Benchmarks

The following tables show benchmarks that compare Ripserer's performance with Ripser, Cubical Ripser, and Eirene.jl. The benchmarking code and more info about the datasets are available here.

All benchmarks were performed on a laptop with an Intel(R) Core(TM) i5-4200U CPU @ 1.60GHz with 8GB of RAM.

We used BenchmarkTools.jl to perform the timing benchmarks and Valgrind's Massif tool to measure peak heap sizes (i.e. total memory footprint).

The benchmarks were performed with Ripserer v0.15, master versions of Ripser (commit hash 286d369) and Cubical Ripser (commit hashes 6edb9c5 for 2D and a063dac for 3D), and Eirene v1.3.5.

The timings show the minimum time taken among five runs of the benchmark.

The heap sizes for Ripserer include the Julia runtime.

Comparison with Ripser

In this experiment, we performed benchmarks with the datasets presented in the Ripser article. We only used the datasets that we were able to run with less than 8GB memory. All datasets were parsed as Float32 as that is what Ripser supports. The time it takes to parse a file is included for both Ripser and Ripserer.

Dense results

Sparse results

These benchmarks were performed with the sparse=true keyword argument.

Alpha-Rips

These benchmarks were performed on sparse matrices that correspond to the 1-skeleta of Delaunay triangulations. The purpose of these is to show performance with very sparse inputs.

Comparison with Cubical Ripser

In these benchmarks, we used some of the datasets presented in the Cubical Ripser article. We limited the 2D image size to 1999×999 as the current master (commit hash 6edb9c5) version of 2D Cubical Ripser throws an assertion error for anything larger. We were also unable to perform 3D 256×256×256 image benchmarks due to Ripserer running out of memory. The eltype of all datasets is Float64, because that is what Cubical Ripser supports. When running Ripserer in the real world, it's a good idea to use the image's native data types. This will slightly reduce the memory footprint and increase performance.

Comparison with Eirene

In these benchmarks, we compare Ripserer to Eirene.jl. Ripserer benchmarks were run with alg=:involuted, so this measures the time it takes to compute representative cycles.