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/fl26/mi6dcl/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 (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(a)). 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.dylib, in preference to using one of the self-contained NAG libraries, libnag_nag.a or libnag_nag.dylib.
The version of Intel MKL supplied is multithreaded. If the environment variable OMP_NUM_THREADS is undefined, MKL may create multiple threads to speed up computation on systems with more than one processor or a multicore chip. If you do not want MKL to make use of multiple cores or processors, OMP_NUM_THREADS must be set to 1, e.g.
setenv OMP_NUM_THREADS 1in the C shell, or
OMP_NUM_THREADS=1 export OMP_NUM_THREADSin the Bourne shell.
Alternatively, set the environment variable to the number of threads required. Note that the Chapter X06 routines do not change the behaviour of MKL threading in serial implementations of the Library.
Please note that this implementation is not compatible with versions of MKL earlier than 10.3.
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.
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/flmi626dcl; 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 MKL libraries, you may link in the following manner:
ifort -I[INSTALL_DIR]/nag_interface_blocks driver.f90 [INSTALL_DIR]/lib/libnag_mkl.a \ [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 \ -framework IOKit -framework CoreFoundation \ [INSTALL_DIR]/rtl/libiomp5.a -lpthread -lc++where driver.f90 is your application program;
or
ifort -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_mkl.dylib \ -L[INSTALL_DIR]/mkl_intel64_11.3.3/lib \ -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core \ -framework IOKit -framework CoreFoundation \ -L[INSTALL_DIR]/rtl -liomp5 -lpthread -lc++if 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 (e.g. libmkl_rt.dylib) explicitly; this requires the environment variable DYLD_LIBRARY_PATH to be set correctly at link time (see below). The exception is when your program calls a BLAS or LAPACK routine by its true name (e.g. DGESV) not the NAG equivalent (e.g. F07AAF). The non-NAG versions are supplied only by the vendor library and hence you must make sure the link line satisfies the additional dependency.
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 -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_nag.a \ -framework IOKit -framework CoreFoundation \ -lpthread -lc++or
ifort -I[INSTALL_DIR]/nag_interface_blocks driver.f90 \ [INSTALL_DIR]/lib/libnag_nag.dylib \ -framework IOKit -framework CoreFoundation \ -lpthread -lc++if the shareable library is required.
If your application has been linked with the shareable NAG and MKL libraries then the environment variable DYLD_LIBRARY_PATH must be set (or extended) to allow run-time linkage.
In the C shell type:
setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3to set DYLD_LIBRARY_PATH, or
setenv DYLD_LIBRARY_PATH \ [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3:${DYLD_LIBRARY_PATH}to extend DYLD_LIBRARY_PATH if you already have it set.
In the Bourne shell, type:
DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3 export DYLD_LIBRARY_PATHto set DYLD_LIBRARY_PATH, or
DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3:${DYLD_LIBRARY_PATH} export DYLD_LIBRARY_PATHto extend DYLD_LIBRARY_PATH if you already have it set.
Note that you may also need to set DYLD_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, ifort, you may need to link against the Intel ifort 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_library
The modules are supplied in pre-compiled form (.mod files) for
use by the Intel Fortran compiler, ifort.
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 the 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 is specified by the argument to the command, e.g.
nag_example_mkl e04nrfwill 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 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.
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 may require a different amount of workspace from the equivalent NAG versions of these routines.
In this implementation calls to the NAG version of the following BLAS and LAPACK routines may be included in the libraries libnag_mkl.a and libnag_mkl.dylib to avoid problems with the vendor version:
None
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.