You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
471 lines
11 KiB
HTML
471 lines
11 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
|
|
|
<!--Converted with LaTeX2HTML 2008 (1.71)
|
|
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 -->
|
|
<HTML>
|
|
<HEAD>
|
|
<TITLE>psb_spsm -- Triangular System Solve</TITLE>
|
|
<META NAME="description" CONTENT="psb_spsm -- Triangular System Solve">
|
|
<META NAME="keywords" CONTENT="userhtml">
|
|
<META NAME="resource-type" CONTENT="document">
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2008">
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
<LINK REL="STYLESHEET" HREF="userhtml.css">
|
|
|
|
<LINK REL="previous" HREF="node58.html">
|
|
<LINK REL="up" HREF="node46.html">
|
|
<LINK REL="next" HREF="node60.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html953"
|
|
HREF="node60.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html949"
|
|
HREF="node46.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html945"
|
|
HREF="node58.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html951"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html954"
|
|
HREF="node60.html">Communication routines</A>
|
|
<B> Up:</B> <A NAME="tex2html950"
|
|
HREF="node46.html">Computational routines</A>
|
|
<B> Previous:</B> <A NAME="tex2html946"
|
|
HREF="node58.html">psb_spmm Sparse</A>
|
|
<B> <A NAME="tex2html952"
|
|
HREF="node1.html">Contents</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<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">
|
|
<!-- 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>
|
|
|
|
<P>
|
|
where:
|
|
<DL>
|
|
<DT><STRONG><IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$"></STRONG></DT>
|
|
<DD>is the global dense matrix <IMG
|
|
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img47.png"
|
|
ALT="$x_{:, :}$">
|
|
</DD>
|
|
<DT><STRONG><IMG
|
|
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img21.png"
|
|
ALT="$y$"></STRONG></DT>
|
|
<DD>is the global dense matrix <IMG
|
|
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img48.png"
|
|
ALT="$y_{:, :}$">
|
|
</DD>
|
|
<DT><STRONG><IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img51.png"
|
|
ALT="$T$"></STRONG></DT>
|
|
<DD>is the global sparse block triangular submatrix <IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img51.png"
|
|
ALT="$T$">
|
|
</DD>
|
|
<DT><STRONG><IMG
|
|
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img52.png"
|
|
ALT="$D$"></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="1804"></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"><IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img51.png"
|
|
ALT="$T$">, <IMG
|
|
WIDTH="14" HEIGHT="13" 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="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img52.png"
|
|
ALT="$D$">, <IMG
|
|
WIDTH="14" HEIGHT="13" 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_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>
|
|
<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="13" 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:f90spsm">13</A>.
|
|
</DD>
|
|
<DT><STRONG>t</STRONG></DT>
|
|
<DD>the global portion of the sparse matrix
|
|
<IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img51.png"
|
|
ALT="$T$">.
|
|
<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
|
|
<IMG
|
|
WIDTH="14" HEIGHT="13" 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:f90spsm">13</A>. The rank of <IMG
|
|
WIDTH="14" HEIGHT="13" 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:f90spsm">13</A>.
|
|
</DD>
|
|
<DT><STRONG>y</STRONG></DT>
|
|
<DD>the local portion of 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 type specified in
|
|
Table <A HREF="#tab:f90spsm">13</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="14" HEIGHT="13" 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>.
|
|
</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: <IMG
|
|
WIDTH="79" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img49.png"
|
|
ALT="$trans = N$">
|
|
<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: <IMG
|
|
WIDTH="76" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img53.png"
|
|
ALT="$unitd = U$">
|
|
<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
|
|
$diag(1) = 1 (no scaling)$
|
|
-->
|
|
<IMG
|
|
WIDTH="165" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img54.png"
|
|
ALT="$diag(1) = 1 (no scaling)$">
|
|
<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 <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$"> 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
|
|
<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: 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>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html953"
|
|
HREF="node60.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html949"
|
|
HREF="node46.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html945"
|
|
HREF="node58.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html951"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html954"
|
|
HREF="node60.html">Communication routines</A>
|
|
<B> Up:</B> <A NAME="tex2html950"
|
|
HREF="node46.html">Computational routines</A>
|
|
<B> Previous:</B> <A NAME="tex2html946"
|
|
HREF="node58.html">psb_spmm Sparse</A>
|
|
<B> <A NAME="tex2html952"
|
|
HREF="node1.html">Contents</A></B>
|
|
<!--End of Navigation Panel-->
|
|
|
|
</BODY>
|
|
</HTML>
|