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Salvatore Filippone
2017-02-12 18:19:15 +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_norm1 -- 1-Norm of Sparse Matrix</TITLE>
<META NAME="description" CONTENT="psb_norm1 -- 1-Norm of Sparse Matrix">
<TITLE>psb_norm2 -- 2-Norm of Vector</TITLE>
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@@ -20,102 +20,120 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION000510000000000000000">
psb_norm1 -- 1-Norm of Sparse Matrix</A>
<H2><A NAME="SECTION00058000000000000000">
psb_norm2 -- 2-Norm of Vector</A>
</H2>
<P>
This function computes the 1-norm of a matrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">:
This function computes the 2-norm of a vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
<P>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a real vector
it computes 2-norm as:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
nrm1 \leftarrow \|A\|_1
nrm2 \leftarrow \sqrt{x^T x}
\end{displaymath}
-->
<IMG
WIDTH="98" HEIGHT="28" BORDER="0"
SRC="img42.png"
ALT="\begin{displaymath}nrm1 \leftarrow \Vert A\Vert _1 \end{displaymath}">
WIDTH="106" HEIGHT="24" BORDER="0"
SRC="img38.png"
ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></STRONG></DT>
<DD>represents the global matrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">
</DD>
</DL>
else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a complex vector then it computes 2-norm as:
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
nrm2 \leftarrow \sqrt{x^H x}
\end{displaymath}
-->
<IMG
WIDTH="108" HEIGHT="24" BORDER="0"
SRC="img39.png"
ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1870"></A>
<DIV ALIGN="CENTER"><A NAME="1950"></A>
<TABLE>
<CAPTION><STRONG>Table 10:</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="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></TD>
WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img40.png"
ALT="$nrm2$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
<TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_genrm2</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
<TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_genrm2</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_genrm2</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_genrm2</TD>
</TR>
</TABLE>
</DIV>
@@ -126,10 +144,9 @@ Data types</CAPTION>
<P>
<PRE>
psb_spnrm1(A, desc_a, info)
psb_norm1(A, desc_a, info)
psb_genrm2(x, desc_a, info)
psb_norm2(x, desc_a, info)
</PRE>
<P>
<DL>
<DT><STRONG>Type:</STRONG></DT>
@@ -138,20 +155,22 @@ psb_norm1(A, desc_a, info)
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>a</STRONG></DT>
<DD>the local portion of the global sparse matrix
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">.
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an object of type spdata<TT>psb_Tspmat_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:f90nrm2">8</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -163,18 +182,21 @@ Type: <B>required</B>
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>Function value</STRONG></DT>
<DD>is the 1-norm of sparse submatrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">.
<DT><STRONG>Function Value</STRONG></DT>
<DD>is the 2-norm of subvector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
Scope: <B>global</B>
<BR>
Type: <B>required</B>
<BR>
Specified as: a long precision real number.
</DD>
<DT><STRONG>info</STRONG></DT>
@@ -193,26 +215,26 @@ An integer value; 0 means no error has been detected.
<P>
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