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Documentation changes. We have barely begun.....
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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>
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<TITLE>psb_geasums -- Generalized 1-Norm of Vector</TITLE>
<META NAME="description" CONTENT="psb_geasums -- Generalized 1-Norm of Vector">
<TITLE>psb_genrm2 -- 2-Norm of Vector</TITLE>
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@@ -20,146 +20,121 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00057000000000000000">
psb_geasums -- Generalized 1-Norm of Vector</A>
<H2><A NAME="SECTION00058000000000000000">
psb_genrm2 -- 2-Norm of Vector</A>
</H2>
<P>
This subroutine computes a series of 1-norms on the columns of
a dense matrix <IMG
This function computes the 2-norm of a vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$x$">:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \max_k |x(k,i)|
\end{displaymath}
-->
<IMG
WIDTH="148" HEIGHT="36" BORDER="0"
SRC="img40.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="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$x$"> is a real vector
it computes 1-norm as:
SRC="img27.png"
ALT="$x$"> is a double precision real vector
it computes 2-norm as:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \|x_i\|
nrm2 \leftarrow \sqrt{x^T x}
\end{displaymath}
-->
<IMG
WIDTH="94" HEIGHT="28" BORDER="0"
SRC="img44.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">
WIDTH="106" HEIGHT="24" BORDER="0"
SRC="img45.png"
ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$x$"> is a complex vector then it computes 1-norm as:
SRC="img27.png"
ALT="$x$"> is double precision complex vector then it computes 2-norm as:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1
nrm2 \leftarrow \sqrt{x^H x}
\end{displaymath}
-->
<IMG
WIDTH="207" HEIGHT="28" BORDER="0"
SRC="img45.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">
WIDTH="108" HEIGHT="24" BORDER="0"
SRC="img46.png"
ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\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="1516"></A>
<DIV ALIGN="CENTER"><A NAME="1445"></A>
<TABLE>
<CAPTION><STRONG>Table 7:</STRONG>
<CAPTION><STRONG>Table 8:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img36.png"
ALT="$res$"></TD>
WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img47.png"
ALT="$nrm2$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$"></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_genrm2</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_genrm2</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_genrm2</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_genrm2</TD>
</TR>
</TABLE>
</DIV>
@@ -168,6 +143,11 @@ Data types</CAPTION>
</DIV><P></P>
<BR>
<P>
<PRE>
psb_genrm2(x, desc_a, info)
</PRE>
<P>
<DL>
<DT><STRONG>Type:</STRONG></DT>
@@ -180,9 +160,8 @@ 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>
@@ -190,9 +169,9 @@ Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a rank one or two array
Specified as: a rank one or two array
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90asums">7</A>.
Table&nbsp;<A HREF="#tab:f90nrm2">8</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -210,18 +189,17 @@ Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
<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
<DT><STRONG>Function Value</STRONG></DT>
<DD>is the 2-norm of subvector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
SRC="img27.png"
ALT="$x$">.
<BR>
Scope: <B>global</B>
<BR>
Intent: <B>out</B>.
Type: <B>required</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.
@@ -239,26 +217,26 @@ An integer value; 0 means no error has been detected.
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