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<H2><A NAME="SECTION000510000000000000000">
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psb_spmm -- Sparse Matrix by Dense Matrix 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">
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<!-- MATH
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\begin{equation}
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y \leftarrow \alpha P_r A P_c x + \beta y
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\end{equation}
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-->
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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="136" 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 P_r A P_c x + \beta y
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\end{displaymath}"></TD>
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<TD WIDTH=10 ALIGN="RIGHT">
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(1)</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">
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<!-- MATH
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\begin{equation}
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y \leftarrow \alpha P_r A^T P_c x + \beta y
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\end{equation}
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-->
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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="145" HEIGHT="27" BORDER="0"
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SRC="img51.png"
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ALT="\begin{displaymath}
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y \leftarrow \alpha P_r A^T P_c x + \beta y
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\end{displaymath}"></TD>
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<TD WIDTH=10 ALIGN="RIGHT">
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(2)</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">
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<!-- MATH
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\begin{equation}
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y \leftarrow \alpha P_r A^H P_c x + \beta y
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\end{equation}
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-->
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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="148" HEIGHT="27" BORDER="0"
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SRC="img52.png"
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ALT="\begin{displaymath}
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y \leftarrow \alpha P_r A^H P_c x + \beta y
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\end{displaymath}"></TD>
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<TD WIDTH=10 ALIGN="RIGHT">
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(3)</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><IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"></STRONG></DT>
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<DD>is the global dense submatrix <IMG
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WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img53.png"
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ALT="$x_{:, :}$">
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</DD>
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<DT><STRONG><IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$"></STRONG></DT>
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<DD>is the global dense submatrix <IMG
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WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img54.png"
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ALT="$y_{:, :}$">
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</DD>
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<DT><STRONG><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="$A$"></STRONG></DT>
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<DD>is the global sparse submatrix <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="$A$">
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</DD>
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<DT><STRONG><IMG
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WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img55.png"
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ALT="$P_r, P_c$"></STRONG></DT>
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<DD>are the permutation matrices.
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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="1426"></A>
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<TABLE>
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<CAPTION><STRONG>Table 11:</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="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$">, <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$">, <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">, <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img28.png"
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ALT="$\alpha$">, <IMG
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WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img29.png"
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ALT="$\beta$"></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 <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img28.png"
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ALT="$\alpha$">.
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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">11</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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<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="$A$">.
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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 spdata<TT>psb_spmat_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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<IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.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:f90spmm">11</A>. The rank of <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> must be the same of <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">.
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</DD>
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<DT><STRONG>beta</STRONG></DT>
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<DD>the scalar <IMG
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WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img29.png"
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ALT="$\beta$">.
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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">11</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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<IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">.
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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
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containing numbers of type specified in
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Table <A HREF="#tab:f90spmm">11</A>. The rank of <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$"> must be the same of <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$">.
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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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</DD>
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<DT><STRONG>trans</STRONG></DT>
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<DD>indicate 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: <IMG
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WIDTH="78" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img56.png"
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ALT="$trans = N$">
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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 <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img26.png"
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ALT="$x$"> and <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$"> 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 submatrix <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img27.png"
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ALT="$y$">.
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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">11</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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