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A matrix file format

Inspired in part by

This repo contains a "straw man" proposal for the next generation openmatrix format. You can review a speed demo in the notebooks folder.

Open Matrix (via ActivitySim)

with resource_usage:
    asim_skims = skim_dict(settings) # loads all skim data into memory
45.8 s: Net 7.11 GB, Total 7.45 GB

It takes some time to load, and a fair bit of RAM. Now we can load values from one of the skim tables, which is quick and easy, and only uses enough extra memory to store the values we have collected.

with resource_usage:
    asim_data1 = asim_skims.get('DISTBIKE').get(otaz,dtaz)
668 ms: Net 277 MB, Total 7.73 GB

Parquet Matrix

Contrast that with the first of two formats of arrow matrix, ParquetMatrix.
As we did above using the skims_dict, let's open the matrix reference itself first.

with resource_usage:
    pqmx = amx.ParquetMatrix('data/mtc_full_skims.pmx')
26.9 ms: Net 1e+03 KB, Total 7.73 GB

The matrix object can be created almost instantly because it doesn't load all the data into RAM, just the schema and metadata. The actual data remains on disk, waiting patiently for us to read it later. So let's do that!

with resource_usage:
    pqmx_data1 = pqmx.get_rc('DISTBIKE', otaz-1, dtaz-1, attach_index=False).to_numpy().reshape(-1).astype('float32')
264 ms: Net 39.8 MB, Total 7.77 GB

Loading this data from the arrow matrix requires barely more memory footprint than the loaded data itself (the array of 10 million double-precision floats uses 76.3 MB).

Well, you may say, that's nothing special. The whole point of the ActivitySim skims module is to be fast, by having the necessary skims preloaded into RAM so they can be read from as fast as possible.

%timeit asim_skims.get('DISTWALK').get(otaz,dtaz)
566 ms ± 23.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

pqmx: "Hold my beer"

%timeit pqmx.get_rc('DISTWALK', otaz-1, dtaz-1, attach_index=False).to_numpy().reshape(-1)
218 ms ± 10.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

Of course, there's no free lunch. Arrow is super fast, but reading data from disk has a high fixed cost. In particular, for Parquet (as configured in this demo, at least) we need to read and decompress the entire source matrix data, to extract what we need. We can beat the pre-loaded ActivitySim skims when the chunk size is very large, but for very small chunk sizes the RAM solution is much faster.

otaz2, dtaz2 = otaz[:50], dtaz[:50]
%timeit asim_skims.get('DISTWALK').get(otaz2,dtaz2)
9.47 µs ± 191 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
%timeit pqmx.get_rc('DISTWALK', otaz2-1, dtaz2-1, attach_index=False).to_numpy().reshape(-1)
19.6 ms ± 858 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

But what if I want the speed of in-memory data, but without actually needing to allocate all that memory?

Feather Matrix

with resource_usage:
    fmx = amx.FeatherMatrix('data/mtc_full_skims_uncompressed.fmx')
1.08 s: Net 620 KB, Total 7.8 GB

Feather is able to point to space on disk and use it like RAM. It's not quite as fast as actual RAM, but these days solid state drives can get kind of close. So, like ParquetMatrix above, we create the object reference almost instantly and with no overhead.

We can contrast now the performance with loading this big chunks...

%timeit fmx.get_rc('DISTBIKE', otaz-1, dtaz-1, attach_index=False).to_numpy().reshape(-1)
200 ms ± 7.69 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

... and the small chunks.

%timeit fmx.get_rc('DISTWALK', otaz2-1, dtaz2-1, attach_index=False).to_numpy().reshape(-1)
140 µs ± 3.25 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Let's plot the relative speed across a variety of chunk sizes.


Assuming a large enough chunk size, either format performs better than the current ActivitySim implementation. Even with a quite small chunk size, the feather format performs reasonably well and with no RAM footprint.

Implementation Details

  • arrowmatrix uses the Apache Arrow table format as its basis. Each matrix data table is stored as a column in this table.

  • As data for matrix tables is stored in a single column (essentially, a vector) and the matrix shape is implicit-- data for matrix tables is stored in the table in row-major order and implementation will need to account for this.

  • While the openmatrix standard includes both two dimensional 'data' and one dimensional 'lookup' arrays, arrowmatrix eschews this (in part due to limitations of the Arrow format), and instead requires that all data elements be exactly the same shape.

  • While the openmatrix standard includes two dimensional 'data' arrays, arrowmatrix allows any number of dimensions. It is still enforced that all data arrays stored in the same file are the same shape.

  • One dimensional lookup values should be stored in Feather format, 'zstd' compressed, as an arrow buffer in the file's metadata. (TODO: provide a demo of this.)

  • arrowmatrix can be any number of dimensions, not just 2. The shape of the matrix is stored in metadata as a bytestring in the representation format of a Python tuple. For example, a matrix file that is 25 by 25 is b'(25,25)'. One dimensional arrays can be stored as lookup metadata, or can also be stored in a different file with shape '(25,)'. Similarly, matrix tables that used to be grouped logically simply by name can instead be arranged explicitly with three or more dimensions, e.g. b'(25,25,3)' for 3 time periods.

  • For debate: should lookup values be bound to the dimensions explicitly? In current openmatrix, they are not, although typically matrix files are square with common lookups or non-square which makes the bindings obvious. By allowing more dimensions, there is more risk of two dimensions having the same cardinality but different meanings.

  • Any data type you can store with Arrow, you can store in an arrowmatrix.

  • Both Parquet and Feather file formats are legit storage formats. Each has distinct advantages and disadvantages, especially with respect to file size and read/write speed. Both formats can store the necessary metadata.

  • Uncompressed Feather data files, while useful in certain applications, should not be used to transfer data between users or over a network. Beyond that, it is unclear whether compressed Feather or Parquet formats will be better for transportation planning applications.

  • Chunk size: this demo uses a full-table chunk size. This may not be the best solution; technical demos with different chunk size (a.k.a. row group size in Parquet) are welcomed.


A matrix file format




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