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.
By default [INSTALL_DIR] (see Installer's Note (in.html)) is /opt/NAG/flmin21d9l; however it could have been changed by the installer. To identify [INSTALL_DIR] for this installation:
f95 driver.f [INSTALL_DIR]/lib/libnag_vl.dylib -framework vecLibwhere driver.f is your application program;
or
f95 driver.f [INSTALL_DIR]/lib/libnag_vl.a -framework vecLibif 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.dylibor
f95 driver.f [INSTALL_DIR]/lib/libnag_nag.aif 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]/libto set DYLD_LIBRARY_PATH, or
setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH}to extend DYLD_LIBRARY_PATH if you already have it set.
In the Bourne shell, type:
DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib export DYLD_LIBRARY_PATHto set DYLD_LIBRARY_PATH, or
DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH} export DYLD_LIBRARY_PATHto extend DYLD_LIBRARY_PATH if you already have it set.
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 and the vecLib library, you may link in the following manner:
f95 driver.f -lnag_vl -framework vecLibThe 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 vecLibPlease 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_nagThe 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.aPlease 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]/libto set DYLD_LIBRARY_PATH, or
setenv DYLD_LIBRARY_PATH [INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH}to extend DYLD_LIBRARY_PATH if you already have it set.
In the Bourne shell, type:
DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib export DYLD_LIBRARY_PATHto set DYLD_LIBRARY_PATH, or
DYLD_LIBRARY_PATH=[INSTALL_DIR]/lib:${DYLD_LIBRARY_PATH} export DYLD_LIBRARY_PATHto extend DYLD_LIBRARY_PATH if you already have it set.
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.
The example program concerned is specified by the argument to the command, e.g.
nag_example e04ucfwill 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.
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 4Thus 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.
These routines are potentially not thread safe and in general output is not recommended in a multithreaded environment.
(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_chapterThese 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
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 dger dgemv zhpevd zheevr dggesx zggesx zgesdd dgels dgelsy dgeqp3 dgeqrf dgelqf
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
X01AAF (PI) = 3.1415926535897932D+00 X01ABF (GAMMA) = 0.5772156649015329D+00
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-308Parameters of other aspects of the computing environment
X02AHF = 1.84467440737095D+19 X02BBF = 2147483647 X02BEF = 15 X02DAF = .FALSE.
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:
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 and NAG product code (in this case FLMIN21D9L).
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http://www.nag.co.uk/, http://www.nag.com/ or http://www.nag-j.co.jp/
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