Julia codes
I use the Julia language for my numerical investigations. Please find a zipped file here containing my Julia codes. The main file to run is Datadriven.jl. It takes as input a data-file containing some timeseries. It then applies a sequence of operations, such as kernel building [4], generator compactification [1], ergodic averaging [3] and computation of the Koopman point spectrum [1]. Please email me at iamsuddhasattwa@gmail.com for more information and help.
I use the Julia language for my numerical investigations. Please find a zipped file here containing my Julia codes. The main file to run is Datadriven.jl. It takes as input a data-file containing some timeseries. It then applies a sequence of operations, such as kernel building [4], generator compactification [1], ergodic averaging [3] and computation of the Koopman point spectrum [1]. Please email me at iamsuddhasattwa@gmail.com for more information and help.
Data_driven.pdfA typical run of the code for performing a quasiperiodically driven reconstruction would be
A typical run of the code for performing a quasiperiodically driven reconstruction would be
julia> include("Data_driven_basis.jl");
julia> Compute_Bisotchastic_SVD();
julia> Compute_RKHS_norms( ; L0=230, ε_2=3.1);
julia> Post_analyze_QpD(; Tqpd=3000);
julia> include("Data_driven_basis.jl");
julia> Compute_Bisotchastic_SVD();
julia> Compute_RKHS_norms( ; L0=230, ε_2=3.1);
julia> Post_analyze_QpD(; Tqpd=3000);
References
[1] D Giannakis, S Das, J Slawinska. Reproducing kernel Hilbert space compactification of unitary evolution groups Appl. Comput. Harm. Anal. (2021) 54. (Preprint here)
[2] S Das, D Giannakis. Koopman spectra in reproducing kernel Hilbert spaces Appl. Comput. Harm. Anal. (2020) 49.2 (Preprint here)
[3] S Das, J Yorke. Super convergence of ergodic averages for quasiperiodic orbits, Nonlinearity, (2018), 31.2, 391. (Preprint here)
[4] S Das, D Giannakis. Delay-coordinate maps and the spectra of Koopman operators J. Stat.Phys. (2019), 175 (Preprint here)