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HREF="node64.html">psb_spmm Sparse</A>
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<B> <A NAME="tex2html1052"
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HREF="node1.html">Contents</A></B>
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<BR></DIV>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION000513000000000000000">
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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" CLASS="mathdisplay">
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<!-- MATH
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\begin{eqnarray*}
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y &\leftarrow& \alpha T^{-1} x + \beta y\\
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y &\leftarrow& \alpha D T^{-1} x + \beta y\\
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y &\leftarrow& \alpha T^{-1} D x + \beta y\\
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y &\leftarrow& \alpha T^{-T} x + \beta y\\
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y &\leftarrow& \alpha D T^{-T} x + \beta y\\
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y &\leftarrow& \alpha T^{-T} D x + \beta y\\
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y &\leftarrow& \alpha T^{-H} x + \beta y\\
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y &\leftarrow& \alpha D T^{-H} x + \beta y\\
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y &\leftarrow& \alpha T^{-H} D x + \beta y\\
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\end{eqnarray*}
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-->
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<IMG
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WIDTH="160" HEIGHT="239" BORDER="0"
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SRC="img54.png"
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ALT="\begin{eqnarray*}
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y &\leftarrow& \alpha T^{-1} x + \beta y\\
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y &\leftarrow& \al...
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...-H} x + \beta y\\
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y &\leftarrow& \alpha T^{-H} D x + \beta y\\
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\end{eqnarray*}"></DIV>
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<BR CLEAR="ALL"><P></P>
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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><SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN></STRONG></DT>
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<DD>is the global dense matrix <SPAN CLASS="MATH"><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="$x_{:, :}$"></SPAN>
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</DD>
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<DT><STRONG><SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN></STRONG></DT>
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<DD>is the global dense matrix <SPAN CLASS="MATH"><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="$y_{:, :}$"></SPAN>
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</DD>
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<DT><STRONG><SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img55.png"
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ALT="$T$"></SPAN></STRONG></DT>
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<DD>is the global sparse block triangular submatrix <SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img55.png"
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ALT="$T$"></SPAN>
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</DD>
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<DT><STRONG><SPAN CLASS="MATH"><IMG
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WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$D$"></SPAN></STRONG></DT>
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<DD>is the scaling diagonal matrix.
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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="2035"></A>
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<TABLE>
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<CAPTION><STRONG>Table 13:</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"><SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img55.png"
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ALT="$T$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$D$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img22.png"
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ALT="$\alpha$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img23.png"
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ALT="$\beta$"></SPAN></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 <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img22.png"
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ALT="$\alpha$"></SPAN>.
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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">13</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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<SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img55.png"
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ALT="$T$"></SPAN>.
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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 object type specified in
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§ <A HREF="node9.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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<SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>.
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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 or an object of type vdata<TT>psb_T_vect_type</TT>
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containing numbers of type specified in
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Table <A HREF="#tab:f90spsm">13</A>. The rank of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> must be the same of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN>.
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</DD>
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<DT><STRONG>beta</STRONG></DT>
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<DD>the scalar <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img23.png"
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ALT="$\beta$"></SPAN>.
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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">13</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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<SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN>.
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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 or an object of type vdata<TT>psb_T_vect_type</TT>
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containing numbers of type specified in
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Table <A HREF="#tab:f90spsm">13</A>. The rank of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN> must be the same of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>.
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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: an object 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>
|
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|
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|
<BR>
|
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|
|
Intent: <B>in</B>.
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|
<BR>
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|
Default: <SPAN CLASS="MATH"><IMG
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|
WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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|
SRC="img53.png"
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ALT="$trans = N$"></SPAN>
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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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|
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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>
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<DD>the operation is with right scaling.
|
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</DD>
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</DL>
|
|
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|
|
Scope: <B>global</B>
|
|
|
|
|
<BR>
|
|
|
|
|
Type: <B>optional</B>
|
|
|
|
|
<BR>
|
|
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|
|
Intent: <B>in</B>.
|
|
|
|
|
<BR>
|
|
|
|
|
Default: <SPAN CLASS="MATH"><IMG
|
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|
WIDTH="76" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img57.png"
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|
ALT="$unitd = U$"></SPAN>
|
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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>choice</STRONG></DT>
|
|
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|
|
<DD>specifies the update of overlap elements to be performed
|
|
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|
on exit:
|
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|
<DL>
|
|
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|
|
<DT></DT>
|
|
|
|
|
<DD><code>psb_none_</code>
|
|
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|
</DD>
|
|
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|
|
<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="img58.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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<B> Next:</B> <A NAME="tex2html1054"
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HREF="node66.html">Communication routines</A>
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<B> Up:</B> <A NAME="tex2html1050"
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HREF="node52.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html1046"
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HREF="node64.html">psb_spmm Sparse</A>
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<B> <A NAME="tex2html1052"
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HREF="node1.html">Contents</A></B> </DIV>
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