SGEFA_OPENMP
Sequential and OpenMP versions of Linpack Solver

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

A comparison is made between

• SGEFA_C, a version of the algorithm with column-oriented updating;
• SGEFA_C_OMP, a version of the algorithm with column-oriented updating and OpenMP.
• SGEFA_R, a version of the algorithm with row-oriented updating;
• SGEFA_R_OMP, a version of the algorithm with row-oriented updating and OpenMP.

Licensing:

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

Languages:

SGEFA_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_S, a FORTRAN77 library which factors and solves systems of linear equations in a variety of formats and arithmetic types.

LINPACK_BENCH, a FORTRAN77 program which measures the time taken by LINPACK to solve a particular linear system.

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_OPENMP, a FORTRAN77 program which compares the performance of plain vanilla Fortran and the FORTRAN90 intrinsic routine MATMUL, for the matrix multiplication problem y=A*x, with and without parallelization by OpenMP.

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

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

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.

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.

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.
4. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
5. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• sgefa_openmp.f, the source code.
• sgefa_openmp.sh, commands to compile and link the source code.

Examples and Tests:

SGEFA_LOCAL runs the program locally.

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

List of Routines:

• MAIN is the main program for the SGEFA_OPENMP test program.
• TEST_SGEFA tests the original version of SGEFA.
• TEST_SGEFA_C tests SGEFA_C.
• TEST_SGEFA_C_OMP tests SGEFA_C_OMP.
• TEST_SGEFA_R tests SGEFA_R.
• TEST_SGEFA_R_OMP tests SGEFA_R_OMP.
• ISAMAX finds the index of element having maximum absolute value.
• MATGEN generates a "random" matrix for testing.
• SAXPY computes constant times a vector plus a vector.
• SDOT forms the dot product of two vectors.
• SGEFA factors a real matrix by gaussian elimination.
• SGEFA_C factors a matrix by gaussian elimination.
• SGEFA_C_OMP factors a matrix by gaussian elimination.
• SGEFA_R factors a matrix by gaussian elimination.
• SGEFA_R_OMP factors a matrix by gaussian elimination.
• SGESL solves a linear system factored by SGEFA.
• SSCAL scales a vector by a constant.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

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