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Fix docs and declare version 3.1
psblas3-final
Salvatore Filippone 12 years ago
parent 2b3d0fda67
commit fbf6dc613e

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@ -56,9 +56,9 @@ University of Rome ``Tor Vergata'', Italy
<BR>
<BR>
<BR>
Software version: 3.0
Software version: 3.1
<BR>
May 25, 2012.
May 2, 2013.
<BR><HR>
<!--Table of Child-Links-->

@ -92,7 +92,7 @@ Intent: <B>in</B>.
<BR>
Specified as: an integer, real or complex variable, which may be a
scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if <IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="18" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img130.png"
ALT="$m$"> is
not specified, size must agree as well.
@ -132,7 +132,7 @@ Specified as: an integer value <!-- MATH
ALT="$0&lt;= m &lt;= size(dat,1)$">.
<BR>
When <IMG
WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img133.png"
ALT="$dat$"> is a rank 2 array, specifies the number of rows to be sent
independently of the leading dimension <IMG
@ -156,7 +156,7 @@ same value on sending and receiving processes.
<OL>
<LI>This subroutine implies a synchronization, but only between the
calling process and the destination process <IMG
WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="25" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img135.png"
ALT="$dst$">.
</LI>

@ -115,7 +115,7 @@ Specified as: an integer value <!-- MATH
ALT="$0&lt;= m &lt;= size(dat,1)$">.
<BR>
When <IMG
WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img133.png"
ALT="$dat$"> is a rank 2 array, specifies the number of rows to be sent
independently of the leading dimension <IMG
@ -142,7 +142,7 @@ Intent: <B>inout</B>.
<BR>
Specified as: an integer, real or complex variable, which may be a
scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if <IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="18" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img130.png"
ALT="$m$"> is
not specified, size must agree as well.
@ -155,7 +155,7 @@ not specified, size must agree as well.
<OL>
<LI>This subroutine implies a synchronization, but only between the
calling process and the source process <IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="26" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img137.png"
ALT="$src$">.
</LI>

@ -135,7 +135,7 @@ subdomain by <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img7.png"
ALT="$\cal I$">, <IMG
WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img8.png"
ALT="$\cal B$"> and <IMG
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
@ -173,7 +173,7 @@ Point classfication.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
WIDTH="318" HEIGHT="285" ALIGN="BOTTOM" BORDER="0"
WIDTH="318" HEIGHT="283" ALIGN="BOTTOM" BORDER="0"
SRC="img13.png"
ALT="\includegraphics[scale=0.65]{figures/points.eps}">
<!-- MATH

@ -89,13 +89,13 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" 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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">, <IMG
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -132,7 +132,7 @@ Data types</CAPTION>
</DD>
<DT><STRONG>alpha</STRONG></DT>
<DD>the scalar <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">.
<BR>
@ -147,7 +147,7 @@ Specified as: a number of the data type indicated in Table&nbsp;<A HREF="#tab:f9
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -160,7 +160,7 @@ Intent: <B>in</B>.
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:f90axpby">1</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -199,7 +199,7 @@ indicated in Table&nbsp;<A HREF="#tab:f90axpby">1</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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>

@ -57,7 +57,7 @@ psb_gedot -- Dot Product</A>
<P>
This function computes dot product between two vectors <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and
<IMG
@ -66,7 +66,7 @@ This function computes dot product between two vectors <IMG
ALT="$y$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -89,7 +89,7 @@ dot \leftarrow x^T y
<BR CLEAR="ALL">
<P></P>
Else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -104,7 +104,7 @@ dot \leftarrow x^H y
-->
<IMG
WIDTH="75" HEIGHT="27" BORDER="0"
WIDTH="76" HEIGHT="27" BORDER="0"
SRC="img25.png"
ALT="\begin{displaymath}dot \leftarrow x^H y\end{displaymath}">
</DIV>
@ -124,10 +124,10 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="25" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$dot$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">, <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -165,7 +165,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -178,7 +178,7 @@ Intent: <B>in</B>.
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:f90dot">2</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -204,7 +204,7 @@ Table&nbsp;<A HREF="#tab:f90dot">2</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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>
@ -226,7 +226,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>Function value</STRONG></DT>
<DD>is the dot product of subvectors <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"

@ -58,7 +58,7 @@ psb_gedots -- Generalized Dot Product</A>
<P>
This subroutine computes a series of dot products among the columns of
two dense matrices <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -81,17 +81,17 @@ res(i) \leftarrow x(:,i)^T y(:,i)
<P></P>
If the matrices are complex, then the
usual convention applies, i.e. the conjugate transpose of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is
used. If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"> are of rank one, then <IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$"> is a scalar, else it
is a rank one array.
@ -109,10 +109,10 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">, <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -150,7 +150,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -163,7 +163,7 @@ Intent: <B>in</B>.
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:f90mdot">3</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -189,7 +189,7 @@ Table&nbsp;<A HREF="#tab:f90mdot">3</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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>
@ -209,7 +209,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>res</STRONG></DT>
<DD>is the dot product of subvectors <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"

@ -58,12 +58,12 @@ psb_geamax -- Infinity-Norm of Vector</A>
<P>
This function computes
the infinity-norm of a vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a real vector
it computes infinity norm as:
@ -83,7 +83,7 @@ amax \leftarrow \max_i |x_i|
<BR CLEAR="ALL">
<P></P>
else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a complex vector then it computes the infinity-norm as:
<BR><P></P>
@ -117,11 +117,11 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img31.png"
ALT="$amax$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
@ -160,7 +160,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
@ -193,7 +193,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>Function value</STRONG></DT>
<DD>is the infinity norm of subvector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>

@ -58,7 +58,7 @@ psb_geamaxs -- Generalized Infinity Norm</A>
<P>
This subroutine computes a series of infinity norms on the columns of
a dense matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">:
<BR><P></P>
@ -70,7 +70,7 @@ res(i) \leftarrow \max_k |x(k,i)|
-->
<IMG
WIDTH="148" HEIGHT="36" BORDER="0"
WIDTH="147" HEIGHT="36" BORDER="0"
SRC="img32.png"
ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">
</DIV>
@ -92,11 +92,11 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
@ -135,7 +135,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -165,7 +165,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>res</STRONG></DT>
<DD>is the infinity norm of the columns of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>

@ -57,12 +57,12 @@ psb_geasum -- 1-Norm of Vector</A>
<P>
This function computes the 1-norm of a vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a real vector
it computes 1-norm as:
@ -82,7 +82,7 @@ asum \leftarrow \|x_i\|
<BR CLEAR="ALL">
<P></P>
else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a complex vector then it computes 1-norm as:
<BR><P></P>
@ -116,11 +116,11 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img35.png"
ALT="$asum$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
@ -159,7 +159,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
@ -192,7 +192,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>Function value</STRONG></DT>
<DD>is the 1-norm of vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>

@ -58,7 +58,7 @@ psb_geasums -- Generalized 1-Norm of Vector</A>
<P>
This subroutine computes a series of 1-norms on the columns of
a dense matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">:
<BR><P></P>
@ -70,19 +70,19 @@ res(i) \leftarrow \max_k |x(k,i)|
-->
<IMG
WIDTH="148" HEIGHT="36" BORDER="0"
WIDTH="147" HEIGHT="36" BORDER="0"
SRC="img32.png"
ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
This function computes the 1-norm of a vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a real vector
it computes 1-norm as:
@ -102,7 +102,7 @@ res(i) \leftarrow \|x_i\|
<BR CLEAR="ALL">
<P></P>
else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a complex vector then it computes 1-norm as:
<BR><P></P>
@ -114,7 +114,7 @@ res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1
-->
<IMG
WIDTH="207" HEIGHT="28" BORDER="0"
WIDTH="206" HEIGHT="28" BORDER="0"
SRC="img37.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">
</DIV>
@ -136,11 +136,11 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
@ -179,7 +179,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
@ -212,7 +212,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>res</STRONG></DT>
<DD>contains the 1-norm of (the columns of) <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>

@ -57,12 +57,12 @@ psb_genrm2 -- 2-Norm of Vector</A>
<P>
This function computes the 2-norm of a vector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
If <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a real vector
it computes 2-norm as:
@ -82,7 +82,7 @@ nrm2 \leftarrow \sqrt{x^T x}
<BR CLEAR="ALL">
<P></P>
else if <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> is a complex vector then it computes 2-norm as:
<BR><P></P>
@ -111,11 +111,11 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img40.png"
ALT="$nrm2$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Function</B></TD>
@ -159,7 +159,7 @@ psb_genrm2(x, desc_a, info)
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -191,7 +191,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>Function Value</STRONG></DT>
<DD>is the 2-norm of subvector <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>

@ -58,7 +58,7 @@ psb_genrm2s -- Generalized 2-Norm of Vector</A>
<P>
This subroutine computes a series of 2-norms on the columns of
a dense matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">:
<BR><P></P>
@ -70,7 +70,7 @@ res(i) \leftarrow \|x(:,i)\|_2
-->
<IMG
WIDTH="126" HEIGHT="28" BORDER="0"
WIDTH="124" HEIGHT="28" BORDER="0"
SRC="img41.png"
ALT="\begin{displaymath}res(i) \leftarrow \Vert x(:,i)\Vert _2 \end{displaymath}">
</DIV>
@ -92,11 +92,11 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img28.png"
ALT="$res$"></TD>
<TD ALIGN="LEFT"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
@ -135,7 +135,7 @@ Data types</CAPTION>
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
@ -168,7 +168,7 @@ Specified as: an object of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>res</STRONG></DT>
<DD>contains the 1-norm of (the columns of) <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>

@ -71,7 +71,7 @@ nrm1 \leftarrow \|A\|_1
-->
<IMG
WIDTH="98" HEIGHT="28" BORDER="0"
WIDTH="97" HEIGHT="28" BORDER="0"
SRC="img42.png"
ALT="\begin{displaymath}nrm1 \leftarrow \Vert A\Vert _1 \end{displaymath}">
</DIV>

@ -71,7 +71,7 @@ nrmi \leftarrow \|A\|_\infty
-->
<IMG
WIDTH="102" HEIGHT="28" BORDER="0"
WIDTH="101" HEIGHT="28" BORDER="0"
SRC="img43.png"
ALT="\begin{displaymath}nrmi \leftarrow \Vert A\Vert _\infty \end{displaymath}">
</DIV>

@ -88,7 +88,7 @@ y \leftarrow \alpha A^T x + \beta y
-->
<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"
WIDTH="112" HEIGHT="27" BORDER="0"
SRC="img45.png"
ALT="\begin{displaymath}
y \leftarrow \alpha A^T x + \beta y
@ -121,7 +121,7 @@ y \leftarrow \alpha A^H x + \beta y
where:
<DL>
<DT><STRONG><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></STRONG></DT>
<DD>is the global dense matrix <IMG
@ -162,13 +162,13 @@ Data types</CAPTION>
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" 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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">, <IMG
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -212,7 +212,7 @@ call psb_spmm(alpha, a, x, beta, y,desc_a, info, &amp;
</DD>
<DT><STRONG>alpha</STRONG></DT>
<DD>the scalar <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">.
<BR>
@ -243,7 +243,7 @@ Specified as: an object of type spdata<TT>psb_Tspmat_type</TT>.
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
@ -257,7 +257,7 @@ Intent: <B>in</B>.
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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -298,7 +298,7 @@ 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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>
@ -335,7 +335,7 @@ Type: <B>optional</B>
Intent: <B>in</B>.
<BR>
Default: <IMG
WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="79" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img49.png"
ALT="$trans = N$">
<BR>
@ -353,7 +353,7 @@ Type: <B>optional</B>
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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> and <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"

@ -88,7 +88,7 @@ y &amp;\leftarrow&amp; \alpha T^{-H} D x + \beta y\\
where:
<DL>
<DT><STRONG><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></STRONG></DT>
<DD>is the global dense matrix <IMG
@ -142,7 +142,7 @@ Data types</CAPTION>
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img51.png"
ALT="$T$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">, <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -151,7 +151,7 @@ Data types</CAPTION>
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img52.png"
ALT="$D$">, <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">, <IMG
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -188,7 +188,7 @@ Data types</CAPTION>
</DD>
<DT><STRONG>alpha</STRONG></DT>
<DD>the scalar <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">.
<BR>
@ -220,7 +220,7 @@ Specified as: an object type specified in
<DT><STRONG>x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
@ -234,7 +234,7 @@ Intent: <B>in</B>.
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:f90spsm">13</A>. The rank of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> must be the same of <IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
@ -275,7 +275,7 @@ Table&nbsp;<A HREF="#tab:f90spsm">13</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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>
@ -310,7 +310,7 @@ Type: <B>optional</B>
Intent: <B>in</B>.
<BR>
Default: <IMG
WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="79" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img49.png"
ALT="$trans = N$">
<BR>
@ -336,7 +336,7 @@ Type: <B>optional</B>
Intent: <B>in</B>.
<BR>
Default: <IMG
WIDTH="76" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="76" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img53.png"
ALT="$unitd = U$">
<BR>
@ -399,7 +399,7 @@ Type: <B>optional</B>
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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> with the
TARGET attribute.

@ -78,7 +78,7 @@ x \leftarrow \alpha x
where:
<DL>
<DT><STRONG><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></STRONG></DT>
<DD>is a global dense submatrix.
@ -95,10 +95,10 @@ Data types</CAPTION>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">, <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
@ -141,7 +141,7 @@ call psb_halo(x, desc_a, info, alpha, work, data)
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -168,7 +168,7 @@ Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>alpha</STRONG></DT>
<DD>the scalar <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$">.
<BR>
@ -195,7 +195,7 @@ Type: <B>optional</B>
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"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
</DD>
@ -217,7 +217,7 @@ index list on which to base the data exchange.
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense result matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
@ -278,7 +278,7 @@ distribution is such that each process will own 32 entries in the
index space, with a halo made of 8 entries placed at local indices 33
through 40. If process 0 assigns an initial value of 1 to its entries
in the <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> vector, and process 1 assigns a value of 2, then after a
call to <code>psb_halo</code> the contents of the local vectors will be the

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