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<H2><A NAME="SECTION000512000000000000000">
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 P_r T^{-1} P_c x + \beta y\\
y &\leftarrow& \alpha D P_r T^{-1} P_c x + \beta y\\
y &\leftarrow& \alpha P_r T^{-1} P_c D x + \beta y\\
y &\leftarrow& \alpha P_r T^{-T} P_c x + \beta y\\
y &\leftarrow& \alpha D P_r T^{-T} P_c x + \beta y\\
y &\leftarrow& \alpha P_r T^{-T} P_c D x + \beta y\\
y &\leftarrow& \alpha P_r T^{-H} P_c x + \beta y\\
y &\leftarrow& \alpha D P_r T^{-H} P_c x + \beta y\\
y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\
\end{eqnarray*}
-->
<IMG
WIDTH="194" HEIGHT="239" BORDER="0"
SRC="img57.png"
ALT="\begin{eqnarray*}
y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\
y &\leftar...
...\beta y\\
y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\
\end{eqnarray*}"></DIV>
<BR CLEAR="ALL"><P></P>
<P>
where:
<DL>
<DT><STRONG><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.png"
ALT="$x$"></STRONG></DT>
<DD>is the global dense submatrix <IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img53.png"
ALT="$x_{:, :}$">
</DD>
<DT><STRONG><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img28.png"
ALT="$y$"></STRONG></DT>
<DD>is the global dense submatrix <IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img54.png"
ALT="$y_{:, :}$">
</DD>
<DT><STRONG><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img58.png"
ALT="$T$"></STRONG></DT>
<DD>is the global sparse block triangular submatrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img58.png"
ALT="$T$">
</DD>
<DT><STRONG><IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img59.png"
ALT="$D$"></STRONG></DT>
<DD>is the scaling diagonal matrix.
</DD>
<DT><STRONG><IMG
WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img55.png"
ALT="$P_r, P_c$"></STRONG></DT>
<DD>are the permutation matrices.
</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="1449"></A>
<TABLE>
<CAPTION><STRONG>Table 12:</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="img58.png"
ALT="$T$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.png"
ALT="$x$">, <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img28.png"
ALT="$y$">, <IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img59.png"
ALT="$D$">, <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img29.png"
ALT="$\alpha$">, <IMG
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img30.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="14" ALIGN="BOTTOM" BORDER="0"
SRC="img29.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">12</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="img58.png"
ALT="$T$">.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a structured data type specified in
§ <A HREF="node8.html#sec:datastruct">3</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="img27.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
containing numbers of type specified in
Table <A HREF="#tab:f90spsm">12</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img28.png"
ALT="$y$">.
</DD>
<DT><STRONG>beta</STRONG></DT>
<DD>the scalar <IMG
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img30.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">12</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="img28.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
containing numbers of type specified in
Table <A HREF="#tab:f90spsm">12</A>. The rank of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img28.png"
ALT="$y$"> must be the same of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.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: a structured data 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="15" ALIGN="BOTTOM" BORDER="0"
SRC="img56.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="15" ALIGN="BOTTOM" BORDER="0"
SRC="img60.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="164" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img61.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">12</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="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.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="img28.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">12</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>
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