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 the OpenMP threading model. Lower-level threading models such as Pthreads are not supported.
http://www.nag.co.uk/doc/inun/fs22/ai6dal/postrelease.html
for details of any new information related to the applicability or usage of this implementation.
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/fsai622dal or /usr/local/NAG/fsai622dal depending on your system; however it could have been changed by the person who did the installation. To identify [INSTALL_DIR] for this installation:
xlf_r -q64 -qsmp=omp -qnosave -qxlf77=nopersistent:leadzero driver.f \
[INSTALL_DIR]/lib/libnagsmp.a -lesslsmp
where driver.f is your application program
; or
xlf_r -q64 -qsmp=omp -qnosave -qxlf77=nopersistent:leadzero driver.f \
[INSTALL_DIR]/lib/libnagsmp.so -lesslsmp
if the shareable library is required.
The library can be used with or without the compiler flag -qextname.
If the compiled NAG Library for SMP & Multicore libraries and the ESSL libraries are installed in, or are pointed at by symbolic links from, directories in the search path of the linker, such as /usr/lib, then you may alternatively link in the following manner:
xlf_r -q64 -qsmp=omp -qnosave -qxlf77=nopersistent:leadzero driver.f \
-lnagsmp -lesslsmp
This will usually link to the static library in preference to the
shareable library if both the libraries are at the same location.
To use the shared library libnagsmp.so you need to use the -brtl compiler flag as follows:
xlf_r -q64 -qsmp=omp -qnosave -qxlf77=nopersistent:leadzero -brtl driver.f \
-lnagsmp -lesslsmp
If your application uses the NAG shareable library then the environment variable LIBPATH must be set or extended, as follows, to allow run time linkage.
In the C shell, type:
setenv LIBPATH [INSTALL_DIR]/libto set LIBPATH, or
setenv LIBPATH [INSTALL_DIR]/lib:${LIBPATH}
to extend LIBPATH if you already have it set.
In the Bourne shell, type:
LIBPATH=[INSTALL_DIR]/lib export LIBPATHto set LIBPATH, or
LIBPATH=[INSTALL_DIR]/lib:${LIBPATH}
export LIBPATH
to extend LIBPATH if you already have it set.
This implementation is not compatible with previous versions of XLF (i.e. XLF 12 and earlier).
The shared library is only recommended for use with the exact compiler version used to create this implementation (IBM XLF version 13.1.0.3). If this is not the default compiler installation on your system, the environment variable LIBPATH must be set to point to the library directory of the IBM XLF version 13.1.0.3 installation. Given this compatibility issue, users are advised to use the static library whenever possible.
In the C shell type:
setenv OMP_NUM_THREADS NIn the Bourne shell, type:
OMP_NUM_THREADS=N export OMP_NUM_THREADSwhere N is the number of processors required. OMP_NUM_THREADS may be re-set between each execution of the program, as desired.
(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.
These interface blocks have been generated automatically by analysing the source code for the NAG Library for SMP & Multicore. As a consequence, and because these files have been thoroughly tested, their use is recommended in preference to writing your own declarations.
The NAG Library for SMP & Multicore 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_chapterThese are supplied in pre-compiled form (.mod files) and they can be accessed by specifying the -Ipathname option on each compiler invocation, where pathname (e.g. [INSTALL_DIR]/nag_interface_blocks) is the path of the directory containing the compiled interface blocks. The interface block files are also supplied in source form, but these are only required if the precompiled form is incompatible with the compiler in use.
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 Library for SMP & Multicore 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
* Mark 14 Revised. NAG Copyright 1989.
*****************************************************
* Add USE statements for relevant chapters *
USE NAG_F77_D_CHAPTER, ONLY: D01DAF
* *
*****************************************************
* .. Parameters ..
INTEGER NOUT
PARAMETER (NOUT=6)
* .. Local Scalars ..
DOUBLE PRECISION ABSACC, ANS, YA, YB
INTEGER IFAIL, NPTS
* .. External Functions ..
DOUBLE PRECISION FA, FB, PHI1, PHI2A, PHI2B
EXTERNAL FA, FB, PHI1, PHI2A, PHI2B
* .. External Subroutines ..
******************************************************
* EXTERNAL declarations need to be removed. *
* EXTERNAL D01DAF
* *
******************************************************
* .. Executable Statements ..
WRITE (NOUT,*) 'D01DAF Example Program Results'
YA = 0.0D0
YB = 1.0D0
ABSACC = 1.0D-6
WRITE (NOUT,*)
IFAIL = 1
*
CALL D01DAF(YA,YB,PHI1,PHI2A,FA,ABSACC,ANS,NPTS,IFAIL)
*
IF (IFAIL.LT.0) THEN
WRITE (NOUT,99998) ' ** D01DAF returned with IFAIL = ', IFAIL
ELSE
*
WRITE (NOUT,*) 'First formulation'
WRITE (NOUT,99999) 'Integral =', ANS
WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
WRITE (NOUT,*)
WRITE (NOUT,*) 'Second formulation'
IFAIL = 1
*
CALL D01DAF(YA,YB,PHI1,PHI2B,FB,ABSACC,ANS,NPTS,IFAIL)
*
WRITE (NOUT,99999) 'Integral =', ANS
WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
END IF
*
99999 FORMAT (1X,A,F9.4)
99998 FORMAT (1X,A,I5)
END
*
DOUBLE PRECISION FUNCTION PHI1(Y)
* .. Scalar Arguments ..
DOUBLE PRECISION Y
* .. Executable Statements ..
PHI1 = 0.0D0
RETURN
END
*
DOUBLE PRECISION FUNCTION PHI2A(Y)
* .. Scalar Arguments ..
DOUBLE PRECISION Y
* .. Intrinsic Functions ..
INTRINSIC SQRT
* .. Executable Statements ..
PHI2A = 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 PHI2B(Y)
*****************************************************
* Add USE statements for relevant chapters *
USE NAG_F77_X_CHAPTER, ONLY: X01AAF
* *
*****************************************************
* .. Scalar Arguments ..
DOUBLE PRECISION Y
* .. External Functions ..
******************************************************
* Function Type declarations need to be removed. *
* DOUBLE PRECISION X01AAF
* *
******************************************************
******************************************************
* EXTERNAL declarations need to be removed. *
* EXTERNAL X01AAF
* *
******************************************************
* .. Executable Statements ..
PHI2B = 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
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 two scripts nagsmp_example and nagsmp_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, presenting its output to stdout, which is redirected to a file.
The example program concerned, and the number of OpenMP threads to use, are specified by the arguments to the command, e.g.
nagsmp_example e04ucf 4will copy the example program e04ucfe.f and its data file e04ucfe.d into the current directory and process them with 4 OpenMP threads to produce the example program results in the file e04ucfe.r.
In order to support all implementations of the Library, the Manual has adopted a convention of using bold italics to distinguish terms which have different interpretations in different implementations.
For this double precision implementation, the bold italicised terms used in the Library Manual should be interpreted as follows:
real means REAL double precision means DOUBLE PRECISION complex means COMPLEX complex*16 means COMPLEX*16 (or equivalent) basic precision means DOUBLE PRECISION additional precision means quadruple precision reduced precision means REAL
Another important bold italicised term is machine precision, which denotes the relative precision to which double precision floating-point numbers are stored in the computer, e.g. in an implementation with approximately 16 decimal digits of precision, machine precision has a value of approximately 1.0D-16.
The precise value of machine precision is given by the routine X02AJF. Other routines in Chapter X02 return the values of other implementation-dependent constants, such as the overflow threshold, or the largest representable integer. Refer to the X02 Chapter Introduction for more details.
The bold italicised term block size is used only in Chapters F07 and F08. It denotes the block size used by block algorithms in these chapters. You only need to be aware of its value when it affects the amount of workspace to be supplied – see the parameters WORK and LWORK of the relevant routine documents and the Chapter Introduction.
In Chapters F06, F07 and F08, alternate routine names are available for BLAS and LAPACK derived routines. For details of the alternate routine names please refer to the relevant Chapter Introduction. Note that applications should reference routines by their BLAS/LAPACK names, rather than their NAG-style names, for optimum performance.
DCFT DCFT2 DCFT3 DCRFT DRCFTAs a result the following C06 chapter routines have implementation specific workspace requirements:
C06PAF C06PCF C06PFF C06PJF C06PKF C06PQF C06PRF C06PSF C06PUF C06PXFThe following table lists formulae to help calculate the required size of the workspace array WORK for each routine. These values may be considerable overestimates depending upon the parameters used (and thus the radices used within the FFT routines).
Routine Minimum length of WORK
C06PAF MAX( 3*N+15 , N+2+MAX(22000,20000+NINT(1.64*DBLE(N))) )
C06PCF MAX( 2*N+15 , N+10000+NINT(1.14*DBLE(N)) )
C06PFF MAX( ML*NL+NL+15 , ML*NL+10000+NINT(1.14*DBLE(NL)) ), where
NL = ND(L), ML = MK if MI=1; ML = MI otherwise, where
MI = Product of ND(1:L-1), MK = Product of ND(L+1:NDIM)
In the example program, we simplify (at the expense of grossly
overestimating workspace requirements in many cases) to give
N+10000+NINT(1.14*DBLE(N))
C06PJF As for C06PCF if NDIM=1;
ND(1)*ND(2)+10000+NINT(1.14*DBLE(MAX(ND(1),ND(2)))), if NDIM=2;
max LWORK value from C06PFF for L=1,NDIM otherwise.
In the example program, we simplify (at the expense of grossly
overestimating workspace requirements in many cases) to give
N+10000+NINT(1.14*DBLE(N))
C06PKF MAX( 2*N+15 , N+10000+NINT(1.14*DBLE(N)) )
C06PQF (M+2)*N+MAX(22000,20000+NINT(1.64*DBLE(N)))
C06PRF As for C06PCF if M=1;
MAX( M*N+2*N+15 , M*N+10000+NINT(1.14*DBLE(N)) ) otherwise
C06PSF As for C06PCF if M=1;
M*N+10000+NINT(1.14*DBLE(N)) otherwise
C06PUF M*N + 20000 + NINT(1.14*DBLE(M+N))
C06PXF Calls C06PUF as a 2D problem if MIN(N1,N2,N3) = 1;
N1*N2*N3 + 20000 + NINT(1.14*DBLE(N1+N2+N3)) otherwise
On exit from these routines, the real part of WORK(1) will contain the
minimum workspace required for the specific combination of parameters used.
In this implementation calls to Basic Linear Algebra Subprograms (BLAS) and the Linear Algebra PACKage (LAPACK) routines are implemented by calls to ESSL,
except for the following routines:
BLAS_DMAX_VAL BLAS_DMIN_VAL DBDSDC DBDSQR DDISNA DGBBRD DGBCON DGBEQU DGBRFS DGBSV DGBSVX DGBTRF DGBTRS DGEBAK DGEBAL DGEBRD DGEEQU DGEES DGEESX DGEEV DGEEVX DGEHRD DGELQF DGELS DGELSD DGELSS DGELSY DGEQLF DGEQP3 DGEQPF DGEQRF DGERFS DGERQF DGESDD DGESV DGESVD DGESVX DGETRF DGETRS DGGBAK DGGBAL DGGES DGGESX DGGEV DGGEVX DGGGLM DGGHRD DGGLSE DGGQRF DGGRQF DGGSVD DGGSVP DGTCON DGTRFS DGTSV DGTSVX DGTTRF DGTTRS DHGEQZ DHSEIN DHSEQR DLAGTM DLALS0 DLALSD DLANGT DLANST DLASDA DLASDQ DOPGTR DOPMTR DORGBR DORGHR DORGLQ DORGQL DORGQR DORGRQ DORGTR DORMBR DORMHR DORMLQ DORMQL DORMQR DORMRQ DORMRZ DORMTR DPBCON DPBEQU DPBRFS DPBSTF DPBSV DPBSVX DPBTRF DPBTRS DPOEQU DPORFS DPOSV DPOSVX DPOTRF DPOTRS DPPEQU DPPRFS DPPSV DPPSVX DPTCON DPTEQR DPTRFS DPTSV DPTSVX DPTTRF DPTTRS DROTI DSBEV DSBEVD DSBEVX DSBGST DSBGV DSBGVD DSBGVX DSBTRD DSGESV DSPCON DSPEV DSPEVD DSPEVX DSPGST DSPGV DSPGVD DSPGVX DSPRFS DSPSV DSPSVX DSPTRD DSPTRF DSPTRI DSPTRS DSTEBZ DSTEDC DSTEGR DSTEIN DSTEQR DSTERF DSTEV DSTEVD DSTEVR DSTEVX DSYCON DSYEV DSYEVD DSYEVR DSYEVX DSYGST DSYGV DSYGVD DSYGVX DSYRFS DSYSV DSYSVX DSYTRD DSYTRF DSYTRI DSYTRS DTBCON DTBRFS DTBTRS DTGEVC DTGEXC DTGSEN DTGSJA DTGSNA DTGSYL DTPCON DTPRFS DTPTRS DTRCON DTREVC DTREXC DTRRFS DTRSEN DTRSNA DTRSYL DTRTRS DTZRZF ZBDSQR ZCGESV ZGBBRD ZGBCON ZGBEQU ZGBRFS ZGBSV ZGBSVX ZGBTRF ZGBTRS ZGEBAK ZGEBAL ZGEBRD ZGEEQU ZGEES ZGEESX ZGEEV ZGEEVX ZGEHRD ZGELQF ZGELS ZGELSD ZGELSS ZGELSY ZGEQLF ZGEQP3 ZGEQPF ZGEQRF ZGERFS ZGERQF ZGESDD ZGESV ZGESVD ZGESVX ZGETRF ZGETRS ZGGBAK ZGGBAL ZGGES ZGGESX ZGGEV ZGGEVX ZGGGLM ZGGHRD ZGGLSE ZGGQRF ZGGRQF ZGGSVD ZGGSVP ZGTCON ZGTRFS ZGTSV ZGTSVX ZGTTRF ZGTTRS ZHBEV ZHBEVD ZHBEVX ZHBGST ZHBGV ZHBGVD ZHBGVX ZHBTRD ZHECON ZHEEV ZHEEVD ZHEEVR ZHEEVX ZHEGST ZHEGV ZHEGVD ZHEGVX ZHERFS ZHESV ZHESVX ZHETRD ZHETRF ZHETRI ZHETRS ZHGEQZ ZHPCON ZHPEV ZHPEVD ZHPEVX ZHPGST ZHPGV ZHPGVD ZHPGVX ZHPRFS ZHPSV ZHPSVX ZHPTRD ZHPTRF ZHPTRI ZHPTRS ZHSEIN ZHSEQR ZLAGTM ZLALS0 ZLALSD ZLANGT ZLANHT ZPBCON ZPBEQU ZPBRFS ZPBSTF ZPBSV ZPBSVX ZPBTRF ZPBTRS ZPOEQU ZPORFS ZPOSV ZPOSVX ZPOTRF ZPOTRS ZPPEQU ZPPRFS ZPPSV ZPPSVX ZPTCON ZPTEQR ZPTRFS ZPTSV ZPTSVX ZPTTRF ZPTTRS ZSPCON ZSPMV ZSPRFS ZSPSV ZSPSVX ZSPTRF ZSPTRI ZSPTRS ZSTEDC ZSTEGR ZSTEIN ZSTEQR ZSYCON ZSYMV ZSYRFS ZSYSV ZSYSVX ZSYTRF ZSYTRI ZSYTRS ZTBCON ZTBRFS ZTBTRS ZTGEVC ZTGEXC ZTGSEN ZTGSJA ZTGSNA ZTGSYL ZTPCON ZTPRFS ZTPTRS ZTRCON ZTREVC ZTREXC ZTRRFS ZTRSEN ZTRSNA ZTRSYL ZTRTRS ZTZRZF ZUNGBR ZUNGHR ZUNGLQ ZUNGQL ZUNGQR ZUNGRQ ZUNGTR ZUNMBR ZUNMHR ZUNMLQ ZUNMQL ZUNMQR ZUNMRQ ZUNMRZ ZUNMTR ZUPGTR ZUPMTR
F07GDF/DPPTRF F07GEF/DPPTRS F07GRF/ZPPTRF F07GSF/ZPPTRS
S07AAF F_1 = 1.0E+13
F_2 = 1.0E-14
S10AAF E_1 = 1.8715E+1
S10ABF E_1 = 7.080E+2
S10ACF E_1 = 7.080E+2
S13AAF X_hi = 7.083E+2
S13ACF X_hi = 1.0E+16
S13ADF X_hi = 1.0E+17
S14AAF IFAIL = 1 if X > 1.70E+2
IFAIL = 2 if X < -1.70E+2
IFAIL = 3 if abs(X) < 2.23E-308
S14ABF IFAIL = 2 if X > X_big = 2.55E+305
S15ADF X_hi = 2.65E+1
S15AEF X_hi = 2.65E+1
S15AFF underflow trap was necessary
S15AGF IFAIL = 1 if X >= 2.53E+307
IFAIL = 2 if 4.74E+7 <= X < 2.53E+307
IFAIL = 3 if X < -2.66E+1
S17ACF IFAIL = 1 if X > 1.0E+16
S17ADF IFAIL = 1 if X > 1.0E+16
IFAIL = 3 if 0.0E0 < X <= 2.23E-308
S17AEF IFAIL = 1 if abs(X) > 1.0E+16
S17AFF IFAIL = 1 if abs(X) > 1.0E+16
S17AGF IFAIL = 1 if X > 1.038E+2
IFAIL = 2 if X < -5.7E+10
S17AHF IFAIL = 1 if X > 1.041E+2
IFAIL = 2 if X < -5.7E+10
S17AJF IFAIL = 1 if X > 1.041E+2
IFAIL = 2 if X < -1.9E+9
S17AKF IFAIL = 1 if X > 1.041E+2
IFAIL = 2 if X < -1.9E+9
S17DCF IFAIL = 2 if abs(Z) < 3.92223E-305
IFAIL = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
IFAIL = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
S17DEF IFAIL = 2 if imag(Z) > 7.00921E+2
IFAIL = 3 if abs(Z) or FNU+N-1 > 3.27679E+4
IFAIL = 4 if abs(Z) or FNU+N-1 > 1.07374E+9
S17DGF IFAIL = 3 if abs(Z) > 1.02399E+3
IFAIL = 4 if abs(Z) > 1.04857E+6
S17DHF IFAIL = 3 if abs(Z) > 1.02399E+3
IFAIL = 4 if abs(Z) > 1.04857E+6
S17DLF IFAIL = 2 if abs(Z) < 3.92223E-305
IFAIL = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
IFAIL = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
S18ADF IFAIL = 2 if 0.0E0 < X <= 2.23E-308
S18AEF IFAIL = 1 if abs(X) > 7.116E+2
S18AFF IFAIL = 1 if abs(X) > 7.116E+2
S18DCF IFAIL = 2 if abs(Z) < 3.92223E-305
IFAIL = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
IFAIL = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
S18DEF IFAIL = 2 if real(Z) > 7.00921E+2
IFAIL = 3 if abs(Z) or FNU+N-1 > 3.27679E+4
IFAIL = 4 if abs(Z) or FNU+N-1 > 1.07374E+9
S19AAF IFAIL = 1 if abs(X) >= 5.04818E+1
S19ABF IFAIL = 1 if abs(X) >= 5.04818E+1
S19ACF IFAIL = 1 if X > 9.9726E+2
S19ADF IFAIL = 1 if X > 9.9726E+2
S21BCF IFAIL = 3 if an argument < 1.583E-205
IFAIL = 4 if an argument >= 3.765E+202
S21BDF IFAIL = 3 if an argument < 2.813E-103
IFAIL = 4 if an argument >= 1.407E+102
X01AAF (pi) = 3.1415926535897932 X01ABF (gamma) = 0.5772156649015328
X02BHF = 2 X02BJF = 53 X02BKF = -1021 X02BLF = 1024 X02DJF = .TRUE.Derived parameters of the floating-point arithmetic
X02AJF = 1.11022302462516E-16 X02AKF = 2.22507385850721E-308 X02ALF = 1.79769313486231E+308 X02AMF = 2.22507385850721E-308 X02ANF = 2.22507385850721E-308Parameters of other aspects of the computing environment
X02AHF = 8.11296384146067E+31 X02BBF = 2147483647 X02BEF = 15 X02DAF = .TRUE.
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/FL/FSdocumentation.asp.
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