CAROM::MatrixInterpolator Class Reference

#include <MatrixInterpolator.h>

Inheritance diagram for CAROM::MatrixInterpolator:

Public Member Functions
	MatrixInterpolator (std::vector< Vector * > parameter_points, std::vector< Matrix * > rotation_matrices, std::vector< Matrix * > reduced_matrices, int ref_point, std::string matrix_type, std::string rbf="G", std::string interp_method="LS", double closest_rbf_val=0.9)
	Constructor. More...
Matrix *	interpolate (Vector *point, bool orthogonalize=false)
	Obtain the interpolated reduced matrix of the unsampled parameter point. More...

Additional Inherited Members
Protected Member Functions inherited from CAROM::Interpolator
	Interpolator (std::vector< Vector * > parameter_points, std::vector< Matrix * > rotation_matrices, int ref_point, std::string rbf, std::string interp_method, double closest_rbf_val=0.9)
	Constructor. More...
Protected Attributes inherited from CAROM::Interpolator
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_ref_point
	The index within the vector of parameter points to the reference point.
std::string	d_rbf
	The RBF type (gaussian, multiquadric, inverse quadratic, inverse multiquadric)
std::string	d_interp_method
	The interpolation method (linear solve, inverse distance weighting, lagrangian polynomials)
double	d_epsilon
	The RBF parameter that determines the width of influence. a small epsilon: larger influential width a large epsilon: smaller influential width.
std::vector< Vector * >	d_parameter_points
	The sampled parameter points.
std::vector< Matrix * >	d_rotation_matrices
	The reduced bases with compatible coordinates.
Matrix *	d_lambda_T
	The RHS of the linear solve in tangential space.

Detailed Description

MatrixInterpolator interpolates reduced matrices of a set of parameter points and returns an interpolated reduced matrix for an unseen parameter point. The performance of this algorithm depends on the matrix sizes being small because of its computational complexity due to direct matrix inversion. The interpolation algorithm was adapted from "Gradient-based Constrained Optimization Using a Database of Linear Reduced-Order Models" by Y. Choi et al.

Definition at line 34 of file MatrixInterpolator.h.

Constructor & Destructor Documentation

MatrixInterpolator()

CAROM::MatrixInterpolator::MatrixInterpolator	(	std::vector< Vector * >	parameter_points,
		std::vector< Matrix * >	rotation_matrices,
		std::vector< Matrix * >	reduced_matrices,
		int	ref_point,
		std::string	matrix_type,
		std::string	rbf = "G",
		std::string	interp_method = "LS",
		double	closest_rbf_val = 0.9
	)

Constructor.

Parameters

[in]	parameter_points	The parameter points.
[in]	rotation_matrices	The rotation matrices associated with each parameter point.
[in]	reduced_matrices	The reduced matrices associated with each parameter point.
[in]	ref_point	The index within the vector of parameter points to the reference point
[in]	matrix_type	The type of matrix (R = real, B = basis [also real, but Steifel in specific] NS = nonsingular, SPD = symmetric positive-definite)
[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

Definition at line 40 of file MatrixInterpolator.cpp.

Member Function Documentation

interpolate()

Matrix * CAROM::MatrixInterpolator::interpolate	(	Vector *	point,
		bool	orthogonalize = false
	)

Obtain the interpolated reduced matrix of the unsampled parameter point.

Parameters

[in]	point	The unsampled parameter point.
[in]	orthogonalize	Whether to orthogonalize the resulting interpolated matrix.

Definition at line 119 of file MatrixInterpolator.cpp.

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

• lib/algo/manifold_interp/MatrixInterpolator.h
• lib/algo/manifold_interp/MatrixInterpolator.cpp