In addition, NAG recommends that before calling any Library routine you should read the following reference material from the Library Manual (see Section 5):
(a) How to Use the NAG Library and its Documentation
(b) Chapter Introduction
(c) Routine Document
http://www.nag.co.uk/doc/inun/fs26/l6idcl/supplementary.html
for details of any new information related to the applicability or usage of this implementation.
This implementation of the NAG Fortran Library provides static and shareable libraries that use the Intel ® Math Kernel Library for Linux (MKL), a third-party vendor performance library, to provide Basic Linear Algebra Subprograms (BLAS) and Linear Algebra PACKage (LAPACK) routines (except for any routines listed in Section 4). It also provides static and shareable libraries that use the NAG versions of these routines (referred to as the self-contained libraries). This implementation has been tested with version 11.3.3 of MKL, which is supplied as a part of this product. Please see the Intel website for further information about MKL (https://software.intel.com/intel-mkl). For best performance, we recommend that you use one of the variants of the NAG Fortran Library which is based on the supplied MKL, i.e. libnag_mkl.a or libnag_mkl.so, in preference to using one of the self-contained NAG libraries, libnag_nag.a or libnag_nag.so.
If you intend to use the NAG library within a multithreaded application please refer to Section 3.12.1 of the document How to Use the NAG Library and its Documentation for more information. 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.
The libraries supplied with this implementation have been compiled with OpenMP. However, the OpenMP runtime libraries of different compilers may not be compatible, thus you are recommended to only use this implementation in conjunction with your own OpenMP code (including any OpenMP statements required in the user-supplied functions of the routines listed in Section 4) when using the compiler and corresponding OpenMP runtime listed in the Installer's Note, Section 2.2. Note that the system's default thread stacksize may not be sufficient for running all NAG Fortran Library routines within multithreaded applications; you may increase this stacksize using the OpenMP environment variable OMP_STACKSIZE.
Intel have introduced a conditional bitwise reproducibility (BWR) option in MKL. Provided a user's code adheres to certain conditions (see https://software.intel.com/en-us/node/528579), BWR can be forced by setting the MKL_CBWR environment variable. See the MKL documentation for further details. It should be noted, however, that many NAG routines do not adhere to these conditions. This means that for a given NAG library built on top of MKL, it may not be possible to ensure BWR for all NAG routines across different CPU architectures by setting MKL_CBWR. See Section 3.11.1 of How to Use the NAG Library and its Documentation for more general information on bitwise reproducibility.
Please note that this implementation is not compatible with versions of MKL earlier than 10.3.
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 $HOME/NAG/fsl6i26dcl; however it could have been changed by the person who did the installation, in which case you should consult that person.
To use the NAG Fortran Library and the supplied Intel MKL libraries, you may link in the following manner:
ifort -qopenmp -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_mkl.a \ -Wl,--start-group \ [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_intel_lp64.a \ [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_intel_thread.a \ [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_core.a \ -Wl,--end-group \ [INSTALL_DIR]/rtl/intel64/libiomp5.a -lpthread -lm -ldl -lstdc++where driver.f90 is your application program; or
ifort -qopenmp -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_mkl.so \ -L[INSTALL_DIR]/mkl_intel64_11.3.3/lib \ -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core \ -L[INSTALL_DIR]/rtl/intel64 -liomp5 -lpthread -lm -ldlif the shareable library is required.
However, if you prefer to link to a version of the NAG Fortran Library which does not require the use of MKL you may wish to use the self-contained libraries as follows:
ifort -qopenmp -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_nag.a -lstdc++or
ifort -qopenmp -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_nag.soif the shareable library is required.
Please note the shareable libraries are 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).
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]/mkl_intel64_11.3.3/libto set LD_LIBRARY_PATH, or
setenv LD_LIBRARY_PATH \to extend LD_LIBRARY_PATH if you already have it set.
[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib:${LD_LIBRARY_PATH}
In the Bourne shell, type:
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib export LD_LIBRARY_PATHto set LD_LIBRARY_PATH, or
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib:${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 a newer version of the compiler.
If you are using a different compiler, or indeed a different version of the Intel compiler, you may need to link against the Intel compiler run-time libraries provided in [INSTALL_DIR]/rtl/intel64.
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. The environment variable OMP_NUM_THREADS may be re-set between each execution of the program, as desired. If you wish to change the number of threads to use for different parts of your program during execution, routines are provided in Chapter X06 of the NAG Library to assist with this process.
Multiple levels of OpenMP parallelism may be present in some NAG Library and MKL routines, and you may also call these multithreaded routines from within an OpenMP parallel region in your own application. By default, OpenMP nested parallelism is disabled, so only the outermost parallel region will actually be active, using N threads in the example above. The inner level(s) will not be active, i.e. they will run on one thread. You can check if OpenMP nested parallelism is enabled and choose to enable/disable it by either querying and setting the OMP_NESTED OpenMP environment variable or using the appropriate routines in Chapter X06. If OpenMP nested parallelism is enabled, the above example will create N threads at each parallel region for each thread at a higher level, thus N*N threads in total if there are two levels of OpenMP parallelism, etc. To provide more detailed control of nested parallelism, the environment variable OMP_NUM_THREADS can be set to be a comma separated list to specify the number of threads desired at each level.
In the C shell, type:
setenv OMP_NUM_THREADS N,PIn the Bourne shell, type:
OMP_NUM_THREADS=N,P export OMP_NUM_THREADSThis will create N threads for the first level of parallelism, and then P threads for each outer level thread when an inner level of parallelism is encountered.
Note: If the environment variable OMP_NUM_THREADS is not set, the default value can vary from compiler to compiler, and for different vendor libraries, usually to either be 1 or else equal to the maximum number of cores available on your system. The latter could be an issue if you are sharing the system with other users, or are running a higher level of parallelism within your own application. Thus it is recommended that you always set OMP_NUM_THREADS explicitly to your desired value.
In general, the maximum number of threads you are recommended to use is the number of physical cores on your shared memory system. However, most Intel processors support a facility known as Hyper-Threading Technology, 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 making use of the additional logical cores, to determine the best choice for you. This can normally be achieved simply by an appropriate choice for the number of threads to use, via OMP_NUM_THREADS. Completely disabling hyper-threading normally requires setting the desired choice in the BIOS on your system at boot time.
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) for the Intel compiler They can be accessed by specifying the
The .mod module files were compiled with the compiler shown in Section 2.2 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 recompile the interface blocks with your own compiler version. A recompiled set of interface blocks can be created in a separate directory (e.g. nag_interface_blocks_alt) using the supplied script command
[INSTALL_DIR]/scripts/nag_recompile_mods nag_interface_blocks_altfrom the [INSTALL_DIR] directory. This script uses the version of the Intel Fortran compiler from your PATH environment; to specify an alternative version it is safest to first run any Intel Fortran compiler environment scripts for that version prior to running [INSTALL_DIR]/scripts/nag_recompile_mods.
To make the new set of compiled modules the default set, move the directory [INSTALL_DIR]/nag_interface_blocks to [INSTALL_DIR]/nag_interface_blocks_original, and then move the directory containing the new set of modules [INSTALL_DIR]/nag_interface_blocks_alt to [INSTALL_DIR]/nag_interface_blocks.
You should now be able to use the newly compiled module files in the usual way.
The distributed example results are those obtained with the static library libnag_mkl.a (i.e. using the MKL BLAS and LAPACK routines). Running the examples with NAG BLAS or LAPACK may give slightly different results.
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 example programs are most easily accessed by using one of the following scripts, which are located in the directory [INSTALL_DIR]/scripts:
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), with the results being sent to a file and to the command window.
The example program concerned, and the number of OpenMP threads to use, are specified by the arguments to the command, e.g.
nag_example_mkl e04nrf 4will copy the example program and its data and options files (e04nrfe.f90, e04nrfe.d and e04nrfe.opt) into the current directory, compile and link the program and run it using 4 OpenMP threads 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. See Section 4.4 of How to Use the NAG Library and its Documentation for details.
In this implementation, the following routines make calls to user functions from within OpenMP parallel regions located inside the NAG routines:
D03RAF D03RBF E05SAF E05SBF E05UCF E05USF F01ELF F01EMF F01FLF F01FMF F01JBF F01JCF F01KBF F01KCF
Thus orphaned OpenMP directives can be used in user functions, unless you are using a different compiler from the one used to build your NAG Library implementation, as listed in the Installer's Note, Section 2.2. You must also ensure that you use the user workspace arrays IUSER and RUSER in a thread safe manner, which is best achieved by only using them to supply read-only data to the user functions.
C06PAF C06PCF C06PFF C06PJF C06PKF C06PPF C06PQF C06PRF C06PSF C06PUF C06PVF C06PWF C06PXF C06PYF C06PZF C06RAF C06RBF C06RCF C06RDFThe 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.
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 in the non-self-contained NAG libraries
are implemented by calls to MKL, except for the following routines:
BLAS_DAMAX_VAL BLAS_DAMIN_VAL BLAS_DAXPBY BLAS_DDOT BLAS_DMAX_VAL BLAS_DMIN_VAL BLAS_DSUM BLAS_DWAXPBY BLAS_ZAMAX_VAL BLAS_ZAMIN_VAL BLAS_ZAXPBY BLAS_ZSUM BLAS_ZWAXPBYThe following NAG named routines in the non-self-contained NAG libraries 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 F08GEF/DSPTRD F08GFF/DOPGTR F08GSF/ZHPTRD F08GTF/ZUPGTR F08JEF/DSTEQR F08JSF/ZSTEQR F08KEF/DGEBRD F08KSF/ZGEBRD F08MEF/DBDSQR F08MSF/ZBDSQR
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 = 1024
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
The Library Manual is available as a separate installation, 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/content/nag-fortran-library-manual.
The Library Manual is supplied in the following formats:
The following main index files have been provided for these formats:
nagdoc_fl26/html/frontmatter/manconts.html nagdoc_fl26/pdf/frontmatter/manconts.pdf nagdoc_fl26/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_fl26/index.html
Advice on viewing and navigating the formats available can be found in http://www.nag.co.uk/numeric/fl/nagdoc_fl26/html/genint/essint.html.
In addition the following are provided:
http://www.nag.co.uk/content/nag-technical-support-service
for information about the NAG Technical Support Service, including details of the NAG Technical Support Service contact points. We would also be delighted to receive your feedback on NAG's products and services.
http://www.nag.co.uk/content/worldwide-contact-information
for worldwide contact details for the Numerical Algorithms Group.