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Updated docs with fnd_owner adn set_p_adjcncy
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Salvatore Filippone
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@@ -3,8 +3,8 @@
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<TITLE>psb_gedot -- Dot Product</TITLE>
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<TITLE>Heap data structure</TITLE>
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<B> Next:</B> <A NAME="tex2html924"
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HREF="node55.html">psb_gedots Generalized</A>
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<B> Up:</B> <A NAME="tex2html920"
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HREF="node52.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html914"
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HREF="node53.html">psb_geaxpby General</A>
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<B> <A NAME="tex2html922"
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<B> Next:</B> <A NAME="tex2html920"
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HREF="node55.html">Computational routines</A>
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<B> Up:</B> <A NAME="tex2html916"
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HREF="node9.html">Data Structures and Classes</A>
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<B> Previous:</B> <A NAME="tex2html912"
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HREF="node53.html">Preconditioner data structure</A>
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<B> <A NAME="tex2html918"
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HREF="node1.html">Contents</A></B>
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<BR>
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<BR></DIV>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00052000000000000000">
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psb_gedot -- Dot Product</A>
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<H2><A NAME="SECTION00045000000000000000">
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Heap data structure</A>
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</H2>
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<P>
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This function computes dot product between two vectors <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> and
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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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If <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> and <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> are real vectors
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it computes dot-product as:
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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<!-- MATH
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\begin{displaymath}
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dot \leftarrow x^T y
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\end{displaymath}
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-->
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<IMG
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WIDTH="74" HEIGHT="27" BORDER="0"
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SRC="img24.png"
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ALT="\begin{displaymath}dot \leftarrow x^T y\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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Else if <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> and <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> are complex vectors then it computes dot-product as:
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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<!-- MATH
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\begin{displaymath}
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dot \leftarrow x^H y
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\end{displaymath}
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-->
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<IMG
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WIDTH="76" HEIGHT="27" BORDER="0"
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SRC="img25.png"
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ALT="\begin{displaymath}dot \leftarrow x^H y\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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<P>
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<PRE>
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psb_gedot(x, y, desc_a, info [,global])
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</PRE>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="2024"></A>
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<TABLE>
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<CAPTION><STRONG>Table 2:</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="25" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$dot$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" 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></TD>
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<TD ALIGN="LEFT"><B>Function</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_gedot</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_gedot</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_gedot</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_gedot</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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Among the tools routines of sec. <A HREF="node74.html#sec:toolsrout">6</A>, we have a number
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of sorting utilities; the heap sort is implemented in terms of heaps
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having the following signatures:
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Synchronous.
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<DT><STRONG><TT>psb_T_heap</TT></STRONG></DT>
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<DD>: a heap containing elements of type T, where T
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can be <code>i,s,c,d,z</code> for integer, real and complex data;
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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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<SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" 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:f90dot">2</A>. The rank of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" 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>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>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:f90dot">2</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="13" 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>global</STRONG></DT>
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<DD>Specifies whether the computation should include the
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global reduction across all processes.
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<BR>
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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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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a logical scalar.
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Default: <code>global=.true.</code>
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<BR>
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<P>
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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>Function value</STRONG></DT>
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<DD>is the dot product of vectors <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> and <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>global</B> unless the optional variable
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<code>global=.false.</code> has been specified
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<BR>
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Specified as: a number of the data type indicated 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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<DT><STRONG><TT>psb_T_idx_heap</TT></STRONG></DT>
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<DD>: a heap containing elements of type T, as
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above, together with an integer index.
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</DD>
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</DL>
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Given a heap object, the following methods are defined on it:
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<DL>
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<DT><STRONG>init</STRONG></DT>
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<DD>Initialize memory; also choose ascending or descending
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order;
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</DD>
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<DT><STRONG>howmany</STRONG></DT>
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<DD>Current heap occupancy;
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</DD>
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<DT><STRONG>insert</STRONG></DT>
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<DD>Add an item (or an item and its index);
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</DD>
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<DT><STRONG>get_first</STRONG></DT>
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<DD>Remove and return the first element;
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</DD>
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<DT><STRONG>dump</STRONG></DT>
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<DD>Print on file;
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</DD>
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<DT><STRONG>free</STRONG></DT>
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<DD>Release memory.
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</DD>
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</DL>
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These objects are used in MLD2P4 to implement the factorization
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algorithms.
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<P>
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<BIG CLASS="LARGE"><B>Notes</B></BIG>
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<OL>
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<LI>The computation of a global result requires a global
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communication, which entails a significant overhead. It may be
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necessary and/or advisable to compute multiple dot products at the same
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time; in this case, it is possible to improve the runtime efficiency
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by using the following scheme:
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<BR>
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<IMG
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WIDTH="499" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
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SRC="img27.png"
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ALT="\begin{lstlisting}
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vres(1) = psb_gedot(x1,y1,desc_a,info,global=.false.)
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vres(...
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...,y3,desc_a,info,global=.false.)
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call psb_sum(ictxt,vres(1:3))
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\end{lstlisting}">
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<BR>
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In this way the global communication, which for small sizes is a
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latency-bound operation, is invoked only once.
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</LI>
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</OL>
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<P>
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<B> Next:</B> <A NAME="tex2html924"
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HREF="node55.html">psb_gedots Generalized</A>
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<B> Up:</B> <A NAME="tex2html920"
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HREF="node52.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html914"
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HREF="node53.html">psb_geaxpby General</A>
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<B> <A NAME="tex2html922"
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HREF="node1.html">Contents</A></B> </DIV>
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