**Index of MultipleRank1Lattice.tar.gz Contents**

Title of paper: *A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size*

Authors: *Craig Gross, Mark A. Iwen, Lutz Kaemmerer, and Toni Volkmer*

File: figure_generator.m

Type: MATLAB Code

Contents: Central code which computes all data used in figures.

Justification: Allows for easy reproduction of all data in section 3 of paper.

File: test_mr1l_approx_symhceven.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Algorithm 2.1 for even hyperbolic crosses starting with CBC construction.

Justification: Used to generate Figures 3.1a, 3.1a, 3.4a.

File: coord_symhc2even.m

Type: MATLAB Code

Contents: Helper function to construct even hyperbolic cross index sets.

Justification: Used throughout numerical tests for even hyperbolic cross examples.

File: coord_symhc2_parfor.m

Type: MATLAB Code

Contents: Computes hyperbolic cross index sets in parallel.

Justification: Used throughout numerical tests for even hyperbolic cross examples.

File: coord_symhc.m

Type: MATLAB Code

Contents: Computes hyperbolic cross index sets.

Justification: Used throughout numerical tests for even hyperbolic cross examples.

File: get_cbc_recor1l_symhceven.m

Type: MATLAB Code

Contents: Lookup for CBC constructed rank-1 lattices for even hyperbolic crosses.

Justification: Used throughout numerical tests for even hyperbolic cross examples.

File: symhc_lattices_even_ad_new.mat

Type: MATLAB Data File

Contents: CBC constructed rank-1 lattices suitable for various even hyperbolic crosses.

Justification: Used throughout numerical tests for even hyperbolic cross examples.

File: deterministic_mr1l_approx_get_lattice_sizes.m

Type: MATLAB Code

Contents: Computes multiple rank-1 lattices by Algorithm 2.1.

Justification: Code which implements the primary algorithm of interest.

File: get_reconstructable_freq.m

Type: MATLAB Code

Contents: Determines which frequencies a lattice keeps collision free.

Justification: Used throughout numerical tests.

File: test_mr1l_approx_symhceven.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Algorithm 2.1 for even hyperbolic crosses starting with exponential lattices for the full grid.

Justification: Used to generate Figures 3.1b, 3.2b.

File: test_mr1l_approx_rand_cbc.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Algorithm 2.1 for random frequency sets crosses starting with CBC construction.

Justification: Used to generate Figure 3.3a, 3.4b.

File: lfft_gen_lattice_algo23mod.m

Type: MATLAB Code

Contents: Generates a reconstructing rank-1 lattice using CBC construction for random frequency set.

Justification: Used throughout numerical tests for random frequency set examples.

File: lfft_lattice_size_reduce_mex_23.c

Type: C Code

Contents: Reduces lattice sizes for CBC constructions.

Justification: Generates mex file.

File: lfft_lattice_size_reduce_mex_23.mexa64

Type: MATLAB Mex Binary (compiled for Linux systems)

Contents: Reduces lattice sizes for CBC constructions.

Justification: Used throughout numerical tests for random frequency set examples.

File: test_mr1l_approx_rand_fulllattice1.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Algorithm 2.1 for random frequency sets crosses starting with exponential lattices for the full grid.

Justification: Used to generate Figure 3.3b.

File: testG3_dmr1l_symhceven_fulllattice1_results.m

Type: MATLAB Code

Contents: Computes the error in using a series of multiple rank-1 lattices for approximation on even hyperbolic crosses starting with exponential lattices for the full grid.

Justification: Used to generate Figure 3.5.

File: testG3_mlfft2_run.m

Type: MATLAB Code

Contents: Computes the error in using multiple rank-1 lattices for approximation on even hyperbolic crosses starting with exponential lattices for the full grid.

Justification: Used to generate Figure 3.5.

File: fct_Gp.m

Type: MATLAB Code

Contents: Computes value of G_p^d at lattice points.

Justification: Used in all function approximation examples.

File: fct_gp_1d.m

Type: MATLAB Code

Contents: Computes value of factors of G_p^d.

Justification: Used in all function approximation examples.

File: multi_lattice_ifft_noniter_avg.m

Type: MATLAB Code

Contents: Uses multiple rank-1 lattice FFTs to reconstruct all Fourier coefficients.

Justification: Used in all function approximation examples.

File: lfft.m

Type: MATLAB Code

Contents: Computes rank-1 lattice FFT.

Justification: Used in all function approximation examples.

File: fct_Gp_hat.m

Type: MATLAB Code

Contents: Computes values of Fourier coefficients of G_p^d.

Justification: Used in all function approximation examples.

File: fct_gp_hat_1d.m

Type: MATLAB Code

Contents: Computes value of factors of Fourier coefficients of G_p^d.

Justification: Used in all function approximation examples.

File: fct_G3_normA.m

Type: MATLAB Code

Contents: Computes Wiener algebra norm of G_3^d.

Justification: Used in all function approximation examples.

File: fct_Gp_hat_mp.m

Type: MATLAB Code

Contents: Computes values of Fourier coefficients of G_p^d in multiple precision.

Justification: Used in all function approximation examples.

File: fct_gp_hat_1d_mp.m

Type: MATLAB Code

Contents: Computes value of factors of Fourier coefficients of G_p^d in multiple precision.

Justification: Used in all function approximation examples.

File: fct_Gp_norm.m

Type: MATLAB Code

Contents: Computes norm of G_3^d in L_2.

Justification: Used in all function approximation examples.

File: test_mr1l_largeMstartS_symhceven.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Theorem 2.8 for even hyperbolic crosses starting with CBC construction.

Justification: Used to generate Figure 3.6a.

File: deterministic_mr1l_get_lattice_sizes_largeMstartS.m

Type: MATLAB Code

Contents: Computes multiple rank-1 lattices by Theorem 2.8.

Justification: Implements a main algorithm of interest.

File: check_iterative_MR1L.m

Type: MATLAB Code

Contents: Checks whether a set of frequencies can be reconstructed with given multiple rank-1 lattices.

Justification: Used for testing multiple rank-1 lattices constructed by the technique in Theorem 2.8.

File: test_mr1l_largeMstartS_symhceven_fulllattice1.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Theorem 2.8 for even hyperbolic crosses starting with starting with exponential lattices for the full grid.

Justification: Used to generate Figure 3.6b.

File: test_mr1l_largeMstartS_rand_cbc.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Theorem 2.8 for random frequency sets crosses starting with CBC construction.

Justification: Used to generate Figure 3.6c.

File: test_mr1l_largeMstartS_rand_fulllattice1.m

Type: MATLAB Code

Contents: Computes the number of samples in multiple rank-1 lattices constructed by Theorem 2.8 for random frequency sets crosses starting with exponential lattices for the full grid.

Justification: Used to generate Figure 3.6d.