FLAI321DAL Users' Note

NAG Fortran Library, Mark 21

FLAI321DAL - License Managed

IBM RISC, 32-bit, AIX, xlf, Double Precision

Users' Note

1. Introduction
2. Availability of Routines
3. General Information
4. Routine-specific Information
5. Documentation
6. Support from NAG
7. User Feedback
Appendix - Contact Addresses

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 those manuals refer 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

If you intend to use the NAG library within a multithreaded application please refer to the document on Thread Safety in the NAG Fortran Library Manual (see Section 5).

The libraries supplied with this implementation have 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

This section shows two ways of accessing the library depending on the location of the compiled libraries.

3.1.1. Libraries NOT in the linker search path

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/flai321dal or /usr/local/NAG/flai321dal depending on your system; however it could have been changed by the installer. To identify [INSTALL_DIR] for this installation:

if /opt/NAG/flai321dal exists, then this is [INSTALL_DIR]
if /usr/local/NAG/flai321dal exists, then this is [INSTALL_DIR]
consult the installer for the directory [INSTALL_DIR].

To use the NAG Fortran Library and the IBM ESSL/BLAS libraries, you may link in the following manner:

 xlf driver.f [INSTALL_DIR]/lib/libnag_essl.a -lessl -lblas -lpthreads

where driver.f is your application program;

  xlf driver.f [INSTALL_DIR]/lib/libnag_essl.so -lessl -lblas -lpthreads

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 the IBM ESSL/BLAS libraries, you may wish to use the self-contained libraries as follows:

  xlf driver.f [INSTALL_DIR]/lib/libnag_nag.a -lpthreads

  xlf driver.f [INSTALL_DIR]/lib/libnag_nag.so -lpthreads

if the shareable library is required.

Please note that using a self-contained library may result in some degradation in the performance of your application.

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

In the C shell type:

   setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib

to set LD_LIBRARY_PATH, or

   setenv LD_LIBRARY_PATH ${LD_LIBRARY_PATH}:[INSTALL_DIR]/lib

to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

   LD_LIBRARY_PATH=[INSTALL_DIR]/lib
   export LD_LIBRARY_PATH

to set LD_LIBRARY_PATH, or

   LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:[INSTALL_DIR]/lib
   export LD_LIBRARY_PATH

to extend LD_LIBRARY_PATH if you already have it set.

3.1.2. Libraries in the linker search path

In this section we assume that the compiled libraries are pointed at by symbolic links from a directory in the search path of the linker, such as /usr/lib.

To use the NAG Fortran Library and the IBM ESSL/BLAS libraries, you may link in the following manner:

  xlf driver.f -lnag_essl -lessl -lblas -lpthreads

To use the static library libnag_essl.a you need the -static loader flag to switch static binding on:

  xlf -static driver.f -lnag_essl -lessl -lblas -lpthreads

However, if you prefer to link to a version of the NAG library which does not require the use of the IBM ESSL/BLAS libraries, you may wish to use the self-contained libraries as follows:

  xlf driver.f -lnag_nag -lpthreads

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

To use the static library libnag_nag.a you need the -static loader flag:

  xlf -static driver.f -lnag_nag -lpthreads

Please note that using a self-contained library may result in some degradation in the performance of your application.

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

In the C shell type:

   setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib

to set LD_LIBRARY_PATH, or

   setenv LD_LIBRARY_PATH ${LD_LIBRARY_PATH}:[INSTALL_DIR]/lib

to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

   LD_LIBRARY_PATH=[INSTALL_DIR]/lib
   export LD_LIBRARY_PATH

to set LD_LIBRARY_PATH, or

   LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:[INSTALL_DIR]/lib
   export LD_LIBRARY_PATH

to extend LD_LIBRARY_PATH if you already have it set.

3.2. Example Programs

The directory [INSTALL_DIR]/scripts contains four scripts nagexample_essl, nagexample_shar_essl, nagexample and nagexample_shar.

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

nagexample_essl, to link with the NAG static library libnag_essl.a and the IBM ESSL/BLAS libraries
nagexample_shar_essl, to link with the NAG shareable library libnag_essl.so and the IBM ESSL/BLAS libraries
nagexample, to link with the NAG self-contained static library libnag_nag.a
nagexample_shar, to link with the NAG self-contained shareable library libnag_nag.so

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.

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

nagexample d01ajf

will copy the example program into the file d01ajfe.f in the current directory and process it to produce the example program results.

The example programs are supplied in machine-readable form. They are suitable for immediate execution. 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 static library libnag_nag.a, (using the NAG BLAS and LAPACK routines). Running the examples with vendor 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) and they can be accessed by specifying the -Ipathname option on each f90/95 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:

Add a USE statement for each of the module files for the chapters of the NAG Fortran Library that your program calls directly. Only one USE statement will be required. The interface blocks for the BLAS and LAPACK routines are in nag_f77_f_chapter.
Delete all EXTERNAL statements for NAG Fortran Library routines (including BLAS and LAPACK routines). These are now declared in the module(s).
Delete the type declarations for any NAG Fortran Library functions. These are now declared in the module(s).

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.

D03
The example programs for D03RAF and D03RBF take much longer to run than other examples.
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 ESSL 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 libraries libnag_essl.a and libnag_essl.so to avoid problems with the vendor version:
```
DAXPYI   DDOTI   DGTHR    DGTHRZ   DROTI    DSBMV   DSCTR   ZAXPYI   
ZDOTCI  ZDOTUI   ZGTHR    ZGTHRZ   ZSCTR 
DGEEV    DGELS   DGETRF   DGEQRF   DPOTRF   DPPSV   DPPTRF  DSPEV    
DSPSV    DSYGV   ZGEEV    ZGETRF   ZPOTRF   ZHPEV   ZHPSV
```
G02
The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0D-13.
P01
On hard failure, P01ABF writes the error message to the error message unit specified by X04AAF and then stops.

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

X01

The values of the mathematical constants are:

X01AAF (PI)    = 3.1415926535897932D+00
X01ABF (GAMMA) = 0.5772156649015329D+00

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 = 8.11296384146067D+31 
X02BBF = 2147483647
X02BEF = 15
X02DAF = .FALSE.

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 nagdoc_fl21 directory. The introductory material is also provided as HTML files in the nagdoc_fl21 directory.
A main index file has been provided (nagdoc_fl21/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:
- un.html - Users' Note (this document)
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 FLAI321DAL).
(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.
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. Please contact your local NAG Response Centre (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: infodesk@nag.com

Tel: +1 630 971 2337                    Tel: +1 630 971 2345
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
```

NAG Fortran Library, Mark 21

FLAI321DAL - License Managed

IBM RISC, 32-bit, AIX, xlf, Double Precision

Users' Note

Contents

D03

F06, F07 and F08

G02

P01

S07 - S21

X01

X02

X04

(a) Contact with NAG

(b) NAG Response Centres

(c) NAG Websites

(d) NAG Electronic Newsletter