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Salvatore Filippone
2017-02-12 18:19:15 +00:00
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>psb_spmm -- Sparse Matrix by Dense Matrix Product</TITLE>
<META NAME="description" CONTENT="psb_spmm -- Sparse Matrix by Dense Matrix Product">
<TITLE>psb_norm1 -- 1-Norm of Sparse Matrix</TITLE>
<META NAME="description" CONTENT="psb_norm1 -- 1-Norm of Sparse Matrix">
<META NAME="keywords" CONTENT="userhtml">
<META NAME="resource-type" CONTENT="document">
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@@ -20,130 +20,70 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION000512000000000000000">
psb_spmm -- Sparse Matrix by Dense Matrix
Product</A>
<H2><A NAME="SECTION000510000000000000000">
psb_norm1 -- 1-Norm of Sparse Matrix</A>
</H2>
<P>
This subroutine computes the Sparse Matrix by Dense Matrix Product:
This function computes the 1-norm of a matrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">:
<BR>
<P>
<BR>
<DIV ALIGN="RIGHT">
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{equation}
y \leftarrow \alpha A x + \beta y
\end{equation}
\begin{displaymath}
nrm1 \leftarrow \|A\|_1
\end{displaymath}
-->
<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="111" 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>
<IMG
WIDTH="98" HEIGHT="28" BORDER="0"
SRC="img42.png"
ALT="\begin{displaymath}nrm1 \leftarrow \Vert A\Vert _1 \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><IMG
WIDTH="13" 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
<DD>represents the global matrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">
@@ -152,9 +92,9 @@ where:
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1872"></A>
<DIV ALIGN="CENTER"><A NAME="1952"></A>
<TABLE>
<CAPTION><STRONG>Table 12:</STRONG>
<CAPTION><STRONG>Table 10:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
@@ -162,32 +102,20 @@ Data types</CAPTION>
<TR><TD ALIGN="LEFT"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">, <IMG
WIDTH="13" 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>
ALT="$A$"></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_spmm</TD>
<TD ALIGN="LEFT">psb_spnrm1</TD>
</TR>
</TABLE>
</DIV>
@@ -198,10 +126,9 @@ Data types</CAPTION>
<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>
psb_spnrm1(A, desc_a, info)
psb_norm1(A, desc_a, info)
</PRE>
<P>
<DL>
@@ -211,23 +138,8 @@ call psb_spmm(alpha, a, x, beta, y,desc_a, info, &amp;
<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
<DD>the local portion of the global sparse matrix
<IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
@@ -241,66 +153,6 @@ 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="13" 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="13" 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="13" 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>
@@ -312,73 +164,18 @@ 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="13" 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="$y$">.
<DT><STRONG>Function value</STRONG></DT>
<DD>is the 1-norm of sparse submatrix <IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">.
<BR>
Scope: <B>local</B>
Scope: <B>global</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>.
Specified as: a long precision real number.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
@@ -396,26 +193,26 @@ An integer value; 0 means no error has been detected.
<P>
<HR>
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