CAROM Namespace Reference

Classes
class	AdaptiveDMD
class	IOptimizable
class	DifferentialEvolution
struct	DMDInternal
class	DMD
class	DMDc
class	GreedyCustomSampler
class	GreedyRandomSampler
struct	GreedyErrorIndicatorPoint
class	GreedySampler
class	Interpolator
class	MatrixInterpolator
class	VectorInterpolator
class	NonuniformDMD
class	Hyperreduction
struct	RowInfo
	Struct to hold the local maximum absolute value of a basis vector, the row it is in, and the processor that owns it. We will reduce this to find the global row containing the maximum of a basis vector.
class	BasisGenerator
class	BasisReader
class	BasisWriter
class	Matrix
struct	EigenPair
struct	ComplexEigenPair
struct	SerialSVDDecomposition
class	NNLSSolver
class	Options
class	IncrementalSVD
class	IncrementalSVDBrand
class	IncrementalSVDFastUpdate
class	IncrementalSVDStandard
class	RandomizedSVD
class	StaticSVD
class	SVD
class	Vector
class	SampleMeshManager
class	SampleDOFSelector
class	CSVDatabase
class	Database
class	HDFDatabase
class	HDFDatabaseMPIO
class	ParallelBuffer
struct	Utilities

Enumerations
enum	SamplingType { deim , gnat , qdeim , sopt }
enum class	NNLS_termination { LINF , L2 }
	Termination criterion for NNLS solver: LINF: L-infinity norm (maximum value) of the residual L2: L2 norm of the residual.

Functions
struct GreedyErrorIndicatorPoint	createGreedyErrorIndicatorPoint (Vector *point, Vector *localROM)
	Create a greedy error indicator point. More...
struct GreedyErrorIndicatorPoint	createGreedyErrorIndicatorPoint (Vector *point, std::shared_ptr< Vector > &localROM)
	Create a greedy error indicator point. More...
Vector	getNearestPoint (std::vector< Vector > paramPoints, Vector point)
	Given a vector, find the nearest point in a domain. More...
int	getNearestPointIndex (std::vector< Vector > paramPoints, Vector point)
	Given a vector, find the nearest point in a domain. More...
double	getNearestPoint (std::vector< double > paramPoints, double point)
	Given a double, find the nearest point in a domain. More...
int	getNearestPointIndex (std::vector< double > paramPoints, double point)
	Given a double, find the nearest point in a domain. More...
std::vector< double >	obtainRBFToTrainingPoints (std::vector< Vector * > parameter_points, std::string interp_method, std::string rbf, double epsilon, Vector *point)
	Compute the RBF from the parameter points with the unsampled parameter point. More...
double	rbfWeightedSum (std::vector< double > &rbf)
	Compute the sum of the RBF weights. More...
double	obtainRBF (std::string rbf, double epsilon, Vector *point1, Vector *point2)
	Compute the RBF between two points. More...
double	convertClosestRBFToEpsilon (std::vector< Vector * > parameter_points, std::string rbf, double closest_rbf_val)
	Convert closest RBF value to an epsilon value. More...
std::vector< Matrix * >	obtainRotationMatrices (std::vector< Vector * > parameter_points, std::vector< Matrix * > bases, int ref_point)
	Obtain the rotation matrices for all the parameter points using the basis of the reference point. More...
Vector *	obtainInterpolatedVector (std::vector< Vector * > data, Matrix *f_T, std::string interp_method, std::vector< double > &rbf)
Matrix *	solveLinearSystem (std::vector< Vector * > parameter_points, std::vector< Vector * > data, std::string interp_method, std::string rbf, double &epsilon)
template<class T >
void	getParametricDMD (T *&parametric_dmd, std::vector< Vector * > &parameter_points, std::vector< T * > &dmds, Vector *desired_point, std::string rbf="G", std::string interp_method="LS", double closest_rbf_val=0.9, bool reorthogonalize_W=false)
	Constructor. More...
template<class T >
void	getParametricDMD (T *&parametric_dmd, std::vector< Vector * > &parameter_points, std::vector< std::string > &dmd_paths, Vector *desired_point, std::string rbf="G", std::string interp_method="LS", double closest_rbf_val=0.9, bool reorthogonalize_W=false)
	Constructor. More...
template<class T >
void	getParametricDMDc (T *&parametric_dmdc, std::vector< Vector * > &parameter_points, std::vector< T * > &dmdcs, std::vector< Matrix * > controls, Matrix *&controls_interpolated, Vector *desired_point, std::string rbf="G", std::string interp_method="LS", double closest_rbf_val=0.9, bool reorthogonalize_W=false)
	Constructor. More...
template<class T >
void	getParametricDMDc (T *&parametric_dmdc, std::vector< Vector * > &parameter_points, std::vector< std::string > &dmdc_paths, std::vector< Matrix * > controls, Matrix *&controls_interpolated, Vector *desired_point, std::string rbf="G", std::string interp_method="LS", double closest_rbf_val=0.9, bool reorthogonalize_W=false)
	Constructor. More...
void	DEIM (const Matrix *f_basis, int num_f_basis_vectors_used, std::vector< int > &f_sampled_row, std::vector< int > &f_sampled_rows_per_proc, Matrix &f_basis_sampled_inv, int myid, int num_procs)
	Computes the DEIM algorithm on the given basis. More...
void	GNAT (const Matrix *f_basis, const int num_f_basis_vectors_used, std::vector< int > &f_sampled_row, std::vector< int > &f_sampled_rows_per_proc, Matrix &f_basis_sampled_inv, const int myid, const int num_procs, const int num_samples_req=-1, std::vector< int > *init_samples=NULL)
	Computes the GNAT algorithm on the given basis. More...
void	QDEIM (const Matrix *f_basis, int num_f_basis_vectors_used, std::vector< int > &f_sampled_row, std::vector< int > &f_sampled_rows_per_proc, Matrix &f_basis_sampled_inv, const int myid, const int num_procs, const int num_samples_req)
	Computes the QDEIM algorithm on the given basis. More...
void	S_OPT (const Matrix *f_basis, int num_f_basis_vectors_used, std::vector< int > &f_sampled_row, std::vector< int > &f_sampled_rows_per_proc, Matrix &f_basis_sampled_inv, const int myid, const int num_procs, const int num_samples_req=-1, std::vector< int > *init_samples=NULL, bool qr_factorize=false)
	Computes the S_OPT algorithm on the given basis. More...
void	SampleTemporalIndices (const Matrix *s_basis, const Matrix *t_basis, const int num_f_basis_vectors_used, int *t_samples, const int myid, const int num_procs, const int num_samples_req, const bool excludeFinalTime)
void	SampleSpatialIndices (const Matrix *s_basis, const Matrix *t_basis, const int num_f_basis_vectors_used, const int num_t_samples, int *t_samples, int *s_sampled_row, int *s_sampled_rows_per_proc, Matrix &f_basis_sampled, const int myid, const int num_procs, const int num_samples_req)
void	SpaceTimeSampling (const Matrix *s_basis, const Matrix *t_basis, const int num_f_basis_vectors_used, std::vector< int > &t_samples, int *f_sampled_row, int *f_sampled_rows_per_proc, Matrix &s_basis_sampled, const int myid, const int num_procs, const int num_t_samples_req, const int num_s_samples_req, const bool excludeFinalTime)
void	GetSampledSpaceTimeBasis (std::vector< int > const &t_samples, const Matrix *t_basis, Matrix const &s_basis_sampled, Matrix &f_basis_sampled_inv)
Matrix	outerProduct (const Vector &v, const Vector &w)
	Computes the outer product of two Vectors, v and w. More...
Matrix	DiagonalMatrixFactory (const Vector &v)
	Factory function to make a diagonal matrix with nonzero entries as in its Vector argument. The rows of this diagonal matrix are distributed in the same fashion as its Vector argument. More...
Matrix	IdentityMatrixFactory (const Vector &v)
	Factory function to make an identity matrix with rows distributed in the same fashion as its Vector argument. This function is provided for convenience due to the ubiquity of identity matrices (and operators) in mathematics. More...
struct EigenPair	SymmetricRightEigenSolve (Matrix *A)
	Computes the eigenvectors/eigenvalues of an NxN real symmetric matrix. More...
struct ComplexEigenPair	NonSymmetricRightEigenSolve (Matrix *A)
	Computes the eigenvectors/eigenvalues of an NxN real nonsymmetric matrix. More...
void	SerialSVD (Matrix *A, Matrix *U, Vector *S, Matrix *V)
	Computes the SVD of a undistributed matrix in serial. More...
struct SerialSVDDecomposition	SerialSVD (Matrix *A)
	Computes the SVD of a undistributed matrix in serial. More...
Matrix *	SpaceTimeProduct (const CAROM::Matrix *As, const CAROM::Matrix *At, const CAROM::Matrix *Bs, const CAROM::Matrix *Bt, const std::vector< double > *tscale, const bool At0at0, const bool Bt0at0, const bool lagB, const bool skip0)
void	blacs_get_ (int *, int *, int *)
void	blacs_pinfo_ (int *, int *)
void	blacs_gridinit_ (int *, char *, int *, int *)
void	blacs_gridinfo_ (int *, int *, int *, int *, int *)
void	blacs_gridexit_ (int *icontxt)
void	blacs_freebuff_ (int *icontxt, int *wait)
void	blacs_exit_ (int *cont)
void	descinit_ (int *DESC, int *M, int *N, int *MB, int *NB, int *IRSRC, int *ICSRC, int *ICTXT, int *LLD, int *INFO)
void	pdormqr_ (char *SIDE, char *TRANS, int *M, int *N, int *K, double *A, int *IA, int *JA, int *DESCA, double *TAU, double *C, int *IC, int *JC, int *DESCC, double *WORK, int *LWORK, int *INFO)
void	pdgeqrf_ (int *M, int *N, double *A, int *IA, int *JA, int *DESCA, double *TAU, double *WORK, int *LWORK, int *INFO)
void	pdtrsm_ (char *SIDE, char *UPLO, char *TRANS, char *DIAG, int *M, int *N, double *ALPHA, double *A, int *IA, int *JA, int *DESCA, double *B, int *IB, int *JB, int *DESCB)
void	pdgemr2d_ (int *m, int *n, double *A, int *IA, int *JA, int *descA, double *B, int *IB, int *JB, int *descB, int *gcontext)
void	pdlacpy_ (char *UPLO, int *M, int *N, double *A, int *IA, int *JA, int *DESCA, double *B, int *IB, int *JB, int *DESCB)
int	numroc_ (int *N, int *NB, int *IPROC, int *ISRCPROC, int *NPROCS)
void	pdgemv_ (char *TRANS, int *M, int *N, double *ALPHA, double *A, int *IA, int *JA, int *DESCA, double *X, int *IX, int *JX, int *DESCX, int *INCX, double *BETA, double *Y, int *IY, int *JY, int *DESCY, int *INCY)
int	getCenterPoint (std::vector< Vector * > &points, bool use_centroid)
	Get center point of a group of points.
int	getCenterPoint (std::vector< Vector > &points, bool use_centroid)
	Get center point of a group of points.
int	getClosestPoint (std::vector< Vector * > &points, Vector *test_point)
	Get closest point to a test point among a group of points.
int	getClosestPoint (std::vector< Vector > &points, Vector test_point)
	Get closest point to a test point among a group of points.
void	FindStencilElements (const vector< int > &sample_dofs_gid, set< int > &elements, ParFiniteElementSpace &fespace)
void	FindSampledMeshEntities (const int type, const vector< int > &sample_dofs_gid, set< int > &entities, ParFiniteElementSpace &fespace)
void	GetLocalSampleMeshElements (ParMesh &pmesh, ParFiniteElementSpace &fespace, const vector< int > &sample_dofs, const vector< int > &local_num_sample_dofs, set< int > &elems, bool getSampledEntities, set< int > &intElems, set< int > &faces, set< int > &edges, set< int > &vertices)
void	SplitDofsIntoBlocks (const vector< int > &Ntrue, const vector< int > &dofs, const vector< int > &local_num_dofs, vector< vector< int >> &dofs_block, vector< vector< int >> &dofs_block_todofs, vector< vector< int >> &local_num_dofs_block)
void	InsertElementDofs (ParFiniteElementSpace &fespace, const int elId, const int offset, set< int > &element_dofs)
void	AugmentDofListWithOwnedDofs (vector< int > &mixedDofs, vector< ParFiniteElementSpace * > &fespace)
void	BuildSampleMesh (ParMesh &pmesh, vector< ParFiniteElementSpace * > &fespace, const set< int > &elems, Mesh *&sample_mesh, vector< int > &stencil_dofs, vector< int > &elemLocalIndices, vector< map< int, int > > &elemLocalIndicesInverse)
void	GetLocalDofsToLocalElementMap (ParFiniteElementSpace &fespace, const vector< int > &dofs, const vector< int > &localNumDofs, const set< int > &elems, vector< int > &dofToElem, vector< int > &dofToElemDof, const bool useTDof)
void	Set_s2sp (const int myid, const int num_procs, vector< int > const &spNtrue, const int global_num_sample_dofs, const vector< int > &local_num_sample_dofs, const vector< vector< int > > &local_num_sample_dofs_sub, const vector< vector< int > > &localSampleDofsToElem_sub, const vector< vector< int > > &localSampleDofsToElemDof_sub, const vector< vector< int > > &sample_dofs_sub_to_sample_dofs, const vector< map< int, int > > &elemLocalIndicesInverse, vector< ParFiniteElementSpace * > &spfespace, vector< int > &s2sp)
void	Finish_s2sp_augmented (const int rank, const int nprocs, vector< ParFiniteElementSpace * > &fespace, vector< vector< int >> &dofs_block, vector< vector< int > > &dofs_sub_to_sdofs, vector< vector< int > > &local_num_dofs_sub, const bool dofsTrue, vector< int > &s2sp_)
void	ParaViewPrintAttributes (const string &fname, Mesh &mesh, int entity_dim, const Array< int > *el_number=nullptr, const Array< int > *vert_number=nullptr)
void	GatherDistributedMatrixRows_aux (const CAROM::Matrix &B, const int rdim, const int os0, const int os1, const int ossp, ParFiniteElementSpace &fespace, const vector< int > &st2sp, const vector< int > &sprows, const vector< int > &all_sprows, CAROM::Matrix &Bsp)
void	SampleVisualization (ParMesh *pmesh, set< int > const &elems, set< int > const &intElems, set< int > const &faces, set< int > const &edges, set< int > const &vertices, string const &filename, mfem::Vector *elemCount, double elementScaling)
void	ComputeCtAB (const HypreParMatrix &A, const CAROM::Matrix &B, const CAROM::Matrix &C, CAROM::Matrix &CtAB)
	This function computes a reduced, non-distributed matrix C^t AB stored identically (redundantly) on every process. More...
void	ComputeCtAB_vec (const HypreParMatrix &A, const HypreParVector &B, const CAROM::Matrix &C, CAROM::Vector &CtAB_vec)
	This function computes a reduced, non-distributed vector C^t AB stored identically (redundantly) on every process. More...
void	verify_within_portion (const mfem::Vector &bb_min, const mfem::Vector &bb_max, const mfem::Vector &t, const double limit)
	Helper function to ensure that t is within a given percentage of the domain relative to the center of the mesh. Performs the check for each dimension of the mesh (works if mesh is 2D or 3D). More...
double	map_to_ref_mesh (const double &bb_min, const double &bb_max, const double &fraction)
	Maps a value from [-1, 1] to the corresponding mesh domain [bb_min, bb_max]. More...
double	map_from_ref_mesh (const double &bb_min, const double &bb_max, const double &value)
	Maps a value within mesh domain [bb_min, bb_max] to the corresponding value between [-1, 1]. More...
bool	fileExists (const std::string &name)
int	split_dimension (const int dim, const MPI_Comm &comm=MPI_COMM_WORLD)
	Distribute the global size dim into MPI processes as equally as possible. More...
int	get_global_offsets (const int local_dim, std::vector< int > &offsets, const MPI_Comm &comm=MPI_COMM_WORLD)
	Save integer offsets for each MPI rank under MPI communicator comm, where each rank as the size of local_dim. the sum of local_dim over all MPI processes is returned as the total dimension. More...
bool	is_same (int x, const MPI_Comm &comm=MPI_COMM_WORLD)
	Check if an integer is equal over all MPI processes. More...

Detailed Description

Copyright (c) 2013-2024, Lawrence Livermore National Security, LLC and other libROM project developers. See the top-level COPYRIGHT file for details.

SPDX-License-Identifier: (Apache-2.0 OR MIT)

Author: Milos Stojanovic Stojke (milsto) Adapted by Kevin Huynh from DifferentialEvolution.h from milsto's Github repo, https://github.com/milsto/differential-evolution, permission granted by milsto/differential-evolution's MIT license.

SPDX-License-Identifier: (MIT)

Function Documentation

ComputeCtAB()

void CAROM::ComputeCtAB	(	const HypreParMatrix &	A,
		const CAROM::Matrix &	B,
		const CAROM::Matrix &	C,
		CAROM::Matrix &	CtAB
	)

This function computes a reduced, non-distributed matrix C^t AB stored identically (redundantly) on every process.

Parameters

[in]	A	The distributed HypreParMatrix (an MFEM class) A in C^t AB.
[in]	B	The distributed Matrix B in C^t AB.
[in]	C	The distributed Matrix C in C^t AB.
[out]	CtAB	The non-distributed Matrix C^t AB.

Definition at line 15 of file Utilities.cpp.

ComputeCtAB_vec()

void CAROM::ComputeCtAB_vec	(	const HypreParMatrix &	A,
		const HypreParVector &	B,
		const CAROM::Matrix &	C,
		CAROM::Vector &	CtAB_vec
	)

This function computes a reduced, non-distributed vector C^t AB stored identically (redundantly) on every process.

Parameters

[in]	A	The distributed HypreParMatrix (an MFEM class) A in C^t AB.
[in]	B	The distributed HypreParVector B in C^t AB.
[in]	C	The distributed Matrix C in C^t AB.
[out]	CtAB	The non-distributed Vector C^t AB.

Definition at line 47 of file Utilities.cpp.

convertClosestRBFToEpsilon()

double CAROM::convertClosestRBFToEpsilon	(	std::vector< Vector * >	parameter_points,
		std::string	rbf,
		double	closest_rbf_val
	)

Convert closest RBF value to an epsilon value.

Parameters

[in]	parameter_points	The parameter points.
[in]	rbf	Which RBF to compute.
[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

Definition at line 176 of file Interpolator.cpp.

createGreedyErrorIndicatorPoint() [1/2]

struct GreedyErrorIndicatorPoint CAROM::createGreedyErrorIndicatorPoint	(	Vector *	point,
		std::shared_ptr< Vector > &	localROM
	)

Create a greedy error indicator point.

Parameters

[in]	point	The error indicator point.
[in]	localROM	The point of the nearest ROM.

Returns

A struct holding the point and the location of the nearest local ROM or NULL if no point is required.

Definition at line 1 of file GreedySampler.cpp.

createGreedyErrorIndicatorPoint() [2/2]

struct GreedyErrorIndicatorPoint CAROM::createGreedyErrorIndicatorPoint	(	Vector *	point,
		Vector *	localROM
	)

Create a greedy error indicator point.

Parameters

[in]	point	The error indicator point.
[in]	localROM	The point of the nearest ROM.

Returns

A struct holding the point and the location of the nearest local ROM or NULL if no point is required.

Definition at line 1 of file GreedySampler.cpp.

DEIM()

void CAROM::DEIM	(	const Matrix *	f_basis,
		int	num_f_basis_vectors_used,
		std::vector< int > &	f_sampled_row,
		std::vector< int > &	f_sampled_rows_per_proc,
		Matrix &	f_basis_sampled_inv,
		int	myid,
		int	num_procs
	)

Computes the DEIM algorithm on the given basis.

Implemented from Saifon Chaturantabut and Danny C. Sorensen "Nonlinear Model Reduction via Discrete Empirical Interpolation", SIAM J. Sci. Comput., 32(5), 2737–2764. (28 pages)

Parameters

[in]	f_basis	The basis vectors for the RHS.
[in]	num_f_basis_vectors_used	The number of basis vectors in f_basis to use in the algorithm.
[out]	f_sampled_row	The local row ids of each sampled row. This will contain the sampled rows from all processors. Use f_sampled_rows_per_proc to index into this array for the sampled rows from a specific processor.
[out]	f_sampled_rows_per_proc	The number of sampled rows for each processor.
[out]	f_basis_sampled_inv	The inverse of the sampled basis of the RHS.
[in]	myid	The rank of this process.
[in]	num_procs	The total number of processes.

Definition at line 29 of file DEIM.cpp.

DiagonalMatrixFactory()

Matrix CAROM::DiagonalMatrixFactory

(

const Vector &

v

)

Factory function to make a diagonal matrix with nonzero entries as in its Vector argument. The rows of this diagonal matrix are distributed in the same fashion as its Vector argument.

Parameters

[in]

v

Vector of elements that will be on the diagonal of the output matrix.

Postcondition

diagonalMatrix.distributed() == v.distributed()

diagonalMatrix.numRows() == v.dim()

Returns

The diagonal matrix created by this function.

Get the number of rows on each process; these process row counts must be summed to get the number of columns on each process.

Compute the row starting index and total number of rows over all processes – which is also the total number of columns. Also compute the starting row index on each process.

Assume that Matrix rows are contiguous sets of row indices, e.g., if a four row matrix is partititioned over two processes, then process zero on the MPI_Comm owns rows 0 and 1, and process one on the MPI_Comm owns rows 2 and 3.

Create the diagonal matrix and assign process local entries in v to process local entries in the diagonal matrix.

Off-diagonal matrix entries are zero; diagonal matrix entries come from the input Vector.

Definition at line 2073 of file Matrix.cpp.

get_global_offsets()

int CAROM::get_global_offsets	(	const int	local_dim,
		std::vector< int > &	offsets,
		const MPI_Comm &	comm = MPI_COMM_WORLD
	)

Save integer offsets for each MPI rank under MPI communicator comm, where each rank as the size of local_dim. the sum of local_dim over all MPI processes is returned as the total dimension.

Parameters

[in]	local_dim	Input local dimension specified for each MPI rank.
[out]	offsets	Resulting global integer offsets split by local_dim.
[in]	comm	MPI communicator. default value MPI_COMM_WORLD.
[out]	dim	(Returned value) Global dimension as the sum of all local_dim.

Definition at line 41 of file mpi_utils.cpp.

getNearestPoint() [1/2]

double CAROM::getNearestPoint	(	std::vector< double >	paramPoints,
		double	point
	)

Given a double, find the nearest point in a domain.

Parameters

[in]	paramPoints	The domain to search.
[in]	point	The specified point.

Returns

A double representing the nearest point in a domain.

Definition at line 74 of file GreedySampler.cpp.

getNearestPoint() [2/2]

Vector CAROM::getNearestPoint	(	std::vector< Vector >	paramPoints,
		Vector	point
	)

Given a vector, find the nearest point in a domain.

Parameters

[in]	paramPoints	The domain to search.
[in]	point	The specified point.

Returns

A vector representing the nearest point in a domain.

Definition at line 44 of file GreedySampler.cpp.

getNearestPointIndex() [1/2]

int CAROM::getNearestPointIndex	(	std::vector< double >	paramPoints,
		double	point
	)

Given a double, find the nearest point in a domain.

Parameters

[in]	paramPoints	The domain to search.
[in]	point	The specified point.

Returns

The index of the nearest point in a domain.

Definition at line 82 of file GreedySampler.cpp.

getNearestPointIndex() [2/2]

int CAROM::getNearestPointIndex	(	std::vector< Vector >	paramPoints,
		Vector	point
	)

Given a vector, find the nearest point in a domain.

Parameters

[in]	paramPoints	The domain to search.
[in]	point	The specified point.

Returns

The index of the nearest point in a domain.

Definition at line 52 of file GreedySampler.cpp.

getParametricDMD() [1/2]

template<class T >

void CAROM::getParametricDMD	(	T *&	parametric_dmd,
		std::vector< Vector * > &	parameter_points,
		std::vector< std::string > &	dmd_paths,
		Vector *	desired_point,
		std::string	rbf = "G",
		std::string	interp_method = "LS",
		double	closest_rbf_val = 0.9,
		bool	reorthogonalize_W = false
	)

Constructor.

Parameters

[in]	parameter_points	The parameter points.
[in]	dmd_paths	The paths to the saved DMD objects associated with each 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.

Definition at line 141 of file ParametricDMD.h.

getParametricDMD() [2/2]

template<class T >

void CAROM::getParametricDMD	(	T *&	parametric_dmd,
		std::vector< Vector * > &	parameter_points,
		std::vector< T * > &	dmds,
		Vector *	desired_point,
		std::string	rbf = "G",
		std::string	interp_method = "LS",
		double	closest_rbf_val = 0.9,
		bool	reorthogonalize_W = false
	)

Constructor.

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.

Definition at line 52 of file ParametricDMD.h.

getParametricDMDc() [1/2]

template<class T >

void CAROM::getParametricDMDc	(	T *&	parametric_dmdc,
		std::vector< Vector * > &	parameter_points,
		std::vector< std::string > &	dmdc_paths,
		std::vector< Matrix * >	controls,
		Matrix *&	controls_interpolated,
		Vector *	desired_point,
		std::string	rbf = "G",
		std::string	interp_method = "LS",
		double	closest_rbf_val = 0.9,
		bool	reorthogonalize_W = false
	)

Constructor.

Parameters

[in]	parameter_points	The parameter points.
[in]	dmdc_paths	The paths to the saved DMD objects associated with each parameter point.
[in]	desired_point	The desired point at which to create a parametric DMD.
[in]	controls	The matrices of controls from previous runs which we use to interpolate.
[in]	controls_interpolated	The interpolated controls.
[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.

Definition at line 164 of file ParametricDMDc.h.

getParametricDMDc() [2/2]

template<class T >

void CAROM::getParametricDMDc	(	T *&	parametric_dmdc,
		std::vector< Vector * > &	parameter_points,
		std::vector< T * > &	dmdcs,
		std::vector< Matrix * >	controls,
		Matrix *&	controls_interpolated,
		Vector *	desired_point,
		std::string	rbf = "G",
		std::string	interp_method = "LS",
		double	closest_rbf_val = 0.9,
		bool	reorthogonalize_W = false
	)

Constructor.

Parameters

[in]	parametric_dmdc	The interpolant DMDc model at the desired point.
[in]	parameter_points	The training parameter points.
[in]	dmdcs	The DMDc 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 DMDc.
[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.

Definition at line 56 of file ParametricDMDc.h.

GNAT()

void CAROM::GNAT	(	const Matrix *	f_basis,
		const int	num_f_basis_vectors_used,
		std::vector< int > &	f_sampled_row,
		std::vector< int > &	f_sampled_rows_per_proc,
		Matrix &	f_basis_sampled_inv,
		const int	myid,
		const int	num_procs,
		const int	num_samples_req = -1,
		std::vector< int > *	init_samples = NULL
	)

Computes the GNAT algorithm on the given basis.

Implemented from Kevin Carlberg, Charbel Farhat, Julien Cortial, and David Amsallem "The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows", Journal of Computational Physics Volume 242, 1 June 2013, Pages 623-647.

Parameters

[in]	f_basis	The basis vectors for the RHS.
[in]	num_f_basis_vectors_used	The number of basis vectors in f_basis to use in the algorithm.
[out]	f_sampled_row	The local row ids of each sampled row. This will contain the sampled rows from all processors. Use f_sampled_rows_per_proc to index into this array for the sampled rows from a specific processor.
[out]	f_sampled_rows_per_proc	The number of sampled rows for each processor.
[out]	f_basis_sampled_inv	The inverse of the sampled basis of the RHS.
[in]	myid	The rank of this process.
[in]	num_procs	The total number of processes.
[in]	num_samples_req	The minimum number of samples required.
[in]	init_samples	Samples to initialize the GNAT algorithm.

Definition at line 27 of file GNAT.cpp.

IdentityMatrixFactory()

Matrix CAROM::IdentityMatrixFactory

(

const Vector &

v

)

Factory function to make an identity matrix with rows distributed in the same fashion as its Vector argument. This function is provided for convenience due to the ubiquity of identity matrices (and operators) in mathematics.

Parameters

[in]

v

Vector of elements that will be on the diagonal of the output matrix.

Postcondition

diagonalMatrix.distributed() == v.distributed()

diagonalMatrix.numRows() == v.dim()

Returns

The identity matrix created by this function.

Definition at line 2149 of file Matrix.cpp.

is_same()

bool CAROM::is_same	(	int	x,
		const MPI_Comm &	comm = MPI_COMM_WORLD
	)

Check if an integer is equal over all MPI processes.

Parameters

[in]	x	Input integer value to test equality.
[in]	comm	MPI communicator. default value MPI_COMM_WORLD.

Definition at line 72 of file mpi_utils.cpp.

map_from_ref_mesh()

double CAROM::map_from_ref_mesh	(	const double &	bb_min,
		const double &	bb_max,
		const double &	value
	)

Maps a value within mesh domain [bb_min, bb_max] to the corresponding value between [-1, 1].

Parameters

bb_min	Minimum value of domain
bb_max	Maximum value of domain
value	Value between [bb_min, bb_max] to map

Returns

value mapped to [-1, 1]

See also

map_to_ref_mesh

Definition at line 96 of file Utilities.cpp.

map_to_ref_mesh()

double CAROM::map_to_ref_mesh	(	const double &	bb_min,
		const double &	bb_max,
		const double &	fraction
	)

Maps a value from [-1, 1] to the corresponding mesh domain [bb_min, bb_max].

Parameters

bb_min	Minimum value of domain
bb_max	Maximum value of domain
fraction	Value between [-1, 1] to map

Returns

fraction mapped to [bb_min, bb_max]

See also

map_from_ref_mesh

Definition at line 88 of file Utilities.cpp.

NonSymmetricRightEigenSolve()

struct ComplexEigenPair CAROM::NonSymmetricRightEigenSolve

(

Matrix *

A

)

Computes the eigenvectors/eigenvalues of an NxN real nonsymmetric matrix.

Parameters

[in]

A

The NxN real nonsymmetric matrix to be eigendecomposed.

Returns

The eigenvectors and eigenvalues of the eigensolve. The eigenvector matrices contained within the returning struct must be destroyed by the user.

Definition at line 2149 of file Matrix.cpp.

obtainRBF()

double CAROM::obtainRBF	(	std::string	rbf,
		double	epsilon,
		Vector *	point1,
		Vector *	point2
	)

Compute the RBF between two points.

Parameters

[in]	rbf	Which RBF to compute.
[in]	epsilon	The RBF parameter that determines the width of influence.
[in]	point1	The first point.
[in]	point2	The second point.

Definition at line 149 of file Interpolator.cpp.

obtainRBFToTrainingPoints()

std::vector< double > CAROM::obtainRBFToTrainingPoints	(	std::vector< Vector * >	parameter_points,
		std::string	interp_method,
		std::string	rbf,
		double	epsilon,
		Vector *	point
	)

Compute the RBF from the parameter points with the unsampled parameter point.

Parameters

[in]	parameter_points	The parameter points.
[in]	interp_method	The interpolation method type ("LS" == linear solve, "IDW" == inverse distance weighting, "LP" == lagrangian polynomials)
[in]	rbf	Which RBF to compute.
[in]	epsilon	The RBF parameter that determines the width of influence.
[in]	point	The unsampled parameter point.

Definition at line 70 of file Interpolator.cpp.

obtainRotationMatrices()

std::vector< Matrix * > CAROM::obtainRotationMatrices	(	std::vector< Vector * >	parameter_points,
		std::vector< Matrix * >	bases,
		int	ref_point
	)

Obtain the rotation matrices for all the parameter points using the basis of the reference point.

Parameters

[in]	parameter_points	The parameter points.
[in]	bases	The spatial basis associated with each parameter point.
[in]	ref_point	The index within the vector of parameter points to the reference point

Definition at line 219 of file Interpolator.cpp.

outerProduct()

Matrix CAROM::outerProduct	(	const Vector &	v,
		const Vector &	w
	)

Computes the outer product of two Vectors, v and w.

Postcondition

The number of rows in the returned matrix equals the dimension of v

The number of cols in the returned matrix equals the dimension of w, if w is not distributed. If w is distributed, the number of columns equals the total number of entries of w, summed over all processes.

If v is distributed, so is the returned matrix.

Parameters

[in]	v	The first vector in the outer product
[in]	w	The second vector in the outer product

Returns

The product of v and the transpose of w.

Definition at line 1973 of file Matrix.cpp.

QDEIM()

void CAROM::QDEIM	(	const Matrix *	f_basis,
		int	num_f_basis_vectors_used,
		std::vector< int > &	f_sampled_row,
		std::vector< int > &	f_sampled_rows_per_proc,
		Matrix &	f_basis_sampled_inv,
		const int	myid,
		const int	num_procs,
		const int	num_samples_req
	)

Computes the QDEIM algorithm on the given basis.

Implemented from Zlatko Drmac, Serkan Gugercin, "A new selection operator for the discrete empirical interpolation method – Improved a priori error bound and extensions", SIAM Journal on Scientific Computing, Volume 38, Issue 2, pages A631-A648, 2016.

Oversampling uses GappyPOD+E from Peherstorfer, Drmac, Gugercin, "Stability of discrete empirical interpolation and gappy proper orthogonal decomposition with randomized and deterministic sampling points", preprint May 20, 2020.

Parameters

[in]	f_basis	The basis vectors for the RHS.
[in]	num_f_basis_vectors_used	The number of basis vectors in f_basis to use in the algorithm.
[out]	f_sampled_row	The local row ids of each sampled row. This will contain the sampled rows from all processors. Use f_sampled_rows_per_proc to index into this array for the sampled rows from a specific processor.
[out]	f_sampled_rows_per_proc	The number of sampled rows for each processor.
[out]	f_basis_sampled_inv	The inverse of the sampled basis of the RHS.
[in]	myid	The rank of this process.
[in]	num_procs	The total number of processes.
[in]	num_samples_req	The minimum number of samples required.

Definition at line 25 of file QDEIM.cpp.

rbfWeightedSum()

double CAROM::rbfWeightedSum

(

std::vector< double > &

rbf

)

Compute the sum of the RBF weights.

Parameters

[in]

rbf

The vector holding the rbfs of the training points.

Definition at line 139 of file Interpolator.cpp.

S_OPT()

void CAROM::S_OPT	(	const Matrix *	f_basis,
		int	num_f_basis_vectors_used,
		std::vector< int > &	f_sampled_row,
		std::vector< int > &	f_sampled_rows_per_proc,
		Matrix &	f_basis_sampled_inv,
		const int	myid,
		const int	num_procs,
		const int	num_samples_req = -1,
		std::vector< int > *	init_samples = NULL,
		bool	qr_factorize = false
	)

Computes the S_OPT algorithm on the given basis.

Implemented from Yeonjong Shin and Dongbin Xiu's "Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression", SIAM J. Sci. Comput., 38(1), A385-A411. (26 pages)

Parameters

[in]	f_basis	The basis vectors for the RHS.
[in]	num_f_basis_vectors_used	The number of basis vectors in f_basis to use in the algorithm.
[out]	f_sampled_row	The local row ids of each sampled row. This will contain the sampled rows from all processors. Use f_sampled_rows_per_proc to index into this array for the sampled rows from a specific processor.
[out]	f_sampled_rows_per_proc	The number of sampled rows for each processor.
[out]	f_basis_sampled_inv	The inverse of the sampled basis of the RHS.
[in]	myid	The rank of this process.
[in]	num_procs	The total number of processes.
[in]	num_samples_req	The minimum number of samples required.
[in]	init_samples	Samples to initialize the S_OPT algorithm.
[in]	qr_factorize	Whether to factorize the incoming matrix. If true and if the incoming matrix is a basis, the unnecessary computation of a QR factorization will be performed.

Definition at line 30 of file S_OPT.cpp.

SerialSVD() [1/2]

struct SerialSVDDecomposition CAROM::SerialSVD

(

Matrix *

A

)

Computes the SVD of a undistributed matrix in serial.

Parameters

[in]

A

The MxN undistributed matrix to be eigendecomposed.

Returns

The singular value decomposition within a struct. The matrices and vector contained within the returning struct must be destroyed by the user.

Definition at line 2279 of file Matrix.cpp.

SerialSVD() [2/2]

void CAROM::SerialSVD	(	Matrix *	A,
		Matrix *	U,
		Vector *	S,
		Matrix *	V
	)

Computes the SVD of a undistributed matrix in serial.

Parameters

[in]	A	The MxN undistributed matrix to be eigendecomposed.
[in]	U	The matrix to write the left singular vectors into.
[in]	S	The vector to write the singular values into.
[in]	V	The matrix to write the right singular vectors into.

Returns

The singular value decomposition within the input parameters U, S, and V.

Definition at line 2279 of file Matrix.cpp.

SpaceTimeSampling()

void CAROM::SpaceTimeSampling	(	const Matrix *	s_basis,
		const Matrix *	t_basis,
		const int	num_f_basis_vectors_used,
		std::vector< int > &	t_samples,
		int *	f_sampled_row,
		int *	f_sampled_rows_per_proc,
		Matrix &	s_basis_sampled,
		const int	myid,
		const int	num_procs,
		const int	num_t_samples_req = -1,
		const int	num_s_samples_req = -1,
		const bool	excludeFinalTime = false
	)

Parameters

[in]	s_basis	The spatial basis vectors.
[in]	t_basis	The temporal basis vectors.
[in]	num_f_basis_vectors_used	The number of basis vectors in f_basis to use in the algorithm.
[out]	t_samples	Array of temporal samples.
[out]	f_sampled_row	The local row ids of each sampled row. This will contain the sampled rows from all processors. Use f_sampled_rows_per_proc to index into this array for the sampled rows from a specific processor.
[out]	f_sampled_rows_per_proc	The number of sampled rows for each processor.
[out]	f_basis_sampled_inv	The inverse of the sampled basis of the RHS.
[in]	myid	The rank of this process.
[in]	num_procs	The total number of processes.
[in]	num_t_samples_req	The number of temporal samples to compute.
[in]	num_s_samples_req	The number of spatial samples to compute.
[in]	excludeFinalTime	Whether to exclude the final time index as a temporal sample.

Definition at line 510 of file STSampling.cpp.

split_dimension()

int CAROM::split_dimension	(	const int	dim,
		const MPI_Comm &	comm = MPI_COMM_WORLD
	)

Distribute the global size dim into MPI processes as equally as possible.

Parameters

[in]	dim	Input global size.
[in]	comm	MPI communicator. default value MPI_COMM_WORLD.
[out]	local_dim	(Returned value) Local size assigned to the current MPI process.

Definition at line 23 of file mpi_utils.cpp.

SymmetricRightEigenSolve()

struct EigenPair CAROM::SymmetricRightEigenSolve

(

Matrix *

A

)

Computes the eigenvectors/eigenvalues of an NxN real symmetric matrix.

Parameters

[in]

A

The NxN real symmetric matrix to be eigendecomposed.

Returns

The eigenvectors and eigenvalues of the eigensolve. The eigenvector matrices contained within the returning struct must be destroyed by the user.

Definition at line 2149 of file Matrix.cpp.

verify_within_portion()

void CAROM::verify_within_portion	(	const mfem::Vector &	bb_min,
		const mfem::Vector &	bb_max,
		const mfem::Vector &	t,
		const double	limit
	)

Helper function to ensure that t is within a given percentage of the domain relative to the center of the mesh. Performs the check for each dimension of the mesh (works if mesh is 2D or 3D).

Parameters

bb_min	Minimum corner of mesh bounding box. See mfem::Mesh::GetBoundingBox().
bb_max	Maximum corner of mesh bounding box. See mfem::Mesh::GetBoundingBox().
t	Point to check if within given limit percentage of mesh domain relative to mesh center.
limit	Fractional percentage (from [0, 1]) of mesh domain to check bounds of t.

Note

This will throw an error and exit if the check fails.

Definition at line 65 of file Utilities.cpp.