NAG Library for SMP & Multicore, Mark 24

FSW6I24DDL - License Managed

Microsoft Windows x64, 64-bit integers, Intel Fortran Double Precision

Users' Note



Contents


1. Introduction

This document is essential reading for every user of the NAG Library for SMP & Multicore implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Mark 24 Library Manual (which we will refer to as the Library Manual). Wherever that manual refers to the "Users' Note for your implementation", you should consult this note.

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).

2. Post Release Information

Please check the following URL:

http://www.nag.co.uk/doc/inun/fs24/w6iddl/postrelease.html

for details of any new information related to the applicability or usage of this implementation.

3. General Information

3.1. Accessing the Library

The NAG Library for SMP & Multicore has been built using the version of Intel Fortran described in the Installer's Note. To call the library from a program compiled with a different version of Intel Fortran, you may need to move or rename the files libifcoremd.dll, libmmd.dll and svml_dispmd.dll in the install dir\bin folder, so that the correct Intel Fortran runtime DLLs are picked up. To facilitate this, the batch file hide_ifort_rtls.bat has been provided in the install dir\bin folder. This file will rename the Intel Fortran run-time libraries libifcoremd.dll, libmmd.dll and svml_dispmd.dll in that folder. The file expose_ifort_rtls.bat, also in that folder, is provided to convert the names back again. (Note that appropriate access permissions may need to be in place for these batch files to work.)

In this section we assume that the library has been installed in the default folder:

  c:\Program Files\NAG\FS24\fsw6i24ddl
If 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|FS24|NAG Library for SMP and Multicore
       (FSW6I24DDL)|FSW6I24DDL Command Prompt

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.)

To ensure that the NAG DLL is accessible at runtime, the PATH environment variable must be set such that the location of the NAG DLL, specifically the folder install_dir\bin, is on the path. The install_dir\MKL_intel64_11.0\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 some linear algebra routines (BLAS or LAPACK) are included in FSW6I24DD.dll. (See Section 4 for details.)

Note that it is particularly important when compiling a user-supplied procedure which is to be passed to a NAG routine as a callback function to make sure that any local variables in the procedure are safe for use in a parallel environment. This is because the callback may be called from inside a parallel region in the NAG library. In particular, you should ensure that local variables are not statically allocated, but are created dynamically on entry to the procedure and destroyed on exit. It may be necessary to use compiler-dependent switches to make this happen. Also, you should avoid the use of any compiler switches with names like -save that cause local variables to be statically allocated, since this is the opposite of what is required.

3.1.1. Setting the number of threads to use

Set the environment variable OMP_NUM_THREADS to the number of processors required, up to maximum available on your system, e.g. in a command window type:
  set OMP_NUM_THREADS=N
where 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.

3.1.2. From a command window

To access this implementation from a command window some environment variables need to be set.

The shortcut:

  Start|All Programs|NAG|FS24|NAG Library for SMP and Multicore
       (FSW6I24DDL)|FSW6I24DDL 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\FS24\fsw6i24ddl\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing fsw6i24ddl.

You may then compile and link to the NAG Library on the command line using one of the following commands:

  ifort /MD /4I8 /Qopenmp driver.f90 FSW6I24DD_static.lib mkl_intel_ilp64.lib
      mkl_intel_thread.lib mkl_core.lib user32.lib
where driver.f90 is your application program; or
  ifort /MD /4I8 /Qopenmp driver.f90 FSW6I24DD.lib
if the DLL version of the library is required. Note that in the DLL case it is not necessary to explicitly link to the MKL library.

Note that the /4I8 switch tells the compiler to use 64-bit integer and logical types instead of the default 32-bits.

Notice that in both cases we compile using the /MD compiler flag. This tells the compiler that we wish to link to multi-threaded DLL versions of compiler run-time libraries. This flag is important to ensure compatibility with this implementation of the NAG Library for SMP and Multicore.

The /Qopenmp flag tells the compiler to heed any OpenMP directives that may be present in your own code. It also causes the linker to link to the compiler threading library, libiomp5md.lib. For older versions of the Intel compiler, a different threading library (named libguide) was used by default. If you are using an older compiler (such as ifort 10.1) then you may need to add libiomp5md.lib explicitly to the compile line, e.g.

  ifort /MD /4I8 /Qopenmp driver.f90 FSW6I24DD_static.lib mkl_intel_ilp64.lib
      mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib
or
  ifort /MD /4I8 /Qopenmp driver.f90 FSW6I24DD.lib libiomp5md.lib
to avoid error messages at link or run time.

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.

3.1.3. From MS Visual Studio .NET

The instructions given here are for Visual Studio .NET 2005/2008/2010 with Intel Fortran Compiler 13.0. Other versions may vary.

To ensure that the NAG DLL is accessible at runtime, the PATH environment variable must be set such that the location of the NAG DLL, specifically the folder install dir\bin, is on the path. The location of the MKL DLLs, install dir\MKL_intel64_11.0\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:

  1. Select the Tools pull down menu, and click on Options.

  2. In the Options window, click on Intel(R) Fortran (or Intel(R) Visual Fortran or Intel Composer XE/Visual Fortran/Compiler) and then choose Compilers in the left window pane. (In some versions of Visual Studio you may need to click on Show all settings to see the Intel compiler options.)

  3. In the right window pane, click on the '...' to the right of the Libraries panel.

  4. Add the path to the NAG DLL import library to the Set Directory List window. The default location is:
      c:\Program Files\NAG\FS24\fsw6i24ddl\lib
    

  5. In this implementation, for the DLL version of the library there is no need to add the path to the MKL import libraries, since the BLAS and LAPACK symbols are exported from the NAG import library (FSW6I24DD.lib). (Note that this behaviour may be different from some other NAG Library implementations.) However, any MKL library folders in the Libraries path must come after the path to the NAG Library, as it is important that these are not picked up before the NAG Library, as explained in Section 3.1.

  6. Click on the OK button in the Set Directory List window.

  7. In the right window pane, click on the '...' to the right of the Includes panel.

  8. Add the path to the NAG interface blocks to the Set Directory List window. The default location is:
      c:\Program Files\NAG\FS24\fsw6i24ddl\nag_interface_blocks
    

  9. Click on the OK button in the Set Directory List window.

  10. Click on the OK button in the Options window.

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 FSW6I24DD_static.lib mkl_intel_ilp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib in this location to use the FSW6I24DD_static.lib library and MKL. Please note that the library names are separated by a space only and that FSW6I24DD_static.lib must be the first one. Press the OK button. Similary, to use the DLL version of the NAG library, insert FSW6I24DD.lib 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 DLL. After you select the correct run-time library press the OK button.

As described earlier when compiling from the command line, you should also tell the compiler to use the /Qopenmp switch. From the Properties form, click Fortran in the leftmost panel and then choose Language. Click on the Process OpenMP Directives entry in the right hand panel and select Generate Parallel Code (/QopenMP) from the drop-down list.

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.

Since this version of the NAG library uses 64-bit integer and logical types, it is important that your program should do the same. By default, Fortran integer and logical types are 32-bit. You must either explicitly declare your variables like this:

  integer (kind=8) i, j, k
  logical (kind=8) p
or you can set the appropriate compiler flag to promote the types automatically. This can be done by going to the project properties page under Fortran / Data, and setting Default Integer KIND to 8 (/integer_size64).

Important: in the Visual Studio "Configuration Manager", ensure the Active Solution Platform is set to x64 (to ensure compatibility with this 64-bit implementation of the NAG Library). If x64 is not shown in the list of available platforms, choose New... and type or choose x64, copying settings from Win32. Failure to set the platform to x64 will result in linker errors when you build your project.

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).

3.1.4. From Visual Basic for Applications 7 / Excel

The Fortran DLL provided in this implementation are ideally suited for use within an Excel spreadsheet. The routines may be called from Visual Basic for Applications 7.0 (VBA7) code. The information here applies to 64-bit versions of Excel.

Examples of use of the DLL 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 DLL from within Excel spreadsheets.

Key information:

This has been tested using Microsoft Office Excel 2010.

3.1.5. From Visual Basic .NET

Many of the library routines are callable from Visual Basic .NET (VB.NET). Examples of use of the DLL from VB.NET are given in the install dir\samples\vb.net64_examples folder. (These examples were created using Visual Studio 2005; if loaded into Visual Studio 2008 or later, the solution and project files will be converted by the Visual Studio Conversion Wizard.)

Key information:

This has been tested using Visual Studio 2005, 2008 and 2010.

3.1.6. Calling the Library from Microsoft or Intel C or C++

With care, the NAG Library for SMP and Multicore may be used from within a C or C++ environment. To assist the user make the mapping between Fortran and C types, a C/C++ header file (nagmk24.h) is provided. It is recommended that users wishing to use a Fortran Library routine either copy and paste the relevant section of the file into their C or C++ application (making sure that the relevant #defines etc. are also copied from the top of the file) or simply include the header file with their application.

Examples of the use of the DLL from C and C++ are given in the install dir\samples\c_examples and install dir\samples\cpp_examples folders.

A document, techdoc.html, giving more detailed advice on calling the DLL 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|FS24|NAG Library for SMP and Multicore
       (FSW6I24DDL)|Calling FSW6I24DDL from C & C++
by 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:

Assuming that the folder containing the libraries has been added to the LIB environment variable, you may compile and link your C application program to the DLL version of the NAG Library on the command line in the following manner (assuming you are using Microsoft C):
  cl /MD driver.c FSW6I24DD.lib
where driver.c is your application program. This assumes that the folder containing the header file has been added to the INCLUDE environment variable. If not, you could use:
  cl /MD /I"install dir\c_headers" driver.c FSW6I24DD.lib
To link to the static library instead of the 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 FSW6I24DD_static.lib
      mkl_intel_ilp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib
The 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.

3.1.7. Calling the Library from Microsoft C#

With care, the NAG Library may also be used from within a C# environment. To assist the user make the mapping between Fortran and C# types, a C# header file (flcsdnet64.cs) is provided, in folder install dir\cs_headers. It is recommended that users wishing to use a Fortran Library routine copy and paste the relevant sections of the file into their C# application.

Examples of the use of the DLL from C# are given in the install dir\samples\cs_examples folder. At a command line prompt, these can easily be compiled using the C# compiler csc like this:

  csc driver.cs
where driver.cs is the name of any of the example programs.

For further information, see also http://www.nag.co.uk/numeric/csharpinfo.asp.

3.1.8. Calling the Library from NAG Fortran Builder

It is possible to link to the DLL versions of the NAG library using nagfor, the Fortran Compiler which comes with NAG Fortran Builder. Interface blocks for use with version 5.3 of Fortran Builder are supplied in folder install dir\nag_interface_blocks_nagfor. It is important to note that you must link to the DLL itself, not the associated import library.

From a DOS command prompt, first make sure that the PATH environment variable is correctly set, as described in Section 3.1.2.

You may then compile and link to the NAG Library for SMP and Multicore on the command line using one of the following commands:

  nagfor -i8 -thread_safe -I"install dir\nag_interface_blocks_nagfor" driver.f90
         "install dir\bin\FSW6I24DD.dll" -o driver.exe
Note that the -i8 switch promotes integer and logical types to 64-bit instead of the default 32-bit, in order to maintain compatibility with this NAG library implementation. Also note that the -thread_safe compiler switch ensures that local variables are not statically allocated, as discussed in Section 3.1. In this context, it is also important to note that you should definitely not use nagfor's -save switch, since that has the opposite effect on local variables to that required.

Using the DLL from within the Fortran Builder IDE itself is also easy, following steps like these:

3.1.9. Accessibility Check

To check whether the DLL included in this library implementation is accessible from the current environment, run the program NAG_Fortran_DLL_info.exe which is available from the Start Menu shortcut
  Start|All Programs|NAG|FS24|NAG Library for SMP and Multicore
       (FSW6I24DDL)|Check NAG DLL Accessibility for FSW6I24DDL
See Section 4.2.3 of the Installer's Note for details of this utility.

3.2. Interface Blocks

The NAG Library interface blocks define the type and arguments of each user callable NAG Library routine. These are not essential to calling the NAG Library from Fortran programs. However, they are required if the supplied examples are used. Their purpose is to allow the Fortran compiler to check that NAG Library routines are called correctly. The interface blocks enable the compiler to check that:

(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 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.

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 3.1.2), and the Intel ifort compiler, you can use any of the commands described in Section 3.1.2 to access these modules since the environment variable INCLUDE will be set.

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, as described here.

Create a folder named nag_interface_blocks_original in a location of your choice (the exact folder name is not important), and copy the contents of nag_interface_blocks to nag_interface_blocks_original, thus saving the original set of interface blocks.

Then in folder nag_interface_blocks recompile all the .f90 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 /4I8 -c nag_precisions.f90
  ifort /4I8 -c nag_a_ib.f90
  ifort /4I8 -c nag_blast_ib.f90
  ifort /4I8 -c nag_blas_consts.f90
  ifort /4I8 -c nag_blas_ib.f90
  ifort /4I8 -c nag_c_ib.f90
  ifort /4I8 -c nag_d_ib.f90
  ifort /4I8 -c nag_e_ib.f90
  ifort /4I8 -c nag_f_ib.f90
  ifort /4I8 -c nag_g_ib.f90
  ifort /4I8 -c nag_h_ib.f90
  ifort /4I8 -c nag_lapack_ib.f90
  ifort /4I8 -c nag_m_ib.f90
  ifort /4I8 -c nag_omp_ib.f90
  ifort /4I8 -c nag_s_ib.f90
  ifort /4I8 -c nag_w_ib.f90
  ifort /4I8 -c nag_x_ib.f90
  ifort /4I8 -c nag_long_names.f90
  ifort /4I8 -c nag_library.f90
The object files generated by the compilation may be discarded - only the module files are needed.

You should now be able to use the newly compiled module files in the usual way.

3.3. Example Programs

The example results distributed were generated at Mark 24, using the software described in Section 2.2 of the Installer's Note. These example results may not be exactly reproducible if the example programs are run in a slightly different environment (for example, a different Fortran compiler, a different compiler library, or a different set of Basic Linear Algebra Subprograms (BLAS) or Linear Algebra PACKage (LAPACK) routines). The results which are most sensitive to such differences are: eigenvectors (which may differ by a scalar multiple, often -1, but sometimes complex); numbers of iterations and function evaluations; and residuals and other "small" quantities of the same order as the machine precision.

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 the batch files nagsmp_example_static.bat or nagsmp_example_dll.bat which are in the folder install_dir\batch.

The batch files need the environment variable NAG_FSW6I24DDL.

As mentioned in Section 3.1.2, the installation procedure provides a shortcut which starts a Command Prompt with local environment variables. The environment variables include NAG_FSW6I24DDL. This shortcut is placed in the Start Menu under

  Start|All Programs|NAG|FS24|NAG Library for SMP and Multicore
       (FSW6I24DDL)|FSW6I24DDL Command Prompt
If 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\FS24\fsw6i24ddl\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing FSW6I24DDL.

The batch script nagsmp_example_static.bat will provide you with a copy of an example program (and its data, if any), compile the program and link it with the library FSW6I24DD_static.lib and the MKL. Finally, the executable program will be run.

The example program concerned, and the number of OpenMP threads to use, are specified by the arguments to nagsmp_example_static.bat, e.g.

  nagsmp_example_static e04ucf 4
will copy the example program e04ucfe.f and its data file e04ucfe.d into the current directory and process them to produce the example program results in the file e04ucfe.r.

Alternatively you could use:

  nagsmp_example_dll e04ucf 4

The difference between nagsmp_example_static.bat and nagsmp_example_dll.bat is that while nagsmp_example_static.bat links to the static version of the NAG SMP and MKL Libraries, nagsmp_example_dll.bat links to the DLL version of the libraries.

3.4. Fortran Types and Interpretation of Bold Italicised Terms

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 1.0D-16.

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.

3.5. Explicit Output from NAG Routines

Certain routines produce explicit error messages and advisory messages via output units which have default values that can be reset by using X04AAF for error messages and X04ABF for advisory messages. (The default values are given in Section 4.) These routines are potentially not thread safe and in general output is not recommended in a multithreaded environment.

4. Routine-specific Information

Any further information which applies to one or more routines in this implementation is listed below, chapter by chapter.
  1. C06

    In this implementation calls to the Intel Discrete Fourier Transforms Interface (DFTI) routines, from the supplied MKL library, are made whenever possible in the following NAG routines:
     C06PAF  C06PCF  C06PFF  C06PJF  C06PKF  C06PPF  C06PQF  C06PRF
     C06PSF  C06PUF  C06PVF  C06PWF  C06PXF  C06PYF  C06PZF  C06RAF
     C06RBF  C06RCF  C06RDF
    
    The 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.

  2. C09

    Due to limitations in the current version of the Intel compiler, the following routines are serial in this implementation:
     C09FAF  C09FBF  C09FCF  C09FDF
    

  3. F06, F07, F08 and F16

    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 Intel 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:

    DGERFS    DGGEVX    DGGGLM    DSBEV     DSBEVX    DSBTRD    ZGEESX    ZHBEV
    ZHBEVX    ZHBTRD    ZTRSEN
    

    The following NAG named routines are wrappers to call LAPACK routines from the vendor library:
    F07ADF/DGETRF    F07AEF/DGETRS    F07ARF/ZGETRF    F07ASF/ZGETRS
    F07AVF/ZGERFS    F07BDF/DGBTRF    F07BEF/DGBTRS    F07BHF/DGBRFS
    F07BRF/ZGBTRF    F07BSF/ZGBTRS    F07BVF/ZGBRFS    F07CHF/DGTRFS
    F07CVF/ZGTRFS    F07FDF/DPOTRF    F07FEF/DPOTRS    F07FHF/DPORFS
    F07FJF/DPOTRI    F07FRF/ZPOTRF    F07FSF/ZPOTRS    F07FVF/ZPORFS
    F07GEF/DPPTRS    F07GHF/DPPRFS    F07GSF/ZPPTRS    F07GVF/ZPPRFS
    F07HEF/DPBTRS    F07HHF/DPBRFS    F07HSF/ZPBTRS    F07HVF/ZPBRFS
    F07JHF/DPTRFS    F07JVF/ZPTRFS    F07MHF/DSYRFS    F07MVF/ZHERFS
    F07NVF/ZSYRFS    F07PHF/DSPRFS    F07PVF/ZHPRFS    F07QVF/ZSPRFS
    F07THF/DTRRFS    F07TVF/ZTRRFS    F07UEF/DTPTRS    F07UHF/DTPRFS
    F07USF/ZTPTRS    F07UVF/ZTPRFS    F07VEF/DTBTRS    F07VHF/DTBRFS
    F07VSF/ZTBTRS    F07VVF/ZTBRFS    F08AEF/DGEQRF    F08AFF/DORGQR
    F08AGF/DORMQR    F08ASF/ZGEQRF    F08ATF/ZUNGQR    F08AUF/ZUNMQR
    F08FEF/DSYTRD    F08FFF/DORGTR    F08FSF/ZHETRD    F08FTF/ZUNGTR
    F08GFF/DOPGTR    F08GTF/ZUPGTR    F08JEF/DSTEQR    F08JJF/DSTEBZ
    F08JKF/DSTEIN    F08JSF/ZSTEQR    F08JXF/ZSTEIN    F08KEF/DGEBRD
    F08KSF/ZGEBRD    F08MEF/DBDSQR    F08MSF/ZBDSQR    F08NEF/DGEHRD
    F08NGF/DORMHR    F08NSF/ZGEHRD    F08PEF/DHSEQR    F08PKF/DHSEIN
    F08PSF/ZHSEQR    F08PXF/ZHSEIN    F08TAF/DSPGV     F08TBF/DSPGVX
    F08TCF/DSPGVD    F08TNF/ZHPGV     F08TPF/ZHPGVX    F08TQF/ZHPGVD
    

  4. G02

    The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0D-13.

  5. P01

    On hard failure, P01ABF writes the error message to the error message unit specified by X04AAF and then stops.

  6. S07 - S21

    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
    

  7. X01

    The values of the mathematical constants are:
    X01AAF (pi) = 3.1415926535897932
    X01ABF (gamma) = 0.5772156649015328
    

  8. X02

    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   = 9223372036854775807
    X02BEF   = 15
    

  9. X04

    The default output units for error and advisory messages for those routines which can produce explicit output are both Fortran Unit 6.
  10. Routines that call User Functions within OpenMP Parallel Regions

    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 OpenMP directives or pragmas within the user functions should be avoided, unless you are using the same OpenMP runtime library (which normally means using the same compiler) as that used to build your NAG Library implementation, as listed in the Installers' Note. 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.

5. Documentation

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_fl24/html/FRONTMATTER/manconts.html
	nagdoc_fl24/pdf/FRONTMATTER/manconts.pdf
	nagdoc_fl24/pdf/FRONTMATTER/manconts.html
Use 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:

Please see the Intel web site for further information about MKL (http://www.intel.com/software/products/mkl).

6. Support from NAG

(a) Contact with NAG

Queries concerning this document or the implementation generally should be directed to NAG at one of the addresses given in the Appendix. Users subscribing to the support service are encouraged to contact one of the NAG Response Centres (see below).

(b) NAG Response Centres

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 FSW6I24DDL).

(c) NAG Websites

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:

http://www.nag.co.uk/, http://www.nag.com/, http://www.nag-j.co.jp/ or http://www.nag-gc.com/

(d) NAG Electronic Newsletter

If you would like to be kept up to date with news from NAG then please register to receive our free electronic newsletter, which will alert you to announcements about new products or product/service enhancements, technical tips, customer stories and NAG's event diary. You can register via one of our websites, or by contacting us at nagnews@nag.co.uk.

(e) Product Registration

To ensure that you receive information on updates and other relevant announcements, please register this product with us. For NAG Library products this may be accomplished by filling in the online registration form at http://www.nag.co.uk/numeric/Library_Registration.asp.

7. User Feedback

Many factors influence the way that NAG's products and services evolve, and your ideas are invaluable in helping us to ensure that we meet your needs. If you would like to contribute to this process, we would be delighted to receive your comments. Please contact any of the NAG Response Centres (shown below).

Appendix - Contact Addresses

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