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265 lines
6.8 KiB
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265 lines
6.8 KiB
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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>
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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 <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>:
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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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="148" HEIGHT="36" BORDER="0"
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SRC="img34.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 <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>.
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<BR>
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If <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> 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" CLASS="mathdisplay">
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<!-- MATH
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\begin{displaymath}
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res(i) \leftarrow \|x_i\|
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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="img39.png"
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ALT="\begin{displaymath}res(i) \leftarrow \Vert x_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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else if <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN> is a complex vector then it computes 1-norm as:
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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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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\end{displaymath}
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-->
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<IMG
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WIDTH="207" HEIGHT="28" BORDER="0"
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SRC="img40.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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</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="2015"></A>
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<TABLE>
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<CAPTION><STRONG>Table 7:</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"><SPAN CLASS="MATH"><IMG
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WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img29.png"
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ALT="$res$"></SPAN></TD>
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<TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN></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_geasums</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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</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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</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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</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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<SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>.
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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 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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</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: an object 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) <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></SPAN>.
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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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Short 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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<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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<B> Next:</B> <A NAME="tex2html984"
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HREF="node60.html">psb_norm2 2-Norm</A>
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HREF="node52.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html974"
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HREF="node58.html">psb_norm1 1-Norm</A>
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