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Use it in GENPDE. Update docs
This commit is contained in:
Salvatore Filippone
+142
-186
@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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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_spsm -- Triangular System Solve</TITLE>
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<META NAME="description" CONTENT="psb_spsm -- Triangular System Solve">
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<TITLE>psb_spmm -- Sparse Matrix by Dense Matrix Product</TITLE>
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<META NAME="description" CONTENT="psb_spmm -- Sparse Matrix by Dense Matrix Product">
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<META NAME="keywords" CONTENT="userhtml">
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<META NAME="resource-type" CONTENT="document">
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<META NAME="distribution" CONTENT="global">
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@@ -18,77 +18,111 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<LINK REL="STYLESHEET" HREF="userhtml.css">
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<LINK REL="next" HREF="node61.html">
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<LINK REL="previous" HREF="node59.html">
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<LINK REL="up" HREF="node47.html">
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<LINK REL="up" HREF="node48.html">
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<LINK REL="next" HREF="node61.html">
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</HEAD>
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<BODY >
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<!--Navigation Panel-->
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<A NAME="tex2html974"
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<A NAME="tex2html979"
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HREF="node61.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
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<A NAME="tex2html970"
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HREF="node47.html">
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<A NAME="tex2html975"
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HREF="node48.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
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<A NAME="tex2html966"
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<A NAME="tex2html969"
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HREF="node59.html">
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<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
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<A NAME="tex2html972"
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<A NAME="tex2html977"
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HREF="node1.html">
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html975"
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HREF="node61.html">Communication routines</A>
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<B> Up:</B> <A NAME="tex2html971"
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HREF="node47.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html967"
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HREF="node59.html">psb_spmm Sparse</A>
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<B> <A NAME="tex2html973"
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<B> Next:</B> <A NAME="tex2html980"
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HREF="node61.html">psb_spsm Triangular</A>
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<B> Up:</B> <A NAME="tex2html976"
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HREF="node48.html">Computational routines</A>
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<B> Previous:</B> <A NAME="tex2html970"
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HREF="node59.html">psb_normi Infinity</A>
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<B> <A NAME="tex2html978"
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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="SECTION000513000000000000000">
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psb_spsm -- Triangular System Solve</A>
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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 Triangular System Solve:
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This subroutine computes the Sparse Matrix by Dense Matrix Product:
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<P>
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<P></P>
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<DIV ALIGN="CENTER">
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<BR>
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<DIV ALIGN="RIGHT">
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<!-- MATH
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\begin{eqnarray*}
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y &\leftarrow& \alpha T^{-1} x + \beta y\\
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y &\leftarrow& \alpha D T^{-1} x + \beta y\\
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y &\leftarrow& \alpha T^{-1} D x + \beta y\\
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y &\leftarrow& \alpha T^{-T} x + \beta y\\
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y &\leftarrow& \alpha D T^{-T} x + \beta y\\
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y &\leftarrow& \alpha T^{-T} D x + \beta y\\
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y &\leftarrow& \alpha T^{-H} x + \beta y\\
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y &\leftarrow& \alpha D T^{-H} x + \beta y\\
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y &\leftarrow& \alpha T^{-H} D x + \beta y\\
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\end{eqnarray*}
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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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<IMG
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WIDTH="160" HEIGHT="239" BORDER="0"
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SRC="img50.png"
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ALT="\begin{eqnarray*}
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y &\leftarrow& \alpha T^{-1} x + \beta y\\
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y &\leftarrow& \al...
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...-H} x + \beta y\\
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y &\leftarrow& \alpha T^{-H} D x + \beta y\\
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\end{eqnarray*}"></DIV>
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<BR CLEAR="ALL"><P></P>
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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="img44.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 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 A^T 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="112" HEIGHT="27" BORDER="0"
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SRC="img45.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 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 A^H 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="114" HEIGHT="27" BORDER="0"
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SRC="img46.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 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="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$"></STRONG></DT>
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<DD>is the global dense matrix <IMG
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@@ -107,50 +141,34 @@ where:
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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="img51.png"
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ALT="$T$"></STRONG></DT>
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<DD>is the global sparse block triangular submatrix <IMG
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SRC="img1.png"
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ALT="$A$"></STRONG></DT>
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<DD>is the global sparse matrix <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img51.png"
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ALT="$T$">
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</DD>
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<DT><STRONG><IMG
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WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img52.png"
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ALT="$D$"></STRONG></DT>
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<DD>is the scaling diagonal matrix.
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SRC="img1.png"
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ALT="$A$">
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</DD>
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</DL>
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<P>
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<PRE>
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call psb_spsm(alpha, t, x, beta, y, desc_a, info)
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call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
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& trans, unit, choice, diag, work)
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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="1825"></A>
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<DIV ALIGN="CENTER"><A NAME="1858"></A>
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<TABLE>
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<CAPTION><STRONG>Table 13:</STRONG>
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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"><IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img51.png"
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ALT="$T$">, <IMG
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WIDTH="14" HEIGHT="13" 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="img20.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="img21.png"
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ALT="$y$">, <IMG
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WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img52.png"
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ALT="$D$">, <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img22.png"
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ALT="$\alpha$">, <IMG
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@@ -160,16 +178,16 @@ Data types</CAPTION>
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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_spsm</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_spsm</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_spsm</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_spsm</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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@@ -178,6 +196,13 @@ Data types</CAPTION>
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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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@@ -199,14 +224,14 @@ Type: <B>required</B>
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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:f90spsm">13</A>.
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Table <A HREF="#tab:f90spmm">12</A>.
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</DD>
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<DT><STRONG>t</STRONG></DT>
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<DD>the global portion of the sparse matrix
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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="img51.png"
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ALT="$T$">.
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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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@@ -214,13 +239,12 @@ 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 type specified in
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§ <A HREF="node9.html#sec:datastruct">3</A>.
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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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<IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img20.png"
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ALT="$x$">.
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@@ -233,8 +257,8 @@ 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:f90spsm">13</A>. The rank of <IMG
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WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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Table <A HREF="#tab:f90spmm">12</A>. The rank of <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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||||
SRC="img20.png"
|
||||
ALT="$x$"> must be the same of <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
@@ -253,7 +277,7 @@ Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a number of the data type indicated in Table <A HREF="#tab:f90spsm">13</A>.
|
||||
Specified as: a number of the data type indicated in Table <A HREF="#tab:f90spmm">12</A>.
|
||||
</DD>
|
||||
<DT><STRONG>y</STRONG></DT>
|
||||
<DD>the local portion of global dense matrix
|
||||
@@ -271,11 +295,11 @@ 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 <A HREF="#tab:f90spsm">13</A>. The rank of <IMG
|
||||
Table <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="13" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$">.
|
||||
</DD>
|
||||
@@ -291,16 +315,18 @@ Intent: <B>in</B>.
|
||||
Specified as: an object of type descdata<TT>psb_desc_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>trans</STRONG></DT>
|
||||
<DD>specify with <EM>unitd</EM> the operation to perform.
|
||||
<DD>indicates what kind of operation to perform.
|
||||
<DL>
|
||||
<DT><STRONG>trans = 'N'</STRONG></DT>
|
||||
<DD>the operation is with no transposed matrix
|
||||
<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 with transposed matrix.
|
||||
<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 with conjugate transposed matrix.
|
||||
<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>
|
||||
@@ -315,82 +341,11 @@ Default: <IMG
|
||||
ALT="$trans = N$">
|
||||
<BR>
|
||||
Specified as: a character variable.
|
||||
</DD>
|
||||
<DT><STRONG>unitd</STRONG></DT>
|
||||
<DD>specify with <EM>trans</EM> the operation to perform.
|
||||
<DL>
|
||||
<DT><STRONG>unitd = 'U'</STRONG></DT>
|
||||
<DD>the operation is with no scaling
|
||||
</DD>
|
||||
<DT><STRONG>unitd = 'L'</STRONG></DT>
|
||||
<DD>the operation is with left scaling
|
||||
</DD>
|
||||
<DT><STRONG>unitd = 'R'</STRONG></DT>
|
||||
<DD>the operation is with right scaling.
|
||||
</DD>
|
||||
</DL>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <IMG
|
||||
WIDTH="76" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img53.png"
|
||||
ALT="$unitd = U$">
|
||||
<BR>
|
||||
Specified as: a character variable.
|
||||
</DD>
|
||||
<DT><STRONG>choice</STRONG></DT>
|
||||
<DD>specifies the update of overlap elements to be performed
|
||||
on exit:
|
||||
<DL>
|
||||
<DT></DT>
|
||||
<DD><code>psb_none_</code>
|
||||
</DD>
|
||||
<DT></DT>
|
||||
<DD><code>psb_sum_</code>
|
||||
</DD>
|
||||
<DT></DT>
|
||||
<DD><code>psb_avg_</code>
|
||||
</DD>
|
||||
<DT></DT>
|
||||
<DD><code>psb_square_root_</code>
|
||||
</DD>
|
||||
</DL>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <code>psb_avg_</code>
|
||||
<BR>
|
||||
Specified as: an integer variable.
|
||||
</DD>
|
||||
<DT><STRONG>diag</STRONG></DT>
|
||||
<DD>the diagonal scaling matrix.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <!-- MATH
|
||||
$diag(1) = 1 (no scaling)$
|
||||
-->
|
||||
<IMG
|
||||
WIDTH="165" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img54.png"
|
||||
ALT="$diag(1) = 1 (no scaling)$">
|
||||
<BR>
|
||||
Specified as: a rank one array containing numbers of the type
|
||||
indicated in Table <A HREF="#tab:f90spsm">13</A>.
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG>work</STRONG></DT>
|
||||
<DD>a work array.
|
||||
<DD>work array.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
@@ -399,10 +354,13 @@ Type: <B>optional</B>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array of the same type of <IMG
|
||||
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
||||
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img20.png"
|
||||
ALT="$x$"> with the
|
||||
TARGET attribute.
|
||||
ALT="$x$"> and <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$"> with
|
||||
the TARGET attribute.
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
@@ -410,12 +368,10 @@ TARGET attribute.
|
||||
<DD>
|
||||
</DD>
|
||||
<DT><STRONG>y</STRONG></DT>
|
||||
<DD>the local portion of global dense matrix
|
||||
<IMG
|
||||
<DD>the local portion of result matrix <IMG
|
||||
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img21.png"
|
||||
ALT="$y$">.
|
||||
|
||||
ALT="$y$">.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
@@ -425,7 +381,7 @@ Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: an array of rank one or two
|
||||
containing numbers of type specified in
|
||||
Table <A HREF="#tab:f90spsm">13</A>.
|
||||
Table <A HREF="#tab:f90spmm">12</A>.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Error code.
|
||||
@@ -443,26 +399,26 @@ An integer value; 0 means no error has been detected.
|
||||
<P>
|
||||
<HR>
|
||||
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|
||||
<A NAME="tex2html974"
|
||||
<A NAME="tex2html979"
|
||||
HREF="node61.html">
|
||||
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
||||
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|
||||
HREF="node47.html">
|
||||
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|
||||
HREF="node48.html">
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||||
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
||||
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|
||||
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|
||||
HREF="node59.html">
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||||
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|
||||
<A NAME="tex2html972"
|
||||
<A NAME="tex2html977"
|
||||
HREF="node1.html">
|
||||
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
||||
<BR>
|
||||
<B> Next:</B> <A NAME="tex2html975"
|
||||
HREF="node61.html">Communication routines</A>
|
||||
<B> Up:</B> <A NAME="tex2html971"
|
||||
HREF="node47.html">Computational routines</A>
|
||||
<B> Previous:</B> <A NAME="tex2html967"
|
||||
HREF="node59.html">psb_spmm Sparse</A>
|
||||
<B> <A NAME="tex2html973"
|
||||
<B> Next:</B> <A NAME="tex2html980"
|
||||
HREF="node61.html">psb_spsm Triangular</A>
|
||||
<B> Up:</B> <A NAME="tex2html976"
|
||||
HREF="node48.html">Computational routines</A>
|
||||
<B> Previous:</B> <A NAME="tex2html970"
|
||||
HREF="node59.html">psb_normi Infinity</A>
|
||||
<B> <A NAME="tex2html978"
|
||||
HREF="node1.html">Contents</A></B>
|
||||
<!--End of Navigation Panel-->
|
||||
|
||||
|
||||
Reference in New Issue
Block a user