#include <DMDc.h>

Public Member Functions
	DMDc (int dim, int dim_c, double dt, Vector *state_offset=NULL)
	Constructor. Basic DMDc with uniform time step size. More...

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

virtual	~DMDc ()
	Destroy the DMDc object.

virtual void	setOffset (Vector *offset_vector)
	Set the state offset.

virtual void	takeSample (double u_in, double t, double f_in, bool last_step=false)
	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 *B=NULL)
	Train the DMDc model with energy fraction criterion. The control matrix B may be available and used in training. It is yet to be implemented and requires consideration in sparse matrix multiplication in general. (See Section III.B. in https://arxiv.org/pdf/1409.6358.pdf) In default, the control matrix is unknown, with B = NULL. More...

virtual void	train (int k, const Matrix *B=NULL)
	Train the DMDc model with specified reduced dimension. The control matrix B may be available and used in training. It is yet to be implemented and requires consideration in sparse matrix multiplication in general. (See Section III.B. in https://arxiv.org/pdf/1409.6358.pdf) In default, the control matrix is unknown, with B = NULL. More...

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

Vector *	predict (double t)
	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 DMDc record in CSV files.

Protected Member Functions
	DMDc (int dim, int dim_c, Vector *state_offset=NULL)
	Constructor. Variant of DMDc with non-uniform time step size. More...

	DMDc (std::vector< std::complex< double >> eigs, Matrix phi_real, Matrix phi_imaginary, Matrix B_tilde, int k, double dt, double t_offset, Vector state_offset, Matrix *basis=nullptr)
	Constructor. Specified from DMDc components. More...

	DMDc ()
	Unimplemented default constructor.

	DMDc (const DMDc &other)
	Unimplemented copy constructor.

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

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

void	constructDMDc (const Matrix f_snapshots, const Matrix f_controls, int rank, int num_procs, const Matrix *B)
	Construct the DMDc object.

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

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)
	Add the state 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.

int	d_dim_c
	The total dimension of the control 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_controls
	std::vector holding the controls.

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 DMDc 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 DMDc modes.

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

Matrix *	d_basis = NULL
	The left singular vector basis.

Matrix *	d_A_tilde = NULL
	A_tilde.

Matrix *	d_B_tilde = NULL
	B_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.

Matrix *	d_projected_controls_real = NULL
	The real part of the projected controls.

Matrix *	d_projected_controls_imaginary = NULL
	The imaginary part of the projected controls.

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

Friends
void	getParametricDMDc (DMDc &parametric_dmdc, std::vector< Vector > &parameter_points, std::vector< DMDc * > &dmdcs, std::vector< Matrix * > controls, Matrix &controls_interpolated, 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 DMDc implements the DMDc algorithm on a given snapshot matrix.

Definition at line 32 of file DMDc.h.

Constructor & Destructor Documentation

◆ DMDc() [1/4]

CAROM::DMDc::DMDc	(	int	dim,
		int	dim_c,
		double	dt,
		Vector *	state_offset = `NULL`
	)

Constructor. Basic DMDc with uniform time step size.

Parameters

[in]	dim	The full-order state dimension.
[in]	dim_c	The control dimension.
[in]	dt	The dt between samples.
[in]	state_offset	The state offset.

Definition at line 68 of file DMDc.cpp.

◆ DMDc() [2/4]

CAROM::DMDc::DMDc ( std::string base_file_name )

Constructor. DMDc 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 91 of file DMDc.cpp.

◆ DMDc() [3/4]

CAROM::DMDc::DMDc	(	int	dim,
		int	dim_c,
		Vector *	state_offset = `NULL`
	)

protected

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

Parameters

[in]	dim	The full-order state dimension.
[in]	dim_c	The control dimension.
[in]	state_offset	The state offset.

Definition at line 47 of file DMDc.cpp.

◆ DMDc() [4/4]

CAROM::DMDc::DMDc	(	std::vector< std::complex< double >>	eigs,
		Matrix *	phi_real,
		Matrix *	phi_imaginary,
		Matrix *	B_tilde,
		int	k,
		double	dt,
		double	t_offset,
		Vector *	state_offset,
		Matrix *	basis = `nullptr`
	)

protected

Constructor. Specified from DMDc components.

Parameters

[in]	eigs	d_eigs
[in]	phi_real	d_phi_real
[in]	phi_imaginary	d_phi_imaginary
[in]	B_tilde	d_B_tilde
[in]	k	d_k
[in]	dt	d_dt
[in]	t_offset	d_t_offset
[in]	state_offset	d_state_offset
[in]	basis	d_basis, set by DMDc class for offline stages. When interpolating a new DMDc, we enter the interpolated basis explicitly

Definition at line 108 of file DMDc.cpp.

Member Function Documentation

◆ getNumSamples()

int CAROM::DMDc::getNumSamples ( ) const

inline

Returns the number of samples taken.

Returns: The number of samples taken.

Definition at line 135 of file DMDc.h.

◆ load() [1/2]

void CAROM::DMDc::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 945 of file DMDc.cpp.

◆ load() [2/2]

void CAROM::DMDc::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.

Definition at line 856 of file DMDc.cpp.

◆ predict()

Vector * CAROM::DMDc::predict ( double t )

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

Definition at line 717 of file DMDc.cpp.

◆ project()

void CAROM::DMDc::project	(	const Vector *	init,
		const Matrix *	controls,
		double	t_offset = `-1.0`
	)

Project U using d_phi, where U is the initial condition and the controls. Calculate pinv(phi) x U, or more precisely, (phi* x phi)^{-1} x phi* x U, where phi* is the conjugate transpose.

Parameters

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

Definition at line 589 of file DMDc.cpp.

◆ save() [1/2]

void CAROM::DMDc::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 1040 of file DMDc.cpp.

◆ save() [2/2]

void CAROM::DMDc::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.

Definition at line 951 of file DMDc.cpp.

◆ takeSample()

void CAROM::DMDc::takeSample	(	double *	u_in,
		double	t,
		double *	f_in,
		bool	last_step = `false`
	)

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.
[in]	f_in	The control.
[in]	last_step	Whether it is the last step.

Definition at line 162 of file DMDc.cpp.

◆ train() [1/2]

void CAROM::DMDc::train	(	double	energy_fraction,
		const Matrix *	B = `NULL`
	)

virtual

Train the DMDc model with energy fraction criterion. The control matrix B may be available and used in training. It is yet to be implemented and requires consideration in sparse matrix multiplication in general. (See Section III.B. in https://arxiv.org/pdf/1409.6358.pdf) In default, the control matrix is unknown, with B = NULL.

Parameters

[in]	energy_fraction	The energy fraction to keep after doing SVD.
[in]	B	(Optional) The control matrix B.

Definition at line 212 of file DMDc.cpp.

◆ train() [2/2]

void CAROM::DMDc::train	(	int	k,
		const Matrix *	B = `NULL`
	)

virtual

Train the DMDc model with specified reduced dimension. The control matrix B may be available and used in training. It is yet to be implemented and requires consideration in sparse matrix multiplication in general. (See Section III.B. in https://arxiv.org/pdf/1409.6358.pdf) In default, the control matrix is unknown, with B = NULL.

Parameters

[in]	k	The number of modes to keep after doing SVD.
[in]	B	(Optional) The control matrix B.

Definition at line 225 of file DMDc.cpp.

Friends And Related Function Documentation

◆ getParametricDMDc

void getParametricDMDc	(	DMDc *&	parametric_dmdc,
		std::vector< Vector * > &	parameter_points,
		std::vector< DMDc * > &	dmdcs,
		std::vector< Matrix * >	controls,
		Matrix *&	controls_interpolated,
		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_dmdc	The interpolant DMD model at the desired point.
[in]	parameter_points	The training parameter points.
[in]	dmdcs	The DMD objects associated with each training parameter point.
[in]	controls	The matrices of controls from previous runs which we use to interpolate.
[in]	controls_interpolated	The interpolated controls.
[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/DMDc.h
lib/algo/DMDc.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ DMDc() [1/4]

◆ DMDc() [2/4]

◆ DMDc() [3/4]

◆ DMDc() [4/4]

Member Function Documentation

◆ getNumSamples()

◆ load() [1/2]

◆ load() [2/2]

◆ predict()

◆ project()

◆ save() [1/2]

◆ save() [2/2]

◆ takeSample()

◆ train() [1/2]

◆ train() [2/2]

Friends And Related Function Documentation

◆ getParametricDMDc