You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
267 lines
6.6 KiB
HTML
267 lines
6.6 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
|
|
|
<!--Converted with LaTeX2HTML 2008 (1.71)
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
* with significant contributions from:
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
<HTML>
|
|
<HEAD>
|
|
<TITLE>psb_geasums -- Generalized 1-Norm of Vector</TITLE>
|
|
<META NAME="description" CONTENT="psb_geasums -- Generalized 1-Norm of Vector">
|
|
<META NAME="keywords" CONTENT="userhtml">
|
|
<META NAME="resource-type" CONTENT="document">
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2008">
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
<LINK REL="STYLESHEET" HREF="userhtml.css">
|
|
|
|
<LINK REL="next" HREF="node55.html">
|
|
<LINK REL="previous" HREF="node53.html">
|
|
<LINK REL="up" HREF="node47.html">
|
|
<LINK REL="next" HREF="node55.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html904"
|
|
HREF="node55.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html900"
|
|
HREF="node47.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html894"
|
|
HREF="node53.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html902"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html905"
|
|
HREF="node55.html">psb_norm2 2-Norm</A>
|
|
<B> Up:</B> <A NAME="tex2html901"
|
|
HREF="node47.html">Computational routines</A>
|
|
<B> Previous:</B> <A NAME="tex2html895"
|
|
HREF="node53.html">psb_norm1 1-Norm</A>
|
|
<B> <A NAME="tex2html903"
|
|
HREF="node1.html">Contents</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H2><A NAME="SECTION00057000000000000000">
|
|
psb_geasums -- Generalized 1-Norm of Vector</A>
|
|
</H2>
|
|
|
|
<P>
|
|
This subroutine computes a series of 1-norms on the columns of
|
|
a dense matrix <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$">:
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
res(i) \leftarrow \max_k |x(k,i)|
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="147" HEIGHT="36" BORDER="0"
|
|
SRC="img32.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 <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$">.
|
|
<BR>
|
|
If <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$"> is a real vector
|
|
it computes 1-norm as:
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
res(i) \leftarrow \|x_i\|
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="94" HEIGHT="28" BORDER="0"
|
|
SRC="img36.png"
|
|
ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
else if <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$"> is a complex vector then it computes 1-norm as:
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="206" HEIGHT="28" BORDER="0"
|
|
SRC="img37.png"
|
|
ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
|
|
<P>
|
|
<PRE>
|
|
call psb_geasums(res, x, desc_a, info)
|
|
</PRE>
|
|
|
|
<P>
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER"><A NAME="1819"></A>
|
|
<TABLE>
|
|
<CAPTION><STRONG>Table 7:</STRONG>
|
|
Data types</CAPTION>
|
|
<TR><TD>
|
|
<DIV ALIGN="CENTER">
|
|
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
|
|
<TR><TD ALIGN="LEFT"><IMG
|
|
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img28.png"
|
|
ALT="$res$"></TD>
|
|
<TD ALIGN="LEFT"><IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$"></TD>
|
|
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
|
|
<TD ALIGN="LEFT">Short Precision Real</TD>
|
|
<TD ALIGN="LEFT">psb_geasums</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
|
|
<TD ALIGN="LEFT">Long Precision Real</TD>
|
|
<TD ALIGN="LEFT">psb_geasums</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
|
|
<TD ALIGN="LEFT">Short Precision Complex</TD>
|
|
<TD ALIGN="LEFT">psb_geasums</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
|
|
<TD ALIGN="LEFT">Long Precision Complex</TD>
|
|
<TD ALIGN="LEFT">psb_geasums</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
|
|
<IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$">.
|
|
|
|
<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:f90asums">7</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>.
|
|
|
|
<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) <IMG
|
|
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img20.png"
|
|
ALT="$x$">.
|
|
<BR>
|
|
Scope: <B>global</B>
|
|
<BR>
|
|
Intent: <B>out</B>.
|
|
<BR>
|
|
Short as: a long precision real number.
|
|
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>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html904"
|
|
HREF="node55.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html900"
|
|
HREF="node47.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html894"
|
|
HREF="node53.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html902"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html905"
|
|
HREF="node55.html">psb_norm2 2-Norm</A>
|
|
<B> Up:</B> <A NAME="tex2html901"
|
|
HREF="node47.html">Computational routines</A>
|
|
<B> Previous:</B> <A NAME="tex2html895"
|
|
HREF="node53.html">psb_norm1 1-Norm</A>
|
|
<B> <A NAME="tex2html903"
|
|
HREF="node1.html">Contents</A></B>
|
|
<!--End of Navigation Panel-->
|
|
|
|
</BODY>
|
|
</HTML>
|