NAG Fortran Library, Mark 19


DEC Alpha Digital UNIX 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 Fortran Library Manual and Introductory Guide. Wherever those manuals refer to the "Users' Note for your implementation", you should consult this note.

NAG recommends that you read the following minimum reference material before calling any library routine:

(a) Essential Introduction
(b) Chapter Introduction
(c) Routine Document
(d) Implementation-specific Users' Note

Items (a), (b) and (c) are included in the NAG Fortran Library Manual; items (a) and (b) are also included in the NAG Fortran Library Introductory Guide; item (d) is this document which is provided in HTML form. Item (a) is also supplied in plain text form.

2. Availability of Routines

All routines listed in the chapter contents documents of the NAG Fortran Library Manual, Mark 19 are available in this implementation. At Mark 19, 68 new primary ("user-callable") routines have been introduced, and 15 deleted. Please consult the file doc/news.html (see Section 3.5) for lists of these routines and for a list of routines scheduled for withdrawal at Mark 20 or later.

3. General Information

3.1. Accessing the Library

Assuming that libnag.a has been installed in a directory in the search path of the linker, such as /usr/lib, then you may link to the NAG Fortran Library in the following manner:

f77 driver.f -lnag
f90 driver.f -lnag
where driver.f is your application program.

Assuming that libnagdx.a has been installed in a directory in the search path of the linker, then if you wish to access the BLAS and/or LAPACK routines supplied in the Digital Extended Math Library (DXML) this can be done in the following manner:

f77 driver.f -lnagdx -ldxml
f90 driver.f -lnagdx -ldxml

If either of the shareable versions of the libraries ( and have been created and installed in a directory in the search path of the linker, these will be linked with instead of the static versions.

3.2. Example Programs

The example programs are most easily accessed by the command nagexample, which will provide you with a copy of an example program (and its data, if any), compile the program and link it with the library (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. The example program concerned is specified by the argument to nagexample, e.g.
nagexample c06eaf
will copy the example program and its data into the files c06eafe.f and c06eafe.d in the current directory and process them to produce the example program results.

In the NAG Fortran Library Manual, routine documents that have been typeset since Mark 12 present the example programs in a generalised form, using bold italicised terms as described in Section 3.3.

In other routine documents, the example programs are in single precision and require modification for use with double precision routines. This conversion can entail:

The example programs supplied to a site in machine-readable form have been modified as necessary so that they are suitable for immediate execution. Note that all the distributed example programs have been revised and do not correspond exactly with the programs published in the manual, unless the documents have been recently typeset. The distributed example programs should be used in preference wherever possible.

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:

real                 - DOUBLE PRECISION (REAL*8)
basic precision      - double precision
complex              - COMPLEX*16
additional precision - quadruple precision (REAL*16)
machine precision    - the machine precision, see the value
                       returned by X02AJF in Section 4                          

Thus a parameter described as real 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.

In routine documents that have been newly typeset since Mark 12 additional bold italicised terms are used in the published example programs and they must be interpreted as follows:

real as an intrinsic function name - DBLE
imag                               - DIMAG
cmplx                              - DCMPLX
conjg                              - DCONJG
e in constants, e.g. 1.0e-4        - D, e.g. 1.0D-4
e in formats, e.g. e12.4           - D, e.g. D12.4

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. The LAPACK name is precision dependent, and hence the name appears in a bold italicised typeface.

The typeset examples use the single precision form of the LAPACK name. To convert this name to its double precision form, change the first character either from S to D or C to Z as appropriate.
For example:

sgetrf refers to the LAPACK routine name - DGETRF
cpotrs                                   - ZPOTRS

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. User Documentation

The following machine-readable information files are provided in the doc directory:

See Section 5 for additional documentation available from NAG.

3.6. 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 programs. Their purpose is to allow the Fortran 90 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, they are more reliable than 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 -I"pathname" option on each f90 invocation, where "pathname" is the path of the directory containing the .mod files.

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

These changes are illustrated by showing the conversion of the Fortran 77 version of the example program for NAG Fortran Library routine S18DEF. 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.

*     S18DEF Example Program Text
*     Mark 14 Revised.  NAG Copyright 1989.
* Add USE statement for relevant chapters                         *
*                                                                 *
*     .. Parameters ..
      INTEGER          NIN, NOUT
      PARAMETER        (NIN=5,NOUT=6)
      INTEGER          N
      PARAMETER        (N=2)
*     .. Local Scalars ..
      COMPLEX*16       Z
      INTEGER          IFAIL, NZ
      CHARACTER*1      SCALE
*     .. Local Arrays ..
      COMPLEX*16       CY(N)
*     .. External Subroutines ..
* EXTERNAL declarations need to be removed (and type declarations *
*  for functions).                                                *
C      EXTERNAL         S18DEF
*                                                                 *
*     .. Executable Statements ..
      WRITE (NOUT,*) 'S18DEF Example Program Results'
*     Skip heading in data file
      READ (NIN,*)
      WRITE (NOUT,*)
      WRITE (NOUT,99999) 'Calling with N =', N
      WRITE (NOUT,*)
      WRITE (NOUT,*)
     +'   FNU            Z        SCALE       CY(1)              CY(2)
     +   NZ IFAIL'
      WRITE (NOUT,*)
   20 READ (NIN,*,END=40) FNU, Z, SCALE
      IFAIL = 0
      WRITE (NOUT,99998) FNU, Z, SCALE, CY(1), CY(2), NZ, IFAIL
      GO TO 20
   40 STOP
99999 FORMAT (1X,A,I2)
99998 FORMAT (1X,F7.4,'  (',F7.3,',',F7.3,')   ',A,
     +       2('  (',F7.3,',',F7.3,')'),I4,I4)

4. Routine-specific Information

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

(a) D03

The example programs for D03RAF and D03RBF take much longer to run than other examples.

(b) F06, F07 and F08

In this implementation calls to the Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) can be resolved by calls to the Digital Extended Math Library (DXML) if it is available. The only exceptions to this are DGER, DDOT, DGEMV and ZGBTRS.

(c) G02

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

(d) P01

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

(e) 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)   = 18.50
S10ABF  E(1)   = 708.0
S10ACF  E(1)   = 708.0

S13AAF  x(hi)  = 708.3
S13ACF  x(hi)  = 1.0D+16
S13ADF  x(hi)  = 1.0D+17

S14AAF  IFAIL  = 1 if X > 170.0
        IFAIL  = 2 if X < -170.0
        IFAIL  = 3 if abs(X) < 2.23D-308
S14ABF  IFAIL  = 2 if X > 2.55D+305

S15ADF  x(hi)  = 26.6
        x(low) = -6.25
S15AEF  x(hi)  = 6.25

S17ACF  IFAIL  = 1 if X > 1.0D+16
S17ADF  IFAIL  = 1 if X > 1.0D+16
        IFAIL  = 3 if 0.0 < 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 > 103.8
        IFAIL  = 2 if X < -5.6D+10
S17AHF  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -5.6D+10
S17AJF  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -1.8D+9
S17AKF  IFAIL  = 1 if X > 104.1
        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) > 700.0
        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 0.0 < X <= 2.23D-308
S18AEF  IFAIL  = 1 if abs(X) > 711.6
S18AFF  IFAIL  = 1 if abs(X) > 711.6
S18CDF  IFAIL  = 2 if 0.0 < 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) > 700.0
        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) >= 49.50
S19ABF  IFAIL  = 1 if abs(x) >= 49.50
S19ACF  IFAIL  = 1 if X > 997.26
S19ADF  IFAIL  = 1 if X > 997.26

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

(f) X01

The values of the mathematical constants are:
X01AAF (PI)    = 3.1415926535897932
X01ABF (GAMMA) = 0.5772156649015329

(g) X02

The values of the machine constants are:

The basic parameters of the model

X02BHF = 2
X02BJF = 53
X02BKF = -1021
X02BLF = 1024
Derived parameters of the floating-point arithmetic
X02AJF = Z'3CA0000000000001' ( 1.11022302462516D-16 )
X02AKF = Z'0010000000000000' ( 2.22507385850721D-308 )
X02ALF = Z'7FEFFFFFFFFFFFFF' ( 1.79769313486231D+308 )
X02AMF = Z'0010000000000000' ( 2.22507385850721D-308 )
X02ANF = Z'0036A09E667F3BCD' ( 1.25869185119309D-307 )
Parameters of other aspects of the computing environment
X02AHF = Z'4950000000000000' ( 1.42724769270596D+45 )
X02BBF = 2147483647
X02BEF = 15

(h) X04

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

(i) X05

The finest granularity of wall-clock time available on this system is one second, so the seventh element of the integer array passed as a parameter to X05AAF will always be returned with the value 0.

5. Documentation

Each supported NAG Fortran Library site is currently provided with a printed copy of the NAG Fortran Library Manual (or Update) and Introductory Guide. Additional copies are available for purchase; please refer to the NAG documentation order form (available on the NAG Website, see Section 6 (c)) for details of current prices.

On-line documentation is bundled with this implementation. Please see the Readme file on the distribution medium for further information.

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 write to 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 please quote your NAG site reference and NAG product code (in this case FLDAU19DA).

(c) NAG Website

The NAG Website is an information service providing items of interest to users and prospective users of NAG products and services. The information is reviewed and updated regularly and includes implementation availability, descriptions of products, downloadable software, product documentation and technical reports. The NAG Website can be accessed at

or (in the USA)

Appendix - Contact Addresses

Wilkinson House
Jordan Hill Road
OXFORD  OX2 8DR                         NAG Ltd Response Centre
United Kingdom                          email:
Tel: +44 (0)1865 511245                 Tel: +44 (0)1865 311744
Fax: +44 (0)1865 310139                 Fax: +44 (0)1865 311755
1400 Opus Place, Suite 200
Downers Grove
IL 60515-5702                           NAG Inc Response Center
USA                                     email:
Tel: +1 630 971 2337                    Tel: +1 630 971 2345
Fax: +1 630 971 2706                    Fax: +1 630 971 2346
Schleissheimerstrasse 5
85748 Garching
Tel: +49 (0)89 320 7395
Fax: +49 (0)89 320 7396

Nihon NAG KK
Nagashima Building 2F
2-24-3 Higashi

Tel: +81 (0)3 5485 2901
Fax: +81 (0)3 5485 2903