NAG Fortran Library, Mark 22

FLL3A22D9L - License Managed

Linux (x86-32), NAG Fortran Compiler, Double Precision

Users' Note


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 22 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.

2. Post Release Information

Please check the following URL:

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

3. General Information

For best performance, we recommend that you should use the variant of the NAG Fortran Library which is based on the supplied AMD Core Math Library (ACML) 4.2.1 i.e. libnag_acml.a or However if you use a version of ACML different from the version used in creating this implementation and you have problems when calling a NAG routine, we suggest that you use one of the above libraries with the supplied ACML, or one of the self-contained libraries libnag_nag.a or

3.1. Accessing the Library

In this section we assume that the library has been installed in the directory [INSTALL_DIR].

By default [INSTALL_DIR] (see Installer's Note (in.html)) is /opt/NAG/fll3a22d9l or /usr/local/NAG/fll3a22d9l depending on your system; however it could have been changed by the person who did the installation. To identify [INSTALL_DIR] for this installation:

To use the NAG Fortran Library and the supplied ACML libraries, you may link in the following manner: 
   nagfor driver.f [INSTALL_DIR]/lib/libnag_acml.a [INSTALL_DIR]/acml/libacml.a -lpthread
where driver.f is your application program;


   nagfor driver.f [INSTALL_DIR]/lib/ [INSTALL_DIR]/acml/ -lpthread
if the shareable library is required.

However, if you prefer to link to a version of the NAG Library which does not require the use of ACML you may wish to use the self-contained libraries as follows:

   nagfor driver.f [INSTALL_DIR]/lib/libnag_nag.a
   nagfor driver.f [INSTALL_DIR]/lib/    
if the shareable library is required.

If the compiled libraries and the supplied ACML libraries are pointed at by symbolic links from a directory in the search path of the linker, such as /usr/lib, then you may alternatively link in the following manner:

   nagfor driver.f -lnag_acml -lacml -lpthread

Similarly for the self-contained libraries the commands

   nagfor driver.f -lnag_nag

may be used. This will usually link to the shareable library in preference to the static library if both libraries are in the same location.

If your application has been linked with the shareable NAG and ACML libraries then the environment variable LD_LIBRARY_PATH must be set (or extended) to allow run time linkage.

In the C shell type:

to set LD_LIBRARY_PATH, or
to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

to set LD_LIBRARY_PATH, or
to extend LD_LIBRARY_PATH if you already have it set.

Note that you may also need to set LD_LIBRARY_PATH to point at other things such as compiler run-time libraries, for example if you are using a newer version of the compiler.

3.2. 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 programs. Their purpose is to allow the Fortran 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; and
(d) all arguments match in type and structure.

These interface blocks have been generated automatically by analysing the source code for the NAG Fortran Library. As a consequence, and because these files have been thoroughly tested, their use is recommended in preference to writing your own declarations.

The NAG Fortran Library interface block files are organised by Library chapter. The module names are:

These are supplied in pre-compiled form (.mod files) and they can be accessed by specifying the -Ipathname option on each compiler invocation, where pathname ([INSTALL_DIR]/nag_interface_blocks) is the path of the directory containing the compiled interface blocks.

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
*     Mark 14 Revised. NAG Copyright 1989.
* Add USE statements for relevant chapters          *
*                                                   *
*     .. Parameters ..
      INTEGER          NOUT
      PARAMETER        (NOUT=6)
*     .. Local Scalars ..
      INTEGER          IFAIL, NPTS
*     .. External Functions ..
      EXTERNAL         FA, FB, PHI1, PHI2A, PHI2B
*     .. External Subroutines ..
* EXTERNAL declarations need to be removed.          *
*     EXTERNAL         D01DAF
*                                                    *
*     .. Executable Statements ..
      WRITE (NOUT,*) 'D01DAF Example Program Results'
      YA = 0.0D0
      YB = 1.0D0
      ABSACC = 1.0D-6
      WRITE (NOUT,*)
      IFAIL = 1
      IF (IFAIL.LT.0) THEN
         WRITE (NOUT,99998) ' ** D01DAF returned with IFAIL = ', IFAIL
         WRITE (NOUT,*) 'First formulation'
         WRITE (NOUT,99999) 'Integral =', ANS
         WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
         IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
         WRITE (NOUT,*)
         WRITE (NOUT,*) 'Second formulation'
         IFAIL = 1
         WRITE (NOUT,99999) 'Integral =', ANS
         WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
         IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
      END IF
99999 FORMAT (1X,A,F9.4)
99998 FORMAT (1X,A,I5)
*     .. Scalar Arguments ..
*     .. Executable Statements ..
      PHI1 = 0.0D0
*     .. Scalar Arguments ..
*     .. Intrinsic Functions ..
      INTRINSIC        SQRT
*     .. Executable Statements ..
      PHI2A = SQRT(1.0D0-Y*Y)
*     .. Scalar Arguments ..
*     .. Executable Statements ..
      FA = X + Y
* Add USE statements for relevant chapters          *
*                                                   *
*     .. Scalar Arguments ..
*     .. External Functions ..
* Function Type declarations need to be removed.     *
*                                                    *
* EXTERNAL declarations need to be removed.          *
*     EXTERNAL         X01AAF
*                                                    *
*     .. Executable Statements ..
      PHI2B = 0.5D0*X01AAF(0.0D0)
*     .. Scalar Arguments ..
*     .. Intrinsic Functions ..
      INTRINSIC        COS, SIN
*     .. Executable Statements ..
      FB = Y*Y*(COS(X)+SIN(X))

3.3. Example Programs

The example results distributed were generated at Mark 22, 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 BLAS or 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 directory [INSTALL_DIR]/scripts contains four scripts nag_example_acml, nag_example_shar_acml, nag_example and nag_example_shar.

The example programs are most easily accessed by one of the commands

Each command will provide you with a copy of an example program (and its data, if any), compile the program and link it with the appropriate libraries (showing you the compile command so that you can recompile your own version of the program). Finally, the executable program will be run, presenting its output to stdout, which is redirected to a file.

The example program concerned is specified by the argument to the command, e.g.

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

The distributed example results are those obtained with the static library libnag_acml.a (using the ACML BLAS and LAPACK routines). Running the examples with the self-contained library (using the NAG BLAS and LAPACK routines) may give slightly different results.

3.4. Interpretation of Bold Italicised Terms

In order to support all implementations of the Library, the Manual has adopted a convention of using bold italics to distinguish terms which have different interpretations in different implementations.

For this double precision implementation, the bold italicised terms used in the Library Manual should be interpreted as follows:

real                  means REAL
double precision      means DOUBLE PRECISION
complex               means COMPLEX
complex*16            means COMPLEX*16 (or equivalent)
basic precision       means DOUBLE PRECISION
additional precision  means quadruple precision
reduced precision     means REAL

Another 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.

In Chapters F06, F07 and F08, alternate routine names are available for BLAS and LAPACK derived routines. For details of the alternate routine names please refer to the relevant Chapter Introduction. Note that applications should reference routines by their BLAS/LAPACK names, rather than their NAG-style names, for optimum performance.

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.) The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified. These routines are potentially not thread safe and in general output is not recommended from multithreaded applications.

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 ACML may require a different amount of workspace from the equivalent NAG versions of these routines. Care should be taken when using the workspace query mechanism.

    In this implementation calls to the NAG version of the following Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) are included in the libraries libnag_acml.a and to avoid problems with the vendor version:

    dsgesv zcgesv zscal zsptrf zhpgv zhpgvx zpotrf dtpsv
  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 NAG Fortran 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 > 1.69E+2
            IFAIL  = 2 if X < -1.69E+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 0.0E0 < 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 imag(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 0.0E0 < 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
  5. X01

    The values of the mathematical constants are:
    X01AAF (pi)    = 3.1415926535897932
    X01ABF (gamma) = 0.5772156649015328
  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 = 1.11022302462516E-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 = 1.84467440737095E+19
    X02BBF = 2147483647
    X02BEF = 15
    X02DAF = .TRUE.
  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 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

The Library Manual is supplied in the following formats:

The following main index files have been provided for these formats:

Use your web browser to navigate from here.

Advice on viewing and navigating the formats available can be found in the Online Documentation document.

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 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 and NAG product code (in this case FLL3A22D9L).

(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:, or

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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

(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

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

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Tel: +44 (0)1865 511245                 Tel: +44 (0)1865 311744
Fax: +44 (0)1865 310139                 Fax: +44 (0)1865 310139

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USA                                     email:

Tel: +1 630 971 2337                    Tel: +1 630 971 2337
Fax: +1 630 971 2706                    Fax: +1 630 971 2706

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