QUAD_MPI
Quadrature using MPI

QUAD_MPI is a FORTRAN90 program which approximates a multidimensional integral using a quadrature rule. The computation is done in parallel by using MPI.

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;

Usage:

quad_mpi file_root

Related Data and Programs:

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

HEAT_MPI is a FORTRAN90 program which solves the 1D Time Dependent Heat Equation using MPI.

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

MPI is a library of routines for doing parallel programming in a distributed memory environment, using message passing.

OPEN_MP is a library of routines, and a set of compiler directives, which enable parallel programming in a shared memory environment.

PESSL is a parallel mathematical library for use on IBM SP systems.

PETSC is a scientific library for parallel computations.

PRODUCT_RULE is a FORTRAN90 program which constructs a product quadrature rule from identical 1D factor rules.

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

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

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.

RANDOM_MPI, a FORTRAN90 program which demonstrates one way to generate the same sequence of random numbers for both sequential execution and parallel execution under MPI.

SATISFIABILITY_MPI is a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using MPI to carry out the calculation in parallel.

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.

Reference:

1. William Gropp, Steven Huss-Lederman, Andrew Lumsdaine, Ewing Lusk, Bill Nitzberg, William Saphir, Marc Snir,
   MPI: The Complete Reference,
   Volume II: The MPI-2 Extensions,
   Second Edition,
   MIT Press, 1998.
2. William Gropp, Ewing Lusk, Anthony Skjellum,
   Using MPI: Portable Parallel Programming with the Message-Passing Interface,
   Second Edition,
   MIT Press, 1999,
   ISBN: 0262571323.
3. William Gropp, Ewing Lusk, Rajiv Thakur,
   Using MPI-2: Advanced Features of the Message-Passing Interface,
   Second Edition,
   MIT Press, 1999,
   ISBN: 0262571331.
4. Stan Openshaw, Ian Turton,
   High Performance Computing and the Art of Parallel Programming: an Introduction for Geographers, Social Scientists, and Engineers,
   Routledge, 2000,
   ISBN: 0415156920.
5. Peter Pacheco,
   Parallel Programming with MPI,
   Morgan Kaufman, 1996,
   ISBN: 1558603395,
   LC: QA76.642.P3.
6. Sudarshan Raghunathan,
   Making a Supercomputer Do What You Want: High Level Tools for Parallel Programming,
   Computing in Science and Engineering,
   Volume 8, Number 5, September/October 2006, pages 70-80.
7. Marc Snir, Steve Otto, Steven Huss-Lederman, David Walker, Jack Dongarra,
   MPI: The Complete Reference,
   Volume I: The MPI Core,
   Second Edition,
   MIT Press, 1998,
   ISBN: 0-262-69216-3,
   LC: QA76.642.M65.
8. Scott Vetter, Yukiya Aoyama, Jun Nakano,
   RS/600 SP: Practical MPI Programming,
   IBM Redbooks, 1999,
   ISBN: 0738413658.
9. The MPI web site at Argonne National Lab: http://www-unix.mcs.anl.gov/mpi/
10. The Message Passing Interface Forum,
    MPI: A Message Passing Interface Standard,
    1995,
    Available online from the MPI Forum.
11. The Message Passing Interface Forum,
    MPI-2: Extensions to the Message Passing Interface,
    1997,
    Available online from the MPI Forum.

Source Code:

• quad_mpi.f90, the source code.
• quad_mpi_sysx.sh, BASH commands to compile, link and load the source code on System X.

Examples and Tests:

CC_D2_LEVEL5 is a quadrature rule for dimension 2, of the fifth level of fineness. Our test involves having the program read this rule, and apply it to estimate the integral of a test function.

• cc_d2_level5_r.txt, the "R" file for the quadrature rule, which defines the region.
• cc_d2_level5_w.txt, the "W" file for the quadrature rule, which defines the weights.
• cc_d2_level5_x.txt, the "X" file for the quadrature rule, which defines the abscissas.
• cc_d2_level5_output.txt, the output file.
• cc_d2_level5.sh, BASH commands submitted to PBS on System X, to execute the program using the CC_D2_LEVEL5 quadrature rule.

List of Routines:

• MAIN is the main program for QUAD_MPI.
• 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.
• I4_DIV_ROUNDED computes the rounded result of I4 division.
• I4_HUGE returns a "huge" I4.
• I4_SIGN evaluates the sign of an I4.
• 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.
• P28_EXACT returns the exact integral for problem 28.
• P28_F evaluates the integrand for problem 28.

You can go up one level to the FORTRAN90 source codes.