I would like to dedicate today’s post to a not-well-known performance trick from my book, that could significantly improve the speed when computing the convolution of two data arrays. Matlab’s internal implementation of convolution (conv, conv2 and convn) appears to rely on a sliding window approach, using implicit (internal) multithreading for speed.

However, this can often be sped up significantly if we use the Convolution Theorem, which states in essence that conv(a,b) = ifft(fft(a,N) .* fft(b,N)), an idea proposed by Bruno Luong. In the following usage example we need to remember to zero-pad the data to get comparable results:

% Prepare the input vectors (1M elements each)
x = rand(1e6,1);
y = rand(1e6,1);

% Compute the convolution using the builtin conv()
tic, z1 = conv(x,y); toc
 => Elapsed time is 360.521187 seconds.

% Now compute the convolution using fft/ifft: 780x faster!
n = length(x) + length(y) - 1;  % we need to zero-pad
tic, z2 = ifft(fft(x,n) .* fft(y,n)); toc
 => Elapsed time is 0.463169 seconds.

% Compare the relative accuracy (the results are nearly identical)
disp(max(abs(z1-z2)./abs(z1)))
 => 2.75200348450538e-10

This latest result shows that the results are nearly identical, up to a tiny difference, which is certainly acceptable in most cases when considering the enormous performance speedup (780x in this specific case). Bruno’s implementation (convnfft) is made even more efficient by using MEX in-place data multiplications, power-of-2 FFTs, and use of GPU/Jacket where available.

It should be noted that the builtin Matlab functions can still be faster for relatively small data arrays, or if your machine has a large number of CPU cores and free memory that Matlab’s builtin conv* functions can utilize, and of course also depending on the Matlab release. So, your mileage might well vary. But given the significant speedup potential, I contend that you should give it a try and see how well it performs on your specific system and data.

If you have read my book, please be kind enough to post your feedback about it on Amazon (link), for the benefit of others. Thanks in advance!

The post Convolution performance appeared first on Undocumented Matlab.

• Demonstrates how to profile MATLAB code for performance and resource usage, enabling users to focus on the program’s actual hotspots
• Considers tradeoffs in performance tuning, horizontal vs. vertical scalability, latency vs. throughput, and perceived vs. actual performance
• Explains generic speedup techniques used throughout the software industry and their adaptation for Matlab, plus methods specific to Matlab
• Analyzes the effects of various data types and processing functions
• Covers vectorization, parallelization (implicit and explicit), distributed computing, optimization, memory management, chunking, and caching
• Explains Matlab’s memory model and shows how to profile memory usage and optimize code to reduce memory allocations and data fetches
• Describes the use of GPU, MEX, FPGA, and other forms of compiled code
• Details acceleration techniques for GUI, graphics, I/O, Simulink, object-oriented Matlab, Matlab startup, and deployed applications
• Discusses a wide variety of MathWorks and third-party functions, utilities, libraries, and toolboxes that can help to improve performance

Ideal for novices and professionals alike, the book leaves no stone unturned. It covers all aspects of Matlab, taking a comprehensive approach to boosting Matlab performance. It is packed with thousands of helpful tips, code examples, and online references. Supported by this active website, the book will help readers rapidly attain significant reductions in development costs and program run times.
Additional information about the book, including detailed Table-of-Contents, book structure, reviews, resources and errata list, can be found in a dedicated webpage that I’ve prepared for this book and plan to maintain.

The post New book: Accelerating MATLAB Performance appeared first on Undocumented Matlab.

% Serialize the data into a 1D array of uint8 bytes
dataInBytes = getByteStreamFromArray(data);
% Parse the requested output filename (full path name)
[fpath,fname,fext] = fileparts(filepath);
% Compress in memory and save to the requested file in ZIP format
fos = java.io.FileOutputStream(filepath);
%fos = java.io.BufferedOutputStream(fos, 8*1024);  % not really important (*ZipOutputStream are already buffered), but doesn't hurt
if strcmpi(fext,'.gz')
    % Gzip variant:
    zos = java.util.zip.GZIPOutputStream(fos);  % note the capitalization
else
    % Zip variant:
    zos = java.util.zip.ZipOutputStream(fos);  % or: org.apache.tools.zip.ZipOutputStream as used by Matlab's zip.m
    ze  = java.util.zip.ZipEntry('data.dat');  % or: org.apache.tools.zip.ZipEntry as used by Matlab's zip.m
    ze.setSize(originalDataSizeInBytes);
    zos.setLevel(9);  % set the compression level (0=none, 9=max)
    zos.putNextEntry(ze);
end
zos.write(dataInBytes, 0, numel(dataInBytes));
zos.finish;
zos.close;

This will directly create a zip archive file in the current folder. The archive will contain a single entry (data.dat) that contains our original data. Note that data.dat is entirely virtual: it was never actually created, saving us its associated I/O costs. In fact we could have called it simply data, or whatever other valid file name.
Saving to a gzip file is even simpler, since GZIP files have single file entries. There is no use for a ZipEntry as in zip archives that may contain multiple file entries.
Note that while the resulting ZIP/GZIP file is often smaller in size than the corresponding MAT file generated by Matlab’s save, it is not necessarily faster. In fact, except on slow disks or network drives, save may well outperform this mechanism. However, in some cases, the reduced file size may save enough I/O to offset the extra processing time. Moreover, GZIP is typically much faster than either ZIP or Matlab’s save.

Loading data from ZIP/GZIP

Similar logic applies to reading compressed data: We could indeed use unzip/gunzip/untar, but these would increase the I/O costs by reading the compressed file, saving the uncompressed version, and then reading that uncompressed file into Matlab.
A better solution would be to read the compressed file directly into Matlab. Unfortunately, the corresponding input-stream classes do not have a read() method that returns a byte array. We therefore use a small hack to copy the input stream into a ByteArrayOutputStream, using Matlab’s own stream-copier class that is used within all of Matlab’s compression and decompression functions:

% Parse the requested output filename (full path name)
[fpath,fname,fext] = fileparts(filepath);
% Get the serialized data
streamCopier = com.mathworks.mlwidgets.io.InterruptibleStreamCopier.getInterruptibleStreamCopier;
baos = java.io.ByteArrayOutputStream;
fis  = java.io.FileInputStream(filepath);
if strcmpi(fext,'.gz')
    % Gzip variant:
    zis  = java.util.zip.GZIPInputStream(fis);
else
    % Zip variant:
    zis  = java.util.zip.ZipInputStream(fis);
    % Note: although the ze & fileName variables are unused in the Matlab
    % ^^^^  code below, they are essential in order to read the ZIP!
    ze = zis.getNextEntry;
    fileName = char(ze.getName);  %#ok => 'data.dat' (virtual data file)
end
streamCopier.copyStream(zis,baos);
fis.close;
data = baos.toByteArray;  % array of Matlab int8
% Deserialize the data back into the original Matlab data format
% Note: the zipped data is int8 => need to convert into uint8:
% Note2: see discussion with Martin in the comments section below
if numel(data) < 1e5
    data = uint8(mod(int16(data),256))';
else
    data = typecast(data, 'uint8');
end
data = getArrayFromByteStream(data);

Note that when we deserialize, we have to convert the unzipped int8 byte-stream into a uint8 byte-stream that getArrayFromByteStream can process (we don't need to do this during serialization).

The SAVEZIP utility

I have uploaded a utility called SAVEZIP to the Matlab File Exchange which includes the savezip and loadzip functions. These include the code above, plus some extra sanity checks and data processing. Usage is quite simple:

savezip('myData', magic(4))   %save data to myData.zip in current folder
savezip('myData', 'myVar')    %save myVar to myData.zip in current folder
savezip('myData.gz', 'myVar') %save data to myData.gz in current folder
savezip('data\myData', magic(4))    %save data to .\data\myData.zip
savezip('data\myData.gz', magic(4)) %save data to .\data\myData.gz
myData = loadzip('myData');
myData = loadzip('myData.zip');
myData = loadzip('data\myData');
myData = loadzip('data\myData.gz');

Jan Berling has written another variant of the idea of using getByteStreamFromArray and getArrayFromByteStream for saving/loading data from disk, in this case in an uncompressed manner. He put it all in his Bytestream Save Toolbox on the File Exchange.

Transmitting compressed data via the network

If instead of saving to a file we wish to transmit the compressed data to a remote process (or to save it ourselves later), we can simply wrap our ZipOutputStream with a ByteArrayOutputStream rather than a FileOutputStream. For example, on the way out:

baos = java.io.ByteArrayOutputStream;
if isGzipVarant
    zos = java.util.zip.GZIPOutputStream(baos);
else  % Zip variant
    zos = java.util.zip.ZipOutputStream(baos);
    ze  = java.util.zip.ZipEntry('data.dat');
    ze.setSize(numel(data));
    zos.setLevel(9);
    zos.putNextEntry(ze);
end
dataInBytes = int8(data);  % or: getByteStreamFromArray(data)
zos.write(dataInBytes,0,numel(dataInBytes));
zos.finish;
zos.close;
compressedDataArray = baos.toByteArray;  % array of Matlab int8

I leave it as an exercise to the reader to make the corresponding changes for the receiving end.

New introductory Matlab book

Matlab has a plethora of introductory books. But I have a special affection to one that was released only a few days ago: MATLAB Succinctly by Dmitri Nesteruk, for which I was a technical editor/reviewer. It's a very readable and easy-to-follow book, and it's totally free, so go ahead and download.
This title adds to the large (and growing) set of free ~100-page introductory titles by Syncfusion, on a wide variety of programming languages and technologies. Go ahead and download these books as well. While you're at it, take a look at Syncfusion's set of professional components and spread the word. If Syncfusion gets enough income from such incoming traffic, they may continue to support their commendable project of similar free IT-related titles.
This may be a good place to update that my own [second] book, Accelerating MATLAB Performance, is nearing completing, and is currently in advanced copy-editing stage. It turned out that there was a lot more to Matlab performance than I initially realized. The book size (and writing time) doubled, and it turned out to be a hefty ~750 pages packed full with performance improvement tips. I'm still considering the cover image (ideas anyone?) and working on the index, but the end is now in sight. The book should be in your favorite bookstore this December. If you can't wait until then, and/or if you'd rather use the real McCoy, consider inviting me for a consulting session...
Addendum December 16, 2014: I am pleased to announce that my book, Accelerating MATLAB Performance, is now published (additional information).

The post savezip utility appeared first on Undocumented Matlab.

The question of a new book

As with any birth, the initial exhilaration completely overwhelms, letting me forget how hard it has been to write the book. So while this “high” lasts, I wanted to ask you my readers for your opinion regarding a possible future book.
Which of the following books by me, possibly co-authored with another writer, would you be interested to read and/or have in your library?

1. Professional Matlab application development
2. Professional Matlab GUI
3. Matlab performance tuning
4. Undocumented Matlab – the non-Java parts
5. Some other subject (please specify)
6. None of the above

Please choose only a single item, or prioritize your choices. It will be a book about only one of the above topics, not several topics. I’m not going to write another 700-page monster that takes 5 years to prepare…
There are of course many factors going into a decision about whether or not to enter a book-writing project. It is a multi-year commitment that requires lots of effort, time, focus, and attention to detail. It affects the writer in a way that influences the entire family. In fact, my wife has already voted an emphatic “NO!” on this subject, and I’m pretty ambivalent about this issue myself.
Please do let me know what you think in a short comment. Happy Holidays everyone!

The post Ideas for a new book appeared first on Undocumented Matlab.

• The Matlab programming environment relies on Java for numerous tasks, including networking, data-processing algorithms and graphical user-interface (GUI)
• We can use Matlab for easy access to external Java functionality, either third-party or user-created
• Using Java, we can extensively customize the Matlab environment and application GUI, enabling the creation of visually appealing and usable applications

No prior Java knowledge is required. All code snippets and examples are self-contained and can generally be used as-is. Advanced Java concepts are sometimes used, but understanding them is not required to run the code. Java-savvy readers will find it easy to tailor code samples for their particular needs; for Java newcomers, an introduction to Java and numerous online references are provided.
More info about the book, including detailed Table-of-Contents, book structure and FAQ, can be found on the book’s webpage.

The post New book: Undocumented Secrets of MATLAB-Java Programming appeared first on Undocumented Matlab.