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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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<B> Next:</B> <A NAME="tex2html522"
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HREF="node29.html">psb_geamax Infinity-Norm</A>
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<B> Up:</B> <A NAME="tex2html518"
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HREF="node25.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html512"
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HREF="node27.html">psb_gedot Dot</A>
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<B> <A NAME="tex2html520"
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HREF="node1.html">Contents</A></B>
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<H2><A NAME="SECTION00053000000000000000">
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psb_gedots -- Generalized Dot Product</A>
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</H2>
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<P>
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This subroutine computes a series of dot products among the columns of
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two dense matrices <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> and <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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res(i) \leftarrow x(:,i)^T y(:,i)
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\end{displaymath}
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-->
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<IMG
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WIDTH="150" HEIGHT="28" BORDER="0"
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SRC="img33.png"
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ALT="\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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If the matrices are complex, then the
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usual convention applies, i.e. the conjugate transpose of <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> is
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used. If <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> and <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$"> are of rank one, then <IMG
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WIDTH="26" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img34.png"
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ALT="$res$"> is a scalar, else it
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is a rank one array.
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<P>
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<PRE>
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call psb_gedots(res, x, y, desc_a, info)
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</PRE>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1418"></A>
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<TABLE>
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<CAPTION><STRONG>Table 3:</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="26" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img34.png"
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ALT="$res$">, <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$">, <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$"></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_gedots</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_gedots</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_gedots</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_gedots</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>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="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.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: an array of rank one or two
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containing numbers of type specified in
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Table <A HREF="#tab:f90mdot">3</A>. The rank of <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> must be the same of <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">.
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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="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.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>in</B>.
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<BR>
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table <A HREF="#tab:f90mdot">3</A>. The rank of <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$"> must be the same of <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.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><B>On Return</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>res</STRONG></DT>
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<DD>is the dot product of subvectors <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> and <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">.
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<BR>
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Scope: <B>global</B>
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<BR>
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Intent: <B>out</B>.
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<BR>
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Specified as: a number or a rank-one array of the data type indicated
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in Table <A HREF="#tab:f90dot">2</A>.
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</DD>
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<DT><STRONG>info</STRONG></DT>
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<DD>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>out</B>.
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<BR>
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An integer value; 0 means no error has been detected.
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</DD>
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</DL>
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