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Announcing NMath 6.0 and NMath Stats 4.0

Tuesday, August 19th, 2014

We’re pleased to announce new versions of the NMath libraries – NMath 6.0, and NMath Stats 4.0.

Added functionality includes:

  • Upgraded to Intel MKL 11.1 Update 3 with resulting performance increases.
  • Added Adaptive Bridge™ technology to NMath Premium edition, with support for multiple GPUs, per-thread control for binding threads to GPUs, and automatic performance tuning of individual CPU–GPU routing to insure optimal hardware usage.
  • NMath linear programming, nonlinear programming, and quadratic programming classes are now built on the Microsoft Solver Foundation (MSF). The Standard Edition of MSF is included with NMath.
  • Added classes for solving nonlinear programming problems using the Stochastic Hill Climbing algorithm, for solving quadratic programming problems using an interior point algorithm, and for solving constrained least squares problems using quadratic programming methods.
  • Added support for MKL Conditional Numerical Reproducibility (CNR).

For more complete changelogs, see here and here.

Upgrades are provided free of charge to customers with current annual maintenance contracts. To request an upgrade, please contact sales@centerspace.net. Maintenance contracts are available through our webstore.

CenterSpace in Chicago and Singapore

Wednesday, June 18th, 2014

NVIDIA GPU Technology Workshop in SE Asia

CenterSpace will be giving a presentation at the upcoming GPU Technology Workshop South East Asia on July 10. The conference will be held at the Suntec Singapore Convention & Exhibition Centre. For a full schedule of talks see the agenda.


Abstract

From CPU to GPU: a comparative case study / Andy Gray – CenterSpace Software

In this code-centric presentation, we will compare and contrast several approaches to a simple algorithmic problem: a straightforward implementation using managed code, a multi-CPU approach using a parallelization library, coupling object-oriented managed abstractions with high-performance native code, and seamlessly leveraging the power of a GPU for massive parallelization without code changes.

Andy Gray, a technology evangelist for CenterSpace Software, will be delivering the talk. We hope to see you there!

Parallel Computing in Finance Lecture

The June 5-6 conference at the University of Chicago titled, Recent Developments in Parallel Computing in Finance hosted talks by various academics in finance, Microsoft, Intel, and CenterSpace. CenterSpace was invited to give a two hour lecture and tutorial on GPU computing at the Stevanovich Center at the University of Chicago. We will post up the tutorial video from the talk as soon as it becomes available.


Abstract

Lecture by Trevor Misfeldt

CenterSpace Software, a leading provider of numerical component libraries for the .NET platform, will give an overview of their NMath math and statistics libraries and how they are being used in industry. The Premium Edition of NMath offers GPU parallelization. Xeon Phi, C++ AMP and CUDA are technologies of interest. Support for each will be discussed. Also discussed will be CenterSpace’s Adapative Bridge™ technology, which provides intelligent, adaptive routing of computations between CPU and GPUs. The presentation will finish with a demonstration followed by performance charts.

Tutorial by Andy Gray

In this hands-on programming tutorial, we will compare and contrast several approaches to a simple algorithmic problem: a straightforward implementation using managed code, a multi-CPU approach using a parallelization library, coupling object-oriented managed abstractions with high-performance native code, and seamlessly leveraging the power of a GPU for massive parallelization.

Fast Arction charts with NMath

Tuesday, March 15th, 2011

Our partners at Arction have created some great video showcasing their very fast signal processing charts using NMath.

More at Arction including information on our partner bundle.

– Trevor

NMath and Silverlight

Tuesday, March 1st, 2011

Customers have asked about using NMath from a Silverlight application.

NMath uses unmanaged code–specifically, Intel’s Math Kernel Library (MKL), an implementation of the BLAS and LAPACK standard.

In Silverlight 4.0, you can use NMath in two ways. You can either use JavaScript to talk to the server and have NMath running there, or you can register classes as COM objects on the local machine and call into them.

In Silverlight 5.0, you will be able to call unmanaged code directly on the client. NMath will have to exist in the client, but interfacing with it should be quite simple.

– Trevor

Finding Peaks in Data with NMath

Wednesday, October 13th, 2010

Finding peaks in experimental data is a very common computing activity, and because of its intuitive nature there are many established techniques and literally dozens of heuristics built on top of those. CenterSpace Software has jumped into this algorithmic fray with a new peak finding class based on smooth Savitzy-Golay polynomials. If you are not familiar with Savitzy-Golay polynomial smoothing, take a look at our previous blog article. When used for peak finding, we simply report the zero crossing derivatives of the smoothing, locally-fit, Savitzy-Golay polynomials. This is a very fast peak finder because the Savitzy-Golay smoothing algorithm can be slightly altered to directly report the first derivatives, which remarkably, can be done with a convolve operation. Because this peak finder is based on Savitzy-Golay polynomials, it requires that the data be sampled at regular intervals.

An Introductory Example

Suppose we have the following sampled data.

graph of example data

Simple data with a single peak.

The following C# code builds the test data and locates the single peak in this simple data set.

Using CenterSpace.NMath.Core;
 
DoubleVector d = new DoubleVector(0,-1, 1.5, 2, 3, 4, 4.5, 4, 3, 2.2, 1.0, -3.0, 0);
PeakFinderSavitzkyGolay pfa = new PeakFinderSavitzkyGolay(d, 5, 4);
pfa.LocatePeaks();

The peak data reported back by the Savitzky-Golay peak finder can be either the (x,y) location of the peak, or the index lying on or preceding the found peak.

Peak found at x:6.00, y:4.50
Peak found at index: 6

The peak finding PeakFinderSavitzkyGolay class requires three parameters: a data vector, the filter window width, and the degree of the smoothing polynomial.

A More Complex Example

To build a peak finder on top on this class for some domain specific data, we need to understand the basic parameters that control which peaks are reported. For this second example, let’s use the complex signal show below, which contains a mixture of isolated peaks, adjacent peaks, and narrow and broad peaks.

Example peaks

Peaks of various widths and heights

This signal also includes some very subtle peaks near x = 23.5 and x = 29. Applying the PeakFinderSavitzkyGolay class as shown below, all 15 peaks are found (the top of the first peak is off the scale in our image).

PeakFinderSavitzkyGolay pfa = new PeakFinderSavitzkyGolay(signal, 10, 5);
pfa.AbscissaInterval = 0.1;
pfa.LocatePeaks();
Console.WriteLine("Number of peaks found: " + pfa.NumberPeaks.ToString());
Console.WriteLine(String.Format("Peak found at x:{0:0.00}, y:{1:0.00}", pfa[4].X, pfa[4].Y));

The position of the fifth peak is reported to the console, using indexing notation, pfa[4].X, pfa[4].Y, on the peak finder object.

Number of peaks found: 15
Peak found at x:9.03, y:0.35

By setting the AbsciassaInterval to the signal sample rate (in this example 0.1 seconds) the class can scale the x-axis according to your units, and supply the (x, y) positions of all found peaks. If you only need the peak location down to the resolution of the sample interval, the peak finder will just report the index that either precedes or lies on the peak abscissa location. This avoids the an extra interpolation step to locate the inter-sample peak abcissa, and increases performance.

Now supposing that we want to eliminate all broad peaks and can increase the peak finders selectivity.

PeakFinderSavitzkyGolay pfa = new PeakFinderSavitzkyGolay(signal, 10, 5);
pfa.AbscissaInterval = 0.1;
pfa.SlopeSelectivity = 0.003;
pfa.LocatePeaks();

The property SlopeSelectivity defaults to zero, causing the peak finder to report all found peaks. By increasing the selectivity a hair to 0.003, the peak finder no longer reports the last three peaks. Both the two subtle peaks are eliminated along with the final broad peak near 26. The slope selectivity is simply the slope of the smoothed first derivative of the Savitzy-Golay polynomial at each zero crossing – so as it’s value is increased only the more pronounced peaks (with steeply diving smoothed first derivatives) are reported.

If we want to heavily filter the peaks and only see the peaks of the general trend line, we could increase the filter width dramatically from 10 to 80.

PeakFinderSavitzkyGolay pfa = new PeakFinderSavitzkyGolay(signal, 80, 5);
pfa.AbscissaInterval = 0.1;
pfa.SlopeSelectivity = 0.0;
pfa.LocatePeaks();

Using these parameters, we find only the four peaks that capture the low frequency variation of the signal above.

Peak found at x:7.53, y:0.34
Peak found at x:14.27, y:0.26
Peak found at x:20.28, y:0.25
Peak found at x:26.76, y:0.24

Note that the y-values here correspond to the smoothed, fitted polynomial not the actual data at the x value. This demonstrates the ability of the this peak finder to act as a low pass filter, which can be use to sort out the peaks of interest from higher frequency noise. This is why Savitzy-Golay data smoothing is often used for baseline subtraction (for example in pre-processing mass spectrometry data before peak finding).

Summary & Performance

The first example used a smoothing polynomial of degree 4, and the second example a polynomial degree of 5. Experience shows that typically a polynomial degree between 3-7 will be best suited to smooth measurement data and correctly locate peaks. However, there is no hard and fast rule, so feel free to experiment. Having said that, the polynomial degree must always be strictly less than the window width or an exception will be thrown.

polynomial degree < window width

Because, after object construction, this peak finder boils down to a convolution, it's performance is far better that many peak finders. On my 2.8Ghz Intel i7 Quad Core, I can find peaks in 3 million data points in about 80 ms, and in 30 million data that requires about 700ms. That would give us the ability to do peak finding in a real time system running with a sample rate of ~43 MHz. In a real system there would likely be other peak filtering overhead, but we would still be able to process data at a very high rate - suitable for most real-time data sampling applications.

Happy Computing

-Paul Shirkey