# Tag Archives: ILNumerics

## Installing ILNumerics – Unexpected behavior

At ILNumerics we get a lot of support requests every day. During the last couple of months some questions were related to installing ILNumerics. In some cases an unexpected error message appears. The easy solution is to manually uninstall our extension from all Visual Studio instances and then reinstall ILNumerics. This issue will be resolved once we release our new installer.

## ILNumerics for Science – How did you do the Visualization?

In the third part of our series we focus on the visualization of scientific data. You learn how to easily display your data with ILNumerics and the ILPanels.

## Plotting Fun with ILNumerics and IronPython

Since the early days of IronPython, I keep shifting one bullet point down on my ToDo list:

* Evaluate options to use ILNumerics from IronPython

Several years ago there has been some attempts from ILNumerics users who successfully utilized ILNumerics from within IronPython. But despite our fascination for these attempts, we were not able to catch up and deeply evaluate all options for joining both projects. Years went by and Microsoft has dropped support for IronPython in the meantime. Nevertheless, a considerably large community seems to be active on IronPython. Finally, today is the day I am going to give this a first quick shot.

## ILNumerics Language Features: Limitations for C#, Part II: Compound operators and ILArray

A while ago I blogged about why the CSharp var keyword cannot be used with local ILNumerics arrays (ILArray<T>, ILCell, ILLogical). This post is about the other one of the two main limitations on C# language features in ILNumerics: the use of compound operators in conjunction with ILArray<T>. In the online documentation we state the rule as follows:

The following features of the C# language are not compatible with the memory management of ILNumerics and its use is not supported:

• The C# var keyword in conjunction with any ILNumerics array types, and
• Any compound operator, like +=, -=, /=, *= a.s.o. Exactly spoken, these operators are not allowed in conjunction with the indexer on arrays. So A += 1; is allowed. A[0] += 1; is not!

Let’s take a closer look at the second rule. Most developers think of compound operators as being just syntactic sugar for some common expressions:

int i = 1;
i += 2;

… would simply expand to:

int i = 1;
i  = i + 2; 

For such simple types like an integer variable the actual effect will be indistinguishable from that expectation. However, compound operators introduce a lot more than that. Back in his times at Microsoft, Eric Lippert blogged about those subtleties. The article is worth reading for a deep understanding of all side effects. In the following, we will focus on the single fact, which becomes important in conjunction with ILNumerics arrays: when used with a compound operator, i in the example above is only evaluated once! In difference to that, in i = i + 2, i is evaluated twice.

Evaluating an int does not cause any side effects. However, if used on more complex types, the evaluation may does cause side effects. An expression like the following:

ILArray<double> A = 1;
A += 2;

… evaluates to something similiar to this:

ILArray<double> A = 1;
A = (ILArray<double>)(A + 2); 

There is nothing wrong with that! A += 2 will work as expected. Problems arise, if we include indexers on A:

ILArray<double> A = ILMath.rand(1,10);
A[0] += 2;
// this transforms to something similar to the following:
var index = (ILRetArray<double>)0;
receiver[index] = receiver[index] + 2; 

In order to understand what exactly is going on here, we need to take a look at the definition of indexers on ILArray:

public ILRetArray<ElementType> this[params ILBaseArray[] range] { ...

The indexer expects a variable length array of ILBaseArray. This gives most flexibility for defining subarrays in ILNumerics. Indexers allow not only scalars of builtin system types as in our example, but arbitrary ILArray and string definitions. In the expression A[0], 0 is implicitly converted to a scalar ILNumerics array before the indexer is invoked. Thus, a temporary array is created as argument. Keep in mind, due to the memory management of ILNumerics, all such implicitly created temporary arrays are immediately disposed off after the first use.

Since both, the indexing expression 0 and the object where the indexer is defined for (i.e.: A) are evaluated only once, we run into a problem: index is needed twice. At first, it is used to acquire the subarray at receiver[index]. The indexer get { ...}  function is used for that. Once it returns, all input arguments are disposed – an important foundation of ILNumerics memory efficency! Therefore, if we invoke the index setter function with the same index variable, it will find the array being disposed already – and throws an exception.

It would certainly be possible to circumvent that behavior by converting scalar system types to ILArray instead of ILRetArray:

ILArray A = ...;
A[(ILArray)0] += 2;

However, the much less expressive syntax aside, this would not solve our problem in general either. The reason lies in the flexibility required for the indexer arguments. The user must manually ensure, all arguments in the indexer argument list are of some non-volatile array type. Casting to ILArray<T> might be an option in some situations. However, in general, compound operators require much more attention due to the efficient memory management in ILNumerics. We considered the risk of failing to provide only non-volatile arguments too high. So we decided not to support compound operators at all.

See: General Rules for ILNumerics, Function Rules, Subarrays

## Troubleshooting: Adding ILNumerics 3D Controls to the VS Toolbox

Adding ILNumerics visualizations to Visual Studio based projects has become a quite convenient task: It’s easy to use the ILNumerics math library for own projects in .NET. However, from time to time users have problems adding the ILNumerics controls to their Visual Studio Toolbox window.

Update: Since ILNumerics Ultimate VS version 4 this issue has been solved once for all. Simply install the MSI installer and find the ILNumerics ILPanel in the toolbox for all applicable situations.

That’s what a post on Stack Overflow from earlier this year was about: A developer who wanted to use our C# math library for 3d visualizations and simulations wasn’t able to access the ILNumerics controls. “How can I locate it?”, he was wondering. “Do I have to make some changes to my VS?”

## Adding ILNumerics Controls to the Visual Studio Toolbox manually

If the ILNumerics Ultimate VS math library is installed on a system, normally the ILNumerics controls are automatically listed in the Visual Studio toolbox on all supported versions of Visual Studio. However, if that’s not the case there’s a way to a add them manually: After clicking right onto the toolbox, you can select “Choose Item”. The dialog allows you to select the assambly to load the controls from – that’s it! You will find the ILNumerics.dll in the installation folder on your system. By default this directory is located at:  “C:\Program Files (x86)\ILNumerics\ILNumerics Ultimate VS\bin\ILNumerics.dll”.

However, if that doesn’t work straightaway, it often helps to clear the toolbox from any copies of custom controls before – simply right-click it and choose “Reset Toolbox”.

## Need help? ILNumerics Documentation and Support

You want to know more about our math library and its installation? Check out our documentation and the Quick Start Guide! If you have any technical questions, have a look at our Support Section.

## Scientific Computing Online: IPython Notebook, Shiny (R) and ILNumerics

It seems that we’re facing a trend at the moment: scientific computing, math and visualization software for web browsers. With our interactive web examples we have taken a step into that direction, too: Visitors of our website can change the C# code of our plotting and visualization demos in order to create a new SVG, PNG, JPG or EXE output. This allows people to easily try out the ILNumerics syntax and our powerful 2d and 3d visualization features for .NET. In addition to that, ILView allows a convenient way to interactively explore scenes that are created with ILNumerics.

There are two other web applications that cause a lot of excitement in the scientific community at the moment: The IPython Notebook and Shiny, a tool for creating web applications in R. Let’s have a closer look…

## IPython Notebook: “Interactive Computational Environment”

The IPython Notebook adresses the huge amount of Python users in the scientific community. It basically offers a new way for writing papers: It’s a web based editor for code execution, math, text and visualization. Because the IPython Notebook combines all parts you normally need to write a scientific paper, you won’t have to import / export different elements from several domain specific software applications: “Everything related to my analysis is located in one unified place”, explains Philip J. Guo in his blog (http://www.pgbovine.net/ipython-notebook-first-impressions.htm). Once you have finished your paper, you can share your IPython Notebook as HTML and PDF with your colleagues, your professor etc.

## Shiny: “Easy web applications in R”

Shiny stands for a different approach: It allows you to implement own analysis into web applications. While IPython obviously adresses Python users, Shiny is based on R, a still very popular programming language among statisticians. What makes Shiny interesting are its interactivity features: Most demos on the Shiny website offer the opportunity to choose input parameters from text fields or drop-downs to dynamically change the output visualization. The code seems to be quite similar to R, so users who are familiar with that language will easily be able to create interactive data visualization applications for their websites using Shiny.

Both approaches make web browsers accesable for specific needs of scientific visualization: The IPython Notebook offers a convenient tool to share the results of analytics related research; Shiny allows R developers to publish particular interactive plots on the web.

However, both projects are limited – namely because of technological issues. The level of performance that can be realized with both platforms is restricted: You’ll face that at the latest when you start creating complex 3d scenes with either Python or R. This holds true for the platforms’ web applications, too…

## Outlook: Scientific Computing online

For certain purposes web based scientific computing software offers new convenient solutions. But if you want to realize complex interactive 3d visualizations, you still won’t use any of them but an application on your local machine instead.

Our interactive web examples point the direction we want to go. In order to make scientific computing more powerful, we’re working on the next step of our approach: a full WebGL support for ILNumerics. Stay tuned…

## High Performance Fast Fourier Transformation in .NET

„I started using ILNumerics for the FFT routines. The quality and speed are excellent in a .NET environment.“

The Fourier Transform (named after French mathematician and physicist Joseph Fourier) allows scientists to transform signals between time domain and frequency domain. This way, an arbitrary periodic function can be expressed as a sum of cosine terms. Think of the equalizer of your mp3-player: It expresses your music’s signal in terms of the frequencies it is composed of.

The Fast Fourier Transform (FFT) is an algorithm for the rapid computation of discrete Fourier Transforms’ values. Being one of the most popular numerical algorithms, it is used in physics, engineering, math and many other domains.

In terms of software engineering, the Fast Fourier Transform is a very demanding algorithm: In the .NET-framework, a naive approach would cause very low execution speeds. That’s the reason why many .NET-developers have to implement native C-libraries when it comes to FFTs.

ILNumerics uses Intel’s® MKL for Fast Fourier Transforms: That’s why our users don’t have to implement native library’s themselves for high performance FFTs. No matter if they have a scientific or an industrial background, many developers rely on ILNumerics because of its implementation of the Fast Fourier Transform. It’s the fastest you can get today – even for big amounts of data.

ILNumerics provides interfaces to forward and backward Fourier Transformations, for real and complex floating point data, in single and double precision, in one, two or n dimensions. In addition to the MKL’s FFTs, prepared interfaces for FFTW and for AMDs ACML exist.

Learn more about the ILNumerics library and its implementation of Fast Fourier Transformation in C#/.NET in the online documentation!

## Putting on a Good Show with HDF5, ILNumerics, and PowerShell

It is certainly nice to have the option to do all kinds of numeric stuff right in your .NET application layer – without the need for interfacing any unmanaged module. But for some tasks, this still seems overkill.

Lets say, you went to that conference and want to give your new friends some insight into your brand new simulation results. The PC in the internet cafe enables you to fetch the data from your NAT storage at home. But will you be able to do anything with it on that plain Windows PC?

Or you want to localize a certain test data set but cannot remember its rather cryptic name. Or you might want to manage the latest measurement results from todays atmospheric observation satellite scans. The data are huge but often require some sort of preprocessing. There should be some easy way to filter them by the meta data within the files, right?

Other than getting the data from some application layer, we now want to interface plain old file objects. Of course, you store your data in HDF5 format, right? You do so, because HDF5 is portable, very efficient, flexible and you are in good company.

Let’s see. We have a fresh Windows PC and we know every Windows installation nowadays comes with Powershell. Powershell itself is based on the .NET framework and hence efficiently handles any .NET assembly. It should be easy to use ILNumerics with Powershell! All we still need is some way to access the HDF5 files. ILNumerics, natively is able to read and write Matlab mat files up to version 6. It currently lags on native HDF5 support.

Luckily, the HDF Group provides a large collection of high quality tools for HDF support. Among them you’ll find a .NET wrapper and … a brand new Powershell module: PSH5X! Together with Gerd Heber, the leading inventor of PSH5X, we did a feasibility study with the goal to investigate the options of utilizing HDF5 and ILNumerics together in Powershell. It can be downloaded here. We were quite impressed by the options this brings.

This blog post will describe the necessary steps to setup Powershell for ILNumerics and HDF5.

# Getting Started

Basically, the installation process for any Powershell module consists of

1. Getting the module files and its dependencies from somewhere,
2. Deploying the module files into a special folder on your machine, and
3. Importing the module in your session.

The PSH5X homepage gives all information on how to get ready using the HDF5 Powershell module. Just download the package and follow the three steps on the page. At the end, HDF5 signals you a successful installation by displaying its version numbers.

Since ILNumerics depends on several other modules, we provide a small bootstrapper script. Just open up your favorite Powershell IDE (PowerShell_ISE.exe comes with any recent Windows) and copy/paste the following line:

(new-object Net.WebClient).DownloadString('http://ilnumerics.net/media/InstallILNumericsPSM.ps1') | iex

If you are curious, what this does – just ommit the trailing | iex and the script is not executed but displayed for your inspection.

The installer will ask for the installation folder (global under System32/ or local in your user profile), fetches the latest ILNumerics package for the current platform from the official nuget repository and install it into the selected module folder. In addition it loads the TypeAccelerator Powershell module and installs it into the same module directory. Note, the accelerators have been slightly modified in order to make them work with Powershell 3 and hence are fetched from our ILNumerics server. However, credits fully belong to poshoholic for his great work.

Note, the installation has to be done only once. Afterwards, on the next Powershell session, simply re-import needed modules by typing – lets say:

PS> Import-Module ILNumerics

# Go!

If everything was setup correctly, we can now use the full spectrum of the involved modules:

PS> [ilmath]::rand(4,5).ToString()
<Double> [5,4]
0,72918    0,87547    0,43167    0,94942
0,58024    0,75562    0,96125    0,83148
0,22454    0,20583    0,82285    0,83144
0,13300    0,40047    0,58829    0,87012
0,50751    0,05496    0,02814    0,48764 

Nice. But what about the MKL? Are the correct binaries really installed as well?

PS> [ilf64] $A = [ilmath]::rand(1000,1000) PS> Measure-Command { [ilf64]$C = [ilmath]::rank($A) } Days : 0 Hours : 0 Minutes : 0 Seconds : 0 Milliseconds : 920 Ticks : 9202311 TotalDays : 1,06508229166667E-05 TotalHours : 0,00025561975 TotalMinutes : 0,015337185 TotalSeconds : 0,9202311 TotalMilliseconds : 920,2311 PS>$C.ToString()
1000

We have almost all options from C#:

PS> [ilf64] $part =$A['10:15;993:end']
PS> $part.ToString() <Double> [11,7] 0,08522 0,87217 0,59997 0,57363 0,22956 0,02006 0,02359 0,33479 0,49003 0,65269 0,97772 0,28322 0,69505 0,70372 0,30072 0,68705 0,47112 0,68627 0,65030 0,40454 0,63026 0,15639 0,30391 0,22992 0,69310 0,65716 0,51797 0,68110 0,72854 0,60188 0,50740 0,74499 0,13459 0,88481 0,12445 0,80525 0,60180 0,69256 0,74825 0,64388 0,16792 0,45266  Lets sort the first row of$part, keeping track of original positions:

PS> [ilf64] $indices = 0.0 PS> [ilf64]$sorted = [ilmath]::sort($part['0,1;:'],$indices,0,$false) PS>$sorted.ToString()
<Double> [2,7]
0,02006    0,02359    0,08522    0,22956    0,57363    0,59997    0,87217
0,28322    0,33479    0,49003    0,65269    0,69505    0,70372    0,97772
PS> \$indices.ToString()
<Double> [2,7]
5          6          0          4          3          2          1
4          0          1          2          5          6          3 

This is all interactive. Of course, we can write complete functions and even complex algorithms that way.
One of the best things: Even in Powershell ILNumerics saves your memory and meets all expectations regarding execution speed. Powershell allows you to consequently use ILNumerics’ typing and scoping rules.

In our feasibility study with Gerd Heber, we show how easy it gets to access an HDF5 file, to convert its data to ILNumerics arrays (implicitly), filter and manipulate a little and even create a full interactive 3D surface graph from it. We demonstrate how to use the type accelerators and to mimic the using statement for artificial scoping. Take a look and let us know, what you think!

## ILNumerics and LINQ

As you may have noticed, ILNumerics arrays implement the IEnumerable interface. This makes them compatible with ‘foreach’ loops and all the nice features of LINQ!

Consider the following example: (Dont forget to include ‘using System.Linq’ and derive your class from ILNumerics.ILMath!)

ILArray<double> A = vec(0, 10);
Console.WriteLine(String.Join(Environment.NewLine, A));

Console.WriteLine("Evens from A:");
var evens = from a in A where a % 2 == 0 select a;
Console.WriteLine(String.Join(Environment.NewLine, evens));
return;


Some people like the Extensions syntax more:


var evens = A.Where(a => a % 2 == 0);


I personally find both equivalently expressive.

## Considerations for IEnumerable<T> on ILArray<T>

No option exist in IEnumerable<T> to specify a dimensionality. Therefore, and since ILNumerics arrays store their elements in column major order, enumerating an ILNumerics array will be done along the first dimension. Therefore, when used on a matrix, the enumerator runs along the columns:

ILArray<double> A = counter(3,4);
Console.WriteLine(A + Environment.NewLine);

Console.WriteLine("IEnumerable:");
foreach(var a in A)
Console.WriteLine(a);


… will give the following:

<Double> [3,4]
1          4          7         10
2          5          8         11
3          6          9         12

IEnumerable:
1
2
3
4
5
6
7
8
9
10
11
12


Secondly, as is well known, accessing elements returned from IEnumerable<T> is only possible in a read-only manner! In order to alter elements of ILNumerics arrays, one should use the explicit API provided by our arrays. See SetValue, SetRange, A[..] = .. and GetArrayForWrite()

Lastly, performance considerations arise by excessive utilization of IEnumerable<T> in such situations, where high performance computations are desirable. ILNumerics does integrate well with IEnumerable<T> – but how well IEnumerable<T> does integrate into the memory management of ILNumerics should be investigated with help of your favorite profiler. I would suspect, most every day scenarios do work out pretty good with LINQ since it concatenates all expressions and queries and iterates the ILNumerics array only once. However, let us know your experiences!

## Microsoft.Numerics, Cloud Numerics for Azure – a short Review

Today I found some time to take a look at the Cloud Numerics project at Microsoft. I started with the overview/ introduction post by Ronnie Hoogerwerf found at the Cloud Numerics blog at msdn.

The project aims at computations on very large distributed data sets and is intended for Azure. Interesting news for me: the library shows quite some similarities to ILNumerics. It provides array classes on top of native wrappers, utilizing MPI, PBLAS and ScaLAPACK. A runtime is deployed with the project binaries: Microsoft.Numerics, which provides all the classes described here.

## ‘Local’ Arrays in “Cloud Numerics”

The similarity is most obvious when comparing the array implementations: Both, ILNumerics and Cloud Numerics utilize multidimensional generic arrays. Cloud Numerics arrays all derive from Microsoft.Numerics.IArray<T> – not to be confused with ILNumerics local arrays ILArray<T> ;)!

Important properties of arrays in ILNumerics are provided by the concrete array implementation of an array A (A.Size.NumberOfElements, A.Size.NumberOfDimensions, A.Reshape, A.T for the Transpose a.s.o.). On the Cloud Numerics side, those properties are provided by the interface IArray<T>: A.NumberOfDimensions, A.NumberOfElements, A.Reshape(), A.Transpose() a.s.o).

A similar analogy is found in the element types supported by ILArray<T> and Microsoft.Numerics.IArray<T>. Both allow the regular System numeric value types, as System.Int32, System.Double and System.Single. Interestingly – both do not rely on System.Numerics.Complex as the main double precisioin complex data element type but rather implement their own for both: single precision and double precision.

Both array types support vector expansion, at least Cloud Numerics promises to do so in the next release. For now, only scalar binary operations are allowed for arrays. For an explanation of the feature it refers to NumPy rather than ILNumerics though.

## Arrays Storage in “Cloud Numerics”

The similarities end when it comes to internal array storage. Both do store multidimensional arrays as one dimensional arrays internally. But Cloud Numerics stores its elements in native one dimensional arrays. They argue with the 2GB limit introduced for .NET objects and further elaborate:

Additionally, the underlying native array types in the “Cloud Numerics” runtime are sufficiently flexible that they can be easily wrapped in environments other than .NET (say Python or R) with very little additional effort.

It is hard follow that view. Out of my experience, .NET arrays are perfectly suitable for such interaction with native libraries, since at the end it is just a pointer to memory passed to thoses libs. Regarding the limit of 2GB: I assume a ‘problem size’ of more than 2GB would hardly be handled on one node. Especially a framework for distributed memory I would have expected to switch over to shared memory about at this limit at least?

In the consequence, interaction between Cloud Numerics and .NET arrays becomes somehow clumsy and – if it comes to really large datasets – with an expected performance hit (disclaimer: untested, of course).

Differences keep coming: indexing features are somehow basic in Cloud Numerics. By now, they support scalar element specification only and restrict the number of dimension specifier to be the same as the number of dimensions in the array. Therefore, subarrays seems to be impossible to work with. I will have an eye on it, if the project will support array features like A[full, end / 2 + 1] in one of the next releases

I wonder, how the memory management is done in Cloud Numerics. The library provides overloaded operators and hence faces the same problems, which have led to the sophisticated memory management in ILNumerics: if executed in tight loops, expression like

A = 0.5 * (A + A') + 0.5 * (A - A')

on ‘large’ arrays A will inevitably lead to memory pollution if run without deterministic disposal! Not to speak about (virtual) memory fragmentation and the problems introduced by heavy unmanaged resources in conjunction with .NET objects and the GC … I could not find the time to really test it live, but I am almost sure, the targeted audience with really large problem sizes somehow contradicts this approach. Unless there is some hidden mechanism in the runtime (which I doubt, because the use of ‘var’ and regular C#, hence without the option to overload the assignment operator), this could evolve to a real nuissance IMO.

## Distributed Arrays

This part seems straightforward. It follows the established scheme known from MPI but offers a nicer interface to the user. Also the Cloud Numerics Runtime wraps away the overhead of cluster management, array slicing to a good extend. However, the question of memory management again arises on the distributed side as well. Since the API exposed to the user (obviously?) does not take care of disposal of temporary arrays in a timely fashion, the performance for large arrays will most likely be suffering.

As soon as I find out more details about their internal memeory management I will post them here – hopefully together with some corrections of my assumptions.