NAG Fortran Library, Mark 21

FLW3221DML - License Managed

Windows NT/2000/XP/Vista, Intel Visual Fortran (/MT)

Users' Note



Contents


1. Introduction

This document is essential reading for every user of the NAG Fortran Library implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Mark 21 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 the use of multiple threads.

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. Availability of Routines

All routines listed in the chapter contents documents of the Library Manual are available in this implementation. Please consult Mark 21 News (see Section 5) for a list of new routines and for a list of routines scheduled for withdrawal at future Marks. Your suggestions for new algorithms for future releases of the Library are welcomed (see Section 7).

3. General Information

3.1. Accessing the Library

In this section we assume that the Library has been installed in the default folder:
  c:\Program Files\NAG\FL21\flw3221dml
If this folder does not exist, please consult the system manager (or the person who did the installation).

We also assume that the default shortcut for the Library command prompt is placed in the Start Menu under:

  Start|All Programs|NAG|FL21|

If this shortcut does not exist, please consult the system manager (or the person who did the installation).

3.1.1. 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|FL21|NAG Fortran Library -
      Intel Visual Fortran compiler(FLW3221DML). 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\FL21\flw3221dml\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw3221dml.

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

  ifort /MT driver.f nag_mkl.lib libguide.lib mkl_c.lib
  ifort /MT driver.f nag_nag.lib
where driver.f is your application program. The order of the libraries in the first command is important because certain parts of the MKL should not be used.

The /MT option MUST be used to specify linking with the correct static multithreaded run time library.

The first command will use the library without the NAG version of the BLAS/LAPACK procedures (nag_mkl.lib) with the MKL libraries mkl_c.lib and libguide.lib.

The second command will use the library with the NAG version of the BLAS/LAPACK procedures (nag_nag.lib).

In the case where more than one library is used, you could simplify the command line by using the librarian to combine the libraries into a single library. For example you could use:

  lib /out:my_nag_mkl.lib nag_mkl.lib libguide.lib mkl_c.lib
(as mentioned before the order of the libraries is important because certain parts of the MKL should not be used (see Section 4)), you can then replace the first command with:
  ifort /MT driver.f my_nag_mkl.lib
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 of the compiler.

3.1.2. From MS Visual Studio .NET

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, move the mouse over Options and left-click on it.
  2. In the Options window, move the mouse over the left window pane to Intel(R) Fortran and left-click on it.
  3. Move the mouse to the right window pane and left-click on the '...' to the right of the Libraries panel.
  4. Add the path to the NAG Library to the Set Directory List window. The default location is:
    "c:\Program Files\NAG\FL21\flw3221dml\lib"
  5. If you intend to use the MKL libraries then you need to add the path to the MKL libraries after the path to the NAG Library. The default location is:
    "c:\Program Files\NAG\FL21\flw3221dml\MKL_ia32_9.1\lib"
  6. Left-click on the OK button in the Set Directory List window.
  7. Move the mouse to the right window pane and left-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\FL21\flw3221dml\nag_interface_blocks"
  9. Left-click on the OK button in the Set Directory List window.
  10. Left-click on the OK button in the Options window.
From now, if an Intel Fortran project requires a library or NAG interface block then the library and interface block do not need the full path to be specified.

The interface block is simply accessed by inserting a USE statement as described in greater detail in Section 3.5.

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 designed 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. If you work in Debug mode, you may receive a warning message about conflicting C runtime libraries. This is usually harmless.

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 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.lib libguide.lib mkl_c.lib in this location to use the nag_mkl.lib library and MKL. Please note that the three libraries are separated by a space only and that nag_mkl.lib must be the first one. Press the OK button. If you wish to use the self-contained NAG Library then you need to add nag_nag.lib instead.

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. As in the paragraph above, 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 the names of the relevant libraries in this location. Press the OK button.

Before you can compile the project you need to specify that multithreaded runtime libraries need to be used. 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 then press the OK button.

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 the current version of Visual Studio .NET.

3.2. Example Programs

The example programs are most easily accessed by the batch files nag_example.bat or nag_example_mkl.bat.

The batch files need the environment variable NAG_FLW3221DML.

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_FLW3221DML. This shortcut is placed in the Start Menu under

  Start|All Programs|NAG|FL21|NAG Fortran Library -
      Intel Visual Fortran compiler(FLW3221DML). Command Prompt
If the shortcut is not used, you need to set this environment variable. You can set this environment variable by running the batch file envvars.bat for this implementation. The default location of this file is:
  c:\Program Files\NAG\FL21\flw3221dml\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw3221dml.

nag_example_mkl.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 nag_mkl.lib and the MKL. Finally, the executable program will be run. The example program concerned is specified by the argument to nag_example_mkl.bat, e.g.

  nag_example_mkl  e04ucf
will copy the example program and its data into the files e04ucfe.f and e04ucfe.d in the current folder and process them to produce the example program results in the file e04ucfe.r.

Alternatively you could use:

  nag_example  e04ucf

The difference between nag_example_mkl.bat and nag_example.bat is that while nag_example_mkl.bat uses the library nag_mkl.lib and the MKL libraries, nag_example.bat uses the self-contained library nag_nag.lib.

The example programs are supplied in machine-readable form. They are suitable for immediate usage. Note that the distributed example programs are those used in this implementation and may not correspond exactly with the programs published in the Library Manual. The distributed example programs should be used in preference wherever possible.

The distributed example results are those obtained with the NAG self-contained library nag_nag.lib, (using the NAG BLAS and LAPACK routines). Running the examples with MKL BLAS or LAPACK may give slightly different results.

3.3. Interpretation of Bold Italicised Terms

For this double precision implementation, the bold italicised terms used in the Library Manual should be interpreted as follows:
real or double precision  - DOUBLE PRECISION (REAL*8)
basic precision           - double precision
complex or complex*16     - COMPLEX*16
additional precision      - quadruple precision (REAL*16,COMPLEX*32)
machine precision         - the machine precision, see the value
                            returned by X02AJF in Section 4
Thus a parameter described as real or double precision should be declared as DOUBLE PRECISION in your program. If a routine accumulates an inner product in additional precision, it is using software to simulate quadruple precision.

All references to routines in Chapter F07 - Linear Equations (LAPACK) and Chapter F08 - Least-squares and Eigenvalue Problems (LAPACK) use the LAPACK name, not the NAG F07/F08 name.

3.4. Explicit Output from NAG Routines

Certain routines produce explicit error messages and advisory messages via output units which either have default values or can be reset by using X04AAF for error messages and X04ABF for advisory messages. (The default values are given in Section 4.) The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified.

3.5. Interface Blocks

The NAG Fortran Library Interface Blocks define the type and arguments of each user callable NAG Fortran Library routine. These are not essential to calling the NAG Fortran Library from Fortran 90/95 programs. Their purpose is to allow the Fortran 90/95 compiler to check that NAG Fortran 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
(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_f77_a_chapter
  nag_f77_c_chapter
  nag_f77_d_chapter
  nag_f77_e_chapter
  nag_f77_f_chapter
  nag_f77_g_chapter
  nag_f77_h_chapter
  nag_f77_m_chapter
  nag_f77_p_chapter
  nag_f77_s_chapter
  nag_f77_x_chapter
These are supplied in pre-compiled form (.mod files).

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.

In order to make use of these modules from existing Fortran 77 code, the following changes need to be made:

The above steps need to be done for each unit (main program, function or subroutine) in your code.

These changes are illustrated by showing the conversion of the Fortran 77 version of the example program for NAG Fortran Library routine D01DAF. Please note that this is not exactly the same as the example program that is distributed with this implementation. Each change is surrounded by comments boxed with asterisks.

*     D01DAF Example Program Text
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_D_CHAPTER
*                                                   *
*****************************************************
*     .. Parameters ..
      INTEGER          NOUT
      PARAMETER        (NOUT=6)
*     .. Local Scalars ..
      DOUBLE PRECISION ABSACC, ANS, YA, YB
      INTEGER          IFAIL, NPTS
*     .. External Functions ..
      DOUBLE PRECISION FA, FB, P1, P2A, P2B
      EXTERNAL         FA, FB, P1, P2A, P2B
*     .. External Subroutines ..
******************************************************
* EXTERNAL declarations need to be removed.          *
C     EXTERNAL         D01DAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      WRITE (NOUT,*) 'D01DAF Example Program Results'
      YA = 0.0D0
      YB = 1.0D0
      ABSACC = 1.0D-6
      WRITE (NOUT,*)
      WRITE (NOUT,*) 'First formulation'
      IFAIL = 1
*
      CALL D01DAF(YA,YB,P1,P2A,FA,ABSACC,ANS,NPTS,IFAIL)
*
      WRITE (NOUT,99999) 'Integral =', ANS
      WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
      IF (IFAIL.GT.0) WRITE (NOUT,99997) 'IFAIL = ', IFAIL
      WRITE (NOUT,*)
      WRITE (NOUT,*) 'Second formulation'
      IFAIL = 1
*
      CALL D01DAF(YA,YB,P1,P2B,FB,ABSACC,ANS,NPTS,IFAIL)
*
      WRITE (NOUT,99999) 'Integral =', ANS
      WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
      IF (IFAIL.GT.0) WRITE (NOUT,99997) 'IFAIL = ', IFAIL
      STOP
*
99999 FORMAT (1X,A,F9.4)
99998 FORMAT (1X,A,I5)
99997 FORMAT (1X,A,I2)
      END
*
      DOUBLE PRECISION FUNCTION P1(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION             Y
*     .. Executable Statements ..
      P1 = 0.0D0
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION P2A(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION              Y
*     .. Intrinsic Functions ..
      INTRINSIC                     SQRT
*     .. Executable Statements ..
      P2A = SQRT(1.0D0-Y*Y)
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION FA(X,Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION             X, Y
*     .. Executable Statements ..
      FA = X + Y
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION P2B(Y)
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_X_CHAPTER
*                                                   *
*****************************************************
*     .. Scalar Arguments ..
      DOUBLE PRECISION              Y
*     .. External Functions ..
******************************************************
* Function Type declarations need to be removed.     *
C     DOUBLE PRECISION              X01AAF
*                                                    *
******************************************************
******************************************************
* EXTERNAL declarations need to be removed.          *
C     EXTERNAL                      X01AAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      P2B = 0.5D0*X01AAF(0.0D0)
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION FB(X,Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION             X, Y
*     .. Intrinsic Functions ..
      INTRINSIC                    COS, SIN
*     .. Executable Statements ..
      FB = Y*Y*(COS(X)+SIN(X))
      RETURN
      END

4. Routine-specific Information

Any further information which applies to one or more routines in this implementation is listed below, chapter by chapter.
  1. F06, F07 and F08

    Many LAPACK routines have a "workspace query" mechanism which allows a caller to interrogate the routine to determine how much workspace to supply. Note that LAPACK routines from the MKL library may require a different amount of workspace than 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 library nag_mkl.lib to avoid problems with the vendor version:

      ZGEEVX    DBDSQR    ZBDSQR
    
  2. G02

    The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0D-13.
  3. P01

    On hard failure, P01ABF writes the error message to the error message unit specified by X04AAF and then stops.
  4. S07 - S21

    Functions in this chapter will give error messages if called with illegal or unsafe arguments. The constants referred to in the Library Manual have the following values in this implementation:
    S07AAF  F(1)   = 1.0D+13
            F(2)   = 1.0D-14
    
    S10AAF  E(1)   = 1.8500D+1
    S10ABF  E(1)   = 7.080D+2
    S10ACF  E(1)   = 7.080D+2
    
    S13AAF  x(hi)  = 7.083D+2
    S13ACF  x(hi)  = 1.0D+16
    S13ADF  x(hi)  = 1.0D+17
    
    S14AAF  IFAIL  = 1 if X > 1.70D+2
            IFAIL  = 2 if X < -1.70D+2
            IFAIL  = 3 if abs(X) < 2.23D-308
    S14ABF  IFAIL  = 2 if X > 2.55D+305
    
    S15ADF  x(hi)  = 2.66D+1
            x(low) = -6.25D+0
    S15AEF  x(hi)  = 6.25D+0
    
    S17ACF  IFAIL  = 1 if X > 1.0D+16
    S17ADF  IFAIL  = 1 if X > 1.0D+16
            IFAIL  = 3 if 0.0D+00 < X <= 2.23D-308
    S17AEF  IFAIL  = 1 if abs(X) > 1.0D+16
    S17AFF  IFAIL  = 1 if abs(X) > 1.0D+16
    S17AGF  IFAIL  = 1 if X > 1.038D+2
            IFAIL  = 2 if X < -5.6D+10
    S17AHF  IFAIL  = 1 if X > 1.041D+2
            IFAIL  = 2 if X < -5.6D+10
    S17AJF  IFAIL  = 1 if X > 1.041D+2
            IFAIL  = 2 if X < -1.8D+9
    S17AKF  IFAIL  = 1 if X > 1.041D+2
            IFAIL  = 2 if X < -1.8D+9
    S17DCF  IFAIL  = 2 if abs (Z) < 3.93D-305
            IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
            IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
    S17DEF  IFAIL  = 2 if imag (Z) > 7.00D+2
            IFAIL  = 3 if abs (Z) or FNU+N-1 > 3.27D+4
            IFAIL  = 4 if abs (Z) or FNU+N-1 > 1.07D+9
    S17DGF  IFAIL  = 3 if abs (Z) > 1.02D+3
            IFAIL  = 4 if abs (Z) > 1.04D+6
    S17DHF  IFAIL  = 3 if abs (Z) > 1.02D+3
            IFAIL  = 4 if abs (Z) > 1.04D+6
    S17DLF  IFAIL  = 2 if abs (Z) < 3.93D-305
            IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
            IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
    
    S18ADF  IFAIL  = 2 if 0.0D+00 < X <= 2.23D-308
    S18AEF  IFAIL  = 1 if abs(X) > 7.116D+2
    S18AFF  IFAIL  = 1 if abs(X) > 7.116D+2
    S18CDF  IFAIL  = 2 if 0.0D+00 < X <= 2.23D-308
    S18DCF  IFAIL  = 2 if abs (Z) < 3.93D-305
            IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
            IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
    S18DEF  IFAIL  = 2 if real (Z) > 7.00D+2
            IFAIL  = 3 if abs (Z) or FNU+N-1 > 3.27D+4
            IFAIL  = 4 if abs (Z) or FNU+N-1 > 1.07D+9
    
    S19AAF  IFAIL  = 1 if abs(x) >= 4.95000D+1
    S19ABF  IFAIL  = 1 if abs(x) >= 4.95000D+1
    S19ACF  IFAIL  = 1 if X > 9.9726D+2
    S19ADF  IFAIL  = 1 if X > 9.9726D+2
    
    S21BCF  IFAIL  = 3 if an argument < 1.579D-205
            IFAIL  = 4 if an argument >= 3.774D+202
    S21BDF  IFAIL  = 3 if an argument < 2.820D-103
            IFAIL  = 4 if an argument >= 1.404D+102
    
  5. X01

    The values of the mathematical constants are:
    X01AAF (PI)    = 3.1415926535897932D+00
    X01ABF (GAMMA) = 0.5772156649015329D+00
    
  6. X02

    The values of the machine constants are:

    The basic parameters of the model

    X02BHF =     2
    X02BJF =    53
    X02BKF =  -1021
    X02BLF =  1024
    X02DJF =  .TRUE.
    

    Derived parameters of the floating-point arithmetic

    X02AJF = 1.11022302462516D-16
    X02AKF = 2.22507385850721D-308
    X02ALF = 1.79769313486231D+308
    X02AMF = 2.22507385850721D-308
    X02ANF = 4.45014771701441D-308
    

    Parameters of other aspects of the computing environment

    X02AHF = 1.42724769270596D+45
    X02BBF = 2147483647
    X02BEF = 15
    X02DAF = .FALSE.
    
  7. X04

    The default output units for error and advisory messages for those routines which can produce explicit output are both Fortran Unit 6.

    5. Documentation

    The Library Manual is supplied in the form of Portable Document Format (PDF) files, with an HTML index, in the manual folder (either installed locally or on the distribution CD). The introductory material is also provided as HTML files in the manual folder.

    A main index file has been provided (manual\html\mark21.html) which contains a fully linked contents document pointing to all the available PDF (and where available HTML) files. This index file is available from the Start Menu under

      Start|All Programs|NAG|FL21|NAG Fortran Library Manual
    
    by default. Use your HTML browser to navigate from here.

    In addition the following are provided:

    This is available from the Start Menu under
      Start|All Programs|NAG|FL21|NAG Fortran Library -
          Intel Visual Fortran compiler(FLW3221DML). Users' Note
    
    by default.

    6. Support from NAG

    (a) Contact with NAG

    Queries concerning this document or the implementation generally should be directed initially to your local Advisory Service. If you have difficulty in making contact locally, you can contact NAG directly 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

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    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 and NAG product code (in this case FLW3221DML).

    (c) NAG Websites

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

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    Appendix - Contact Addresses

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