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<H2><A NAME="SECTION00052000000000000000">
psb_gedot -- Dot Product</A>
</H2>
<P>
This function computes dot product between two vectors <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> and
<SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN>.
<BR>
If <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> and <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN> are real vectors
it computes dot-product as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
dot \leftarrow x^T y
\end{displaymath}
-->
<IMG
WIDTH="74" HEIGHT="27" BORDER="0"
SRC="img24.png"
ALT="\begin{displaymath}dot \leftarrow x^T y\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
Else if <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> and <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN> are complex vectors then it computes dot-product as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
dot \leftarrow x^H y
\end{displaymath}
-->
<IMG
WIDTH="75" HEIGHT="27" BORDER="0"
SRC="img25.png"
ALT="\begin{displaymath}dot \leftarrow x^H y\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
<P>
<PRE>
psb_gedot(x, y, desc_a, info [,global])
</PRE>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="2024"></A>
<TABLE>
<CAPTION><STRONG>Table 2:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$dot$"></SPAN>, <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>, <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_gedot</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>x</STRONG></DT>
<DD>the local portion of global dense matrix
<SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<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:f90dot">2</A>. The rank of <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> must be the same of <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN>.
</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>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:f90dot">2</A>. The rank of <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN> must be the same of <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
</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>global</STRONG></DT>
<DD>Specifies whether the computation should include the
global reduction across all processes.
<BR>
Scope: <B>global</B>
<BR>
Type: <B>optional</B>.
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a logical scalar.
Default: <code>global=.true.</code>
<BR>
<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>Function value</STRONG></DT>
<DD>is the dot product of vectors <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> and <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN>.
<BR>
Scope: <B>global</B> unless the optional variable
<code>global=.false.</code> has been specified
<BR>
Specified as: a number of the data type indicated in Table <A HREF="#tab:f90dot">2</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>
<BIG CLASS="LARGE"><B>Notes</B></BIG>
<OL>
<LI>The computation of a global result requires a global
communication, which entails a significant overhead. It may be
necessary and/or advisable to compute multiple dot products at the same
time; in this case, it is possible to improve the runtime efficiency
by using the following scheme:
<BR>
<IMG
WIDTH="500" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
SRC="img27.png"
ALT="\begin{lstlisting}
vres(1) = psb_gedot(x1,y1,desc_a,info,global=.false.)
vres(...
...,y3,desc_a,info,global=.false.)
call psb_sum(ictxt,vres(1:3))
\end{lstlisting}">
<BR>
In this way the global communication, which for small sizes is a
latency-bound operation, is invoked only once.
</LI>
</OL>
<P>
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