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<B> Next:</B> <A NAME="tex2html996"
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HREF="node61.html">psb_genrm2s Generalized</A>
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<B> Up:</B> <A NAME="tex2html992"
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HREF="node52.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html986"
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HREF="node59.html">psb_geasums Generalized</A>
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<B> <A NAME="tex2html994"
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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="SECTION00058000000000000000">
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psb_norm2 -- 2-Norm of Vector</A>
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</H2>
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<P>
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This function computes the 2-norm of a vector <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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If <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> is a real vector
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it computes 2-norm 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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nrm2 \leftarrow \sqrt{x^T x}
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\end{displaymath}
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-->
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<IMG
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WIDTH="106" HEIGHT="24" BORDER="0"
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SRC="img41.png"
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ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\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="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> is a complex vector then it computes 2-norm 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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nrm2 \leftarrow \sqrt{x^H x}
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\end{displaymath}
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-->
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<IMG
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WIDTH="108" HEIGHT="24" BORDER="0"
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SRC="img42.png"
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ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\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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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="2016"></A>
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<TABLE>
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<CAPTION><STRONG>Table 8:</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="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img43.png"
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ALT="$nrm2$"></SPAN></TD>
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<TD ALIGN="LEFT"><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></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">Short Precision Real</TD>
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<TD ALIGN="LEFT">psb_genrm2</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">Long Precision Real</TD>
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<TD ALIGN="LEFT">psb_genrm2</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">Short Precision Complex</TD>
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<TD ALIGN="LEFT">psb_genrm2</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">Long Precision Complex</TD>
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<TD ALIGN="LEFT">psb_genrm2</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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<PRE>
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psb_genrm2(x, desc_a, info [,global])
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psb_norm2(x, desc_a, info [,global])
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</PRE>
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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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<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:f90nrm2">8</A>.
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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 2-norm of vector <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>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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Type: <B>required</B>
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<BR>
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Specified as: a long precision real number.
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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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<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 norms 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="481" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
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SRC="img44.png"
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ALT="\begin{lstlisting}
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vres(1) = psb_genrm2(x1,desc_a,info,global=.false.)
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vres(2)...
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...x3,desc_a,info,global=.false.)
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call psb_nrm2(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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