QUAD_OPEN_MP
Quadrature using OpenMP

QUAD_OPEN_MP is a FORTRAN90 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	0.0019 seconds
2	cc_d10_level4	0.0011 seconds
4	cc_d10_level4	0.0012 seconds
1	cc_d10_level5	0.0086 seconds
2	cc_d10_level5	0.0045 seconds
4	cc_d10_level5	0.0046 seconds

Usage:

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

        export OMP_NUM_THREADS=2
        quad_open_mp file_root
      

Licensing:

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

Related Data and Programs:

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

FFT_OPEN_MP is a FORTRAN90 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

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

MD_OPEN_MP is a FORTRAN90 program which carries out a molecular dynamics simulation using OpenMP.

MPI is a directory of FORTRAN90 examples which illustrate the use of the MPI application program interface for carrying out parallel computatioins in a distributed memory environment.

MXV_OPEN_MP is a FORTRAN90 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.

OPEN_MP is a directory of FORTRAN90 examples which illustrate the use of the OpenMP application program interface for carrying out parallel computatioins in a shared memory environment.

OPEN_MP_ITHACA FORTRAN90 programs which illustrate the use of OpenMP on the Virginia Tech ITHACA cluster.

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

QUAD_MPI is a FORTRAN90 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using MPI.

QUAD_OPEN_MP is also available in a C version and a C++ version and a FORTRAN77 version.

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.

PETSC is a scientific library for parallel computations.

SATISFIABILITY_OPEN_MP is a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SGEFA_OPEN_MP is a FORTRAN90 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

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

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

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

ZIGGURAT_OPEN_MP, a FORTRAN90 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,
   open_mp_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:

• quad_open_mp.f90, the source code.
• quad_open_mp.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_OPEN_MP.
• 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 FORTRAN90 source codes.