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Salvatore Filippone
2011-12-16 16:45:25 +00:00
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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_gedot -- Dot Product</TITLE>
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<TITLE>psb_gedots -- Generalized Dot Product</TITLE>
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@@ -20,132 +20,117 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00052000000000000000">
psb_gedot -- Dot Product</A>
<H2><A NAME="SECTION00053000000000000000">
psb_gedots -- Generalized Dot Product</A>
</H2>
<P>
This function computes dot product between two vectors <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="img28.png"
ALT="$x$"> and
<IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
ALT="$y$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
ALT="$y$"> are real vectors
it computes dot-product as:
SRC="img28.png"
ALT="$y$">:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
dot \leftarrow x^T y
res(i) \leftarrow x(:,i)^T y(:,i)
\end{displaymath}
-->
<IMG
WIDTH="74" HEIGHT="27" BORDER="0"
SRC="img32.png"
ALT="\begin{displaymath}dot \leftarrow x^T y\end{displaymath}">
WIDTH="150" HEIGHT="28" BORDER="0"
SRC="img34.png"
ALT="\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
Else if <IMG
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="img28.png"
SRC="img27.png"
ALT="$x$"> is
used. If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
ALT="$y$"> are complex vectors then it computes dot-product as:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
dot \leftarrow x^H y
\end{displaymath}
-->
<IMG
WIDTH="75" HEIGHT="27" BORDER="0"
SRC="img33.png"
ALT="\begin{displaymath}dot \leftarrow x^H y\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
SRC="img28.png"
ALT="$y$"> are of rank one, then <IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img35.png"
ALT="$res$"> is a scalar, else it
is a rank one array.
<P>
<PRE>
psb_gedot(x, y, desc_a, info)
call psb_gedots(res, x, y, desc_a, info)
</PRE>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1511"></A>
<DIV ALIGN="CENTER"><A NAME="1440"></A>
<TABLE>
<CAPTION><STRONG>Table 2:</STRONG>
<CAPTION><STRONG>Table 3:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img34.png"
ALT="$dot$">, <IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img35.png"
ALT="$res$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$">, <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
SRC="img28.png"
ALT="$y$"></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_gedot</TD>
<TD ALIGN="LEFT">psb_gedots</TD>
</TR>
</TABLE>
</DIV>
@@ -166,8 +151,8 @@ Data types</CAPTION>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$x$">.
SRC="img27.png"
ALT="$x$">.
<BR>
Scope: <B>local</B>
<BR>
@@ -177,19 +162,19 @@ Intent: <B>in</B>.
<BR>
Specified as: an array of rank one or two
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90dot">2</A>. The rank of <IMG
Table&nbsp;<A HREF="#tab:f90mdot">3</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
SRC="img28.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="img29.png"
SRC="img28.png"
ALT="$y$">.
<BR>
Scope: <B>local</B>
@@ -200,12 +185,12 @@ Intent: <B>in</B>.
<BR>
Specified as: an array of rank one or two
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90dot">2</A>. The rank of <IMG
Table&nbsp;<A HREF="#tab:f90mdot">3</A>. The rank of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
SRC="img28.png"
ALT="$y$"> must be the same of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$">.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
@@ -218,24 +203,25 @@ Type: <B>required</B>
Intent: <B>in</B>.
<BR>
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>Function value</STRONG></DT>
<DT><STRONG>res</STRONG></DT>
<DD>is the dot product of subvectors <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img29.png"
SRC="img28.png"
ALT="$y$">.
<BR>
Scope: <B>global</B>
<BR>
Specified as: a number of the data type indicated in Table&nbsp;<A HREF="#tab:f90dot">2</A>.
Intent: <B>out</B>.
<BR>
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.
@@ -253,26 +239,26 @@ An integer value; 0 means no error has been detected.
<P>
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