dynamic_synch

Matlab files with proposed dynamic synchronization algorithms.

Description:

**main script files **:

1. sim_eType1_varyT_MultExps.m: Performance of algos for different value of T (for both Wigner and Outliers noise models)
2. sim_eType2_varyNoise_MultExps.m: Performance of algos for different values of noise (for both Wigner and Outliers noise models)
3. sim_eType2_PPM_varyNoise_MultExps.m: Performance of PPM for different values of noise (for both Wigner and Outliers noise models)

dynamic SO2 synchronization algorithms (names coincide with algos in the draft):

1. algo_spectral_so2.m
2. algo_spectral_local.m
3. algo_GTRS_DynSync.m
4. algo_LTRS_GS_DynSync.m
5. algo_LTRS_GMD_DynSync.m
6. algo_ppm_DynSync.m

**data generation **:

1. generate_ground_truth.m (sample random angles and impose smoothness by projection)
2. generate_AGN_data/generate_AGN_data_sparse.m (spike wigner model, add Gaussian noise to ground truth generated by generate_ground_truth.m)
3. generate_Outlier_data_sparse.m (outlier model, random contamination of the ground truth)
   

useful/auxiliary functions:

1. complextoreal.m (real representation of complex vectors/matrices, doubles the dimension)
2. realtocomplex.m (do the inverse of complextoreal.m)
3. laplacian_path.m (create a laplacian mat. of a path graph of given size)
4. proj_C.m (project a complex vector such that every coordinate is on the complex circle)
5. proj_2.m (anchors a complex vector such that the first coordinate is one, done blockwise)
6. projmat_smalleigs_lap.m (define a low freq. projection matrix based on path laplacian)
7. TRSgep (trs solver, coded by Yuji Nakatsukasa).