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Updated description of DOT and friends to account for optional GLOBAL

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Salvatore Filippone
2018-04-20 15:57:26 +01:00
parent eaaa701c2e
commit 4a6c0857f1
281 changed files with 15338 additions and 14268 deletions
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@@ -22,26 +22,26 @@
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@@ -70,7 +70,7 @@ call psb_hsort(x,ix,dir,flag)
<P>
These serial routines sort a sequence <SPAN CLASS="MATH"><IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img114.png"
SRC="img118.png"
ALT="$X$"></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
@@ -96,7 +96,7 @@ Type:<B>optional</B>.
<BR>
Specified as: an integer array of (at least) the same size as <SPAN CLASS="MATH"><IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img114.png"
SRC="img118.png"
ALT="$X$"></SPAN>.
</DD>
<DT><STRONG>dir</STRONG></DT>
@@ -120,7 +120,7 @@ default <code>psb_lsort_up_</code>.
<DT><STRONG>flag</STRONG></DT>
<DD>Whether to keep the original values in <SPAN CLASS="MATH"><IMG
WIDTH="27" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img115.png"
SRC="img119.png"
ALT="$IX$"></SPAN>.
<BR>
Type:<B>optional</B>.
@@ -182,10 +182,10 @@ position as the corresponding entries in <SPAN CLASS="MATH"><IMG
-->
<SPAN CLASS="MATH"><IMG
WIDTH="180" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img116.png"
SRC="img120.png"
ALT="$flag = psb\_sort\_ovw\_idx\_$"></SPAN> then the entries in <SPAN CLASS="MATH"><IMG
WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img117.png"
SRC="img121.png"
ALT="$ix(1:n)$"></SPAN>
where <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
@@ -199,7 +199,7 @@ position as the corresponding entries in <SPAN CLASS="MATH"><IMG
-->
<SPAN CLASS="MATH"><IMG
WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img118.png"
SRC="img122.png"
ALT="$ix(i) \leftarrow
i$"></SPAN>; thus, upon return from the subroutine, for each
index <SPAN CLASS="MATH"><IMG
@@ -207,10 +207,10 @@ i$"></SPAN>; thus, upon return from the subroutine, for each
SRC="img4.png"
ALT="$i$"></SPAN> we have in <SPAN CLASS="MATH"><IMG
WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img119.png"
SRC="img123.png"
ALT="$ix(i)$"></SPAN> the position that the item <SPAN CLASS="MATH"><IMG
WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img120.png"
SRC="img124.png"
ALT="$x(i)$"></SPAN>
occupied in the original data sequence;
</LI>
@@ -219,16 +219,16 @@ i$"></SPAN>; thus, upon return from the subroutine, for each
-->
<SPAN CLASS="MATH"><IMG
WIDTH="185" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img121.png"
SRC="img125.png"
ALT="$flag = psb\_sort\_keep\_idx\_$"></SPAN> the routine will assume that
the entries in <SPAN CLASS="MATH"><IMG
WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img122.png"
SRC="img126.png"
ALT="$ix(:)$"></SPAN> have already been initialized by the user;
</LI>
<LI>The three sorting algorithms have a similar <SPAN CLASS="MATH"><IMG
WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img123.png"
SRC="img127.png"
ALT="$O(n \log n)$"></SPAN> expected
running time; in the average case quicksort will be the
fastest and merge-sort the slowest. However note that:
@@ -236,7 +236,7 @@ i$"></SPAN>; thus, upon return from the subroutine, for each
<OL>
<LI>The worst case running time for quicksort is <SPAN CLASS="MATH"><IMG
WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="img124.png"
SRC="img128.png"
ALT="$O(n^2)$"></SPAN>; the algorithm
implemented here follows the well-known median-of-three heuristics,
but the worst case may still apply;
@@ -244,7 +244,7 @@ i$"></SPAN>; thus, upon return from the subroutine, for each
<LI>The worst case running time for merge-sort and heap-sort is
<SPAN CLASS="MATH"><IMG
WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img123.png"
SRC="img127.png"
ALT="$O(n \log n)$"></SPAN> as the average case;
</LI>
<LI>The merge-sort algorithm is implemented to take advantage of
@@ -264,26 +264,26 @@ i$"></SPAN>; thus, upon return from the subroutine, for each
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