#include <DMD.h>

Inheritance diagram for CAROM::DMD:

Public Member Functions
	DMD (int dim, double dt, bool alt_output_basis=false, Vector *state_offset=NULL)
	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 (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...

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

virtual void	train (int k, const Matrix *W0=NULL, double linearity_tol=0.0)
	Train the DMD model with specified reduced dimension. 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...

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

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
	DMD (int dim, bool alt_output_basis=false, Vector *state_offset=NULL)
	Constructor. Variant of DMD with non-uniform time step size. More...

	DMD (std::vector< std::complex< double >> eigs, Matrix phi_real, Matrix phi_imaginary, int k, double dt, double t_offset, 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< Matrix , 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.

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

Protected Attributes
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< Vector * >	d_snapshots
	std::vector holding the snapshots.

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

Vector *	d_state_offset = NULL
	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.

Matrix *	d_basis = NULL
	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.

Matrix *	d_A_tilde = NULL
	A_tilde.

Matrix *	d_phi_real = NULL
	The real part of d_phi.

Matrix *	d_phi_imaginary = NULL
	The imaginary part of d_phi.

Matrix *	d_phi_real_squared_inverse = NULL
	The real part of d_phi_squared_inverse.

Matrix *	d_phi_imaginary_squared_inverse = NULL
	The imaginary part of d_phi_squared_inverse.

Vector *	d_projected_init_real = NULL
	The real part of the projected initial condition.

Vector *	d_projected_init_imaginary = NULL
	The imaginary part of the projected initial condition.

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

Friends
void	getParametricDMD (DMD &parametric_dmd, std::vector< Vector > &parameter_points, std::vector< DMD * > &dmds, 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...

Detailed Description

Class DMD implements the DMD algorithm on a given snapshot matrix.

Definition at line 70 of file DMD.h.

Constructor & Destructor Documentation

◆ DMD() [1/4]

CAROM::DMD::DMD	(	int	dim,
		double	dt,
		bool	alt_output_basis = `false`,
		Vector *	state_offset = `NULL`
	)

Constructor. Basic DMD with uniform time step size.

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 66 of file DMD.cpp.

◆ DMD() [2/4]

CAROM::DMD::DMD ( std::string base_file_name )

Constructor. DMD from saved models.

Parameters

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

Definition at line 88 of file DMD.cpp.

◆ DMD() [3/4]

CAROM::DMD::DMD	(	int	dim,
		bool	alt_output_basis = `false`,
		Vector *	state_offset = `NULL`
	)

protected

Constructor. Variant of DMD with non-uniform time step size.

Parameters

[in]	dim	The full-order state dimension.
[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 46 of file DMD.cpp.

◆ DMD() [4/4]

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

protected

Constructor. Specified from DMD components.

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

Definition at line 105 of file DMD.cpp.

Member Function Documentation

◆ getNumSamples()

int CAROM::DMD::getNumSamples ( ) const

inline

Returns the number of samples taken.

Returns: The number of samples taken.

Definition at line 166 of file DMD.h.

◆ load() [1/2]

void CAROM::DMD::load ( const char * base_file_name )

Load the object state from a file.

Parameters

[in] base_file_name The base part of the filename to load the database from.

Definition at line 844 of file DMD.cpp.

◆ load() [2/2]

void CAROM::DMD::load ( std::string base_file_name )

virtual

Load the object state from a file.

Parameters

[in] base_file_name The base part of the filename to load the database from.

Reimplemented in CAROM::NonuniformDMD.

Definition at line 759 of file DMD.cpp.

◆ predict()

Vector * CAROM::DMD::predict	(	double	t,
		int	deg = `0`
	)

Predict state given a time. Uses the projected initial condition of the training dataset (the first column).

Parameters

[in]	t	The time of the output state
[in]	deg	The derivative degree of the output state

Definition at line 645 of file DMD.cpp.

◆ projectInitialCondition()

void CAROM::DMD::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.

Parameters

[in]	init	The initial condition.
[in]	t_offset	The initial time offset.

Definition at line 541 of file DMD.cpp.

◆ save() [1/2]

void CAROM::DMD::save ( const char * base_file_name )

Save the object state to a file.

Parameters

[in] base_file_name The base part of the filename to save the database to.

Definition at line 933 of file DMD.cpp.

◆ save() [2/2]

void CAROM::DMD::save ( std::string base_file_name )

virtual

Save the object state to a file.

Parameters

[in] base_file_name The base part of the filename to save the database to.

Reimplemented in CAROM::NonuniformDMD.

Definition at line 850 of file DMD.cpp.

◆ takeSample()

void CAROM::DMD::takeSample	(	double *	u_in,
		double	t
	)

virtual

Sample the new state, u_in. Any samples in d_snapshots taken at the same or later time will be erased.

Precondition: u_in != 0; t >= 0.0

Parameters

[in]	u_in	The new state.
[in]	t	The time of the newly sampled state.

Definition at line 159 of file DMD.cpp.

◆ train() [1/2]

void CAROM::DMD::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 in CAROM::AdaptiveDMD.

Definition at line 203 of file DMD.cpp.

◆ train() [2/2]

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

virtual

Train the DMD model with specified reduced dimension.

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 in CAROM::AdaptiveDMD.

Definition at line 214 of file DMD.cpp.

Friends And Related Function Documentation

◆ getParametricDMD

void getParametricDMD	(	DMD *&	parametric_dmd,
		std::vector< Vector * > &	parameter_points,
		std::vector< DMD * > &	dmds,
		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/DMD.h
lib/algo/DMD.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ DMD() [1/4]

◆ DMD() [2/4]

◆ DMD() [3/4]

◆ DMD() [4/4]

Member Function Documentation

◆ getNumSamples()

◆ load() [1/2]

◆ load() [2/2]

◆ predict()

◆ projectInitialCondition()

◆ save() [1/2]

◆ save() [2/2]

◆ takeSample()

◆ train() [1/2]

◆ train() [2/2]

Friends And Related Function Documentation

◆ getParametricDMD