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<H2><A NAME="SECTION000512000000000000000">
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psb_spmm -- Sparse Matrix by Dense Matrix
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Product</A>
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</H2>
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<P>
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This subroutine computes the Sparse Matrix by Dense Matrix Product:
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<P>
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<BR>
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<DIV ALIGN="RIGHT" CLASS="mathdisplay">
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<!-- MATH
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\begin{equation}
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y \leftarrow \alpha A x + \beta y
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\end{equation}
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-->
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<A NAME="eq:f90spmm_no_tra"></A>
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<TABLE WIDTH="100%" ALIGN="CENTER">
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<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:f90spmm_no_tra"></A><IMG
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WIDTH="102" HEIGHT="27" BORDER="0"
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SRC="img48.png"
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ALT="\begin{displaymath}
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y \leftarrow \alpha A x + \beta y
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\end{displaymath}"></TD>
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<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
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(<SPAN CLASS="arabic">1</SPAN>)</TD></TR>
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</TABLE>
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<BR CLEAR="ALL"></DIV><P></P>
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<BR>
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<DIV ALIGN="RIGHT" CLASS="mathdisplay">
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<!-- MATH
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\begin{equation}
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y \leftarrow \alpha A^T x + \beta y
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\end{equation}
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-->
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<A NAME="eq:f90spmm_tra"></A>
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<TABLE WIDTH="100%" ALIGN="CENTER">
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<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:f90spmm_tra"></A><IMG
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WIDTH="111" HEIGHT="27" BORDER="0"
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SRC="img49.png"
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ALT="\begin{displaymath}
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y \leftarrow \alpha A^T x + \beta y
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\end{displaymath}"></TD>
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<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
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(<SPAN CLASS="arabic">2</SPAN>)</TD></TR>
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</TABLE>
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<BR CLEAR="ALL"></DIV><P></P>
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<BR>
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<DIV ALIGN="RIGHT" CLASS="mathdisplay">
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<!-- MATH
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\begin{equation}
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y \leftarrow \alpha A^H x + \beta y
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\end{equation}
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-->
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<A NAME="eq:f90spmm_con"></A>
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<TABLE WIDTH="100%" ALIGN="CENTER">
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<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:f90spmm_con"></A><IMG
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WIDTH="114" HEIGHT="27" BORDER="0"
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SRC="img50.png"
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ALT="\begin{displaymath}
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y \leftarrow \alpha A^H x + \beta y
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\end{displaymath}"></TD>
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<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
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(<SPAN CLASS="arabic">3</SPAN>)</TD></TR>
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</TABLE>
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<BR CLEAR="ALL"></DIV><P></P>
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<P>
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where:
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<DL>
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<DT><STRONG><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></STRONG></DT>
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<DD>is the global dense matrix <SPAN CLASS="MATH"><IMG
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WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img51.png"
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ALT="$x_{:, :}$"></SPAN>
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</DD>
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<DT><STRONG><SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN></STRONG></DT>
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<DD>is the global dense matrix <SPAN CLASS="MATH"><IMG
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WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img52.png"
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ALT="$y_{:, :}$"></SPAN>
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</DD>
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<DT><STRONG><SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$"></SPAN></STRONG></DT>
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<DD>is the global sparse matrix <SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$"></SPAN>
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</DD>
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</DL>
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="2020"></A>
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<TABLE>
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<CAPTION><STRONG>Table 12:</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="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$"></SPAN>, <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>, <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img22.png"
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ALT="$\alpha$"></SPAN>, <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img23.png"
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ALT="$\beta$"></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">psb_spmm</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">psb_spmm</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
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<TD ALIGN="LEFT">psb_spmm</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
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<TD ALIGN="LEFT">psb_spmm</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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<PRE>
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call psb_spmm(alpha, a, x, beta, y, desc_a, info)
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call psb_spmm(alpha, a, x, beta, y,desc_a, info, &
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& trans, work)
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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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<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>alpha</STRONG></DT>
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<DD>the scalar <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img22.png"
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ALT="$\alpha$"></SPAN>.
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<BR>
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Scope: <B>global</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 number of the data type indicated in
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Table <A HREF="#tab:f90spmm">12</A>.
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</DD>
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<DT><STRONG>a</STRONG></DT>
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<DD>the local portion of the sparse matrix
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<SPAN CLASS="MATH"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$"></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: an object of type spdata<TT>psb_Tspmat_type</TT>.
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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:f90spmm">12</A>. The rank 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> must be the same of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN>.
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</DD>
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<DT><STRONG>beta</STRONG></DT>
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<DD>the scalar <SPAN CLASS="MATH"><IMG
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WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img23.png"
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ALT="$\beta$"></SPAN>.
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<BR>
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Scope: <B>global</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 number of the data type indicated in Table <A HREF="#tab:f90spmm">12</A>.
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</DD>
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<DT><STRONG>y</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="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></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>inout</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:f90spmm">12</A>. The rank of <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN> must be the same 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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</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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</DD>
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<DT><STRONG>trans</STRONG></DT>
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<DD>indicates what kind of operation to perform.
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<DL>
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<DT><STRONG>trans = N</STRONG></DT>
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<DD>the operation is specified by equation <A HREF="#eq:f90spmm_no_tra">1</A>
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</DD>
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<DT><STRONG>trans = T</STRONG></DT>
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<DD>the operation is specified by equation
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<A HREF="#eq:f90spmm_tra">2</A>
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</DD>
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<DT><STRONG>trans = C</STRONG></DT>
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<DD>the operation is specified by equation
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<A HREF="#eq:f90spmm_con">3</A>
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</DD>
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</DL>
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Scope: <B>global</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Default: <SPAN CLASS="MATH"><IMG
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WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img53.png"
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ALT="$trans = N$"></SPAN>
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<BR>
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Specified as: a character variable.
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<P>
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</DD>
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<DT><STRONG>work</STRONG></DT>
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<DD>work array.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Intent: <B>inout</B>.
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<BR>
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Specified as: a rank one array of the same type 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> and <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></SPAN> with
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the TARGET attribute.
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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>y</STRONG></DT>
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<DD>the local portion of result matrix <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$y$"></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>inout</B>.
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<BR>
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table <A HREF="#tab:f90spmm">12</A>.
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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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