QUAD2_OPENMP
Quadrature using OpenMP

QUAD2_OPENMP is a FORTRAN77 program which approximates a multidimensional integral using a quadrature rule. The quadrature computation is done with OpenMP.

The quadrature rule is defined by three text files:

1. the "X" file lists the abscissas (N rows, M columns);
2. the "W" file lists the weights (N rows);
3. the "R" file lists the integration region corners (2 rows, M columns);

The program assumes that the names of the three files can be deduced from the file_root. For instance, if the file_root was "cc_d2_level5", this implies that

1. the "X" file is cc_d2_level5_x.txt;
2. the "W" file is cc_d2_level5_w.txt;
3. the "R" file is cc_d2_level5_r.txt;

On an Apple PowerPC G5 with two processors, the following results were observed:

Threads	Quadrature rule	Time
1	cc_d10_level4	0.0026 seconds
2	cc_d10_level4	0.0015 seconds
4	cc_d10_level4	0.0015 seconds
1	cc_d10_level5	0.012 seconds
2	cc_d10_level5	0.0077 seconds
4	cc_d10_level5	0.0065 seconds

Usage:

        export OMP_NUM_THREADS=2
        ./quad2_openmp file_root
      

Licensing:

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

Languages:

QUAD2_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

CLENSHAW_CURTIS is a FORTRAN90 library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.

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

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

HEATED_PLATE_OPENMP is 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.

INTEGRAL_TEST is a FORTRAN90 program which uses test integrals to evaluate sets of quadrature points.

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

MPI is a directory of FORTRAN77 examples which illustrate the use of the MPI application program interface for carrying out parallel computatioins in a distributed memory environment.

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 is 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 is a directory of FORTRAN77 examples which illustrate the use of the OpenMP application program interface for carrying out parallel computatioins in a shared memory environment.

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

PRODUCT_RULE is a FORTRAN90 program which can create a multidimensional quadrature rule as a product of one dimensional rules.

QUAD_MPI is a FORTRAN77 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using MPI.

QUADRATURE_RULES is a dataset directory which contains many examples of files that define quadrature rules.

QUADRATURE_TEST is a FORTRAN90 program which reads files defining a quadrature rule, and applies them to all the test integrals defined by TEST_NINT.

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

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

STROUD is a FORTRAN90 library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TEST_NINT is a FORTRAN90 library which defines a set of integrand functions to be used for testing multidimensional quadrature rules and routines.

TESTPACK is a FORTRAN90 library which defines a set of integrands used to test multidimensional quadrature.

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. 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.
2. Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,
   Using OpenMP: Portable Shared Memory Parallel Processing,
   MIT Press, 2007,
   ISBN13: 978-0262533027.
3. Tim Mattson, Rudolf Eigenmann,
   OpenMP: An API for Writing Portable SMP Application Software,
   a slide presentation,
   openmp_slides.pdf.
4. libgomp.pdf,
   The GNU OpenMP Implementation.
5. The OpenMP web site
6. OpenMP Architecture Review Board,
   OpenMP C and C++ Application Program Interface,
   Version 2.0,
   March 2002.
7. OpenMP Architecture Review Board,
   OpenMP Fortran Application Program Interface,
   Version 2.0,
   November 2000.

Source Code:

• quad2_openmp.f, the source code.
• quad2_openmp.sh, BASH commands to compile and load the source code.

Examples and Tests:

CC_D10_LEVEL4 is a Clenshaw-Curtis sparse grid rule for a 10 dimensional hypercube, at the 4th level of fineness.

• cc_d10_level4_r.txt, the "R" file.
• cc_d10_level4_w.txt, the "W" file.
• cc_d10_level4_x.txt, the "X" file.
• cc_d10_level4_nt1_output.txt, the output file, using 1 thread (on a 2 processor machine).
• cc_d10_level4_nt2_output.txt, the output file, using 2 threads (on a 2 processor machine).
• cc_d10_level4_nt4_output.txt, the output file, using 4 threads (on a 2 processor machine).

CC_D10_LEVEL5 is a Clenshaw-Curtis sparse grid rule for a 10 dimensional hypercube, at the 5th level of fineness.

• cc_d10_level5_r.txt, the "R" file.
• cc_d10_level5_w.txt, the "W" file.
• cc_d10_level5_x.txt, the "X" file.
• cc_d10_level5_nt1_output.txt, the output file, using 1 thread (on a 2 processor machine).
• cc_d10_level5_nt2_output.txt, the output file, using 2 threads (on a 2 processor machine).
• cc_d10_level5_nt4_output.txt, the output file, using 4 threads (on a 2 processor machine).

List of Routines:

• MAIN is the main program for QUAD_OPENMP.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads data from a DTABLE file.
• DTABLE_HEADER_READ reads the header from a DTABLE file.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• S_TO_I4 reads an I4 from a string.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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