lawn81.tex

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 Tests completed
\end{verbatim}
The file \texttt{lsame.f} is automatically copied to
\texttt{LAPACK/BLAS/SRC/} and \texttt{LAPACK/SRC/}. 
The function LSAME is needed by both the BLAS and LAPACK, so it is safer
to have it in both libraries as long as this does not cause trouble
in the link phase when both libraries are used.

\subsubsection{Installing SLAMCH and DLAMCH}

SLAMCH and DLAMCH are real functions with a single character parameter
that indicates the machine parameter to be returned.  The test 
program in \texttt{slamchtst.f}
simply prints out the different values computed by SLAMCH,
so you need to know something about what the values should be. 
For example, the output of the test program executable \texttt{testslamch}
for SLAMCH on a Sun SPARCstation is
\begin{verbatim}
 Epsilon                      =     5.96046E-08
 Safe minimum                 =     1.17549E-38
 Base                         =     2.00000
 Precision                    =     1.19209E-07
 Number of digits in mantissa =     24.0000
 Rounding mode                =     1.00000
 Minimum exponent             =    -125.000
 Underflow threshold          =     1.17549E-38
 Largest exponent             =     128.000
 Overflow threshold           =     3.40282E+38
 Reciprocal of safe minimum   =     8.50706E+37
\end{verbatim}
On a Cray machine, the safe minimum underflows its output
representation and the overflow threshold overflows its output
representation, so the safe minimum is printed as 0.00000 and overflow
is printed as R.  This is normal.
If you would prefer to print a representable number, you can modify
the test program to print SFMIN*100. and RMAX/100. for the safe
minimum and overflow thresholds.

Likewise, the test executable \texttt{testdlamch} is run for DLAMCH.

If both tests were successful, go to Section~\ref{second}.

If SLAMCH (or DLAMCH) returns an invalid value, you will have to create
your own version of this function.  The following options are used in
LAPACK and must be set:

\begin{list}{}{}
\item {`B': }  Base of the machine
\item {`E': }  Epsilon (relative machine precision)
\item {`O': }  Overflow threshold
\item {`P': }  Precision = Epsilon*Base
\item {`S': }  Safe minimum (often same as underflow threshold)
\item {`U': }  Underflow threshold
\end{list}

Some people may be familiar with R1MACH (D1MACH), a primitive
routine for setting machine parameters in which the user must
comment out the appropriate assignment statements for the target
machine.  If a version of R1MACH is on hand, the assignments in
SLAMCH can be made to refer to R1MACH using the correspondence

\begin{list}{}{}
\item {SLAMCH( `U' )}  $=$ R1MACH( 1 )
\item {SLAMCH( `O' )}  $=$ R1MACH( 2 )
\item {SLAMCH( `E' )}  $=$ R1MACH( 3 )
\item {SLAMCH( `B' )}  $=$ R1MACH( 5 )
\end{list}

\noindent
The safe minimum returned by SLAMCH( 'S' ) is initially set to the
underflow value, but if $1/(\mathrm{overflow}) \geq (\mathrm{underflow})$
it is recomputed as $(1/(\mathrm{overflow})) * ( 1 + \varepsilon )$,
where $\varepsilon$ is the machine precision.

BE AWARE that the initial call to SLAMCH or DLAMCH is expensive.  
We suggest that installers run it once, save the results, and hard-code
the constants in the version they put in their library.

\subsubsection{Installing SECOND and DSECND}\label{second}

Both the timing routines\footnotemark[\value{footnote}]  and the test routines call SECOND
(DSECND), a real function with no arguments that returns the time
in seconds from some fixed starting time.
Our version of this routine 
returns only ``user time'', and not ``user time $+$ system time''. 
The following version of SECOND in \texttt{second\_EXT\_ETIME.f, second\_INT\_ETIME.f} calls 
ETIME, a Fortran library routine available on some computer systems.
If ETIME is not available or a better local timing function exists,
you will have to provide the correct interface to SECOND and DSECND
on your machine.

Since LAPACK 3.1.1 we provide 5 different flavours of the SECOND and DSECND routines.
The version that will be used depends on the value of the TIMER variable in the make.inc

\begin{itemize}
\item If ETIME is available as an external function, set the value of the TIMER variable in your 
make.inc to \texttt{EXT\_ETIME}:\texttt{second\_EXT\_ETIME.f} and \texttt{dsecnd\_EXT\_ETIME.f} will be used.
Usually on HPPA architectures,
the compiler and loader flag \texttt{+U77} should be included to access
the function \texttt{ETIME}.

\item If ETIME\_ is available as an external function, set the value of the TIMER variable in your make.inc 
to \texttt{EXT\_ETIME\_}:\texttt{second\_EXT\_ETIME\_.f} and \texttt{dsecnd\_EXT\_ETIME\_.f} will be used.
It is the case on some IBM architectures such as IBM RS/6000s.

\item If ETIME is available as an internal function, set the value of the TIMER variable in your make.inc
to \texttt{INT\_ETIME}:\texttt{second\_INT\_ETIME.f}  and \texttt{dsecnd\_INT\_ETIME.f} will be used. 
This is the case with gfortan.

\item If CPU\_TIME is available as an internal function, set the value of the TIMER variable in your make.inc
to \texttt{INT\_CPU\_TIME}:\texttt{second\_INT\_CPU\_TIME.f} and \texttt{dsecnd\_INT\_CPU\_TIME.f} will be used.

\item If none of these function is available, set the value of the TIMER variable in your make.inc
to \texttt{NONE:}\texttt{second\_NONE.f} and \texttt{dsecnd\_NONE.f} will be used.
These routines will always return zero.
\end{itemize}

The test program in \texttt{secondtst.f}
performs a million operations using 5000 iterations of 
the SAXPY operation $y := y + \alpha x$ on a vector of length 100.
The total time and megaflops for this test is reported, then
the operation is repeated including a call to SECOND on each of
the 5000 iterations to determine the overhead due to calling SECOND.
The test program executable is called \texttt{testsecond} (or \texttt{testdsecnd}).
There is no single right answer, but the times
in seconds should be positive and the megaflop ratios should be 
appropriate for your machine.

\subsubsection{Testing IEEE arithmetic and ILAENV}\label{testieee}

%\textbf{If you are installing LAPACK on a non-IEEE machine, you MUST 
%modify ILAENV!  Otherwise, ILAENV will crash .  By default, ILAENV
%assumes an IEEE machine, and does a test for IEEE-754 compliance.}

As some new routines in LAPACK rely on IEEE-754 compliance,
two settings (\texttt{ISPEC=10} and \texttt{ISPEC=11}) have been added to ILAENV
(\texttt{LAPACK/SRC/ilaenv.f}) to denote IEEE-754 compliance for NaN and
infinity arithmetic, respectively.  By default, ILAENV assumes an IEEE
machine, and does a test for IEEE-754 compliance.  \textbf{NOTE:  If you
are installing LAPACK on a non-IEEE machine, you MUST modify ILAENV,
as this test inside ILAENV will crash!}

If \texttt{ILAENV( 10, $\ldots$ )} or \texttt{ILAENV( 11, $\ldots$ )} is 
issued, then \texttt{ILAENV=1} is returned to signal IEEE-754 compliance,
and \texttt{ILAENV=0} if the architecture is non-IEEE-754 compliant.

Thus, for non-IEEE machines, the user must hard-code the setting of
(\texttt{ILAENV=0}) for (\texttt{ISPEC=10} and \texttt{ISPEC=11}) in the version
of \texttt{LAPACK/SRC/ilaenv.f} to be put in
his library.  There are also specialized testing and timing\footnotemark[\value{footnote}] versions of
ILAENV that will also need to be modified.
\begin{itemize}
\item Testing/timing version of \texttt{LAPACK/TESTING/LIN/ilaenv.f}
\item Testing/timing version of \texttt{LAPACK/TESTING/EIG/ilaenv.f}
\item Testing/timing version of \texttt{LAPACK/TIMING/LIN/ilaenv.f}
\item Testing/timing version of \texttt{LAPACK/TIMING/EIG/ilaenv.f}
\end{itemize}

%Some new routines in LAPACK rely on IEEE-754 compliance, and if non-compliance
%is detected (via a call to the function ILAENV), alternative (slower)
%algorithms will be chosen.
%For further details, refer to the leading comments of routines such
%as \texttt{LAPACK/SRC/sstevr.f}.

The test program in \texttt{LAPACK/INSTALL/tstiee.f} checks an installation
architecture
to see if infinity arithmetic and NaN arithmetic are IEEE-754 compliant.  
A warning message to the user is printed if non-compliance is detected.
This same test is performed inside the function ILAENV.  If
\texttt{ILAENV( 10, $\ldots$ )} or \texttt{ILAENV( 11, $\ldots$ )} is 
issued, then \texttt{ILAENV=1} is returned to signal IEEE-754 compliance,
and \texttt{ILAENV=0} if the architecture is non-IEEE-754 compliant.

To avoid this IEEE test being run every time you call
\texttt{ILAENV( 10, $\ldots$)} or \texttt{ILAENV( 11, $\ldots$ )}, we suggest
that the user hard-code the setting of
\texttt{ILAENV=1} or \texttt{ILAENV=0} in the version of \texttt{LAPACK/SRC/ilaenv.f} to be put in
his library.  As aforementioned, there are also specialized testing and
timing\footnotemark[\value{footnote}] versions of ILAENV that will also need to be modified.

\subsection{Create the BLAS Library} 

Ideally, a highly optimized version of the BLAS library already
exists on your machine. 
In this case you can go directly to Section~\ref{testblas} to
make the BLAS test programs.  

\begin{itemize}
\item[a)]
Go to \texttt{LAPACK} and edit the definition of \texttt{blaslib} in the
file \texttt{Makefile} to specify the data types desired, as in the example
in Section~\ref{toplevelmakefile}.

If you already have some of the BLAS, you will need to edit the file
\texttt{LAPACK/BLAS/SRC/Makefile} to comment out the lines 
defining the BLAS you have.  

\item[b)]
Type \texttt{make blaslib}.
The make command can be run more than once to add another
data type to the library if necessary.  
\end{itemize}

\noindent
The BLAS library is created in \texttt{LAPACK/blas\_PLAT.a}, where
\texttt{PLAT} is the user-defined architecture suffix specified in the file
\texttt{LAPACK/make.inc}.

\subsection{Run the BLAS Test Programs}\label{testblas}

Test programs for the Level 1, 2, and 3 BLAS are in the directory 
\texttt{LAPACK/BLAS/TESTING}.

To compile and run the Level 1, 2, and 3 BLAS test programs,
go to \texttt{LAPACK} and type \texttt{make blas\_testing}.  The executable
files are called \texttt{xblat\_s}, \texttt{xblat\_d}, \texttt{xblat\_c}, and
\texttt{xblat\_z}, where the \_ (underscore) is replaced by 1, 2, or 3,
depending upon the level of BLAS that it is testing.  All executable and
output files are created in \texttt{LAPACK/BLAS/}.
For the Level 1 BLAS tests, the output file names are \texttt{sblat1.out},
\texttt{dblat1.out}, \texttt{cblat1.out}, and \texttt{zblat1.out}.  For the Level
2 and 3 BLAS, the name of the output file is indicated on the first line of the
input file and is currently defined to be \texttt{sblat2.out} for
the Level 2 REAL version, and \texttt{sblat3.out} for the Level 3 REAL
version, with similar names for the other data types.

If the tests using the supplied data files were completed successfully,
consider whether the tests were sufficiently thorough.
For example, on a machine with vector registers, at least one value
of $N$ greater than the length of the vector registers should be used;
otherwise, important parts of the compiled code may not be
exercised by the tests. 
If the tests were not successful, either because the program did not
finish or the test ratios did not pass the threshold, you will
probably have to find and correct the problem before continuing. 
If you have been testing a system-specific
BLAS library, try using the Fortran BLAS for the routines that
did not pass the tests.
For more details on the BLAS test programs, 
see \cite{BLAS2-test} and \cite{BLAS3-test}.

\subsection{Create the LAPACK Library}

\begin{itemize}
\item[a)]
Go to the directory \texttt{LAPACK} and edit the definition of
\texttt{lapacklib} in the file \texttt{Makefile} to specify the data types desired,
as in the example in Section~\ref{toplevelmakefile}.

\item[b)]
Type \texttt{make lapacklib}.
The make command can be run more than once to add another
data type to the library if necessary.  

\end{itemize}

\noindent
The LAPACK library is created in \texttt{LAPACK/lapack\_PLAT.a}, where
\texttt{PLAT} is the user-defined architecture suffix specified in the file
\texttt{LAPACK/make.inc}.

\subsection{Create the Test Matrix Generator Library}

\begin{itemize}
\item[a)]
Go to the directory \texttt{LAPACK} and edit the definition of \texttt{tmglib}
in the file \texttt{Makefile} to specify the data types desired, as in the
example in Section~\ref{toplevelmakefile}.

\item[b)]
Type \texttt{make tmglib}.
The make command can be run more than once to add another
data type to the library if necessary.  

\end{itemize}

\noindent
The test matrix generator library is created in \texttt{LAPACK/tmglib\_PLAT.a},
where \texttt{PLAT} is the user-defined architecture suffix specified in the 
file \texttt{LAPACK/make.inc}.

\subsection{Run the LAPACK Test Programs}

There are two distinct test programs for LAPACK routines
in each data type, one for the linear equation routines and
one for the eigensystem routines.
In each data type, there is one input file for testing the linear
equation routines and eighteen input files for testing the eigenvalue
routines.
The input files reside in \texttt{LAPACK/TESTING}.
For more information on the test programs and how to modify the
input files, please refer to LAPACK Working Note 41~\cite{WN41}.
% see Section~\ref{moretesting}. 

If you do not wish to run each of the tests individually, you can
go to \texttt{LAPACK}, edit the definition \texttt{lapack\_testing} in the file
\texttt{Makefile} to specify the data types desired, and type \texttt{make
lapack\_testing}.  This will
compile and run the tests as described in sections~\ref{testlin} 
and ~\ref{testeig}.