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Salvatore Filippone
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>psb_geamaxs -- Generalized Infinity Norm</TITLE>
<META NAME="description" CONTENT="psb_geamaxs -- Generalized Infinity Norm">
<TITLE>psb_gedots -- Generalized Dot Product</TITLE>
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@@ -20,73 +20,90 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00055000000000000000">
psb_geamaxs -- Generalized Infinity Norm</A>
<H2><A NAME="SECTION00053000000000000000">
psb_gedots -- Generalized Dot Product</A>
</H2>
<P>
This subroutine computes a series of infinity norms on the columns of
a dense matrix <IMG
This subroutine computes a series of dot products among the columns of
two dense matrices <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">:
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$">:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \max_k |x(k,i)|
res(i) \leftarrow x(:,i)^T y(:,i)
\end{displaymath}
-->
<IMG
WIDTH="148" HEIGHT="36" BORDER="0"
SRC="img32.png"
ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">
WIDTH="150" HEIGHT="28" BORDER="0"
SRC="img27.png"
ALT="\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
If the matrices are complex, then the
usual convention applies, i.e. the conjugate transpose of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is
used. If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"> are of rank one, then <IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$"> is a scalar, else it
is a rank one array.
<P>
<PRE>
call psb_geamaxs(res, x, desc_a, info)
call psb_gedots(res, x, y, desc_a, info)
</PRE>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1865"></A>
<DIV ALIGN="CENTER"><A NAME="1945"></A>
<TABLE>
<CAPTION><STRONG>Table 5:</STRONG>
<CAPTION><STRONG>Table 3:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
@@ -94,28 +111,26 @@ Data types</CAPTION>
<TR><TD ALIGN="LEFT"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$"></TD>
<TD ALIGN="LEFT"><IMG
ALT="$res$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
ALT="$x$">, <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></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_geamaxs</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_geamaxs</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_geamaxs</TD>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_geamaxs</TD>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
</TABLE>
</DIV>
@@ -145,9 +160,38 @@ 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:f90mamax">5</A>.
Table&nbsp;<A HREF="#tab:f90mdot">3</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$">.
</DD>
<DT><STRONG>y</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$">.
<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&nbsp;<A HREF="#tab:f90mdot">3</A>. The rank of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"> must be the same of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -164,16 +208,20 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
<DD>
</DD>
<DT><STRONG>res</STRONG></DT>
<DD>is the infinity norm of the columns of <IMG
<DD>is the dot product of subvectors <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$">.
<BR>
Scope: <B>global</B>
<BR>
Intent: <B>out</B>.
<BR>
Specified as: a number or a rank-one array of long precision real numbers.
Specified as: a number or a rank-one array of the data type indicated
in Table&nbsp;<A HREF="#tab:f90dot">2</A>.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
@@ -191,26 +239,26 @@ An integer value; 0 means no error has been detected.
<P>
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