Okay, here we go with what I came up with after some discussion plus trial and error. I hope I've kept it somewhat comprehensible. However, it seems you are very new to a lot of this, so you probably have a lot of reading to do regarding how certain libraries and data types work.
Analyzing the algorithm
Let's start with taking a closer look at your computation:
for Pass in range(Passes:
for Row in range(StartRow,EndRow):
Rand = randrange(ArrayCount)
Value1 = Decimal(DataSet[Row][0]) + Decimal(DataSet[Row][1])
Value2 = Decimal(DataSet[Rand][0]) + Decimal(DataSet[Rand][1])
Value3 = Value1 - Value2
NewValue = Decimal(DataSet[Row][7]) + Value3
DataSet[Row][7] = str(NewValue)
So basically, we update a single row through a computation involving another random row.
Assumptions that I make:
- the real algorithm does a bit more stuff, otherwise it is hard to see what you want to achieve
- the access pattern of the real algorithm stays the same
Following our discussion, there are no functional reasons for the following aspects:
- Computation in Decimal is unnecessary. float will do just fine
- The values don't need to be stored as string. We can use an array of float
At this point it is clear that we can save tremendous amounts of runtime by using a numpy array instead of a list of string.
There is an additional hazard here for parallelization: We use random numbers. When we use multiple processes, the random number generators need to be set up for parallel generation. We'll cross that bridge when we get there.
Notably, the output column is no input for the next pass. The inputs per pass stay constant.
Input / Output
The input file format seems to be a simple CSV mostly filled with floating point numbers (using only one decimal place) and one column not being a floating point number. The text based format coupled with your information that there are gigabytes of data means that a significant amount of time will be spent just parsing the input file or formatting the output. I'll try to be efficient in both but keep things simple enough that extensions in both are possible.
Optimizing the sequential algorithm
It is always advisable to first optimize the sequential case before parallelizing. So we start here. We begin with parsing the input file into a numpy array.
import numpy as np
def ReadInputs(Filename):
"""Read a CSV file containing 10 columns
The 7th column is skipped because it doesn't contains floating point values
Return value:
2D numpy array of floats
"""
UsedColumns = (0, 1, 2, 3, 4, 5, 7, 8, 9)
return np.loadtxt(Filename, delimiter=',', usecols=UsedColumns)
Since we are using numpy, we switch over to its random number generators. This is the setup routine. It allows us to force deterministic values for easier debugging.
def MakeRandomGenerator(Deterministic=False):
"""Initializes the random number generator avoiding birthday paradox
Arguments:
Deterministic -- if True, the same same random numbers are being used
Return value:
numpy random number generator
"""
SeedInt = 0 if Deterministic else None
Seed = np.random.SeedSequence(SeedInt)
return np.random.default_rng(Seed)
And now the main computation. Numpy makes this very straight-forward.
def ComputePass(DataSets, RandomGenerator):
"""The main computation
Arguments:
DataSets -- 2D numpy array. Changed in place
RandomGenerator -- numpy random number generator
"""
Count = len(DataSets)
RandomIndices = RandomGenerator.integers(
low=0, high=Count, size=Count)
RandomRows = DataSets[RandomIndices]
# All rows: first column + second column
Value1 = DataSets[:, 0] + DataSets[:, 1]
Value2 = RandomRows[:, 0] + RandomRows[:, 1]
Value3 = Value1 - Value2
# This change is in-place of the whole DataSets array
DataSets[:, 7] += Value3
I've kept the structure the same. That means there are a few optimizations that we can still do:
We never use most columns. Columns that are unnecessary should be removed from the array (skipped in input parsing) to reduce memory consumption and improve locality of data. If necessary for output, it is better to merge in the output stage, maybe by re-reading the input file to gather the remaining columns
Since Value1 and Value2 never change, we could pre-compute Value3 for all rows and just use that. Again, if we don't need the first two columns in memory, better to remove them
If we transpose the array (or store in Fortran order), we improve vectorization. This will make the use of MPI harder, but not impossible
I've not done any of this because I do not want to stray too far from the original algorithm.
The last step is the output. Here I go with a pure Python route to keep things simple and replicate the input file format:
def WriteOutputs(Filename, DataSets):
LineFormat = "{:.1f}, " * 6 + "+" + ", {:.1f}" * 3 + "\n"
with open(Filename, 'w') as OutFile:
for Row in DataSets:
OutFile.write(LineFormat.format(*Row))
Now the entire operation is rather simple:
def main():
InFilename = "indata.csv"
OutFilename = "outdata.csv"
Passes = 20
RandomGenerator = MakeRandomGenerator()
DataSets = ReadInputs(InFilename)
for _ in range(Passes):
ComputePass(DataSets, RandomGenerator)
WriteOutputs(OutFilename, DataSets)
if __name__ == '__main__':
main()
Parallelization framework
There are two main concerns for parallelization:
For every row, we need access to the entire input data set to pick a random entry
The amount of calculation per row is very low
So we need to find a way that keeps overhead per row small and shares the input data set efficiently.
The first choice is multiprocessing since, you know, standard library and all that. However, I think that the normal usage patterns have too much overhead. It's certainly possible but I would like to use MPI for this to give us as much performance as possible. Also, your first attempt at parallelization used a pattern that matches MPI's preferred pattern. So it is a good fit.
A word towards the concept of MPI: multiprocessing.Pool works with a main process that distributes work items among a set of worker processes. MPI start N processes that all execute the same code. There is no main process. The only distinguishing feature is the process "rank", which is a number [0, N). If you need a main process, the one with rank 0 is usually chosen. Other than that, the idea is that all processes execute the same code, only picking different indices or offsets based on their rank. If processes need to communicate, there are a couple of "collective" communication patterns such as broadcasting, scattering, and gathering.
Option 1: Pure MPI
Let's rewrite the code. The main idea is this: We distribute rows in the data set among all processes. Then each process calculates all passes for its own set of rows. Input and output take considerable time, so we try to do as much as possible parallelized, too.
We start by defining a helper function that defines how we distribute rows among all processes. This is very similar to what you had in your original version.
from mpi4py import MPI
def MakeDistribution(NumberOfRows):
"""Computes how the data set should be distributed across processes
Arguments:
NumberOfRows -- size of the whole dataset
Return value:
(Offsets, Counts) numpy integer arrays. One entry per process
"""
Comm = MPI.COMM_WORLD
WorldSize = Comm.Get_size()
SameSize, Tail = divmod(NumberOfRows, WorldSize)
Counts = np.full(WorldSize, SameSize, dtype=int)
Counts[:Tail] += 1
# Start offset per process
Offsets = np.cumsum(Counts) - Counts[0]
return Offsets, Counts
A second helper function is used to distribute the data sets among all processes. MPI's allgather function is used to collect results of a computation among all processes into one array. The normal function gather collects the whole array on one process. Allgather collects it in all processes. Since all processes need access to all data sets for their random access, we use allgather. Allgatherv is a generalized version that allows different number of entries per process. We need this because we cannot guarantee that all processes have the same number of rows in their local data set.
This function uses the "buffer" interface of mpi4py. This is the more efficient version but also very error-prone. If we mess up an index or the size of a data type, we risk data corruption.
def DistributeDataSets(DataSets, Offsets, Counts):
"""Shares the datasets with all other processes
Arguments:
DataSets -- numpy array of floats. Changed in place
Offsets, Counts -- See MakeDistribution
Return value:
DataSets. Most likely a reference to the original.
Might be an updated copy
"""
# Sanitize the input. Better safe than sorry and shouldn't cost anything
DataSets = np.ascontiguousarray(DataSets, dtype='f8')
assert len(DataSets) == np.sum(Counts)
# MPI works best if we pretend to have 1-dimensional data
InnerSize = np.prod(DataSets.shape[1:], dtype=int)
# I really wish mpi4py had a helper for this
BufferDescr = (DataSets,
Counts * InnerSize,
Offsets * InnerSize,
MPI.DOUBLE)
MPI.COMM_WORLD.Allgatherv(MPI.IN_PLACE, BufferDescr)
return DataSets
We split reading the input data into two parts. First we read all lines in a single process. This is relatively cheap and we need to know the total number of rows before we can distribute the datasets. Then we scatter the lines among all processes and let each process parse its own set of rows. After that, we use the DistributeDataSets function to let each process know all the results.
Scattering the lines uses mpi4py's pickle interface that can transfer arbitrary objects among processes. It's slower but more convenient. For stuff like lists of strings it's very good.
def ParseLines(TotalLines, Offset, OwnLines):
"""Allocates a data set and parses the own segment of it
Arguments:
TotalLines -- number of rows in the whole data set across all processes
Offset -- starting offset of the set of rows parsed by this process
OwnLines -- list of lines to be parsed by the local process
Return value:
a 2D numpy array. The rows [Offset:Offset+len(OwnLines)] are initialized
with the parsed values
"""
UsedColumns = (0, 1, 2, 3, 4, 5, 7, 8, 9)
DataSet = np.empty((TotalLines, len(UsedColumns)), dtype='f8')
OwnEnd = Offset + len(OwnLines)
for Row, Line in zip(DataSet[Offset:OwnEnd], OwnLines):
Columns = Line.split(',')
# overwrite in-place with new values
Row[:] = [float(Columns[Column]) for Column in UsedColumns]
return DataSet
def DistributeInputs(Filename):
"""Read input from the file and distribute it among processes
Arguments:
Filename -- path to the CSV file to parse
Return value:
(DataSets, Offsets, Counts) with
DataSets -- 2D array containing all values in the CSV file
Offsets -- Row indices (one per rank) where each process starts its own
processing
Counts -- number of rows per process
"""
Comm = MPI.COMM_WORLD
Rank = Comm.Get_rank()
Lines = None
LineCount = None
if not Rank:
# Read the data. We do as little work as possible here so that other
# processes can help with the parsing
with open(Filename) as InFile:
Lines = InFile.readlines()
LineCount = len(Lines)
# broadcast so that all processes know the number of datasets
LineCount = Comm.bcast(LineCount, root=0)
Offsets, Counts = MakeDistribution(LineCount)
# reshape into one list per process
if not Rank:
Lines = [Lines[Offset:Offset+Count]
for Offset, Count
in zip(Offsets, Counts)]
# distribute strings for parsing
Lines = Comm.scatter(Lines, root=0)
# parse into a float array
DataSets = ParseLines(LineCount, Offsets[Rank], Lines)
del Lines # release strings because this is a huge array
# Share the parsed result
DataSets = DistributeDataSets(DataSets, Offsets, Counts)
return DataSets, Offsets, Counts
Now we need to update the way the random number generator is initialized. What we need to prevent is that each process has the same state and generates the same random numbers. Thankfully, numpy gives us a convenient way of doing this.
def MakeRandomGenerator(Deterministic=False):
"""Initializes the random number generator avoiding birthday paradox
Arguments:
Deterministic -- if True, the same number of processes should always result
in the same random numbers being used
Return value:
numpy random number generator
"""
Comm = MPI.COMM_WORLD
Rank = Comm.Get_rank()
AllSeeds = None
if not Rank:
# the root process (rank=0) generates a seed sequence for everyone else
WorldSize = Comm.Get_size()
SeedInt = 0 if Deterministic else None
OwnSeed = np.random.SeedSequence(SeedInt)
AllSeeds = OwnSeed.spawn(WorldSize)
# mpi4py can scatter Python objects. This is the simplest way
OwnSeed = Comm.scatter(AllSeeds, root=0)
return np.random.default_rng(OwnSeed)
The computation itself is almost unchanged. We just need to limit it to the rows for which the individual process is responsible.
def ComputePass(DataSets, Offset, Count, RandomGenerator):
"""The main computation
Arguments:
DataSets -- 2D numpy array. Changed in place
Offset, Count -- rows that should be updated by this process
RandomGenerator -- numpy random number generator
"""
RandomIndices = RandomGenerator.integers(
low=0, high=len(DataSets), size=Count)
RandomRows = DataSets[RandomIndices]
# Creates a "view" into the whole dataset for the given slice
OwnDataSets = DataSets[Offset:Offset + Count]
# All rows: first column + second column
Value1 = OwnDataSets[:, 0] + OwnDataSets[:, 1]
Value2 = RandomRows[:, 0] + RandomRows[:, 1]
Value3 = Value1 - Value2
# This change is in-place of the whole DataSets array
OwnDataSets[:, 7] += Value3
Now we come to writing the output. The most expensive part is formatting the floating point numbers into strings. So we let each process format its own data. MPI has a file IO interface that allows all processes to write a single file together. Unfortunately, for text files, we need to calculate the offsets before writing the data. So we format all rows into one huge string per process, then write the file.
import io
def WriteOutputs(Filename, DataSets, Offset, Count):
"""Writes all DataSets to a CSV file
We parse all rows to a string (one per process), then write it
collectively using MPI
Arguments:
Filename -- output path
DataSets -- all values among all processes
Offset, Count -- the rows for which the local process is responsible
"""
StringBuf = io.StringIO()
LineFormat = "{:.6f}, " * 6 + "+" + ", {:.6f}" * 3 + "\n"
for Row in DataSets[Offset:Offset+Count]:
StringBuf.write(LineFormat.format(*Row))
StringBuf = StringBuf.getvalue() # to string
StringBuf = StringBuf.encode() # to bytes
Comm = MPI.COMM_WORLD
BytesPerProcess = Comm.allgather(len(StringBuf))
Rank = Comm.Get_rank()
OwnOffset = sum(BytesPerProcess[:Rank])
FileLength = sum(BytesPerProcess)
AccessMode = MPI.MODE_WRONLY | MPI.MODE_CREATE
OutFile = MPI.File.Open(Comm, Filename, AccessMode)
OutFile.Set_size(FileLength)
OutFile.Write_ordered(StringBuf)
OutFile.Close()
The main process is almost unchanged.
def main():
InFilename = "indata.csv"
OutFilename = "outdata.csv"
Passes = 20
RandomGenerator = MakeRandomGenerator()
DataSets, Offsets, Counts = DistributeInputs(InFilename)
Rank = MPI.COMM_WORLD.Get_rank()
Offset = Offsets[Rank]
Count = Counts[Rank]
for _ in range(Passes):
ComputePass(DataSets, Offset, Count, RandomGenerator)
WriteOutputs(OutFilename, DataSets, Offset, Count)
if __name__ == '__main__':
main()
You need to call this script with mpirun or mpiexec. E.g. mpiexec python3 script_name.py
Using shared memory
The MPI pattern has one significant drawback: Each process needs its own copy of the whole data set. Given its size, this is very inconvenient. We might run out of memory before we run out of CPU cores for multithreading. As a different idea, we can use shared memory. Shared memory allows multiple processes to access the same physical memory without any extra cost. This has some drawbacks:
We need a very recent python version. 3.8 IIRC
Python's implementation may behave differently on various operating systems. I could only test it on Linux. There is a chance that it will not work on any different system
IMHO python's implementation is not great. You will notice that the final version will print some warnings which I think are harmless. Maybe I'm using it wrong but I don't see a more correct way of using it
It limits you to a single PC. MPI itself is perfectly capable (and indeed designed to) operate across multiple systems on a network. Shared memory works only locally.
The major benefit is that the memory consumption does not increase with the number of processes.
We start by allocating such a data set.
From here on, we put in "barriers" at various points where processes may have to wait for one another. For example because all processes need to access the same shared memory segment, they all have to open it before we can unlink it.
from multiprocessing import shared_memory
def AllocateSharedDataSets(NumberOfRows, NumberOfCols=9):
"""Creates a numpy array in shared memory
Arguments:
NumberOfRows, NumberOfCols -- basic shape
Return value:
(DataSets, Buf) with
DataSets -- numpy array shaped (NumberOfRows, NumberOfCols).
Datatype float
Buf -- multiprocessing.shared_memory.SharedMemory that backs the array.
Close it when no longer needed
"""
length = NumberOfRows * NumberOfCols * np.float64().itemsize
Comm = MPI.COMM_WORLD
Rank = Comm.Get_rank()
Buf = None
BufName = None
if not Rank:
Buf = shared_memory.SharedMemory(create=True, size=length)
BufName = Buf.name
BufName = Comm.bcast(BufName)
if Rank:
Buf = shared_memory.SharedMemory(name=BufName, size=length)
DataSets = np.ndarray((NumberOfRows, NumberOfCols), dtype='f8',
buffer=Buf.buf)
Comm.barrier()
if not Rank:
Buf.unlink() # this may differ among operating systems
return DataSets, Buf
The input parsing also changes a little because have to put the data into the previously allocated array
def ParseLines(DataSets, Offset, OwnLines):
"""Reads lines into a preallocated array
Arguments:
DataSets -- [Rows, Cols] numpy array. Will be changed in-place
Offset -- starting offset of the set of rows parsed by this process
OwnLines -- list of lines to be parsed by the local process
"""
UsedColumns = (0, 1, 2, 3, 4, 5, 7, 8, 9)
OwnEnd = Offset + len(OwnLines)
OwnDataSets = DataSets[Offset:OwnEnd]
for Row, Line in zip(OwnDataSets, OwnLines):
Columns = Line.split(',')
Row[:] = [float(Columns[Column]) for Column in UsedColumns]
def DistributeInputs(Filename):
"""Read input from the file and stores it in shared memory
Arguments:
Filename -- path to the CSV file to parse
Return value:
(DataSets, Offsets, Counts, Buf) with
DataSets -- [Rows, 9] array containing two copies of all values in the
CSV file
Offsets -- Row indices (one per rank) where each process starts its own
processing
Counts -- number of rows per process
Buf -- multiprocessing.shared_memory.SharedMemory object backing the
DataSets object
"""
Comm = MPI.COMM_WORLD
Rank = Comm.Get_rank()
Lines = None
LineCount = None
if not Rank:
# Read the data. We do as little work as possible here so that other
# processes can help with the parsing
with open(Filename) as InFile:
Lines = InFile.readlines()
LineCount = len(Lines)
# broadcast so that all processes know the number of datasets
LineCount = Comm.bcast(LineCount, root=0)
Offsets, Counts = MakeDistribution(LineCount)
# reshape into one list per process
if not Rank:
Lines = [Lines[Offset:Offset+Count]
for Offset, Count
in zip(Offsets, Counts)]
# distribute strings for parsing
Lines = Comm.scatter(Lines, root=0)
# parse into a float array
DataSets, Buf = AllocateSharedDataSets(LineCount)
try:
ParseLines(DataSets, Offsets[Rank], Lines)
Comm.barrier()
return DataSets, Offsets, Counts, Buf
except:
Buf.close()
raise
Output writing is exactly the same. The main process changes slightly because now we have to manage the life time of the shared memory.
import contextlib
def main():
InFilename = "indata.csv"
OutFilename = "outdata.csv"
Passes = 20
RandomGenerator = MakeRandomGenerator()
Comm = MPI.COMM_WORLD
Rank = Comm.Get_rank()
DataSets, Offsets, Counts, Buf = DistributeInputs(InFilename)
with contextlib.closing(Buf):
Offset = Offsets[Rank]
Count = Counts[Rank]
for _ in range(Passes):
ComputePass(DataSets, Offset, Count, RandomGenerator)
WriteOutputs(OutFilename, DataSets, Offset, Count)
Results
I've not benchmarked the original version. The sequential version requires 2 GiB memory and 3:20 minutes for 12500000 lines and 20 passes.
The pure MPI version requires 6 GiB and 42 seconds with 6 cores.
The shared memory version requires a bit over 2 GiB of memory and 38 seconds with 6 cores.
