在MATLAB中将大型数组直接写入磁盘时，是否需要预先分配？

Question

I need to write an array that is too large to fit into memory to a .mat binary file. This can be accomplished with the matfile function, which allows random access to a .mat file on disk.

Normally, the accepted advice is to preallocate arrays, because expanding them on every iteration of a loop is slow. However, when I was asking how to do this , it occurred to me that this may not be good advice when writing to disk rather than RAM.

Will the same performance hit from growing the array apply , and if so, will it be significant when compared to the time it takes to write to disk anyway?

(Assume that the whole file will be written in one session , so the risk of serious file fragmentation is low .)

Answer 1

Q: Will the same performance hit from growing the array apply, and if so will it be significant when compared to the time it takes to write to disk anyway?

A: Yes, performance will suffer if you significantly grow a file on disk without pre-allocating. The performance hit will be a consequence of fragmentation. As you mentioned, fragmentation is less of a risk if the file is written in one session, but will cause problems if the file grows significantly.

A related question was raised on the MathWorks website, and the accepted answer was to pre-allocate when possible.

If you don't pre-allocate, then the extent of your performance problems will depend on:

• your filesystem (how data are stored on disk, the cluster-size),
• your hardware (HDD seek time, or SSD access times),
• the size of your mat file (whether it moves into non-contiguous space),
• and the current state of your storage (existing fragmentation / free space).

Let's pretend that you're running a recent Windows OS, and so are using the NTFS file-system . Let's further assume that it has been set up with the default 4 kB cluster size. So, space on disk gets allocated in 4 kB chunks and the locations of these are indexed to the Master File Table. If the file grows and contiguous space is not available then there are only two choices:

1. Re-write the entire file to a new part of the disk, where there is sufficient free space.
2. Fragment the file, storing the additional data at a different physical location on disk.

The file system chooses to do the least-bad option, #2, and updates the MFT record to indicate where the new clusters will be on disk.

Now, the hard disk needs to physically move the read head in order to read or write the new clusters, and this is a (relatively) slow process. In terms of moving the head, and waiting for the right area of disk to spin underneath it ... you're likely to be looking at a seek time of about 10ms . So for every time you hit a fragment, there will be an additional 10ms delay whilst the HDD moves to access the new data. SSDs have much shorter seek times (no moving parts). For the sake of simplicity, we're ignoring multi-platter systems and RAID arrays!

If you keep growing the file at different times, then you may experience a lot of fragmentation. This really depends on when / how much the file is growing by, and how else you are using the hard disk. The performance hit that you experience will also depend on how often you are reading the file, and how frequently you encounter the fragments.

MATLAB stores data in Column-major order , and from the comments it seems that you're interested in performing column-wise operations (sums, averages) on the dataset. If the columns become non-contiguous on disk then you're going to hit lots of fragments on every operation!

As mentioned in the comments, both read and write actions will be performed via a buffer. As @user3666197 points out the OS can speculatively read-ahead of the current data on disk, on the basis that you're likely to want that data next. This behaviour is especially useful if the hard disk would be sitting idle at times - keeping it operating at maximum capacity and working with small parts of the data in buffer memory can greatly improve read and write performance. However, from your question it sounds as though you want to perform large operations on a huge (too big for memory) .mat file. Given your use-case, the hard disk is going to be working at capacity anyway , and the data file is too big to fit in the buffer - so these particular tricks won't solve your problem.

So ...Yes, you should pre-allocate. Yes, a performance hit from growing the array on disk will apply. Yes, it will probably be significant (it depends on specifics like amount of growth, fragmentation, etc). And if you're going to really get into the HPC spirit of things then stop what you're doing, throw away MATLAB , shard your data and try something like Apache Spark! But that's another story.

Does that answer your question?

PS Corrections / amendments welcome! I was brought up on POSIX inodes, so sincere apologies if there are any inaccuracies in here...

Answer 2

Preallocating a variable in RAM and preallocating on the disk don't solve the same problem.

In RAM

To expand a matrix in RAM, MATLAB creates a new matrix with the new size and copies the values of the old matrix into the new one and deletes the old one. This costs a lot of performance.

If you preallocated the matrix, the size of it does not change. So there is no more reason for MATLAB to do this matrix copying anymore.

On the hard-disk

The problem on the hard-disk is fragmentation as GnomeDePlume said. Fragmentation will still be a problem, even if the file is written in one session.

Here is why: The hard disk will generally be a little fragmentated. Imagine

• # to be memory blocks on the hard disk that are full
• M to be memory blocks on the hard disk that will be used to save data of your matrix
• - to be free memory blocks on the hard disk

Now the hard disk could look like this before you write the matrix onto it:

###--##----#--#---#--------------------##-#---------#---#----#------

When you write parts of the matrix (eg MMM blocks) you could imagine the process to look like this >!(I give an example where the file system will just go from left to right and use the first free space that is big enough - real file systems are different):

1. First matrix part:
   ###--##MMM-#--#---#--------------------##-#---------#---#----#------
2. Second matrix part: ###--##MMM-#--#MMM#--------------------##-#---------#---#----#------
3. Third matrix part: ###--##MMM-#--#MMM#MMM-----------------##-#---------#---#----#------
4. And so on ...

Clearly the matrix file on the hard disk is fragmented although we wrote it without doing anything else in the meantime.

This can be better if the matrix file was preallocated. In other words, we tell the file system how big our file would be, or in this example, how many memory blocks we want to reserve for it.

Imagine the matrix needed 12 blocks: MMMMMMMMMMMM . We tell the file system that we need so much by preallocating and it will try to accomodate our needs as best as it can. In this example, we are lucky: There is free space with >= 12 memory blocks.

1. Preallocating (We need 12 memory blocks):
   ###--##----#--#---# (------------) --------##-#---------#---#----#------
   The file system reserves the space between the parentheses for our matrix and will write into there.
2. First matrix part:
   ###--##----#--#---# (MMM---------) --------##-#---------#---#----#------
3. Second matrix part:
   ###--##----#--#---# (MMMMMM------) --------##-#---------#---#----#------
4. Third matrix part:
   ###--##----#--#---# (MMMMMMMMM---) --------##-#---------#---#----#------
5. Fourth and last part of the matrix:
   ###--##----#--#---# (MMMMMMMMMMMM) --------##-#---------#---#----#------

Voilá, no fragmentation!

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Analogy

Generally you could imagine this process as buying cinema tickets for a large group. You would like to stick together as a group, but there are already some seats in the theatre reserved by other people. For the cashier to be able to accomodate to your request (large group wants to stick together), he/she needs knowledge about how big your group is (preallocating).

Answer 3

A quick answer to the whole discussion (in case you do not have the time to follow or the technical understanding):

• Pre-allocation in Matlab is relevant for operations in RAM. Matlab does not give low-level access to I/O operations and thus we cannot talk about pre-allocating something on disk.
• When writing a big amount of data to disk, it has been observed that the fewer the number of writes, the faster is the execution of the task and smaller is the fragmentation on disk.

Thus, if you cannot write in one go, split the writes in big chunks .

Answer 4

Prologue

This answer is based on both the original post and the clarifications ( both ) provided by the author during the recent week.

The question of adverse performance hit (s) introduced by a low-level, physical-media-dependent, "fragmentation" , introduced by both a file-system & file-access layers is further confronted both in a TimeDOMAIN magnitudes and in ComputingDOMAIN repetitiveness of these with the real-use problems of such an approach.

Finally a state-of-art, principally fastest possible solution to the given task was proposed , so as to minimise damages from both wasted efforts and mis-interpretation errors from idealised or otherwise not valid assumptions, alike that a risk of "serious file fragmentation is low" due to an assumption, that the whole file will be written in one session ( which is simply principally not possible during many multi-core / multi-process operations of the contemporary O/S in real-time over a time-of-creation and a sequence of extensive modification(s) ( ref. the MATLAB size limits ) of a TB-sized BLOB file-object(s) inside contemporary COTS FileSystems ).

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One may hate the facts, however the facts remain true out there until a faster & better method moves in

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First, before considering performance, realise the gaps in the concept

1. The real performance adverse hit is not caused by HDD-IO or related to the file fragmentation

2. RAM is not an alternative for the semi-permanent storage of the .mat file

3. Additional operating system limits and interventions + additional driver and hardware-based abstractions were ignored from assumptions on un-avoidable overheads
4. The said computational scheme was omited from the review of what will have the biggest impact / influence on the resulting performance

Given:

• The whole processing is intended to be run just once , no optimisation / iterations, no continuous processing

• Data have 1E6 double Float-values x 1E5 columns = about 0.8 TB (+ HDF5 overhead)

• In spite of original post, there is no random IO associated with the processing

• Data acquisition phase communicates with a .NET to receive DataELEMENT s into MATLAB

  That means, since v7.4,

  a 1.6 GB limit on MATLAB WorkSpace in a 32bit Win ( 2.7 GB with a 3GB switch )

  a 1.1 GB limit on MATLAB biggest Matrix in wXP / 1.4 GB wV / 1.5 GB

  a bit "released" 2.6 GB limit on MATLAB WorkSpace + 2.3 GB limit on a biggest Matrix in a 32bit Linux O/S.

  Having a 64bit O/S will not help any kind of a 32bit MATLAB 7.4 implementation and will fail to work due to another limit , the maximum number of cells in array, which will not cover the 1E12 requested here.

  The only chance is to have both

  • both a 64bit O/S ( wXP, Linux, Solaris )

  • and a 64bit MATLAB 7.5+

    MathWorks' source for R2007a cited above, for newer MATLAB R2013a you need a User Account there

• Data storage phase assumes block-writes of a row-ordered data blocks ( a collection of row-ordered data blocks ) into a MAT-file on an HDD-device

• Data processing phase assumes to re-process the data in a MAT-file on an HDD-device, after all inputs have been acquired and marshalled to a file-based off-RAM-storage, but in a column-ordered manner

• just column-wise mean() -s / max() -es are needed to calculate ( nothing more complex )

Facts:

• MATLAB uses a "restricted" implementation of an HDF5 file-structure for binary files.

Review performance measurements on real-data & real-hardware ( HDD + SSD ) to get feeling of scales of the un-avoidable weaknesses thereof

The Hierarchical Data Format ( HDF ) was born on 1987 at the National Center for Supercomputing Applications ( NCSA ), some 20 years ago. Yes, that old. The goal was to develop a file format that combine flexibility and efficiency to deal with extremely large datasets. Somehow the HDF file was not used in the mainstream as just a few industries were indeed able to really make use of it's terrifying capacities or simply did not need them.

FLEXIBILITY means that the file-structure bears some overhead, one need not use if the content of the array is not changing ( you pay the cost without consuming any benefit of using it ) and an assumption, that HDF5 limits on overall size of the data it can contain sort of helps and saves the MATLAB side of the problem is not correct.

MAT-files are good in principle, as they avoid an otherwise persistent need to load a whole file into RAM to be able to work with it.

Nevertheless, MAT-files are not serving well the simple task as was defined and clarified here. An attempt to do that will result in just a poor performance and HDD-IO file-fragmentation ( adding a few tens of milliseconds during write-through -s and something less than that on read-ahead -s during the calculations ) will not help at all in judging the core-reason for the overall poor performance.

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A professional solution approach

Rather than moving the whole gigantic set of 1E12 DataELEMENT s into a MATLAB in-memory proxy data array, that is just scheduled for a next coming sequenced stream of HDF5 / MAT-file HDD-device IO-s ( write-through s and O/S vs. hardware-device-chain conflicting/sub-optimised read-ahead s ) so as to have all the immenses work "just [married] ready" for a few & trivially simple calls of mean() / max() MATLAB functions( that will do their best to revamp each of the 1E12 DataELEMENT s in just another order ( and even TWICE -- yes -- another circus right after the first job-processing nightmare gets all the way down, through all the HDD-IO bottlenecks ) back into MATLAB in-RAM-objects, do redesign this very step into a pipe-line BigDATA processing from the very beginning.

while true                                          % ref. comment Simon W Oct 1 at 11:29
   [ isStillProcessingDotNET,   ...                 %      a FLAG from .NET reader function
     aDotNET_RowOfVALUEs ...                        %      a ROW  from .NET reader function
     ] = GetDataFromDotNET( aDtPT )                 %                  .NET reader
   if ( isStillProcessingDotNET )                   % Yes, more rows are still to come ...
      aRowCOUNT = aRowCOUNT + 1;                    %      keep .INC for aRowCOUNT ( mean() )
      for i = 1:size( aDotNET_RowOfVALUEs )(2)      %      stepping across each column
         aValue     = aDotNET_RowOfVALUEs(i);       %      
         anIncrementalSumInCOLUMN(i) = ...
         anIncrementalSumInCOLUMN(i) + aValue;      %      keep .SUM for each column ( mean() )
         if ( aMaxInCOLUMN(i) < aValue )            %      retest for a "max.update()"
              aMaxInCOLUMN(i) = aValue;             %      .STO a just found "new" max
         end
      endfor
      continue                                      %      force re-loop
   else
      break
   endif
end
%-------------------------------------------------------------------------------------------
% FINALLY:
% all results are pre-calculated right at the end of .NET reading phase:
%
% -------------------------------
% BILL OF ALL COMPUTATIONAL COSTS ( for given scales of 1E5 columns x 1E6 rows ):
% -------------------------------
% HDD.IO:          **ZERO**
% IN-RAM STORAGE:
%                  Attr Name                       Size                     Bytes  Class
%                  ==== ====                       ====                     =====  =====
%                       aMaxInCOLUMNs              1x100000                800000  double
%                       anIncrementalSumInCOLUMNs  1x100000                800000  double
%                       aRowCOUNT                  1x1                          8  double
%
% DATA PROCESSING:
%
% 1.000.000x .NET row-oriented reads ( same for both the OP and this, smarter BigDATA approach )
%         1x   INT   in aRowCOUNT,                 %%       1E6 .INC-s
%   100.000x FLOATs  in aMaxInCOLUMN[]             %% 1E5 * 1E6 .CMP-s
%   100.000x FLOATs  in anIncrementalSumInCOLUMN[] %% 1E5 * 1E6 .ADD-s
% -----------------
% about 15 sec per COLUMN of 1E6 rows
% -----------------
%                  --> mean()s are anIncrementalSumInCOLUMN./aRowCOUNT
%-------------------------------------------------------------------------------------------
% PIPE-LINE-d processing takes in TimeDOMAIN "nothing" more than the .NET-reader process
%-------------------------------------------------------------------------------------------

Your pipe-line d BigDATA computation strategy will in a smart way principally avoid interim storage buffering in MATLAB as it will progressively calculate the results in not more than about 3 x 1E6 ADD/CMP-registers, all with a static layout, avoid proxy-storage into HDF5 / MAT-file , absolutely avoid all HDD-IO related bottlenecks and low BigDATA sustained-read-s' speeds ( not speaking at all about interim/BigDATA sustained-writes... ) and will also avoid ill-performing memory-mapped use just for counting mean-s and max-es.

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Epilogue

The pipeline processing is nothing new under the Sun.

It re-uses what speed-oriented HPC solutions already use for decades

[ generations before BigDATA tag has been "invented" in Marketing Dept's. ]

Forget about zillions of HDD-IO blocking operations & go into a pipelined distributed process-to-process solution.

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There is nothing faster than this

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If it were , all FX business and HFT Hedge Fund Monsters would already be there...