MXV_OPENMP
Matrix Vector Multiplication Timings with OpenMP

MXV_OPENMP is a FORTRAN77 program which sets up several matrix vector multiplication problems y=A*x, and carries them out using

• "plain vanilla" FORTRAN;
• "plain vanilla" FORTRAN plus OpenMP parallelization;

The calculations are carried out for a variety of matrix shapes and sizes, and the elapsed wall clock time is measured and reported. The results are up to the user to analyze and explain!

Usage:

In the BASH shell, the program could be run with 2 threads using the commands:

        export OMP_NUM_THREADS=2
        ./mxv_openmp
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

MXV_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

DIJKSTRA_OPENMP, a FORTRAN77 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a FORTRAN77 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN77 program which prints out "Hello, world!" using the OpenMP parallel programming environment.

LINPACK_BENCH, a FORTRAN77 program which measures the time needed to factor and solve a "large" (N=1000) dense linear system of equations, and is used as a benchmark.

MANDELBROT_OPENMP, a FORTRAN77 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

MD_OPENMP, a FORTRAN77 program which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a FORTRAN77 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a FORTRAN77 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

MXV, a FORTRAN77 program which compares the performance of (DO I, DO J) loops and (DO J, DO I ) loops for computing the product of an MxN matrix A and an N vector X.

OPENMP, FORTRAN77 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

POISSON_OPENMP, a FORTRAN77 program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

PRIME_OPENMP, a FORTRAN77 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a FORTRAN77 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a FORTRAN77 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a FORTRAN77 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a FORTRAN77 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a FORTRAN77 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

TIMER, FORTRAN77 programs which demonstrate how to compute CPU time or elapsed time.

ZIGGURAT_OPENMP, a FORTRAN77 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

Reference:

1. Peter Arbenz, Wesley Petersen,
   Introduction to Parallel Computing - A practical guide with examples in C,
   Oxford University Press,
   ISBN: 0-19-851576-6,
   LC: QA76.58.P47.
2. Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan, Jeff McDonald, Ramesh Menon,
   Parallel Programming in OpenMP,
   Morgan Kaufmann, 2001,
   ISBN: 1-55860-671-8,
   LC: QA76.642.P32.
3. Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,
   Using OpenMP: Portable Shared Memory Parallel Processing,
   MIT Press, 2007,
   ISBN13: 978-0262533027,
   LC: QA76.642.C49.

Source Code:

• mxv_openmp.f, the source code.

Examples and Tests:

MXV_LOCAL runs the program locally.

• mxv_local.sh, commands to compile the program and run with 1, 2, 4, and 8 threads.
• mxv_local_output.txt, the output file.

MXV_ITHACA runs the program through ITHACA's batch system.

• mxv_ithaca.sh, commands to compile the program and run with 1, 2, 4, and 8 threads.
• mxv_ithaca_output.txt, the output file.

List of Routines:

• MAIN is the main program for MXV_OPENMP.
• TEST01 compares various algorithms for a given matrix size MxN.
• MATGEN generates a random matrix A and vector X.
• MXV_PLAIN computes y = A * x, using "plain" code.
• MXV_PLAIN_OPENMP computes y = A * x, using OpenMP parallel directives.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.