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Courseware - Numeric Algorithm Examples

  • Parallel algorithm implementing Strassen’s Algorithm for matrix-matrix multiplication ( Akshay Singh)
  • Material Type:

    Coding example, Problem set

    ISN Logo

    Technical Format:

    PDF document, zip archive, text file

    Location:

    Go to materials

    Date Added:

    04/12/2010

    Date Modified:

    04/12/2010

    Author

    Akshay Singh, Intel Threading Challenge
    Description:

    The included source code implements Strassen’s Algorithm for matrix-matrix multiplication in parallel, as described in the included problem description text file. The parallel algorithm uses Pthreads to implement a thread pool and the standard recursive algorithm to create smaller instances of the matrix multiplication. The smaller instances become tasks that can be assigned to threads within the thread pool. The code was intended for Linux OS and includes a makefile to build the application.

    Recommended Audience:
    Programmers experienced in C/C++ and Pthreads; students of linear algebra with C/C++ and parallel programming skill

    DISCLAIMER: This code is provided by the author as a submitted contest entry, and is intended for educational use only. The code is not guaranteed to solve all instances of the input data sets and may require modifications to work in your own specific environment.

    Recommended Audience:

    Advanced programmers, Beginning programmers, Undergraduate students

    Language:

    English

    Keywords:

    Strassens Algorithm, matrixmatrix multiplication, POSIX Threads, linear algebra, Pthreads, thread pool
  • Parallel algorithm implementing Strassen’s Algorithm for matrix-matrix multiplication (Bradley Kuszmaul)
  • Material Type:

    Coding example, Problem set

    ISN Logo

    Technical Format:

    text file, zip archive, PDF document

    Location:

    Go to materials

    Date Added:

    04/12/2010

    Date Modified:

    04/12/2010

    Author

    Bradley Kuszmaul, MIT Computer Science and Artificial Intelligence Laboratory
    Description:

    The included source code implements Strassen’s Algorithm for matrix-matrix multiplication in parallel, as described in the included problem description text file. The included write-up gives an overview of Cilk++ and some of the tools available for Cilk programming. Six different methods for computing matrix-matrix multiplication are discussed. The pros and cons of the parallelization (using Cilk++) of each method and the performance of each on different sized matrices are provided within the write-up. Source files for the alternate algorithms are provided and these alternatives can be built for comparison against each other. The code was intended for Linux OS and includes a makefile to build the applications.

    Recommended Audience:
    Programmers experienced in C/C++ (some exposure to Cilk++ and parallel programming is helpful); students of linear algebra with C/C++ and parallel programming skill.

    DISCLAIMER: This code is provided by the author as a submitted contest entry, and is intended for educational use only. The code is not guaranteed to solve all instances of the input data sets and may require modifications to work in your own specific environment.

    Recommended Audience:

    Advanced programmers, Beginning programmers, Undergraduate students

    Language:

    English

    Keywords:

    Strassens Algorithm, matrixmatrix multiplication, Cilk++, linear algebra, Goto BLAS, Intel Math Kernel Library MKL, divide and conquer, MKL
  • Parallel algorithm implementing Strassen’s Algorithm for matrix-matrix multiplication ( G. Koloskov)
  • Material Type:

    Coding example, Problem set

    ISN Logo

    Technical Format:

    text file, PDF document, zip archive

    Location:

    Go to materials

    Date Added:

    04/12/2010

    Date Modified:

    04/12/2010

    Author

    G Koloskov, Intel Threading Challenge
    Description:

    The included source code implements Strassen’s Algorithm for matrix-matrix multiplication in parallel, as described in the included problem description text file. The parallel algorithm uses OpenMP* to implement the standard recursive algorithm. However, to better load balance the work assigned to threads, the code has been written to handle non-square matrix instances by detecting small matrix dimensions and not subdividing such matrices. The code was intended for Linux OS and includes a makefile to build the application.

    DISCLAIMER: This code is provided by the author as a submitted contest entry, and is intended for educational use only. The code is not guaranteed to solve all instances of the input data sets and may require modifications to work in your own specific environment.

    Recommended Audience:

    Advanced programmers, Beginning programmers, Undergraduate students

    Language:

    English

    Keywords:

    Strassens Algorithm, matrixmatrix multiplication, OpenMP, linear algebra, load balance
  • Parallel algorithm implementing Strassen’s Algorithm for matrix-matrix multiplication (Intel)
  • Material Type:

    Coding example, Problem set

    ISN Logo

    Technical Format:

    PDF document, text file, zip archive

    Location:

    Go to materials

    Date Added:

    04/12/2010

    Date Modified:

    04/12/2010

    Author

    Byung Kim, Intel
    Description:

    The included source code implements Strassen’s Algorithm for matrix-matrix multiplication in parallel, as described in the included problem description text file. The parallel algorithm uses Intel Threading Building Blocks (TBB) to implement the parallelization from the standard recursive algorithm. Three alternatives for creating TBB tasks are examined: Breadth-First spawning (uses too much memory), Depth-First spawning (less memory, but less parallelism), and Half-and-Half (best features of previous methods). The implemented code has two phases of tasks generated. The temporary matrices used in the first phase are used in the second phase to cut down the memory requirements. The write-up projects that there are enough tasks and sub-tasks generated by the Half-and-Half method to keep at least 8 cores busy. The code was intended for Linux OS and includes a makefile to build the application.

    DISCLAIMER: This code is provided by the author as a submitted contest entry, and is intended for educational use only. The code is not guaranteed to solve all instances of the input data sets and may require modifications to work in your own specific environment.

    Recommended Audience:

    Advanced programmers, Beginning programmers, Undergraduate students

    Language:

    English

    Keywords:

    Strassens Algorithm, Intel Threading Building Blocks, TBB, tasks, linear algebra, matrixmatrix multiplication, BreadthFirst spawning, DepthFirst spawning
  • Implementing Strassen’s Algorithm for matrix-matrix multiplication with OpenMP* 3.0 tasks (Intel)
  • Material Type:

    Lecture / Presentation, Coding example, Problem set

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    Technical Format:

    text file, .docx, .pptx, .icproj, .sln, .suo, .vcproj, zip archive

    Location:

    Go to materials

    Date Added:

    03/31/2010

    Date Modified:

    03/31/2010

    Author

    Clay Breshears, Intel Software
    Description:

    he included source code implements Strassen’s Algorithm for matrix-matrix multiplication in parallel using OpenMP* 3.0 tasks. Microsoft Visual Studio* solution and project files are included to build the application for testing. The PowerPoint* lecture foils describe 1) the standard triple-nested algorithm and how different insertion points of OpenMP* pragmas will affect the parallelism to be expected, 2) a recursive algorithm with the same number of multiplication operations, and 3) the Strassen’s Algorithm and how to use OpenMP* 3.0 task constructs to parallelize the recursive calls. The write-up follows the outline in the PowerPoint presentation. Potential modifications to the included code that may have an effect on parallel performance are postualted in both the PowerPoint and written description of the code development for Strassen’s Algorithm. These modifications could be assigned as lab exercises by students to determine if there is any significant performance benefit to the potential optimizations.

    Recommended Audience
    Programmers experienced in C/C++ and OpenMP* 3.0 task constructs; students of linear algebra with C/C++ and parallel programming skill

    Recommended Audience:

    Beginning programmers, Undergraduate students

    Language:

    English

    Keywords:

    matrixmatrix multiplication, OpenMP, OpenMP task constructs, recursion, linear algebra, C++, Strassens Algorithm