Bdot

Fast Matrix Multiply on Pretty Big Data

Bdot does big dot products (by making your RAM bigger on the inside). It's based on Bcolz and includes transparent disk-based storage.

Supports matrix . vector and matrix . matrix for most common numpy numeric data types (numpy.int64, numpy.int32, numpy.float64, numpy.float32)

Install

pip install bdot

or build from source (requires bcolz >= 0.9.0)

python setup.py build_ext --inplace
python setup.py install

Usage

Matrix . Vector

Multiply a matrix (carray) with a vector (numpy.ndarray), returns a vector (numpy.ndarray)

import bdot
import numpy as np

matrix = np.random.random_integers(0, 12000, size=(300000, 100))
bcarray = bdot.carray(matrix, chunklen=2**13, cparams=bdot.cparams(clevel=2))

v = bcarray[0]

result = bcarray.dot(v)
expected = matrix.dot(v)

# should return True
(expected == result).all()

Matrix . Matrix

Multiply a matrix (carray) with the transpose of a matrix (carray), returns a matrix (carray)

import bdot
import numpy as np

matrix = np.random.random_integers(0, 120, size=(1000, 100))
bcarray1 = bdot.carray(matrix, chunklen=2**9, cparams=bdot.cparams(clevel=2))
bcarray2 = bdot.carray(matrix, chunklen=2**9, cparams=bdot.cparams(clevel=2))

# calculates bcarray1 . bcarray2.T (transpose)
result = bcarray1.dot(bcarray2)
expected = matrix.dot(matrix.T)

# should return True
(expected == result).all()

Save Result to Disk (Experimental)

Save really big results directly to disk

# create correctly sized container (helper method, not required)
output = bcarray1.empty_dot(bcarray2, rootdir='/path/to/bcolz/output')

# generate results directly on disk
bcarray1.dot(bcarray2, out=output)

# make sure the last bits get written
output.flush()

This method can also be used to get carray output for ndarray vector input, just leave off the rootdir parameter in empty_dot, or create your own carray container.

Test

nosetests bdot

Simple Benchmarks

Benchmarks were done on data structures generated by the above code, are very informal, and vary a bit across data sets.

Space

numpy ~229MB
bdot ~64MB

compression ratio: 3.5

Time

numpy ~33 ms
bdot ~48 ms

percent performance: 68%

Goals

This project has three goals, each slightly more fantastic than the last:

Allow computation on (compressed) data which is (~5-10x) larger than RAM at approximately the same speed as numpy.dot
Allow computation on (slightly compressed) data at speeds that improve on numpy.dot
Allow computation on (compressed) data which resides on disk at some sizable percentage (~50-30%) of the speed of numpy.dot

So far, the first goal has been met.

Acknowledgements

This library wouldn't be possible without all the talented people who worked hard to create Bcolz (and the libraries on which it's based). Initial code was also heavily influenced by Bquery.

Awesome TARDIS can be found here

flrgsr / bdot