Get Stated

Setup

The support Matlab releases for running mhodlr: MATLAB2023a, MATLAB2023b, MATLAB2024a, MATLAB2024b.

Platform Compatibility: Windows, macOS, Linux.

One can easily install mhodlr by simply downloading the software from the GitHub Link (https://github.com/chenxinye/mhodlr)

Or use the bash command if git is installed:

git clone https://github.com/chenxinye/mhodlr.git

After downloading the package, in Matlab terminal, add enviromental variables like

Or one can put the code in the corresponding location and perform the computing.

The alternative way to download is from FileExchange.

Quick start

Simply construct HODLR representation for array A via

A = spdiags(ones(10, 1) * [1 5  -1],  -1:1, 10, 10);
hA = hodlr(A, 3, 5, 'svd', 1.0e-8); % or simply use ``hA = hodlr(A)`` by omitting other parameters as default

By printing out the variable hA, one can obtain:

hA =

hodlr with properties:

               U1: [5×1 double]
               V2: [-1 0 0 0 0]
               U2: [5×1 double]
               V1: [0 0 0 0 1]
               D: []
               A11: [1×1 hodlr]
               A22: [1×1 hodlr]
            level: 1
            shape: [10 10]
         max_level: 3
      bottom_level: 1
            vareps: 1.0000e-08
   min_block_size: 5

Then you can recover your HODLR representation by built-in function recover.

RA = recover(hA);
err = norm(full(RA - A), 2); % check how much error of the approxiamtion
disp(err);

Note

You can speficy four paramters for your initialization: The first parameter is the matrix to be converted; the second and the third refer to the maximum level and minimum block size for the cluster tree, respectively; the fourth is to specify the method low rank approximation, which default is ‘svd’, the other options: ‘qr’; the fifth parameter is the tolerance for the low rank approximation; the sixth parameter is used to determine the norm used for the truncation, where only two norms, i.e., Frobenius and 2 norm, are supported, and the Frobenius norm only used with ``method``=’svd’.

One can perform hierarchical matrix-vector product via hdot

x = rand(10);
b = hdot(A, x, 'dense');

err = norm(b - x, 2); # Compute forward
disp(err);

Note

The third parameter is specified as ‘dense’ to indicate the output is dense format, the other option is ‘hodlr’.