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 not been compiled in a manner that facilitates the use of multiple threads.
http://www.nag.co.uk/doc/inun/fl24/l6adpl/postrelease.html
for details of any new information related to the applicability or usage of this implementation.
If your machine has more than one processor or a multicore chip, then it is recommended that you set the environment variable OMP_NUM_THREADS to the number of available threads, e.g.
setenv OMP_NUM_THREADS 4in the C shell, or
OMP_NUM_THREADS=4 export OMP_NUM_THREADSin the Bourne shell. This will enable the ACML BLAS to make use of the extra processor(s) / core(s) and will thus speed up the computation of many of the Library procedures.
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/fll6a24dpl or /usr/local/NAG/fll6a24dpl depending on your system; however it could have been changed by the person who did the installation. To identify [INSTALL_DIR] for this installation:
pgf90 -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_acml.a [INSTALL_DIR]/acml/libacml_mp.awhere driver.f90 is your application program;
or
pgf90 -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_acml.so [INSTALL_DIR]/acml/libacml_mp.soif the shareable library is required. Please note that the shareable library is fully resolved so that you need not link against other run-time libraries explicitly; this requires the environment variable LD_LIBRARY_PATH to be set correctly at link time (see below).
However, if you prefer to link to a version of the NAG Library which does not require the use of ACML you may wish to use the self-contained libraries as follows:
pgf90 -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_nag.aor
pgf90 -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_nag.soif the shareable library is required.
If your application has been linked with the shareable NAG and ACML libraries then the environment variable LD_LIBRARY_PATH must be set (or extended) to allow run-time linkage.
In the C shell type:
setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/acmlto set LD_LIBRARY_PATH, or
setenv LD_LIBRARY_PATH \ [INSTALL_DIR]/lib:[INSTALL_DIR]/acml:${LD_LIBRARY_PATH}to extend LD_LIBRARY_PATH if you already have it set.
In the Bourne shell, type:
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml export LD_LIBRARY_PATHto set LD_LIBRARY_PATH, or
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml:${LD_LIBRARY_PATH} export LD_LIBRARY_PATHto 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 items such as compiler run-time libraries, for example if you are using another version of the compiler.
If you are using a different compiler, you may need to link against the PGI pgf90 run-time libraries provided in [INSTALL_DIR]/rtl.
A document, techdoc.html, giving advice on calling the NAG Fortran Library from C and C++ is also available in [INSTALL_DIR]/c_headers.
(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 Fortran Library 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/fl24/l6adpl/postrelease.html
where more information may be available, or contact NAG for further help.
The distributed example results are those obtained with the static library libnag_acml.a, (i.e. using the ACML BLAS and LAPACK routines).
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 four scripts: nag_example_acml, nag_example_shar_acml, nag_example and nag_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 is specified by the argument to the command, e.g.
nag_example_acml e04nrfwill 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 to produce the example program results in the file e04nrfe.r.
This implementation of the NAG Fortran Library uses 32-bit integers.
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 Fortran Library 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.
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 ACML 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 the NAG version of the following BLAS and LAPACK routines are included in the libraries libnag_acml.a and libnag_acml.so to avoid problems with the vendor version:
DDOT DGELSS DGEMV DGGES DGGESX DGGESVX DTRSV
The behaviour of functions in these Chapters may depend on implementation-specific values.
General details are given in the Library Manual, but the specific values used in this implementation are as follows:
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 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 AIMAG(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 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
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 = 1024Derived 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 = 1.42724769270596E+45 X02BBF = 2147483647 X02BEF = 15
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/FLdocumentation.asp.
The Library Manual is supplied in the following formats:
The following main index files have been provided for these formats:
nagdoc_fl24/html/FRONTMATTER/manconts.html nagdoc_fl24/pdf/FRONTMATTER/manconts.pdf nagdoc_fl24/pdf/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_fl24/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 FLL6A24DPL).
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