Document DESC%CNV method and MOLD arguments to CDASB and PREC%BUILD
Salvatore Filippone
7 years ago
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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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HREF="node117.html">hb_read Read</A>
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<B> Previous:</B> <A NAME="tex2html1696"
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HREF="node115.html">psb_rcv Receive</A>
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HREF="node1.html">Contents</A></B>
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<BR></DIV>
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<H1><A NAME="SECTION000100000000000000000"></A>
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<A NAME="sec:util"></A>
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<BR>
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Utilities
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<H1><A NAME="SECTION00090000000000000000">
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Error handling</A>
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</H1>
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<P>
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We have some utitlities available for input and output of
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sparse matrices; the interfaces to these routines are available in the
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module <code>psb_util_mod</code>.
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<P>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html1704"
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HREF="node117.html">hb_read -- Read a sparse matrix from a file in the
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Harwell-Boeing format</A>
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<LI><A NAME="tex2html1705"
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HREF="node118.html">hb_write -- Write a sparse matrix to a file
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in the Harwell-Boeing format</A>
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<LI><A NAME="tex2html1706"
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HREF="node119.html">mm_mat_read -- Read a sparse matrix from a
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file in the MatrixMarket format</A>
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<LI><A NAME="tex2html1707"
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HREF="node120.html">mm_array_read -- Read a dense array from a
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file in the MatrixMarket format</A>
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<LI><A NAME="tex2html1708"
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HREF="node121.html">mm_mat_write -- Write a sparse matrix to a
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file in the MatrixMarket format</A>
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<LI><A NAME="tex2html1709"
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HREF="node122.html">mm_array_write -- Write a dense array from a
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file in the MatrixMarket format</A>
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</UL>
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<!--End of Table of Child-Links-->
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<BR><HR>
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The PSBLAS library error handling policy has been completely rewritten
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in version 2.0. The idea behind the design of this new error handling
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strategy is to keep error messages on a stack allowing the user to
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trace back up to the point where the first error message has been
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generated. Every routine in the PSBLAS-2.0 library has, as last
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non-optional argument, an integer <code>info</code> variable; whenever,
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inside the routine, an error is detected, this variable is set to a
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value corresponding to a specific error code. Then this error code is
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also pushed on the error stack and then either control is returned to
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the caller routine or the execution is aborted, depending on the users
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choice. At the time when the execution is aborted, an error message is
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printed on standard output with a level of verbosity than can be
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chosen by the user. If the execution is not aborted, then, the caller
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routine checks the value returned in the <code>info</code> variable and, if
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not zero, an error condition is raised. This process continues on all the
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levels of nested calls until the level where the user decides to abort
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the program execution.
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<P>
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Figure <A HREF="#fig:routerr">9</A> shows the layout of a generic <code>psb_foo</code>
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routine with respect to the PSBLAS-2.0 error handling policy. It is
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possible to see how, whenever an error condition is detected, the
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<code>info</code> variable is set to the corresponding error code which is,
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then, pushed on top of the stack by means of the
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<code>psb_errpush</code>. An error condition may be directly detected inside
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a routine or indirectly checking the error code returned returned by a
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called routine. Whenever an error is encountered, after it has been
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pushed on stack, the program execution skips to a point where the
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error condition is handled; the error condition is handled either by
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returning control to the caller routine or by calling the
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<code>psb\_error</code> routine which prints the content of the error stack
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and aborts the program execution, according to the choice made by the
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user with <code>psb_set_erraction</code>. The default is to print the error
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and terminate the program, but the user may choose to handle the error
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explicitly.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:routerr"></A><A NAME="7265"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 9:</STRONG>
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The layout of a generic <TT>psb_foo</TT>
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routine with respect to PSBLAS-2.0 error handling policy.</CAPTION>
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<TR><TD>
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<BR>
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<DIV ALIGN="CENTER">
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<!-- MATH
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$\fbox{\TheSbox}$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="562" HEIGHT="482" ALIGN="MIDDLE" BORDER="0"
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SRC="img142.png"
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ALT="\fbox{\TheSbox}"></SPAN>
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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Figure <A HREF="#fig:errormsg">10</A> reports a sample error message generated by
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the PSBLAS-2.0 library. This error has been generated by the fact that
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the user has chosen the invalid “FOO” storage format to represent
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the sparse matrix. From this error message it is possible to see that
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the error has been detected inside the <code>psb_cest</code> subroutine
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called by <code>psb_spasb</code> ... by process 0 (i.e. the root process).
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:errormsg"></A><A NAME="7266"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 10:</STRONG>
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A sample PSBLAS-2.0 error
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message. Process 0 detected an error condition inside the psb_cest subroutine</CAPTION>
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<TR><TD>
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<BR>
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<DIV ALIGN="CENTER">
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<!-- MATH
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$\fbox{\TheSbox}$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="562" HEIGHT="482" ALIGN="MIDDLE" BORDER="0"
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SRC="img142.png"
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ALT="\fbox{\TheSbox}"></SPAN>
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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ifstarsubroutinesubroutinepsb_errpushPushes an error code onto the error
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stack
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<P>
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<BR>
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<IMG
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WIDTH="423" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img144.png"
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ALT="\begin{lstlisting}
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call psb_errpush(err_c, r_name, i_err, a_err)
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\end{lstlisting}">
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<BR>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Asynchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>err_c</STRONG></DT>
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<DD>the error code
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: an integer.
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</DD>
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<DT><STRONG>r_name</STRONG></DT>
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<DD>the soutine where the error has been caught.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a string.
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<BR></DD>
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<DT><STRONG>i_err</STRONG></DT>
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<DD>addional info for error code
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Specified as: an integer array
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<BR></DD>
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<DT><STRONG>a_err</STRONG></DT>
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<DD>addional info for error code
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Specified as: a string.
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<BR></DD>
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</DL>
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<P>
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ifstarsubroutinesubroutinepsb_errorPrints the error stack content and aborts
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execution
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<P>
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<BR>
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<IMG
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WIDTH="214" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img145.png"
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ALT="\begin{lstlisting}
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call psb_error(icontxt)
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\end{lstlisting}">
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<BR>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Asynchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>icontxt</STRONG></DT>
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<DD>the communication context.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: an integer.
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</DD>
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</DL>
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<P>
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ifstarsubroutinesubroutinepsb_set_errverbositySets the verbosity of error
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messages.
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<P>
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<BR>
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<IMG
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WIDTH="261" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img146.png"
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ALT="\begin{lstlisting}
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call psb_set_errverbosity(v)
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\end{lstlisting}">
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<BR>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Asynchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>v</STRONG></DT>
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<DD>the verbosity level
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: an integer.
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</DD>
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</DL>
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<P>
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ifstarsubroutinesubroutinepsb_set_erractionSet the type of action to be
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taken upon error condition.
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<P>
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<BR>
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<IMG
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WIDTH="291" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
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SRC="img147.png"
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ALT="\begin{lstlisting}
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call psb_set_erraction(err_act)
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\end{lstlisting}">
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<BR>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Asynchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>err_act</STRONG></DT>
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<DD>the type of action.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: an integer. Possible values: <code>psb_act_ret</code>,
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<code>psb_act_abort</code>.
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</DD>
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</DL>
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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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||||
* with significant contributions from:
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||||
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<!--Converted with LaTeX2HTML 2017.2 (Released Jan 23, 2017) -->
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<TITLE>hb_read -- Read a sparse matrix from a file in the Harwell-Boeing format</TITLE>
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<BR></DIV>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION000101000000000000000">
|
||||
hb_read -- Read a sparse matrix from a file in the
|
||||
Harwell-Boeing format</A>
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
<BR>
|
||||
<IMG
|
||||
WIDTH="462" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img148.png"
|
||||
ALT="\begin{lstlisting}
|
||||
call hb_read(a, iret, iunit, filename, b, mtitle)
|
||||
\end{lstlisting}">
|
||||
<H1><A NAME="SECTION000100000000000000000"></A>
|
||||
<A NAME="sec:util"></A>
|
||||
<BR>
|
||||
Utilities
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Asynchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry </B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>filename</STRONG></DT>
|
||||
<DD>The name of the file to be read.
|
||||
<BR>
|
||||
Type:<B>optional</B>.
|
||||
<BR>
|
||||
Specified as: a character variable containing a valid file name, or
|
||||
<code>-</code>, in which case the default input unit 5 (i.e. standard input
|
||||
in Unix jargon) is used. Default: <code>-</code>.
|
||||
</DD>
|
||||
<DT><STRONG>iunit</STRONG></DT>
|
||||
<DD>The Fortran file unit number.
|
||||
<BR>
|
||||
Type:<B>optional</B>.
|
||||
<BR>
|
||||
Specified as: an integer value. Only meaningful if filename is not <code>-</code>.
|
||||
</DD>
|
||||
</DL>
|
||||
We have some utitlities available for input and output of
|
||||
sparse matrices; the interfaces to these routines are available in the
|
||||
module <code>psb_util_mod</code>.
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>a</STRONG></DT>
|
||||
<DD>the sparse matrix read from file.
|
||||
<BR>
|
||||
Type:<B>required</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>b</STRONG></DT>
|
||||
<DD>Rigth hand side(s).
|
||||
<BR>
|
||||
Type: <B>Optional</B>
|
||||
<BR>
|
||||
An array of type real or complex, rank 2 and having the ALLOCATABLE
|
||||
attribute; will be allocated and filled in if the input file contains
|
||||
a right hand side, otherwise will be left in the UNALLOCATED state.
|
||||
</DD>
|
||||
<DT><STRONG>mtitle</STRONG></DT>
|
||||
<DD>Matrix title.
|
||||
<BR>
|
||||
Type: <B>Optional</B>
|
||||
<BR>
|
||||
A charachter variable of length 72 holding a copy of the
|
||||
matrix title as specified by the Harwell-Boeing format and contained
|
||||
in the input file.
|
||||
</DD>
|
||||
<DT><STRONG>iret</STRONG></DT>
|
||||
<DD>Error code.
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
</DD>
|
||||
</DL>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
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<P>
|
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<HR>
|
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<!--End of Navigation Panel-->
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|
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<LI><A NAME="tex2html1719"
|
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HREF="node118.html">hb_read -- Read a sparse matrix from a file in the
|
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Harwell-Boeing format</A>
|
||||
<LI><A NAME="tex2html1720"
|
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HREF="node119.html">hb_write -- Write a sparse matrix to a file
|
||||
in the Harwell-Boeing format</A>
|
||||
<LI><A NAME="tex2html1721"
|
||||
HREF="node120.html">mm_mat_read -- Read a sparse matrix from a
|
||||
file in the MatrixMarket format</A>
|
||||
<LI><A NAME="tex2html1722"
|
||||
HREF="node121.html">mm_array_read -- Read a dense array from a
|
||||
file in the MatrixMarket format</A>
|
||||
<LI><A NAME="tex2html1723"
|
||||
HREF="node122.html">mm_mat_write -- Write a sparse matrix to a
|
||||
file in the MatrixMarket format</A>
|
||||
<LI><A NAME="tex2html1724"
|
||||
HREF="node123.html">mm_array_write -- Write a dense array from a
|
||||
file in the MatrixMarket format</A>
|
||||
</UL>
|
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<!--End of Table of Child-Links-->
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<BR><HR>
|
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|
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</BODY>
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</HTML>
|
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|
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@ -1,141 +1,98 @@
|
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
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|
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original version by: Nikos Drakos, CBLU, University of Leeds
|
||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
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* with significant contributions from:
|
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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|
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|
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HREF="node123.html">Preconditioner routines</A>
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HREF="node123.html">mm_array_write Write</A>
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HREF="node1.html">Contents</A></B>
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<!--End of Navigation Panel-->
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|
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<H2><A NAME="SECTION000111000000000000000">
|
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init -- Initialize a preconditioner</A>
|
||||
</H2>
|
||||
<H1><A NAME="SECTION000110000000000000000"></A>
|
||||
<A NAME="sec:precs"></A>
|
||||
<BR>
|
||||
Preconditioner routines
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
call prec%init(ptype, info)
|
||||
</PRE>
|
||||
<A NAME="sec:psprecs"></A>The base PSBLAS library contains the implementation of two simple
|
||||
preconditioning techniques:
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Asynchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>ptype</STRONG></DT>
|
||||
<DD>the type of preconditioner.
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a character string, see usage notes.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Exit</B></STRONG></DT>
|
||||
<DD><P>
|
||||
</DD>
|
||||
<DT><STRONG>prec</STRONG></DT>
|
||||
<DD>Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a preconditioner data structure precdata<TT>psb_prec_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Error code: if no error, 0 is returned.
|
||||
</DD>
|
||||
</DL>
|
||||
<FONT SIZE="+1"><B>Notes</B></FONT>Legal inputs to this subroutine are interpreted depending on the
|
||||
<IMG
|
||||
WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img154.png"
|
||||
ALT="$ptype$"> string as follows<A NAME="tex2html31"
|
||||
HREF="footnode.html#foot7601"><SUP>4</SUP></A>:
|
||||
<DL>
|
||||
<DT><STRONG>NONE</STRONG></DT>
|
||||
<DD>No preconditioning, i.e. the preconditioner is just a copy
|
||||
operator.
|
||||
</DD>
|
||||
<DT><STRONG>DIAG</STRONG></DT>
|
||||
<DD>Diagonal scaling; each entry of the input vector is
|
||||
multiplied by the reciprocal of the sum of the absolute values of
|
||||
the coefficients in the corresponding row of matrix <IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">;
|
||||
</DD>
|
||||
<DT><STRONG>BJAC</STRONG></DT>
|
||||
<DD>Precondition by a factorization of the
|
||||
block-diagonal of matrix <IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">, where block boundaries are determined
|
||||
by the data allocation boundaries for each process; requires no
|
||||
communication. Only the incomplete factorization <IMG
|
||||
WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img155.png"
|
||||
ALT="$ILU(0)$"> is
|
||||
currently implemented.
|
||||
</DD>
|
||||
</DL>
|
||||
<UL>
|
||||
<LI>Diagonal Scaling
|
||||
</LI>
|
||||
<LI>Block Jacobi with ILU(0) factorization
|
||||
</LI>
|
||||
</UL>
|
||||
The supporting data type and subroutine interfaces are defined in the
|
||||
module <code>psb_prec_mod</code>.
|
||||
The old interfaces <code>psb_precinit</code> and <code>psb_precbld</code> are still supported for
|
||||
backward compatibility
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL CLASS="ChildLinks">
|
||||
<LI><A NAME="tex2html1807"
|
||||
HREF="node125.html">init -- Initialize a preconditioner</A>
|
||||
<LI><A NAME="tex2html1808"
|
||||
HREF="node126.html">build -- Builds a preconditioner</A>
|
||||
<LI><A NAME="tex2html1809"
|
||||
HREF="node127.html">apply -- Preconditioner application
|
||||
routine</A>
|
||||
<LI><A NAME="tex2html1810"
|
||||
HREF="node128.html">descr -- Prints a description of current
|
||||
preconditioner</A>
|
||||
<LI><A NAME="tex2html1811"
|
||||
HREF="node129.html">clone -- clone current
|
||||
preconditioner</A>
|
||||
<LI><A NAME="tex2html1812"
|
||||
HREF="node130.html">free -- Free a preconditioner</A>
|
||||
</UL>
|
||||
<!--End of Table of Child-Links-->
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
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</HTML>
|
||||
|
||||
@ -1,433 +1,76 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
||||
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
|
||||
|
||||
<!--Converted with LaTeX2HTML 2012 (1.2)
|
||||
original version by: Nikos Drakos, CBLU, University of Leeds
|
||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||||
* with significant contributions from:
|
||||
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
||||
<!--Converted with LaTeX2HTML 2017.2 (Released Jan 23, 2017) -->
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<HTML>
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<HEAD>
|
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<TITLE>psb_krylov -- Krylov Methods Driver Routine</TITLE>
|
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|
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<TITLE>Iterative Methods</TITLE>
|
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HREF="node130.html">Iterative Methods</A>
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HREF="node130.html">Iterative Methods</A>
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<B> <A NAME="tex2html1888"
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<B> Next:</B> <A NAME="tex2html1894"
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HREF="node132.html">psb_krylov Krylov</A>
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HREF="node1.html">Contents</A></B>
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<BR>
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<BR>
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<BR></DIV>
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<!--End of Navigation Panel-->
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|
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<H2><A NAME="SECTION000121000000000000000"></A><A NAME="krylov"></A>
|
||||
<BR>
|
||||
psb_krylov -- Krylov Methods Driver
|
||||
Routine
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
This subroutine is a driver that provides a general interface for all
|
||||
the Krylov-Subspace family methods implemented in PSBLAS version 2.
|
||||
|
||||
<P>
|
||||
The stopping criterion can take the following values:
|
||||
<DL>
|
||||
<DT><STRONG>1</STRONG></DT>
|
||||
<DD>normwise backward error in the infinity
|
||||
norm; the iteration is stopped when
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="205" HEIGHT="44" BORDER="0"
|
||||
SRC="img157.png"
|
||||
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
</DD>
|
||||
<DT><STRONG>2</STRONG></DT>
|
||||
<DD>Relative residual in the 2-norm; the iteration is stopped
|
||||
when
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
err = \frac{\|r_i\|}{\|b\|_2} < eps
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="121" HEIGHT="44" BORDER="0"
|
||||
SRC="img158.png"
|
||||
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
</DD>
|
||||
<DT><STRONG>3</STRONG></DT>
|
||||
<DD>Relative residual reduction in the 2-norm; the iteration is stopped
|
||||
when
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
err = \frac{\|r_i\|}{\|r_0\|_2} < eps
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="129" HEIGHT="44" BORDER="0"
|
||||
SRC="img159.png"
|
||||
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert r_0\Vert _2} < eps \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
</DD>
|
||||
</DL>
|
||||
The behaviour is controlled by the istop argument (see
|
||||
later). In the above formulae, <IMG
|
||||
WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img160.png"
|
||||
ALT="$x_i$"> is the tentative solution and
|
||||
<IMG
|
||||
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img161.png"
|
||||
ALT="$r_i=b-Ax_i$"> the corresponding residual at the <IMG
|
||||
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img4.png"
|
||||
ALT="$i$">-th iteration.
|
||||
|
||||
<P>
|
||||
<BR>
|
||||
<IMG
|
||||
WIDTH="482" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img162.png"
|
||||
ALT="\begin{lstlisting}
|
||||
call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
|
||||
& itmax,iter,err,itrace,irst,istop,cond)
|
||||
\end{lstlisting}">
|
||||
<BR>
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Synchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>method</STRONG></DT>
|
||||
<DD>a string that defines the iterative method to be
|
||||
used. Supported values are:
|
||||
<DL>
|
||||
<DT><STRONG>CG:</STRONG></DT>
|
||||
<DD>the Conjugate Gradient method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>CGS:</STRONG></DT>
|
||||
<DD>the Conjugate Gradient Stabilized method;
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG>GCR:</STRONG></DT>
|
||||
<DD>the Generalized Conjugate Residual method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>FCG:</STRONG></DT>
|
||||
<DD>the Flexible Conjugate Gradient method<A NAME="tex2html32"
|
||||
HREF="footnode.html#foot8038"><SUP>5</SUP></A>;
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG>BICG:</STRONG></DT>
|
||||
<DD>the Bi-Conjugate Gradient method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>BICGSTAB:</STRONG></DT>
|
||||
<DD>the Bi-Conjugate Gradient Stabilized method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>BICGSTABL:</STRONG></DT>
|
||||
<DD>the Bi-Conjugate Gradient Stabilized method with restarting;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>RGMRES:</STRONG></DT>
|
||||
<DD>the Generalized Minimal Residual method with restarting.
|
||||
|
||||
</DD>
|
||||
</DL>
|
||||
</DD>
|
||||
<DT><STRONG>a</STRONG></DT>
|
||||
<DD>the local portion of global sparse matrix
|
||||
<IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>prec</STRONG></DT>
|
||||
<DD>The data structure containing the preconditioner.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type precdata<TT>psb_prec_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>b</STRONG></DT>
|
||||
<DD>The RHS vector.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>The initial guess.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>eps</STRONG></DT>
|
||||
<DD>The stopping tolerance.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>desc_a</STRONG></DT>
|
||||
<DD>contains data structures for communications.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>itmax</STRONG></DT>
|
||||
<DD>The maximum number of iterations to perform.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <IMG
|
||||
WIDTH="99" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img164.png"
|
||||
ALT="$itmax = 1000$">.
|
||||
<BR>
|
||||
Specified as: an integer variable <IMG
|
||||
WIDTH="76" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img165.png"
|
||||
ALT="$itmax \ge 1$">.
|
||||
</DD>
|
||||
<DT><STRONG>itrace</STRONG></DT>
|
||||
<DD>If <IMG
|
||||
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img111.png"
|
||||
ALT="$>0$"> print out an informational message about
|
||||
convergence every <IMG
|
||||
WIDTH="45" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img166.png"
|
||||
ALT="$itrace$"> iterations.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR></DD>
|
||||
<DT><STRONG>irst</STRONG></DT>
|
||||
<DD>An integer specifying the restart parameter.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>.
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Values: <IMG
|
||||
WIDTH="60" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img167.png"
|
||||
ALT="$irst>0$">. This is employed for the BiCGSTABL or RGMRES
|
||||
methods, otherwise it is ignored.
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG>istop</STRONG></DT>
|
||||
<DD>An integer specifying the stopping criterion.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>.
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Values: 1: use the normwise backward error, 2: use the scaled 2-norm
|
||||
of the residual, 3: use the residual reduction in the 2-norm. Default: 2.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>The computed solution.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>iter</STRONG></DT>
|
||||
<DD>The number of iterations performed.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: an integer variable.
|
||||
</DD>
|
||||
<DT><STRONG>err</STRONG></DT>
|
||||
<DD>The convergence estimate on exit.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<H1><A NAME="SECTION000120000000000000000"></A>
|
||||
<A NAME="sec:methods"></A>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>cond</STRONG></DT>
|
||||
<DD>An estimate of the condition number of matrix <IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">; only
|
||||
available with the <IMG
|
||||
WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img168.png"
|
||||
ALT="$CG$"> method on real data.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: a real number. A correct result will be greater than or
|
||||
equal to one; if specified for non-real data, or an error occurred,
|
||||
zero is returned.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Error code.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
Iterative Methods
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
In this chapter we provide routines for preconditioners and iterative
|
||||
methods. The interfaces for Krylov subspace methods are available in
|
||||
the module <code>psb_krylov_mod</code>.
|
||||
|
||||
<P>
|
||||
<HR>
|
||||
<!--Navigation Panel-->
|
||||
<A NAME="tex2html1889"
|
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|
||||
<B> Next:</B> <A NAME="tex2html1890"
|
||||
HREF="node132.html">Bibliography</A>
|
||||
<B> Up:</B> <A NAME="tex2html1886"
|
||||
HREF="node130.html">Iterative Methods</A>
|
||||
<B> Previous:</B> <A NAME="tex2html1882"
|
||||
HREF="node130.html">Iterative Methods</A>
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<B> <A NAME="tex2html1888"
|
||||
HREF="node1.html">Contents</A></B>
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<!--End of Navigation Panel-->
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL CLASS="ChildLinks">
|
||||
<LI><A NAME="tex2html1895"
|
||||
HREF="node132.html">psb_krylov -- Krylov Methods Driver
|
||||
Routine</A>
|
||||
</UL>
|
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<!--End of Table of Child-Links-->
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
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</HTML>
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|
||||
@ -1,173 +1,431 @@
|
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
||||
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
|
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|
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<!--Converted with LaTeX2HTML 2012 (1.2)
|
||||
original version by: Nikos Drakos, CBLU, University of Leeds
|
||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||||
* with significant contributions from:
|
||||
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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HREF="node131.html">psb_krylov Krylov</A>
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<H2><A NAME="SECTION000130000000000000000">
|
||||
Bibliography</A>
|
||||
</H2><DL COMPACT><DD><P></P><DT><A NAME="DesPat:11">1</A>
|
||||
<DD>
|
||||
D. Barbieri, V. Cardellini, S. Filippone and D. Rouson
|
||||
<EM>Design Patterns for Scientific Computations on Sparse Matrices</EM>,
|
||||
HPSS 2011, Algorithms and Programming Tools for Next-Generation High-Performance Scientific Software, Bordeaux, Sep. 2011
|
||||
<H2><A NAME="SECTION000121000000000000000"></A><A NAME="krylov"></A>
|
||||
<BR>
|
||||
psb_krylov -- Krylov Methods Driver
|
||||
Routine
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="PARA04FOREST">2</A>
|
||||
<DD>
|
||||
G. Bella, S. Filippone, A. De Maio and M. Testa,
|
||||
<EM>A Simulation Model for Forest Fires</EM>,
|
||||
in J. Dongarra, K. Madsen, J. Wasniewski, editors,
|
||||
Proceedings of PARA 04 Workshop on State of the Art
|
||||
in Scientific Computing, pp. 546-553, Lecture Notes in Computer Science,
|
||||
Springer, 2005.
|
||||
<P></P><DT><A NAME="2007d">3</A>
|
||||
<DD> A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,<BR>
|
||||
2LEV-D2P4: a package of high-performance preconditioners,<BR>
|
||||
Applicable Algebra in Engineering, Communications and Computing,
|
||||
Volume 18, Number 3, May, 2007, pp. 223-239<P></P><DT><A NAME="2007c">4</A>
|
||||
<DD> P. D'Ambra, S. Filippone, D. Di Serafino<BR>
|
||||
On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners
|
||||
<BR>
|
||||
Applied Numerical Mathematics, Elsevier Science,
|
||||
Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196.
|
||||
This subroutine is a driver that provides a general interface for all
|
||||
the Krylov-Subspace family methods implemented in PSBLAS version 2.
|
||||
|
||||
<P>
|
||||
The stopping criterion can take the following values:
|
||||
<DL>
|
||||
<DT><STRONG>1</STRONG></DT>
|
||||
<DD>normwise backward error in the infinity
|
||||
norm; the iteration is stopped when
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="205" HEIGHT="44" BORDER="0"
|
||||
SRC="img157.png"
|
||||
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
</DD>
|
||||
<DT><STRONG>2</STRONG></DT>
|
||||
<DD>Relative residual in the 2-norm; the iteration is stopped
|
||||
when
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
err = \frac{\|r_i\|}{\|b\|_2} < eps
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="121" HEIGHT="44" BORDER="0"
|
||||
SRC="img158.png"
|
||||
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
</DD>
|
||||
<DT><STRONG>3</STRONG></DT>
|
||||
<DD>Relative residual reduction in the 2-norm; the iteration is stopped
|
||||
when
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
err = \frac{\|r_i\|}{\|r_0\|_2} < eps
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="129" HEIGHT="44" BORDER="0"
|
||||
SRC="img159.png"
|
||||
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert r_0\Vert _2} < eps \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
</DD>
|
||||
</DL>
|
||||
The behaviour is controlled by the istop argument (see
|
||||
later). In the above formulae, <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img160.png"
|
||||
ALT="$x_i$"></SPAN> is the tentative solution and
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img161.png"
|
||||
ALT="$r_i=b-Ax_i$"></SPAN> the corresponding residual at the <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img4.png"
|
||||
ALT="$i$"></SPAN>-th iteration.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="BLAS2">5</A>
|
||||
<DD>
|
||||
Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R.,
|
||||
An Extended Set of Fortran Basic Linear Algebra Subprograms,
|
||||
ACM Trans. Math. Softw. vol. 14, 1-17, 1988.
|
||||
<P></P><DT><A NAME="BLAS3">6</A>
|
||||
<DD>
|
||||
Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I.,
|
||||
A Set of level 3 Basic Linear Algebra Subprograms,
|
||||
ACM Trans. Math. Softw. vol. 16, 1-17, 1990.<P></P><DT><A NAME="BLACS">7</A>
|
||||
<DD>
|
||||
J. J. Dongarra and R. C. Whaley,
|
||||
<EM>A User's Guide to the BLACS v. 1.1</EM>,
|
||||
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
|
||||
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="sblas97">8</A>
|
||||
<DD>
|
||||
I. Duff, M. Marrone, G. Radicati and C. Vittoli,
|
||||
<EM>Level 3 Basic Linear Algebra Subprograms for Sparse Matrices:
|
||||
a User Level Interface</EM>,
|
||||
ACM Transactions on Mathematical Software, 23(3), pp. 379-401, 1997.<P></P><DT><A NAME="sblas02">9</A>
|
||||
<DD>
|
||||
I. Duff, M. Heroux and R. Pozo,
|
||||
<EM>An Overview of the Sparse Basic Linear
|
||||
Algebra Subprograms: the New Standard from the BLAS Technical Forum</EM>,
|
||||
ACM Transactions on Mathematical Software, 28(2), pp. 239-267, 2002.
|
||||
<P></P><DT><A NAME="PSBLAS">10</A>
|
||||
<DD>
|
||||
S. Filippone and M. Colajanni,
|
||||
<EM>PSBLAS: A Library for Parallel Linear Algebra
|
||||
Computation on Sparse Matrices</EM>,
|
||||
<BR>
|
||||
ACM Transactions on Mathematical Software, 26(4), pp. 527-550, 2000.<P></P><DT><A NAME="Sparse03">11</A>
|
||||
<DD>
|
||||
S. Filippone and A. Buttari,
|
||||
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>,
|
||||
<IMG
|
||||
WIDTH="482" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img162.png"
|
||||
ALT="\begin{lstlisting}
|
||||
call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
|
||||
& itmax,iter,err,itrace,irst,istop,cond)
|
||||
\end{lstlisting}">
|
||||
<BR>
|
||||
ACM Transactions on Mathematical Software, 38(4), 2012.<P></P><DT><A NAME="KIVA3PSBLAS">12</A>
|
||||
<DD>
|
||||
S. Filippone, P. D'Ambra, M. Colajanni,
|
||||
<EM>Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics
|
||||
Applications Code on Linux Clusters</EM>,
|
||||
in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors,
|
||||
Parallel Computing - Advances & Current Issues,
|
||||
pp. 441-448, Imperial College Press, 2002. <P></P><DT><A NAME="DesignPatterns">13</A>
|
||||
<DD>
|
||||
Gamma, E., Helm, R., Johnson, R., and Vlissides,
|
||||
J. 1995.
|
||||
<EM>Design Patterns: Elements of Reusable Object-Oriented Software</EM>.
|
||||
Addison-Wesley.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="METIS">14</A>
|
||||
<DD>
|
||||
Karypis, G. and Kumar, V.,
|
||||
<EM>METIS: Unstructured Graph Partitioning and Sparse Matrix
|
||||
Ordering System</EM>.
|
||||
Minneapolis, MN 55455: University of Minnesota, Department of
|
||||
Computer Science, 1995.
|
||||
Internet Address: <code>http://www.cs.umn.edu/~karypis</code>.
|
||||
<P></P><DT><A NAME="BLAS1">15</A>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Synchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||
<DD>
|
||||
Lawson, C., Hanson, R., Kincaid, D. and Krogh, F.,
|
||||
Basic Linear Algebra Subprograms for Fortran usage,
|
||||
ACM Trans. Math. Softw. vol. 5, 38-329, 1979.
|
||||
</DD>
|
||||
<DT><STRONG>method</STRONG></DT>
|
||||
<DD>a string that defines the iterative method to be
|
||||
used. Supported values are:
|
||||
<DL>
|
||||
<DT><STRONG>CG:</STRONG></DT>
|
||||
<DD>the Conjugate Gradient method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>CGS:</STRONG></DT>
|
||||
<DD>the Conjugate Gradient Stabilized method;
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="machiels">16</A>
|
||||
<DD>
|
||||
Machiels, L. and Deville, M.
|
||||
<EM>Fortran 90: An entry to object-oriented programming for the solution
|
||||
of partial differential equations.</EM>
|
||||
ACM Trans. Math. Softw. vol. 23, 32-49.
|
||||
<P></P><DT><A NAME="metcalf">17</A>
|
||||
<DD>
|
||||
Metcalf, M., Reid, J. and Cohen, M.
|
||||
<EM>Fortran 95/2003 explained.</EM>
|
||||
Oxford University Press, 2004.<P></P><DT><A NAME="RouXiaXu:11">18</A>
|
||||
<DD>
|
||||
Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The
|
||||
Object-Oriented Way. Cambridge University Press (2011)
|
||||
</DD>
|
||||
<DT><STRONG>GCR:</STRONG></DT>
|
||||
<DD>the Generalized Conjugate Residual method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>FCG:</STRONG></DT>
|
||||
<DD>the Flexible Conjugate Gradient method<A NAME="tex2html32"
|
||||
HREF="footnode.html#foot8093"><SUP><SPAN CLASS="arabic">5</SPAN></SUP></A>;
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="MPI1">19</A>
|
||||
</DD>
|
||||
<DT><STRONG>BICG:</STRONG></DT>
|
||||
<DD>the Bi-Conjugate Gradient method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>BICGSTAB:</STRONG></DT>
|
||||
<DD>the Bi-Conjugate Gradient Stabilized method;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>BICGSTABL:</STRONG></DT>
|
||||
<DD>the Bi-Conjugate Gradient Stabilized method with restarting;
|
||||
|
||||
</DD>
|
||||
<DT><STRONG>RGMRES:</STRONG></DT>
|
||||
<DD>the Generalized Minimal Residual method with restarting.
|
||||
|
||||
</DD>
|
||||
</DL>
|
||||
</DD>
|
||||
<DT><STRONG>a</STRONG></DT>
|
||||
<DD>the local portion of global sparse matrix
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$"></SPAN>.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>prec</STRONG></DT>
|
||||
<DD>The data structure containing the preconditioner.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type precdata<TT>psb_prec_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>b</STRONG></DT>
|
||||
<DD>The RHS vector.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>The initial guess.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>eps</STRONG></DT>
|
||||
<DD>The stopping tolerance.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>desc_a</STRONG></DT>
|
||||
<DD>contains data structures for communications.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>itmax</STRONG></DT>
|
||||
<DD>The maximum number of iterations to perform.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="99" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img164.png"
|
||||
ALT="$itmax = 1000$"></SPAN>.
|
||||
<BR>
|
||||
Specified as: an integer variable <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="76" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img165.png"
|
||||
ALT="$itmax \ge 1$"></SPAN>.
|
||||
</DD>
|
||||
<DT><STRONG>itrace</STRONG></DT>
|
||||
<DD>If <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img111.png"
|
||||
ALT="$>0$"></SPAN> print out an informational message about
|
||||
convergence every <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="45" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img166.png"
|
||||
ALT="$itrace$"></SPAN> iterations.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR></DD>
|
||||
<DT><STRONG>irst</STRONG></DT>
|
||||
<DD>An integer specifying the restart parameter.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>.
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Values: <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="60" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img167.png"
|
||||
ALT="$irst>0$"></SPAN>. This is employed for the BiCGSTABL or RGMRES
|
||||
methods, otherwise it is ignored.
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG>istop</STRONG></DT>
|
||||
<DD>An integer specifying the stopping criterion.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>.
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Values: 1: use the normwise backward error, 2: use the scaled 2-norm
|
||||
of the residual, 3: use the residual reduction in the 2-norm. Default: 2.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra,
|
||||
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
|
||||
MIT Press, 1998.</DL>
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>The computed solution.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>iter</STRONG></DT>
|
||||
<DD>The number of iterations performed.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: an integer variable.
|
||||
</DD>
|
||||
<DT><STRONG>err</STRONG></DT>
|
||||
<DD>The convergence estimate on exit.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>cond</STRONG></DT>
|
||||
<DD>An estimate of the condition number of matrix <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$"></SPAN>; only
|
||||
available with the <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img168.png"
|
||||
ALT="$CG$"></SPAN> method on real data.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: a real number. A correct result will be greater than or
|
||||
equal to one; if specified for non-real data, or an error occurred,
|
||||
zero is returned.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Error code.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
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HREF="node1.html">Contents</A></B>
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<H2><A NAME="SECTION00042000000000000000"></A>
|
||||
<A NAME="sec:spmat"></A>
|
||||
<H3><A NAME="SECTION000411200000000000000"></A>
|
||||
<A NAME="sec:cd_constants"></A>
|
||||
<BR>
|
||||
Sparse Matrix class
|
||||
</H2>
|
||||
The spdata<TT>psb_Tspmat_type</TT> class
|
||||
contains all information about the local portion of the sparse matrix and
|
||||
its storage mode. Its design is
|
||||
based on the STATE design pattern [<A
|
||||
HREF="node132.html#DesignPatterns">13</A>] as detailed
|
||||
in [<A
|
||||
HREF="node132.html#Sparse03">11</A>]; the type declaration is shown in
|
||||
figure <A HREF="#fig:spmattype">4</A> where <code>T</code> is a placeholder for the
|
||||
data type and precision variants
|
||||
Named Constants
|
||||
</H3>
|
||||
<DL>
|
||||
<DT><STRONG>S</STRONG></DT>
|
||||
<DD>Single precision real;
|
||||
<DT><STRONG>psb_none_</STRONG></DT>
|
||||
<DD>Generic no-op;
|
||||
</DD>
|
||||
<DT><STRONG>D</STRONG></DT>
|
||||
<DD>Double precision real;
|
||||
<DT><STRONG>psb_root_</STRONG></DT>
|
||||
<DD>Default root process for broadcast and scatter operations;
|
||||
</DD>
|
||||
<DT><STRONG>C</STRONG></DT>
|
||||
<DD>Single precision complex;
|
||||
<DT><STRONG>psb_nohalo_</STRONG></DT>
|
||||
<DD>Do not fetch halo elements;
|
||||
</DD>
|
||||
<DT><STRONG>Z</STRONG></DT>
|
||||
<DD>Double precision complex.
|
||||
<DT><STRONG>psb_halo_</STRONG></DT>
|
||||
<DD>Fetch halo elements from neighbouring processes;
|
||||
</DD>
|
||||
</DL>
|
||||
The actual data is contained in the polymorphic component <code>a%a</code>
|
||||
of type spbasedata<TT>psb_T_base_sparse_mat</TT>; its
|
||||
specific layout can be chosen dynamically among the predefined types,
|
||||
or an entirely new storage layout can be implemented and passed to the
|
||||
library at runtime via the <code>psb_spasb</code> routine.
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:spmattype"></A><A NAME="920"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
|
||||
The PSBLAS defined data type that
|
||||
contains a sparse matrix.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV><TABLE WIDTH="85%">
|
||||
<TR><TD>
|
||||
<PRE>
|
||||
type :: psb_Tspmat_type
|
||||
class(psb_T_base_sparse_mat), allocatable :: a
|
||||
end type psb_Tspmat_type
|
||||
</PRE></TD></TR>
|
||||
</TABLE>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV></TD></TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
The following very common formats are precompiled in PSBLAS and thus
|
||||
are always available:
|
||||
<DL>
|
||||
<DT><STRONG>psb_T_coo_sparse_mat</STRONG></DT>
|
||||
<DD>Coordinate storage;
|
||||
<DT><STRONG>psb_sum_</STRONG></DT>
|
||||
<DD>Sum overlapped elements
|
||||
</DD>
|
||||
<DT><STRONG>psb_T_csr_sparse_mat</STRONG></DT>
|
||||
<DD>Compressed storage by rows;
|
||||
<DT><STRONG>psb_avg_</STRONG></DT>
|
||||
<DD>Average overlapped elements
|
||||
</DD>
|
||||
<DT><STRONG>psb_T_csc_sparse_mat</STRONG></DT>
|
||||
<DD>Compressed storage by columns;
|
||||
<DT><STRONG>psb_comm_halo_</STRONG></DT>
|
||||
<DD>Exchange data based on the <code>halo_index</code>
|
||||
list;
|
||||
</DD>
|
||||
</DL>
|
||||
The inner sparse matrix has an associated state, which can take the
|
||||
following values:
|
||||
<DL>
|
||||
<DT><STRONG>Build:</STRONG></DT>
|
||||
<DD>State entered after the first allocation, and before the
|
||||
first assembly; in this state it is possible to add nonzero entries.
|
||||
<DT><STRONG>psb_comm_ext_</STRONG></DT>
|
||||
<DD>Exchange data based on the <code>ext_index</code>
|
||||
list;
|
||||
</DD>
|
||||
<DT><STRONG>Assembled:</STRONG></DT>
|
||||
<DD>State entered after the assembly; computations using
|
||||
the sparse matrix, such as matrix-vector products, are only possible
|
||||
in this state;
|
||||
<DT><STRONG>psb_comm_ovr_</STRONG></DT>
|
||||
<DD>Exchange data based on the <code>ovrlap_index</code>
|
||||
list;
|
||||
</DD>
|
||||
<DT><STRONG>Update:</STRONG></DT>
|
||||
<DD>State entered after a reinitalization; this is used to
|
||||
handle applications in which the same sparsity pattern is used
|
||||
multiple times with different coefficients. In this state it is only
|
||||
possible to enter coefficients for already existing nonzero entries.
|
||||
<DT><STRONG>psb_comm_mov_</STRONG></DT>
|
||||
<DD>Exchange data based on the <code>ovr_mst_idx</code>
|
||||
list;
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
</DL>
|
||||
The only storage variant supporting the build state is COO; all other
|
||||
variants are obtained by conversion to/from it.
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL>
|
||||
<LI><A NAME="tex2html505"
|
||||
HREF="node23.html">Sparse Matrix Methods</A>
|
||||
<LI><A NAME="tex2html506"
|
||||
HREF="node24.html">get_nrows -- Get number of rows in a sparse matrix</A>
|
||||
<LI><A NAME="tex2html507"
|
||||
HREF="node25.html">get_ncols -- Get number of columns in a sparse
|
||||
matrix</A>
|
||||
<LI><A NAME="tex2html508"
|
||||
HREF="node26.html">get_nnzeros -- Get number of nonzero elements
|
||||
in a sparse matrix</A>
|
||||
<LI><A NAME="tex2html509"
|
||||
HREF="node27.html">get_size -- Get maximum number of nonzero elements
|
||||
in a sparse matrix</A>
|
||||
<LI><A NAME="tex2html510"
|
||||
HREF="node28.html">sizeof -- Get memory occupation in bytes
|
||||
of a sparse matrix</A>
|
||||
<LI><A NAME="tex2html511"
|
||||
HREF="node29.html">get_fmt -- Short description of the dynamic type</A>
|
||||
<LI><A NAME="tex2html512"
|
||||
HREF="node30.html">is_bld, is_upd, is_asb -- Status check</A>
|
||||
<LI><A NAME="tex2html513"
|
||||
HREF="node31.html">is_lower, is_upper, is_triangle, is_unit --
|
||||
Format check</A>
|
||||
<LI><A NAME="tex2html514"
|
||||
HREF="node32.html">cscnv -- Convert to a different storage format</A>
|
||||
<LI><A NAME="tex2html515"
|
||||
HREF="node33.html">csclip -- Reduce to a submatrix</A>
|
||||
<LI><A NAME="tex2html516"
|
||||
HREF="node34.html">clean_zeros -- Eliminate zero coefficients</A>
|
||||
<LI><A NAME="tex2html517"
|
||||
HREF="node35.html">get_diag -- Get main diagonal</A>
|
||||
<LI><A NAME="tex2html518"
|
||||
HREF="node36.html">clip_diag -- Cut out main diagonal</A>
|
||||
<LI><A NAME="tex2html519"
|
||||
HREF="node37.html">tril -- Return the lower triangle</A>
|
||||
<LI><A NAME="tex2html520"
|
||||
HREF="node38.html">triu -- Return the upper triangle</A>
|
||||
<LI><A NAME="tex2html521"
|
||||
HREF="node39.html">psb_set_mat_default -- Set default storage format</A>
|
||||
<LI><A NAME="tex2html522"
|
||||
HREF="node40.html">clone -- Clone current object</A>
|
||||
<LI><A NAME="tex2html523"
|
||||
HREF="node41.html">Named Constants</A>
|
||||
</UL>
|
||||
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|
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|
||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||||
* with significant contributions from:
|
||||
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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Sparse Matrix Methods</A>
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</H3>
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<H2><A NAME="SECTION00042000000000000000"></A>
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<A NAME="sec:spmat"></A>
|
||||
<BR>
|
||||
Sparse Matrix class
|
||||
</H2>
|
||||
The spdata<TT>psb_Tspmat_type</TT> class
|
||||
contains all information about the local portion of the sparse matrix and
|
||||
its storage mode. Its design is
|
||||
based on the STATE design pattern [<A
|
||||
HREF="node133.html#DesignPatterns">13</A>] as detailed
|
||||
in [<A
|
||||
HREF="node133.html#Sparse03">11</A>]; the type declaration is shown in
|
||||
figure <A HREF="#fig:spmattype">4</A> where <code>T</code> is a placeholder for the
|
||||
data type and precision variants
|
||||
<DL>
|
||||
<DT><STRONG>S</STRONG></DT>
|
||||
<DD>Single precision real;
|
||||
</DD>
|
||||
<DT><STRONG>D</STRONG></DT>
|
||||
<DD>Double precision real;
|
||||
</DD>
|
||||
<DT><STRONG>C</STRONG></DT>
|
||||
<DD>Single precision complex;
|
||||
</DD>
|
||||
<DT><STRONG>Z</STRONG></DT>
|
||||
<DD>Double precision complex.
|
||||
</DD>
|
||||
</DL>
|
||||
The actual data is contained in the polymorphic component <code>a%a</code>
|
||||
of type spbasedata<TT>psb_T_base_sparse_mat</TT>; its
|
||||
specific layout can be chosen dynamically among the predefined types,
|
||||
or an entirely new storage layout can be implemented and passed to the
|
||||
library at runtime via the <code>psb_spasb</code> routine.
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:spmattype"></A><A NAME="934"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
|
||||
The PSBLAS defined data type that
|
||||
contains a sparse matrix.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV><TABLE WIDTH="85%">
|
||||
<TR><TD>
|
||||
<PRE>
|
||||
type :: psb_Tspmat_type
|
||||
class(psb_T_base_sparse_mat), allocatable :: a
|
||||
end type psb_Tspmat_type
|
||||
</PRE></TD></TR>
|
||||
</TABLE>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV></TD></TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
The following very common formats are precompiled in PSBLAS and thus
|
||||
are always available:
|
||||
<DL>
|
||||
<DT><STRONG>psb_T_coo_sparse_mat</STRONG></DT>
|
||||
<DD>Coordinate storage;
|
||||
</DD>
|
||||
<DT><STRONG>psb_T_csr_sparse_mat</STRONG></DT>
|
||||
<DD>Compressed storage by rows;
|
||||
</DD>
|
||||
<DT><STRONG>psb_T_csc_sparse_mat</STRONG></DT>
|
||||
<DD>Compressed storage by columns;
|
||||
</DD>
|
||||
</DL>
|
||||
The inner sparse matrix has an associated state, which can take the
|
||||
following values:
|
||||
<DL>
|
||||
<DT><STRONG>Build:</STRONG></DT>
|
||||
<DD>State entered after the first allocation, and before the
|
||||
first assembly; in this state it is possible to add nonzero entries.
|
||||
</DD>
|
||||
<DT><STRONG>Assembled:</STRONG></DT>
|
||||
<DD>State entered after the assembly; computations using
|
||||
the sparse matrix, such as matrix-vector products, are only possible
|
||||
in this state;
|
||||
</DD>
|
||||
<DT><STRONG>Update:</STRONG></DT>
|
||||
<DD>State entered after a reinitalization; this is used to
|
||||
handle applications in which the same sparsity pattern is used
|
||||
multiple times with different coefficients. In this state it is only
|
||||
possible to enter coefficients for already existing nonzero entries.
|
||||
</DD>
|
||||
</DL>
|
||||
The only storage variant supporting the build state is COO; all other
|
||||
variants are obtained by conversion to/from it.
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL CLASS="ChildLinks">
|
||||
<LI><A NAME="tex2html520"
|
||||
HREF="node24.html">Sparse Matrix Methods</A>
|
||||
<LI><A NAME="tex2html521"
|
||||
HREF="node25.html">get_nrows -- Get number of rows in a sparse matrix</A>
|
||||
<LI><A NAME="tex2html522"
|
||||
HREF="node26.html">get_ncols -- Get number of columns in a sparse
|
||||
matrix</A>
|
||||
<LI><A NAME="tex2html523"
|
||||
HREF="node27.html">get_nnzeros -- Get number of nonzero elements
|
||||
in a sparse matrix</A>
|
||||
<LI><A NAME="tex2html524"
|
||||
HREF="node28.html">get_size -- Get maximum number of nonzero elements
|
||||
in a sparse matrix</A>
|
||||
<LI><A NAME="tex2html525"
|
||||
HREF="node29.html">sizeof -- Get memory occupation in bytes
|
||||
of a sparse matrix</A>
|
||||
<LI><A NAME="tex2html526"
|
||||
HREF="node30.html">get_fmt -- Short description of the dynamic type</A>
|
||||
<LI><A NAME="tex2html527"
|
||||
HREF="node31.html">is_bld, is_upd, is_asb -- Status check</A>
|
||||
<LI><A NAME="tex2html528"
|
||||
HREF="node32.html">is_lower, is_upper, is_triangle, is_unit --
|
||||
Format check</A>
|
||||
<LI><A NAME="tex2html529"
|
||||
HREF="node33.html">cscnv -- Convert to a different storage format</A>
|
||||
<LI><A NAME="tex2html530"
|
||||
HREF="node34.html">csclip -- Reduce to a submatrix</A>
|
||||
<LI><A NAME="tex2html531"
|
||||
HREF="node35.html">clean_zeros -- Eliminate zero coefficients</A>
|
||||
<LI><A NAME="tex2html532"
|
||||
HREF="node36.html">get_diag -- Get main diagonal</A>
|
||||
<LI><A NAME="tex2html533"
|
||||
HREF="node37.html">clip_diag -- Cut out main diagonal</A>
|
||||
<LI><A NAME="tex2html534"
|
||||
HREF="node38.html">tril -- Return the lower triangle</A>
|
||||
<LI><A NAME="tex2html535"
|
||||
HREF="node39.html">triu -- Return the upper triangle</A>
|
||||
<LI><A NAME="tex2html536"
|
||||
HREF="node40.html">psb_set_mat_default -- Set default storage format</A>
|
||||
<LI><A NAME="tex2html537"
|
||||
HREF="node41.html">clone -- Clone current object</A>
|
||||
<LI><A NAME="tex2html538"
|
||||
HREF="node42.html">Named Constants</A>
|
||||
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|
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HREF="node41.html">clone Clone</A>
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HREF="node1.html">Contents</A></B>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00043000000000000000"></A>
|
||||
<A NAME="sec:vecttype"></A>
|
||||
<H3><A NAME="SECTION000421900000000000000"></A>
|
||||
<A NAME="sec:sp_constants"></A>
|
||||
<BR>
|
||||
Dense Vector Data Structure
|
||||
</H2>
|
||||
The vdata<TT>psb_T_vect_type</TT> data structure
|
||||
encapsulates the dense vectors in a way similar to sparse matrices,
|
||||
i.e. including a base type vbasedata<TT> psb_T_base_vect_type</TT>.
|
||||
The user will not, in general, access the vector components directly,
|
||||
but rather via the routines of sec. <A HREF="node70.html#sec:toolsrout">6</A>. Among other
|
||||
simple things, we define here an extraction method that can be used to
|
||||
get a full copy of the part of the vector stored on the local
|
||||
process.
|
||||
|
||||
<P>
|
||||
The type declaration is shown in
|
||||
figure <A HREF="#fig:vectype">5</A> where <code>T</code> is a placeholder for the
|
||||
data type and precision variants
|
||||
Named Constants
|
||||
</H3>
|
||||
<DL>
|
||||
<DT><STRONG>I</STRONG></DT>
|
||||
<DD>Integer;
|
||||
<DT><STRONG>psb_dupl_ovwrt_</STRONG></DT>
|
||||
<DD>Duplicate coefficients should be overwritten
|
||||
(i.e. ignore duplications)
|
||||
</DD>
|
||||
<DT><STRONG>psb_dupl_add_</STRONG></DT>
|
||||
<DD>Duplicate coefficients should be added;
|
||||
</DD>
|
||||
<DT><STRONG>S</STRONG></DT>
|
||||
<DD>Single precision real;
|
||||
<DT><STRONG>psb_dupl_err_</STRONG></DT>
|
||||
<DD>Duplicate coefficients should trigger an error conditino
|
||||
</DD>
|
||||
<DT><STRONG>D</STRONG></DT>
|
||||
<DD>Double precision real;
|
||||
<DT><STRONG>psb_upd_dflt_</STRONG></DT>
|
||||
<DD>Default update strategy for matrix coefficients;
|
||||
</DD>
|
||||
<DT><STRONG>C</STRONG></DT>
|
||||
<DD>Single precision complex;
|
||||
<DT><STRONG>psb_upd_srch_</STRONG></DT>
|
||||
<DD>Update strategy based on search into the data structure;
|
||||
</DD>
|
||||
<DT><STRONG>Z</STRONG></DT>
|
||||
<DD>Double precision complex.
|
||||
<DT><STRONG>psb_upd_perm_</STRONG></DT>
|
||||
<DD>Update strategy based on additional
|
||||
permutation data (see tools routine description).
|
||||
</DD>
|
||||
</DL>
|
||||
The actual data is contained in the polymorphic component <code>v%v</code>;
|
||||
the separation between the application and the actual data is
|
||||
essential for cases where it is necessary to link to data storage made
|
||||
available elsewhere outside the direct control of the
|
||||
compiler/application, e.g. data stored in a graphics accelerator's
|
||||
private memory.
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:vectype"></A><A NAME="923"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
|
||||
The PSBLAS defined data type that
|
||||
contains a dense vector.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV><TABLE WIDTH="85%">
|
||||
<TR><TD>
|
||||
<PRE>
|
||||
type psb_T_base_vect_type
|
||||
TYPE(KIND_), allocatable :: v(:)
|
||||
end type psb_T_base_vect_type
|
||||
|
||||
type psb_T_vect_type
|
||||
class(psb_T_base_vect_type), allocatable :: v
|
||||
end type psb_T_vect_type
|
||||
</PRE></TD></TR>
|
||||
</TABLE>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV></TD></TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL>
|
||||
<LI><A NAME="tex2html762"
|
||||
HREF="node43.html">Vector Methods</A>
|
||||
<LI><A NAME="tex2html763"
|
||||
HREF="node44.html">get_nrows -- Get number of rows in a dense vector</A>
|
||||
<LI><A NAME="tex2html764"
|
||||
HREF="node45.html">sizeof -- Get memory occupation in bytes
|
||||
of a dense vector</A>
|
||||
<LI><A NAME="tex2html765"
|
||||
HREF="node46.html">set -- Set contents of the vector</A>
|
||||
<LI><A NAME="tex2html766"
|
||||
HREF="node47.html">get_vect -- Get a copy of the vector contents</A>
|
||||
<LI><A NAME="tex2html767"
|
||||
HREF="node48.html">clone -- Clone current object</A>
|
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Vector Methods</A>
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</H3>
|
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<H2><A NAME="SECTION00043000000000000000"></A>
|
||||
<A NAME="sec:vecttype"></A>
|
||||
<BR>
|
||||
Dense Vector Data Structure
|
||||
</H2>
|
||||
The vdata<TT>psb_T_vect_type</TT> data structure
|
||||
encapsulates the dense vectors in a way similar to sparse matrices,
|
||||
i.e. including a base type vbasedata<TT> psb_T_base_vect_type</TT>.
|
||||
The user will not, in general, access the vector components directly,
|
||||
but rather via the routines of sec. <A HREF="node71.html#sec:toolsrout">6</A>. Among other
|
||||
simple things, we define here an extraction method that can be used to
|
||||
get a full copy of the part of the vector stored on the local
|
||||
process.
|
||||
|
||||
<P>
|
||||
The type declaration is shown in
|
||||
figure <A HREF="#fig:vectype">5</A> where <code>T</code> is a placeholder for the
|
||||
data type and precision variants
|
||||
<DL>
|
||||
<DT><STRONG>I</STRONG></DT>
|
||||
<DD>Integer;
|
||||
</DD>
|
||||
<DT><STRONG>S</STRONG></DT>
|
||||
<DD>Single precision real;
|
||||
</DD>
|
||||
<DT><STRONG>D</STRONG></DT>
|
||||
<DD>Double precision real;
|
||||
</DD>
|
||||
<DT><STRONG>C</STRONG></DT>
|
||||
<DD>Single precision complex;
|
||||
</DD>
|
||||
<DT><STRONG>Z</STRONG></DT>
|
||||
<DD>Double precision complex.
|
||||
</DD>
|
||||
</DL>
|
||||
The actual data is contained in the polymorphic component <code>v%v</code>;
|
||||
the separation between the application and the actual data is
|
||||
essential for cases where it is necessary to link to data storage made
|
||||
available elsewhere outside the direct control of the
|
||||
compiler/application, e.g. data stored in a graphics accelerator's
|
||||
private memory.
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:vectype"></A><A NAME="937"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
|
||||
The PSBLAS defined data type that
|
||||
contains a dense vector.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV><TABLE WIDTH="85%">
|
||||
<TR><TD>
|
||||
<PRE>
|
||||
type psb_T_base_vect_type
|
||||
TYPE(KIND_), allocatable :: v(:)
|
||||
end type psb_T_base_vect_type
|
||||
|
||||
type psb_T_vect_type
|
||||
class(psb_T_base_vect_type), allocatable :: v
|
||||
end type psb_T_vect_type
|
||||
</PRE></TD></TR>
|
||||
</TABLE>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV></TD></TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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|
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HREF="node44.html">Vector Methods</A>
|
||||
<LI><A NAME="tex2html778"
|
||||
HREF="node45.html">get_nrows -- Get number of rows in a dense vector</A>
|
||||
<LI><A NAME="tex2html779"
|
||||
HREF="node46.html">sizeof -- Get memory occupation in bytes
|
||||
of a dense vector</A>
|
||||
<LI><A NAME="tex2html780"
|
||||
HREF="node47.html">set -- Set contents of the vector</A>
|
||||
<LI><A NAME="tex2html781"
|
||||
HREF="node48.html">get_vect -- Get a copy of the vector contents</A>
|
||||
<LI><A NAME="tex2html782"
|
||||
HREF="node49.html">clone -- Clone current object</A>
|
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|
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|
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<TITLE>psb_geaxpby -- General Dense Matrix Sum</TITLE>
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HREF="node1.html">Contents</A></B>
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<H2><A NAME="SECTION00051000000000000000">
|
||||
psb_geaxpby -- General Dense Matrix Sum</A>
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
This subroutine is an interface to the computational kernel for
|
||||
dense matrix sum:
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
y \leftarrow \alpha\> x+ \beta y
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="93" HEIGHT="27" BORDER="0"
|
||||
SRC="img19.png"
|
||||
ALT="\begin{displaymath}y \leftarrow \alpha\> x+ \beta y \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
<P>
|
||||
<PRE>
|
||||
call psb_geaxpby(alpha, x, beta, y, desc_a, info)
|
||||
</PRE>
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="1948"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 1:</STRONG>
|
||||
Data types</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
|
||||
<TR><TD ALIGN="LEFT"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">, <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$">, <IMG
|
||||
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img22.png"
|
||||
ALT="$\alpha$">, <IMG
|
||||
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img23.png"
|
||||
ALT="$\beta$"></TD>
|
||||
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
|
||||
<TD ALIGN="LEFT">psb_geaxpby</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
|
||||
<TD ALIGN="LEFT">psb_geaxpby</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
|
||||
<TD ALIGN="LEFT">psb_geaxpby</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
|
||||
<TD ALIGN="LEFT">psb_geaxpby</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
</TD></TR>
|
||||
</TABLE>
|
||||
</DIV><P></P>
|
||||
<BR>
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Synchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>alpha</STRONG></DT>
|
||||
<DD>the scalar <IMG
|
||||
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img22.png"
|
||||
ALT="$\alpha$">.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a number of the data
|
||||
type indicated in Table <A HREF="#tab:f90axpby">1</A>.
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>the local portion of global dense matrix
|
||||
<IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
|
||||
containing numbers of type
|
||||
specified in Table <A HREF="#tab:f90axpby">1</A>. The rank of <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"> must be the same of <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$">.
|
||||
</DD>
|
||||
<DT><STRONG>beta</STRONG></DT>
|
||||
<DD>the scalar <IMG
|
||||
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img23.png"
|
||||
ALT="$\beta$">.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a number of the data type indicated in Table <A HREF="#tab:f90axpby">1</A>.
|
||||
</DD>
|
||||
<DT><STRONG>y</STRONG></DT>
|
||||
<DD>the local portion of the global dense matrix
|
||||
<IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT> containing numbers of the type
|
||||
indicated in Table <A HREF="#tab:f90axpby">1</A>. The rank of <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"> must be the same of <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">.
|
||||
</DD>
|
||||
<DT><STRONG>desc_a</STRONG></DT>
|
||||
<DD>contains data structures for communications.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: an object of type descdata<TT>psb_desc_type</TT>.
|
||||
<P>
|
||||
</DD>
|
||||
</DL>
|
||||
<H1><A NAME="SECTION00050000000000000000">
|
||||
Computational routines</A>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>y</STRONG></DT>
|
||||
<DD>the local portion of result submatrix <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT> containing numbers of the type
|
||||
indicated in Table <A HREF="#tab:f90axpby">1</A>.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Error code.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
</DD>
|
||||
</DL>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<P>
|
||||
<HR>
|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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HREF="node1.html">Contents</A></B>
|
||||
<!--End of Navigation Panel-->
|
||||
<UL CLASS="ChildLinks">
|
||||
<LI><A NAME="tex2html887"
|
||||
HREF="node53.html">psb_geaxpby -- General Dense Matrix Sum</A>
|
||||
<LI><A NAME="tex2html888"
|
||||
HREF="node54.html">psb_gedot -- Dot Product</A>
|
||||
<LI><A NAME="tex2html889"
|
||||
HREF="node55.html">psb_gedots -- Generalized Dot Product</A>
|
||||
<LI><A NAME="tex2html890"
|
||||
HREF="node56.html">psb_normi -- Infinity-Norm of Vector</A>
|
||||
<LI><A NAME="tex2html891"
|
||||
HREF="node57.html">psb_geamaxs -- Generalized Infinity Norm</A>
|
||||
<LI><A NAME="tex2html892"
|
||||
HREF="node58.html">psb_norm1 -- 1-Norm of Vector</A>
|
||||
<LI><A NAME="tex2html893"
|
||||
HREF="node59.html">psb_geasums -- Generalized 1-Norm of Vector</A>
|
||||
<LI><A NAME="tex2html894"
|
||||
HREF="node60.html">psb_norm2 -- 2-Norm of Vector</A>
|
||||
<LI><A NAME="tex2html895"
|
||||
HREF="node61.html">psb_genrm2s -- Generalized 2-Norm of Vector</A>
|
||||
<LI><A NAME="tex2html896"
|
||||
HREF="node62.html">psb_norm1 -- 1-Norm of Sparse Matrix</A>
|
||||
<LI><A NAME="tex2html897"
|
||||
HREF="node63.html">psb_normi -- Infinity Norm of Sparse Matrix</A>
|
||||
<LI><A NAME="tex2html898"
|
||||
HREF="node64.html">psb_spmm -- Sparse Matrix by Dense Matrix
|
||||
Product</A>
|
||||
<LI><A NAME="tex2html899"
|
||||
HREF="node65.html">psb_spsm -- Triangular System Solve</A>
|
||||
</UL>
|
||||
<!--End of Table of Child-Links-->
|
||||
<BR><HR>
|
||||
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||||
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</HTML>
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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|
||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||||
* with significant contributions from:
|
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|
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<DIV CLASS="navigation"><!--Navigation Panel-->
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<BR>
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<B> Next:</B> <A NAME="tex2html1050"
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HREF="node66.html">psb_halo Halo</A>
|
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<B> Up:</B> <A NAME="tex2html1046"
|
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HREF="userhtml.html">userhtml</A>
|
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<B> Previous:</B> <A NAME="tex2html1040"
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<B> Next:</B> <A NAME="tex2html1053"
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HREF="node66.html">Communication routines</A>
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<B> Up:</B> <A NAME="tex2html1049"
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HREF="node52.html">Computational routines</A>
|
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<B> Previous:</B> <A NAME="tex2html1045"
|
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HREF="node64.html">psb_spmm Sparse</A>
|
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<B> <A NAME="tex2html1051"
|
||||
HREF="node1.html">Contents</A></B>
|
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<BR>
|
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<BR>
|
||||
<BR></DIV>
|
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<!--End of Navigation Panel-->
|
||||
|
||||
<H1><A NAME="SECTION00060000000000000000">
|
||||
Communication routines</A>
|
||||
</H1>The routines in this chapter implement various global communication operators
|
||||
on vectors associated with a discretization mesh. For auxiliary communication
|
||||
routines not tied to a discretization space see <A HREF="node70.html#sec:toolsrout">6</A>.
|
||||
<H2><A NAME="SECTION000513000000000000000">
|
||||
psb_spsm -- Triangular System Solve</A>
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
This subroutine computes the Triangular System Solve:
|
||||
|
||||
<P>
|
||||
<P></P>
|
||||
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
||||
<!-- MATH
|
||||
\begin{eqnarray*}
|
||||
y &\leftarrow& \alpha T^{-1} x + \beta y\\
|
||||
y &\leftarrow& \alpha D T^{-1} x + \beta y\\
|
||||
y &\leftarrow& \alpha T^{-1} D x + \beta y\\
|
||||
y &\leftarrow& \alpha T^{-T} x + \beta y\\
|
||||
y &\leftarrow& \alpha D T^{-T} x + \beta y\\
|
||||
y &\leftarrow& \alpha T^{-T} D x + \beta y\\
|
||||
y &\leftarrow& \alpha T^{-H} x + \beta y\\
|
||||
y &\leftarrow& \alpha D T^{-H} x + \beta y\\
|
||||
y &\leftarrow& \alpha T^{-H} D x + \beta y\\
|
||||
\end{eqnarray*}
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="160" HEIGHT="239" BORDER="0"
|
||||
SRC="img50.png"
|
||||
ALT="\begin{eqnarray*}
|
||||
y &\leftarrow& \alpha T^{-1} x + \beta y\\
|
||||
y &\leftarrow& \al...
|
||||
...-H} x + \beta y\\
|
||||
y &\leftarrow& \alpha T^{-H} D x + \beta y\\
|
||||
\end{eqnarray*}"></DIV>
|
||||
<BR CLEAR="ALL"><P></P>
|
||||
<BR CLEAR="ALL"><P></P>
|
||||
|
||||
<P>
|
||||
where:
|
||||
<DL>
|
||||
<DT><STRONG><SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></SPAN></STRONG></DT>
|
||||
<DD>is the global dense matrix <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img47.png"
|
||||
ALT="$x_{:, :}$"></SPAN>
|
||||
</DD>
|
||||
<DT><STRONG><SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"></SPAN></STRONG></DT>
|
||||
<DD>is the global dense matrix <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img48.png"
|
||||
ALT="$y_{:, :}$"></SPAN>
|
||||
</DD>
|
||||
<DT><STRONG><SPAN CLASS="MATH"><IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img51.png"
|
||||
ALT="$T$"></SPAN></STRONG></DT>
|
||||
<DD>is the global sparse block triangular submatrix <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img51.png"
|
||||
ALT="$T$"></SPAN>
|
||||
</DD>
|
||||
<DT><STRONG><SPAN CLASS="MATH"><IMG
|
||||
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img52.png"
|
||||
ALT="$D$"></SPAN></STRONG></DT>
|
||||
<DD>is the scaling diagonal matrix.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
call psb_spsm(alpha, t, x, beta, y, desc_a, info)
|
||||
call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
|
||||
& trans, unit, choice, diag, work)
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="1989"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 13:</STRONG>
|
||||
Data types</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
|
||||
<TR><TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img51.png"
|
||||
ALT="$T$"></SPAN>, <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></SPAN>, <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"></SPAN>, <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img52.png"
|
||||
ALT="$D$"></SPAN>, <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img22.png"
|
||||
ALT="$\alpha$"></SPAN>, <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img23.png"
|
||||
ALT="$\beta$"></SPAN></TD>
|
||||
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
|
||||
<TD ALIGN="LEFT">psb_spsm</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
|
||||
<TD ALIGN="LEFT">psb_spsm</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
|
||||
<TD ALIGN="LEFT">psb_spsm</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
|
||||
<TD ALIGN="LEFT">psb_spsm</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
</TD></TR>
|
||||
</TABLE>
|
||||
</DIV><P></P>
|
||||
<BR>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL>
|
||||
<LI><A NAME="tex2html1051"
|
||||
HREF="node66.html">psb_halo -- Halo Data Communication</A>
|
||||
<LI><A NAME="tex2html1052"
|
||||
HREF="node67.html">psb_ovrl -- Overlap Update</A>
|
||||
<LI><A NAME="tex2html1053"
|
||||
HREF="node68.html">psb_gather -- Gather Global Dense Matrix</A>
|
||||
<LI><A NAME="tex2html1054"
|
||||
HREF="node69.html">psb_scatter -- Scatter Global Dense Matrix</A>
|
||||
</UL>
|
||||
<!--End of Table of Child-Links-->
|
||||
<BR><HR>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Synchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>alpha</STRONG></DT>
|
||||
<DD>the scalar <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img22.png"
|
||||
ALT="$\alpha$"></SPAN>.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a number of the data type indicated in
|
||||
Table <A HREF="#tab:f90spsm">13</A>.
|
||||
</DD>
|
||||
<DT><STRONG>t</STRONG></DT>
|
||||
<DD>the global portion of the sparse matrix
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img51.png"
|
||||
ALT="$T$"></SPAN>.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: an object type specified in
|
||||
§ <A HREF="node9.html#sec:datastruct">3</A>.
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>the local portion of global dense matrix
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></SPAN>.
|
||||
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
|
||||
containing numbers of type specified in
|
||||
Table <A HREF="#tab:f90spsm">13</A>. The rank of <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></SPAN> must be the same of <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"></SPAN>.
|
||||
</DD>
|
||||
<DT><STRONG>beta</STRONG></DT>
|
||||
<DD>the scalar <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img23.png"
|
||||
ALT="$\beta$"></SPAN>.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a number of the data type indicated in Table <A HREF="#tab:f90spsm">13</A>.
|
||||
</DD>
|
||||
<DT><STRONG>y</STRONG></DT>
|
||||
<DD>the local portion of global dense matrix
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"></SPAN>.
|
||||
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
|
||||
containing numbers of type specified in
|
||||
Table <A HREF="#tab:f90spsm">13</A>. The rank of <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"></SPAN> must be the same of <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></SPAN>.
|
||||
</DD>
|
||||
<DT><STRONG>desc_a</STRONG></DT>
|
||||
<DD>contains data structures for communications.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: an object of type descdata<TT>psb_desc_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>trans</STRONG></DT>
|
||||
<DD>specify with <EM>unitd</EM> the operation to perform.
|
||||
<DL>
|
||||
<DT><STRONG>trans = 'N'</STRONG></DT>
|
||||
<DD>the operation is with no transposed matrix
|
||||
</DD>
|
||||
<DT><STRONG>trans = 'T'</STRONG></DT>
|
||||
<DD>the operation is with transposed matrix.
|
||||
</DD>
|
||||
<DT><STRONG>trans = 'C'</STRONG></DT>
|
||||
<DD>the operation is with conjugate transposed matrix.
|
||||
</DD>
|
||||
</DL>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img49.png"
|
||||
ALT="$trans = N$"></SPAN>
|
||||
<BR>
|
||||
Specified as: a character variable.
|
||||
</DD>
|
||||
<DT><STRONG>unitd</STRONG></DT>
|
||||
<DD>specify with <EM>trans</EM> the operation to perform.
|
||||
<DL>
|
||||
<DT><STRONG>unitd = 'U'</STRONG></DT>
|
||||
<DD>the operation is with no scaling
|
||||
</DD>
|
||||
<DT><STRONG>unitd = 'L'</STRONG></DT>
|
||||
<DD>the operation is with left scaling
|
||||
</DD>
|
||||
<DT><STRONG>unitd = 'R'</STRONG></DT>
|
||||
<DD>the operation is with right scaling.
|
||||
</DD>
|
||||
</DL>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="76" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img53.png"
|
||||
ALT="$unitd = U$"></SPAN>
|
||||
<BR>
|
||||
Specified as: a character variable.
|
||||
</DD>
|
||||
<DT><STRONG>choice</STRONG></DT>
|
||||
<DD>specifies the update of overlap elements to be performed
|
||||
on exit:
|
||||
<DL>
|
||||
<DT></DT>
|
||||
<DD><code>psb_none_</code>
|
||||
</DD>
|
||||
<DT></DT>
|
||||
<DD><code>psb_sum_</code>
|
||||
</DD>
|
||||
<DT></DT>
|
||||
<DD><code>psb_avg_</code>
|
||||
</DD>
|
||||
<DT></DT>
|
||||
<DD><code>psb_square_root_</code>
|
||||
</DD>
|
||||
</DL>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <code>psb_avg_</code>
|
||||
<BR>
|
||||
Specified as: an integer variable.
|
||||
</DD>
|
||||
<DT><STRONG>diag</STRONG></DT>
|
||||
<DD>the diagonal scaling matrix.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <!-- MATH
|
||||
$diag(1) = 1 (no scaling)$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="164" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img54.png"
|
||||
ALT="$diag(1) = 1 (no scaling)$"></SPAN>
|
||||
<BR>
|
||||
Specified as: a rank one array containing numbers of the type
|
||||
indicated in Table <A HREF="#tab:f90spsm">13</A>.
|
||||
</DD>
|
||||
<DT><STRONG>work</STRONG></DT>
|
||||
<DD>a work array.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array of the same type of <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></SPAN> with the
|
||||
TARGET attribute.
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>y</STRONG></DT>
|
||||
<DD>the local portion of global dense matrix
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"></SPAN>.
|
||||
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: an array of rank one or two
|
||||
containing numbers of type specified in
|
||||
Table <A HREF="#tab:f90spsm">13</A>.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Error code.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
|
||||
<DIV CLASS="navigation"><HR>
|
||||
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|
||||
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|
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||||
<BR>
|
||||
<B> Next:</B> <A NAME="tex2html1053"
|
||||
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|
||||
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||||
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||||
<B> Previous:</B> <A NAME="tex2html1045"
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||||
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@ -1,638 +1,77 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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original version by: Nikos Drakos, CBLU, University of Leeds
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||||
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||||
* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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||||
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||||
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||||
<TITLE>psb_halo -- Halo Data Communication</TITLE>
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||||
<META NAME="description" CONTENT="psb_halo -- Halo Data Communication">
|
||||
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<B> <A NAME="tex2html1064"
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<B> Next:</B> <A NAME="tex2html1065"
|
||||
HREF="node67.html">psb_halo Halo</A>
|
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<B> Up:</B> <A NAME="tex2html1061"
|
||||
HREF="userhtml.html">userhtml</A>
|
||||
<B> Previous:</B> <A NAME="tex2html1055"
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|
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HREF="node1.html">Contents</A></B>
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<BR>
|
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<BR></DIV>
|
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<!--End of Navigation Panel-->
|
||||
|
||||
<H2><A NAME="SECTION00061000000000000000">
|
||||
psb_halo -- Halo Data Communication</A>
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
These subroutines gathers the values of the halo
|
||||
elements:
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER">
|
||||
<!-- MATH
|
||||
\begin{displaymath}
|
||||
x \leftarrow x
|
||||
\end{displaymath}
|
||||
-->
|
||||
|
||||
<IMG
|
||||
WIDTH="43" HEIGHT="24" BORDER="0"
|
||||
SRC="img55.png"
|
||||
ALT="\begin{displaymath}x \leftarrow x \end{displaymath}">
|
||||
</DIV>
|
||||
<BR CLEAR="ALL">
|
||||
<P></P>
|
||||
where:
|
||||
<DL>
|
||||
<DT><STRONG><IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></STRONG></DT>
|
||||
<DD>is a global dense submatrix.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="3338"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 14:</STRONG>
|
||||
Data types</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
|
||||
<TR><TD ALIGN="LEFT"><IMG
|
||||
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img22.png"
|
||||
ALT="$\alpha$">, <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"></TD>
|
||||
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Integer</TD>
|
||||
<TD ALIGN="LEFT">psb_halo</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
|
||||
<TD ALIGN="LEFT">psb_halo</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
|
||||
<TD ALIGN="LEFT">psb_halo</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
|
||||
<TD ALIGN="LEFT">psb_halo</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
|
||||
<TD ALIGN="LEFT">psb_halo</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
</TD></TR>
|
||||
</TABLE>
|
||||
</DIV><P></P>
|
||||
<BR>
|
||||
|
||||
<P>
|
||||
<BR>
|
||||
<IMG
|
||||
WIDTH="395" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img56.png"
|
||||
ALT="\begin{lstlisting}
|
||||
call psb_halo(x, desc_a, info)
|
||||
call psb_halo(x, desc_a, info, work, data)
|
||||
\end{lstlisting}">
|
||||
<BR>
|
||||
<H1><A NAME="SECTION00060000000000000000">
|
||||
Communication routines</A>
|
||||
</H1>
|
||||
The routines in this chapter implement various global communication operators
|
||||
on vectors associated with a discretization mesh. For auxiliary communication
|
||||
routines not tied to a discretization space see <A HREF="node71.html#sec:toolsrout">6</A>.
|
||||
|
||||
<P>
|
||||
<DL>
|
||||
<DT><STRONG>Type:</STRONG></DT>
|
||||
<DD>Synchronous.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>global dense matrix <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
|
||||
containing numbers of type specified in
|
||||
Table <A HREF="#tab:f90halo">14</A>.
|
||||
</DD>
|
||||
<DT><STRONG>desc_a</STRONG></DT>
|
||||
<DD>contains data structures for communications.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>work</STRONG></DT>
|
||||
<DD>the work array.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array of the same type of <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">.
|
||||
</DD>
|
||||
<DT><STRONG>data</STRONG></DT>
|
||||
<DD>index list selector.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Specified as: an integer. Values:<code>psb_comm_halo_</code>,<code>psb_comm_mov_</code>,
|
||||
<code>psb_comm_ext_</code>, default: <code>psb_comm_halo_</code>. Chooses the
|
||||
index list on which to base the data exchange.
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>global dense result matrix <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Returned as: a rank one or two array
|
||||
containing numbers of type specified in
|
||||
Table <A HREF="#tab:f90halo">14</A>.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>the local portion of result submatrix <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value that contains an error code.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:try8x8"></A><A NAME="3340"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7:</STRONG>
|
||||
Sample discretization mesh.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
<IMG
|
||||
WIDTH="358" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img58.png"
|
||||
ALT="\includegraphics[scale=0.45]{figures/try8x8.eps}">
|
||||
|
||||
<!-- MATH
|
||||
$\rotatebox{-90}{\includegraphics[scale=0.45]{figures/try8x8}}$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="1" HEIGHT="2" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img57.png"
|
||||
ALT="\rotatebox{-90}{\includegraphics[scale=0.45]{figures/try8x8}}">
|
||||
|
||||
</DIV></TD></TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<FONT SIZE="+1"><B>Usage Example</B></FONT>
|
||||
Consider the discretization mesh depicted in fig. <A HREF="#fig:try8x8">7</A>,
|
||||
partitioned among two processes as shown by the dashed line; the data
|
||||
distribution is such that each process will own 32 entries in the
|
||||
index space, with a halo made of 8 entries placed at local indices 33
|
||||
through 40. If process 0 assigns an initial value of 1 to its entries
|
||||
in the <IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"> vector, and process 1 assigns a value of 2, then after a
|
||||
call to <code>psb_halo</code> the contents of the local vectors will be the
|
||||
following:
|
||||
<BR>
|
||||
<DIV ALIGN="CENTER">
|
||||
<TABLE CELLPADDING=3 ALIGN="CENTER">
|
||||
<TR><TD ALIGN="CENTER" COLSPAN=3><FONT SIZE="-1">
|
||||
Process 0</FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="CENTER" COLSPAN=3><FONT SIZE="-1">
|
||||
Process 1</FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
I </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> GLOB(I) </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> X(I) </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> I </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> GLOB(I) </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> X(I) </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
1 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 1 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 33 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
2 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 2 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 34 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
3 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 3 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 3 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 35 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
4 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 4 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 4 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 36 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
5 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 5 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 5 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 37 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
6 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 6 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 6 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 38 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
7 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 7 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 7 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 39 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
8 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 8 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 8 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 40 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
9 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 9 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 9 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 41 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
10 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 10 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 10 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 42 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
11 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 11 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 11 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 43 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
12 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 12 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 12 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 44 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
13 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 13 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 13 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 45 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
14 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 14 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 14 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 46 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
15 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 15 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 15 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 47 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
16 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 16 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 16 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 48 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
17 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 17 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 17 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 49 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
18 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 18 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 18 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 50 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
19 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 19 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 19 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 51 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
20 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 20 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 20 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 52 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
21 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 21 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 21 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 53 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
22 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 22 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 22 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 54 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
23 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 23 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 23 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 55 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
24 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 24 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 24 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 56 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
25 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 25 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 25 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 57 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
26 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 26 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 26 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 58 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
27 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 27 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 27 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 59 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
28 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 28 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 28 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 60 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
29 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 29 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 29 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 61 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
30 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 30 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 30 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 62 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
31 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 31 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 31 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 63 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
32 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 32 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 32 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 64 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
33 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 33 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 33 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 25 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
34 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 34 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 34 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 26 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
35 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 35 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 35 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 27 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
36 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 36 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 36 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 28 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
37 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 37 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 37 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 29 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
38 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 38 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 38 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 30 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
39 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 39 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 39 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 31 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
|
||||
40 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 40 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
|
||||
<TD ALIGN="LEFT"> </TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 40 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 32 </FONT></TD>
|
||||
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
|
||||
</TR>
|
||||
</TABLE></DIV>
|
||||
<BR>
|
||||
|
||||
<P>
|
||||
<HR>
|
||||
<!--Navigation Panel-->
|
||||
<A NAME="tex2html1065"
|
||||
HREF="node67.html">
|
||||
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
||||
<A NAME="tex2html1061"
|
||||
HREF="node65.html">
|
||||
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
||||
<A NAME="tex2html1055"
|
||||
HREF="node65.html">
|
||||
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
||||
<A NAME="tex2html1063"
|
||||
HREF="node1.html">
|
||||
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
||||
<BR>
|
||||
<B> Next:</B> <A NAME="tex2html1066"
|
||||
HREF="node67.html">psb_ovrl Overlap</A>
|
||||
<B> Up:</B> <A NAME="tex2html1062"
|
||||
HREF="node65.html">Communication routines</A>
|
||||
<B> Previous:</B> <A NAME="tex2html1056"
|
||||
HREF="node65.html">Communication routines</A>
|
||||
<B> <A NAME="tex2html1064"
|
||||
HREF="node1.html">Contents</A></B>
|
||||
<!--End of Navigation Panel-->
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL CLASS="ChildLinks">
|
||||
<LI><A NAME="tex2html1066"
|
||||
HREF="node67.html">psb_halo -- Halo Data Communication</A>
|
||||
<LI><A NAME="tex2html1067"
|
||||
HREF="node68.html">psb_ovrl -- Overlap Update</A>
|
||||
<LI><A NAME="tex2html1068"
|
||||
HREF="node69.html">psb_gather -- Gather Global Dense Matrix</A>
|
||||
<LI><A NAME="tex2html1069"
|
||||
HREF="node70.html">psb_scatter -- Scatter Global Dense Matrix</A>
|
||||
</UL>
|
||||
<!--End of Table of Child-Links-->
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
|
||||
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