From 2f514d1959c9b5ed953c6fce7c925de5787c1f02 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Tue, 30 Sep 2025 19:09:03 +0200 Subject: [PATCH] Update sorting docs --- docs/html/userhtmlse6.html | 120 +- docs/psblas-3.9.pdf | 3482 ++++++++++++++++++------------------ docs/src/toolsrout.tex | 20 +- 3 files changed, 1842 insertions(+), 1780 deletions(-) diff --git a/docs/html/userhtmlse6.html b/docs/html/userhtmlse6.html index 7d23f86f..f5be71d9 100644 --- a/docs/html/userhtmlse6.html +++ b/docs/html/userhtmlse6.html @@ -3872,72 +3872,76 @@ class="cmtt-10">integer(psb_long_int_k_) number. id="x12-1050006.27">Sorting utilities —

psb_msort — Sorting by the Merge-sort algorithm +class="pplb7t-x-x-120">_isort — Sorting by the Insertion-sort algorithm

psb_qsort — Sorting by the Quicksort algorithm +class="pplb7t-x-x-120">_msort — Sorting by the Merge-sort algorithm

psb_qsort — Sorting by the Quicksort algorithm +

psb_hsort — Sorting by the Heapsort algorithm 

+call psb_isort(x,ix,dir,flag)
 call psb_msort(x,ix,dir,flag)
 call psb_qsort(x,ix,dir,flag)
 call psb_hsort(x,ix,dir,flag)
-

-

These serial routines sort a sequence

+

These serial routines sort a sequence 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). +argument meaning is identical for all calls; the only difference is the algorithm used +to accomplish the task (see Usage Notes below).

-

+

Type:

-

Asynchronous. +

Asynchronous.

-

+

On Entry

-

+

-

+

x

-

The sequence to be sorted.

The sequence to be sorted.
Type:required.
Specified as: an integer, real or complex array of rank 1.

-

+

ix

-

A vector of indices.

A vector of indices.
Type:optional.
Specified as: an integer array of (at least) the same size as X.

-

+

dir

-

The desired ordering.

The desired ordering.
Type:optional.
Specified as: an integer value:

-

+

Integer and real data:

-

psb_sort_up_, psb_sort_down_, psb_asort_up_, @@ -3948,11 +3952,11 @@ class="cmtt-10">psb_sort_up_.

-

+

Complex data:

-

psb_lsort_up_, psb_lsort_down_, psb_asort_up_, @@ -3960,11 +3964,11 @@ class="cmtt-10">psb_asort_up_, class="cmtt-10">psb_asort_down_; default psb_lsort_up_.

-

+

flag

-

Whether to keep the original values in

Whether to keep the original values in IX.
Type:optional.
psb_sort_keep_idx_; default psb_sort_ovw_idx_.

-

+

-

+

On Return

-

+

-

+

x

-

The sequence of values, in the chosen ordering.

The sequence of values, in the chosen ordering.
Type:required.
Specified as: an integer, real or complex array of rank 1.

-

+

ix

-

A vector of indices.

A vector of indices.
Type: Optional
An integer array of rank 1, whose entries are moved to the same position as the corresponding entries in x.

-

Notes

  1. -

    For integer or real data the sorting can be performed in the up/down +

    For integer or real data the sorting can be performed in the up/down direction, on the natural or absolute values;

  2. -

    For complex data the sorting can be done in a lexicographic order (i.e.: +

    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; @@ -4020,15 +4024,15 @@ class="pplb7t-x-x-120">Notes

  3. -

    The routines return the items in the chosen ordering; the output +

    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; + original input. With the insertion-sort or merge-sort algorithms ties are + preserved in the same relative order as they had in the original sequence, + while this is not guaranteed for quicksort or heapsort;

  4. -

    If

    If flag = psb_) occupied

  5. -

    If

    If flag = psb_(:) have already been initialized by the user;

  6. -

    The three sorting algorithms have a similar

    Three sorting algorithms have a similar O(n log n) expected running time; +class="zplmr7t-">) expected running time, + whereas insertion sort has an expected running time O(n2); of the other three, in the average case quicksort will be the fastest and merge-sort the slowest. However note that:

    1. -

      The worst case running time +

      The the best case running time for insertion sort is Ω(n) while the + average and worst case are O(n2); however for very short input + sequences this is likely to be the fastest method; +

      2. +
    2. +

      The worst case running time for quicksort is O(); the algorithm implemented here follows the apply;

    3. -

      The worst case running time for merge-sort and heap-sort is + class="enumerate" id="x12-105018x3"> +

      The worst case running time for merge-sort and heap-sort is O(n log n) as the average case; + + +

    4. -

      The merge-sort algorithm is implemented to take advantage of + class="enumerate" id="x12-105020x4"> +

      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.

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F@ FA FB FC FD FE FF FG FH FI FJ FK FL FM FN FO FP FQ FR FS FT FU FV FW FX FY FZ F[ F\ F] F^ F_ F` Fa Fb Fc +}4 +{+~ endstream endobj startxref -2848054 +2850453 %%EOF diff --git a/docs/src/toolsrout.tex b/docs/src/toolsrout.tex index d026f585..d58faadc 100644 --- a/docs/src/toolsrout.tex +++ b/docs/src/toolsrout.tex @@ -1780,6 +1780,9 @@ Returned as: an \verb|integer(psb_long_int_k_)| number. \clearpage\subsection{Sorting utilities --- } %\addcontentsline{toc}{subsection}{Sorting utilities} +{\par\noindent\large\bfseries psb\_isort --- Sorting by the Insertion-sort + algorithm} + {\par\noindent\large\bfseries psb\_msort --- Sorting by the Merge-sort algorithm} @@ -1788,13 +1791,14 @@ Returned as: an \verb|integer(psb_long_int_k_)| number. {\par\noindent\large\bfseries psb\_hsort --- Sorting by the Heapsort algorithm} \begin{verbatim} +call psb_isort(x,ix,dir,flag) call psb_msort(x,ix,dir,flag) call psb_qsort(x,ix,dir,flag) call psb_hsort(x,ix,dir,flag) \end{verbatim} These serial routines sort a sequence $X$ into ascending or -descending order. The argument meaning is identical for the three +descending order. The argument meaning is identical for all calls; the only difference is the algorithm used to accomplish the task (see Usage Notes below). \begin{description} @@ -1843,7 +1847,7 @@ position as the corresponding entries in $x$. the imaginary part) or on the absolute values; \item 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 + equal value) in the original input. With the insertion-sort or merge-sort algorithms ties are preserved in the same relative order as they had in the original sequence, while this is not guaranteed for quicksort or heapsort; @@ -1854,11 +1858,15 @@ position as the corresponding entries in $x$. occupied in the original data sequence; \item If $flag = psb\_sort\_keep\_idx\_$ the routine will assume that the entries in $ix(:)$ have already been initialized by the user; -\item The three sorting algorithms have a similar $O(n \log n)$ expected - running time; in the average case quicksort will be the +\item Three sorting algorithms have a similar $O(n \log n)$ expected + running time, whereas insertion sort has an expected running time + $O(n^2)$; of the other three, in the average case quicksort will be the fastest and merge-sort the slowest. However note that: -\begin{enumerate} -\item The worst case running time for quicksort is $O(n^2)$; the algorithm + \begin{enumerate} + \item The the best case running time for insertion sort is $\Omega(n)$ while the average + and worst case are $O(n^2)$; however for very short input sequences this is + likely to be the fastest method; + \item The worst case running time for quicksort is $O(n^2)$; the algorithm implemented here follows the well-known median-of-three heuristics, but the worst case may still apply; \item The worst case running time for merge-sort and heap-sort is