NAG Fortran Library, Mark 19

FLDVV19SA

DEC VAX/VMS Single Precision

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 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 both HTML form and plain text 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 NEWS.DOC (see Section 3.5) for lists of these routines and for a list of routines scheduled for withdrawal at Mark 20 or later. Your suggestions for new algorithms for future releases of the Library are welcomed (see Section 7).

3. General Information

3.1. Accessing the Library

To compile a Fortran program, type 
FORTRAN <program>
where <program> is the name of a .FOR file containing your program.

To link a program with the NAG Library, assuming that the library has been associated with a LNK$LIBRARY logical, type 

LINK <program>
where <program> is the name of a .OBJ file containing your compiled program.

To run the program, type 

ASSIGN <data>    FOR005
ASSIGN <results> FOR006
RUN    <program>
where <program> is the name of a .EXE file containing your linked program, <data> is data to be read from Fortran channel 5, and <results> are results to be written to Fortran channel 6.

3.2. Example Programs

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. All printed example programs show routine names ending in F not E (see Section 3.6).

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 single precision implementation, the bold italicised terms used in the NAG Fortran Library Manual should be interpreted as: 

real                 - REAL (REAL*4)
basic precision      - single precision
complex              - COMPLEX (COMPLEX*8)
additional precision - double precision (REAL*8)
machine precision    - the machine precision, see the value
                       returned by X02AJE in Section 4

Thus a parameter described as real should be declared as REAL in your program. If a routine accumulates an inner product in additional precision, it is using double 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 - REAL
imag                               - AIMAG
cmplx                              - CMPLX
conjg                              - CONJG
e in constants, e.g. 1.0e-4        - E, e.g. 1.0E-4
e in formats, e.g. e12.4           - E, e.g. E12.4

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.
For example: 

sgetrf refers to the LAPACK routine name - SGETRF
cpotrs                                   - CPOTRS

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 X04AAE for error messages and X04ABE 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:

See Section 5 for additional documentation available from NAG.

3.6. Naming of Routines

To ensure a single precision implementation is completely distinct from any double precision version also available, all single precision routine names have been modified by changing the sixth character from F to E. Thus, for example: 
A02AAF  denotes the double precision version
A02AAE  denotes the single precision version

The names of auxiliary routines have also been modified by interchanging the first three and the last three characters, e.g. C02AFZ has been changed to AFZC02.

In the NAG Fortran Library Manual all library routine names end in F. Therefore, when using the manual in conjunction with this single precision implementation, all such names must be understood to refer to the single precision versions with names ending in E. Some routines in the Library require users to specify particular auxiliary routines. Again, when using this implementation it is necessary to specify the amended names.

The names of COMMON blocks have also been modified, e.g. AC02AF is renamed AFC02A. This is unlikely to affect the user.

4. Routine-specific Information

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

(a) D02

D02GBE  In the example program the value of TOL has to be set to 1.0E-02 in 
        order to obtain a solution
 
D02MVE  In the example program the value of ATOL(1) has to be set to 5.0E-04 in 
        order to obtain a solution
 
D02PWE  In the example program the value of TOL has to be set to 1.0E-03 for 
        the first solution and to 1.0E-04 for the second solution in order to 
        obtain solutions which demonstrate increasing accuracy with smaller 
        values of TOL
 
D02PZE  In the example program the value of TOL has to be set to 1.0E-05 in 
        order to obtain a solution
 
D02TKE  The example program results exhibit failure with IFAIL=2. Users are 
        recommended to use a double precision implementation

D02TVE  The example program results exhibit failure with IFAIL=4; results 
        should be treated with extreme caution. Users are recommended to use a 
        double precision implementation

D02TXE  The example program results exhibit failure with IFAIL=2. Users are 
        recommended to use a double precision implementation

(b) D03

The example programs for D03RAE and D03RBE take much longer to run than other examples. 
D03PCE  In the example program the value of ACC has to be set to 1.0E-03 in 
        order to obtain a solution
 
D03PFE  In the example program the value of ACC(1) has to be set to 1.0E-05 in 
        order to obtain a solution
 
D03RBE  This routine may fail to solve many problems using this single 
        precision implementation. The use of a double precision implementation 
        is recommended for this routine

(c) D05

D05BDE      D05BEE      D05BYE
These routines may fail to solve many problems using this single precision implementation. The use of a double precision implementation is recommended for these routines.

(d) G02

The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0E-4.

(e) P01

On hard failure, P01ABE writes the error message to the error message unit specified by X04AAE and then stops.

(f) S07 - S21

The constants referred to in the NAG Fortran Library Manual have the following values in this implementation: 
S07AAE  F(1)   = 1.0E+05
        F(2)   = 1.0E-06
 
S10AAE  E(1)   = 9.25
S10ABE  E(1)   = 88.0
S10ACE  E(1)   = 88.0
 
S13AAE  x(hi)  = 88.02
S13ACE  x(hi)  = 1.0E+08
S13ADE  x(hi)  = 1.0E+09
 
S14AAE  IFAIL  = 1 if X > 33.0
        IFAIL  = 2 if X < -33.0
        IFAIL  = 3 if abs(X) < 5.88E-39
S14ABE  IFAIL  = 2 if X > 2.05E+36
 
S15ADE  x(hi)  = 9.38
        x(low) = -4.50
S15AEE  x(hi)  = 5.00
 
S17ACE  IFAIL  = 1 if X > 1.0E+07
S17ADE  IFAIL  = 1 if X > 1.0E+07
        IFAIL  = 3 if 0.0 < X <= 5.88E-39
S17AEE  IFAIL  = 1 if abs(X) > 1.0E+07
S17AFE  IFAIL  = 1 if abs(X) > 1.0E+07
S17AGE  IFAIL  = 1 if X > 25.52
        IFAIL  = 2 if X < -8.5E+04
S17AHE  IFAIL  = 1 if X > 25.93
        IFAIL  = 2 if X < -8.5E+04
S17AJE  IFAIL  = 1 if X > 25.84
        IFAIL  = 2 if X < -1.8E+04
S17AKE  IFAIL  = 1 if X > 25.93
        IFAIL  = 2 if X < -1.8E+04
S17DCE  IFAIL  = 2 if abs (Z) < 5.80E-36
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 2.89E+03
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 8.38E+06
S17DEE  IFAIL  = 2 if imag (Z) > 81.10
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 2.89E+03
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 8.38E+06
S17DGE  IFAIL  = 3 if abs (Z) > 203.0
        IFAIL  = 4 if abs (Z) > 4.12E+04
S17DHE  IFAIL  = 3 if abs (Z) > 203.0
        IFAIL  = 4 if abs (Z) > 4.12E+04
S17DLE  IFAIL  = 2 if abs (Z) < 5.80E-36
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 2.89E+03
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 8.38E+06
 
S18ADE  IFAIL  = 2 if 0.0 < X <= 5.88E-39
S18AEE  IFAIL  = 1 if abs(X) > 90.28
S18AFE  IFAIL  = 1 if abs(X) > 90.28
S18CDE  IFAIL  = 2 if 0.0 < X <= 5.88E-39
S18DCE  IFAIL  = 2 if abs (Z) < 5.80E-36
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 2.89E+03
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 8.38E+06
S18DEE  IFAIL  = 2 if real (Z) > 81.10
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 2.89E+03
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 8.38E+06
 
S19AAE  IFAIL  = 1 if abs(x) >= 18.75
S19ABE  IFAIL  = 1 if abs(x) >= 18.75
S19ACE  IFAIL  = 1 if X > 121.42
S19ADE  IFAIL  = 1 if X > 121.42
 
S21BCE  IFAIL  = 3 if an argument < 6.512E-26
        IFAIL  = 4 if an argument >= 8.473E+23
S21BDE  IFAIL  = 3 if an argument < 1.806E-13
        IFAIL  = 4 if an argument >= 2.193E+12

(g) X01

The values of the mathematical constants are: 
X01AAE (PI)    = 3.1415927
X01ABE (GAMMA) = 0.5772157

(h) X02

The values of the machine constants are:

The basic parameters of the model 

X02BHE = 2
X02BJE = 24
X02BKE = -127
X02BLE = 127
X02DJE = .TRUE.
Derived parameters of the floating-point arithmetic 
X02AJE = '00003480'X ( 5.96046E-08 )
X02AKE = '00000080'X ( 2.93874E-39 )
X02ALE = 'FFFF7FFF'X ( 1.70141E+38 )
X02AME = '00130100'X ( 5.87749E-39 )
X02ANE = '00010200'X ( 2.35099E-38 )
Parameters of other aspects of the computing environment 
X02AHE = '00007F80'X ( 8.50705E+37 )
X02BBE = 2147483647
X02BEE = 6
X02DAE = .FALSE.

(i) 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

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 websites, see Section 6 (c)) for details of current prices.

A full on-line version of the NAG Fortran Library Manual is available in the form of Portable Document Format (PDF) files. Please contact NAG if you are interested in this.

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 please quote your NAG site reference and NAG product code (in this case FLDVV19SA).

(c) NAG Websites

The NAG websites are 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 websites can be accessed at

http://www.nag.co.uk/

or

http://www.nag.com/ (in North America)

or

http://www.nag-j.co.jp/ (in Japan)

(d) NAG Electronic Newsletter

If you would like to be kept up to date with news from NAG you may want to register to receive our electronic newsletter, which will alert you to special offers, announcements about new products or product/service enhancements, case studies and NAG's event diary. To register simply visit one of our websites or contact us at nagnews@nag.co.uk.

7. User Feedback

Many factors influence the way 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. We have provided a short survey on our website at www.nag.co.uk/local/feedback to enable you to provide this feedback. Alternatively feel free to contact the appropriate NAG Response Centre who will be happy either to record your comments or to send you a printed copy of the survey.

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
 
Nihon NAG KK
Yaesu Nagaoka Building No. 6 
1-9-8 Minato
Chuo-ku
Tokyo
Japan
email: help@nag-j.co.jp

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

[NP3464/UN]