NAG Fortran Library, Mark 21

FLMI621D9L - License Managed

Intel-based Mac, Mac OS X 64, NAGWare f95, Double 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 Mark 21 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 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 Library Manual 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/flmi621d9l; however it could have been changed by the installer. To identify [INSTALL_DIR] for this installation:

To use the NAG Fortran Library and the vecLib library, you may link in the following manner:
  f95 driver.f [INSTALL_DIR]/lib/libnag_vl.dylib -framework vecLib
where driver.f is your application program;

or

  f95 driver.f [INSTALL_DIR]/lib/libnag_vl.a -framework vecLib
if the static library is required.

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

  f95 driver.f [INSTALL_DIR]/lib/libnag_nag.dylib
or
  f95 driver.f [INSTALL_DIR]/lib/libnag_nag.a
if the static 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 NAG shareable library then the environment variable DYLD_LIBRARY_PATH must be set (or extended) to include the directory containing the NAG shareable library.

In the C shell, type:

   setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib
to set DYLD_LIBRARY_PATH, or
   setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH}
to extend DYLD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

   DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib
   export DYLD_LIBRARY_PATH
to set DYLD_LIBRARY_PATH, or
   DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH}
   export DYLD_LIBRARY_PATH
to extend DYLD_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 that requires the vecLib library, you may link in the following manner:

  f95 driver.f -lnag_vl -framework vecLib
The linker will, by default, pick up the shared library libnag_vl.dylib. To force the use of the static library libnag_vl.a you will have to specify the library in full on your command line:
  f95 driver.f /usr/lib/libnag_vl.a -framework vecLib
Please note that if the symbolic links were created in a directory other than /usr/lib this directory must be used in place of /usr/lib in the above statement.

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

  f95 driver.f -lnag_nag
The linker will, by default, pick up the shared library libnag_nag.dylib. To force the use of the static library libnag_nag.a you will have to specify the library in full on your command line:
  f95 driver.f /usr/lib/libnag_nag.a
Please note that if the symbolic links were created in a directory other than /usr/lib this directory must be used in place of /usr/lib in the above statement.

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 NAG shareable library then the environment variable DYLD_LIBRARY_PATH must be set (or extended) to include the directory containing the NAG shareable library.

In the C shell, type:

   setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib
to set DYLD_LIBRARY_PATH, or
   setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH}
to extend DYLD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

   DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib
   export DYLD_LIBRARY_PATH
to set DYLD_LIBRARY_PATH, or
   DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH}
   export DYLD_LIBRARY_PATH
to extend DYLD_LIBRARY_PATH if you already have it set.

3.2. Example Programs

The directory [INSTALL_DIR]/scripts contains four scripts nag_example_vl, nag_example_shar_vl, 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, and its output will be saved.

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

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

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 Library 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 Library Manual should be interpreted as follows:
real or double precision  - DOUBLE PRECISION (REAL*8)
basic precision           - double precision
complex or 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 real or 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.

These routines are potentially not thread safe and in general output is not recommended in a multithreaded environment.

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:

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.
  • 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 vecLib 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_vl.a and libnag_vl.dylib to avoid problems with the vendor version:

    daxpyi   ddoti    dgthr    dgthrz   droti    dsctr    zaxpyi
    zdotci   zdotui   zgthr    zgthrz   zsctr    zdotc    zdotu
    zhpevd   zheevr   zgesdd   dggesx   zggesx
    
  • 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 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 = 1.84467440737095D+19
    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

    The Library Manual is supplied in the form of Portable Document Format (PDF) files, with an HTML index, in the nagdoc_mk21 directory. The introductory material is also provided as HTML files in the nagdoc_mk21 directory.

    A main index file has been provided (nagdoc_mk21/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

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    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 FLMI621D9L).

    (c) NAG Websites

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    http://www.nag.co.uk/, http://www.nag.com/ or http://www.nag-j.co.jp/

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    Appendix - Contact Addresses

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    Tel: +44 (0)1865 511245                 Tel: +44 (0)1865 311744
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    Tel: +1 630 971 2337                    Tel: +1 630 971 2337
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    104-0032
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    email: help@nag-j.co.jp
    
    Tel: +81 (0)3 5542 6311
    Fax: +81 (0)3 5542 6312