Mathematics

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The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. At present, it provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.

 

http://math-atlas.sourceforge.net/

 

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Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.

Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It is easily extensible and customizable via user-defined functions written in Octave's own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages.

 

http://www.gnu.org/software/octave/

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Maple 12 is the essential technical computing software for today’s engineers and scientists. Whether you need to do quick calculations, develop design sheets, or produce sophisticated high-fidelity simulation models, Maple 12 provides the necessary technology to reduce errors and dramatically increase your analytical productivity at every stage of the design process.

http://www.maplesoft.com/products/Maple/professional/index.aspx

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Mathematica includes numerical, graphical and symbolic computation capabilities, all linked to the Mathematica programming language. Introduced in 2005, Version 5.2 supports 64-bit memory addressing and 64-bit long number partitioning. It also supports threading of numerical linear algebra over multiple CPUs and multi-core processors.

 

http://www.wolfram.com/

 

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MATLAB® is a high-level language and interactive environment that enables you to perform computationally intensive tasks faster than with traditional programming languages such as C, C++, and FORTRAN.

 

http://www.mathworks.com/products/matlab/

 

 

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The Star-P open software platform delivers revolutionary results to scientists, engineers and analysts by enabling them to transparently use high performance computing resources, using familiar desktop tools.

 

Star-P software is a client-server parallel-computing platform that’s been designed to work with multiple Very High Level Language (VHLL) client applications such as MATLAB®, or Python and has built-in tools to expand VHLL computing capability through addition of libraries and hardware-based accelerators.

 

• Star-P Client

  The Star-P client connects the desktop application to the parallel server, and outsources to it the most computationally-intensive operations. It resides on the user’s desktop, intercepts calls to VHLL function libraries, and forwards them to the parallel libraries on the server if parallel computing is needed. Star-P Client also handles all Star-P specific commands.

• Star-P Interactive Engine

  Star-P’s interactive engine runs on top of the server operating system, and manages the multiple interactive sessions in a multi-user environment, giving client applications interactive access to the server’s processors, memory, and file system.

• Star-P Computation Engine

  Star-P’s computation engine consists of two key elements: Built-in parallel computing and add-on parallel computing, accessible via Star-P Connect. Both support data- and task- parallel computations.

  • Data-Parallel Computations are for high-level matrix and vector operations on large data sets. and involve inter-processor communication during the computation.
  • Task-Parallel Computations are for carrying out many independent calculations in parallel, such as Monte Carlo simulations, or "un-rolling" serial FOR loops. Task-parallel computations do not involve inter-processor communication during the computation.
• Star-P Connect Library API Link

  Star-P Connect library API link enables you to extend the functionality of the Star-P compute engine based on your particular application and algorithm requirements. You can plug in existing serial and parallel libraries, access them via the desktop tools such as MATLAB® and Python, and execute them in a task- and data-parallel modes.

• Hardware Accelerators

  Hardware accelerators such as FPGAs and GPUs give technical computing users significant computation, I/O and memory bandwidth advantages over traditional CPU-only solutions. Through the Star-P Connect library API link, compute-intensive algorithms embedded in hardware appear as standard library functions, and can be easily called from the high-level desktop application.

 

http://www.interactivesupercomputing.com/products/

 

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The IMSL Numerical Libraries have been the cornerstone of high-performance and desktop computing as well as predictive analytics applications in science, technical and business environments for well over three decades. These embeddable mathematical and statistical algorithms, written in C, C#/.NET, Java™, and Fortran, are used in a broad range of applications -- from programs that help airplanes fly to allowing people to predict the weather, to those that enable innovative ways to study the human genome as well as applications that predict stock market behavior and provide risk management and portfolio optimization. The IMSL Libraries can also be used from Python using PyIMSL Studio or the PyIMSL wrappers.

 

The IMSL Libraries are regarded as the most sophisticated, flexible, scalable and highly accessible technology available for numerical analysis in the most important mainstream programming environments in use today.

 

The IMSL Libraries are a comprehensive set of mathematical and statistical functions that programmers can embed into their software applications. The libraries save development time by providing pre-written mathematical and statistical algorithms that can be embedded into C, C# for .NET, Java™ and Fortran applications or accessed from Python, enhancing return on investment and programmer productivity. The libraries free users from developing their own internal code by providing pre-written mathematical and statistical algorithms that can be embedded into C, C#/.NET, Java™, and Fortran applications.

 

Its robust, accurate, reliable mathematical and statistical library provides functionality in a wide range of numerical computing areas including:

 

• Optimization
• FFT's
• Interpolation
• Differential equations
• Correlation
• Regression
• Time series analysis
• and many more

 

The IMSL Libraries reflect ongoing numerical analysis research and development, and embody research expertise in both numerical and scientific computing. The IMSL Libraries computing environment and support services emphasize user productivity and cost-effectiveness. Visual Numerics provides a significant return on investment by saving up to 95% of the time and cost of developing numerical algorithms.

 

Programmers at major corporations, research laboratories and academic institutions have used the IMSL Library tools to build software applications in fields including engineering, research and development, financial engineering, physics, business analysis, data mining, biotechnology, plus many more.

 

 

Developers using the IMSL Libraries find significant benefits in the products ability to accelerate development time, reduce coding hassle, improve quality, and reduce development costs.

 

 

http://www.vni.com/products/imsl/

 

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The PV-WAVE Family of products, which includes PV-WAVE, TS-WAVE, and JWAVE, provides software developers with the tools needed to efficiently and accurately meet data analysis requirements. PV-WAVE solutions allow users to rapidly import, manipulate, analyze and visualize data.

 

The PV-WAVE Family includes robust time series analysis software as well as the ability to share analysis results across the enterprise with a Java™-based solution. Unlike other products, PV-WAVE Advantage includes a sophisticated set of analysis routines based on the industry-standard IMSL Numerical Libraries.

 

PV-WAVE charting capabilities, such as this X Bar and R chart are used in many technical and business applications.

 

• PV-WAVE

  PV-WAVE is an array oriented fourth-generation programming language used to build and deploy VDA applications.

  • Manipulate and visualize simple to complex datasets
  • Detect and display patterns, trends, anomalies and other vital information
  • Deliver powerful image and signal processing, data import and export, 3-D surface, plot, histogram, contour, animation, color editor and a database table display
  • Incorporate sophisticated analysis routines based on the industry-standard IMSL Numerical Libraries for reliable and precise numerical analysis
• TS-WAVE

  TS-WAVE is the time series analysis component of the PV-WAVE Family of products.

   

  • Perform plot creation and batch processing of time series data
  • Use any of the four general functional areas provided: time history, tabular data, x-y plotting and batch processing
  • Customizable for proprietary data formats
• JWAVE

  JWAVE is for network-based visual data analysis applications.

  • Provide quick access to and greater understanding of data from anywhere, at anytime
  • Quickly create 3-D surfaces, X-Y plots, polar plots, animations, contours, bar charts, histograms and more
  • Rapidly analyze, visualize and share critical information immediately across the organization, regardless of the computer platform

 

http://www.vni.com/products/wave/

 

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