NAG Library for SMP & Multicore, Mark 23

FSL6I23DCL - License Managed

Linux 64 (Intel 64 / AMD64), Intel 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 23 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 libraries supplied with this implementation have been compiled in a manner that facilitates their use within a multithreaded application. If you intend to use the NAG library within a multithreaded application please refer to the document on Thread Safety in the Library Manual (see Section 5).

Further information about using the supplied Intel MKL libraries with threaded applications is available at http://software.intel.com/en-us/articles/intel-math-kernel-library-intel-mkl-using-intel-mkl-with-threaded-applications.

2. Post Release Information

Please check the following URL:

http://www.nag.co.uk/doc/inun/fs23/l6idcl/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/fsl6i23dcl or /usr/local/NAG/fsl6i23dcl 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 supplied Intel MKL libraries, you may link in the following manner:
  ifort -openmp -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \
      [INSTALL_DIR]/lib/libnagsmp.a -Wl,--start-group [INSTALL_DIR]/mkl10.3/libmkl_intel_lp64.a \
      [INSTALL_DIR]/mkl10.3/libmkl_intel_thread.a [INSTALL_DIR]/mkl10.3/libmkl_core.a -Wl,--end-group
where driver.f90 is your application program ; or
  ifort -openmp -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \
      [INSTALL_DIR]/lib/libnagsmp.so [INSTALL_DIR]/mkl10.3/libmkl_rt.so 
if the shareable library is required. Please note the shareable library is fully resolved so that, as long as the environment variable LD_LIBRARY_PATH is set correctly at link time (see below), you need not link against other run-time libraries explicitly.

If your application has been linked with the shareable NAG and MKL libraries then the environment variable LD_LIBRARY_PATH must be set or extended, as follows, to allow run-time linkage.

In the C shell, type:

  setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3
to set LD_LIBRARY_PATH, or
  setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3:${LD_LIBRARY_PATH}
to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

  LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3
  export LD_LIBRARY_PATH
to set LD_LIBRARY_PATH, or
  LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3:${LD_LIBRARY_PATH}
  export LD_LIBRARY_PATH
to extend LD_LIBRARY_PATH if you already have it set.

Note that you may also need to set LD_LIBRARY_PATH to point at other things such as compiler run-time libraries, for example if you are using a newer version of the compiler.

If you are using a different compiler, you may need to link against the Intel ifort compiler run-time libraries provided in [INSTALL_DIR]/rtl.

3.1.1. Setting the number of threads to use

Set the environment variable OMP_NUM_THREADS to the number of threads required, up to the maximum available on your system.

In the C shell type:

  setenv OMP_NUM_THREADS N
In the Bourne shell, type:
  OMP_NUM_THREADS=N
  export OMP_NUM_THREADS
where N is the number of threads required. OMP_NUM_THREADS may be re-set between each execution of the program, as desired.

In general, the maximum number of threads you are recommended to use is the number of physical cores on your SMP system. However, newer Intel processors (Nehalem or later) support a facility known as Hyperthreading, which allows each physical core to support up to two threads at the same time and thus appear to the operating system as two logical cores. It may be beneficial to make use of this functionality, but this choice will depend on the particular algorithms and problem size(s) used. You are advised to benchmark performance critical applications with and without Hyperthreading enabled, to determine the best choice for you. Enabling and disabling Hyperthreading normally requires setting the desired choice in the BIOS on your system.

The supplied Intel MKL libraries include additional environment variables to allow greater control of the threading within MKL. These are discussed at http://software.intel.com/en-us/articles/intel-math-kernel-library-intel-mkl-intel-mkl-100-threading. Many NAG routines make calls to routines within MKL, thus the MKL environment variables may indirectly affect the operation of the NAG library as well. The default settings of the MKL environment variables should be suitable for most purposes, thus it is recommended that you do not explicitly set these variables. Please contact NAG for further advice if required.

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. However, they are required if the supplied examples are used. 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.

The NAG Library for SMP & Multicore interface block files are organised by Library chapter. They are aggregated into one module named

  nag_library
The modules are supplied in pre-compiled form (.mod files) and they can be accessed by specifying the -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 .mod module files were compiled with the compiler shown in Section 2.1 of the Installer's Note. Such module files are compiler-dependent, so if you wish to use the NAG example programs, or use the interface blocks in your own programs, when using a compiler that is incompatible with these modules, you will first need to create your own module files. See the Post Release Information page

http://www.nag.co.uk/doc/inun/fs23/l6idcl/postrelease.html

where more information may be available, or contact NAG for further help.

3.3. Example Programs

The example results distributed were generated at Mark 23, 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 Basic Linear Algebra Subprograms (BLAS) or Linear Algebra PACKage (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 two scripts nagsmp_example and nagsmp_example_shar.

The example programs are most easily accessed by one of the commands

Each command will provide you with a copy of an example program (and its data and options file, 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 with appropriate arguments specifying data, options and results files as needed.

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

nagsmp_example e04nrf 4
will copy the example program and its data and options files (e04nrfe.f90, e04nrfe.d and e04nrfe.opt) into the current directory, compile the program and run it using 4 OpenMP threads to produce the example program results in the file e04nrfe.r.

3.4. Fortran Types and Interpretation of Bold Italicised Terms

The NAG Library and documentation use parameterized types for floating-point variables. Thus, the type

      REAL(KIND=nag_wp)
appears in documentation of all NAG Library for SMP & Multicore routines, where nag_wp is a Fortran KIND parameter. The value of nag_wp will vary between implementations, and its value can be obtained by use of the nag_library module. We refer to the type nag_wp as the NAG Library "working precision" type, because most floating-point arguments and internal variables used in the library are of this type.

In addition, a small number of routines use the type

      REAL(KIND=nag_rp)
where nag_rp stands for "reduced precision type". Another type, not currently used in the library, is
      REAL(KIND=nag_hp)
for "higher precision type" or "additional precision type".

For correct use of these types, see almost any of the example programs distributed with the Library.

For this implementation, these types have the following meanings:

      REAL (kind=nag_rp)      means REAL (i.e. single precision)
      REAL (kind=nag_wp)      means DOUBLE PRECISION
      COMPLEX (kind=nag_rp)   means COMPLEX (i.e. single precision complex)
      COMPLEX (kind=nag_wp)   means double precision complex (e.g. COMPLEX*16)

In addition, the Manual has adopted a convention of using bold italics to distinguish some terms.

One 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.

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.) These routines are potentially not thread safe and in general output is not recommended in a multithreaded environment.

4. Routine-specific Information

Any further information which applies to one or more routines in this implementation is listed below, chapter by chapter.
  1. C06

    In this implementation calls to the Intel Discrete Fourier Transforms Interface (DFTI) routines, from the supplied MKL library, are made whenever possible in the following NAG routines:
     C06PAF  C06PCF  C06PFF  C06PJF  C06PKF  C06PPF  C06PQF  C06PRF
     C06PSF  C06PUF  C06PXF  C06RAF  C06RBF  C06RCF  C06RDF
    
    The Intel DFTI routines allocate their own workspace internally, so no changes are needed to the size of workspace array WORK passed to the NAG C06 routines listed above from that specified in their respective library documents.
  2. F06, F07, F08 and F16

    In Chapters F06, F07, F08 and F16, 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.

    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 MKL 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 BLAS and LAPACK routines are implemented by calls to MKL, except for the following routines:

    BLAS_DMAX_VAL    BLAS_DMIN_VAL
    DASUM     DBDSDC    DDOT      DGBRFS    DGBSV     DGBSVX    DGBTRF    DGECON
    DGEES     DGEESX    DGEEV     DGEEVX    DGELS     DGELSD    DGELSS    DGELSY
    DGEQP3    DGERFS    DGESDD    DGESV     DGESVD    DGESVX    DGGES     DGGESX
    DGGEV     DGGEVX    DGGGLM    DGGLSE    DGGQRF    DGGRQF    DGTRFS    DGTSVX
    DHSEIN    DOPGTR    DORGBR    DORGHR    DORGQR    DORGTR    DORMBR    DORMHR
    DORMTR    DPBRFS    DPBSV     DPBSVX    DPORFS    DPOSV     DPOSVX    DPPRFS
    DPPSV     DPPSVX    DPPTRF    DPTEQR    DPTRFS    DPTSVX    DSBEV     DSBEVD
    DSBEVX    DSBGV     DSBGVD    DSBGVX    DSBTRD    DSGESV    DSPEV     DSPEVD
    DSPEVX    DSPGV     DSPGVD    DSPGVX    DSPRFS    DSPSVX    DSTEBZ    DSTEDC
    DSTEGR    DSTEIN    DSTEV     DSTEVD    DSTEVR    DSTEVX    DSYEV     DSYEVD
    DSYEVR    DSYEVX    DSYGV     DSYGVD    DSYGVX    DSYRFS    DSYSV     DSYSVX
    DSYTRF    DTBRFS    DTBTRS    DTGSYL    DTPRFS    DTPTRS    DTRRFS    ZCGESV
    ZGBRFS    ZGBSV     ZGBSVX    ZGBTRF    ZGEES     ZGEESX    ZGEEV     ZGEEVX
    ZGELS     ZGELSD    ZGELSS    ZGELSY    ZGEQP3    ZGERFS    ZGESDD    ZGESV
    ZGESVD    ZGESVX    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    ZHESVX    ZHPEV     ZHPEVD    ZHPEVX    ZHPGV
    ZHPGVD    ZHPGVX    ZHPRFS    ZHPSVX    ZHSEIN    ZPBRFS    ZPBSV     ZPBSVX
    ZPORFS    ZPOSV     ZPOSVX    ZPPRFS    ZPPSV     ZPPSVX    ZPTEQR    ZPTRFS
    ZPTSVX    ZSPRFS    ZSPSVX    ZSTEDC    ZSTEGR    ZSTEIN    ZSYRFS    ZSYSVX
    ZTBRFS    ZTBTRS    ZTGSYL    ZTPRFS    ZTPTRS    ZTRRFS    ZUNGBR    ZUNGHR
    ZUNGQR    ZUNGTR    ZUNMBR    ZUNMHR    ZUNMTR    ZUPGTR
    

    The following NAG named routines are wrappers to call LAPACK routines from the vendor library:
    F07ADF/DGETRF    F07AEF/DGETRS    F07ARF/ZGETRF    F07ASF/ZGETRS
    F07BEF/DGBTRS    F07BSF/ZGBTRS    F07FDF/DPOTRF    F07FEF/DPOTRS
    F07FRF/ZPOTRF    F07FSF/ZPOTRS    F07GEF/DPPTRS    F07GSF/ZPPTRS
    F07HEF/DPBTRS    F07HSF/ZPBTRS    F08AEF/DGEQRF    F08AGF/DORMQR
    F08ASF/ZGEQRF    F08AUF/ZUNMQR    F08FEF/DSYTRD    F08FSF/ZHETRD
    F08JEF/DSTEQR    F08JSF/ZSTEQR    F08KEF/DGEBRD    F08KSF/ZGEBRD
    F08MEF/DBDSQR    F08MSF/ZBDSQR
    
  3. G02

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

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

    Functions in these Chapters will give error messages if called with illegal or unsafe arguments.

    The constants referred to in the 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 = 1.0E+16
    S13ADF  x_hi = 1.0E+17
    
    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 > 1.0E+16
    S17ADF  IFAIL = 1 if X > 1.0E+16
            IFAIL = 3 if 0 < X <= 2.23E-308
    S17AEF  IFAIL = 1 if abs(X) > 1.0E+16
    S17AFF  IFAIL = 1 if abs(X) > 1.0E+16
    S17AGF  IFAIL = 1 if X > 1.038E+2
            IFAIL = 2 if X < -5.7E+10
    S17AHF  IFAIL = 1 if X > 1.041E+2
            IFAIL = 2 if X < -5.7E+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 Im(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 < 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 Re(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
    
  6. X01

    The values of the mathematical constants are:

    X01AAF (pi) = 3.1415926535897932
    X01ABF (gamma) = 0.5772156649015328
    
  7. 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 = 2.22507385850721E-308

    Parameters of other aspects of the computing environment

    X02AHF = 1.42724769270596E+45 X02BBF = 2147483647 X02BEF = 15 X02DAF = .TRUE.
  8. 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_fl23/xhtml/FRONTMATTER/manconts.xml
	nagdoc_fl23/pdf/FRONTMATTER/manconts.pdf
	nagdoc_fl23/html/FRONTMATTER/manconts.html
Use your web browser to navigate from here. For convenience, a master index file containing links to the above files has been provided at
	nagdoc_fl23/index.html

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

In addition the following are provided:

Please see the Intel web site for further information about MKL (http://www.intel.com/software/products/mkl).

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 FSL6I23DCL).

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

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(e) Product Registration

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

Many factors influence the way that NAG's products and services evolve, and your ideas are invaluable in helping us to ensure that we meet your needs. If you would like to contribute to this process, we would be delighted to receive your comments. Please contact any of the NAG Response Centres (shown below).

Appendix - Contact Addresses

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