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 the use of multiple threads.
http://www.nag.co.uk/doc/inun/fl23/w6idcl/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 default folder:
c:\Program Files\NAG\FL23\flw6i23dclIf this folder does not exist, please consult the system manager (or the person who did the installation). In some of the following subsections, this folder is referred to as install_dir.
We also assume that the default shortcut for the Library command prompt is placed in the Start Menu under:
Start|All Programs|NAG|FL23|NAG Fortran Library - Intel Fortran (FLW6I23DCL)
If this shortcut does not exist, please consult the system manager (or the person who did the installation). (Other shortcuts created as part of the Library installation procedure are also assumed to be in this location.)
If you are using one of the DLL forms of the Library (see Section 3.1.1), you need to ensure that the NAG DLL (FLW6I23DC_mkl.dll or FLW6I23DC_nag.dll) is accessible at run time; therefore the install_dir\bin folder must be on the path. If an MKL-based version of the Library is to be used, the install_dir\MKL_intel64_10.3\bin folder must also be on the path, but should appear later in the path than the install_dir\bin folder, since the NAG versions of a few Basic Linear Algebra Subprograms (BLAS) / linear algebra routines (LAPACK) are included in the NAG Libraries to avoid problems with the vendor versions. (See Section 4 for details.)
To check the accessibility of the NAG DLLs, run the program NAG_Fortran_DLL_info.exe which is available from the Start Menu shortcut
Start|All Programs|NAG|FL23|NAG Fortran Library - Intel Fortran (FLW6I23DCL)| Check NAG DLL Accessibility (FLW6I23DCL)See Section 4.2.3 of the Installer's Note for details of this utility.
The shortcut:
Start|All Programs|NAG|FL23|NAG Fortran Library - Intel Fortran (FLW6I23DCL)| FLW6I23DCL Command Prompt
may be used to start a command prompt window with the correct settings for the INCLUDE, LIB and PATH environment variables for the Library and the supplied MKL.
If the shortcut is not used, you can set the environment variables by running the batch file envvars.bat for this implementation. The default location of this file is:
c:\Program Files\NAG\FL23\flw6i23dcl\batch\envvars.batIf the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw6i23dcl.
You may then compile and link to the NAG Fortran Library on the command line using one of the following commands:
ifort /MT driver.f90 nag_mkl_MT.lib user32.lib mkl_intel_lp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5mt.lib ifort /MT driver.f90 nag_nag_MT.lib user32.lib ifort /MD driver.f90 nag_mkl_MD.lib user32.lib mkl_intel_lp64_dll.lib mkl_intel_thread_dll.lib mkl_core_dll.lib libiomp5md.lib ifort /MD driver.f90 nag_nag_MD.lib user32.lib ifort /MD driver.f90 FLW6I23DC_mkl.lib ifort /MD driver.f90 FLW6I23DC_nag.libwhere driver.f90 is your application program.
The order of the libraries is important because certain parts of the MKL should not be used (see Section 4).
The first two commands use libraries compiled with the /MT option. The first command will use the static library without the NAG version of the BLAS/LAPACK procedures (nag_mkl_MT.lib) in addition to the MKL static libraries. The second command will use the library containing the NAG version of the BLAS/LAPACK procedures (nag_nag_MT.lib). The option /MT must be used to ensure linking with the correct run-time libraries (multithreaded static run-time libraries in this case).
The third and fourth commands use static libraries compiled with the /MD option. The third command will use the static library without the NAG version of the BLAS/LAPACK procedures (nag_mkl_MD.lib) in addition to the MKL DLLs. The fourth command will use the library containing the NAG version of the BLAS/LAPACK procedures (nag_nag_MD.lib). The option /MD must be used to ensure linking with the correct run-time libraries (multithreaded dynamic link run-time libraries in this case).
The last two commands use DLL import libraries compiled with the /MD option. The fifth command will use the DLL without the NAG version of the BLAS/LAPACK procedures (FLW6I23DC_mkl.lib) in addition to the MKL DLLs. The last command will use the DLL containing the NAG version of the BLAS/LAPACK procedures (FLW6I23DC_nag.lib). The option /MD must be used to ensure linking with the correct run-time libraries.
Note that /MT is equivalent to specifying
Please note that the Intel Visual Fortran compiler environment variables must be set in the command window. For more details refer to the User's Guide for the compiler.
To ensure that the NAG DLLs are accessible at runtime, the PATH environment variable must be set such that the location of the NAG DLLs, specifically the folder install_dir\bin, is on the path. If the MKL version of the DLL is required, the location of the MKL DLLs, install_dir\MKL_intel64_10.3\bin must also be on the path, but should appear after the install_dir\bin folder.
Once Visual Studio has been opened, it is possible to set up the directories for use with Intel Fortran in this and all subsequent projects which use this compiler. One way to do so is:
c:\Program Files\NAG\FL23\flw6i23dcl\lib
c:\Program Files\NAG\FL23\flw6i23dcl\nag_interface_blocks
Having done this, if an Intel Fortran project requires a library or NAG interface block during the compilation and linking process then the full path to the library and interface block do not need to be specified.
Whilst the above changes will apply to every Intel Fortran project, the following tasks need to be performed for each individual Intel Fortran project.
The library is intended to be run in fully optimised mode, so to avoid any warning messages, you might decide to set the active configuration to Release. You can do this from the Toolbar or alternatively via the Build|Configuration Manager menus. Note that if you work in Debug mode, you may receive a warning message about conflicting C run-time libraries.
There are a number of ways to add the NAG Library to the project. We describe just two; choose the one that most suits you.
If the Solution Explorer window is open then make sure that the group project (the first line) is NOT selected. From the Project menu, choose the project Properties item. (Alternatively right-click on a specific single project in the Solution Explorer and choose Properties.)
From the form, click Linker in the leftmost panel and then choose Input. The right hand panel will now have an Additional Dependencies entry, and you need to type nag_mkl_MT.lib user32.lib mkl_intel_lp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5mt.lib in this location to use the nag_mkl_MT.lib library and MKL. Please note that the six libraries are separated by a space only and that nag_mkl_MT.lib must be the first one. Press the OK button. If you wish to use the self-contained NAG Library nag_nag_MT.lib then you need to add nag_nag_MT.lib user32.lib instead of the six libraries above. Similary, to use one of the other NAG Libraries, insert the appropriate library or libraries (as detailed in Section 3.1.1) in the Additional Dependencies field.
Before you can compile the project you need to specify the correct run-time library needed.
From the Properties Window, click Fortran in the leftmost panel and then choose Libraries. The right hand panel will now have a Runtime Library entry, and you need to select Multithreaded if your project uses one of the two libraries nag_nag_MT.lib or nag_mkl_MT.lib. If your projects uses any of the other NAG libraries you need to select Multithreaded DLL. After you select the correct run-time library press the OK button.
The Properties information may also be accessed via the Toolbar. With the project selected in Solution Explorer, choose the Properties Window button on the Toolbar. In the ensuing window choose then the rightmost Property Pages icon. Select the appropriate settings as detailed in the paragraphs above.
In summary, the setting of the project Additional Dependencies, the project Runtime Library and the PATH environment variable must be consistent as follows:
The project should now compile and link using the appropriate choice from the Build menu.
To run a program that does not require input or output redirected from standard input or standard output, from within the Microsoft Development Environment, the program may be executed via the Debug menu (by selecting Start Without Debugging, for example).
If a data file needs to be attached to the standard input or the output of a program needs to be redirected to the standard output, we recommend that you run the executable from a command prompt window to avoid the limitations of Visual Studio .NET.
Examples of use of the DLLs from within Excel are given in the install_dir\samples\excel64_examples folder. The folder install_dir\samples\excel64_examples\linear_algebra contains the file xls_demo_64.html. This file gives some hints about using NAG DLLs from within Excel spreadsheets.
Key information:
This has been tested using Microsoft Office Excel 2010.
Key information:
Imports System.Runtime.InteropServices
This has been tested using Visual Studio 2005, 2008 and 2010.
Examples of the use of the DLLs from C and C++ are given in the install_dir\samples\c_examples and install_dir\samples\cpp_examples folders. (Note that if the e04cbfcppclass.sln file is loaded into Visual Studio 2005 or later, the Conversion Wizard will update the files in the project/solution as necessary.)
A document, techdoc.html, giving more detailed advice on calling the DLLs from C and C++ is available in install_dir\c_headers. There is also a shortcut to this document on the Start Menu under
Start|All Programs|NAG|FL23|NAG Fortran Library (FLW6I23DCL)| C & C++ Header File Informationby default. Note that some changes will be needed if you paste code from one of the C examples given there into a C++ file since, if __cplusplus is defined, the header file provided uses C++ reference arguments for scalars, and therefore the "address of" operator should not be used. See Section 3 of the techdoc.html document for more details.
Key information:
cl driver.c FLW6I23DC_mkl.libor
cl driver.c FLW6I23DC_nag.libwhere driver.c is your application program. This assumes that the folder containing the header files has been added to the INCLUDE environment variable. If not, you could use:
cl /I"install_dir\c_headers" driver.c FLW6I23DC_mkl.libor
cl /I"install_dir\c_headers" driver.c FLW6I23DC_nag.libTo link to one of the static libraries instead of a DLL, you will also need access to the compiler run-time library directory install_dir\rtl. It is most convenient if you add that directory to your LIB environment variable, then use, for example:
cl /MD /I"install_dir\c_headers" driver.c nagc_nag_MD.lib user32.libor
cl /MT /I"install_dir\c_headers" driver.c nagc_nag_MT.lib user32.libThe Intel C compiler icl may be used in the same way as the Microsoft compiler cl, though it may not be necessary to add the rtl directory to your LIB environment variable.
Start|All Programs|NAG|FL23|NAG Fortran Library - Intel Fortran (FLW6I23DCL)| Check NAG DLL Accessibility (FLW6I23DCL)See Section 4.2.3 of the Installer's Note for details of this utility.
(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.
These interface blocks have been generated automatically by analysing the source code for the NAG Fortran Library. As a consequence, and because these files have been thoroughly tested, their use is recommended in preference to writing your own declarations.
The NAG Fortran Library interface block files are organised by Library chapter. The module names are:
nag_precisions nag_blas_consts nag_a_ib nag_c_ib nag_d_ib nag_e_ib nag_f_ib nag_g_ib nag_h_ib nag_m_ib nag_p_ib nag_s_ib nag_x_ib nag_long_namesand these are also aggregated into one module named
nag_libraryA program calling a NAG routine may then use a module for a specific chapter (e.g. nag_s_ib) or for the whole library (i.e. nag_library).
The modules are supplied in pre-compiled form (.mod files) for use by the Intel Fortran compiler, ifort.
If you use the Library command prompt shortcut or set the environment variables by running the batch file envvars.bat for this implementation (see Section 3.1.1), you can use any of the commands described in Section 3.1.1 to access these modules since the environment variable INCLUDE will be set.
If you wish to use NAG modules with a version of the Intel Fortran compiler other than the one used to build this NAG Library, you may need to recompile the interface blocks with your own compiler version, as described here.
Copy all the .f90 files from the nag_interface_blocks folder to a new folder of your choice, for example nag_interface_blocks_ifort10. Then compile all the files into objects using your compiler. Because the interface blocks contain some inter-dependencies, the order of compilation is important, but the following compilation order should work:
ifort -c nag_precisions.f90 ifort -c nag_blas_consts.f90 ifort -c nag_a_ib.f90 ifort -c nag_c_ib.f90 ifort -c nag_d_ib.f90 ifort -c nag_e_ib.f90 ifort -c nag_f_ib.f90 ifort -c nag_g_ib.f90 ifort -c nag_h_ib.f90 ifort -c nag_m_ib.f90 ifort -c nag_p_ib.f90 ifort -c nag_s_ib.f90 ifort -c nag_x_ib.f90 ifort -c nag_long_names.f90 ifort -c nag_library.f90The object files generated by the compilation may be discarded - only the module files are needed.
To use the newly compiled module files, you will need a compiler-dependent switch to tell the compiler where to find them when you are compiling programs. For example, the command
ifort -I nag_interface_blocks_ifort10will tell the compiler to look in the new folder for module files.
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 one of the following batch files:
nag_mkl_MT.lib and nag_nag_MT.lib use the static multithreaded run-time library, whilst nag_mkl_MD.lib, nag_nag_MD.lib, FLW6I23DC_mkl.lib and FLW6I23DC_nag.lib use the multithreaded DLL run-time library.
The batch files need the environment variable NAG_FLW6I23DCL.
As mentioned in Section 3.1.1, the installation procedure provides a shortcut which starts a Command Prompt with local environment variables. The environment variables include NAG_FLW6I23DCL. This shortcut is, by default, placed in the Start Menu under
Start|All Programs|NAG|FL23|NAG Fortran Library - Intel Fortran (FLW6I23DCL)| FLW6I23DCL Command PromptIf the shortcut is not used, you need to set this environment variable. It can be set by running the batch file envvars.bat for this implementation. The default location of this file is:
c:\Program Files\NAG\FL23\flw6i23dcl\batch\envvars.batIf the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw6i23dcl.
Each of the nag_example* batch files mentioned above will provide you with a copy of an example program (and its data, 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, writing its output to a file.
The example program concerned is specified by the argument to the command, e.g.
nag_example_mkl_MT e04ucfwill copy the example program and its data into the files e04ucfe.f90 and e04ucfe.d in the current folder and process them to produce the example program results in the file e04ucfe.r.
The distributed example results are those obtained with the static library nag_mkl_MT.lib, (using the MKL BLAS and LAPACK routines). Running the examples with the self-contained library (using the NAG BLAS and LAPACK routines) may give slightly different results.
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 MKL 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 Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) are included in the libraries nag_mkl_MT.lib, nag_mkl_MD.lib and FLW6I23DC_mkl.dll to avoid problems with the vendor version:
DBDSQR DGEBAL DGEESX DGEEVX DGEHRD DGGESX DHSEQR ZBDSQR ZGEBAL ZGEEVX ZHPEVD ZHSEQR ZTRSEN ZTRSV
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
X01AAF (pi) = 3.1415926535897932 X01ABF (gamma) = 0.5772156649015328
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 = 4.45014771701441E-308
Parameters of other aspects of the computing environment
X02AHF = 1.42724769270596E+45 X02BBF = 2147483647 X02BEF = 15 X02DAF = .TRUE.
The Library Manual is available as a separate installation, via download from the NAG website, or from the distribution CD if you have one. It is also available directly on the CD. 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_fl23\xhtml\FRONTMATTER\manconts.xml nagdoc_fl23\pdf\FRONTMATTER\manconts.pdf nagdoc_fl23\html\FRONTMATTER\manconts.htmlIf the Library Manual has been installed locally, these index files are available from the Start Menu under
Start|All Programs|NAG|FL23|NAG Fortran Library Manual (XHTML + MathML) Start|All Programs|NAG|FL23|NAG Fortran Library Manual (PDF) Start|All Programs|NAG|FL23|NAG Fortran Library Manual (PDF + HTML Index)respectively, by default. Use your web browser to navigate from here.
Advice on viewing and navigating the formats available can be found in the Online Documentation document.
Note that if you are using Internet Explorer, all links within the XHTML/MathML version to example source, data and results files and PDF files will be diverted from the local file system to the NAG website to avoid security restrictions which prevent the display of these pages. If you are using any other browser then local links to examples and PDF files are retained.
The Library Manual is also available as an HTML Help file. In order to display the mathematical expressions correctly, you will need to install Design Science's MathPlayer plug-in. MathPlayer may optionally be installed with this NAG Library product, or may be downloaded from Design Science's website:
http://www.dessci.com/en/products/mathplayer/download.htm
The HTML Help version of the Library Manual is available from the Start Menu under
Start|All Programs|NAG|FL23|NAG Fortran Library Manual HTML HelpIf the NAG Library materials have been installed on a network drive, you may need to copy the HTML Help file (nagdoc_fl23.chm) to a local drive. If you still have trouble seeing the correct help file materials, e.g. if you see a message such as
Navigation to the webpage was canceledthe file might have been blocked by security updates in Windows or Internet Explorer. Right-click on nagdoc_fl23.chm in Windows Explorer and select Properties from the pop-up menu. If there is an Unblock button at the bottom click on it to unblock the file and then click on OK to close the Properties dialog box.
In addition the following are provided:
Start|All Programs|NAG|FL23|NAG Fortran Library - Intel Fortran (FLW6I23DCL)| Users' Noteby default.
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 no. and NAG product code (in this case FLW6I23DCL).
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