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<H2><A NAME="SECTION000512000000000000000">
psb_spmm -- Sparse Matrix by Dense Matrix
  Product</A>
</H2>

<P>
This subroutine computes the Sparse Matrix by Dense Matrix Product:

<P>
<BR>
<DIV ALIGN="RIGHT">

<!-- MATH
 \begin{equation}
y \leftarrow \alpha  A  x + \beta y
\end{equation}
 -->
<TABLE WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:f90spmm_no_tra"></A><IMG
 WIDTH="102" HEIGHT="27" BORDER="0"
 SRC="img44.png"
 ALT="\begin{displaymath}
y \leftarrow \alpha A x + \beta y
\end{displaymath}"></TD>
<TD WIDTH=10 ALIGN="RIGHT">
(1)</TD></TR>
</TABLE>
<BR CLEAR="ALL"></DIV><P></P>
<BR>
<DIV ALIGN="RIGHT">

<!-- MATH
 \begin{equation}
y \leftarrow \alpha  A^T x + \beta y
\end{equation}
 -->
<TABLE WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:f90spmm_tra"></A><IMG
 WIDTH="112" HEIGHT="27" BORDER="0"
 SRC="img45.png"
 ALT="\begin{displaymath}
y \leftarrow \alpha A^T x + \beta y
\end{displaymath}"></TD>
<TD WIDTH=10 ALIGN="RIGHT">
(2)</TD></TR>
</TABLE>
<BR CLEAR="ALL"></DIV><P></P>
<BR>
<DIV ALIGN="RIGHT">

<!-- MATH
 \begin{equation}
y \leftarrow \alpha  A^H  x + \beta y
\end{equation}
 -->
<TABLE WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:f90spmm_con"></A><IMG
 WIDTH="114" HEIGHT="27" BORDER="0"
 SRC="img46.png"
 ALT="\begin{displaymath}
y \leftarrow \alpha A^H x + \beta y
\end{displaymath}"></TD>
<TD WIDTH=10 ALIGN="RIGHT">
(3)</TD></TR>
</TABLE>
<BR CLEAR="ALL"></DIV><P></P>

<P>
where:
<DL>
<DT><STRONG><IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></STRONG></DT>
<DD>is the global dense matrix <IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img47.png"
 ALT="$x_{:, :}$">
</DD>
<DT><STRONG><IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$"></STRONG></DT>
<DD>is the global dense matrix <IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img48.png"
 ALT="$y_{:, :}$">
</DD>
<DT><STRONG><IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$A$"></STRONG></DT>
<DD>is the global sparse matrix <IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$A$">
</DD>
</DL>

<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1954"></A>
<TABLE>
<CAPTION><STRONG>Table 12:</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="$A$">, <IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">, <IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$">, <IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img22.png"
 ALT="$\alpha$">, <IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.png"
 ALT="$\beta$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>

<P>
<PRE>
call psb_spmm(alpha, a, x, beta, y, desc_a, info)
call psb_spmm(alpha, a, x, beta, y,desc_a, info, &amp;
             &amp; trans, work)
</PRE> 

<P>
<DL>
<DT><STRONG>Type:</STRONG></DT>
<DD>Synchronous.
</DD>
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>alpha</STRONG></DT>
<DD>the scalar <IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img22.png"
 ALT="$\alpha$">.
<BR>
Scope: <B>global</B> 
<BR>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a number of the data type indicated in
Table&nbsp;<A HREF="#tab:f90spmm">12</A>. 
</DD>
<DT><STRONG>a</STRONG></DT>
<DD>the local portion of the sparse matrix
<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$A$">. 
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an object of type spdata<TT>psb_Tspmat_type</TT>.
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">. 
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>in</B>.
<BR>
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:f90spmm">12</A>.  The rank of <IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"> must be the same of <IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$">. 
</DD>
<DT><STRONG>beta</STRONG></DT>
<DD>the scalar <IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.png"
 ALT="$\beta$">.
<BR>
Scope: <B>global</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a number of the data type indicated in Table&nbsp;<A HREF="#tab:f90spmm">12</A>.
</DD>
<DT><STRONG>y</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$">. 
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>inout</B>.
<BR>
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:f90spmm">12</A>. The rank of <IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$"> must be the same of <IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">. 
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>trans</STRONG></DT>
<DD>indicates what kind of operation to perform.
<DL>
<DT><STRONG>trans = N</STRONG></DT>
<DD>the operation is specified by equation <A HREF="#eq:f90spmm_no_tra">1</A>
</DD>
<DT><STRONG>trans = T</STRONG></DT>
<DD>the operation is specified by equation
<A HREF="#eq:f90spmm_tra">2</A>
</DD>
<DT><STRONG>trans = C</STRONG></DT>
<DD>the operation is specified by equation
<A HREF="#eq:f90spmm_con">3</A>
</DD>
</DL>
Scope: <B>global</B> 
<BR>
Type: <B>optional</B>
<BR>
Intent: <B>in</B>.
<BR>
Default: <IMG
 WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img49.png"
 ALT="$trans = N$">
<BR>
Specified as: a character variable.
<P>
</DD>
<DT><STRONG>work</STRONG></DT>
<DD>work array.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>optional</B>
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a rank one array of the same type of <IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"> and <IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$"> with
the TARGET attribute. 

<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>y</STRONG></DT>
<DD>the local portion of result matrix <IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$">.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: an array of rank one or two
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90spmm">12</A>.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>out</B>.
<BR>
An integer value; 0 means no error has been detected. 
</DD>
</DL>

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