README.rst

Benchmark repository for Approximate Joint Diagonalization

BenchOpt is a package to simplify and make more transparent and reproducible the comparisons of optimization algorithms. This benchmark considers the approximate joint diagonalization (AJD) of positive matrices. Given $n$ square symmetric positive matrices $C^i$, it consists of solving the following problem:

$$ \min_B \frac{1}{2n} \sum_{i=1}^n \log | \textrm{diag} (B C^i B^{\top}) | - \log | B C^i B^{\top} | $$

where | | stands for the matrix determinant and $\textrm{diag}$ stands for the operator that keeps only the diagonal elements of a matrix. Optionally, the matrix $B$ can be enforced to be orthogonal.

Install

This benchmark can be run using the following commands:

$ pip install -U benchopt
$ git clone https://github.com/benchopt/benchmark_jointdiag
$ benchopt run ./benchmark_jointdiag

Use benchopt run -h for more details about these options, or visit https://benchopt.github.io/api.html.

Troubleshooting

If you run into some errors when running the examples present in this Readme, try installing the development version of benchopt:

$ pip install -U git+https://github.com/benchopt/benchopt