In addition, NAG recommends that before calling any Library routine you should read the following reference material from the Library Manual (see Section 5):
(a) How to Use the NAG Library
(b) Chapter Introduction
(c) Routine Document
https://www.nag.com/doc/inun/nl27/mi6dgl/supplementary.html
for details of any new information related to the applicability or usage of this implementation.
This implementation of the NAG Library provides static and shareable libraries that use Apple vecLib (Accelerate Framework), a third-party vendor performance library, to provide Basic Linear Algebra Subprograms (BLAS) and Linear Algebra PACKage (LAPACK) routines (except for any routines listed in Section 4). It also provides static and shareable libraries that use the NAG versions of these routines (referred to as the self-contained libraries). This implementation has been tested with version 3.11 of vecLib. Please see the Apple web site for further information about vecLib (https://developer.apple.com/documentation/accelerate/veclib.) For best performance, we recommend that you use one of the variants of the NAG Library which is based on vecLib, i.e. libnag_vl.a or libnag_vl.dylib, in preference to using one of the self-contained NAG libraries, libnag_nag.a or libnag_nag.dylib.
The NAG AD Library is not included in this implementation.
Note that the NAG Library is carefully designed so that any memory used can be reclaimed – either by the Library itself or, for C routines, by the user invoking calls of NAG_FREE(). However, the Library does itself depend on the use of compiler run-time and other libraries which may sometimes leak memory, and memory tracing tools used on programs linked to the NAG Library may report this. The amount of memory leaked will vary from application to application, but should not be excessive and should never increase without limit as more calls are made to the NAG Library.
If you intend to use the NAG library within a multithreaded application please refer to the document CL Interface Multithreading or FL Interface Multithreading (as appropriate) for more information.
The libraries supplied with this implementation do not contain OpenMP or any other threading mechanisms. However, vecLib may employ multithreading to enhance performance.
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 $HOME/NAG/nlmi627dgl; however it could have been changed by the person who did the installation, in which case you should consult that person. Note that the environment variable DYLD_LIBRARY_PATH must be set correctly at link time and run time to point to the appropriate library locations underneath [INSTALL_DIR]. See below for how to do this.
The NAG Library is a combined replacement for users of both the NAG C Library and the NAG Fortran Library (including the C wrappers to the Fortran Library interfaces). To help with calling the different libraries included with this implementation the scripts nagvars.sh and nagvars.csh are included to set NAG-specific environment variables to assist with compiling and linking applications that call any of the NAG routines. They also amend the standard environment variables PATH and DYLD_LIBRARY_PATH so that NAG executable programs and libraries can be found at compile, link and run time.
The nagvars scripts are designed to be used as follows:
. [INSTALL_DIR]/scripts/nagvars.sh [-help] [-unset] [-quiet] {int32} \
{vendor,nag} {static,dynamic}
or
source [INSTALL_DIR]/scripts/nagvars.csh [-help] [-unset] [-quiet] {int32} \
{vendor,nag} {static,dynamic}
where:
source [INSTALL_DIR]/scripts/nagvars.sh int32 vendor dynamicThe NAG-specific environment variables set are:
For C programs:
${NAGLIB_CC} ${NAGLIB_CFLAGS} ${NAGLIB_INCLUDE} program.c ${NAGLIB_CLINK}
or for C++ programs:
${NAGLIB_CXX} ${NAGLIB_CXXFLAGS} ${NAGLIB_INCLUDE} program.cpp ${NAGLIB_CXXLINK}
or for Fortran programs:
${NAGLIB_F77} ${NAGLIB_FFLAGS} ${NAGLIB_INCLUDE} program.f90 ${NAGLIB_FLINK}
You will also need to edit the variable _nag_compiler_runtimedir in the script files nagvars.csh and nagvars.sh so that it points to the location of the appropriate lib directory. If you are not using the scripts, then set DYLD_LIBRARY_PATH to point to the compiler run-time libraries.
Their purpose is to allow the Fortran compiler to check that NAG 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; and
(d) all arguments match in type and structure.
The NAG Library interface block files are organised by Library chapter. They are aggregated into one module named
nag_libraryThe modules are supplied in compiled form (.mod files) for the GNU gfortran compiler. They can be accessed by specifying the
The .mod module files were compiled with the Fortran compiler shown in Section 2.2 of the Installer's Note. Such module files are compiler-dependent, so if you wish to use the NAG example programs, or use the interface blocks in your own programs, when using a compiler that is incompatible with these modules, you will first need to recompile the interface blocks with your own compiler version. A recompiled set of interface blocks can be created in a separate directory (e.g. nag_interface_blocks_alt) using the supplied script command
[INSTALL_DIR]/scripts/nag_recompile_mods {int32} nag_interface_blocks_alt
from the [INSTALL_DIR] directory.
This script uses the version of the
GNU Fortran compiler
from your PATH environment; to specify an alternative version
it is safest to first run any
GNU Fortran compiler
environment scripts for that version prior
to running [INSTALL_DIR]/scripts/nag_recompile_mods.
To make the new set of compiled modules the default set, you may use the following commands (with [INSTALL_DIR] substituted by the actual directory path as appropriate):
mv [INSTALL_DIR]/lp64/nag_interface_blocks [INSTALL_DIR]/lp64/nag_interface_blocks_original mv [INSTALL_DIR]/lp64/nag_interface_blocks_alt [INSTALL_DIR]/lp64/nag_interface_blocks
You should now be able to use the newly compiled module files in the usual way.
The distributed example results are those obtained with the static library libnag_vl.a (i.e. using the vecLib BLAS and LAPACK routines). Running the examples with NAG BLAS or LAPACK may give slightly different results.
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 example programs are most easily accessed by using the script nag_example, which is located in the directory [INSTALL_DIR]/scripts.
This script 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. Finally, the executable program will be run (with appropriate arguments specifying data, options and results files as needed), with the results being sent to a file and to the command window. By default nag_example selects to use static linking to the self-contained libnag_nag.a library. These choices can be changed by optional switches -shared and -vendor respectively. The -quiet option may be specified to minimize printing of both comments and the commands being executed at each of the stages described above. Run
nag_example -helpto display a list of the available options.
The nag_example script demonstrates use of the nagvars script discussed in Section 3.1, but note that it does not alter the environment in the calling shell.
The example program concerned is specified by the argument to the command, e.g. for a NAG C routine
nag_example e04uccwill copy the example program and its data and options files (e04ucce.c, e04ucce.d and e04ucce.opt) into the current directory, compile and link the program and run it to produce the example program results in the file e04ucce.r.
Similarly, for a NAG Fortran routine
nag_example e04nrfwill copy the example program and its data and options files (e04nrfe.f90, e04nrfe.d and e04nrfe.opt) into the current directory, compile and link the program and run it to produce the example program results in the file e04nrfe.r.
You will need to set the variable _nag_compiler_runtimedir with the location of the appropriate compiler run-time libraries in the script nagvars.sh as this is used by the nag_example script. See Section 3.1 for details.
| NAG Type | C Type | Size (bytes) |
|---|---|---|
| Integer | int | 4 |
| Pointer | void * | 8 |
The values for sizeof(Integer) and sizeof(Pointer) are also given by the a00aac example program. Information on other NAG data types is available in Section 3.1.1 of the NAG CL Interface Introduction component of the Library Manual (see Section 5 below).
This implementation of the NAG Library includes libraries for 32-bit integers only. The libraries are located in [INSTALL_DIR]/lp64/lib.
The NAG Library and documentation use parameterized types for floating-point variables. Thus, the type
REAL(KIND=nag_wp)
appears in the documentation of all NAG Library routines,
where nag_wp
is a Fortran KIND parameter. The value of nag_wp will vary
between implementations,
and its value can be obtained by use of the nag_library
module. We refer to the type
nag_wp as the NAG Library "working precision" type, because
most floating-point
arguments and internal variables used in the Library are of this type.
In addition, a small number of routines use the type
REAL(KIND=nag_rp)
where nag_rp stands for "reduced precision" type. Another
type, not currently
used in the Library, is
REAL(KIND=nag_hp)
for "higher precision" type or "additional precision" type.
For correct use of these types, see almost any of the example programs distributed with the Library.
For this implementation, these types have the following meanings:
REAL (kind=nag_rp) means REAL (i.e. single precision)
REAL (kind=nag_wp) means DOUBLE PRECISION
COMPLEX (kind=nag_rp) means COMPLEX (i.e. single precision complex)
COMPLEX (kind=nag_wp) means double precision complex (e.g. COMPLEX*16)
In addition, the FL Interface section of the Manual has adopted a convention of using bold italics to distinguish some terms. See Section 2.5 of the FL Interface Introduction for details.
A document, alt_c_interfaces.html, giving advice on calling the Fortran routines in the NAG Library from C and C++ is also available. (In previous Marks of the NAG Library, this document was called techdoc.html.)
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 from the equivalent NAG versions of these routines. Care should be taken when using the workspace query mechanism.
In this implementation, calls to BLAS and LAPACK routines in the non-self-contained NAG libraries
are implemented by calls to vecLib, except for the following routines:
blas_damax_val blas_damin_val blas_daxpby blas_ddot blas_dmax_val blas_dmin_val blas_dsum blas_dwaxpby blas_zamax_val blas_zamin_val blas_zaxpby blas_zsum blas_zwaxpby daxpyi dbdsvdx ddoti dgeesx dgehrd dgejsv dgemqrt dgemv dgeqrt dgesvdx dgesvj dgetrs dgges dgges3 dggev3 dggevx dgghd3 dggsvd3 dggsvp3 dgthr dgthrz dhgeqz dorcsd drot droti dsctr dsgesv dtpmqrt dtpqrt dtrsen dtrsm dznrm2 sasum scasum sdot zaxpyi zcgesv zcopy zdotc zdotci zdotu zdotui zgeesx zgejsv zgelsy zgemqrt zgeqp3 zgeqrt zgesvdx zgesvj zgges3 zggev3 zgghd3 zggsvd3 zggsvp3 zgthr zgthrz zsctr ztgsen ztpmqrt ztpqrt zuncsd zunmrz
The behaviour of functions in these Chapters may depend on implementation-specific values.
General details are given in the Library Manual, but the specific values used in this implementation are as follows:
s07aa[f] (nag[f]_specfun_tan)
F_1 = 1.0e+13
F_2 = 1.0e-14
s10aa[fc] (nag[f]_specfun_tanh)
E_1 = 1.8715e+1
s10ab[fc] (nag[f]_specfun_sinh)
E_1 = 7.080e+2
s10ac[fc] (nag[f]_specfun_cosh)
E_1 = 7.080e+2
s13aa[fc] (nag[f]_specfun_integral_exp)
x_hi = 7.083e+2
s13ac[fc] (nag[f]_specfun_integral_cos)
x_hi = 1.0e+16
s13ad[fc] (nag[f]_specfun_integral_sin)
x_hi = 1.0e+17
s14aa[fc] (nag[f]_specfun_gamma)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.70e+2
ifail = 2 (NE_REAL_ARG_LT) if x < -1.70e+2
ifail = 3 (NE_REAL_ARG_TOO_SMALL) if abs(x) < 2.23e-308
s14ab[fc] (nag[f]_specfun_gamma_log_real)
ifail = 2 (NE_REAL_ARG_GT) if x > x_big = 2.55e+305
s15ad[fc] (nag[f]_specfun_erfc_real)
x_hi = 2.65e+1
s15ae[fc] (nag[f]_specfun_erf_real)
x_hi = 2.65e+1
s15ag[fc] (nag[f]_specfun_erfcx_real)
ifail = 1 (NW_HI) if x >= 2.53e+307
ifail = 2 (NW_REAL) if 4.74e+7 <= x < 2.53e+307
ifail = 3 (NW_NEG) if x < -2.66e+1
s17ac[fc] (nag[f]_specfun_bessel_y0_real)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.0e+16
s17ad[fc] (nag[f]_specfun_bessel_y1_real)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.0e+16
ifail = 3 (NE_REAL_ARG_TOO_SMALL) if 0 < x <= 2.23e-308
s17ae[fc] (nag[f]_specfun_bessel_j0_real)
ifail = 1 (NE_REAL_ARG_GT) if abs(x) > 1.0e+16
s17af[fc] (nag[f]_specfun_bessel_j1_real)
ifail = 1 (NE_REAL_ARG_GT) if abs(x) > 1.0e+16
s17ag[fc] (nag[f]_specfun_airy_ai_real)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.038e+2
ifail = 2 (NE_REAL_ARG_LT) if x < -5.7e+10
s17ah[fc] (nag[f]_specfun_airy_bi_real)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.041e+2
ifail = 2 (NE_REAL_ARG_LT) if x < -5.7e+10
s17aj[fc] (nag[f]_specfun_airy_ai_deriv)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.041e+2
ifail = 2 (NE_REAL_ARG_LT) if x < -1.9e+9
s17ak[fc] (nag[f]_specfun_airy_bi_deriv)
ifail = 1 (NE_REAL_ARG_GT) if x > 1.041e+2
ifail = 2 (NE_REAL_ARG_LT) if x < -1.9e+9
s17dc[fc] (nag[f]_specfun_bessel_y_complex)
ifail = 2 (NE_OVERFLOW_LIKELY) if abs(z) < 3.92223e-305
ifail = 4 (NW_SOME_PRECISION_LOSS) if abs(z) or fnu+n-1 > 3.27679e+4
ifail = 5 (NE_TOTAL_PRECISION_LOSS) if abs(z) or fnu+n-1 > 1.07374e+9
s17de[fc] (nag[f]_specfun_bessel_j_complex)
ifail = 2 (NE_OVERFLOW_LIKELY) if AIMAG(z) > 7.00921e+2
ifail = 3 (NW_SOME_PRECISION_LOSS) if abs(z) or fnu+n-1 > 3.27679e+4
ifail = 4 (NE_TOTAL_PRECISION_LOSS) if abs(z) or fnu+n-1 > 1.07374e+9
s17dg[fc] (nag[f]_specfun_airy_ai_complex)
ifail = 3 (NW_SOME_PRECISION_LOSS) if abs(z) > 1.02399e+3
ifail = 4 (NE_TOTAL_PRECISION_LOSS) if abs(z) > 1.04857e+6
s17dh[fc] (nag[f]_specfun_airy_bi_complex)
ifail = 3 (NW_SOME_PRECISION_LOSS) if abs(z) > 1.02399e+3
ifail = 4 (NE_TOTAL_PRECISION_LOSS) if abs(z) > 1.04857e+6
s17dl[fc] (nag[f]_specfun_hankel_complex)
ifail = 2 (NE_OVERFLOW_LIKELY) if abs(z) < 3.92223e-305
ifail = 4 (NW_SOME_PRECISION_LOSS) if abs(z) or fnu+n-1 > 3.27679e+4
ifail = 5 (NE_TOTAL_PRECISION_LOSS) if abs(z) or fnu+n-1 > 1.07374e+9
s18ad[fc] (nag[f]_specfun_bessel_k1_real)
ifail = 2 (NE_REAL_ARG_TOO_SMALL) if 0 < x <= 2.23e-308
s18ae[fc] (nag[f]_specfun_bessel_i0_real)
ifail = 1 (NE_REAL_ARG_GT) if abs(x) > 7.116e+2
s18af[fc] (nag[f]_specfun_bessel_i1_real)
ifail = 1 (NE_REAL_ARG_GT) if abs(x) > 7.116e+2
s18dc[fc] (nag[f]_specfun_bessel_k_complex)
ifail = 2 (NE_OVERFLOW_LIKELY) if abs(z) < 3.92223e-305
ifail = 4 (NW_SOME_PRECISION_LOSS) if abs(z) or fnu+n-1 > 3.27679e+4
ifail = 5 (NE_TOTAL_PRECISION_LOSS) if abs(z) or fnu+n-1 > 1.07374e+9
s18de[fc] (nag[f]_specfun_bessel_i_complex)
ifail = 2 (NE_OVERFLOW_LIKELY) if REAL(z) > 7.00921e+2
ifail = 3 (NW_SOME_PRECISION_LOSS) if abs(z) or fnu+n-1 > 3.27679e+4
ifail = 4 (NE_TOTAL_PRECISION_LOSS) if abs(z) or fnu+n-1 > 1.07374e+9
s19aa[fc] (nag[f]_specfun_kelvin_ber)
ifail = 1 (NE_REAL_ARG_GT) if abs(x) >= 5.04818e+1
s19ab[fc] (nag[f]_specfun_kelvin_bei)
ifail = 1 (NE_REAL_ARG_GT) if abs(x) >= 5.04818e+1
s19ac[fc] (nag[f]_specfun_kelvin_ker)
ifail = 1 (NE_REAL_ARG_GT) if x > 9.9726e+2
s19ad[fc] (nag[f]_specfun_kelvin_kei)
ifail = 1 (NE_REAL_ARG_GT) if x > 9.9726e+2
s21bc[fc] (nag[f]_specfun_ellipint_symm_2)
ifail = 3 (NE_REAL_ARG_LT) if an argument < 1.583e-205
ifail = 4 (NE_REAL_ARG_GE) if an argument >= 3.765e+202
s21bd[fc] (nag[f]_specfun_ellipint_symm_3)
ifail = 3 (NE_REAL_ARG_LT) if an argument < 2.813e-103
ifail = 4 (NE_REAL_ARG_GT) if an argument >= 1.407e+102
The values of the mathematical constants are:
x01aa[fc] (nag[f]_math_pi)
= 3.1415926535897932
x01ab[fc] (nag[f]_math_euler)
= 0.5772156649015328
The values of the machine constants are:
The basic parameters of the model
x02bh[fc] (nag[f]_machine_model_base)
= 2
x02bj[fc] (nag[f]_machine_model_digits)
= 53
x02bk[fc] (nag[f]_machine_model_minexp)
= -1021
x02bl[fc] (nag[f]_machine_model_maxexp)
= 1024
Derived parameters of the floating-point arithmetic
x02aj[fc] (nag[f]_machine_precision)
= 1.11022302462516e-16
x02ak[fc] (nag[f]_machine_real_smallest)
= 2.22507385850721e-308
x02al[fc] (nag[f]_machine_real_largest)
= 1.79769313486231e+308
x02am[fc] (nag[f]_machine_real_safe)
= 2.22507385850721e-308
x02an[fc] (nag[f]_machine_complex_safe)
= 4.78687214269110e-168
Parameters of other aspects of the computing environment
x02ah[fc] (nag[f]_machine_sinarg_max)
= 1.42724769270596e+45
x02bb[fc] (nag[f]_machine_integer_max)
= 2147483647
x02be[fc] (nag[f]_machine_decimal_digits)
= 15
The Library Manual is available as a separate installation, via download from the NAG website. The most up-to-date version of the documentation is accessible via the NAG website at https://www.nag.com/numeric/nl/nagdoc_27/.
The Library Manual is supplied in HTML5, a fully linked version of the manual using HTML and MathML. These documents can be accessed using your web browser.
The following master index file has been provided:
nagdoc_27/index.htmlUse your web browser to navigate from here.
Advice on viewing and navigating the documentation can be found in https://www.nag.com/numeric/nl/nagdoc_27/nlhtml/genint/naglibdoc.html.
In addition the following are provided:
https://www.nag.com/content/nag-technical-support-service
for information about the NAG Technical Support Service, including details of the NAG Technical Support Service contact points. We would also be delighted to receive your feedback on NAG's products and services.
https://www.nag.com/content/worldwide-contact-information
for worldwide contact details for the Numerical Algorithms Group.