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Added entrywise inversion and documentation for vec-vec operation

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cirdans-home
2019-11-21 13:56:22 +01:00
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<!--Converted with LaTeX2HTML 2018 (Released Feb 1, 2018) -->
<HTML>
<HEAD>
<TITLE>psb_nrm2 -- Global 2-norm reduction</TITLE>
<META NAME="description" CONTENT="psb_nrm2 -- Global 2-norm reduction">
<TITLE>psb_min -- Global minimum</TITLE>
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<H2><A NAME="SECTION000815000000000000000">
psb_nrm2 -- Global 2-norm reduction</A>
<H2><A NAME="SECTION000812000000000000000">
psb_min -- Global minimum</A>
</H2>
<P>
<PRE>
call psb_nrm2(icontxt, dat, root)
call psb_min(icontxt, dat, root)
</PRE>
<P>
This subroutine implements a 2-norm value reduction
This subroutine implements a minimum value reduction
operation based on the underlying communication library.
<DL>
<DT><STRONG>Type:</STRONG></DT>
@@ -88,13 +88,13 @@ Type: <B>required</B>.
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a real variable, which may be a
scalar, or a rank 1 array. Kind, rank and size must agree on all processes.
Specified as: an integer or real variable, which may be a
scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes.
</DD>
<DT><STRONG>root</STRONG></DT>
<DD>Process to hold the final value, or <SPAN CLASS="MATH"><IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img82.png"
WIDTH="24" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img88.png"
ALT="$-1$"></SPAN> to make it available
on all processes.
<BR>
@@ -108,8 +108,8 @@ Specified as: an integer value <!-- MATH
$-1<= root <= np-1$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="165" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img141.png"
WIDTH="165" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img147.png"
ALT="$-1&lt;= root &lt;= np-1$"></SPAN>, default -1.
<BR></DD>
</DL>
@@ -120,7 +120,7 @@ Specified as: an integer value <!-- MATH
<DD>
</DD>
<DT><STRONG>dat</STRONG></DT>
<DD>On destination process(es), the result of the 2-norm reduction.
<DD>On destination process(es), the result of the minimum operation.
<BR>
Scope: <B>global</B>.
<BR>
@@ -128,10 +128,10 @@ Type: <B>required</B>.
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a real variable, which may be a
scalar, or a rank 1 array.
Specified as: an integer or real variable, which may be a
scalar, or a rank 1 or 2 array.
<BR>
Kind, rank and size must agree on all processes.
Type, kind, rank and size must agree on all processes.
</DD>
</DL>
@@ -139,70 +139,38 @@ Kind, rank and size must agree on all processes.
<BIG CLASS="LARGE"><B>Notes</B></BIG>
<OL>
<LI>This reduction is appropriate to compute the results of multiple
(local) NRM2 operations at the same time.
</LI>
<LI>Denoting by <SPAN CLASS="MATH"><IMG
WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img142.png"
ALT="$dat_i$"></SPAN> the value of the variable <SPAN CLASS="MATH"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img143.png"
ALT="$dat$"></SPAN> on process
<SPAN CLASS="MATH"><IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"></SPAN>, the output <SPAN CLASS="MATH"><IMG
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img29.png"
ALT="$res$"></SPAN> is equivalent to the computation of
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
res = \sqrt{\sum_i dat_i^2},
\end{displaymath}
-->
<IMG
WIDTH="119" HEIGHT="55" BORDER="0"
SRC="img144.png"
ALT="\begin{displaymath}res = \sqrt{\sum_i dat_i^2},\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
with care taken to avoid unnecessary overflow.
</LI>
<LI>The <code>dat</code> argument is both input and output, and its
value may be changed even on processes different from the final
result destination.
</LI>
<LI>The <code>dat</code> argument may also be a long integer scalar.
</LI>
</OL>
<P>
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