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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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<B> Next:</B> <A NAME="tex2html811"
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HREF="node48.html">psb_spmm Sparse</A>
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<B> <A NAME="tex2html809"
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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="SECTION000512000000000000000">
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psb_spsm -- Triangular System Solve</A>
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</H2>
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<P>
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This subroutine computes the Triangular System Solve:
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<P>
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<P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{eqnarray*}
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y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\
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y &\leftarrow& \alpha D P_r T^{-1} P_c x + \beta y\\
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y &\leftarrow& \alpha P_r T^{-1} P_c D x + \beta y\\
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y &\leftarrow& \alpha P_r T^{-T} P_c x + \beta y\\
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y &\leftarrow& \alpha D P_r T^{-T} P_c x + \beta y\\
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y &\leftarrow& \alpha P_r T^{-T} P_c D x + \beta y\\
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y &\leftarrow& \alpha P_r T^{-H} P_c x + \beta y\\
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y &\leftarrow& \alpha D P_r T^{-H} P_c x + \beta y\\
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y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\
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\end{eqnarray*}
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-->
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<IMG
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WIDTH="193" HEIGHT="239" BORDER="0"
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SRC="img55.png"
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ALT="\begin{eqnarray*}
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y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\
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y &\leftar...
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...\beta y\\
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y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\
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\end{eqnarray*}"></DIV>
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<BR CLEAR="ALL"><P></P>
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<P>
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where:
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<DL>
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<DT><STRONG><IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$"></STRONG></DT>
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<DD>is the global dense submatrix <IMG
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WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img51.png"
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ALT="$x_{:, :}$">
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</DD>
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<DT><STRONG><IMG
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WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img26.png"
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ALT="$y$"></STRONG></DT>
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<DD>is the global dense submatrix <IMG
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WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img52.png"
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ALT="$y_{:, :}$">
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</DD>
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<DT><STRONG><IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$T$"></STRONG></DT>
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<DD>is the global sparse block triangular submatrix <IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$T$">
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</DD>
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<DT><STRONG><IMG
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WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img57.png"
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ALT="$D$"></STRONG></DT>
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<DD>is the scaling diagonal matrix.
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</DD>
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<DT><STRONG><IMG
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WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img53.png"
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ALT="$P_r, P_c$"></STRONG></DT>
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<DD>are the permutation matrices.
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</DD>
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</DL>
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<P>
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<PRE>
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call psb_spsm(alpha, t, x, beta, y, desc_a, info)
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call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
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& trans, unit, choice, diag, work)
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</PRE>
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1527"></A>
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<TABLE>
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<CAPTION><STRONG>Table 12:</STRONG>
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Data types</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
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<TR><TD ALIGN="LEFT"><IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$T$">, <IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">, <IMG
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WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img26.png"
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ALT="$y$">, <IMG
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WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img57.png"
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ALT="$D$">, <IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img27.png"
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ALT="$\alpha$">, <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img28.png"
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ALT="$\beta$"></TD>
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<TD ALIGN="LEFT"><B>Subroutine</B></TD>
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</TR>
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<TR><TD ALIGN="LEFT">Short Precision Real</TD>
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<TD ALIGN="LEFT">psb_spsm</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Long Precision Real</TD>
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<TD ALIGN="LEFT">psb_spsm</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
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<TD ALIGN="LEFT">psb_spsm</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
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<TD ALIGN="LEFT">psb_spsm</TD>
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</TR>
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</TABLE>
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</DIV>
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</TD></TR>
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</TABLE>
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</DIV><P></P>
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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>Synchronous.
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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>alpha</STRONG></DT>
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<DD>the scalar <IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img27.png"
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ALT="$\alpha$">.
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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: a number of the data type indicated in
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Table <A HREF="#tab:f90spsm">12</A>.
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</DD>
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<DT><STRONG>t</STRONG></DT>
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<DD>the global portion of the sparse matrix
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<IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$T$">.
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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 structured data type specified in
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§ <A HREF="node8.html#sec:datastruct">3</A>.
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</DD>
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<DT><STRONG>x</STRONG></DT>
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<DD>the local portion of global dense matrix
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<IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">.
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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 rank one or two array
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containing numbers of type specified in
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Table <A HREF="#tab:f90spsm">12</A>. The rank of <IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$"> must be the same of <IMG
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WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img26.png"
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ALT="$y$">.
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</DD>
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<DT><STRONG>beta</STRONG></DT>
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<DD>the scalar <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img28.png"
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ALT="$\beta$">.
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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: a number of the data type indicated in Table <A HREF="#tab:f90spsm">12</A>.
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</DD>
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<DT><STRONG>y</STRONG></DT>
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<DD>the local portion of global dense matrix
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<IMG
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WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img26.png"
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ALT="$y$">.
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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>inout</B>.
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<BR>
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Specified as: a rank one or two array
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containing numbers of type specified in
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Table <A HREF="#tab:f90spsm">12</A>. The rank of <IMG
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WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img26.png"
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ALT="$y$"> must be the same of <IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">.
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</DD>
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<DT><STRONG>desc_a</STRONG></DT>
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<DD>contains data structures for communications.
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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 structured data of type descdata<TT>psb_desc_type</TT>.
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</DD>
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<DT><STRONG>trans</STRONG></DT>
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<DD>specify with <EM>unitd</EM> the operation to perform.
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<DL>
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<DT><STRONG>trans = 'N'</STRONG></DT>
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<DD>the operation is with no transposed matrix
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</DD>
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<DT><STRONG>trans = 'T'</STRONG></DT>
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<DD>the operation is with transposed matrix.
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</DD>
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<DT><STRONG>trans = 'C'</STRONG></DT>
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<DD>the operation is with conjugate transposed matrix.
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|
</DD>
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|
</DL>
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|
Scope: <B>global</B>
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|
<BR>
|
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|
|
Type: <B>optional</B>
|
|
|
|
|
<BR>
|
|
|
|
|
Intent: <B>in</B>.
|
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|
|
<BR>
|
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|
|
|
Default: <IMG
|
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|
|
WIDTH="78" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img54.png"
|
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ALT="$trans = N$">
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|
<BR>
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|
Specified as: a character variable.
|
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|
</DD>
|
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<DT><STRONG>unitd</STRONG></DT>
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<DD>specify with <EM>trans</EM> the operation to perform.
|
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<DL>
|
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<DT><STRONG>unitd = 'U'</STRONG></DT>
|
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|
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|
<DD>the operation is with no scaling
|
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</DD>
|
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<DT><STRONG>unitd = 'L'</STRONG></DT>
|
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|
|
<DD>the operation is with left scaling
|
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</DD>
|
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|
<DT><STRONG>unitd = 'R'</STRONG></DT>
|
|
|
|
|
<DD>the operation is with right scaling.
|
|
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|
|
</DD>
|
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|
|
|
</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="img58.png"
|
|
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|
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
|
|
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|
|
on exit:
|
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|
|
<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="img59.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="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img25.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="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img26.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>
|
|
|
|
|
<HR>
|
|
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|
|
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<B> Next:</B> <A NAME="tex2html811"
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HREF="node50.html">Communication routines</A>
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<B> Up:</B> <A NAME="tex2html807"
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HREF="node37.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html803"
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HREF="node48.html">psb_spmm Sparse</A>
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<B> <A NAME="tex2html809"
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HREF="node1.html">Contents</A></B>
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