The programs below are based on the paper:
### Fast QMC matrix vector product for lattice rules

The main program is:
fast_QMC_matrix_lattice_rule.m

It requires the following additional programs:

fastrank1pt_mod.m This is a slight modification of Dirk Nuyens' program which can be found here.

fastrank1od_mod.m This is a slight modification of Dirk Nuyens' program which can be found here.

generatorp.m This code is from Dirk Nuyens website.

powmod.m This code is from Dirk Nuyens website.

Here are two Examples to illustrate how fast_QMC_matrix_lattice_rule.m is used:

Example1.m Generates normally distributed points with a random covariance matrix.

Example2.m Performs a fast QMC matrix vector multiplication using a random matrix.

### Fast QMC matrix vector product for the union of all Korobov lattice point sets

Here is Matlab code to perform a fast QMC matrix vector multiplication:
fast_QMC_matrix_p_set.m

It requires the following additional programs:

generatorp.m This code is from Dirk Nuyens website.

Here are two Examples to illustrate how fast_QMC_matrix_lattice_rule.m is used:

Example1.m Generates normally distributed points with a random covariance matrix.

Example2.m Performs a fast QMC matrix vector multiplication using a random matrix.

The union of all Korobov lattice point sets has been studied by Korobov and Hua and Wang. Some background information can be found in the following papers:

- J. Dick, Q. T. Le Gia, F. Y. Kuo and Ch. Schwab, Fast QMC matrix-vector multiplication. SIAM J. Sci. Comput., 37, A1436--A1450, 2015. DOI: 10.1137/151005518 For the arXiv version see here.

It requires the following additional programs:

fastrank1pt_mod.m This is a slight modification of Dirk Nuyens' program which can be found here.

fastrank1od_mod.m This is a slight modification of Dirk Nuyens' program which can be found here.

generatorp.m This code is from Dirk Nuyens website.

powmod.m This code is from Dirk Nuyens website.

Here are two Examples to illustrate how fast_QMC_matrix_lattice_rule.m is used:

Example1.m Generates normally distributed points with a random covariance matrix.

Example2.m Performs a fast QMC matrix vector multiplication using a random matrix.

It requires the following additional programs:

generatorp.m This code is from Dirk Nuyens website.

Here are two Examples to illustrate how fast_QMC_matrix_lattice_rule.m is used:

Example1.m Generates normally distributed points with a random covariance matrix.

Example2.m Performs a fast QMC matrix vector multiplication using a random matrix.

The union of all Korobov lattice point sets has been studied by Korobov and Hua and Wang. Some background information can be found in the following papers:

- J. Dick, Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine-, and Walsh series. J. Approx. Theory, 183, 14--30, 2014. DOI: 10.1016/j.jat.2014.03.015 For the arXiv version see here.
- J. Dick and F. Pillichshammer, The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. To appear in the Proceedings of the conference Sequences and their Applications 2014. For the arXiv version see here.
- J. Dick and F. Pillichshammer, The weighted star discrepancy of Korobov's p-sets. To appear in Proc. Amer. Math. Soc., 2015. For the arXiv version see here.