NAG Library for SMP & Multicore, Mark 22

FSFL622DA

Fujitsu HX600, Linux 64, Fujitsu Fortran, Double Precision

Users' Note



Contents


1. Introduction

This document is essential reading for every user of the NAG Library for SMP & Multicore implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Mark 22 Library Manual (which we will refer to as the Library Manual). Wherever that manual refers to the "Users' Note for your implementation", you should consult this note.

In addition, NAG recommends that before calling any Library routine you should read the following reference material (see Section 5):

(a) Essential Introduction
(b) Chapter Introduction
(c) Routine Document

The library supplied with this implementation has been compiled in a manner that facilitates the use of the OpenMP threading model. Lower-level threading models such as Pthreads are not supported.

2. Post Release Information

Please check the following URL:

http://www.nag.co.uk/doc/inun/fs22/fl6da/postrelease.html

for details of any new information related to the applicability or usage of this implementation.

3. General Information

3.1. Accessing the Library

In this section we assume that the library has been installed in the directory [INSTALL_DIR].

By default [INSTALL_DIR] (see Installer's Note (in.html)) is /opt/NAG/fsfl622da or /usr/local/NAG/fsfl622da depending on your system; however it could have been changed by the person who did the installation. To identify [INSTALL_DIR] for this installation:

To use the NAG Library for SMP & Multicore and the SSL II libraries, you may link in the following manner:
  frt -X9 -fw -Kthreadsafe -KOMP driver.f [INSTALL_DIR]/lib/libnagsmp.a \
-SSL2BLAMP
where driver.f is your application program .

If the compiled NAG Library for SMP & Multicore libraries and the SSL II libraries are installed in, or are pointed at by symbolic links from, directories in the search path of the linker, such as /usr/lib64, then you may alternatively link in the following manner:

  frt -X9 -fw -Kthreadsafe -KOMP driver.f -lnagsmp \
-SSL2BLAMP

3.1.1. Set the number of processors to use

Set the environment variable OMP_NUM_THREADS to the number of processors required, up to maximum available on your system, e.g. In the C shell type:
setenv OMP_NUM_THREADS N
In the Bourne shell, type:
set OMP_NUM_THREADS=N
export OMP_NUM_THREADS
where N is the number of processors required. OMP_NUM_THREADS may be re-set between each execution of the program, as desired.

3.2. Interface Blocks

The NAG Library for SMP & Multicore Interface Blocks define the type and arguments of each user callable NAG Library for SMP & Multicore routine. These are not essential to calling the NAG Library for SMP & Multicore from Fortran programs. Their purpose is to allow the Fortran compiler to check that NAG Library for SMP & Multicore routines are called correctly. The interface blocks enable the compiler to check that:

(a) subroutines are called as such;
(b) functions are declared with the right type;
(c) the correct number of arguments are passed; and
(d) all arguments match in type and structure.

These interface blocks have been generated automatically by analysing the source code for the NAG Library for SMP & Multicore. As a consequence, and because these files have been thoroughly tested, their use is recommended in preference to writing your own declarations.

The NAG Library for SMP & Multicore Interface Block files are organised by Library chapter. The module names are:

  nag_f77_a_chapter
  nag_f77_c_chapter
  nag_f77_d_chapter
  nag_f77_e_chapter
  nag_f77_f_chapter
  nag_f77_g_chapter
  nag_f77_h_chapter
  nag_f77_m_chapter
  nag_f77_p_chapter
  nag_f77_s_chapter
  nag_f77_x_chapter
These are supplied in pre-compiled form (.mod files) and they can be accessed by specifying the -Am -Ipathname option on each compiler invocation, where pathname ([INSTALL_DIR]/nag_interface_blocks) is the path of the directory containing the compiled interface blocks. The interface block files are also supplied in source form, but these are only required if the precompiled form is incompatible with the compiler in use.

In order to make use of these modules from existing Fortran 77 code, the following changes need to be made:

The above steps need to be done for each unit (main program, function or subroutine) in your code.

These changes are illustrated by showing the conversion of the Fortran 77 version of the example program for NAG Library for SMP & Multicore routine D01DAF. Please note that this is not exactly the same as the example program that is distributed with this implementation. Each change is surrounded by comments boxed with asterisks.

*     D01DAF Example Program Text
*     Mark 14 Revised. NAG Copyright 1989.
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_D_CHAPTER, ONLY: D01DAF
*                                                   *
*****************************************************
*     .. Parameters ..
      INTEGER          NOUT
      PARAMETER        (NOUT=6)
*     .. Local Scalars ..
      DOUBLE PRECISION ABSACC, ANS, YA, YB
      INTEGER          IFAIL, NPTS
*     .. External Functions ..
      DOUBLE PRECISION FA, FB, PHI1, PHI2A, PHI2B
      EXTERNAL         FA, FB, PHI1, PHI2A, PHI2B
*     .. External Subroutines ..
******************************************************
* EXTERNAL declarations need to be removed.          *
*     EXTERNAL         D01DAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      WRITE (NOUT,*) 'D01DAF Example Program Results'
      YA = 0.0D0
      YB = 1.0D0
      ABSACC = 1.0D-6
      WRITE (NOUT,*)
      IFAIL = 1
*
      CALL D01DAF(YA,YB,PHI1,PHI2A,FA,ABSACC,ANS,NPTS,IFAIL)
*
      IF (IFAIL.LT.0) THEN
         WRITE (NOUT,99998) ' ** D01DAF returned with IFAIL = ', IFAIL
      ELSE
*
         WRITE (NOUT,*) 'First formulation'
         WRITE (NOUT,99999) 'Integral =', ANS
         WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
         IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
         WRITE (NOUT,*)
         WRITE (NOUT,*) 'Second formulation'
         IFAIL = 1
*
         CALL D01DAF(YA,YB,PHI1,PHI2B,FB,ABSACC,ANS,NPTS,IFAIL)
*
         WRITE (NOUT,99999) 'Integral =', ANS
         WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
         IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
      END IF
*
99999 FORMAT (1X,A,F9.4)
99998 FORMAT (1X,A,I5)
      END
*
      DOUBLE PRECISION FUNCTION PHI1(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION Y
*     .. Executable Statements ..
      PHI1 = 0.0D0
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION PHI2A(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION Y
*     .. Intrinsic Functions ..
      INTRINSIC        SQRT
*     .. Executable Statements ..
      PHI2A = SQRT(1.0D0-Y*Y)
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION FA(X,Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION X, Y
*     .. Executable Statements ..
      FA = X + Y
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION PHI2B(Y)
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_X_CHAPTER, ONLY: X01AAF
*                                                   *
*****************************************************
*     .. Scalar Arguments ..
      DOUBLE PRECISION Y
*     .. External Functions ..
******************************************************
* Function Type declarations need to be removed.     *
*     DOUBLE PRECISION X01AAF
*                                                    *
******************************************************
******************************************************
* EXTERNAL declarations need to be removed.          *
*     EXTERNAL         X01AAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      PHI2B = 0.5D0*X01AAF(0.0D0)
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION FB(X,Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION X, Y
*     .. Intrinsic Functions ..
      INTRINSIC        COS, SIN
*     .. Executable Statements ..
      FB = Y*Y*(COS(X)+SIN(X))
      RETURN
      END

3.3. Example Programs

The example results distributed were generated at Mark 22, using the software described in Section 2.2 of the Installer's Note. These example results may not be exactly reproducible if the example programs are run in a slightly different environment (for example, a different Fortran compiler, a different compiler library, or a different set of BLAS or LAPACK routines). The results which are most sensitive to such differences are: eigenvectors (which may differ by a scalar multiple, often -1, but sometimes complex); numbers of iterations and function evaluations; and residuals and other "small" quantities of the same order as the machine precision.

Note that the example material has been adapted, if necessary, from that published in the Library Manual, so that programs are suitable for execution with this implementation with no further changes. The distributed example programs should be used in preference to the versions in the Library Manual wherever possible. The directory [INSTALL_DIR]/scripts contains a script nagsmp_example.

The example programs are most easily accessed by the command nagsmp_example, to link with the NAG static library libnagsmp.a and the SSL II libraries

This command will provide you with a copy of an example program (and its data, if any), compile the program and link it with the appropriate libraries (showing you the compile command so that you can recompile your own version of the program). Finally, the executable program will be run, presenting its output to stdout, which is redirected to a file.

The example program concerned, and the number of OpenMP threads to use, are specified by the arguments to the command, e.g.

nagsmp_example e04ucf 4
will copy the example program e04ucfe.f and its data file e04ucfe.d into the current directory and process them to produce the example program results in the file e04ucfe.r.

3.4. Interpretation of Bold Italicised Terms

In order to support all implementations of the Library, the Manual has adopted a convention of using bold italics to distinguish terms which have different interpretations in different implementations.

For this double precision implementation, the bold italicised terms used in the Library Manual should be interpreted as follows:

real                  means REAL
double precision      means DOUBLE PRECISION
complex               means COMPLEX
complex*16            means COMPLEX*16 (or equivalent)
basic precision       means DOUBLE PRECISION
additional precision  means quadruple precision
reduced precision     means REAL

Another important bold italicised term is machine precision, which denotes the relative precision to which double precision floating-point numbers are stored in the computer, e.g. in an implementation with approximately 16 decimal digits of precision, machine precision has a value of approximately 1.0D-16.

The precise value of machine precision is given by the routine X02AJF. Other routines in Chapter X02 return the values of other implementation-dependent constants, such as the overflow threshold, or the largest representable integer. Refer to the X02 Chapter Introduction for more details.

The bold italicised term block size is used only in Chapters F07 and F08. It denotes the block size used by block algorithms in these chapters. You only need to be aware of its value when it affects the amount of workspace to be supplied – see the parameters WORK and LWORK of the relevant routine documents and the Chapter Introduction.

In Chapters F06, F07 and F08, alternate routine names are available for BLAS and LAPACK derived routines. For details of the alternate routine names please refer to the relevant Chapter Introduction. Note that applications should reference routines by their BLAS/LAPACK names, rather than their NAG-style names, for optimum performance.

3.5. Explicit Output from NAG Routines

Certain routines produce explicit error messages and advisory messages via output units which have default values that can be reset by using X04AAF for error messages and X04ABF for advisory messages. (The default values are given in Section 4.) The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified.

4. Routine-specific Information

Any further information which applies to one or more routines in this implementation is listed below, chapter by chapter.
  1. F06, F07 and F08

    Many LAPACK routines have a "workspace query" mechanism which allows a caller to interrogate the routine to determine how much workspace to supply. Note that LAPACK routines from the Fujitsu Scientific Subroutine Library "SSL II" library may require a different amount of workspace from the equivalent NAG versions of these routines. Care should be taken when using the workspace query mechanism.

    In this implementation calls to Basic Linear Algebra Subprograms (BLAS) and the Linear Algebra PACKage (LAPACK) routines are implemented by calls to Fujitsu Scientific Subroutine Library "SSL II", except for the following routines:

    DBDSDC    DBDSQR    DDOT      DGBRFS    DGBSV     DGBSVX    DGBTRF    DGBTRS
    DGEBAL    DGEBRD    DGEES     DGEESX    DGEEV     DGEEVX    DGELS     DGELSD
    DGELSS    DGELSY    DGEMV     DGEQP3    DGEQRF    DGERFS    DGESDD    DGESV
    DGESVD    DGESVX    DGETRF    DGETRS    DGGES     DGGESX    DGGEV     DGGEVX
    DGGGLM    DGGLSE    DGGQRF    DGGRQF    DGTRFS    DGTSVX    DHSEIN    DLALSD
    DLASDA    DLASDQ    DOPGTR    DORGBR    DORGHR    DORGQR    DORGTR    DORMBR
    DORMHR    DORMQR    DORMTR    DPBRFS    DPBSV     DPBSVX    DPBTRS    DPORFS
    DPOSV     DPOSVX    DPOTRF    DPOTRS    DPPRFS    DPPSV     DPPSVX    DPPTRS
    DPTCON    DPTEQR    DPTRFS    DPTSVX    DSBEV     DSBEVD    DSBEVX    DSBGV
    DSBGVD    DSBGVX    DSBTRD    DSPEV     DSPEVD    DSPEVX    DSPGV     DSPGVD
    DSPGVX    DSPRFS    DSPSVX    DSTEBZ    DSTEDC    DSTEGR    DSTEIN    DSTEQR
    DSTEV     DSTEVD    DSTEVR    DSTEVX    DSYEV     DSYEVD    DSYEVR    DSYEVX
    DSYGV     DSYGVD    DSYGVX    DSYRFS    DSYSV     DSYSVX    DSYTRD    DTBRFS
    DTBTRS    DTPRFS    DTPTRS    DTRRFS    ZBDSQR    ZGBRFS    ZGBSV     ZGBSVX
    ZGBTRF    ZGBTRS    ZGEBAL    ZGEBRD    ZGEES     ZGEESX    ZGEEV     ZGEEVX
    ZGELS     ZGELSD    ZGELSS    ZGELSY    ZGEQP3    ZGEQRF    ZGERFS    ZGESDD
    ZGESV     ZGESVD    ZGESVX    ZGETRF    ZGETRS    ZGGES     ZGGESX    ZGGEV
    ZGGEVX    ZGGGLM    ZGGLSE    ZGGQRF    ZGGRQF    ZGTRFS    ZGTSVX    ZHBEV
    ZHBEVD    ZHBEVX    ZHBGV     ZHBGVD    ZHBGVX    ZHBTRD    ZHEEV     ZHEEVD
    ZHEEVR    ZHEEVX    ZHEGV     ZHEGVD    ZHEGVX    ZHERFS    ZHESV     ZHESVX
    ZHETRD    ZHPEV     ZHPEVD    ZHPEVX    ZHPGV     ZHPGVD    ZHPGVX    ZHPRFS
    ZHPSVX    ZHSEIN    ZLALSD    ZPBRFS    ZPBSV     ZPBSVX    ZPBTRS    ZPORFS
    ZPOSV     ZPOSVX    ZPOTRF    ZPOTRS    ZPPRFS    ZPPSV     ZPPSVX    ZPPTRS
    ZPTEQR    ZPTRFS    ZPTSVX    ZSPRFS    ZSPSVX    ZSTEDC    ZSTEGR    ZSTEIN
    ZSTEQR    ZSYCON    ZSYRFS    ZSYSV     ZSYSVX    ZSYTRF    ZTBRFS    ZTBTRS
    ZTPRFS    ZTPTRS    ZTRRFS    ZUNGBR    ZUNGHR    ZUNGQR    ZUNGTR    ZUNMBR
    ZUNMHR    ZUNMQR    ZUNMTR    ZUPGTR
    
  2. G02

    The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0D-13.
  3. P01

    On hard failure, P01ABF writes the error message to the error message unit specified by X04AAF and then stops.
  4. S07 - S21

    Functions in these chapters will give error messages if called with illegal or unsafe arguments. The constants referred to in the NAG Fortran Library Manual have the following values in this implementation:
    S07AAF  F_1   = 1.0E+13
            F_2   = 1.0E-14
    
    S10AAF  E_1   = 1.8715E+1
    S10ABF  E_1   = 7.080E+2
    S10ACF  E_1   = 7.080E+2
    
    S13AAF  X_hi  = 7.083E+2
    S13ACF  X_hi  = 2.2E+15
    S13ADF  X_hi  = 2.2E+15
    
    S14AAF  IFAIL  = 1 if X > 1.70E+2
            IFAIL  = 2 if X < -1.70E+2
            IFAIL  = 3 if abs(X) < 2.23E-308
    S14ABF  IFAIL  = 2 if X > X_big = 2.55E+305
    
    S15ADF  X_hi  = 2.65E+1
    S15AEF  X_hi  = 2.65E+1
    S15AFF  underflow trap was necessary
    S15AGF  IFAIL  = 1 if X >= 2.53E+307
            IFAIL  = 2 if 4.74E+7 <= X < 2.53E+307
            IFAIL  = 3 if X < -2.66E+1
    
    S17ACF  IFAIL  = 1 if X > 2.2E+15
    S17ADF  IFAIL  = 1 if X > 2.2E+15
            IFAIL  = 3 if 0.0E0 < X <= 2.23E-308
    S17AEF  IFAIL  = 1 if abs(X) > 2.2E+15
    S17AFF  IFAIL  = 1 if abs(X) > 2.2E+15
    S17AGF  IFAIL  = 1 if X > 1.038E+2
            IFAIL  = 2 if X < -2.3E+10
    S17AHF  IFAIL  = 1 if X > 1.041E+2
            IFAIL  = 2 if X < -2.3E+10
    S17AJF  IFAIL  = 1 if X > 1.041E+2
            IFAIL  = 2 if X < -1.9E+9
    S17AKF  IFAIL  = 1 if X > 1.041E+2
            IFAIL  = 2 if X < -1.9E+9
    S17DCF  IFAIL  = 2 if abs(Z) < 3.92223E-305
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
    S17DEF  IFAIL  = 2 if imag(Z) > 7.00921E+2
            IFAIL  = 3 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 1.07374E+9
    S17DGF  IFAIL  = 3 if abs(Z) > 1.02399E+3
            IFAIL  = 4 if abs(Z) > 1.04857E+6
    S17DHF  IFAIL  = 3 if abs(Z) > 1.02399E+3
            IFAIL  = 4 if abs(Z) > 1.04857E+6
    S17DLF  IFAIL  = 2 if abs(Z) < 3.92223E-305
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
    
    S18ADF  IFAIL  = 2 if 0.0E0 < X <= 2.23E-308
    S18AEF  IFAIL  = 1 if abs(X) > 7.116E+2
    S18AFF  IFAIL  = 1 if abs(X) > 7.116E+2
    S18DCF  IFAIL  = 2 if abs(Z) < 3.92223E-305
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
    S18DEF  IFAIL  = 2 if real(Z) > 7.00921E+2
            IFAIL  = 3 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 1.07374E+9
    
    S19AAF  IFAIL  = 1 if abs(X) >= 5.04818E+1
    S19ABF  IFAIL  = 1 if abs(X) >= 5.04818E+1
    S19ACF  IFAIL  = 1 if X > 9.9726E+2
    S19ADF  IFAIL  = 1 if X > 9.9726E+2
    
    S21BCF  IFAIL  = 3 if an argument < 1.583E-205
            IFAIL  = 4 if an argument >= 3.765E+202
    S21BDF  IFAIL  = 3 if an argument < 2.813E-103
            IFAIL  = 4 if an argument >= 1.407E+102
    
  5. X01

    The values of the mathematical constants are:
    X01AAF (pi)    = 3.1415926535897932
    X01ABF (gamma) = 0.5772156649015328
    
  6. X02

    The values of the machine constants are:
    The basic parameters of the model
    X02BHF = 2
    X02BJF = 53
    X02BKF = -1021
    X02BLF = 1024
    X02DJF = .TRUE.
    
    Derived parameters of the floating-point arithmetic
    X02AJF = 1.11022302462516E-16
    X02AKF = 2.22507385850721E-308
    X02ALF = 1.79769313486231E+308
    X02AMF = 2.22507385850721E-308
    X02ANF = 4.45014771701441E-308
    
    Parameters of other aspects of the computing environment
    X02AHF = 2.25179981368524E+15
    X02BBF = 2147483647
    X02BEF = 15
    X02DAF = .TRUE.
    
  7. X04

    The default output units for error and advisory messages for those routines which can produce explicit output are both Fortran Unit 6.

5. Documentation

The Library Manual is available as part of the installation or via download from the NAG website. The most up-to-date version of the documentation is accessible via the NAG website at http://www.nag.co.uk/numeric/FL/FSdocumentation.asp.

The Library Manual is supplied in the following formats:

The following main index files have been provided for these formats:

	nagdoc_fl22/xhtml/FRONTMATTER/manconts.xml
	nagdoc_fl22/pdf/FRONTMATTER/manconts.pdf
	nagdoc_fl22/html/FRONTMATTER/manconts.html
Use your web browser to navigate from here.

Advice on viewing and navigating the formats available can be found in the Online Documentation document.

In addition the following are provided:

6. Support from NAG

(a) Contact with NAG

Queries concerning this document or the implementation generally should be directed to NAG at one of the addresses given in the Appendix. Users subscribing to the support service are encouraged to contact one of the NAG Response Centres (see below).

(b) NAG Response Centres

The NAG Response Centres are available for general enquiries from all users and also for technical queries from sites with an annually licensed product or support service.

The Response Centres are open during office hours, but contact is possible by fax, email and phone (answering machine) at all times.

When contacting a Response Centre, it helps us deal with your enquiry quickly if you can quote your NAG site reference or account number and NAG product code (in this case FSFL622DA).

(c) NAG Websites

The NAG websites provide information about implementation availability, descriptions of products, downloadable software, product documentation and technical reports. The NAG websites can be accessed at the following URLs:

http://www.nag.co.uk/, http://www.nag.com/ or http://www.nag-j.co.jp/

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To ensure that you receive information on updates and other relevant announcements, please register this product with us. For NAG Library products this may be accomplished by filling in the online registration form at http://www.nag.co.uk/numeric/Library_Registration.asp.

7. User Feedback

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Appendix - Contact Addresses

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