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psblas3:
base/internals/psi_idx_ins_cnv.f90 base/modules/psb_base_tools_mod.f90 base/modules/psb_gen_block_map_mod.f90 base/modules/psb_hash_map_mod.f90 base/modules/psb_indx_map_mod.f90 base/modules/psb_list_map_mod.f90 base/modules/psb_repl_map_mod.f90 base/modules/psi_i_mod.f90 base/tools/psb_cdins.f90 docs/html/footnode.html docs/html/index.html docs/html/node1.html docs/html/node10.html docs/html/node100.html docs/html/node101.html docs/html/node102.html docs/html/node103.html docs/html/node104.html docs/html/node105.html docs/html/node106.html docs/html/node107.html docs/html/node108.html docs/html/node109.html docs/html/node11.html docs/html/node110.html docs/html/node111.html docs/html/node112.html docs/html/node113.html docs/html/node114.html docs/html/node115.html docs/html/node116.html docs/html/node117.html docs/html/node118.html docs/html/node119.html docs/html/node12.html docs/html/node120.html docs/html/node13.html docs/html/node14.html docs/html/node15.html docs/html/node16.html docs/html/node17.html docs/html/node18.html docs/html/node19.html docs/html/node2.html docs/html/node20.html docs/html/node21.html docs/html/node22.html docs/html/node23.html docs/html/node24.html docs/html/node25.html docs/html/node26.html docs/html/node27.html docs/html/node28.html docs/html/node29.html docs/html/node3.html docs/html/node30.html docs/html/node31.html docs/html/node32.html docs/html/node33.html docs/html/node34.html docs/html/node35.html docs/html/node36.html docs/html/node37.html docs/html/node38.html docs/html/node39.html docs/html/node4.html docs/html/node40.html docs/html/node41.html docs/html/node42.html docs/html/node43.html docs/html/node44.html docs/html/node45.html docs/html/node46.html docs/html/node47.html docs/html/node48.html docs/html/node49.html docs/html/node5.html docs/html/node50.html docs/html/node51.html docs/html/node52.html docs/html/node53.html docs/html/node54.html docs/html/node55.html docs/html/node56.html docs/html/node57.html docs/html/node58.html docs/html/node59.html docs/html/node6.html docs/html/node60.html docs/html/node61.html docs/html/node62.html docs/html/node63.html docs/html/node64.html docs/html/node65.html docs/html/node66.html docs/html/node67.html docs/html/node68.html docs/html/node69.html docs/html/node7.html docs/html/node70.html docs/html/node71.html docs/html/node72.html docs/html/node73.html docs/html/node74.html docs/html/node75.html docs/html/node76.html docs/html/node77.html docs/html/node78.html docs/html/node79.html docs/html/node8.html docs/html/node80.html docs/html/node81.html docs/html/node82.html docs/html/node83.html docs/html/node84.html docs/html/node85.html docs/html/node86.html docs/html/node87.html docs/html/node88.html docs/html/node89.html docs/html/node9.html docs/html/node90.html docs/html/node91.html docs/html/node92.html docs/html/node93.html docs/html/node94.html docs/html/node95.html docs/html/node96.html docs/html/node97.html docs/html/node98.html docs/html/node99.html docs/html/userhtml.html docs/psblas-3.0.pdf docs/src/intro.tex New docs for LIDX. New LIDX parm in idx_cnv_ins.
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Salvatore Filippone
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@@ -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>Sorting utilities</TITLE>
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<TITLE>psb_sizeof -- Memory occupation</TITLE>
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@@ -18,276 +18,111 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> Next:</B> <A NAME="tex2html1234"
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HREF="node83.html">Parallel environment routines</A>
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<B> Up:</B> <A NAME="tex2html1230"
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HREF="node55.html">Data management routines</A>
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<B> Previous:</B> <A NAME="tex2html1226"
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HREF="node81.html">psb_sizeof Memory</A>
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<B> <A NAME="tex2html1232"
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<B> Next:</B> <A NAME="tex2html1237"
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HREF="node83.html">Sorting utilities</A>
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<B> Up:</B> <A NAME="tex2html1233"
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HREF="node56.html">Data management routines</A>
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<B> Previous:</B> <A NAME="tex2html1227"
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HREF="node81.html">psb_sp_getrow Extract</A>
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<B> <A NAME="tex2html1235"
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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="SECTION000727000000000000000">
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Sorting utilities</A>
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<H2><A NAME="SECTION000726000000000000000">
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psb_sizeof -- Memory occupation</A>
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</H2>
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<P>
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<FONT SIZE="+1"><B>psb_msort -- Sorting by the Merge-sort
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algorithm</B></FONT>
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This function computes the memory occupation of a PSBLAS object.
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<P>
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<FONT SIZE="+1"><B>psb_qsort -- Sorting by the Quicksort
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algorithm</B></FONT>
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<P>
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<FONT SIZE="+1"><B>psb_hsort -- Sorting by the Heapsort algorithm</B></FONT>
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<PRE>
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call psb_msort(x,ix,dir,flag)
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call psb_qsort(x,ix,dir,flag)
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call psb_hsort(x,ix,dir,flag)
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isz = psb_sizeof(a)
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isz = psb_sizeof(desc_a)
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isz = psb_sizeof(prec)
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</PRE>
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<P>
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These serial routines sort a sequence <IMG
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WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img106.png"
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ALT="$X$"> into ascending or
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descending order. The argument meaning is identical for the three
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calls; the only difference is the algorithm used to accomplish the
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task (see Usage Notes below).
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Asynchronous.
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</DD>
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<DT><STRONG><B>On Entry </B></STRONG></DT>
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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>x</STRONG></DT>
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<DD>The sequence to be sorted.
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<DT><STRONG>a</STRONG></DT>
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<DD>A 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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Type:<B>required</B>.
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Scope: <B>local</B>
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<BR>
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Specified as: an integer, real or complex array of rank 1.
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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_Tspmat_type</TT>.
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</DD>
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<DT><STRONG>ix</STRONG></DT>
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<DD>A vector of indices.
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<DT><STRONG>desc_a</STRONG></DT>
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<DD>Communication descriptor.
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<BR>
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Type:<B>optional</B>.
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Scope: <B>local</B>
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<BR>
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Specified as: an integer array of (at least) the same size as <IMG
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WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img106.png"
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ALT="$X$">.
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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>dir</STRONG></DT>
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<DD>The desired ordering.
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<DT><STRONG>prec</STRONG></DT>
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<DD>Scope: <B>local</B>
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<BR>
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Type:<B>optional</B>.
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Type: <B>required</B>
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<BR>
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Specified as: an integer value: <DL>
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<DT><STRONG>Integer and real data:</STRONG></DT>
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<DD><code>psb_sort_up_</code>,
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<code>psb_sort_down_</code>, <code>psb_asort_up_</code>, <code>psb_asort_down_</code>;
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default <code>psb_sort_up_</code>.
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</DD>
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<DT><STRONG>Complex data:</STRONG></DT>
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<DD><code>psb_lsort_up_</code>,
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<code>psb_lsort_down_</code>, <code>psb_asort_up_</code>, <code>psb_asort_down_</code>;
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default <code>psb_lsort_up_</code>.
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</DD>
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</DL>
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</DD>
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<DT><STRONG>flag</STRONG></DT>
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<DD>Whether to keep the original values in <IMG
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WIDTH="27" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img107.png"
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ALT="$IX$">.
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Intent: <B>in</B>.
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<BR>
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Type:<B>optional</B>.
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<BR>
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Specified as: an integer value <code>psb_sort_ovw_idx_</code> or
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<code>psb_sort_keep_idx_</code>; default <code>psb_sort_ovw_idx_</code>.
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<P>
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Specified as: a preconditioner data structure precdata<TT>psb_prec_type</TT>.
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</DD>
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</DL>
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<P>
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<DL>
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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>x</STRONG></DT>
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<DD>The sequence of values, in the chosen ordering.
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<DT><STRONG>Function value</STRONG></DT>
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<DD>The memory occupation of the object specified in
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the calling sequence, in bytes.
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<BR>
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Type:<B>required</B>.
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Scope: <B>local</B>
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<BR>
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Specified as: an integer, real or complex array of rank 1.
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</DD>
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<DT><STRONG>ix</STRONG></DT>
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<DD>A vector of indices.
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<BR>
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Type: <B>Optional</B>
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<BR>
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An integer array of rank 1, whose entries are moved to the same
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position as the corresponding entries in <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="$x$">.
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Returned as: an <code>integer(psb_long_int_k_)</code> number.
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</DD>
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</DL>
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<P>
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<P>
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<FONT SIZE="+1"><B>Notes</B></FONT>
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<OL>
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<LI>For integer or real data the sorting can be performed in the up/down direction, on the
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natural or absolute values;
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</LI>
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<LI>For complex data the sorting can be done in a lexicographic
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order (i.e.: sort on the real part with ties broken according to
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the imaginary part) or on the absolute values;
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</LI>
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<LI>The routines return the items in the chosen ordering; the
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output difference is the handling of ties (i.e. items with an
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equal value) in the original input. With the merge-sort algorithm
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ties are preserved in the same relative order as they had in the
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original sequence, while this is not guaranteed for quicksort or
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heapsort;
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</LI>
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<LI>If <!-- MATH
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$flag = psb\_sort\_ovw\_idx\_$
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-->
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<IMG
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WIDTH="180" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img108.png"
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ALT="$flag = psb\_sort\_ovw\_idx\_$"> then the entries in <IMG
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WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img109.png"
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ALT="$ix(1:n)$">
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where <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img16.png"
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ALT="$n$"> is the size of <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="$x$"> are initialized to <!-- MATH
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$ix(i) \leftarrow
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i$
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-->
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<IMG
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WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img110.png"
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ALT="$ix(i) \leftarrow
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i$">; thus, upon return from the subroutine, for each
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index <IMG
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WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$i$"> we have in <IMG
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WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img111.png"
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ALT="$ix(i)$"> the position that the item <IMG
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WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img112.png"
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ALT="$x(i)$">
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occupied in the original data sequence;
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</LI>
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<LI>If <!-- MATH
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$flag = psb\_sort\_keep\_idx\_$
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-->
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<IMG
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WIDTH="185" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img113.png"
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ALT="$flag = psb\_sort\_keep\_idx\_$"> the routine will assume that
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the entries in <IMG
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WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img114.png"
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ALT="$ix(:)$"> have already been initialized by the user;
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</LI>
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<LI>The three sorting algorithms have a similar <IMG
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WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img115.png"
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ALT="$O(n \log n)$"> expected
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running time; in the average case quicksort will be the
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fastest and merge-sort the slowest. However note that:
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<OL>
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<LI>The worst case running time for quicksort is <IMG
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WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
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SRC="img116.png"
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ALT="$O(n^2)$">; the algorithm
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implemented here follows the well-known median-of-three heuristics,
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but the worst case may still apply;
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</LI>
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<LI>The worst case running time for merge-sort and heap-sort is
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<IMG
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WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img115.png"
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ALT="$O(n \log n)$"> as the average case;
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</LI>
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<LI>The merge-sort algorithm is implemented to take advantage of
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subsequences that may be already in the desired ordering prior to
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the subroutine call; this situation is relatively common when
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dealing with groups of indices of sparse matrix entries, thus
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merge-sort is the preferred choice when a sorting is needed
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by other routines in the library.
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</LI>
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</OL>
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</LI>
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</OL>
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<P>
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<P>
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Reference in New Issue
Block a user