NAG C Library, Mark 23

CLLUX23DCL - License Managed

Linux (x86-32), Intel C/C++

Users' Note



Contents


1. Introduction

This document is essential reading for every user of the NAG C Library implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Mark 23 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:

http://www.nag.co.uk/doc/inun/cl23/luxdcl/postrelease.html

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 C Library which is based on the supplied Intel ® Math Kernel Library (MKL) i.e. libnagc_mkl.a or libnagc_mkl.so. However if you use a version of the MKL 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 MKL, or one of the self-contained libraries libnagc_nag.a or libnagc_nag.so.

3.1. Accessing the Library

In this section we assume that the library and the NAG include files have been installed in the directory [INSTALL_DIR].

By default [INSTALL_DIR] (see Installer's Note (in.html)) is /opt/NAG/cllux23dcl or /usr/local/NAG/cllux23dcl 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 C Library and the supplied MKL libraries, you may link in the following manner:
  icc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.a \
      -Wl,--start-group \
      [INSTALL_DIR]/mkl/libmkl_intel.a \
      [INSTALL_DIR]/mkl/libmkl_intel_thread.a \
      [INSTALL_DIR]/mkl/libmkl_core.a \
      [INSTALL_DIR]/rtl/libiomp5.a \
      -Wl,--end-group \
      -lpthread -lm
where driver.c is your application program;

or

  icc driver.c -I[INSTALL_DIR]/include -L[INSTALL_DIR]/lib -lnagc_mkl \
      -L[INSTALL_DIR]/mkl -lmkl_intel -lmkl_intel_thread -lmkl_core \
      -L[INSTALL_DIR]/rtl -liomp5 \
      -lpthread -lm
if the shareable library is required. Please note that the shareable library is fully resolved so that you need not link against other run-time libraries (e.g. libmkl_rt.so) explicitly; this requires the environment variable LD_LIBRARY_PATH to be set correctly at link time (see below).

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

  icc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.a \
      -lpthread -lm
or
  icc driver.c -I[INSTALL_DIR]/include -L[INSTALL_DIR]/lib -lnagc_nag \
      -lpthread -lm
if the shareable library is required.

In case you want to use a different compiler, for example gcc version 4.1.2 or newer with glibc-2.7-2 or later, you can use one of the following commands:

  gcc driver.c -I[INSTALL_DIR]/include -m32 [INSTALL_DIR]/lib/libnagc_mkl.a \
      -Wl,--start-group \
      [INSTALL_DIR]/mkl/libmkl_intel.a \
      [INSTALL_DIR]/mkl/libmkl_intel_thread.a \
      [INSTALL_DIR]/mkl/libmkl_core.a \
      -Wl,--end-group \
      [INSTALL_DIR]/rtl/libimf.a \
      [INSTALL_DIR]/rtl/libsvml.a \
      [INSTALL_DIR]/rtl/libirc.a \
      [INSTALL_DIR]/rtl/libiomp5.a \
      -lpthread -lm
to access the MKL based NAG Library with static linkage;
  gcc driver.c -I[INSTALL_DIR]/include -m32 -L[INSTALL_DIR]/lib -lnagc_mkl \
      -L[INSTALL_DIR]/mkl -lmkl_intel -lmkl_intel_thread -lmkl_core \
      -L[INSTALL_DIR]/rtl -limf -lsvml -lirc -liomp5 \
      -lpthread -lm
to access the MKL based NAG Library with shared linkage;
  gcc driver.c -I[INSTALL_DIR]/include -m32 [INSTALL_DIR]/lib/libnagc_nag.a \
      [INSTALL_DIR]/rtl/libimf.a \
      [INSTALL_DIR]/rtl/libsvml.a \
      [INSTALL_DIR]/rtl/libirc.a \
      -lpthread -lm
to access the self-contained NAG Library with static linkage;
  gcc driver.c -I[INSTALL_DIR]/include -m32 -L[INSTALL_DIR]/lib -lnagc_nag \
      -L[INSTALL_DIR]/rtl -limf -lsvml -lirc \
      -lgcc_s -lpthread -lm
to access the self-contained NAG Library with shared linkage. Note the link to gcc runtime library libgcc_s which contains some low-level functions.

If your application has been linked with the shareable NAG and MKL libraries 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:[INSTALL_DIR]/mkl:[INSTALL_DIR]/rtl
to set LD_LIBRARY_PATH, or
  setenv LD_LIBRARY_PATH \
      [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl:[INSTALL_DIR]/rtl:${LD_LIBRARY_PATH}
to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

  LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl:[INSTALL_DIR]/rtl
  export LD_LIBRARY_PATH
to set LD_LIBRARY_PATH, or
  LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl:[INSTALL_DIR]/rtl:${LD_LIBRARY_PATH}
  export LD_LIBRARY_PATH
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.

If you are using a different compiler, you may need to link against the Intel icl run-time libraries provided in [INSTALL_DIR]/rtl.

3.2. Example Programs

The example results distributed were generated at Mark 23, 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 C compiler, a different compiler library, or a different set of Basic Linear Algebra Subprograms (BLAS) or Linear Algebra PACKage (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.

The distributed example results are those obtained with the static library libnagc_mkl.a (using the MKL BLAS and LAPACK routines).

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 nagc_example_mkl, nagc_example_shar_mkl, nagc_example and nagc_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 and options file, 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 with appropriate arguments specifying data, options and results files as needed.

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

  nagc_example_mkl e04ucc
will copy the example program and its data and options files (e04ucce.c, e04ucce.d and e04ucce.opt) into the current directory, compile the program and run it to produce the example program results in the file e04ucce.r.

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, f08 and f16

    In this implementation calls to the NAG version of the following BLAS and LAPACK routines are included in the libraries libnagc_mkl.a and libnagc_mkl.so to avoid problems with the vendor version:
      zdotu      zggevx     zdotc      zdotci     zdotui
    
  2. s10 - s21

    Functions in these Chapters will give error messages if called with illegal or unsafe arguments.

    General details are given in the Library Manual, but parameter limits which are implementation specific are given below:

    s07aac  F_1 = 1.0e+13
            F_2 = 1.0e-14
    
    s10aac  E_1 = 1.8715e+1
    s10abc  E_1 = 7.080e+2
    s10acc  E_1 = 7.080e+2
    
    s13aac  x_hi = 7.083e+2
    s13acc  x_hi = 1.0e+16
    s13adc  x_hi = 1.0e+17
    
    s14aac  fail.code = NE_REAL_ARG_GT if x > 1.70e+2
            fail.code = NE_REAL_ARG_LT if x < -1.70e+2
            fail.code = NE_REAL_ARG_TOO_SMALL if abs(x) < 2.23e-308
    s14abc  fail.code = NE_REAL_ARG_GT if x > x_big = 2.55e+305
    
    s15adc  x_hi = 2.65e+1
    s15aec  x_hi = 2.65e+1
    s15afc  underflow trap was necessary
    s15agc  fail.code = NW_HI if x >= 2.53e+307
            fail.code = NW_REAL if 4.74e+7 <= x < 2.53e+307
            fail.code = NW_NEG if x < -2.66e+1
    
    s17acc  fail.code = NE_REAL_ARG_GT if x > 1.0e+16
    s17adc  fail.code = NE_REAL_ARG_GT if x > 1.0e+16
            fail.code = NE_REAL_ARG_TOO_SMALL if 0 < x <= 2.23e-308
    s17aec  fail.code = NE_REAL_ARG_GT if abs(x) > 1.0e+16
    s17afc  fail.code = NE_REAL_ARG_GT if abs(x) > 1.0e+16
    s17agc  fail.code = NE_REAL_ARG_GT if x > 1.038e+2
            fail.code = NE_REAL_ARG_LT if x < -5.7e+10
    s17ahc  fail.code = NE_REAL_ARG_GT if x > 1.041e+2
            fail.code = NE_REAL_ARG_LT if x < -5.7e+10
    s17ajc  fail.code = NE_REAL_ARG_GT if x > 1.041e+2
            fail.code = NE_REAL_ARG_LT if x < -1.9e+9
    s17akc  fail.code = NE_REAL_ARG_GT if x > 1.041e+2
            fail.code = NE_REAL_ARG_LT if x < -1.9e+9
    s17dcc  fail.code = NE_OVERFLOW_LIKELY if abs(z) < 3.92223e-305
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    s17dec  fail.code = NE_OVERFLOW_LIKELY if Im(z) > 7.00921e+2
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    s17dgc  fail.code = NW_SOME_PRECISION_LOSS if abs(z) > 1.02399e+3
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) > 1.04857e+6
    s17dhc  fail.code = NW_SOME_PRECISION_LOSS if abs(z) > 1.02399e+3
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) > 1.04857e+6
    s17dlc  fail.code = NE_OVERFLOW_LIKELY if abs(z) < 3.92223e-305
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    
    s18adc  fail.code = NE_REAL_ARG_TOO_SMALL if 0 < x <= 2.23e-308
    s18aec  fail.code = NE_REAL_ARG_GT if abs(x) > 7.116e+2
    s18afc  fail.code = NE_REAL_ARG_GT if abs(x) > 7.116e+2
    s18dcc  fail.code = NE_OVERFLOW_LIKELY if abs(z) < 3.92223e-305
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    s18dec  fail.code = NE_OVERFLOW_LIKELY if Re(z) > 7.00921e+2
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    
    s19aac  fail.code = NE_REAL_ARG_GT if abs(x) >= 5.04818e+1
    s19abc  fail.code = NE_REAL_ARG_GT if abs(x) >= 5.04818e+1
    s19acc  fail.code = NE_REAL_ARG_GT if x > 9.9726e+2
    s19adc  fail.code = NE_REAL_ARG_GT if x > 9.9726e+2
    
    s21bcc  fail.code = NE_REAL_ARG_LT if an argument < 1.583e-205
            fail.code = NE_REAL_ARG_GE if an argument >= 3.765e+202
    s21bdc  fail.code = NE_REAL_ARG_LT if an argument < 2.813e-103
            fail.code = NE_REAL_ARG_GT if an argument >= 1.407e+102
    
  3. x01

    The values of the mathematical constants are provided in the header file nagx01.h:

    X01AAC (pi) = 3.1415926535897932
    X01ABC (gamma) = 0.5772156649015328
    
  4. x02

    The values of the machine constants are provided in the header file nagx02.h:

    The basic parameters of the model

    X02BHC   = 2
    X02BJC   = 53
    X02BKC   = -1021
    X02BLC   = 1024
    X02DJC   = Nag_TRUE
    

    Derived parameters of the floating-point arithmetic

    X02AJC = 1.11022302462516e-16 X02AKC = 2.22507385850721e-308 X02ALC = 1.79769313486231e+308 X02AMC = 2.22507385850721e-308 X02ANC = 2.22507385850721e-308

    Parameters of other aspects of the computing environment

    X02AHC = 1.42724769270596e+45 X02BBC = 2147483647 X02BEC = 15 X02DAC = Nag_TRUE

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 http://www.nag.co.uk/numeric/CL/CLdocumentation.asp.

The Library Manual is supplied in the following formats:

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

	nagdoc_cl23/html/FRONTMATTER/manconts.html
	nagdoc_cl23/pdf/FRONTMATTER/manconts.pdf
	nagdoc_cl23/pdf/FRONTMATTER/manconts.html
Use your web browser to navigate from here. For convenience, a master index file containing links to the above files has been provided at
	nagdoc_cl23/index.html

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 or account number and NAG product code (in this case CLLUX23DCL).

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

(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 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 nagnews@nag.co.uk.

(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 http://www.nag.co.uk/numeric/Library_Registration.asp.

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

NAG Ltd
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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
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Suite 185
Lisle, IL  60532-4332                   NAG Inc Response Center
USA                                     email: support@nag.com

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

Nihon NAG KK
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4-9-9
Hatchobori
Chuo-ku
Tokyo 104-0032                          Nihon NAG Response Centre
Japan                                   email: support@nag-j.co.jp

Tel: +81 3 5542 6311                    Tel: +81 3 5542 6311
Fax: +81 3 5542 6312                    Fax: +81 3 5542 6312

NAG Taiwan Branch Office
5F.-5, No.36, Sec.3
Minsheng E. Rd.
Taipei City 10480                       NAG Taiwan Response Centre
Taiwan                                  email: support@nag-gc.com

Tel: +886 2 25093288                    Tel: +886 2 25093288
Fax: +886 2 25091798                    Fax: +886 2 25091798