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<TITLE>psb_geasums -- Generalized 1-Norm of Vector</TITLE>
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<H2><A NAME="SECTION00057000000000000000">
psb_geasums -- Generalized 1-Norm of Vector</A>
<H2><A NAME="SECTION00054000000000000000">
psb_normi -- Infinity-Norm of Vector</A>
</H2>
<P>
This subroutine computes a series of 1-norms on the columns of
a dense matrix <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \max_k |x(k,i)|
\end{displaymath}
-->
<IMG
WIDTH="147" HEIGHT="36" BORDER="0"
SRC="img34.png"
ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
This function computes the 1-norm of a vector <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
This function computes
the infinity-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="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> is a real vector
it computes 1-norm as:
ALT="$x$"></SPAN> is a real vector
it computes infinity norm as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \|x_i\|
amax \leftarrow \max_i |x_i|
\end{displaymath}
-->
<IMG
WIDTH="94" HEIGHT="28" BORDER="0"
SRC="img39.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">
WIDTH="119" HEIGHT="36" BORDER="0"
SRC="img30.png"
ALT="\begin{displaymath}amax \leftarrow \max_i \vert x_i\vert\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
else if <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> is a complex vector then it computes 1-norm as:
ALT="$x$"></SPAN> is a complex vector then it computes the infinity-norm as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1
amax \leftarrow \max_i {(|re(x_i)| + |im(x_i)|)}
\end{displaymath}
-->
<IMG
WIDTH="206" HEIGHT="28" BORDER="0"
SRC="img40.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">
WIDTH="233" HEIGHT="36" BORDER="0"
SRC="img31.png"
ALT="\begin{displaymath}amax \leftarrow \max_i {(\vert re(x_i)\vert + \vert im(x_i)\vert)}\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
<P>
<PRE>
call psb_geasums(res, x, desc_a, info)
psb_geamax(x, desc_a, info [,global])
psb_normi(x, desc_a, info [,global])
</PRE>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="2029"></A>
<DIV ALIGN="CENTER"><A NAME="2105"></A>
<TABLE>
<CAPTION><STRONG>Table 7:</STRONG>
<CAPTION><STRONG>Table 4:</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="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img29.png"
ALT="$res$"></SPAN></TD>
WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img32.png"
ALT="$amax$"></SPAN></TD>
<TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></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_geasums</TD>
<TD ALIGN="LEFT">psb_geamax</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_geasums</TD>
<TD ALIGN="LEFT">psb_geamax</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_geasums</TD>
<TD ALIGN="LEFT">psb_geamax</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_geasums</TD>
<TD ALIGN="LEFT">psb_geamax</TD>
</TR>
</TABLE>
</DIV>
@@ -176,7 +158,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
@@ -187,9 +169,9 @@ 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>
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&nbsp;<A HREF="#tab:f90asums">7</A>.
Table&nbsp;<A HREF="#tab:f90amax">4</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -201,24 +183,36 @@ Type: <B>required</B>
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>res</STRONG></DT>
<DD>contains the 1-norm of (the columns of) <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
<DT><STRONG>Function value</STRONG></DT>
<DD>is the infinity 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>
Scope: <B>global</B> unless the optional variable
<code>global=.false.</code> has been specified
<BR>
Intent: <B>out</B>.
<BR>
Short as: a long precision real number.
Specified as: a long precision real number.
Specified as: a long precision real number.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
@@ -233,30 +227,55 @@ 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="img33.png"
ALT="\begin{lstlisting}
vres(1) = psb_geamax(x1,desc_a,info,global=.false.)
vres(2)...
...(x3,desc_a,info,global=.false.)
call psb_amx(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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