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 and its Documentation
(b) Chapter Introduction
(c) Routine Document
https://www.nag.co.uk/doc/inun/cl26/l6i2gl/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 the Intel ® Math Kernel Library (MKL), 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(a)). 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 2018.0.1 of MKL, which is supplied as a part of this product. Please see the Intel website for further information about MKL (https://software.intel.com/intel-mkl). For best performance, we recommend that you use one of the variants of the NAG Library which is based on the supplied MKL, i.e. libnagc_mkl.a or libnagc_mkl.so, in preference to using one of the self-contained NAG libraries, libnagc_nag.a or libnagc_nag.so.
Note that the NAG C Library is carefully designed so that any memory used can be reclaimed – either by the Library itself or 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.
The version of Intel MKL supplied is multithreaded. If the environment variable OMP_NUM_THREADS is undefined, MKL may create multiple threads to speed up computation on systems with more than one processor or a multicore chip. If you do not want MKL to make use of multiple cores or processors, OMP_NUM_THREADS must be set to 1, e.g.
setenv OMP_NUM_THREADS 1in the C shell, or
OMP_NUM_THREADS=1 export OMP_NUM_THREADSin the Bourne shell.
Alternatively, set the environment variable to the number of threads required. Note that the Chapter X06 routines do not change the behaviour of MKL threading in serial implementations of the Library.
Intel have introduced a conditional bitwise reproducibility (BWR) option in MKL. Provided a user's code adheres to certain conditions (see https://software.intel.com/en-us/node/528579), BWR can be forced by setting the MKL_CBWR environment variable. See the MKL documentation for further details. It should be noted, however, that many NAG routines do not adhere to these conditions. This means that for a given NAG library built on top of MKL, it may not be possible to ensure BWR for all NAG routines across different CPU architectures by setting MKL_CBWR. See Section 3.9.1 of How to Use the NAG Library and its Documentation for more general information on bitwise reproducibility.
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 $HOME/NAG/cll6i262gl; however it could have been changed by the person who did the installation, in which case you should consult that person.
Note that the environment variable LD_LIBRARY_PATH must be set correctly at link time and run time (see below).
To use the NAG Library and the supplied MKL libraries, you may link in the following manner:
gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.a \ -Wl,--start-group \ [INSTALL_DIR]/mkl_intel64_2018.0.1/lib/libmkl_gf_lp64.a \ [INSTALL_DIR]/mkl_intel64_2018.0.1/lib/libmkl_gnu_thread.a \ [INSTALL_DIR]/mkl_intel64_2018.0.1/lib/libmkl_core.a \ -Wl,--end-group \ -lgomp -lpthread -lm -ldl -lgfortran -lquadmath -lstdc++where driver.c is your application program;
or
gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.so \ -L[INSTALL_DIR]/mkl_intel64_2018.0.1/lib -Wl,--no-as-needed \ -lmkl_gf_lp64 -lmkl_gnu_thread -lmkl_core -lgomp -lpthread -lm -ldl \ -lgfortran -lquadmath -lstdc++if the shareable library is required.
However, if you prefer to link to a version of the NAG Library which does not require the use of MKL you may wish to use the self-contained libraries as follows:
gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.a \ -lgfortran -lm -lquadmath -lpthread -lstdc++or
gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.so \ -lgfortran -lm -lquadmath -lpthread -lstdc++if the shareable library is required.
To compile and run your application with the shareable NAG and MKL libraries, the environment variable LD_LIBRARY_PATH must be set or extended, as follows.
In the C shell, type:
setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_2018.0.1/libto set LD_LIBRARY_PATH, or
setenv LD_LIBRARY_PATH \ [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_2018.0.1/lib:${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_intel64_2018.0.1/lib export LD_LIBRARY_PATHto set LD_LIBRARY_PATH, or
LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_2018.0.1/lib:${LD_LIBRARY_PATH} export LD_LIBRARY_PATHto 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 items such as compiler run-time libraries, for example if you are using a newer version of the compiler.
The distributed example results are those obtained with the static library libnagc_mkl.a (i.e. using the MKL 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 one of the following scripts, which are located in the directory [INSTALL_DIR]/scripts:
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), with the results being sent to a file and to the command window.
The example program concerned is specified by the argument to the command, e.g.
nagc_example -mkl 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.
In this implementation, the NAG types Integer and Pointer are defined as follows:
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 the How to Use the NAG Library and its Documentation section of the Library Manual (see Section 5).
In this implementation, calls to the NAG version of the following BLAS and LAPACK routines may be included in the libraries libnagc_mkl.a and libnagc_mkl.so to avoid problems with the vendor version:
dgesvj
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:
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 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 AIMAG(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 REAL(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
The values of the mathematical constants are provided in the header file nagx01.h:
X01AAC (pi) = 3.1415926535897932 X01ABC (gamma) = 0.5772156649015328
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
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
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.co.uk/numeric/cl/nagdoc_cl26.2/.
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 main index files have been provided:
nagdoc_26.2/nagdoc_cl26.2/html/frontmatter/manconts.html nagdoc_26.2/nagdoc_fl26.2/html/frontmatter/manconts.htmlUse your web browser to navigate from here. For convenience, a master index file containing links to the above files has been provided at
nagdoc_26.2/index.html
Advice on viewing and navigating the formats available can be found in https://www.nag.co.uk/numeric/cl/nagdoc_cl26.2/html/genint/essint.html#onlinedoc.
In addition the following are provided:
https://www.nag.co.uk/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.co.uk/content/worldwide-contact-information
for worldwide contact details for the Numerical Algorithms Group.