|
|
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
|
|
|
|
"http://www.w3.org/TR/html4/loose.dtd">
|
|
|
|
|
<html >
|
|
|
|
|
<head><title>Sorting utilities — </title>
|
|
|
|
|
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
|
|
|
|
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
|
|
|
|
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
|
|
|
|
<!-- html,3 -->
|
|
|
|
|
<meta name="src" content="userhtml.tex">
|
|
|
|
|
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
|
|
|
|
</head><body
|
|
|
|
|
>
|
|
|
|
|
<!--l. 1780--><div class="crosslinks"><p class="noindent">[<a
|
|
|
|
|
href="userhtmlsu55.html" >prev</a>] [<a
|
|
|
|
|
href="userhtmlsu55.html#tailuserhtmlsu55.html" >prev-tail</a>] [<a
|
|
|
|
|
href="userhtmlsu53.html#tailuserhtmlsu56.html">tail</a>] [<a
|
|
|
|
|
href="userhtmlsu32.html#userhtmlsu58.html" >up</a>] </p></div>
|
|
|
|
|
<h4 class="subsectionHead"><span class="titlemark">6.27 </span> <a
|
|
|
|
|
id="x67-1040006.27"></a>Sorting utilities — </h4>
|
|
|
|
|
<!--l. 1783--><p class="noindent" ><span
|
|
|
|
|
class="cmbx-12">psb</span><span
|
|
|
|
|
class="cmbx-12">_msort — Sorting by the Merge-sort algorithm</span>
|
|
|
|
|
<!--l. 1786--><p class="noindent" ><span
|
|
|
|
|
class="cmbx-12">psb</span><span
|
|
|
|
|
class="cmbx-12">_qsort — Sorting by the Quicksort algorithm</span>
|
|
|
|
|
<!--l. 1789--><p class="noindent" ><span
|
|
|
|
|
class="cmbx-12">psb</span><span
|
|
|
|
|
class="cmbx-12">_hsort — Sorting by the Heapsort algorithm</span>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<pre class="verbatim" id="verbatim-60">
|
|
|
|
|
call psb_msort(x,ix,dir,flag)
|
|
|
|
|
call psb_qsort(x,ix,dir,flag)
|
|
|
|
|
call psb_hsort(x,ix,dir,flag)
|
|
|
|
|
</pre>
|
|
|
|
|
<!--l. 1794--><p class="nopar" >
|
|
|
|
|
<!--l. 1796--><p class="indent" > These serial routines sort a sequence <span
|
|
|
|
|
class="cmmi-10">X </span>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 class="description"><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">Type:</span> </dt><dd
|
|
|
|
|
class="description">Asynchronous.
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">On Entry</span> </dt><dd
|
|
|
|
|
class="description">
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">x</span> </dt><dd
|
|
|
|
|
class="description">The sequence to be sorted.<br
|
|
|
|
|
class="newline" />Type:<span
|
|
|
|
|
class="cmbx-10">required</span>.<br
|
|
|
|
|
class="newline" />Specified as: an integer, real or complex array of rank 1.
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">ix</span> </dt><dd
|
|
|
|
|
class="description">A vector of indices.<br
|
|
|
|
|
class="newline" />Type:<span
|
|
|
|
|
class="cmbx-10">optional</span>.<br
|
|
|
|
|
class="newline" />Specified as: an integer array of (at least) the same size as <span
|
|
|
|
|
class="cmmi-10">X</span>.
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">dir</span> </dt><dd
|
|
|
|
|
class="description">The desired ordering.<br
|
|
|
|
|
class="newline" />Type:<span
|
|
|
|
|
class="cmbx-10">optional</span>.<br
|
|
|
|
|
class="newline" />Specified as: an integer value:
|
|
|
|
|
<dl class="description"><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">Integer and real data:</span> </dt><dd
|
|
|
|
|
class="description"><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_sort_up_</span></span></span>, <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_sort_down_</span></span></span>,
|
|
|
|
|
<span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_asort_up_</span></span></span>, <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_asort_down_</span></span></span>; default <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_sort_up_</span></span></span>.
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">Complex data:</span> </dt><dd
|
|
|
|
|
class="description"><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_lsort_up_</span></span></span>, <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_lsort_down_</span></span></span>, <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_asort_up_</span></span></span>,
|
|
|
|
|
<span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_asort_down_</span></span></span>; default <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_lsort_up_</span></span></span>.</dd></dl>
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">flag</span> </dt><dd
|
|
|
|
|
class="description">Whether to keep the original values in <span
|
|
|
|
|
class="cmmi-10">IX</span>.<br
|
|
|
|
|
class="newline" />Type:<span
|
|
|
|
|
class="cmbx-10">optional</span>.<br
|
|
|
|
|
class="newline" />Specified as: an integer value <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_sort_ovw_idx_</span></span></span> or <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_sort_keep_idx_</span></span></span>;
|
|
|
|
|
default <span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-10">psb_sort_ovw_idx_</span></span></span>.
|
|
|
|
|
</dd></dl>
|
|
|
|
|
<!--l. 1826--><p class="indent" >
|
|
|
|
|
<dl class="description"><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">On Return</span> </dt><dd
|
|
|
|
|
class="description">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">x</span> </dt><dd
|
|
|
|
|
class="description">The sequence of values, in the chosen ordering.<br
|
|
|
|
|
class="newline" />Type:<span
|
|
|
|
|
class="cmbx-10">required</span>.<br
|
|
|
|
|
class="newline" />Specified as: an integer, real or complex array of rank 1.
|
|
|
|
|
</dd><dt class="description">
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-10">ix</span> </dt><dd
|
|
|
|
|
class="description">A vector of indices.<br
|
|
|
|
|
class="newline" />Type: <span
|
|
|
|
|
class="cmbx-10">Optional </span><br
|
|
|
|
|
class="newline" />An integer array of rank 1, whose entries are moved to the same position
|
|
|
|
|
as the corresponding entries in <span
|
|
|
|
|
class="cmmi-10">x</span>.</dd></dl>
|
|
|
|
|
<!--l. 1837--><p class="noindent" ><span
|
|
|
|
|
class="cmbx-12">Notes</span>
|
|
|
|
|
<ol class="enumerate1" >
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104002x1">For integer or real data the sorting can be performed in the up/down
|
|
|
|
|
direction, on the natural or absolute values;
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104004x2">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>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104006x3">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
|
|
|
|
|
class="enumerate" id="x67-104008x4">If <span
|
|
|
|
|
class="cmmi-10">flag </span>= <span
|
|
|
|
|
class="cmmi-10">psb</span>_<span
|
|
|
|
|
class="cmmi-10">sort</span>_<span
|
|
|
|
|
class="cmmi-10">ovw</span>_<span
|
|
|
|
|
class="cmmi-10">idx</span>_ then the entries in <span
|
|
|
|
|
class="cmmi-10">ix</span>(1 : <span
|
|
|
|
|
class="cmmi-10">n</span>) where <span
|
|
|
|
|
class="cmmi-10">n </span>is the size
|
|
|
|
|
of <span
|
|
|
|
|
class="cmmi-10">x </span>are initialized to <span
|
|
|
|
|
class="cmmi-10">ix</span>(<span
|
|
|
|
|
class="cmmi-10">i</span>) <span
|
|
|
|
|
class="cmsy-10">← </span><span
|
|
|
|
|
class="cmmi-10">i</span>; thus, upon return from the subroutine,
|
|
|
|
|
for each index <span
|
|
|
|
|
class="cmmi-10">i </span>we have in <span
|
|
|
|
|
class="cmmi-10">ix</span>(<span
|
|
|
|
|
class="cmmi-10">i</span>) the position that the item <span
|
|
|
|
|
class="cmmi-10">x</span>(<span
|
|
|
|
|
class="cmmi-10">i</span>) occupied
|
|
|
|
|
in the original data sequence;
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104010x5">If <span
|
|
|
|
|
class="cmmi-10">flag </span>= <span
|
|
|
|
|
class="cmmi-10">psb</span>_<span
|
|
|
|
|
class="cmmi-10">sort</span>_<span
|
|
|
|
|
class="cmmi-10">keep</span>_<span
|
|
|
|
|
class="cmmi-10">idx</span>_ the routine will assume that the entries in
|
|
|
|
|
<span
|
|
|
|
|
class="cmmi-10">ix</span>(:) have already been initialized by the user;
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104012x6">The three sorting algorithms have a similar <span
|
|
|
|
|
class="cmmi-10">O</span>(<span
|
|
|
|
|
class="cmmi-10">n</span>log <span
|
|
|
|
|
class="cmmi-10">n</span>) expected running time;
|
|
|
|
|
in the average case quicksort will be the fastest and merge-sort the slowest.
|
|
|
|
|
However note that:
|
|
|
|
|
<ol class="enumerate2" >
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104014x1">The worst case running time for quicksort is <span
|
|
|
|
|
class="cmmi-10">O</span>(<span
|
|
|
|
|
class="cmmi-10">n</span><sup><span
|
|
|
|
|
class="cmr-7">2</span></sup>); the algorithm
|
|
|
|
|
implemented here follows the well-known median-of-three heuristics,
|
|
|
|
|
but the worst case may still apply;
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104016x2">The worst case running time for merge-sort and heap-sort is
|
|
|
|
|
<span
|
|
|
|
|
class="cmmi-10">O</span>(<span
|
|
|
|
|
class="cmmi-10">n</span>log <span
|
|
|
|
|
class="cmmi-10">n</span>) as the average case;
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x67-104018x3">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></ol>
|
|
|
|
|
</li></ol>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<!--l. 3--><div class="crosslinks"><p class="noindent">[<a
|
|
|
|
|
href="userhtmlsu55.html" >prev</a>] [<a
|
|
|
|
|
href="userhtmlsu55.html#tailuserhtmlsu55.html" >prev-tail</a>] [<a
|
|
|
|
|
href="userhtmlsu56.html" >front</a>] [<a
|
|
|
|
|
href="userhtmlsu32.html#userhtmlsu58.html" >up</a>] </p></div>
|
|
|
|
|
<!--l. 3--><p class="indent" > <a
|
|
|
|
|
id="tailuserhtmlsu56.html"></a>
|
|
|
|
|
</body></html>
|
