.

virtual void	computePhi (DMDInternal dmd_internal_obj)
	Compute phi.

virtual std::complex< double >	computeEigExp (std::complex< double > eig, double t)
	Compute the appropriate exponential function when predicting the solution.

virtual void	addOffset (Vector &result, double t=0.0, int deg=0)
	Add the appropriate offset when predicting the solution.

std::unique_ptr< const Matrix >	createSnapshotMatrix (const std::vector< std::shared_ptr< Vector >> &snapshots)
	Get the snapshot matrix contained within d_snapshots.

Friends
void	getParametricDMD (std::unique_ptr< SnapshotDMD > &parametric_dmd, const std::vector< Vector > &parameter_points, std::vector< SnapshotDMD * > &dmds, const Vector &desired_point, std::string rbf, std::string interp_method, double closest_rbf_val, bool reorthogonalize_W)
	Obtain DMD model interpolant at desired parameter point by interpolation of DMD models from training parameter points. More...

Additional Inherited Members
Protected Attributes inherited from CAROM::DMD
int	d_rank
	The rank of the process this object belongs to.

int	d_num_procs
	The number of processors being run on.

int	d_dim
	The total dimension of the sample vector.

double	d_dt = -1.0
	The time step size between samples.

double	d_t_offset
	The time offset of the first sample.

std::vector< std::shared_ptr< Vector > >	d_snapshots
	std::vector holding the snapshots.

std::vector< double >	d_sampled_times
	The stored times of each sample.

std::shared_ptr< Vector >	d_state_offset
	State offset in snapshot.

bool	d_trained
	Whether the DMD has been trained or not.

bool	d_init_projected
	Whether the initial condition has been projected.

int	d_num_singular_vectors
	The maximum number of singular vectors.

std::vector< double >	d_sv
	std::vector holding the signular values.

double	d_energy_fraction
	The energy fraction used to obtain the DMD modes.

int	d_k
	The number of columns used after obtaining the SVD decomposition.

std::shared_ptr< Matrix >	d_basis
	The left singular vector basis.

bool	d_alt_output_basis = false
	Whether to use the alternative basis for output, i.e. phi = U^(+)VOmega^(-1)*X.

std::shared_ptr< Matrix >	d_A_tilde
	A_tilde.

std::shared_ptr< Matrix >	d_phi_real
	The real part of d_phi.

std::shared_ptr< Matrix >	d_phi_imaginary
	The imaginary part of d_phi.

std::unique_ptr< Matrix >	d_phi_real_squared_inverse
	The real part of d_phi_squared_inverse.

std::unique_ptr< Matrix >	d_phi_imaginary_squared_inverse
	The imaginary part of d_phi_squared_inverse.

std::shared_ptr< Vector >	d_projected_init_real
	The real part of the projected initial condition.

std::shared_ptr< Vector >	d_projected_init_imaginary
	The imaginary part of the projected initial condition.

std::vector< std::complex< double > >	d_eigs
	A vector holding the complex eigenvalues of the eigenmodes.

Detailed Description

Definition at line 10 of file SnapshotDMD.h.

Constructor & Destructor Documentation

◆ SnapshotDMD() [1/3]

CAROM::SnapshotDMD::SnapshotDMD	(	int	dim,
		double	dt,
		bool	alt_output_basis = `false`,
		std::shared_ptr< Vector >	state_offset = `nullptr`
	)

inline

Constructor. Basic DMD with uniform time step size. Inherited directly from base DMD class.

Parameters

[in]	dim	The full-order state dimension.
[in]	dt	The dt between samples.
[in]	alt_output_basis	Whether to use the alternative basis for output, i.e. phi = U^(+)VOmega^(-1)*X.
[in]	state_offset	The state offset.

Definition at line 24 of file SnapshotDMD.h.

◆ SnapshotDMD() [2/3]

CAROM::SnapshotDMD::SnapshotDMD ( std::string base_file_name )

inline

Constructor. DMD from saved models. Inherited directly from base DMD class.

Parameters

[in] base_file_name The base part of the filename of the database to load when restarting from a save.

Definition at line 35 of file SnapshotDMD.h.

◆ SnapshotDMD() [3/3]

CAROM::SnapshotDMD::SnapshotDMD	(	std::vector< std::complex< double >> &	eigs,
		std::shared_ptr< Matrix > &	phi_real,
		std::shared_ptr< Matrix > &	phi_imaginary,
		int	k,
		double	dt,
		double	t_offset,
		std::shared_ptr< Vector > &	state_offset
	)

inlineprotected

Constructor.

Parameters

[in]	eigs	d_eigs
[in]	phi_real	d_phi_real
[in]	phi_imaginary	d_phi_imaginary
[in]	k	d_k
[in]	dt	d_dt
[in]	t_offset	d_t_offset
[in]	state_offset	d_state_offset
[in]	derivative_offset	d_derivative_offset

Definition at line 123 of file SnapshotDMD.h.

Member Function Documentation

◆ interpolateToNSnapshots()

void CAROM::SnapshotDMD::interpolateToNSnapshots ( int n )

Interpolate the current snapshots to n, new snapshots distributed uniformly over the currently sampled time domain.

Parameters

[in] n The number of desired snapshots.

Definition at line 49 of file SnapshotDMD.cpp.

◆ train() [1/2]

void CAROM::SnapshotDMD::train	(	double	energy_fraction,
		const Matrix *	W0 = `NULL`,
		double	linearity_tol = `0.0`
	)

virtual

Train the DMD model with energy fraction criterion.

Parameters

[in]	energy_fraction	The energy fraction to keep after doing SVD.
[in]	W0	The initial basis to prepend to W.
[in]	linearity_tol	The tolerance for determining whether a column of W is linearly independent with W0.

Reimplemented from CAROM::DMD.

Definition at line 43 of file SnapshotDMD.cpp.

◆ train() [2/2]

void CAROM::SnapshotDMD::train	(	int	k,
		const Matrix *	W0 = `NULL`,
		double	linearity_tol = `0.0`
	)

virtual

Train the DMD model with specified reduced dimension. If k is too large then new snapshots are computed using interpolateToNSnapshots(k+1).

Parameters

[in]	k	The number of modes to keep after doing SVD.
[in]	W0	The initial basis to prepend to W.
[in]	linearity_tol	The tolerance for determining whether a column of W is linearly independent with W0.

Reimplemented from CAROM::DMD.

Definition at line 26 of file SnapshotDMD.cpp.

Friends And Related Function Documentation

◆ getParametricDMD

void getParametricDMD	(	std::unique_ptr< SnapshotDMD > &	parametric_dmd,
		const std::vector< Vector > &	parameter_points,
		std::vector< SnapshotDMD * > &	dmds,
		const Vector &	desired_point,
		std::string	rbf,
		std::string	interp_method,
		double	closest_rbf_val,
		bool	reorthogonalize_W
	)

friend

Obtain DMD model interpolant at desired parameter point by interpolation of DMD models from training parameter points.

Parameters

[in]	parametric_dmd	The interpolant DMD model at the desired point.
[in]	parameter_points	The training parameter points.
[in]	dmds	The DMD objects associated with each training parameter point.
[in]	desired_point	The desired point at which to create a parametric DMD.
[in]	rbf	The RBF type ("G" == gaussian, "IQ" == inverse quadratic, "IMQ" == inverse multiquadric)
[in]	interp_method	The interpolation method type ("LS" == linear solve, "IDW" == inverse distance weighting, "LP" == lagrangian polynomials)
[in]	closest_rbf_val	The RBF parameter determines the width of influence. Set the RBF value of the nearest two parameter points to a value between 0.0 to 1.0
[in]	reorthogonalize_W	Whether to reorthogonalize the interpolated W (basis) matrix.

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

lib/algo/SnapshotDMD.h
lib/algo/SnapshotDMD.cpp

Public Member Functions

Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SnapshotDMD() [1/3]

◆ SnapshotDMD() [2/3]

◆ SnapshotDMD() [3/3]

Member Function Documentation

◆ interpolateToNSnapshots()

◆ train() [1/2]

◆ train() [2/2]

Friends And Related Function Documentation

◆ getParametricDMD