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This commit is contained in:
Salvatore Filippone
+53
-75
@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
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<TITLE>psb_geasums -- Generalized 1-Norm of Vector</TITLE>
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<META NAME="description" CONTENT="psb_geasums -- Generalized 1-Norm of Vector">
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<TITLE>psb_genrm2 -- 2-Norm of Vector</TITLE>
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<META NAME="description" CONTENT="psb_genrm2 -- 2-Norm of Vector">
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<META NAME="keywords" CONTENT="userhtml">
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<META NAME="resource-type" CONTENT="document">
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<META NAME="distribution" CONTENT="global">
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@@ -20,7 +20,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<LINK REL="next" HREF="node45.html">
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<LINK REL="previous" HREF="node43.html">
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<LINK REL="up" HREF="node37.html">
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<LINK REL="up" HREF="node36.html">
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<LINK REL="next" HREF="node45.html">
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</HEAD>
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@@ -30,7 +30,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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HREF="node45.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
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<A NAME="tex2html748"
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HREF="node37.html">
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HREF="node36.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
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<A NAME="tex2html742"
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HREF="node43.html">
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@@ -40,126 +40,101 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html753"
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HREF="node45.html">psb_genrm2 2-Norm</A>
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HREF="node45.html">psb_genrm2s Generalized</A>
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<B> Up:</B> <A NAME="tex2html749"
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HREF="node37.html">Computational routines</A>
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HREF="node36.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html743"
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HREF="node43.html">psb_geasum 1-Norm</A>
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HREF="node43.html">psb_geasums Generalized</A>
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<B> <A NAME="tex2html751"
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HREF="node1.html">Contents</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00057000000000000000">
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psb_geasums -- Generalized 1-Norm of Vector</A>
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<H2><A NAME="SECTION00058000000000000000">
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psb_genrm2 -- 2-Norm of Vector</A>
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</H2>
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<P>
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This subroutine computes a series of 1-norms on the columns of
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a dense matrix <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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res(i) \leftarrow \max_k |x(k,i)|
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\end{displaymath}
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-->
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<IMG
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WIDTH="147" HEIGHT="36" BORDER="0"
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SRC="img37.png"
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ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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This function computes the 1-norm of a vector <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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This function computes the 2-norm of a vector <IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">.
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<BR>
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If <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$"> is a real vector
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it computes 1-norm as:
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ALT="$x$"> is a real vector
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it computes 2-norm as:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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res(i) \leftarrow \|x_i\|
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nrm2 \leftarrow \sqrt{x^T x}
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\end{displaymath}
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-->
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<IMG
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WIDTH="94" HEIGHT="28" BORDER="0"
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SRC="img41.png"
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ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">
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WIDTH="106" HEIGHT="24" BORDER="0"
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SRC="img43.png"
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ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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else if <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$"> is a complex vector then it computes 1-norm as:
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ALT="$x$"> is a complex vector then it computes 2-norm as:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1
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nrm2 \leftarrow \sqrt{x^H x}
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\end{displaymath}
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-->
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<IMG
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WIDTH="206" HEIGHT="28" BORDER="0"
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SRC="img42.png"
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ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">
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WIDTH="108" HEIGHT="24" BORDER="0"
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SRC="img44.png"
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ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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<P>
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<PRE>
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call psb_geasums(res, x, desc_a, info)
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</PRE>
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1539"></A>
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<DIV ALIGN="CENTER"><A NAME="1578"></A>
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<TABLE>
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<CAPTION><STRONG>Table 7:</STRONG>
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<CAPTION><STRONG>Table 8:</STRONG>
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Data types</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
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<TR><TD ALIGN="LEFT"><IMG
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WIDTH="26" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img33.png"
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ALT="$res$"></TD>
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WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img45.png"
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ALT="$nrm2$"></TD>
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<TD ALIGN="LEFT"><IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$"></TD>
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<TD ALIGN="LEFT"><B>Subroutine</B></TD>
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<TD ALIGN="LEFT"><B>Function</B></TD>
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</TR>
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<TR><TD ALIGN="LEFT">Short Precision Real</TD>
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<TD ALIGN="LEFT">Short Precision Real</TD>
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<TD ALIGN="LEFT">psb_geasums</TD>
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<TD ALIGN="LEFT">psb_genrm2</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Long Precision Real</TD>
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<TD ALIGN="LEFT">Long Precision Real</TD>
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<TD ALIGN="LEFT">psb_geasums</TD>
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<TD ALIGN="LEFT">psb_genrm2</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Short Precision Real</TD>
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<TD ALIGN="LEFT">Short Precision Complex</TD>
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<TD ALIGN="LEFT">psb_geasums</TD>
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<TD ALIGN="LEFT">psb_genrm2</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Long Precision Real</TD>
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<TD ALIGN="LEFT">Long Precision Complex</TD>
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<TD ALIGN="LEFT">psb_geasums</TD>
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<TD ALIGN="LEFT">psb_genrm2</TD>
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</TR>
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</TABLE>
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</DIV>
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@@ -168,6 +143,11 @@ Data types</CAPTION>
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</DIV><P></P>
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<BR>
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<P>
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<PRE>
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psb_genrm2(x, desc_a, info)
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</PRE>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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@@ -179,10 +159,9 @@ Data types</CAPTION>
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<DT><STRONG>x</STRONG></DT>
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<DD>the local portion of global dense matrix
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<IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">.
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ALT="$x$">.
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<BR>
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Scope: <B>local</B>
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<BR>
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@@ -190,9 +169,9 @@ Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
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Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
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containing numbers of type specified in
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Table <A HREF="#tab:f90asums">7</A>.
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Table <A HREF="#tab:f90nrm2">8</A>.
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</DD>
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<DT><STRONG>desc_a</STRONG></DT>
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<DD>contains data structures for communications.
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@@ -210,18 +189,17 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
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<DT><STRONG><B>On Return</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>res</STRONG></DT>
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<DD>contains the 1-norm of (the columns of) <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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<DT><STRONG>Function Value</STRONG></DT>
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<DD>is the 2-norm of subvector <IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img25.png"
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ALT="$x$">.
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<BR>
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Scope: <B>global</B>
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<BR>
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Intent: <B>out</B>.
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Type: <B>required</B>
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<BR>
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Short as: a long precision real number.
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Specified as: a long precision real number.
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Specified as: a long precision real number.
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</DD>
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<DT><STRONG>info</STRONG></DT>
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<DD>Error code.
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@@ -243,7 +221,7 @@ An integer value; 0 means no error has been detected.
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HREF="node45.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
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<A NAME="tex2html748"
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HREF="node37.html">
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HREF="node36.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
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<A NAME="tex2html742"
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HREF="node43.html">
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@@ -253,11 +231,11 @@ An integer value; 0 means no error has been detected.
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html753"
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HREF="node45.html">psb_genrm2 2-Norm</A>
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HREF="node45.html">psb_genrm2s Generalized</A>
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<B> Up:</B> <A NAME="tex2html749"
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HREF="node37.html">Computational routines</A>
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HREF="node36.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html743"
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HREF="node43.html">psb_geasum 1-Norm</A>
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HREF="node43.html">psb_geasums Generalized</A>
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<B> <A NAME="tex2html751"
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HREF="node1.html">Contents</A></B>
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<!--End of Navigation Panel-->
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