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<H2><A NAME="SECTION00056000000000000000">
psb_norm1 -- 1-Norm of Vector</A>
</H2>
<P>
This function computes the 1-norm of a vector <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<BR>
If <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> is a real vector
it computes 1-norm as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
asum \leftarrow \|x_i\|
\end{displaymath}
-->
<IMG
WIDTH="92" HEIGHT="29" BORDER="0"
SRC="img35.png"
ALT="\begin{displaymath}asum \leftarrow \Vert x_i\Vert\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> is a complex vector then it computes 1-norm as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
asum \leftarrow \|re(x)\|_1 + \|im(x)\|_1
\end{displaymath}
-->
<IMG
WIDTH="206" HEIGHT="29" BORDER="0"
SRC="img36.png"
ALT="\begin{displaymath}asum \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
<P>
<PRE>
psb_geasum(x, desc_a, info [,global])
psb_norm1(x, desc_a, info [,global])
</PRE>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="2028"></A>
<TABLE>
<CAPTION><STRONG>Table 6:</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="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img37.png"
ALT="$asum$"></SPAN></TD>
<TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_geasum</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_geasum</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_geasum</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_geasum</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:f90asum">6</A>.
</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 1-norm of vector <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<BR>
Scope: <B>global</B> unless the optional variable
<code>global=.false.</code> has been specified
<BR>
Specified as: a long precision real number.
</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 norms at the same
time; in this case, it is possible to improve the runtime efficiency
by using the following scheme:
<BR>
<IMG
WIDTH="481" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
SRC="img38.png"
ALT="\begin{lstlisting}
vres(1) = psb_geasum(x1,desc_a,info,global=.false.)
vres(2)...
...(x3,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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