NAG Fortran Library, Mark 21

FLW3221DDL - License Managed

Windows NT/2000/XP, Compaq Visual Fortran

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 Fortran 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 not been compiled in a manner that facilitates the use of multiple threads.

2. Availability of Routines

All routines listed in the chapter contents documents of the NAG Fortran Library Manual, Mark 21 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\flw3221ddl
If this folder does not exist, please consult with the system manager (or the person who did the installation).

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

  Start|Programs|NAG|FL21|

If this shortcut does not exist, please consult with 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|Programs|NAG|FL21|NAG Fortran Library - Compaq Visual Fortran compiler. 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\flw3221ddl\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw3221ddl.

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

  f90 driver.f nag_mkl.lib mkl_s.lib libguide.lib
  f90 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 (see Section 4).

The first command will use the library without the NAG version of the BLAS/LAPACK procedures (nag_mkl.lib) with the MKL libraries mkl_s.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 mkl_s.lib libguide.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: 
  f90 driver.f my_nag_mkl.lib
Please note that the Compaq Visual Fortran compiler environment variables must be set in the command window. For more details refer to the User's Guide for the compiler.

3.1.2. From MS Developer Studio

If you are using Developer Studio, after establishing a workspace you should make the system aware of the libraries by clicking on Project, then Settings, then Link and entering the library and relevant MKL libraries under Object/library modules. The installation procedure attempts to make Developer Studio aware of the location of the NAG libraries and of the MKL libraries supplied by NAG. You can confirm that it has been successful by examining the Directories pane when Tools/Options/Directories/Show directories for Libraries has been selected. If the installation had difficulty, perhaps because several versions of Developer Studio were recorded in the registry, then you can set this facility manually in the Directories pane. Otherwise you will have to specify the full path name of the libraries in Object/library modules.

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_FLW3221DDL.

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_FLW3221DDL. This shortcut is placed in the Start Menu under 

  Start|Programs|NAG|FL21|NAG Fortran Library - Compaq Visual Fortran compiler. 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\flw3221ddl\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw3221ddl.

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 f08fdf
will copy the example program and its data into the files f08fdfe.f and f08fdfe.d in the current folder and process them to produce the example program results in the file f08fdfe.r.

Alternatively you could use: 

  nag_example f08fdf
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 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 NAG Fortran Library Manual should be interpreted as: 
double precision     - DOUBLE PRECISION (REAL*8)
basic precision      - double precision
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 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 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: 

    DBDSQR    DDOT     DSYGV     DSYGVX     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

    The constants referred to in the NAG Fortran 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 = 2.22507385850721D-308
    Parameters of other aspects of the computing environment 
    X02AHF = 1.84467440737095D+19
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

A full online version of the NAG Fortran 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. Use your HTML browser to navigate from here.

In addition the following are provided:

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

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 and NAG product code (in this case FLW3221DDL).

(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/ or http://www.nag-j.co.jp/

(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 special offers, announcements about new products or product/service enhancements, 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
1431 Opus Place, Suite 220
Downers Grove
IL 60515-1362                           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
Japan
email: help@nag-j.co.jp

Tel: +81 (0)3 5542 6311
Fax: +81 (0)3 5542 6312