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.
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.
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:
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-groupwhere 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.soif 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]/mkl10.3to set LD_LIBRARY_PATH, or
setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3:${LD_LIBRARY_PATH}to extend LD_LIBRARY_PATH if you already have it set.
In the Bourne shell, type:
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3 export LD_LIBRARY_PATHto set LD_LIBRARY_PATH, or
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl10.3:${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 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.
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, 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.
(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/l6idcl/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.
C06PAF C06PCF C06PFF C06PJF C06PKF C06PPF C06PQF C06PRF C06PSF C06PUF C06PXF 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 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
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
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
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 = 1.42724769270596E+45 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 FSL6I23DCL).
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:
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