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<TITLE>psb_norm1 -- 1-Norm of Sparse Matrix</TITLE>
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<TITLE>psb_geasums -- Generalized 1-Norm of Vector</TITLE>
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<H2><A NAME="SECTION000510000000000000000">
psb_norm1 -- 1-Norm of Sparse Matrix</A>
<H2><A NAME="SECTION00057000000000000000">
psb_geasums -- Generalized 1-Norm of Vector</A>
</H2>
<P>
This function computes the 1-norm of a matrix <SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN>:
<BR>
<P>
This subroutine computes a series of 1-norms on the columns of
a dense matrix <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
nrm1 \leftarrow \|A\|_1
res(i) \leftarrow \max_k |x(k,i)|
\end{displaymath}
-->
<IMG
WIDTH="97" HEIGHT="28" BORDER="0"
SRC="img46.png"
ALT="\begin{displaymath}nrm1 \leftarrow \Vert A\Vert _1 \end{displaymath}">
WIDTH="148" HEIGHT="36" BORDER="0"
SRC="img34.png"
ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN></STRONG></DT>
<DD>represents the global matrix <SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN>
</DD>
</DL>
This function computes the 1-norm of a vector <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<BR>
If <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> is a real vector
it computes 1-norm as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \|x_i\|
\end{displaymath}
-->
<IMG
WIDTH="93" HEIGHT="29" BORDER="0"
SRC="img39.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
else if <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> is a complex vector then it computes 1-norm as:
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1
\end{displaymath}
-->
<IMG
WIDTH="207" HEIGHT="29" BORDER="0"
SRC="img40.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\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="2032"></A>
<DIV ALIGN="CENTER"><A NAME="2108"></A>
<TABLE>
<CAPTION><STRONG>Table 10:</STRONG>
<CAPTION><STRONG>Table 7:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img29.png"
ALT="$res$"></SPAN></TD>
<TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Subroutine</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_geasums</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_geasums</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_geasums</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_geasums</TD>
</TR>
</TABLE>
</DIV>
@@ -121,12 +165,6 @@ Data types</CAPTION>
</DIV><P></P>
<BR>
<P>
<PRE>
psb_spnrm1(A, desc_a, info)
psb_norm1(A, desc_a, info)
</PRE>
<P>
<DL>
<DT><STRONG>Type:</STRONG></DT>
@@ -135,20 +173,23 @@ 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
<SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN>.
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<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:f90asums">7</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -160,19 +201,24 @@ 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 <SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN>.
<DT><STRONG>res</STRONG></DT>
<DD>contains the 1-norm of (the columns of) <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<BR>
Scope: <B>global</B>
<BR>
Specified as: a long precision real number.
Intent: <B>out</B>.
<BR>
Short as: a long precision real number.
Specified as: a long precision real number.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
@@ -188,7 +234,31 @@ An integer value; 0 means no error has been detected.
</DL>
<P>
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