fdurastante/psblas3
1
0
Fork 0
mirror of https://github.com/sfilippone/psblas3.git synced 2026-10-16 10:52:08 +00:00
Code Issues Packages Projects Releases Wiki Activity

psblas3:

Browse Source 
Updated docs.
This commit is contained in:
Salvatore Filippone
2017-02-12 18:19:15 +00:00
parent 9ab0539881
commit 001aa819fa
147 changed files with 22648 additions and 22177 deletions
Download Patch File Download Diff File Expand all files Collapse all files
docs/html/node95.html
+153 -188
View File
@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>Sorting utilities -- </TITLE>
<META NAME="description" CONTENT="Sorting utilities -- ">
<TITLE>psb_sp_getrow -- Extract row(s) from a sparse matrix</TITLE>
<META NAME="description" CONTENT="psb_sp_getrow -- Extract row(s) from a sparse matrix">
<META NAME="keywords" CONTENT="userhtml">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
@@ -18,118 +18,125 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<LINK REL="STYLESHEET" HREF="userhtml.css">
<LINK REL="next" HREF="node96.html">
<LINK REL="previous" HREF="node94.html">
<LINK REL="up" HREF="node68.html">
<LINK REL="up" HREF="node70.html">
<LINK REL="next" HREF="node96.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html1428"
<A NAME="tex2html1436"
HREF="node96.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html1424"
HREF="node68.html">
<A NAME="tex2html1432"
HREF="node70.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html1420"
<A NAME="tex2html1426"
HREF="node94.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
<A NAME="tex2html1426"
<A NAME="tex2html1434"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html1429"
HREF="node96.html">Parallel environment routines</A>
<B> Up:</B> <A NAME="tex2html1425"
HREF="node68.html">Data management routines</A>
<B> Previous:</B> <A NAME="tex2html1421"
HREF="node94.html">psb_sizeof Memory</A>
&nbsp; <B> <A NAME="tex2html1427"
<B> Next:</B> <A NAME="tex2html1437"
HREF="node96.html">psb_sizeof Memory</A>
<B> Up:</B> <A NAME="tex2html1433"
HREF="node70.html">Data management routines</A>
<B> Previous:</B> <A NAME="tex2html1427"
HREF="node94.html">psb_get_overlap Extract</A>
&nbsp; <B> <A NAME="tex2html1435"
HREF="node1.html">Contents</A></B>
<BR>
<BR>
<!--End of Navigation Panel-->
<H2><A NAME="SECTION000727000000000000000">
Sorting utilities -- </A>
<H2><A NAME="SECTION000725000000000000000">
psb_sp_getrow -- Extract row(s) from a sparse
matrix</A>
</H2>
<P>
<FONT SIZE="+1"><B>psb_msort -- Sorting by the Merge-sort
algorithm</B></FONT>
<P>
<FONT SIZE="+1"><B>psb_qsort -- Sorting by the Quicksort
algorithm</B></FONT>
<P>
<FONT SIZE="+1"><B>psb_hsort -- Sorting by the Heapsort algorithm</B></FONT>
<PRE>
call psb_msort(x,ix,dir,flag)
call psb_qsort(x,ix,dir,flag)
call psb_hsort(x,ix,dir,flag)
call psb_sp_getrow(row, a, nz, ia, ja, val, info, &amp;
&amp; append, nzin, lrw)
</PRE>
<P>
These serial routines sort a sequence <IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img114.png"
ALT="$X$"> into ascending or
descending order. The argument meaning is identical for the three
calls; the only difference is the algorithm used to accomplish the
task (see Usage Notes below).
<DL>
<DT><STRONG>Type:</STRONG></DT>
<DD>Asynchronous.
</DD>
<DT><STRONG><B>On Entry </B></STRONG></DT>
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>The sequence to be sorted.
<DT><STRONG>row</STRONG></DT>
<DD>The (first) row to be extracted.
<BR>
Type:<B>required</B>.
Scope:<B>local</B>
<BR>
Specified as: an integer, real or complex array of rank 1.
Type:<B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an integer <IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img111.png"
ALT="$&gt;0$">.
</DD>
<DT><STRONG>ix</STRONG></DT>
<DD>A vector of indices.
<DT><STRONG>a</STRONG></DT>
<DD>the matrix from which to get rows.
<BR>
Type:<B>optional</B>.
Scope:<B>local</B>
<BR>
Specified as: an integer array of (at least) the same size as <IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img114.png"
ALT="$X$">.
Type:<B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
</DD>
<DT><STRONG>dir</STRONG></DT>
<DD>The desired ordering.
<DT><STRONG>append</STRONG></DT>
<DD>Whether to append or overwrite existing output.
<BR>
Type:<B>optional</B>.
Scope:<B>local</B>
<BR>
Specified as: an integer value: <DL>
<DT><STRONG>Integer and real data:</STRONG></DT>
<DD><code>psb_sort_up_</code>,
<code>psb_sort_down_</code>, <code>psb_asort_up_</code>, <code>psb_asort_down_</code>;
default <code>psb_sort_up_</code>.
Type:<B>optional</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a logical value default: false (overwrite).
</DD>
<DT><STRONG>Complex data:</STRONG></DT>
<DD><code>psb_lsort_up_</code>,
<code>psb_lsort_down_</code>, <code>psb_asort_up_</code>, <code>psb_asort_down_</code>;
default <code>psb_lsort_up_</code>.
</DD>
</DL>
</DD>
<DT><STRONG>flag</STRONG></DT>
<DD>Whether to keep the original values in <IMG
WIDTH="27" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img115.png"
ALT="$IX$">.
<DT><STRONG>nzin</STRONG></DT>
<DD>Input size to be appended to.
<BR>
Type:<B>optional</B>.
Scope:<B>local</B>
<BR>
Specified as: an integer value <code>psb_sort_ovw_idx_</code> or
<code>psb_sort_keep_idx_</code>; default <code>psb_sort_ovw_idx_</code>.
Type:<B>optional</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an integer <IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img111.png"
ALT="$&gt;0$">. When append is true, specifies how many
entries in the output vectors are already filled.
</DD>
<DT><STRONG>lrw</STRONG></DT>
<DD>The last row to be extracted.
<BR>
Scope:<B>local</B>
<BR>
Type:<B>optional</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an integer <IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img111.png"
ALT="$&gt;0$">, default: <IMG
WIDTH="31" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img112.png"
ALT="$row$">.
<P>
</DD>
@@ -140,152 +147,110 @@ Specified as: an integer value <code>psb_sort_ovw_idx_</code> or
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>The sequence of values, in the chosen ordering.
<DT><STRONG>nz</STRONG></DT>
<DD>the number of elements returned by this call.
<BR>
Scope:<B>local</B>.
<BR>
Type:<B>required</B>.
<BR>
Specified as: an integer, real or complex array of rank 1.
Intent: <B>out</B>.
<BR>
Returned as: an integer scalar.
</DD>
<DT><STRONG>ix</STRONG></DT>
<DD>A vector of indices.
<DT><STRONG>ia</STRONG></DT>
<DD>the row indices.
<BR>
Type: <B>Optional</B>
Scope:<B>local</B>.
<BR>
An integer array of rank 1, whose entries are moved to the same
position as the corresponding entries in <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
Type:<B>required</B>.
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: an integer array with the <code>ALLOCATABLE</code> attribute.
</DD>
<DT><STRONG>ja</STRONG></DT>
<DD>the column indices of the elements to be inserted.
<BR>
Scope:<B>local</B>.
<BR>
Type:<B>required</B>.
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: an integer array with the <code>ALLOCATABLE</code> attribute.
</DD>
<DT><STRONG>val</STRONG></DT>
<DD>the elements to be inserted.
<BR>
Scope:<B>local</B>.
<BR>
Type:<B>required</B>.
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a real array with the <code>ALLOCATABLE</code> attribute.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
<BR>
Intent: <B>out</B>.
<BR>
An integer value; 0 means no error has been detected.
</DD>
</DL>
<P>
<P>
<FONT SIZE="+1"><B>Notes</B></FONT>
<OL>
<LI>For integer or real data the sorting can be performed in the up/down direction, on the
natural or absolute values;
<LI>The output <IMG
WIDTH="22" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img101.png"
ALT="$nz$"> is always the size of the output generated by
the current call; thus, if <code>append=.true.</code>, the total output
size will be <IMG
WIDTH="74" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img113.png"
ALT="$nzin+nz$">, with the newly extracted coefficients stored in
entries <code>nzin+1:nzin+nz</code> of the array arguments;
</LI>
<LI>For complex data the sorting can be done in a lexicographic
order (i.e.: sort on the real part with ties broken according to
the imaginary part) or on the absolute values;
<LI>When <code>append=.true.</code> the output arrays are reallocated as
necessary;
</LI>
<LI>The routines return the items in the chosen ordering; the
output difference is the handling of ties (i.e. items with an
equal value) in the original input. With the merge-sort algorithm
ties are preserved in the same relative order as they had in the
original sequence, while this is not guaranteed for quicksort or
heapsort;
</LI>
<LI>If <!-- MATH
$flag = psb\_sort\_ovw\_idx\_$
-->
<IMG
WIDTH="180" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img116.png"
ALT="$flag = psb\_sort\_ovw\_idx\_$"> then the entries in <IMG
WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img117.png"
ALT="$ix(1:n)$">
where <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img16.png"
ALT="$n$"> is the size of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"> are initialized to <!-- MATH
$ix(i) \leftarrow
i$
-->
<IMG
WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img118.png"
ALT="$ix(i) \leftarrow
i$">; thus, upon return from the subroutine, for each
index <IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"> we have in <IMG
WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img119.png"
ALT="$ix(i)$"> the position that the item <IMG
WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img120.png"
ALT="$x(i)$">
occupied in the original data sequence;
</LI>
<LI>If <!-- MATH
$flag = psb\_sort\_keep\_idx\_$
-->
<IMG
WIDTH="185" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img121.png"
ALT="$flag = psb\_sort\_keep\_idx\_$"> the routine will assume that
the entries in <IMG
WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img122.png"
ALT="$ix(:)$"> have already been initialized by the user;
</LI>
<LI>The three sorting algorithms have a similar <IMG
WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img123.png"
ALT="$O(n \log n)$"> expected
running time; in the average case quicksort will be the
fastest and merge-sort the slowest. However note that:
<OL>
<LI>The worst case running time for quicksort is <IMG
WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="img124.png"
ALT="$O(n^2)$">; the algorithm
implemented here follows the well-known median-of-three heuristics,
but the worst case may still apply;
</LI>
<LI>The worst case running time for merge-sort and heap-sort is
<IMG
WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img123.png"
ALT="$O(n \log n)$"> as the average case;
</LI>
<LI>The merge-sort algorithm is implemented to take advantage of
subsequences that may be already in the desired ordering prior to
the subroutine call; this situation is relatively common when
dealing with groups of indices of sparse matrix entries, thus
merge-sort is the preferred choice when a sorting is needed
by other routines in the library.
<LI>The row and column indices are returned in the local numbering
scheme; if the global numbering is desired, the user may employ the
<code>psb_loc_to_glob</code> routine on the output.
</LI>
</OL>
</LI>
</OL>
<P>
<P>
<HR>
<!--Navigation Panel-->
<A NAME="tex2html1428"
<A NAME="tex2html1436"
HREF="node96.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html1424"
HREF="node68.html">
<A NAME="tex2html1432"
HREF="node70.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html1420"
<A NAME="tex2html1426"
HREF="node94.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
<A NAME="tex2html1426"
<A NAME="tex2html1434"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html1429"
HREF="node96.html">Parallel environment routines</A>
<B> Up:</B> <A NAME="tex2html1425"
HREF="node68.html">Data management routines</A>
<B> Previous:</B> <A NAME="tex2html1421"
HREF="node94.html">psb_sizeof Memory</A>
&nbsp; <B> <A NAME="tex2html1427"
<B> Next:</B> <A NAME="tex2html1437"
HREF="node96.html">psb_sizeof Memory</A>
<B> Up:</B> <A NAME="tex2html1433"
HREF="node70.html">Data management routines</A>
<B> Previous:</B> <A NAME="tex2html1427"
HREF="node94.html">psb_get_overlap Extract</A>
&nbsp; <B> <A NAME="tex2html1435"
HREF="node1.html">Contents</A></B>
<!--End of Navigation Panel-->