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211 lines
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211 lines
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<H2><A NAME="SECTION000815000000000000000">
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psb_nrm2 -- Global 2-norm reduction</A>
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</H2>
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<P>
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<PRE>
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call psb_nrm2(icontxt, dat, root)
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</PRE>
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<P>
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This subroutine implements a 2-norm value reduction
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operation based on the underlying communication library.
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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>icontxt</STRONG></DT>
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<DD>the communication context identifying the virtual
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parallel machine.
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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: an integer variable.
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</DD>
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<DT><STRONG>dat</STRONG></DT>
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<DD>The local contribution to the global minimum.
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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 real variable, which may be a
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scalar, or a rank 1 array. Kind, rank and size must agree on all processes.
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</DD>
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<DT><STRONG>root</STRONG></DT>
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<DD>Process to hold the final value, or <SPAN CLASS="MATH"><IMG
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WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img82.png"
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ALT="$-1$"></SPAN> to make it available
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on 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: an integer value <!-- MATH
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$-1<= root <= np-1$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="165" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img136.png"
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ALT="$-1<= root <= np-1$"></SPAN>, default -1.
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<BR></DD>
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</DL>
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<P>
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<DL>
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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>dat</STRONG></DT>
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<DD>On destination process(es), the result of the 2-norm reduction.
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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>inout</B>.
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<BR>
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Specified as: a real variable, which may be a
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scalar, or a rank 1 array.
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<BR>
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Kind, rank and size must agree on all processes.
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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>This reduction is appropriate to compute the results of multiple
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(local) NRM2 operations at the same time.
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</LI>
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<LI>Denoting by <SPAN CLASS="MATH"><IMG
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WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img137.png"
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ALT="$dat_i$"></SPAN> the value of the variable <SPAN CLASS="MATH"><IMG
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WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img138.png"
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ALT="$dat$"></SPAN> on process
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<SPAN CLASS="MATH"><IMG
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WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$i$"></SPAN>, the output <SPAN CLASS="MATH"><IMG
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WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img29.png"
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ALT="$res$"></SPAN> is equivalent to the computation of
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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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res = \sqrt{\sum_i dat_i^2},
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\end{displaymath}
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-->
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<IMG
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WIDTH="119" HEIGHT="55" BORDER="0"
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SRC="img139.png"
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ALT="\begin{displaymath}res = \sqrt{\sum_i dat_i^2},\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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with care taken to avoid unnecessary overflow.
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</LI>
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<LI>The <code>dat</code> argument is both input and output, and its
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value may be changed even on processes different from the final
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result destination.
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</LI>
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</OL>
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<P>
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