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274 lines
6.8 KiB
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274 lines
6.8 KiB
HTML
17 years ago
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<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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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_genrm2s -- Generalized 1-Norm of Vector</TITLE>
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<BR>
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<B> Next:</B> <A NAME="tex2html582"
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HREF="node34.html">psb_spnrmi Infinity</A>
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<B> Up:</B> <A NAME="tex2html578"
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HREF="node25.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html572"
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HREF="node32.html">psb_geasums Generalized</A>
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<B> <A NAME="tex2html580"
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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="SECTION00058000000000000000">
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psb_genrm2s -- Generalized 1-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="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.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="img36.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="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.png"
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ALT="$x$">.
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<BR>
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If <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.png"
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ALT="$x$"> is a real vector
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it computes 1-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 \sqrt{x^T x}
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\end{displaymath}
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-->
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<IMG
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WIDTH="107" HEIGHT="28" BORDER="0"
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SRC="img45.png"
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ALT="\begin{displaymath}res(i) \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="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.png"
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ALT="$x$"> is a complex vector then it computes 1-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 \sqrt{x^H x}
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\end{displaymath}
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-->
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<IMG
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WIDTH="109" HEIGHT="28" BORDER="0"
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SRC="img46.png"
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ALT="\begin{displaymath}res(i) \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_genrm2s(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="1422"></A>
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<TABLE>
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<CAPTION><STRONG>Table 9:</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="img32.png"
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ALT="$res$"></TD>
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<TD ALIGN="LEFT"><IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.png"
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ALT="$x$"></TD>
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<TD ALIGN="LEFT"><B>Subroutine</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_genrm2s</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_genrm2s</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_genrm2s</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_genrm2s</TD>
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</TR>
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</TABLE>
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</DIV>
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</TD></TR>
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</TABLE>
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</DIV><P></P>
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<BR>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Synchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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</DD>
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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="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.png"
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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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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
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containing numbers of type specified in
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Table <A HREF="#tab:f90nrm2s">9</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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<BR>
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Scope: <B>local</B>
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<BR>
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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 structured data of type descdata<TT>psb_desc_type</TT>.
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<P>
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</DD>
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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="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img24.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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<BR>
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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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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>out</B>.
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<BR>
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An integer value; 0 means no error has been detected.
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</DD>
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</DL>
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<P>
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<HR>
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HREF="node34.html">psb_spnrmi Infinity</A>
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<B> Up:</B> <A NAME="tex2html578"
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HREF="node25.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html572"
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HREF="node32.html">psb_geasums Generalized</A>
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<B> <A NAME="tex2html580"
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HREF="node1.html">Contents</A></B>
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