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). Note that the system's default thread stacksize may not be sufficient for running all NAG Library for SMP & Multicore routines within multithreaded applications. You may have to increase this stacksize, e.g. using the POSIX threads routine pthread_attr_setstacksize. A value of 1MB should be sufficient in most circumstances, but more may be required if each POSIX thread is creating multiple OpenMP threads. You should consult a POSIX thread programming guide for further information if required.
http://www.nag.co.uk/doc/inun/fs23/ai6dal/postrelease.html
for details of any new information related to the applicability or usage of this implementation.
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/fsai623dal or /usr/local/NAG/fsai623dal depending on your system; however it could have been changed by the person who did the installation. To identify [INSTALL_DIR] for this installation:
xlf_r -q64 -qsmp=omp -qnosave -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \
[INSTALL_DIR]/lib/libnagsmp.a -lesslsmp
where driver.f90 is your application program
; or
xlf_r -q64 -qsmp=omp -qnosave -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \
[INSTALL_DIR]/lib/libnagsmp.so -lesslsmp
if the shareable library is required.
The library can be used with or without the compiler flag -qextname.
If your application has been linked with the shareable NAG library 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]/libto set LD_LIBRARY_PATH, or
setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:${LD_LIBRARY_PATH}
to extend LD_LIBRARY_PATH if you already have it set.
In the Bourne shell, type:
LD_LIBRARY_PATH=[INSTALL_DIR]/lib export LD_LIBRARY_PATHto set LD_LIBRARY_PATH, or
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:${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.
In the C shell type:
setenv OMP_NUM_THREADS NIn the Bourne shell, type:
OMP_NUM_THREADS=N export OMP_NUM_THREADSwhere 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, IBM POWER7 processors support a facility known as SMT, which allows each physical core to support four threads at the same time and thus appear to the operating system four 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 SMT enabled, to determine the best choice for you. Enabling and disabling SMT may require root access to the system, although some sites may have configured different options in their batch queue systems to allow users to more easily access different SMT configurations.
(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_libraryThe 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/ai6dal/postrelease.html
where more information may be available, or contact NAG for further help.
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 4will 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.
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
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.
DCFT DCFT2 DCFT3 DCRFT DRCFTare made whenever possible in the following NAG routines:
C06PAF C06PCF C06PFF C06PJF C06PKF C06PQF C06PRF C06PSF C06PUF C06PXFThe required size of the workspace array WORK for each routine will depend upon the parameters used and thus the choice of ESSL or NAG FFT kernels used within the FFT routines. The values specified in the NAG routine documents should be sufficient in many cases, and where they are insufficient a suitable workspace will be allocated internally.
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 ESSL 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 ESSL,
except for the following routines:
BLAS_DMAX_VAL BLAS_DMIN_VAL DBDSDC DBDSQR DDISNA DGBBRD DGBCON DGBEQU DGBRFS DGBSV DGBSVX DGBTRF DGBTRS DGEBAK DGEBAL DGEBRD DGEEQU DGEES DGEESX DGEEV DGEEVX DGEHRD DGEJSV DGELQF DGELS DGELSD DGELSS DGELSY DGEQLF DGEQP3 DGEQPF DGEQRF DGERFS DGERQF DGESDD DGESV DGESVD DGESVJ DGESVX DGETRF DGETRS DGGBAK DGGBAL DGGES DGGESX DGGEV DGGEVX DGGGLM DGGHRD DGGLSE DGGQRF DGGRQF DGGSVD DGGSVP DGTCON DGTRFS DGTSV DGTSVX DGTTRF DGTTRS DHGEQZ DHSEIN DHSEQR DLANGT DLANSF DLANST DNRM2 DOPGTR DOPMTR DORGBR DORGHR DORGLQ DORGQL DORGQR DORGRQ DORGTR DORMBR DORMHR DORMLQ DORMQL DORMQR DORMRQ DORMRZ DORMTR DPBCON DPBEQU DPBRFS DPBSTF DPBSV DPBSVX DPBTRF DPBTRS DPFTRF DPFTRI DPFTRS DPOEQU DPORFS DPOSV DPOSVX DPOTRS DPPEQU DPPRFS DPPSV DPPSVX DPSTRF DPTCON DPTEQR DPTRFS DPTSV DPTSVX DPTTRF DPTTRS DROTI DROTM DROTMG DSBEV DSBEVD DSBEVX DSBGST DSBGV DSBGVD DSBGVX DSBTRD DSFRK DSGESV DSPCON DSPEV DSPEVD DSPEVX DSPGST DSPGV DSPGVD DSPGVX DSPOSV DSPRFS DSPSV DSPSVX DSPTRD DSPTRF DSPTRI DSPTRS DSTEBZ DSTEDC DSTEGR DSTEIN DSTEQR DSTERF DSTEV DSTEVD DSTEVR DSTEVX DSYCON DSYEV DSYEVD DSYEVR DSYEVX DSYGST DSYGV DSYGVD DSYGVX DSYRFS DSYSV DSYSVX DSYTRD DSYTRF DSYTRI DSYTRS DTBCON DTBRFS DTBTRS DTFSM DTFTRI DTFTTP DTFTTR DTGEVC DTGEXC DTGSEN DTGSJA DTGSNA DTGSYL DTPCON DTPRFS DTPTRS DTPTTF DTPTTR DTRCON DTREVC DTREXC DTRRFS DTRSEN DTRSNA DTRSYL DTRTRS DTRTTF DTRTTP DTZRZF ZBDSQR ZCGESV ZCPOSV ZGBBRD ZGBCON ZGBEQU ZGBRFS ZGBSV ZGBSVX ZGBTRF ZGBTRS ZGEBAK ZGEBAL ZGEBRD ZGEEQU ZGEES ZGEESX ZGEEV ZGEEVX ZGEHRD ZGELQF ZGELS ZGELSD ZGELSS ZGELSY ZGEQLF ZGEQP3 ZGEQPF ZGEQRF ZGERFS ZGERQF ZGESDD ZGESV ZGESVD ZGESVX ZGETRF ZGETRS ZGGBAK ZGGBAL ZGGES ZGGESX ZGGEV ZGGEVX ZGGGLM ZGGHRD ZGGLSE ZGGQRF ZGGRQF ZGGSVD ZGGSVP ZGTCON ZGTRFS ZGTSV ZGTSVX ZGTTRF ZGTTRS ZHBEV ZHBEVD ZHBEVX ZHBGST ZHBGV ZHBGVD ZHBGVX ZHBTRD ZHECON ZHEEV ZHEEVD ZHEEVR ZHEEVX ZHEGST ZHEGV ZHEGVD ZHEGVX ZHERFS ZHESV ZHESVX ZHETRD ZHETRF ZHETRI ZHETRS ZHFRK ZHGEQZ ZHPCON ZHPEV ZHPEVD ZHPEVX ZHPGST ZHPGV ZHPGVD ZHPGVX ZHPRFS ZHPSV ZHPSVX ZHPTRD ZHPTRF ZHPTRI ZHPTRS ZHSEIN ZHSEQR ZLANGT ZLANHF ZLANHT ZPBCON ZPBEQU ZPBRFS ZPBSTF ZPBSV ZPBSVX ZPBTRF ZPBTRS ZPFTRF ZPFTRI ZPFTRS ZPOEQU ZPORFS ZPOSV ZPOSVX ZPOTRS ZPPEQU ZPPRFS ZPPSV ZPPSVX ZPSTRF ZPTCON ZPTEQR ZPTRFS ZPTSV ZPTSVX ZPTTRF ZPTTRS ZSPCON ZSPMV ZSPRFS ZSPSV ZSPSVX ZSPTRF ZSPTRI ZSPTRS ZSTEDC ZSTEGR ZSTEIN ZSTEQR ZSYCON ZSYMV ZSYRFS ZSYSV ZSYSVX ZSYTRF ZSYTRI ZSYTRS ZTBCON ZTBRFS ZTBTRS ZTFSM ZTFTRI ZTFTTP ZTFTTR ZTGEVC ZTGEXC ZTGSEN ZTGSJA ZTGSNA ZTGSYL ZTPCON ZTPRFS ZTPTRS ZTPTTF ZTPTTR ZTRCON ZTREVC ZTREXC ZTRRFS ZTRSEN ZTRSNA ZTRSYL ZTRTRS ZTRTTF ZTRTTP ZTZRZF ZUNGBR ZUNGHR ZUNGLQ ZUNGQL ZUNGQR ZUNGRQ ZUNGTR ZUNMBR ZUNMHR ZUNMLQ ZUNMQL ZUNMQR ZUNMRQ ZUNMRZ ZUNMTR ZUPGTR ZUPMTR
F07FDF/DPOTRF F07FRF/ZPOTRF F07GDF/DPPTRF F07GEF/DPPTRS F07GRF/ZPPTRF F07GSF/ZPPTRS
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 = 1.8E+16
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
The values of the mathematical constants are:
X01AAF (pi) = 3.1415926535897932 X01ABF (gamma) = 0.5772156649015328
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-308Parameters of other aspects of the computing environment
X02AHF = 1.80143985094819E+16 X02BBF = 2147483647 X02BEF = 15 X02DAF = .TRUE.
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.htmlUse 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:
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 FSAI623DAL).
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:
NAG Ltd Wilkinson House Jordan Hill Road OXFORD OX2 8DR NAG Ltd Response Centre United Kingdom email: support@nag.co.uk Tel: +44 (0)1865 511245 Tel: +44 (0)1865 311744 Fax: +44 (0)1865 310139 Fax: +44 (0)1865 310139 NAG Inc 801 Warrenville Road Suite 185 Lisle, IL 60532-4332 NAG Inc Response Center USA email: support@nag.com Tel: +1 630 971 2337 Tel: +1 630 971 2337 Fax: +1 630 971 2706 Fax: +1 630 971 2706 Nihon NAG KK Hatchobori Frontier Building 2F 4-9-9 Hatchobori Chuo-ku Tokyo 104-0032 Nihon NAG Response Centre Japan email: support@nag-j.co.jp Tel: +81 3 5542 6311 Tel: +81 3 5542 6311 Fax: +81 3 5542 6312 Fax: +81 3 5542 6312 NAG Taiwan Branch Office 5F.-5, No.36, Sec.3 Minsheng E. Rd. Taipei City 10480 NAG Taiwan Response Centre Taiwan email: support@nag-gc.com Tel: +886 2 25093288 Tel: +886 2 25093288 Fax: +886 2 25091798 Fax: +886 2 25091798