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.
Fortran 90/95/2003 users are advised that the compiled *.mod files (the interface blocks) have been compiled with the Intel Fortran Compiler 13.0 and are intended for use with that compiler. Users may have to compile the interface blocks themselves if they wish to use them with a different compiler.
for details of any new information related to the applicability or usage of this implementation.
c:\Program Files\NAG\FL24\fldll244mlIf 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:
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.)
(Under Windows 8, the shortcuts appear under the list of all applications. To find this, right-click on the background of the Start screen and select All apps from the bottom right hand corner of the screen. The shortcuts are listed under the NAG section.)
To ensure that the NAG DLL (FLDLL244M_mkl.dll or FLDLL244M_nag.dll) is accessible at run time, the install dir\bin folder must be on the path. If the MKL-based version of the Library is to be used, the install dir\MKL_ia32_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 a few Basic Linear Algebra Subprograms (BLAS) / Linear Algebra PACKage (LAPACK) routines 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|FL24|NAG Fortran Library for Win32 Applications (FLDLL244ML)|Check NAG DLL Accessibility for FLDLL244MLSee Section 4.2.3 of the Installer's Note for details of this utility.
See Section 184.108.40.206 below for information on setting environment variables from a command prompt. The PATH, LIB and INCLUDE environment variables may already have been set globally as part of the installation or this may be done via the Control Panel. (On Windows XP, from Control Panel select System | Advanced | Environment Variables; on Vista, Windows 7 or Windows 8 from the Control Panel home select System and Maintenance (on Vista) / System and Security (on Windows 7 or Windows 8), then System | Advanced System Settings | Environment Variables... .) Either the user variables or the system variables may be edited, although Administrator privileges will be required to edit the system ones. Edit the PATH environment variable to include
c:\Program Files\NAG\FL24\fldll244ml\batch; c:\Program Files\NAG\FL24\fldll244ml\bin; c:\Program Files\NAG\FL24\fldll244ml\MKL_ia32_11.0\bin; existing pathadd or edit the LIB environment variable to include
c:\Program Files\NAG\FL24\fldll244ml\lib; any existing library pathadd or edit the INCLUDE environment variable to include
c:\Program Files\NAG\FL24\fldll244ml\nag_interface_blocks; any existing include pathsubstituting the correct folder where the NAG Fortran DLLs are installed if necessary.
In this DLL implementation, for convenience, the MKL symbols are exported directly from the NAG import library FLDLL244M_mkl.lib, so it is not necessary to specify the MKL interface libraries mkl_intel_s_dll.lib, mkl_intel_thread_dll.lib and mkl_core_dll.lib as well. However, if the MKL interface libraries are specified, it is important that the NAG import library precedes them, i.e. the order should be
FLDLL244M_mkl.lib mkl_intel_s_dll.lib mkl_intel_thread_dll.lib mkl_core_dll.libbecause certain parts of the MKL should not be used (see Section 4).
Information on calling the NAG Fortran DLLs from various different environments is given below. More information on calling NAG Fortran or C DLLs is available on the NAG web site at
http://www.nag.co.uk/numeric/Num_DLLhelp.aspMore information specific to this product may be available from the Post Release Information page:
Start|All Programs|NAG|FL24|NAG Fortran Library for Win32 Applications (FLDLL244ML)|FLDLL244ML 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\FL24\fldll244ml\batch\envvars.batIf the file is not in the default location, you can locate it by searching for the file envvars.bat containing fldll244ml.
You may then compile and link to the NAG Fortran Library on the command line using one of the following commands:
ifort /iface:cvf /MD driver.f90 FLDLL244M_mkl.lib ifort /iface:cvf /MD driver.f90 FLDLL244M_nag.libwhere driver.f90 is your application program.
The first command will use the DLL without the NAG version of the BLAS/LAPACK procedures (FLDLL244M_mkl.lib) in addition to the MKL DLLs. It is not necessary to add the path to the MKL import libraries here, since the BLAS and LAPACK symbols are exported from the NAG import library (FLDLL244M_mkl.lib) in this instance. (Note that this behaviour may be different from some other NAG library implementations.) The second command will use the DLL with the NAG version of the BLAS/LAPACK procedures (FLDLL244M_nag.lib). The option /MD should be used to ensure linking with the correct run-time libraries.
Please note that the Intel Visual Fortran compiler environment variables must be set in the command window. For more details refer to the Users' 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_ia32_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:
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.
The following steps show how to add the NAG Library to the project:
In summary, the setting of the project Additional Dependencies, the project Runtime Library and the PATH environment variable must be consistent as follows:
To run a program from within the Microsoft Development Environment, the program may be executed via the Debug menu (by selecting Start Without Debugging, for example).
For Visual Studio 2005 and later, 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, this can be achieved by selecting the Debugging section on the Properties form and inserting the appropriate commands in the Command Arguments field, e.g.
< input_file > output_fileIf the input and output files are not in the application's working directory, full or relative paths may need to be specified. For NAG examples that use an .opt file, this should be placed in the working directory. This directory may be set via the Working Directory field, which is also on the Debugging page of the Properties form. (Note that input / output redirection is broken in some versions of Visual Studio 2008.)
At a command line, commands such as the following may then be used to call the NAG DLLs from the NAG Fortran Compiler (nagfor):
nagfor -compatible -I "install dir"\nag_interface_blocks_nagfor -o driver.exe driver.f90 "install dir\lib\FLDLL244M_mkl.lib"or
nagfor -compatible -I "install dir"\nag_interface_blocks_nagfor -o driver.exe driver.f90 "install dir\lib\FLDLL244M_nag.lib"where driver.f90 is your application program and driver.exe is the executable produced, and nag_interface_blocks_nagfor is the directory containing the compiled module files.
The full pathname of the FLDLL244M_mkl.lib or FLDLL244M_nag.lib file must be specified and must be enclosed within quotes if it contains spaces.
Using the DLLs from within the Fortran Builder IDE itself is also easy, following steps like these:
It is important to note that the interface file nag_precisions.f90 may need to be modified before it can be compiled with FTN95. The Fortran kind function may not be recognised by the compiler as an intrinsic function. If that is the case, you should delete the intrinsic declarations of kind and selected_int_kind, and change the other parameters to look like this:
INTEGER, PARAMETER :: HP = 2 INTEGER, PARAMETER :: I4B = 3 INTEGER, PARAMETER :: RP = 1 INTEGER, PARAMETER :: WP = 2
In addition, the interface file nag_e_ib.f90 has been observed to fail to compile with FTN95 due to a declaration of the intrinsic function MAX. Simply deleting the declaration should make it work.
Since FTN95 uses a variant of the cdecl calling convention, the compiler must be told that the routines in the DLLs are to be called using the CVF calling convention. This can be accomplished using the /import_lib command line switch as follows:
ftn95 /f_stdcall /mod_path nag_interface_blocks_ftn95 driver.f90 /import_lib "install dir\bin\FLDLL244M_mkl.dll" /linkor
ftn95 /f_stdcall /mod_path nag_interface_blocks_ftn95 driver.f90 /import_lib "install dir\bin\FLDLL244M_nag.dll" /link(This assumes that you have placed the compiled NAG interface blocks into directory nag_interface_blocks_ftn95).
The full pathname of install dir should be specified to the DLLs and should be enclosed within quotes if it contains spaces. The effect of this is to assume that all exported names in the DLL are CVF STDCALL and that any use of them should use the CVF STDCALL calling convention. External names passed via the argument list to a routine in a NAG DLL are automatically adjusted for whether or not they occur in the same source.
It is also possible to compile and link using commands such as
ftn95 /f_stdcall /mod_path nag_interface_blocks_ftn95 driver.f90 slink driver.obj "install dir\bin\FLDLL244M_mkl.dll"As with compilation, the full path to the DLLs should be specified here, within quotes if the pathname contains spaces. It is worth emphasising that the linker should link directly against the DLLs, not the *.lib files.
A possible limitation of the FTN95 compiler means that if the driver program itself contains a Fortran MODULE defining a routine to be passed as an argument to a NAG routine, the argument may not be given the STDCALL attribute, and linking may fail (or the program may fail at run time). This limitation has been observed during testing with version 6.00.0 of FTN95. Internal modules are used in many of the NAG Example Programs. You are advised to replace such internal modules by external routine declarations.
Another minor limitation of FTN95 is that it does not support the Fortran FLUSH statement (which is part of the Fortran 2003 standard). Some NAG example programs use FLUSH to ensure that output from the NAG DLL comes out in the expected order. You may need to comment out calls to FLUSH in order to compile.
Plato3 is the Integrated Development Environment (IDE) that is provided with the more recent versions of FTN95. To use Plato3 for a project involving a NAG routine:
open(6,file='c:\test.res')in the main program before any write statements to channel 6.
Assuming that the LIB and PATH environment variables have been set up appropriately for your installation of the NAG Library, the command for linking to the Mark 24 DLLs using pgf90 is:
pgf90 driver.f90 -module nag_interface_blocks_pgi FLDLL244M_mkl.lib -o driver.exe(for the MKL-based variant of the Library), or
pgf90 driver.f90 -module nag_interface_blocks_pgi FLDLL244M_nag.lib -o driver.exe(for the self-contained variant of the Library). In both cases nag_interface_blocks_pgi is the directory containing your compiled module files.
This has been tested using version
install dir\samples\lahey_fortran_exampleThe advice given here has been tested using Lahey Fortran version 7.2.
There are a few simple changes that must be made to a standard Fortran program to allow the NAG DLLs to be used by Lahey Fortran:
DLL_IMPORT OUTand in the user-supplied subroutine or function insert a DLL_EXPORT statement i.e.
DLL_EXPORT OUTshould be inserted in subroutine OUT.
Remember to declare all these subroutines and functions as EXTERNAL and also to declare the type of any functions used. The names of imported functions are case sensitive; this means that NAG names must be in upper case.
The second family of changes concern the treatment of character arguments which must be adjusted to suit the convention used by the NAG DLLs. Character arguments must be stripped of the hidden length argument that Lahey places at the end of all the arguments; this is accomplished by passing the value of the address of the argument as follows: VAL(POINTER(char_arg)). Then, to conform to the NAG DLL standard, the length argument needs to be added immediately following the character argument. Both arguments are passed by value. Here is an example:
CALL D02CJF (X, XEND2, N, Y, FCN, TOL, VAL(POINTER('Default')), + VAL(LEN('Default')), OUT, G, W, IFAIL)
Use the compiler switch
lf95 d02cjfe.f "install dir\lib\FLDLL244M_mkl.lib" -ml bcor
lf95 d02cjfe.f "install dir\lib\FLDLL244M_nag.lib" -ml bc
Ensure that the DLLs are on the PATH.
Note that, because of the different calling conventions used, when calling the NAG Fortran Library from the Lahey Compiler, it may be easier to use the DLLs included with the product FLW3224DC. Details may be given in the Post Release Notes for that product: http://www.nag.co.uk/doc/inun/fl24/w32dc/postrelease.html
If you wish to use the NAG Fortran Library interface blocks (e.g. if you are compiling a NAG example program) you may first need to create the module files as described in Section 3.2.
Commands such as the following may be used for calling the NAG Fortran Library Mark 24 DLLs from gfortran, where driver.f90 is your application program and driver.exe is the executable produced.
Using gfortran from a Windows Command Prompt:
gfortran -mrtd -Inag_interface_blocks_gfortran driver.f90 "install dir\lib\FLDLL244M_mkl.lib" -o driver.exeor
gfortran -mrtd -Inag_interface_blocks_gfortran driver.f90 "install dir\lib\FLDLL244M_nag.lib" -o driver.exeUsing gfortran from a Cygwin xterm:
gfortran -mrtd -Inag_interface_blocks_gfortran driver.f90 "install dir/lib/FLDLL244M_mkl.lib" -o driver.exeor
gfortran -mrtd -Inag_interface_blocks_gfortran driver.f90 "install dir/lib/FLDLL244M_nag.lib" -o driver.exeIn all cases, nag_interface_blocks_gfortran is the directory containing your compiled module files.
Character string arguments demand special attention. The NAG Library uses the Intel ifort /iface:cvf calling convention, part of which means that the compiler inserts "hidden" arguments immediately after each argument of Fortran type character. These hidden arguments are the lengths of the character strings. The gfortran compiler puts these hidden arguments at the end of the argument list, thus causing a mismatch when calling library routines. If you do not attend to this problem, your code is likely to crash. Currently there is no way to tell gfortran to insert the hidden arguments anywhere but at the end of the argument list.
The solution to this problem is to explicitly insert the values of the hidden arguments.
Immediately after each character string argument in the call of a NAG routine, pass by value the length of the string. For example the first argument of function g01faf is a character tail. Call g01faf like this:
dev = g01faf(tail,%VAL(1),p,ifail)where %VAL(1) tells the compiler to pass the length 1 by value.
Unfortunately, explicitly adding this extra hidden argument means that the call of g01faf no longer matches the NAG interface block declaration of g01faf, so the compiler will complain if you try to USE the interface block. Instead, you should declare g01faf to be external and of the correct type in your program.
In a similar way, in the example program d02cjfe.f90, you need to replace the formal argument relabs (actual argument 'Default') in all the calls to the routine d02cjf by:
'Default',%VAL(7)and declare d02cjf as external rather than getting it from the NAG interface block module.
For library routines where an argument is a character array, pass the length of each array element.
This information has been tested with GNU Fortran 4.3.4 which comes from the Cygwin distribution.
Modified versions of the example programs d02cjfe.f90 and g01fafe.f are provided to illustrate the use of the NAG DLLs with gfortran. These files can be found in the folder
Note that NAG example programs which do not call NAG routines with character arguments need no modification for use with gfortran.
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.
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|FL24|NAG Fortran Library for Win32 Applications (FLDLL244ML)|Calling FLDLL244ML 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.
cl driver.c FLDLL244M_mkl.libor
cl driver.c FLDLL244M_nag.libwhere 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 /I"install dir\c_headers" driver.c FLDLL244M_mkl.libor
cl /I"install dir\c_headers" driver.c FLDLL244M_nag.lib
The following instuctions apply to Visual Studio .NET 2003, Visual Studio 2005 and Visual Studio 2008. Later versions may vary.
If you are working under the Visual Studio IDE, set the following values to enable linking to work. Under the project's Properties, select Configuration Properties | Linker | Input and add FLDLL244M_mkl.lib or FLDLL244M_nag.lib to the Additional Dependencies field. If the LIB environment variable has not been set elsewhere, select Configuration Properties | Linker | General and add install dir\lib to the Additional Library Directories field.
Note that, with Microsoft C++, you may need to use the /EHsc compiler switch with the command line C++ examples.
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 NAG Fortran Library on the command line in the following manner:
icl /I"install dir\c_headers" driver.c FLDLL244M_mkl.libor
icl /I"install dir\c_headers" driver.c FLDLL244M_nag.libwhere driver.c is your application program.
Commands such as the following may be used to call the NAG Fortran Library for Win32 Applications from gcc or g++, where driver.c or driver.cpp is your application program and driver.exe is the executable produced.
Using gcc to compile a C program from a Windows Command Prompt:
gcc -D _WIN32 -I "install dir\c_headers" driver.c "install dir\lib\FLDLL244M_mkl.lib" -o driver.exeor
gcc -D _WIN32 -I "install dir\c_headers" driver.c "install dir\lib\FLDLL244M_nag.lib" -o driver.exe
Using gcc to compile a C program from a Cygwin xterm:
gcc -D _WIN32 -I "install dir/c_headers" driver.c "install dir/lib/FLDLL244M_mkl.lib" -o driver.exeor
gcc -D _WIN32 -I "install dir/c_headers" driver.c "install dir/lib/FLDLL244M_nag.lib" -o driver.exe
Using g++ to compile a C++ program from a Windows Command Prompt:
g++ -D _WIN32 -I "install dir\c_headers" driver.cpp "install dir\lib\FLDLL244M_mkl.lib" -o driver.exeor
g++ -D _WIN32 -I "install dir\c_headers" driver.cpp "install dir\lib\FLDLL244M_nag.lib" -o driver.exe
Using g++ to compile a C++ program from a Cygwin xterm:
g++ -D _WIN32 -I "install dir/c_headers" driver.cpp "install dir/lib/FLDLL244M_mkl.lib" -o driver.exeor
g++ -D _WIN32 -I "install dir/c_headers" driver.cpp "install dir/lib/FLDLL244M_nag.lib" -o driver.exe
This information has been tested with gcc version 4.3.4 from the from the Cygwin distribution.
Examples of use of the DLLs from within Excel are given in the install dir\samples\excel_examples folder. The folder install dir\samples\excel_examples\linear_algebra contains the file xls_demo.html. This file gives some hints about using NAG DLLs from within Excel spreadsheets. See also the VB 6 examples for further illustrations of calling the NAG DLLs from VB 6 / VBA.
This has been tested using Microsoft Office Excel 2003, 2007 and 2010.
Examples of use of the DLLs from Visual Basic 6 are given in the install dir\samples\vb6_examples folder. See also the VBA code within the Excel examples for further illustrations of calling the NAG DLLs from VB 6 / VBA.
This has been tested using Microsoft Visual Basic 6.0.
This has been tested using Visual Studio .NET 2003, 2005, 2008 and 2010.
If running on a 64-bit system, it may be necessary to set the Target CPU to x86 to avoid a BadImageFormatException.
Examples of use of the DLLs from C# are given in the install dir\samples\cs_examples folder. They may be compiled with the C# compiler in a command line like this:
csc driver.cs(Note that the DLL name is embedded in the example files.)
You may also be interested in the NAG Library for .NET – see http://www.nag.co.uk/microsoft_dotnet.asp for details.
However, it is very much easier to use the NAG Library for Java.
or contact us via one of the addresses listed in the Appendix.
Start|All Programs|NAG|FL24|NAG Fortran Library for Win32 Applications (FLDLL244ML)|Check NAG DLL Accessibility for FLDLL244MLSee 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.
The NAG Fortran Library interface block files are organised by Library chapter. They are aggregated into one module named
The modules are supplied in pre-compiled form (.mod files) for 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 220.127.116.11), and the Intel ifort compiler, you can use any of the commands described in Section 18.104.22.168 to access these modules since the environment variable INCLUDE will be set.
The .mod module files were compiled with the compiler shown in Section 2.2 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 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. Here we use the Intel compiler ifort for illustration - you should replace ifort /iface:cvf by the name of the compiler you wish to use along with any necessary compiler switches.
ifort /iface:cvf -c nag_precisions.f90 ifort /iface:cvf -c nag_a_ib.f90 ifort /iface:cvf -c nag_blast_ib.f90 ifort /iface:cvf -c nag_blas_consts.f90 ifort /iface:cvf -c nag_blas_ib.f90 ifort /iface:cvf -c nag_c_ib.f90 ifort /iface:cvf -c nag_d_ib.f90 ifort /iface:cvf -c nag_e_ib.f90 ifort /iface:cvf -c nag_f_ib.f90 ifort /iface:cvf -c nag_g_ib.f90 ifort /iface:cvf -c nag_h_ib.f90 ifort /iface:cvf -c nag_lapack_ib.f90 ifort /iface:cvf -c nag_m_ib.f90 ifort /iface:cvf -c nag_omp_ib.f90 ifort /iface:cvf -c nag_s_ib.f90 ifort /iface:cvf -c nag_w_ib.f90 ifort /iface:cvf -c nag_x_ib.f90 ifort /iface:cvf -c nag_long_names.f90 ifort /iface:cvf -c nag_library.f90The 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.
The distributed example results are those obtained with the DLL library FLDLL244M_mkl.lib, (i.e. using the MKL BLAS and LAPACK routines).
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:
The batch files need the environment variable NAG_FLDLL244ML.
As mentioned in Section 22.214.171.124, the installation procedure provides a shortcut which starts a Command Prompt with local environment variables. The environment variables include NAG_FLDLL244ML. This shortcut is, by default, placed in the Start Menu under
Start|All Programs|NAG|FL24|NAG Fortran Library for Win32 Applications (FLDLL244ML)|FLDLL244ML 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\FL24\fldll244ml\batch\envvars.batIf the file is not in the default location, you can locate it by searching for the file envvars.bat containing fldll244ml.
Each of the nag_example* batch files mentioned above 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 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 folder and process them 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 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
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 BLAS and LAPACK routines are included in the library FLDLL244M_mkl.dll to avoid problems with the vendor version:
DBDSDC DGEES DGEESX DGERFS DGGES DGGESX DGGEVX DSBEV DSBEVX ZGEES ZGEESX ZGGES ZGGESX ZHBEV ZHBEVX ZTRSEN
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 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 arithmeticX02AJF = 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 environmentX02AHF = 1.42724769270596E+45 X02BBF = 2147483647 X02BEF = 15
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