sparsify_dynamics: Matrix Sparsification for SINDy Algorithm

In RobertGM111/havok: Procedures for the Analysis of Nonlinear Dynamical Systems

Matrix Sparsification for SINDy Algorithm

Description

Sparsification function based on sequential thresholded least-squares as shown in the SINDy algorithm in "Discovering governing equations from data: Sparse identification of nonlinear dynamical systems" (Brunton, Proctor, & Kutz, 2016).

Usage

sparsify_dynamics(Theta, dXdt, lambda, loops = 1)

Arguments

Theta	A matrix of candidate functions.
dXdt	A matrix of first order derivatives of the variables of interest with respect to time.
lambda	A numeric value; sparsification threshold.
loops	An integer; number of times sequential thresholded least-squares procedure is repeated.

Value

A matrix of sparse coefficients.

References

Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932-3937.

Examples

## Not run: 
sparsify_dynamics(Theta, dXdt, lambda, n)
sparsify_dynamics(Theta, dXdt, .005, 10)
sparsify_dynamics(pool_data(yIn, 15, 5, TRUE), dXdt, .1, 1)

## End(Not run)

RobertGM111/havok documentation built on July 8, 2023, 8:23 p.m.